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1. 1 12 Objectives and Scop 3 2 6 Del akrasha aap asua Semone 6 2 1 1 Introduction to Expert Systems bitis distet di 6 2 1 1 1 Origins of Expert devo stavo 7 2 1 1 2 Characteristics of Expert 8 2 1 2 Expert Systems 11 2 1 3 Problem Solving Strategies Using Expert Systems eee 16 2 1 3 1 General Approaches a ettet nnne 16 2 1 3 2 Control Strategies eeeeeeeeeeee eese eee 17 2 1 3 3 Handling Uncertainty 19 2 2 Site Screening Model Background sese 24 2 2 1 Geotechnical Properties sssssssee eme 24 2 3 System Design Model Background eee 33 3 PROGRAM AND MODEL APPROACH eee emm 35 3 1 Overview of Concept and Model 35 3 1 1 Site 37 viii TABLE OF CONTENTS Continued Chapter Page SO System Desio Ue ee dir Sui Cha dt etn Doa nung 38 3 12 Calibration MOS etcetera e 39 3 1 2 2
2. 48 0 36 1 75 0 50 0 60 0 60 0 48 0 86 2 75 0 50 0 45 0 60 0 48 0 77 3 75 0 55 0 10 096 50 0 52 0 30 6 75 0 50 0 60 0 50 0 52 0 83 0 75 0 50 0 45 0 50 0 52 0 72 7 75 0 55 0 10 0 50 0 48 0 27 3 75 0 50 0 60 0 50 0 48 0 80 6 75 0 50 0 45 0 50 0 48 0 69 4 75 0 55 0 10 0 40 0 52 0 22 7 75 0 50 0 60 0 40 0 52 0 76 5 75 0 50 0 45 0 40 0 52 0 63 9 75 0 55 0 10 0 40 0 48 0 20 0 75 0 50 0 60 0 40 0 48 0 73 5 75 0 50 0 45 0 40 0 48 0 60 2 146 Clayey Silt Depth Plasticity Consistency Water Table Probability Clayey Silt Depth Plasticity Consistency Water Table Probability Clayey Silt Depth Plasticity Consistency Water Table Probability 75 0 50 0 10 0 60 0 52 0 35 1 75 0 25 0 60 0 60 0 52 0 70 9 75 0 25 0 45 0 60 0 52 0 57 1 75 0 50 0 10 0 60 0 48 0 31 6 75 0 25 0 60 0 60 0 48 0 67 5 75 0 25 0 45 0 60 0 48 0 53 1 75 0 50 0 10 0 50 0 52 0 26 5 75 0 25 0 60 0 50 0 52 0 61 9 75 0 25 0 45 0 50 0 52
3. Determine the aperture 196 Aperture ApertureCalculation Abort ApertureFlag D depth K Modulus Poisson _ PRESdriv RADIUS RADIUSwell R next XX This block checks to see if the square root is negative and if it is it jumps out of the subroutine The number 60 is to convert scfm to scf sec If PRES n 2 lt _ 12 Qres 60 VISCOSITY Gas PRES n Log R_next R_n _ Pi DENSITYGas Aperture 3 Then StarTrek Qres Exit Do End If PRES next PRES n 2 _ 12 Qres 60 VISCOSITYGas PRES n Log R_next R_n _ Pi DENSITYGas Aperture 3 0 5 PRES prop PRESprop Abort Density DENSITYGas depth FractureToughness R n Calculate the Flow by the Flownet method If mnuLeakOffGraphicalKh Kv Checked True Or _ mnuLeakOffGraphicalKh 5Kv Checked True Or _ mnuLeakOffGraphicalKh 10Kv Checked True Then Call Flownet Abort depth PHI R_incr RADIUS XX The value 1 9686 converts conductivity of cm sec to ft min Qleak 1 9686 PneumaticConductivity PRES n PHI Pi _ R next n Qres Qres Qleak Else Else it calulates by the analytical method The value 1 9686 converts conductivity of cm sec to ft min Qleak Kh Kv 0 5 1 9686 _ PRES next PRES n 2 HeadLossDistance _ Pi R next 2 R n 2 Qres Qres 2 Oleak End If StarTrek Qres R next PRES PRES next Loop Exit Function
4. geologic formation types supported by the program are given in Appendix D 3 1 2 1 Calibration Mode Another important function of PF Model s System Design component is the Calibration Mode In this mode the post fracture Young s modulus and pneumatic conductivity can be estimated if a pilot test has been performed at a site Evidence and system data are entered just as in the Fracture Prediction Mode and after a series of calculations the estimated modulus and conductivity can be updated as known evidence for the Fracture Prediction Mode This allows for a more accurate estimate of fracture extent This mode is detailed further in Section 3 4 Calibration Mode 3 1 2 2 Consistency and Strength of Clay Soils As discussed in Section 2 2 1 the consistency of fine grained soils is used as a piece of evidence in the expert system However consistency also plays a major role in the System Design component The pneumatic conductivity and modulus of fine grained formations vary according to 40 consistency Therefore PF Model will select different default values based on formation type and consistency thereby greatly affecting the final estimated aperture and radius It is advantageous then to expand this system utility ie Relative Density Consistency to include other descriptors At times field data may be available in the form of SPT penetration visual description or unconfined compressive strength qu The relationship of
5. 0 40 fracture toughness is K 0 0 and fracturing is above the water table Graphical leakoff method K 5K used CHAPTER 5 RESULTS CONCLUSIONS AND RECOMMENDATIONS 5 Results and Conclusions The objective of this study has been the development of a new computer program called PF Model PF Model is designed to support pneumatic fracturing which is an in situ remediation process that involves the injection of high pressure gas into geologic formations to enhance permeability as well as to introduce liquid and solid amendments Now that the pneumatic fracturing process has been receiving considerable industrial attention there is an increasing need for a computer model to aid in analysis PF Model has been designed with two principal components The first is Site Screening which heuristically evaluates sites with regard to process applicability The second component is System Design which uses the numerical solution of a coupled algorithm to generate preliminary design parameters The following are the results and conclusions of the current study 1 The selection of appropriate technologies is an essential step in successful site remediation The Site Screening component of PF Model was designed as an expert system in order to aid in that analysis An important characteristic of an expert system is that it is limited to a solvable problem The Site Screening component focuses expertise on a well defined process to determine the
6. E4 E5 Dim Formation As String Dim Evidence As Single Formation frmSiteScreening IblGeologyType Caption ProcName GetGeologyTypeEvidence On Error GoTo ErrorHandler Select Case Formation Case Clay Select Case TechnologyFlag Casel Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation Clay Text Case2 Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation Clay Text Case3 Liquid Media Injection 202 Evidence Val frmKnowledgeBase txtLiquidMI Formation Clay Text End Select Case Clayey Sand Select Case TechnologyFlag Casel Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation ClayeySand Text Case2 Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation ClayeySand Text Case3 Liquid Media Injection Evidence Val frmKnowledgeBase txtLiquidMI Formation ClayeySand Text End Select Case Clayey Silt Select Case TechnologyFlag Case Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation ClayeySilt Text Case2 Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation ClayeySilt Text Case3 Liquid Media Injection Evidence Val frmKnowledgeBase txtLiquidMI Formation ClayeySilt Text End Select Case Silty Clay Select Case TechnologyFlag Case Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation SiltyClay Text Case2 Dry Media Injection Evidence Val frmKnowledgeBas
7. and are independent then the occurrence of the first has no effect on the occurrence of the second This suggests a relationship between set theory and probability theory If 4 and are disjoint sets then p A B p A p B and p AC B p A x p B A 10 If the two events are truly independent the set union corresponds to a sum of probabilities and set intersection corresponds to a product of probabilities B can be written in set theory notation as the disjoint union B r A B A A Therefore p B p Br A o Br A p BO A p Br A A 11 p B A x p A p BI A p A Combining equations A 8 and A 11 and rewriting we obtain vip A 12 APY BA E OM This is the basic equation that was stated in Chapter 2 as Equation 2 2 It allows probability theory to manage uncertainty in expert systems and states the conditional 125 probability of 4 given B from the conditional probability of B given A It also allows determination of the probability of A if A is unknown and is observed APPENDIX B DEMPSTER SHAFER THEORY As previously shown in probability theory once the probability of the occurrence is known the probability of the hypothesis negation is fixed ie p H p H 1 Shafer believed that evidence that partially favors a hypothesis should not be construed as also supporting its negation Shafer 1976 The Dempster Shafer theory DST as summarized by Ng an
8. and Veatch R Recent Advances in Hydraulic Fracturing Society of Petroleum Engineers Richardson TX 1989 Giles R Semantics for Fuzzy Reasoning International Journal of Man Machine Studies Vol 17 No 4 pp 401 415 1982 Hall H Investigation Into Fracture Behavior and Longevity of Pneumatically Fractured Fine Grained Formations M S Thesis Department of Chemical Engineering Chemistry and Environmental Science New Jersey Institute of Technology Newark NJ 1995 Ham M Playing by the Rules PC World pp 34 41 Jan 1984 219 REFERENCES Continued Heres R Pneumatic Fracturing Flow Analysis M S Project Department of Civil and Environmental Engineering New Jersey Institute of Technology Newark NJ 1994 Hollinger E Evaluation of Expert Systems in Topics in Expert System Design Guida G and Tasso C eds Pp 377 416 Elsevier North Holland Publishing 1989 Hubbert M and Willis D Mechanics of Hydraulic Fracturing Trans AIME Vol 210 pp 153 166 1957 Hunt V Artificial Intelligence and Expert Systems Sourcebook Chapman and Hall New York NY 1986 Jensen F V An Introduction to Bayesian Networks Springer Verlag New York NY 1996 King T Mechanism of Pneumatic Fracturing M S Thesis Department of Civil and Environmental Engineering New Jersey Institute of Technology Newark NJ 1993 Lambe T and Whitman R Soil Mechanics John Wiley amp Sons Inc N
9. 13 Msg Msg amp Description amp Err Description amp Chr 13 Msg 7 Msg amp Location amp Screen ActiveForm Name amp Chr 13 Msg Msg amp Procedure amp ProcName MsgBox Msg End Sub Public Sub SubjectiveProbability EvidenceCounter E1 E2 E3 E4 E5 Dim Ceaser As Single Temporary variable to hold multiplied values of E Dim Belief As Single ProcName SubjectiveProbability 205 On Error GoTo ErrorHandler Subtract one from the EvidenceCounter since the program will always have one EvidenceCounter when it enters here EvidenceCounter EvidenceCounter 1 Select Case EvidenceCounter Casel 1 peice of evidence is known Ceaser El 0 5 Belief Ceaser Ceaser 1 El 0 5 Case2 2 peices of evidence are known Ceaser El E2 0 5 Belief Ceaser Ceaser 1 El 1 E2 0 5 Case3 3 peices of evidence are known Ceaser E2 0 5 Belief Ceaser Ceaser 1 El 1 E2 1 0 5 Case4 4 peices of evidence are known Ceaser E E2 EA 0 5 Belief Ceaser Ceaser 1 El 1 E2 1 1 E4 0 5 Case5 5 peices of evidence are known Ceaser El E2 E4 E5 0 5 Belief Ceaser Ceaser 1 EI 1 E2 1 1 E4 1 E5 0 5 End Select Display the probability to 1 decimal place Belief CInt Belief 100 frmSiteScreening txtTech
10. 4 35 System op Roco eet he eicit Esc 94 4 3 1 Validation of the System Design Component sess 95 4 3 1 1 Validation of Calibration Mode assis 95 4 3 1 2 Validation of Fracture Prediction 97 4 3 2 Calibration of the System Design Component esses 99 4 3 2 1 Calibration of Fine Grained Soils eie pape hates 101 4 3 2 2 Calibration of Rock Formations 103 4 3 2 3 Calibration of Coarse Grained Soils so 105 5 RESULTS CONCLUSIONS AND RECOMMENDATIONS en 107 CORCLUSIUDSI y usuka 107 5 2 Recommendations bera Vaca A Eai 114 APPENDIX A SUBJECTIVE PROBABILITY THEORY 121 APPENDIX B DEMPSTER SHAFER THEORY aet tet vuv tag eia valigia ds 126 APPENDIX C BAYESIAN NETWORKS APPLIED TO 128 GU Background ees eic ie dede usq sp A E slide 128 C2 GOGO BIG EVIden coe ipia duode o uaque tet atas statuat 128 C 3 AprOae ies coectetuer ee brique Gs me LE ota enean Ea cas at nae as 129 DISCUSSI W oa aska T D 135 TABLE OF CONTENTS Continued Chapter Page APPENDIX D DEFAULT VALUES FOR GEOTECHNICAL PROPERTIES INCBESMCODE E Z S actio c dee as 138 APPENDIX
11. 9 Shale Siltstone Unknown 6 000 L1x107 15 1700 40 0 19 24 1 Widely jointed N R N R N R N R Medium jointed 12 000 9 0x10 15 1700 40 0 20 29 0 Closely jointed 6 000 1 1x107 15 1700 40 2 Sandstone Unknown 8 000 1 3 107 15 1700 40 0 14 23 6 Widely jointed N R N R N R N R Medium jointed 16 000 11 10 15 1700 40 0 12 27 7 Closely jointed 8 000 1 3x10 15 1700 40 0 14 23 6 Limestone Dolomite Unknown 8 000 11 10 15 1700 40 0 17 25 1 Widely jointed N R N R N R N R Medium jointed 16 000 9 0x10 15 1700 40 0 17 30 3 Closely jointed 8 000 11 10 15 1700 40 0 17 25 1 Granite Gneiss Schist Unknown 10 000 11 10 15 1700 40 0 15 25 8 Widely jointed N R N R N R N R Medium jointed 20 000 9 0x10 15 1700 40 0 16 31 2 Closely jointed 10 000 11x10 15 1700 40 0 15 25 8 Basalt Unknown 15 000 1 1x10 15 1700 40 0 13 27 4 Widely jointed NAR N R N R N R Medium jointed 30 000 9 0x10 15 1700 40 0 13 33 2 Closely jointed 15 000 1 1x107 15 1700 40 0 13 27 4 Abbr E Young s modulus K pneumatic conductivity z fracture depth Q injection flow rate maintenance pressure b aperture R radius N R fracturing not recommended Notes Other default values soil density is y 140 pcf Poisson s ratio is v 0 25 fracture toughness is 0 0 and fracturing is above the water table Value based on standard published rock properties only No experience with pneumatic fracturin
12. Poisson _ PRESdriv RADIUS RADIUSwell next XX As Single Dim aperture well As Single ProcName ApertureCalculation On Error GoTo FileError If ApertureFlag 1 then the well aperture is calculated for the final RADIUS If ApertureFlag 1 Then XX RADIUSwell next RADIUSwell End If If mnuSolverLogDistribution Checked True Then ApertureCalculation XX 4 128 D 2 PRESdriv G K _ 2 K Log XX RADIUSwell XX 2 256 D _ 10 K RADIUS 2 RADIUSwell 2 8 16 PRESdriv _ 16 K Log XX RADIUSwell _ K RADIUS 4 64 DD _ RADIUSwell 2 RADIUS 2 32 D Elself mnuSolverConstantPressure Checked True Then ApertureCalculation 3 PRESdriv 1 Poisson 2 XX 4 _ 2 RADIUS 2 XX 2 RADIUS 4 _ 16 Modulus depth 3 Elself mnuSolverAnticlinalPlan Checked True Then ApertureCalculation PRESdriv 1 Poisson 2 4 _ 2 RADIUS 2 2 RADIUS 4 _ 2 Modulus depth 3 Else Lineraly tapering aperture well 3 PRESdriv 1 Poisson 2 RADIUS 4 _ 16 Modulus depth 3 ApertureCalculation aperture well aperture well R next RADIUS End If 199 Exit Function FileError Divide by zero If Err Number 11 Then Msg The algorithm is dividing by zero This is most amp Chr 13 Msg Msg amp likely due to
13. _ I Figure 4 6 The System Design Screen Let s just verify the model solution algorithm s defaults First check leakoff Select LEAKOFF from the Menu Bar Select GRAPHICAL from the Leakoff Menu A check should appear next to the leakoff model default which is K 5K this is also your only choice when using PF MODEL s conductivity default If not Select K 5K from the Graphical Sub menu 19 PNEUMATIC FRACTURING COMPUTER MODEL This choice reflects the fact that many natural geologic formations display some degree of anisotropy with higher conductivity in the longitudinal direction This anisotropy is normally due to stratification and bedding effects Next check on the Deflection Solver used by PF MODEL Select DEFLECTION from the Menu Bar The default is Log Distribution Circular Plan and should already be selected If not Select LOG DISTRIBUTION CIRCULAR PLAN from the Deflection Menu Since everything is now set Click the button CALCULATE After a few seconds PF MODEL will present the estimated aperture and radius below the Calculate button The estimated aperture 15 0 416 in lt lt lt The estimated radius is 14 04 ft lt lt lt If your answers are different than above go back to the beginning of the step by step example and repeat the procedure until you arrive at the above solutions Now you re going to perform some fine tuning with the System Design component for preliminary layout of th
14. e easy one step installation e explanation help facility e menu and or command driven GUI This was the major reason why the programming language used was Visual Basic as discussed previously in Chapter 3 With the click of a mouse button all program files will install in the correct folder locations a technology recommendation can be obtained or the explanation facility can be accessed 90 Different users also prefer different styles of programs For instance some users prefer to work with menu driven programs others command driven or even a combination of both PF Model is menu driven but was designed to be versatile enough so a user can use only a keyboard i e command driven if desired Presentation of Results Several different approaches were explored to present the final technology recommendation of the Site Screening Component Originally the recommendation was simply verbal e g technology recommended However because subjective probability was used in the inference engine it was possible to present technology recommendations numerically thereby reflecting a quantitative belief in the result In addition an explanation facility was developed to aid in interpretation of the numeric as discussed in the next section Clarity of Explanations Another justification for using a numeric was that when a human expert makes a recommendation that recommendation is never absolute Rather it is an opinion that c
15. 0 47 0 75 0 50 0 10 0 50 0 48 0 NO ive Yi 75 0 25 0 60 0 50 0 48 0 58 1 75 0 25 0 45 0 50 0 48 0 43 0 75 0 50 0 10 0 40 0 52 0 19 4 75 0 25 0 60 0 40 0 52 0 52 0 75 0 25 0 45 0 40 0 52 0 37 1 75 0 50 0 10 095 40 0 48 0 17 0 75 0 25 0 60 0 40 0 48 0 48 0 75 0 25 0 45 0 40 0 48 0 33 5 147 Clayey Silt Depth Plasticity Consistency Water Table Probability 75 0 25 0 10 0 60 0 52 0 15 3 75 0 25 0 10 0 60 0 48 0 13 3 75 0 25 0 10 0 50 0 52 0 10 7 75 0 25 0 10 0 50 0 48 0 9 3 75 0 25 0 10 0 40 0 52 0 7 4 75 0 25 0 10 0 40 0 48 0 6 4 148 Formation Depth Relative Density Water Table Silty Sand Depth Relative Density Water Table Probability Silty Sand Depth Relative Density Water Table Probability Silty Sand 6f 6 12ft gt 12 ft above below 45 0 55 0 60 0 52 0 61 9 45 0 50 0 60 0 52 0 57 1 Very loose to loose firm to very firm Dense to very dense 45 0 55 0 60 0 48 0 58 1 45 0 50 0 60 0 48 0 53 1 45 0 25 0 50 0 55 0 40 0 50 0 60 0 52 0
16. 00 2 12 04 2 12E 04 3 04E 04 3 04E 04 1 98E 04 1 98E 04 1 57 1 14 0 0184 14 4348 0 0185 14 142 1 00 1 00 1 72E 04 1 72 04 1 79 2 00 0 0148 16 061 0 0153 16 183 1 03 1 01 1 50 04 1 50 04 1 95 2 00 0 0282 11 786 0 0283 11 798 1 00 1 00 2 54 04 2 54 04 1 37 1 14 0 0168 11 59 0 0165 11 531 0 98 0 99 2 38 2 00 0 0415 18 976 0 0421 19 049 1 01 1 00 1 62 2 00 0 0124 30 733 0 0123 30 685 0 99 1 00 2 88 2 00 0 0993 22 960 0 1013 23 081 1 02 1 01 Tinker 8 23 05 8 23 05 1 44E 05 1 44E 05 6 95 05 6 95 05 Marcus Hook 1 77 04 1 77E 04 2 70 2 00 0 0484 16 061 0 0498 16 183 1 03 1 01 1 18E 04 1 18E 04 2 63 2 00 0 0508 15 867 0 0505 15 842 099 1 00 1 8 E 04 1 81E 04 2 52 2 00 0 0698 15 089 0 0694 15 065 0 99 1 00 Hillsborough 2 7 76 05 7 16E 05 2 79 2 00 0 0325 28 013 0 0323 27 964 099 1 00 6 63E 05 6 63E 05 245 2 00 0 0277 29 956 0 0275 29 908 0 99 1 00 6 84E 05 6 84E 05 1 98 2 00 0 0314 27 624 0 0316 27 073 1 01 1 00 Hillsborough 3 3 50E 05 3 50E 05 2 14 2 00 0 0348 30 345 0 0346 30 296 0 99 1 00 Newark 2 72E 05 2 72E 05 2 50 2 00 0 013 24 903 0 0134 25 049 1 02 1 01 1 83E 05 1 83E 05 1 88 2 00 0 0113 30 345 0 0112 30 296 099 1 00 Flemington 1 20E 04 1 20E 04 1 53 1 14 0 0260 24 515 0 0266 24 660 1 02 1 01 4 02E 05 4 02E 05 1 22 1 14 0 0110 33 454 0 0107 33 308 0 97 1 00 Table J 4 Validation of Graphical Leakoff Method Ky Site Name Frelinghuysen 1 Frelinghuysen 2 Frelinghuysen 3 Tinker Marcus
17. 04 2 25E 04 3 44E 04 1 06E 04 2 47 05 7 76 05 1 98 04 1 38 04 2 22 04 8 18 05 8 08E 05 1 02E 04 5 00E 05 1 55E 04 6 10E 05 K cm sec 4 94E 04 4 94E 04 7 76 04 6 35 04 3 95 04 6 35 04 1 59 03 4 59 04 6 17 04 4 59 04 1 83 03 2 84E 04 5 29E 04 2 4 E 04 2 54E 04 2 25E 04 3 44E 04 1 06E 04 2 47E 05 7 76E 05 1 98E 04 1 38E 04 2 22E 04 8 18E 05 8 08E 05 1 02E 04 5 00 05 3 05E 05 2 72 05 1 55 04 6 10 05 00275 14 7 00150 i163 1890 1 5 00275 11 7 1049 0017 u 000 oo 165 00188 141 1149 17 0058 114 0 050 0 019 0 034 0 033 0 034 0 008 0 024 0 038 0 040 0 016 0 027 0 024 0 019 0 015 0 028 0 016 0 042 0 012 0 100 0 050 0 042 0 049 0 032 0 028 0 033 0 036 0 013 0 011 0 027 0 010 per S Puppala dissertation 42 42 4 43 8 4 8 3 5 7 11 8 8 6 11 4 4 2 12 6 9 6 14 3 16 0 11 8 11 4 19 0 30 7 23 0 16 2 15 8 15 8 27 9 29 5 27 6 29 9 25 0 30 0 24 5 33 0 0 0797 0 0552 0 0205 0 0328 0 0349 0 0373 0 0080 0 0237 0 0388 0 0398 0 0165 0 0282 0 0259 0 0184 0 0153 0 0277 0 0163 0 0420 0 0127 0 1000 0 0502 0 0506 0 0714 0 0319 0 0257 0 0316 0 0331 0 0135 0 0108 0 0267 0 0104 4 227 4 251 4 196 4 252 8 556 8 545 5 817 11 759 8 685 11 369 4 205 12 693 9 694 14 115 16 187 1
18. 16 5 Stiff 6000 2240 10 1500 21 0 14 194 Clayey Sand Unknown 2500 3 8x10 10 1500 21 0 15 l Soft 600 3 810 10 1500 2 035 134 Medium 2500 3 8x10 10 1500 21 0 15 15 7 Stiff 8 000 3 8 10 10 1500 0 08 182 Clayey Silt Unknown 600 3 5x10 10 1500 21 0 42 14 0 Soft 200 3 5x10 10 1500 21 0 84 126 Medium 600 3 5x107 10 1500 21 0 42 14 0 Stiff 3 000 3 5x 07 10 1500 21 0 13 15 7 Silty Clay Unknown 1 000 32x10 10 1500 21 0 38 15 7 Soft 400 32x10 10 1500 2 6 14 2 Medium 1 000 32 10 10 1500 21 0 38 15 7 Stiff 5 000 32x10 10 1500 21 0 12 17 6 Abbr E Young s modulus K pneumatic conductivity z fracture depth Q injection flow rate maintenance pressure b aperture R radius Notes Other default values soil density is y 105 pcf Poisson s ratio is o 0 40 fracture toughness is K 0 0 and fracturing is above the water table Graphical leakoff method K 5K used 103 After the calibration for fine grained soils was completed cases were analyzed as shown in Table 4 7 on the previous page This was done to insure that at extreme instances of consistency and or soil type unexpected behavior would not occur In addition flow rates and depths were varied 4 3 2 2 Calibration of Rock Formations For rock formations most of the available data were for siltstone formations that were closely jointed As for clayey silt and fine grained soils siltstone formed the base case for the calibration of rock A similar ca
19. 48 0 45 0 55 0 50 0 52 0 52 0 45 0 50 0 50 0 52 0 47 0 45 0 55 0 50 0 48 0 48 0 45 0 50 0 50 0 48 0 43 0 Permeability Enhancement 45 0 55 0 40 0 52 0 41 9 45 0 50 0 40 0 52 0 37 1 45 0 55 0 40 0 48 0 38 1 45 0 50 0 40 0 48 0 33 5 149 Silty Sand Depth Relative Density Water Table Probability 45 0 25 0 60 0 52 0 30 7 45 0 25 0 60 0 48 0 27 4 45 0 25 0 50 0 52 0 22 8 45 0 25 0 50 0 48 0 20 1 45 0 25 0 40 0 52 0 16 5 45 0 25 0 40 0 48 0 14 4 150 Formation Shale Siltstone 75 0 Permeability Enhancement Depth lt 4 ft 40 0 4 8 ft 55 0 gt 8 ft 65 0 Weathering slightly wea 45 0 moderately wea 60 0 heavily wea 55 0 Frac Freq widely jointed 20 0 medium jointed 50 0 closely jointed 60 0 Shale Siltstone 75 0 75 0 75 0 75 0 75 0 75 0 75 0 75 0 75 0 Depth 65 0 65 0 65 0 65 0 65 0 65 0 65 0 65 0 65 0 Weathering 55 0 55 0 55 0 60 0 60 0 60 0 45 0 45 0 45 0 Frac Freq 60 0 500 20 0 600 500 20 0 60 096 500 20 0 Probability 91 1 872 63 0 926 89 3 676 872 82 0 53 3 Shale Siltstone 75 0 75 0 75 0 75 0 75 0 75 0 750 75 0 75 0 Depth 55 0 55 0 55 096 55 0 55 099 55 0 55 0 55 0 55
20. 55 0 55 0 Fracturing is below 48 0 45 0 45 0 Notes a Applies only to cohesive soils b Applies only to noncohesive soils c Applies only to rock Formation Clayey Silt 75 0 Permeability Enhancement Depth lt 6 ft 25 0 6 12 ft 50 0 gt 12 ft 55 0 Plasticity w lt PL 60 0 PL lt w lt LL 45 0 w gt LL 10 0 Consistency Very soft to soft 40 0 Medium to stiff 50 0 Very stiff to hard 60 0 Water Table above 52 0 below 48 0 Clayey Silt 75 0 75 0 75 0 75 0 75 0 75 0 Depth 55 0 55 0 55 0 55 0 55 0 55 0 Plasticity 60 0 60 0 60 0 60 0 60 0 60 0 Consistency 60 0 60 0 50 0 50 0 40 0 40 0 Water Table 52 0 48 0 52 0 48 0 52 0 48 0 Probability 89 9 884 85 6 83 5 79 9 77 2 Clayey Silt 75 0 75 0 75 0 75 0 75 0 75 0 Depth 55 0 55 0 55 0 55 0 55 0 55 0 Plasticity 45 0 45 0 45 0 45 0 45 0 45 0 Consistency 60 0 60 0 50 0 50 0 40 0 40 0 Water Table 52 0 48 0 52 0 48 0 52 0 48 0 Probability 83 0 80 6 76 5 73 5 68 4 64 9 Clayey Silt Depth Plasticity Consistency Water Table Probability Clayey Silt Depth Plasticity Consistency Water Table Probability Clayey Silt Depth Plasticity Consistency Water Table Probability 75 0 55 0 10 0 60 0 52 0 39 8 75 0 50 0 60 0 60 0 52 0 88 0 75 0 50 0 45 0 60 0 52 0 80 0 75 0 55 0 10 0 60 0
21. 6 3o COMPONEN FMEN E eee s a Sa i eS eoi Orat Mn Bois 7 S39 EEABSOPE MI aaa Anes 7 Jo hd DEELECHON S S pa Y n pae 8 3 310 ADVANCED Men orm opui an nuo e 8 3 3 1 6 BACKGROUND pectus dps del das 9 4 STEP BY STEP EXAMP IE amisi QNNM RH s a tir LE 11 A0 General OVervIeW usun aa ha edd a Sr a usb aan DE 11 4 1 Description of Problem a e dtd faa arisen ond i es E cose 11 4 2 of Data Set reti tu eate ene dote ee A nc cs 13 PNEUMATIC FRACTURING COMPUTER MODEL CHAPTER 1 GETTING STARTED 1 1 PF MODEL Versions The enclosed disks contain the required files to setup the pneumatic fracturing computer model on your hard rive PF MODEL version 3 0 is currently being distributed on three disks Any future upgrades may be obtained on disk or through e mail To set up PF MODEL on your hard drive read Installing PF MODEL later in this chapter 1 2 Required and Optional Hardware To run PF MODEL you need the following minimum system configuration e Microsoft Windows 95 or higher e 80486 or higher microprocessor and math co processor e 16MB of RAM with approximately 400kb free in lower memory e A high density 1 44 MB floppy drive 3 5 diskettes for software installation e A hard drive with at least 5 MB free e
22. C 7 Bayesian Network Modeling the Success of Pneumatic Fracturing for Plastic Fine Grained Soils C 4 Discussion The most straightforward approach to modeling pneumatic fracturing with a Bayesian Network is to use the BN shown if Figure C 2 However this approach has an almost unmanageable number of distributions at 25 272 These distributions for pneumatic fracturing could be known and implemented albeit at a tremendous amount of effort and time perhaps measured in months Even by utilizing the three minimized BNs discussed an extensive series of back calculations would still have to be carried out with check after check to concur that the 1000 distributions compare exactly to the what the original 25 000 would have produced anyway In effect 25 000 distributions will still have to be known in order to insure that the 1000 mirror exactly the 25 0004 The answer though may lie in the fact that a minimized network will produce probabilities that provide a certain feel for the different states This can be thought of as almost a heuristic afterthought For example it is known fine grained soils will 136 most likely be successful while coarse grained will not If the advantageous evidence is entered and the minimized BN shows that the fine grained soil s probabilities are always higher than the coarse grained the model works and provides the right heuristic feel Using HUGIN a Bayesian Network software progra
23. Calibration Mode will be superior to those made without running it 3 4 1 Calibration Algorithm In many ways the Calibration Mode is similar in logic to the System Design mode discussed previously With some minor differences the same three subroutines of the System Design mode are nested within the main subroutine of the Calibration Mode This is explained in the following section 74 3 4 1 1 Calibration Subroutine The subroutine first regresses the post fracture Young s modulus and then uses the method of bisections to converge on the post fracture pneumatic conductivity of the site The method of bisections was chosen as the model engine for processing speed considerations due to the fact that the Calibration Subroutine converges on two solutions in two separate intervals i e the pneumatic conductivity and the corresponding residual flow rate that satisfy the conductivity in the current iteration The method of bisections keeps the processing times to a manageable level Figure 3 8 on the following page shows the steps involved in the Calibration Subroutine and an explanation of the figure follows Step 1 Data Input The system properties from the pilot test ie the depth of fracturing injection flow rate and maintenance pressure are entered with the resulting measured aperture and radius of fracture Other properties ie unit weight Poisson s ratio etc can also be entered if known or PF Model can assign the defa
24. Consistency and Strength of Clay Soils ui eet pissed 39 Solio Future Components acu e niin bete pios Aes 4 3 2 Site Screening Approach S u L ped ecu inisa isa 42 3 3 System Design Approach eer cix veio eal tex n p tel tal oat 51 Aid cL Physical Processes amna Ha ga asa DO ya ia 51 3 3 2 Coupling the Physical Processes ness Ives Advertencia 55 3 3 2 System Design Ale Orrin TA nO EVE DAP 56 3 3 3 1 System Design Subroutine Dass das bate 56 3 3 3 2 Model Engine Subroutine 61 333 3 PDF Subroutine auda tee Oei ue fepe d ERR Lngd een oo taped 66 Calibration Mode A aca Cas iab uui Sa sd he Uem pedis c UR medi E d 23 344 E Calibration Algorithm u uapa aao Loa uU d al dun 73 34 1 T Calibratiot Subroutine io oe d Gua teet bodie ina vede a 74 3 5 Program Languape and un ads oa Ead unciae d terae EY EHE tire 79 4 VALIDATION AND CALIBRATION OF PF MODEBL treten horti eat 83 d Introduction uere ren nr eto iare diuiu oaa sae escis e Asi Rl o eU Nor iode oed 83 42 Site Screenin t cene eorr rt ddp eile ua ha a a dee 83 42 1 System Validation of Site Screening Component ttes 84 TABLE OF CONTENTS Continued Chapter Page 4 2 2 User Acceptance of Site Screening Component eese 88
25. End Select Case Granite Gneiss Schist Select Case TechnologyFlag Case Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation lgneous Text Case2 Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation lgneous Text Case3 Liquid Media Injection t t 204 Evidence Val frmKnowledgeBase txtLiquidMI Formation Igneous Text End Select Case Basalt Select Case TechnologyFlag Casel Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation Basalt Text Case2 Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation Basalt Text Case3 Liquid Media Injection Evidence Val frmKnowledgeBase txtLiquidMI Formation Basalt Text End Select End Select Sets the Evidence to variable E x based on how many peices of evidence have been entered selected For example if the EvidenceCounter 2 for this block of code then E2 is assigned the probability which is used in the Subjective Probability Equations later Select Case EvidenceCounter Case 1 EI Evidence Case 2 E2 Evidence Case 3 Evidence Case 4 4 Evidence Case 5 5 Evidence End Select EvidenceCounter EvidenceCounter 1 Error code Exit Sub ErrorHandler Msg An untrapped error has occured Please make amp Chr 13 Msg Msg amp note of the following information amp Chr 13 amp Chr 13 Msg Msg amp Error number amp Err Number amp Chr
26. FileError Divide by zero 197 If Err Number 11 Then Msg The algorithm is dividing by zero This is most amp Chr 13 Msg Msg amp likely due to an incorrectly entered system input amp Chr 13 Msg Msg amp or geologic parameter Go back and check your amp Chr 13 Msg Msg amp entered data amp Chr 13 amp Chr 13 Msg Msg amp If the problem persists please make a amp Chr 13 Msg Msg amp note of the following information amp Chr 13 amp Chr 13 Msg Msg amp Error number amp Err Number amp Chr 13 Msg Msg amp Description amp Err Description amp Chr 13 sg Msg amp Location amp Screen ActiveForm Name amp Chr 13 Msg Msg amp Procedure amp ProcName MsgBox Msg Resume ErrorAbort Else Msg An untrapped error has occured Please make a amp Chr 13 Msg Msg amp note of the following information amp Chr 13 amp Chr 13 Msg Msg amp Error number amp Err Number amp Chr 13 Msg Msg amp Description amp Err Description amp Chr 13 Msg Msg amp Location amp Screen ActiveForm Name amp Chr 13 Msg Msg amp Procedure amp ProcName MsgBox Msg Resume ErrorAbort End If ErrorAbort Abort Yes End Function Public Function PRESprop Abort Density DENSITYGas depth FractureToughness R n As Single ProcName PRESprop On Error GoTo FileError PRESprop Density
27. Hook Hillsborough 2 Hillsborough 3 Newark Flemington K cm sec 1 69E 03 1 72E 03 2 99E 03 2 37E 03 1 75E 03 2 85E 03 7 02E 03 2 19E 03 2 82 03 1 88 03 5 38E 03 1 69E 03 2 43E 03 1 30E 03 1 39E 03 1 19E 03 1 69E 03 6 39E 04 1 10E 04 5 29E 04 1 37 03 9 23 04 1 39E 03 6 10E 04 5 1 3 31 04 7 1 50 04 cm sec 1 69E 04 1 72 04 2 99 04 2 37 04 1 75 04 2 85E 04 7 02E 04 2 19E 04 2 82E 04 1 88E 04 5 38E 04 1 69E 04 2 43E 04 1 30E 04 1 39E 04 1 19 04 1 69 04 6 39E 05 1 10E 05 5 29E 05 1 37E 04 9 23E 05 1 39E 04 6 10E 05 5 37E 05 5 31E 05 2 74 05 2 17E 05 1 50E 05 7 75 05 2 62 05 10K Using Bisection Model Engine actual 1 20 1 20 1 20 1 20 1 42 1 42 0 95 1 41 1 43 1 31 0 70 2 10 1 60 1 57 1 79 1 95 1 37 2 38 1 62 2 88 2 70 2 63 2 52 2 79 2 45 1 98 2 14 2 50 1 88 1 53 1 22 used in MCad 1 14 1 14 1 14 1 14 1 14 1 14 1 00 1 14 1 14 1 14 0 71 2 00 2 00 114 2 00 2 00 1 14 2 00 2 00 2 00 2 00 2 00 2 00 2 00 2 00 2 00 2 00 2 00 2 00 1 14 1 14 b R b R Mcad PF Model w single R z useage w full R z useage f f 0 0767 4 182 0 0774 4 188 0 0543 4 231 0 0554 4 249 0 0211 4 231 0 0213 4 237 0 0322 4 231 0 0322 4 225 0 0345 8 531 0 0344 8 518 0 0355 8 433 0 036 8 470 0 0071 5 616 0 0073 5 658 0 0239 11 786 0 0233 11 701 0 0363 8 531
28. Overall the interface design should be as accommodating as possible Explanation Facility n expert system should not just reach a conclusion when faced with a complex problem but be capable of explaining to some extent some of the reasoning that led to that conclusion Since an expert system works on a problem that lacks a rigid control structure this capability takes on some importance in an expert system due to the fact that the validity of the system s findings may come into question Why a particular question is asked allows the user to feel more comfortable with the line of questioning and understand what line of reasoning the system is pursuing 16 Knowledge Acquisition Facility In expert systems knowledge and data are constantly changing and expanding and the knowledge base must be modified accordingly The knowledge acquisition facility is an automatic way for the user to enter knowledge in the system rather than by having the knowledge engineer explicitly code the knowledge Giarratano and Riley 1989 The knowledge acquisition facility acts as an editor allowing new knowledge to be entered or modifying existing knowledge 2 1 3 Problem Solving Strategies Using Expert Systems The search to solve a problem with an expert system begins with known facts or data and ends at a final conclusion or solution This section discusses the various problem solving strategies including general approaches control strategies and handli
29. RMid and RHigh determined from Steps 25 and 26 If the error is less that 0 1 the subroutine has converged on the radius and proceeds to Step 29 66 Step 29 Output Upon reaching this step in the subroutine the values for the aperture and radius as well as subroutine control are passed back to the System Design Subroutine Step 13 Step 30 Input Radius Increasing Engine The input radius for the Increasing Engine starts at the value of the well radius usually 0 25 ft This value is then passed to the PDF Subroutine Step 20 Step 31 Flow Comparison Should the PDF Subroutine return a flow value less than zero then the actual radius has been reached and the subroutine proceeds to provide the output Step 29 Step 32 Increment Radius If the value of Q R from Step 31 is greater than zero the radius Rpoyw is incremented by 0 1 This value is then passed along with control back to the PDF Subroutine Step 20 3 3 3 3 PDF Subroutine Pressure Deflection and Flow This section outlines the logic of the PDF Subroutine which is presented in Figure 3 7 on the following page When the fracture radii Row RMid and are passed to this subroutine the fracture extent is discretized into smaller segments The residual flow Ores and pressure distribution at the fracture tip p are calculated for this first segment If the Ores 15 greater than zero or the pressure at the tip is greater than the propagation pressur
30. Relationship Between Consistency Consolidation and OCR 4 3 3 Assigned Permeability Enhancement Probabilities for the Site Screening CCompohsentor PESMOdSL u a teca a exo 45 3 4 Geologic Properties that Apply to Fine Grained 0115 46 3 5 Geologic Properties that Apply to Coarse Grained Solls sess 47 3 6 Geologic Properties that Apply to Rocks ose distinti 47 3 7 Input Parameters for the System Design Subroutine eese 58 3 8 Deflection solvers and Corresponding Equations een cest hr nent 60 3 9 Rules Interval Determination and Actions for the Bisection Engine 64 3 10 The Coefficient A for Soil and Rock Formations Varying with Injection Flow a aaa u idt fux itd odi bia tegat A Peu iUd 69 3 11 Rules Interval Determination and Actions for the Calibration Mode 78 4 1 System Validation of Permeability Enhancement Variant 87 42 Hierarchical Order of Geotechnical Properties 92 LIST OF TABLES Continued Table Page 4 3 Breakdown of Geotechnical Properties Into Qualifiers sss 93 4 4 Validation of Calibration Mode for Estimating Young s Modulus 96 4 5 Validation of Calibration Mode for Estimating Pneumatic Conductivity 98 4 6 Validation
31. a pilot test since this would allow direct measurement of the post fracture pneumatic conductivity and Young s modulus at the Little Bighorn Refinery Congratulations You ve completed your first preliminary design of a pneumatic fracturing system In summary you found that e Pneumatic fracturing at the Little Bighorn Refinery is likely to be effective e fracture well spacing of 25 ft was preliminarily selected e To obtain 15 ft well spacings injection flow rate 2000 scfm and maintenance pressure 24 psi The user is encouraged now to explore and create new sites for analysis To quit PF MODEL go to the File Menu and select Exit 21 APPENDIX I SELECTIONS OF PROGRAM CODE USED IN PF MODEL L1 Introduction This appendix contains selected portions of code for copyright purposes As programming style varies from individual to individual this section will also allow for the reader to acclimate himself with this programmer s style of coding The following three selections were chosen e selected code from the System Design Subroutine including coded subroutine calls for the Model Engine and PDF Subroutines e selected code for the Site Screening component s expert system showing equations of subjective probability and access to the knowledge base and e coding for the Data Input screen showing mostly its object activation code Please note that PF Model documentation and the code herein are part of
32. an incorrectly entered system input amp Chr 13 Msg Msg amp or geologic parameter Go back and check your amp Chr 13 Msg Msg amp entered data amp Chr 13 amp Chr 13 Msg 7 Msg amp If the problem persists please make a amp Chr 13 Msg Msg amp note of the following information amp Chr 13 amp Chr 13 Msg 7 Msg amp Error number amp Err Number amp Chr 13 Msg Msg amp Description amp Err Description amp Chr 13 Msg Msg amp Location amp Screen ActiveForm Name amp Chr 13 Msg Msg amp Procedure amp ProcName MsgBox Msg Resume ErrorAbort Else Msg An untrapped error has occured Please make a amp Chr 13 Msg Msg amp note of the following information amp Chr 13 amp Chr 13 Msg Msg amp Error number amp Err Number amp Chr 13 Msg Msg amp Description amp Err Description amp Chr 13 Msg Msg amp Location amp Screen ActiveForm Name amp Chr 13 Msg Msg amp Procedure amp ProcName MsgBox Msg Resume ErrorAbort End If ErrorAbort Abort Yes End Function 1 3 Selected Code from the Site Screening Component Option Explicit Evidence variables Dim 1 As Single Dim E2 As Single Dim E3 As Single Dim E4 As Single Dim E5 As Single Dim EvidenceCounter As Integer Flag to select between 3 different technologys Dim TechnologyFlag As Integer 200 Private Sub cmdPermeabilityEnha
33. candidates for the pneumatic fracturing technology since process pressures are not sufficient to break intact rock It is further noted that pneumatic fracturing may also have reduced effectiveness in intensely fractured rock formations due to high leakoff rates The standard scale for fracture frequency for field classification of rocks is given in Table 2 5 on the following page Weathering The breakdown of rocks by weathering involves three processes chemical physical and biological The most important of these as it applies to pneumatic fracturing is by far the chemical process In the chemical process secondary minerals are 32 Table 2 5 Standard Scale for Fracture Frequency for Field Classification of Rocks Description for Structural Features Bedding Fracture Frequency Spacing Foliation or Banding Widely jointed gt 2 ft Thickly to very thickly Medium jointed 8 24 in Medium Closely jointed lt 8 in Thinly to very thinly formed in situ by chemical recombination and crystallization Secondary minerals continue to accumulate as weathering progresses eventually forming a residual soil of various grain sizes from clay to gravel Boggs 1987 It is obvious then that rock formations that are highly weathered will respond to pneumatic fracturing like soil formations and thus can develop new fractures Partially weathered rock formations will
34. code debugging software such as Visual One can also optimize the native code for speed or size in any of the other native code debugging software environments Microsoft 1997 PF Model is a menu driven as opposed to command driven program and this is apparent when the user runs the program and views the GUI The GUI for the model consists of objects such as buttons arrows pull down menus etc all familiar to computer users today The interface reacts with the user by responding to events that 81 occur in the interface The user in turn is able to handle otherwise difficult situations easily and rapidly For example the entry of large amounts of data needed for any application can be daunting Needed information may not be available at all times or it may not be of significant importance for the application to run and produce results for the user This is the situation for example in one of PF Model s advanced functions Input Parameters The approach for alleviating this potential problem was to have the program select default values for certain parameters by activating a button on the GUI Thus with the ease of a mouse click default values are entered and the application can return results to the user This is particularly useful for the pneumatic fracturing computer model since detailed geologic data are not always available for analysis The program manual for PF Model is presented in Appendix
35. deflection of the overburden Pressure loss is modeled based on Poiseuille s law leakoff is modeled using two dimensional Darcian flow while deflection is modeled as a circular plate clamped at its edges and subjected to a logarithmically varying load These processes and their coupling are discussed in detail in Section 3 3 System Design Approach CHAPTER 3 PROGRAM AND MODEL APPROACH 3 1 Overview of Concept and Model Components In order for technologies to advance from the research arena into the industrial sector they must undergo the process of technology transfer The leap of technology transfer is an important yet difficult link to accomplish Pneumatic fracturing is receiving considerable industrial attention since it addresses a problem which has plagued environmental clean up efforts to date ie remediation of low permeability geologic formations It is clear then that the computer model greatly enhances the technology transfer of pneumatic fracturing by linking together the results of numerous laboratory studies pilot field demonstrations and analytical modeling studies Figure 3 1 on the following page illustrates the conceptual role of the computer model in the technology transfer of pneumatic fracturing PF Model is a Windows format program which is interactive with the user The program contains a data library ie the knowledge base of geotechnical probabilities related to pneumatic fracturing based on previou
36. drive The default destination directory is C Program Files PF MODEL but you may modify it Insert the floppy disk titled disk 1 into drive A Run your appropriate Setup program for your operating environment or double click the Setup icon located on Disk 1 then follow the setup instructions PNEUMATIC FRACTURING COMPUTER MODEL 1 4 User Agreement Please note that PF MODEL provides results that are based on academic efforts and research and no claim is made about the reliability or is any responsibility taken for the results obtained from the program The computer program is proprietary Specifically you may not distribute rent sub license or lease the software or documentation alter modify or adapt the software or documentation including but not limited to translating decompiling disassembling or creating derivative works without the prior written consent the New Jersey Institute of Technology 1 5 Running PF MODEL You are now ready to run PF MODEL You can start PF MODEL by using the Start button on the task bar in Windows From the Start Menu select the PF MODEL application icon PNEUMATIC FRACTURING COMPUTER MODEL CHAPTER 2 THEORETICAL BACKGROUND PF MODEL makes extensive use of research on the pneumatic fracturing process performed at the Center for Environmental Engineering and Science CEES at New Jersey Institute of Technology NJIT For more information on model engines deflection solv
37. e the success of the technology Three different approaches were investigated to handle uncertainty in the inference engine They were the Dempster Shafer theory DST Bayesian networks BNs and subjective probability theory 109 Although the Dempster Shafer theory can explicitly express ignorance it suffers by its use of unfamiliar terminology and lack of formal semantics Limiting the theory further was the fact that a huge subset of probability assignments must be assigned by the expert since the representation of all hypotheses in DST is the power set of all possible hypotheses Bayesian networks on the other hand showed promise BNs handle uncertainty using probability theory and the use of formal diagrams where the diagrams show important conceptual information about the network One important advantage of BNs is that probabilities assigned in a network are conditional and quantify conceptual relationships in one s own mind This makes it easier to quantify directed links with local nodes turning a very large network into a globally consistent knowledge base Ultimately however BNs were not chosen for PF Model on account of the difficulty in assigning priori probabihties and interpreting posterior probabilities Subjective probability theory though was finally chosen to handle uncertainty The main advantage of subjective probability 1s that the heuristic knowledge and facts stored in the knowledge base are viewed as subject
38. exhibit an intermediate behavior However a rock formation that is relatively unweathered will contain only discrete discontinuities like those described in the previous section so enhancement results from dilation Water Table The last geotechnical property of concern is water table depth For permeability enhancement there does not appear to be any significant difference in the effectiveness of the pneumatic fracturing process in either the vadose or saturated zone U S EPA 1993 Saturation may have some effect on propagation radius however due to increased unit weight and improved pressure sealing Also if performing a dry media or liquid media injection the vadose zone may be preferred since media transport in the saturated zone is retarded by the pore water 33 2 3 System Design Model Background Fracture propagation radius is one of the most critical and frequently asked questions on pneumatic fracturing projects The design of a project and even the applicability of the pneumatic fracturing technology is based largely on the extent to which fractures will propagate Figure 2 2 provides a schematic of the pneumatic fracturing process showing a typical subsurface fracture pattern Flow Q Pressure p ANAS SAAS NNE NSN EE E Z77 Depth of overburden z Leakoff Distribution Nl rr yu Aperture width b Radius r Figure 2 2 Pneumatic Fracturing Process Fracture propagation has been studied for
39. graphics card and suitable monitor e Microsoft or compatible mouse PNEUMATIC FRAC TURING COMPUTER MODEL The RAM lower memory and math CO processor requirements above are to ensure fast and efficient response times due to math intensive calculations and for drawing graphics A smaller RAM and or lower memory or if your system does not have a math co processor will result in the user noticing a slower performance of PF MODEL as drawing graphics and mathematical operations will take longer to complete Out of memory errors may also result if insufficient RAM is available The following options give PF MODEL more functional capabilities however they are not required A printer with graphics capabilities e More than 16 MB of RAM If you have any problems with your particular system configuration please make sure that you followed the installation instructions exactly see Section 1 3 below If the problem still exists contact your system experts and then finally contact us at New Jersey Institute of Technology 1 3 Installing PF MODEL PF MODEL is distributed currently on three 3 5 1 44 MB diskettes The disks are formatted for standard IBM PCs and compatibles running MS DOS or PC DOS PF MODEL must be installed on your hard disk in order to run The files are compressed and will not run from the disk The procedure below assumes that the installation will be from drive A the source drive to drive C the destination
40. gt 5 3 1 3 Future Components The components of PF Model can be considered modules that can be added or removed from the main program at any time Therefore future model components can be added at a later date as research progresses Two components which are currently planned include Supplemental Media Injection and Contaminant and Transport Analysis and these are discussed briefly below Supplemental Media Injection In some pneumatic fracturing applications liquid or solid supplements are injected into the formation during the fracturing process to enhance in situ treatments e g bioremediation reactive media injection or for the purposes of 42 mechanical propping For example during a recent U S EPA SITE Emerging Technology Project by HSMRC U S EPA 1995 liquid nutrients and buffer solutions were injected into fine grained soils at a refinery site to enhance bioremediation of gasoline contamination Thus there is a clear need for development of a mathematical model to predict the distribution of supplemental media for various flow rates and injection times into the subsurface Once developed it can be added into the computer model Contaminant Transport Analysis After a geologic formation has been pneumatically fractured the ability to treat and or remove contaminants depends on the flow and transport characteristics of the fractured medium Once a fracture network is established in a formation contaminants are
41. known facts to a conclusion Forward chaining is advantageous since most problems begin with the gathering of information and then seeing what conclusions or goals can be reached from it It can also provide information from only a small amount of input data Forward chaining operates by collecting all the initial information into the working memory The information can be obtained from either the data base or inputted from the user The system then scans the rules searching for a match When a rule match is found it is executed or fired placing its conclusion in the working memory The scanning process is repeated again until no additional rules are fired It is possible that during a scan of the rules several rules may be applicable Usually though only one of these rules needs to be fired before the system cycles through the rules again This is called a recognize resolve act cycle Durkin 1994 There is also the process called conflict resolution in which several rules compete but only one is to be 18 fired In this method the rules are given a priority value in which the rule with the highest priority fires Some disadvantages exist with a forward chaining system however There may be no means for the system to recognize that some data might be more important than others The system will also ask all possible questions or require all possible input data for all possible conditions which may not be known or relevant Only a few ques
42. m 2 Yw 3 21 where is a coefficient z is the depth of the fracture zy is the depth to the water table yis the bulk weight of the formation and yw is the specific weight of water If the fracturing occurs in the vadose zone the above equation reduces to Pm Ax zxy 3 22 In the Fracture Prediction Mode the user will rarely know the maintenance pressure so instead the program performs the computation and 69 provides a default value For simplicity Equation 3 22 is used for both the vadose and saturated zones although if fracturing in the latter the coefficient 4 is increased by 1 0 This adjustment accounts for the superior seal and heavier weight of the saturated formation Note that this adjustment would not apply if multiple injections have dewatered the formation In addition prior research has shown that maintenance pressure increases with increasing flow rate Heres 1994 A regression of available data yielded the values of the coefficient A shown in Table 3 10 Examination of Table 3 10 shows that for flow rates above 1600 scfm the coefficient increases linearly by 10 thereby corresponding to a 109 linear increase in maintenance pressure for each 500 scfm increase in flow rate Table 3 10 The Coefficient 4 for Soil and Rock Formations Varying with Injection Flow Rate Coefficient 4 Injection Flow Rate scfm Rocks P 500 1600 3 00 2 50 1600 2100 3 30 2 75 2100 2
43. method of leakoff is selected which can be either the graphical method or the analytical method as discussed previously in Section 3 3 1 Geophysical Processes The graphical method is based on the construction of a flownet and obtaining the shape factor associated with it Appendix G contains the shape factors used as the default in PF Model s advanced menu function Flownet Parameters As this method is believed to give the most accurate representation of leakoff within a fractured formation it will be the default should the user not specify a leakoff method The other method is the analytical method as described by Equation 3 10 The difference in this method is that an effective pneumatic conductivity must be used when calculating leakoff in anisotropic formations It is therefore simpler than the graphical method but less accurate since variations in gradient and formation anisotropy are not accounted for Steps 8 through 12 Selection of Deflection Solver Method PF Model four Deflection Solvers are available each with a different fracture aperture geometry After the user selects the desired Deflection Solver the subroutine then prepares the Solver to be passed to the PDF Subroutine Table 3 8 lists the four Solvers and the corresponding equations 60 Table 3 8 Deflection Solvers and Corresponding Equations Solver Equation fracture geometry 4 b circular plan 128D Tw fract
44. of Analytical Leakoff Method Using Bisection Model Engine 216 xiv LIST OF FIGURES Figure Page 24 Relationship of Expert System Components o Wesen enis 12 222 Pneumatic Fract ring Ata co Edd 33 3 1 Conceptualization of the Technology Transfer Process sse 36 3 2 Top Level Flow Chart Showing the Model Components sese 37 23 Flow Chart of Site Screening S Deere ata ae pdt tib d derum E 43 3 4 Flow Chart Representing How Inference Engine Accesses Probabilities 3 9 Gd C 2 C 4 C 5 C 6 C 7 from Knowledge D 398a adno edocet o h pana rada S Landes a 48 The System Design Subroutine si rill ceed ts qp sasha Exp CE ee e den pres ia dades 57 The Model Engine Subroutine de e reote aiia 62 The PDF Subroutines a odo vit Boda rerit s deu Mu t pop EUR UNE wee ae dut 67 The Calroration Subroutine oae poss pb s edades uidi iu EE 75 Interaction of Components Engines and Data Bases esee 82 Converging CoOBHeCHOB Q u pee Oe dra e pera ebd ga 130 Earliest Version of a Bayesian Network Applied to Pneumatic Fracturing 131 A Bayesian Network for Plastic Fine Grained 50115 132 Bayesian Network for ROCKS una aga aaa epo dU Ux nef Dada iaa Ex 133 Bayesian Netwo
45. other common characteristics First expert systems must perform at a competence level which is equal to or better than an expert in the field It should also reach decisions within a reasonable amount of time Finally the system should have a stable platform and not be subject to crashing or freezing up 2 1 2 Expert Systems Architecture There are three major traits of an expert that are modeled in an expert system 1 the experts knowledge in the specific domain 2 the reasoning used to reach a conclusion or provide an answer and 3 knowledge about the problem being solved To accomplish 12 this the expert system must be designed with a number of interactive working components They have three principal components a knowledge base the working memory and an inference engine Other components that can enhance the model are a user interface explanation facility and knowledge acquisition facility Durkin 1994 Figure 2 1 shows an idealized representation of the architecture of an expert system and the relationship between its components Working User Interface Memory Inference Engine Explanation Facility Knowledge Acquisition Facility Knowledge Base Figure 2 1 Relationship of Expert System Components The remainder of this section will discuss each of these components all of which are needed to build an expert system 13 Knowledge Base The knowledge base is th
46. specific actions or tasks The programs solved equations processed data and scanned data bases for information They were able to do this exceptionally well but they were still not able to reason about the information they were processing Any problem that required human reasoning was performed by a human expert Shapiro 1987 Eventually programmers began coding knowledge about a problem into the computer The knowledge consisted of facts rules and structures of the problem which was coded in symbolic form The problem knowledge was represented as symbols which is simply alphanumeric characters In order to encode and search through the symbolic information symbolic processing languages were developed Some early examples of symbolic languages include LISP and PROLOG Michie 1979 As advances in symbolic programming languages and symbolic knowledge representation were made in the late 1950s programmers began efforts to create programs that displayed intelligent behavior This created a new field of study called Artificial Intelligence or AI Shapiro 1987 AI strives to simulate human intelligence in a computer Early AI research centered around the belief that a few laws of reasoning paired with computers would be able to simulate human intelligence After years of research in developing AI programs it was found that the general problem solving strategies were too weak to solve most complex problems Newell and Simon 1972 T
47. success or failure of the pneumatic fracturing technology 107 2 108 The major components of the expert system architecture for the Site Screening component are the user interface knowledge base and inference engine The functions of the user interface include entry of site data adjustment of rules or facts response to user requests and support of all other communication between the system and the user The knowledge base contains the kasa of the foremost experts in the field of pneumatic fracturing The inference engine uses the information provided from the knowledge base and the user to make a technology recommendation In doing so it simulates the thought process of an expert To increase functionality an explanation facility and a knowledge acquisition facility were added to the expert system The explanation facility can be accessed at any time in order to give an explanation on a certain line of reasoning The knowledge acquisition facility allows the program to acquire knowledge as the expert system is updated and expanded over the lifetime of the system Three different control strategies were investigated to manage the knowledge base forward chaining backward chaining and mixed chaining Forward chaining was selected since it became obvious that pneumatic fracturing experts mostly mirrored forward chaining that is they began with the gathering of site data 7 e evidence in order to reach a decision i
48. there are no efficient algorithmic solutions Biondo 1990 such as the decision of whether a site is a potential candidate for pneumatic fracturing Once PF Model has determined that pneumatic fracturing is an appropriate technology for the site the program will then make preliminary estimations of design parameters such as well spacing injection pressures and fracture intervals This part of the program incorporates current mathematical models developed at the Center for Environmental Engineering and Science CEES Puppala 1998 and King 1993 The coding of this part of the computer model uses conventional programming techniques since mathematical models and algorithmic solutions require rigid control structures The computer model is designed in a Windows format that is interactive with the user The program makes extensive use of graphics and objects thus providing a friendly user interface The computer program also includes a User s Guide for design applications A data base library of probabilities representing geologic evidence necessary for site screening is also included in PF Model This part of the program allows the data base to be updated with new probabilities as desired allowing expert potential users to customize their own proprietary version of the program The library provides the expert system with the needed information ie probabilities to assess pneumatic fracturing applicability dry media injections and l
49. this example which is a clayey silt w lt PL and fracturing occurring at a depth of 17 20 ft pneumatic fracturing is applicable 84 6 of the time conversely it is not applicable 15 4 of the time The Site Screening component s 159 applicability rating of 84 6 coincides with the initial statement that historically sites similar to this proved excellent sites to apply pneumatic fracturing APPENDIX G SHAPE FACTORS USED BY PF MODEL S GRAPHICAL ENGINE This appendix contains the shape factors of flownets for different fracture geometries used by the Graphical Leakoff method of PF Model Table G 1 is for the isotropic condition of when K K Tables G 2 and G 3 are for the anisotropic conditions of K 5K and K 10K respectively The A z ratio is the current iteration s radius divided by the depth of fracturing The R ratio is the iteration s descretized radius divided by the current iteration s radius 160 Table G 1 Shape Factors for Isotropic Condition K 161 R z r R N Riz r R N 0 14 0 1 1 48 0 71 cont 0 6 3 36 0 2 1 59 0 7 3 41 0 3 1 50 0 8 4 31 0 4 1 64 0 9 4 77 0 5 1 60 1 0 11 10 0 6 1 74 0 7 1 80 0 86 0 1 3 06 0 8 1 91 0 2 2 99 0 9 2 63 0 3 3 17 1 0 7 69 0 4 3 05 0 5 3 61 0 29 0 1 1 90 0 6 3 23 0 2 1 90 0 7 4 16 0 3 1 91 0 8 4 18 0 4 2 02 0 9 5 70 0 5 1 95 1 0 11 60 0 6 221 0 7 2 63 1 00 0 1 3 39 0 8 5 47 0 2 3 46 0 9 3 18 0 3 3 32 1 0 8 64 0 4 3 74 0 5 3 50 0 43 0 1 1 89 0 6 3
50. two infinite smooth parallel plates and is given by d 3 5 gp dy dy where is the potential function u is the velocity of the fluid is the dynamic viscosity of the fluid and p is the fluid s density Accounting for compressibility and solving the differential equation yields 12p Qu ntl J n Dn Pu 7 3 3 6 mg pb where and pj4 are pressures at distance rj and ry respectively is the flow between ry and rj b is the fracture aperture and g is acceleration due to gravity Leakoff Model Fracture propagation is also affected by leakoff the physical process where gas escapes from the fracture plane and into the formation Leakoff is modeled in three dimensions to account for pressure variations with respect to the distance from the injection well Formation anisotropy and fluid losses at the fracture tip are also considered The leakoff model uses two approaches to predict the complex pattern of leakoff that occurs in a fracture a graphical method and an analytical method 53 In the graphical or flownet method Darcy s law is modified to account for the variation in leakoff with radial distance Darcy s equation for two dimensional flow is given as ua Oleak gas H Ny 3 7 where is the air flow lost Kgas is the effective pneumatic conductivity of the formation H is the total head driving the flow Nfis the number of flow tubes and Ng is t
51. various types of soil and rock media in relation to several different mechanisms including magma intrusion hydraulic fracturing and explosive fracturing Magma intrusion is a natural phenomena in which molten rock penetrates geologic formations at a relatively low velocity of 0 5 m sec Pollard 1973 Spence and Turcotte 1985 Propagation velocities for hydraulic fracturing are similar to 34 those for magma intrusion Numerous studies of hydraulic fracture propagation have been conducted due to its importance in the petroleum industry Perkins and Kern 1961 Geertsma and de Klerk 1969 Explosive fracturing which causes much higher propagation velocities approximately 330 m sec and greater has been applied to enhance the permeabilities of oil gas and geothermal wells Nilson et al 1985 Pneumatically induced fractures propagate at velocities which are intermediate between the previously cited mechanisms A unique aspect of pneumatic fracture propagation is the profound influence of formation leakoff owing to the lower viscosity of the fracturing fluid The effects of leakoff have been modeled during a recent study at CEES Puppala 1998 This model serves as the basis for the algorithmic logic used in the System Design component of PF Model The approach is developed around the coupling of three physical processes controlling propagation e pressure loss due to frictional effects leakoff into the surrounding formation and e
52. 0 Weathering 55 096 55 0 55 0 600 600 600 45 096 45 0 45 0 Frac Freq 60 0 50 0 20 0 600 50 0 200 60 0 50 0 20 0 Probability 87 1 81 8 52 899 89 296 846 579 81 8 75 0 42 9 tnd Shale Siltstone Depth Weathering Frac Freq Probability 75 0 40 0 55 0 60 0 78 6 75 0 40 0 55 0 50 0 71 0 75 0 40 0 55 0 20 0 37 9 75 0 40 0 60 0 60 0 81 8 75 0 40 0 60 0 50 0 75 0 75 0 40 0 60 0 20 0 42 9 75 0 40 0 45 0 60 0 71 1 75 0 40 0 45 096 50 0 62 1 75 0 40 0 45 0 20 0 29 0 152 Formation Depth Relative Density Water Table Formation Depth Sand Depth Probability Sand 6f 6 12ft gt 12 ft Very loose to loose Firm to very firm Dense to very dense above below Sand 6 ft 6 12 ft gt 12 ft 75 096 75 096 50 0 50 0 75 0 75 0 75 0 40 0 50 0 50 0 75 0 40 0 66 7 Probability 75 0 40 0 50 0 50 0 60 0 55 0 50 0 55 096 45 0 Dry Media Injection 153 Formation Depth Consistency Water Table Silty Clay Depth Consistency Water Table Probability Silty Clay Depth Consistency Water Table Probability Silty Clay 6ft 6 12ft gt 12 ft Very soft to soft Medium to stiff Very stiff t
53. 0 2 79 04 5 58 05 2 00 0 0264 29 567 0 0259 29 422 0 98 1 00 2 76E 04 5 52bE 05 2 00 0 0314 27 628 0 0320 27 770 1 02 101 Hillsborough 3 1 39E 04 2 78E 05 2 00 0 0365 30 733 0 0363 30 685 099 1 00 Newark 1 11E 04 2 22E 05 2 00 0 0131 24 903 00134 25 049 1 002 1 01 7 57 05 1 51E 05 2 00 0 0107 29 956 0 0109 30 102 1 02 1 00 Flemington 4 41E 04 8 82E 05 1 14 0 0260 24 515 0 0255 24 369 098 0 99 1 50 04 3 00 05 1 14 0 0100 32 677 0 0103 32 920 103 1 01 001 101 screened by Puppala 1998 It is acknowledged that field data for calibration purposes are not available for all the formation types that are specified in PF Model The calibration of the program was done in three steps corresponding to the soil grain size or rock type The following sections describe the process 4 3 2 1 Calibration of Fine Grained Soils Fine grained soils were selected as the first formation type to be calibrated since the most field data was available for this formation type Specifically clayey silt had the largest amount of data and therefore was selected as the base case for calibration First using all the clayey silts from Table 4 6 the arithmetic averages for Young s modulus E and pneumatic conductivity K were calculated These values were input into PF Model to observe the general response Next the sensitivity of PF Model was established by slightly varying the values for E and K This process continued until optimum values for modulus and
54. 0 0369 8 567 0 0377 11 203 0 0388 11 288 0 0162 4 182 0 0161 4 176 0 0272 12 563 0 0266 12 490 0 0240 9 502 0 0244 9 539 0 0184 14 118 0 0185 14 142 0 0148 16 061 0 0149 16 085 0 0282 11 786 0 0275 11 701 0 0158 11 397 0 0161 11 458 0 0415 18 976 0 0421 19 049 0 0130 31 122 0 0132 31 268 0 1058 23 349 0 1029 23 179 0 0506 16 255 0 0498 16 183 0 0485 15 672 0 0493 15 745 0 0698 15 089 0 0711 15 162 0 0325 28 03 0 0319 27 867 0 0264 29 567 0 0265 29 616 0 0314 27 624 0 0324 27 867 0 0348 30 345 0 0341 30 199 0 0131 24 903 0 0134 25 049 0 0107 29 956 0 0107 29 907 0 0260 24 515 0 0262 24 563 0 0110 33 454 0 0107 33 308 c VB Mcad 1 0 1 02 1 01 1 00 1 00 1 02 1 03 0 97 1 02 1 03 0 99 0 98 1 02 1 0 1 01 0 98 1 02 1 01 1 02 0 97 0 98 1 02 1 02 0 98 1 00 1 03 0 98 1 02 1 00 1 01 0 97 VB Mcad 1 00 1 00 1 00 1 00 1 00 1 00 1 01 0 99 1 00 1 01 1 00 0 99 1 00 1 00 1 00 0 99 1 0 1 00 1 00 0 99 1 00 1 00 1 00 0 99 1 00 1 01 1 00 1 01 1 00 1 00 1 00 SIZ Table J 5 Validation of Analytical Leakoff Method Using Bisection Model Engine Site Name Frelinghuysen 1 Frelinghuysen 2 Frelinghuysen 3 Tinker Marcus Hook Hillsborough 2 Hillsborough 3 Newark Flemington K cm sec 4 94E 04 4 94E 04 7 76 04 6 35E 04 3 95E 04 6 35E 04 1 59E 03 4 59 04 6 17E 04 4 59 04 1 83E 03 2 84E 04 3 29E 04 241E 04 2 54E
55. 00 Soft 2 7X 10 500 Medium 2 7X 10 2 000 Stiff 22 x07 6 000 Clayey Sand Unknown 3 8x10 2 500 Soft 3 8X10 600 Medium 3 8X 10 2 500 Stiff 3 8X10 8 000 Clayey Silt Unknown 3 5X 10 600 Soft 3 510 200 Medium 3510 600 Stiff 3 5x10 3 000 Silty Clay Unknown 32 10 1 000 Soft 3 2X10 400 Medium 3 2x10 1 000 Stuff 3 25 10 5 000 Notes For all cases the dry unit weight y is 105 lb ft For all cases Poisson s ratio v is 0 40 For all cases fracture toughness K is 0 0 140 Table D 2 Default Values for Coarse Grained Soils Used in PF Model v3 0 ee GEOTECHNICAL PROPERTY DEFAULT post fracture Pneumatic Young s Modulus Conductivity E Formation Type Relative Density cm sec psi Silt Unknown 1 0 10 500 Loose 1 0 10 200 Medium dense Lp 102 500 Dense 1 0x 10 2 500 Silty Sand Unknown 1 0X 10 2 000 Loose 1 0x 10 1 000 Medium dense 1 0x 10 2 000 Dense 1 0 10 5 000 Sand Unknown 5 0X 102 4 000 Loose 5 0X 10 2 000 Medium dense 5 0x 102 4 000 Dense 5 0 102 8 000 Sand and Gravel Unknown 1 0x 10 10 000 Loose 1 0x 10 5 000 Medium dense 1 0x 10 10 000 Dense 1 0x 102 20 000 Gravel Unknown 1 0x10 10 000 Loose 1 0x10 5 000 Medium dense 1 0 10 10 000 Dense 1 0x 10 20 000 Notes For all cases t
56. 1 then chain is stretched The algorithm performs this same sequence of operations each and every time It is this repetitiveness that makes it attractive for conventional programming techniques Heuristic reasoning does not follow a rigid structure of steps Georgeff 1983 Rather it draws a conclusion based on the available information The heuristic approach to determine if the chain is stretched would be as follows IF Chain comes off bike AND Chain is old THEN Suspect stretched chain 11 Notice that heuristic reasoning does not guarantee that the chain is actually stretched but it is a good starting point to begin analysis of the problem The problem may actually have been a faulty rear derailleur or worn chainrings Makes Mistakes lt must be recognized that since expert systems are Segona i with the knowledge of a human expert they are therefore capable of making the same mistakes That is not to say conventional programs with structured algorithms have a significant advantage over expert systems Both types of programs address different types of problems Conventional programs work well where information or data is readily available or certain But if the data is wrong or incomplete a conventional program will return a wrong result or nothing at all Expert systems are designed to work with less information The result may not be exact but it can be reasonable Other Characteristics Expert systems usually exhibit some
57. 1 724 11 507 19 038 30 937 23 004 16 217 15 856 15 181 27 87 29 384 27 683 29 961 25 090 30 021 24 668 32 971 PF Model R Analytical 0 0799 0 0554 0 0206 0 0329 0 0351 0 0373 0 0081 0 0238 0 0389 0 0398 0 0167 0 0282 0 0260 0 0185 0 0153 0 0277 0 0163 0 0421 0 0128 0 1000 0 0503 0 0505 0 0711 0 0319 0 0259 0 0316 0 0333 0 0134 0 0108 0 0266 0 0104 4 225 4 249 4 200 4 249 8 567 8 543 5 828 11 774 8 688 11 361 4 213 12 684 9 709 14 142 16 183 11 725 11 506 19 049 30 976 22 984 16 231 15 842 15 162 27 867 29 422 27 673 30 005 25 049 30 005 24 660 33 017 PF M Mcad 1 00 1 00 1 00 1 00 1 01 1 00 1 01 1 00 1 00 1 00 1 01 1 00 1 00 1 01 1 00 1 00 1 00 1 00 1 01 1 00 1 00 1 00 1 00 1 00 1 01 1 00 1 01 0 99 1 00 1 00 1 00 PF M Mcad 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 91 REFERENCES Adams J A Probability Model of Medical Reasoning and the MYCIN Model Mathematical Biosciences Vol 32 pp 177 186 1976 Adrion W Branstad M and Cherniavsky J Validation Verification and Testing of Computer Software ACM Computing Surveys Vol 4 No 2 pp 159 192 June 1982 ASTM D1586 84 rev 92 Stand
58. 1 and 3 2 The rest of the parents Plasticity Relative Density Consistency Weathering and Fracture Frequency each have three states while Water Table has two The obvious problem with the BN from Figure C 2 is its size With these seven variables there will be 25 272 distributions that need to be specified 13x6x3x3x3x3x2x2 25 272 To enter over 25 000 probabilities without any errors 131 as well as insure that their interactions provide the correct results is daunting to say the least Fracture Type Frequency Figure C 2 Earliest Version of a Bayesian Network Applied to Pneumatic Fracturing Another difficulty with the BN in Figure C 2 is the handling of evidence that applies only to certain geologic formations Specifically there are three instances that need to be addressed The first is that there are six states in the node Depth yet three of these states do not apply to soils and three do not apply to rock Secondly some nodes apply only to soil and rock Relative Density Consistency is pertinent to soils Weathering and Fracture Frequency are pertinent to rock Finally the P asticity node applies only to the four soils with clay minerals Subsequent investigations led to dividing the network into three independent BNs along the same lines as Tables 3 4 through 3 6 Although a single BN is preferable due to programming considerations of the computer model ie it s more time efficient to program one BN instea
59. 2 89 0 8 2 34 0 2 2 89 0 9 2 90 0 3 3 09 1 0 7 68 0 4 3 15 0 5 3 22 0 71 0 1 1 87 0 6 3 32 0 2 1 73 0 7 3 55 0 3 1 73 0 8 4 06 0 4 1 99 0 9 5 11 0 5 1 92 1 0 10 00 Note The number of head drops Nf is 24 for all flownets Table G 3 Shape Factors for Anisotropic Condition K 10K R z r R 0 14 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 0 43 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 0 71 0 1 0 2 0 3 0 4 0 5 Note The number of head drops Ng is 24 for all flownets Ne 1 06 0 92 0 91 1 01 1 01 1 04 1 06 1 23 1 45 7 06 1 23 1 08 1 20 1 21 1 26 1 30 1 39 iB fo i bo Ur INO SN U 1 76 1 62 1 44 1 53 1 69 1 42 R z 0 71 cont r R 0 6 0 8 0 9 1 0 7 08 1 39 1 73 E55 1 84 1 75 2 08 2 23 2 55 3 06 7 11 1 90 1 99 2 10 2 06 2 20 2 45 2 66 3 16 3 50 8 06 163 APPENDIX H USER S MANUAL FOR PF MODEL The following appendix contains the manual for version 3 0 of PF Model Installation disks may be obtained upon request from NJIT CEES address found in binos This version of PF Model contains a Site Screening component and System Design component and future components may be added at a alter date A user should have some familiarity with Windows based computer programs and should have a basic geotechnical background IMPORTANT NOTE This version of the computer model is a 32 bit application Due to comp
60. 31127 1 00 16 857 53 0 0108 30 25171 251662 1 00 Flemington 16 2286 35 00260 24 5 2522 2520 9 1 00 27 1886 75 0 0104 33 10166 10164 8 1 00 Abbr 2 fracture depth Q injected flow rate Pa maintenance pressure b aperture R radius E Young s modulus Notes soil density is y 105 pcf and Poisson s ratio is o 0 40 b rock density is y 140 pcf and Poisson s ratio is v 0 25 97 estimated post fracture modulus determined by PF Model s Calibration Mode If both of these results agree then the post fracture modulus is adequately represented This is indicated in the last column which is the ratio of Epe Epf As can be seen the modulus ratio ranged between 1 00 or 1 01 confirming that the Calibration Mode of PF Model is a valid representation of the mathematical model in estimating post fracture Young s modulus The validation of the post fracture pneumatic conductivity is shown in Table 4 5 on the following page Again the first two columns represent the site data while the third column lists values of post fracture pneumatic conductivity Kme and Kpr which have been calculated using Mathcad and PF Model respectively The final column gives the ratio Kmc Kpf which ranged from 0 94 to 1 06 The average of all the sites was 0 99 thus demonstrating reasonable agreement It is surmised that the slightly higher variation in the ratio Kj Kpf is related to how Mathcad and PF Model handle significant figures Since the con
61. 4 1 94 04 1 14 0 0543 4 231 0 0554 4 249 1 00 1 00 72E 03 3 44E 04 1 14 0 0202 4 182 0 0202 4 176 100 1 00 1 36E 03 2 72 04 1 14 0 0309 4 182 0 0308 4 176 1 00 1 00 Frelinghuysen 2 9 70 04 1 94 04 1 14 0 0345 8 531 0 0347 8 543 1 01 1 00 1 59 03 3 18 04 1 14 0 0370 8 531 0 0369 8 518 1 00 1 00 3 92 03 7 84E 04 1 00 0 0071 5 616 0 0073 5 670 1 04 1 01 1 23E 03 2 46E 04 1 14 0 0224 11 591 0 0233 11 701 1 04 1 0 1 57 03 3 14E 04 1 14 0 0378 8 628 0 0381 8 640 1 0 1 00 1 07E 03 2 14 04 1 14 0 0377 11 203 0 0376 11 190 1 00 1 00 Frelinghuysen 3 3 03E 03 6 06E 04 0 71 0 0162 4 182 0 0161 4 476 0 99 1 00 2 00 0 0272 12 563 0 0278 12 636 1 02 1 01 2 00 0 0259 9 697 0 0200 9 709 1 00 1 00 1 14 0 0184 14 118 0 0185 14 142 1 01 1 00 8 56 04 1 71E 04 1 22 03 2 4412 04 7 23 04 1 45 04 7 09 04 1 42 04 2 00 0 0148 16 061 0 0149 16 085 1 01 1 00 6 13E 04 1 23E 04 2 00 0 0282 11 786 0 0275 11 701 0 98 0 99 9 35 04 1 87 04 1 14 0 0158 11 397 0 0162 11 482 1 03 1 01 Tinker 3 33E 04 6 66E 05 2 00 0 0415 18 976 0 0421 1909 1 01 1 00 5 82 05 1 16 05 2 00 0 0124 30 733 0 0127 30 976 1 02 10 2 79 04 5 58E 05 2 00 0 1058 23 349 0 1029 23 179 0 97 0 99 Marcus Hook 7 14 04 1 43 04 2 00 0 0506 16 255 0 0498 16 183 0 98 1 00 4 80 04 9 60E 05 2 00 0 0508 15 867 0 0505 15842 0 99 1 00 7 18 04 1 44E 04 2 00 0 0732 15 284 0 0737 15 308 1 01 1 00 Hillsborough 2 3 14 04 6 28 05 2 00 0 0325 28 013 0 0327 26 061 1 0 1 0
62. 4 17 0 0158 11 4 5 50e 4 5 66e 4 0 97 Tinker 8 1716 31 0 0417 19 1 32 4 1 32 4 1 00 19 1759 130 0 0125 30 8 2 80 5 2 80 5 1 00 8 1716 28 0 1000 23 9 84 5 9 83 5 1 00 Marcus Hook 6 1200 12 00500 162 3 14e 4 3 16 4 0 99 6 1276 19 00500 158 L8le4 1 81 4 1 00 6 1400 l4 00700 15 1 328e4 3 29 4 1 00 Hillsborough 2 10 1500 21 0 03220 279 L58e4 1 59e 4 0 99 12 1607 25 0 0258 294 1 55 4 1 60 4 0 97 14 1886 30 0 0317 21 1 1 94 4 1 93 4 1 01 Hibar s 14 1029 28 0 0333 30 03e 4 1 04 4 0 99 Newark 10 71 375 0013 25 l6e 5 4 19 5 0 99 16 857 53 00108 30 3 93e 3 95e 5 0 99 Elemington 16 2286 35 0 0260 245 296e 4 2 94 4 1 01 21 1886 75 0 0104 33 9 77e 5 9 74 5 1 00 Abbr z fracture depth Q injected flow rate P maintenance pressure b aperture R radius K pneumatic conductivity Notes a soil density is y 105 pcf and Poisson s ratio is o 0 40 b rock density is y 140 pef and Poisson s ratio is v 0 25 99 Table 4 6 on the following page shows the validation of the graphical leakoff method where K 5K using the bisection model engine which also happens to be the default selections for PF Model The 11 entries in the first two columns represent actual field data This is followed by two entries for R z which is a shape factor for the flownet see Appendix The first is the actual R z value based on site data and the second is the ratio used by the Mathcad model It shoul
63. 44 Density Consistency Figure C 5 Bayesian Network for Non Plastic Soils For all three BNs then the total number of distributions required are 1 116 432 540 144 In effect the original BN that required over 25 000 distributions has been 134 reduced by the use of a modeling trick similar to divorcing Should divorcing be applied directly to the above BNs though the effects would be dramatic Although the question of applying divorcing to pneumatic fracturing BNs requires further investigation the introduction of a mediating variable would reduce further the number of required distributions For example if a mediating variable called ST P Result was introduced into the BN of Figure C 3 the total number of distributions would be reduced from 432 to 72 another significant savings The resulting BN is shown in Figure C 6 Figure C 6 Bayesian Network of Plastic Fine Grained Soils with Example of Divorced Parents Similarly mediating variables may be introduced into any of the BNs previously discussed reducing the required number of distributions overall A different approach to model the success of pneumatic fracturing in plastic fine grained soils is shown in Figure C 7 on the following page Instead of the converging 135 5 In this connection the BN in Figure C 7 uses causal independence and the noisy or network the number of distributions is reduced further to 62 Background Figure
64. 600 3 60 3 00 2600 3000 3 90 3 25 Notes a Coefficient A is increased by 1 0 if fracturing in the saturated zone b Unfractured and highly weathered rocks behave closer to soil and should use the soil coefficient instead 70 The value of the pressure pz required to overcome fracture toughness is given by Sneddon 1946 as 3 23 where is the formation s fracture toughness and r is the fracture radius Steps 35 amp 36 Aperture Calculation The Deflection Solver selected previously during the System Design Subroutine Steps 8 through 12 is called from internal storage Step 35 and is now used to calculate the aperture Step 36 Table 3 8 shown previously summarizes the equations used for each deflection model in the Deflection Solver Step 37 Pressure Distribution Calculation After the aperture has been calculated the pressure model of Section 3 3 1 is solved The pressure distribution in the current segment is calculated using Equation 3 6 which is repeated below 2 n Pn 1 Pn ag 3 3 6 zgpb 12p Qun where pp and py are the pressures at radial distances ry and ry J respectively is the flow between rj and the dynamic viscosity of the gas p is the 71 density of the injected gas 5 is the fracture width g is the acceleration due to gravity Steps 38 amp 39 Leakoff and Residual Flow Calculations The next step in the PDF Subroutine is c
65. 8 are compared in order to determine the value of the radius corresponding to the effective conductivity along the entire interval The comparison rules and actions to be taken are shown in Table 3 11 on the following page Note that the functions R K etc are returning radius values which are based on the conductivity of the current iteration If one of the rules are true the corresponding action to update the conductivity is then executed 7 set K High K Mig etc 78 Table3 11 Rules Interval Determination and Actions taken for the Calibration Mode The conductivity If function is lies within Action R K x lt 0 Kiss to Kwa Set Ku Ky R Kmia x R Ku lt 0 Ky tO Ky Set Ky ww Kyu R K x RK aia 0 Kiow None Steps 14 and 15 Error Calculation and Error Comparison These steps determine if the actual effective conductivity has been reached The relative error is calculated in a similar manner as presented in Equations 3 16 and 3 17 of the Model Engine Subroutine Therefore the relative error is given by KHigh error x 100 3 28 Kyigh As long as this error is greater that 0 1 the subroutine will pass control back to the CC Subroutine Step 7 with new values for Krow KMjg and KHigh determined from Steps 12 and 13 If the error is less that 0 1 the subroutine has converged on the effective conductivity and executes Step 16 Step 16 Output U
66. 94 0 2 2 07 0 7 4 01 0 3 221 0 8 4 65 0 4 241 0 9 5 72 0 5 2 38 1 0 12 59 0 6 2 68 0 7 2 76 1 14 0 1 3 56 0 8 3 11 0 2 3 81 0 9 3 84 0 3 3 57 1 0 9 45 0 4 3 90 0 5 3 94 0 57 0 1 2 53 0 6 4 08 0 2 2 55 0 7 4 59 0 3 2 46 0 8 4 92 0 4 2 76 0 9 6 46 0 5 2 64 1 0 13 32 0 6 2 98 0 7 3 15 2 00 0 1 5 80 0 8 3 68 0 2 5 71 0 9 4 57 0 3 5 97 1 0 10 18 0 4 6 02 0 5 6 11 0 71 0 1 2 98 0 6 6 31 0 2 2 55 0 7 6 75 0 3 3 05 0 8 7 30 0 4 2 90 0 9 8 70 0 5 3 07 1 0 17 47 Note The number of head drops Nf is 24 for all flownets 162 Table G 2 Shape Factors for Anisotropic Condition K 5 _ _ R z r R Ne Riz r R N 0 14 0 1 1 16 0 71 cont 0 6 2 22 0 2 1 35 0 7 2 19 0 3 1 12 0 8 2 71 0 4 1 20 0 9 3 10 0 5 1 13 1 0 7 98 0 6 1 22 0 7 1 32 0 86 0 1 1 95 0 8 1 44 0 2 1 98 0 9 1 77 0 3 1 95 1 0 7 28 0 4 1 98 0 5 2 18 0 29 0 1 1 35 0 6 2 29 0 2 1 69 0 7 2 48 0 3 1 43 0 8 2 59 0 4 1 40 0 9 3 53 0 5 1 42 1 0 7 88 0 6 1 62 0 7 1 69 1 00 0 1 2 05 0 8 1 64 0 2 2 02 0 9 2 18 3 2 01 1 0 7 17 0 4 2 13 0 5 2 19 0 43 0 1 1 49 0 6 2 42 0 2 1 50 0 7 2 68 0 3 1 55 0 8 2 93 0 4 1 63 0 9 3 66 0 5 1 84 1 0 8 43 0 6 1 66 0 7 1 89 1 14 0 1 2 10 0 8 2 20 0 2 2 16 0 9 2 47 0 3 2 11 1 0 7 43 0 4 2 32 0 5 2 32 0 57 0 1 1 78 0 6 2 61 0 2 1 60 0 7 2 57 0 3 1 63 0 8 3 34 0 4 1 74 0 9 3 98 0 5 1 86 1 0 8 57 0 6 1 89 0 7 2 16 2 00 0 1
67. Calibration Subroutine which processes the values as a parallel operation in logic Step 7 Composite Calibration Subroutine The Composite Calibration Subroutine or CC Subroutine receives its name in that it contains the three subroutines found in the System Design component but with three major differences The first is that only the method of bisections is used as the Composite Calibration Subroutine s 77 model engine Second the Deflection Solver in the CC Subroutine is the circular plan fracture subjected to a logarithmically varying load distribution And last the Analytical method is used as the leakoff model It is important to note that this deviates from the Fracture Prediction Mode of PF Model which uses the Graphical method as a default The Analytical method is considered more appropriate for the Calibration Mode since in virtually all instances the actual field results will yield an effective conductivity Keff Subsequent flow charts and process descriptions for these subroutines are not provided since they are basically the same as those shown in Figures 3 5 3 6 and 3 7 but with the obvious modifications as described above Step 8 Internal Storage of CC Subroutine Results As control passes back to the Calibration Subroutine the results of the CC Subroutine are stored internally for later comparison Steps 9 through 13 Conductivity Function and Interval Determination The results held in the internal storage Step
68. Copyright Warning amp Restrictions The copyright law of the United States Title 17 United States Code governs the mahing of photocopies or other reproductions of copyrighted material Under certain conditions specified in the law libraries and archives are authorized to furnish a photocopy or other reproduction One of these specified conditions is that the photocopy or reproduction is not to be used for any purpose other than private study scholarship or research If a user mahes a request for or later uses a photocopy or reproduction for purposes in excess of fair use that user may be liable for copyright infringement This institution reserves the right to refuse to accept a copying order if in its judgment fulfillment of the order would involve violation of copyright law Please Note The author retains the copyright while the New Jersey Institute of Technology reserves the right to distribute this thesis or dissertation Printing note If you do not wish to print this page then select Pages from first page to last page on the print dialog screen The Van Houten library has removed some of the personal information and all signatures from the approval page and biographical sketches of theses and dissertations in order to protect the identity of NJIT graduates and faculty ABSTRACT DEVELOPMENT OF A COMPUTER MODEL AND EXPERT SYSTEM FOR PNEUMATIC FRACTURING OF GEOLOGIC FORMATIONS by Brian Michael Siel
69. Density DENSITYGas depth FractureToughness HeadLossDistance K Kh Kv MaintPres Modulus Poisson PRESdriv RADIUS RADIUSwell R next VISCOSITYGas XX If Abort Yes Then Exit Sub End If If OQlow Qmiddle lt 0 Then RADIUSup RADIUSmiddle FlowFlag 0 Elself Qlow Qmiddle gt 0 Then RADIUSlow RADIUSmiddle FlowFlag 1 Else RADIUSIow RADIUSmiddle 0 Exit Do End If QError Abs RADIUSup RADIUSlow RADIUSup RADIUSlow 100 Loop ApertureFlag 1 Call ShowResults Abort ApertureFlag D Density DENSITYGas depth FractureToughness _ HeadLossDistance K Kh Kv MaintPres Modulus Poisson PRESdriv _ RADIUS RADIUSwell next VISCOSITYGas XX Error Code Exit Sub ErrorHandler Msg An untrapped error has occured Please make a amp Chr 13 Msg Msg amp note of the following information amp Chr 13 amp Chr 13 Msg Msg amp Error number amp Err Number amp Chr 13 Msg Msg amp Description amp Err Description amp Chr 13 Msg Msg amp Location amp Screen ActiveForm Name amp Chr 13 Msg Msg amp Procedure amp ProcName MsgBox Msg End Sub Private Function StarTrek Abort ApertureFlag D Density DENSITY Gas depth _ FractureToughness HeadLossDistance K Kh Kv MaintPres Modulus _ Poisson PRESdriv RADIUS RADIUSwell next VISCOSITYGas _ XX As Single 195 Dim Aperture As Single Dim PneumaticConductivity As Si
70. E BASE This appendix contains the probabilities used in PF Model s expert system the Site Screening component The probabilities for the three domains ie Permeability Enhancement Dry Media Injection and Liquid Media Injection are presented in Table E 1 Following this table of probabilities are five selected examples showing the permutations of technology applicability for the following cases e Clayey Silt Evidence Depth Plasticity Consistency Water Table Technology Permeability Enhancement e Silty Sand Evid Depth Relative Density Water Table Tech Permeability Enhancement e Shale Evid Depth Fracture Frequency Weathering Tech Permeability Enhancement e Sand Evid Depth Tech Dry Media Injection e Silty Clay Evid Depth Consistency Water Table Tech Liquid Media Injection These 5 cases were selected as they are considered representative of the types of formations that are encountered in pneumatic fracturing today The known evidence among the cases varies between one and four pieces of evidence This represents the fact 142 143 that at times certain sites may have very little information available while at others an extensive site characterization has been performed Three of the cases are applied to the Fracturability technology one to the Dry Media Injection technology and one to the Liquid Media Injection technology in order to present the different technologies available w
71. E PROBABILITIES FOR PF MODEL S KNOWLEDGE BASE 142 APPENDIX F SUBJECTIVE PROBABILITY SITE SCREENING EXAMPLE 156 APPENDIX G SHAPE FACTORS USED BY PF MODEL S GRAPHICAL ENGINE a er sona 160 APPENDIX H USER S MANUAL FOR PF MONDBDEL toot rta tnn ronds 164 APPENDIX SELECTIONS OF PROGRAM CODE USED IN PF MODEL 189 IT ecoute ado daas 189 L2 Selected Code for the System Design Routine cerei dx dois 190 L3 Selected Code from the Site Screening Component eis cles een deis ue 199 1 4 Selected Code for the Data Input Screen eese ted Por aeta regalia cs 205 APPENDIX J TABLES USED IN VALIDATION AND CALIBRATION OF PF MODEL Lesa u a m bus tat tum asas 211 REFERENCES aaa upaqa sha aqya E A Bisa ag roit 217 xi LIST OF TABLES Table Page 2 1 Differences Between Conventional Programs and Expert 7 2 2 Particle Size Classifications u Sua itane temerario Ote nea Mins 25 2 3 Description of Atterberg Limit Range tete prints 28 2A Standard Penetr tion Festo etos edt tete ode RE stets 30 2 5 Standard Scale for Fracture Frequency for Field Classification of Rocks 32 3 1 Guide to Consistency and Strength of Clay Soils 40 3 2 Approximate
72. EPA Risk Reduction Engineering Laboratory SITE Demonstration Project Accutech Pneumatic Fracturing Extraction and Hot Gas Injection Phase 1 Applications Analysis Report EPA 540 AR 93 509 July 1993 222 REFERENCES Continued U S EPA Risk Reduction Laboratory SITE Emerging Technology Project Integrated Pneumatic Fracturing and Bioremediation for the In Situ Treatment of Contaminated Soil Project Report for EPA Cooperative Agreement No CR818207 01 0 February 1995 United States Patent No 5 032 042 Method and Apparatus for Eliminating Non naturally Occurring Subsurface Liquid Toxic Contaminants from the Soil July 16 1991 URL hugin Introducing the HUGIN System HUGIN Expert A S 1998 Http www hugin dk hugintro index html March 18 1998 Wise B and Henrion M A Framework for Comparing Uncertain Inference Systems to Probability in Uncertainty in AI Kanal and Lemmer eds Elsevier Science Publishers New York NY 1986 Zadeh L Fuzzy Sets as a Basis for a Theory of Possibility Fuzzy Sets and Systems Vol 1 No 1 pp 2 28 1978
73. H It contains various screen shots of the GUI sample output graphs and a step by step example that will guide the user through both the Site Screening and System Design components By reviewing the manual and working through the step by step example the user becomes acquainted with PF Model s menu driven GUI and the various functions available A quick examination of either the manual or the actual program will show that the key element in the entire program is the Data Input Screen since it interacts with both the Site Screening component and the System Design component The Data Input Screen stores all the required information needed by the other model components to perform their functions The interaction of the data set and the model components allows the user to easily move from one component to another component within the program 82 Figure 3 9 is a schematic of the different screens and components of PF Model showing the global interactions of all the components engines and data bases Calibration Module Flownet Parameters Data Input Screen Knowledge Base Default Library Input Parameters System Design Screen Deflection Leakoff Solver Model Figure 3 9 Interaction of Components Engines and Data Bases Screening Screen Model Engine GLOBAL ACCESS History of PF Case Studies Applications Help Appendix I contains select portions of co
74. ILE option in the top menu bar you are then transferred to the file drop down menu NEW Generates a new PF MODEL data set OPEN Opens an existing PF MODEL data set SAVE AS Saves file under a user specified name PRINT Print the given screen to printer EXIT Ends the program PNEUMATIC FRACTURING COMPUTER MODEL 3 3 1 2 COMPONENT Menu When you choose the COMPONENT option you will see the active model components available to you If a component is not active you must go back to the data input screen and activate the component directly SITE SCREENING Move to the Site Screening component where you can evaluate the applicability of pneumatic fracturing using PF MODEL s expert system SYSTEM DESIGN Move to the System Design component where the estimated results for aperture and radius are found CALIBRATION The Calibration Mode can be used to determine a sites post fracture modulus and conductivity provided data from a pilot test is available The modulus and conductivity values can then be used directly by the System Design component to better estimate the aperture and expected radius for the site RETURN TO DATA INPUT Returns back to the data input screen allowing you to make changes in geology type conductivity etc 3 3 1 3 LEAKOFF Menu The LEAKOFF menu allows you to select from two approaches used to predict the complex pattern of leakoff that occurs in a fracture an analy
75. INTRODUCTION AND OBJECTIVES 1 1 Introduction Over the past 25 years industry government and the general public have become increasingly aware of the need to respond to the hazardous waste problem which has grown steadily over the past 50 years In 1980 Congress enacted the Comprehensive Environmental Response Compensation and Liability Act CERCLA the Superfund Law to provide for liability compensation cleanup and emergency response for hazardous substances released into the environment and the cleanup of inactive waste disposal sites A major difficulty in cleaning up some hazardous waste sites is the relative low permeability of the formation ie fine grained soils and dense bedrock Current remediation technologies such as pump and treat air sparging bioremediation vapor extraction thermal treatment and soil washing work best in formations of relatively high permeability In response to this problem of low permeability formations a research effort was begun in 1987 at the Hazardous Substance Management Research Center HSMRC at New Jersey Institute of Technology NJIT It culminated with the development of a new remediation enhancement technology known as pneumatic fracturing U S Patent 5 032 042 in 1991 Pneumatic fracturing enhances the permeability of contaminated geologic formations by injecting high pressure air creating fractures or fissures in the soil or rock matrix The fractures or fissures occur if th
76. NY 1986 Clancey W The Epistemology of a Rule Based Expert System a Framework for Explanation Artificial Intelligence Vol 20 pp 215 251 1983 217 218 REFERENCES Continued Das B Principles of Geotechnical Engineering Third Edition PWS Publishing Company Boston MA 1994 Dempster A Upper and Lower Probabilities Induced by a Multivalued Mapping Annals of Mathematical Statistics Vol 38 No 2 pp 323 357 1967 Ding Y Theoretical Analysis of Volatile Contaminant Removal by the Pneumatic Fracturing Process Ph D Dissertation Department of Civil and Environmental Engineering New Jersey Institute of Technology Newark NJ 1995 Durkin J Expert Systems Design and Development Macmillan Publishing Company New York NY 1994 Gaschnig J Klahr P Pople H Shortliffe E and Terry A Evaluation of Expert Systems Issues and Case Studies in Building Expert Systems Hayes Roth F Waterman D and Lenat D eds Addison Wesley Reading MA 1983 Geertsma J and de Klerk F A Rapid Method for Predicting the Width and Extent of Hydraulically Induced Fractures Journal of Petroleum Technology Vol 21 No 12 pp 1571 1581 1969 Georgeff M Strategies in Heuristic Search Artificial Intelligence Vol 20 pp 393 425 1983 Giarratano J and Riley G Expert Systems Principles and Programming PWS Kent Publishing Company 1989 Gidley J Holditch S Nierode D
77. Number amp Chr 13 Msg Msg amp Description amp Err Description amp Chr 13 Msg Msg amp Location amp Screen ActiveForm Name amp Chr 13 Msg 7 Msg amp Procedure amp ProcName MsgBox Msg End Sub Public Sub Bisection Abort ApertureFlag D Density DENSITYGas depth _ FractureToughness HeadLossDistance K Kh Kv MaintPres Modulus _ Poisson PRESdriv RADIUSwell R next VISCOSITYGas XX Dim FlowFlag As Integer Dim QError Single Dim Qlow As Single Dim Qmiddle As Single Dim RADIUS As Single Dim RADIUSlow As Single Dim RADIUSmiddle As Single Dim RADIUSup As Single ProcName Bisection On Error GoTo ErrorHandler RADIUSlow 1 RADIUSmiddle 100 RADIUSup 200 QError 100 FlowFlag 1 Do While QError gt 0 1 RADIUSmiddle RADIUSlow RADIUSup 2 If FlowFlag Then RADIUS RADIUSIow Qlow StarTrek Abort ApertureFlag D Density DENSITYGas depth _ FractureToughness HeadLossDistance K Kh Kv MaintPres Modulus _ Poisson PRESdriv RADIUS RADIUSwell R_next VISCOSITY Gas XX 194 If Abort Yes Then Exit Sub RADIUS RADIUSmiddle Qmiddle StarTrek A bort ApertureFlag D Density DENSITYGas depth FractureToughness HeadLossDistance K Kh Kv MaintPres Modulus Poisson PRESdriv RADIUS RADIUSwell next VISCOSITYGas XX If Abort Yes Then Exit Sub Else RADIUS RADIUSmiddle Qmiddle StarTrek Abort ApertureF lag D
78. On the contrary they are intimately related Should the inference engine control the reasoning process at a very low level i e providing solution strategy flexibility the knowledge base must contain concise and specific data On the other hand if the inference engine has a high level reasoning process the knowledge base does not need to be extensive The interaction between the knowledge base and inference engine constitutes the major source of uncertainty in the expert system due to unreliable information 15 incomplete information or a poor combination of knowledge from different experts Therefore the expert system must be capable of handling this uncertainty Three popular methods are subjective probability theory the Dempster Shafer theory and more recently Bayesian networks all of which will be described later in Section 2 1 3 Problem Solving Strategies Using Expert Systems User Interface This is how the user and the expert system communicate The user interface should interact in a natural language style and should be as close as possible to humans in conversation in order to gather as much information as is possible It may also be designed to allow the interface to change information in the working memory should this be desirable for the user The actual interface design can take on many variations Today most interfaces are interactive and make extensive use of menus graphics and specifically designed screens
79. Rating Belief Error code Exit Sub ErrorHandler Msg An untrapped error has occured Please make a amp Chr 13 Msg Msg amp note of the following information amp Chr 13 amp Chr 13 Msg Msg amp Error number amp Err Number amp Chr 13 Msg Msg amp Description amp Err Description amp Chr 13 Msg Msg amp Location amp Screen ActiveForm Name amp Chr 13 Msg Msg amp Procedure amp ProcName MsgBox Msg End Sub L4 Selected Code for the Data Input Screen Option Explicit Delcare variables for various message boxes that appear in this form Dim FlagDepth As Integer Dim FlagSoilRock As Integer Dim FlagWaterTable As Integer Dim FlagWeathering As Integer 206 Sub GeologicalPropertiesOnOffQ This subroutine will turn on or turn off the various geological properties found on the Data Input form depending on the type of soil or rock that is selected by the user Enable Disable the Degree of Weathering and Fracture Frequency boxes depending on if a soil or rock type is selected If cboType Text Clay Or _ cboType Text Clayey Sand Or _ cboType Text Clayey Silt Or _ cboType Text Silty Clay Or _ cboType Text Silt Or _ cboType Text Silty Sand Or _ cboType Text Sand Or _ cboType Text Sand and Gravel Or _ cboType Text Gravel Then cboWeathering Text cboWeathering Enabled False IbIWeathering Enabled False cboFr
80. ability of the hypothesis negation is fixed i e p H 1 Shafer 1976 Bayesian Networks One of the more promising belief networks that plays a central role in handling uncertainty are Bayesian networks Pearl 1988 Bayesian networks handle this uncertainty using probability theory and the formal use of diagrams The diagrams show important conceptual information about the network Bayesian networks are represented by directed acyclic graphs a directed graph is acyclic if there is no directed path A such that A A where each node represents an uncertainty The use of arrows in the directed graphs allow for distinguishing dependencies between nodes by inspection The probabilities assigned in the network are conditional and quantify conceptual relationships in one s own mind e cause and effect These are psychologically meaningful and can be obtained by direct measurement or data analysis Appendix C details Bayesian networks and discusses its possible use as a model for the Site Screening component of PF Model The greatest advantage of using directed graphs such as Bayesian networks is that it is easier to quantify the directed links with local nodes turning the network into a globally consistent knowledge base Pearl 1988 The disadvantage of using a Bayesian network when applied to the Site Screening component as detailed in Appendix C is the subsequent scaling of posterior probabilities and assignment
81. acFrequency Text cboFracFrequency Enabled False IblFracFrequency Enabled False Elself cboType Text Shale Siltstone Or _ cboType Text Sandstone Or _ cboType Text Shale Or _ cboType Text Limestone Dolomite Or _ cboType Text Granite Gneiss Schist Or _ cboType Text Basalt Then cboWeathering Text cboWeathering Enabled True Ibi Weathering Enabled True cboWeathering ListIndex 0 makes weathering unknown upon selection or change in rock formation cboFracFrequency Text cboFracFrequency Enabled True IbiFracFrequency Enabled True cboFracFrequency Listindex 0 makes fracture frequency unknown upon selection or change in rock formation End If Disable Plasticity button if a silt sand rock are selected If cboType Text Silt Or _ cboType Text Silty Sand Or _ cboType Text Sand Or _ cboType Text Sand and Gravel Or _ cboType Text Gravel Or _ cboType Text Shale Siltstone Or _ 207 CboType Text Sandstone Or cboType Text Shale Or _ cboType Text Limestone Dolomite Or cboType Text Granite Gneiss Schist Or cboType Text Basalt Then cmdPlasticityMoisture Enabled False Else Plasticity isinstead true i e a Clayey soil cmdPlasticityMoisture Enabled True End If Disable OCR if a rock type is selected If cboType Text Shale Siltstone Or cboType Text Sandstone Or _ 7 cboType Text Shale Or _ cboType Text Lim
82. academic efforts and research and are proprietary to the author and NJIT Specifically you may not distribute rent sub license or lease the software documentation and code alter modify or adapt the software documentation or code including but not limited to translating 189 190 decompiling disassembling or creating derivative works without the prior written consent of the author and the New Jersey Institute of Technology 1 2 Selected Code for the System Design Subroutine Option Explicit Private Sub emdCalculate MouseUp Button As Integer Shift As Integer _ X As Single Y As Single ProcName cmdCalculate MouseUp On Error GoTo ErrorHandler If Button vbLeftButton Then Screen MousePointer vbHourglass Screen MousePointer 11 Dim ApertureFlag As Integer Dim D As Single Dim Density As Single Dim DENSITY Gas As Single Dim depth As Single Dim FractureToughness As Single Dim HeadLossDistance As Single Dim HeadLossFactor As Single Dim K As Single Dim Kh As Single Dim Kv As Single Dim MaintPres As Single Dim Modulus As Single Dim Poisson As Single Dim PRESdriv As Single Dim RADIUSwell Single Dim next As Single Dim VISCOSITYGas As Single Dim XX As Single Abort No Set the Abort Error Flag to No Density Val frmInputParameters txtFormationDensity Formation density DENSITY Gas Val frmInputParameters txtDensityGas depth Val frmDatalnput txtFractureDepth De
83. ack to the Model Engine Subroutine the results of the PDF Subroutine are stored internally for later comparison using the bisection method Steps 22 through 26 Flow Function and Interval Determination The results held in the internal storage Step 21 are compared in order to determine the location of the radius along the entire interval The comparison is shown in Table 3 9 along with the actions the Bisection Engine is to perform Table 3 9 Rules Interval Determination and Actions for the Bisection Engine If function is The radius lies within Action Q Riow x Q Rnia lt 0 Ius to Ria Set Rin Ria lt 0 R mia tO Ry Set Row Ras QRiow x QR nia 0 Riow None _ l llLLJlLlLLCCxXI5IITSSTSTTSTNTXTNE IIIa h 65 Steps 27 and 28 Error Calculation and Error Comparison These steps determine if the actual radius given the current iteration s flow and pressure conditions has been reached First the relative error is calculated as Rold error x 100 3 16 new Equation 3 16 can be simplified further by making the following substitutions R High Rrow High Rpow Rnew 2 and sos Roa 2 therefore giving as the relative error R High R Low error x 100 3 17 R High Rrow As long as this error is greater that 0 1 the Bisection Engine will pass control back to the PDF Subroutine Step 20 with new values for RZ ow
84. acture pneumatic conductivities were 114 then estimated using the Calibration algorithm In the Calibration Mode PF Model agreed within 5 of the mathematical model 13 The System Design component was calibrated for 14 formation types by establishing default values for 6 parameters They were vasis modulus pneumatic conductivity fracture depth injection flow rate formation density and Poisson s ratio Average values were used for depth flow rate density and Poisson s ratio Post fracture Young s modulus and pneumatic conductivity were established by regression until optimum values were obtained which reproduced in general the average behavior of the actual site data In cases where site data were either limited or not available the calibration was made on a relative basis That is the expected trends between pneumatic conductivity and grain size were used The moduli were calibrated in a similar manner 5 2 Recommendations A number of recommendations are suggested based upon the completed study They are 1 The expert system should go through system validation annually Pneumatic fracturing is an evolving technology and as knowledge increases the expert system needs to be updated concurrently in order for PF Model to be of maximum value to end users All new field data should be collected and archived so that these annual validations will reflect new knowledge or experience The foremost experts of N U 115
85. al Engineering Corp and John Liskowitz President of ARS Technologies Inc for their expert opinion for the pneumatic fracturing knowledge base I would like to thank the past students of the pneumatic fracturing project many of whom I do not know personally Their work and research over the past decade has aided greatly in understanding the technology like to especially thank Suresh Puppala as his research has been invaluable throughout this study Special appreciation is extended to Dr Richard Scherl and Chris Koebel who are responsible for wresting me from the security blanket of subjective probability theory into the cold darkness of Bayesian networks and influence diagrams vi I take great pleasure in recognizing my academic colleagues who have been generous with their time and ideas Michael T Time Galbraith Heather Holistic Hall Jenny Quick Fingers Lin and Chip Their friendship and goodness will always be with me I am greatly indebted to my family and friends for reminding me why it all matters making me feel useful sheltering me from the travails of the real world and surrounding me with so much love support and hope Finally I d like to thank all my maternal and paternal ancestors for providing me with the correct DNA sequence to be here today vil TABLE OF CONTENTS Chapter Page 1 INTRODUCTION AND OBJIEGCTIWES 1 ki Introduction
86. al model Instead of absolute pressure gauge pressure was used in selected steps Further investigation showed that this did not cause a significant error in the program due to the effects of the cubic law since pressure remains relatively constant until it suddenly near the fracture tip In nearly all cases the equation flaw did not affect convergence until the calculation was within 0 0001 in of the final radius Therefore the original calibrations performed by Puppala 1998 are valid despite the use of gauge pressure The coding of the pressure distribution model in the PDF Subroutine was corrected to reflect absolute pressure Validation of PF Model agreed with the earlier calibrations as expected Specific site data were used to validate PF Model The field data consisted of 6 sites comprised of 31 injections previously screened Puppala 1998 The estimated aperture and radius were then calculated using Mathcad The Fracture Prediction Mode was validated by comparing the estimated aperture and radius to these results All four leakoff methods ie Analytical Graphical K Graphical K 5K and Graphical K 10K were validated using the Bisection engine with the Circular Plan Log Distribution Deflection Solver In all instances PF Model agreed within 4 of the mathematical model To validate the Calibration Mode post fracture Young s moduli were regressed using the modified deflection equation Post fr
87. alculated for coarse grained soils are much smaller This is as expected since the degree of flow and pressure confinement is less than for fine grained soils 106 Table 4 9 Calibration of Default Values for Coarse Grained Soils Defaults Predictions E K Z Q P b R psi cm sec ft scfm psi in ft Silt Unknown 500 1 0107 10 1500 21 0 10 9 1 Loose 200 10x10 10 1500 21 0 14 7 8 Medium dense 500 1 0x10 10 1500 21 0 10 9 Dense 2 500 1 0x10 10 1500 21 0 06 12 3 Silty Sand Unknown 2 000 1 0x10 10 1500 21 0 06 11 75 Loose 1 000 1 0x10 10 1500 21 0 08 10 24 Medium dense 2 000 1 0 10 10 1500 21 0 06 11 75 Dense 5 000 10x10 10 1500 21 0 006 14 53 Sand Unknown 4 000 5 0x107 10 500 21 0 04 12 3 Loose 2 000 5 0x107 10 1500 2 0 04 10 3 Medium dense 4 000 5 0x107 10 500 21 0 04 12 3 Dense 8 000 5 0x10 10 1500 21 0 04 14 8 Sand amp Gravel Unknown 10 000 1 0x10 10 1500 21 0 04 15 5 Loose 5 000 1 0x10 10 1500 21 0 04 12 8 Medium dense 10 000 1 0x10 10 1500 21 0 04 15 5 Dense 20 000 1 0x107 10 1500 2 0 04 18 5 Gravel Unknown 10 000 1 0x107 10 1500 21 0 03 14 6 Loose 5 000 1 0x10 10 1500 21 0 03 12 1 Medium dense 10 000 10x10 10 1500 21 0 03 14 6 Dense 20 000 10 10 10 1500 21 0 03 17 5 Abbr E Young s modulus K pneumatic conductivity z fracture depth Q injection flow rate Pn maintenance pressure b aperture R radius Notes Other default values soil density is y 105 pcf Poisson s ratio is o
88. alculation of the residual flow Q es This is done by first calculating the leakoff from the fracture Ojegk One of the two leakoff methods determined during the System Design Subroutine Steps 5 through 7 is called from internal storage Step 38 The related equations were discussed previously in Section 3 3 1 and are repeated below for convenience For the graphical or flownet method leakoff is given by R N Oleak PE gas H ns f zz a r 4 3 9 and for the analytical method leakoff is given by Fn 2 3 10 r R Pd Oleak gt gas K ad ELM l grad The residual flow left in the current segment after leakoff is then found by determining the overall mass balance of the flow Ignoring fracture volume 72 Ores Ores Oleak 3 24 where is the residual flow of the previous segment and Oleak iS the leakoff flow loss of the current segment This step of the subroutine satisfies the leakoff model discussed in Section 3 3 1 Step 40 PDF Criteria Comparison Residual flow fracture pressure distribution and radius at the end of the segment are compared to the conditions that would exist at the fracture tip if in equilibrium as shown in Step 40 of Figure 3 7 If this condition is satisfied control passes to Step 41 otherwise execution is passed to Step 42 Step 41 Increase the Segmentized Fracture Radius 1f the conditions of equilibrium of Step 40 are satisfied t
89. ally for enhancement of pump and treat vapor extraction air sparging and bioremediation Other innovative approaches using the pneumatic fracturing process are also under investigation and include in situ vitrification in situ ultrasonic enhancement and reactive media injection 1 2 Objectives and Scope The objective of this study is to develop a comprehensive pneumatic fracturing computer model called PF Model with two principal functions First the model will assist in deciding whether or not a site is a potential candidate for the technology Second it will generate preliminary design parameters for applying the pneumatic fracturing process at the site Each of these model functions will now be briefly introduced An essential step in the successful remediation of a site is the selection of appropriate technologies In the past the decision when and if to use pneumatic fracturing was made by informal quantitative comparisons with empirical data from past projects by an expert familiar with the capabilities of the technology Now the computer model will make the same judgment by functioning in part as an expert system An expert system is a high performance problem solving computer program capable of simulating human expertise within a narrow domain An expert system either performs the function of a human being or it fulfills the role as an assistant to the human decision maker Expert systems are best suited for conditions in which
90. and re slice the data allowing the analysis to be done faster Eventually it was decided to use Microsoft Visual Basic for PF Model An important reason for selecting Visual Basic was to facilitate future modifications and additions to the program which are inevitable Visual Basic allows those students and 80 faculty not proficient in higher level computer languages the ability to access and modify the program code Like the alternative development tools Visual Basic allows for the creation of robust and powerful applications for Microsoft Windows operating systems yet retains the programming ease of standard Basic Visual Basic also allows programmers to incorporate an extensive graphical user interface GUI into the program A new feature of Visual Basic allows PF Model to be compiled in native code similar to the other development tools This provides for several options for optimizing and debugging that aren t available in standard pseudo code or p code P code is described as an intermediate step between the high level instructions in the actual Basic program and the low level native code executed by the computer processor Normally at run time each p code statement is translated into native code By compiling to native code directly the intermediate p code step is eliminated thereby extending performance up to 20 times faster Microsoft 1997 Another advantage is compiled native code can be debugged with other standard native
91. ant pressure distribution acting on a circular plate to predict the fracture CONSTANT PRESSURE ANTICLINAL PLAN Selects a constant pressure distribution acting on an anticlinal beam LINEARLY TAPERING CIRCULAR PLAN Selects a linearly tapering pressure distribution acting on a circular plate 3 3 1 5 ADVANCED Menu The advanced functions of PF MODEL should only be accessed by expert users of the program and the pneumatic fracturing technology These options add greater functionality to the program thereby increasing the versatility of any analysis performed by the model Itis also possible to tailor your version of PF MODEL with proprietary information MODEL ENGINE Expands to another drop down menu The engines models two different approaches to arrive at a solution Bisection and Increasing The default engine 15 Bisection which decreases the processing time considerably by converging rapidly towards the solution yet maintains the accuracy of the Increasing engine The Increasing Engine is included for use during research INPUT PARAMETERS the Input Parameter screen allowing you to change geotechnical properties or system properties for the PNEUMATIC FRACTURING COMPUTER MODEL O 9 M n current data set Some of the properties include Young s modulus formation density fracture toughness density of the inje
92. ard Test Method for Penetration Test and Split Barrel Sampling of Soils in Annual Book of ASTM Standards Vol 4 08 pp 129 133 American Society for Testing and Materials Standards Philadelphia PA 1994 ASTM D4318 93 Standard Test Method for Liquid Limit Plastic Limit and Plasticity Index of Soils in Annual Book of ASTM Standards Vol 4 08 pp 551 561 American Society for Testing and Materials Standards Philadelphia PA 1994 Bates R and Jackson J Dictionary of Geological Terms Doubleday New York NY 1984 Bielawski L and Lewand R Expert Systems Development Building PC Based Applications QED Information Sciences Inc Wellesley MA 1988 Biondo S Fundamentals of Expert Systems Technology Ablex Publishing Norwood NJ 1990 Boggs Jr S Principles of Sedimentology and Stratigraphy Merrill Publishing Company Columbus OH 1987 Burmister D Soil Components Fractions Terms and Abbreviations for Visual Identification of Soils ASTM Special Technical Publication 479 5th Edition American Society for Testing and Materials Standards Philadelphia PA 1970 Canino M Potential Effects of Pneumatic Fracturing on Existing Structures and Utilities M S Thesis Department of Civil and Environmental Engineering New Jersey Institute of Technology Newark NJ 1997 Cheeseman P Probabilistic vs Fuzzy Reasoning in Uncertainty in AI Kanal and Lemmer eds Elsevier Science Publishers New York
93. ated which uses a non linear distribution to predict a tapering fracture Canino 1997 and Puppala 1998 Field observations have shown ground surface heave contours circular in shape Therefore overburden can be modeled as the bending of an elastic circular plate clamped atthe edges The derived deflection equation is 4 r r b 2 3k 2kln Pa 3k ze 2 r 2 r 8kpa 8k 16 2 3 11 kn Um 5 64D 32D 3 where K a ae 2 12 1 Fw b is the fracture aperture at a distance r from the injection well pg is the driving pressure at the well r is the well radius R 15 the radial extent of the fracture E is Young s Modulus v is Poisson s ratio and z is the depth of fracturing 3 3 2 Coupling the Physical Processes By coupling the three physical processes pressure distribution leakoff and deflection the extent of fracture propagation can be determined This is due to the dependency of the physical processes with each other Each physical process is expressed below as a function of its formation and system parameters Pr fO igas Peas b Pre 3 12 56 N Oleak TE E r a 3 13 b f R E V prz 3 14 The above equations demonstrate this interdependency since each dependent variable appears within one of the other processes list of independent variables This coupling of the physical processes is handled with an algorithm that is described i
94. atibility issues it is recommended that this program be run only on 32 bit operating systems e g Windows 95 or Windows 98 164 QUICK START Q 1 Basics If you don t have much time to devote to reading a user s manual and are familiar with running computer software this Quick Start shows you 1 how to install PF MODEL and 2 where in this manual you can find a step by step tutorial Q 2 Installing PF MODEL You install PF MODEL on your computer using the Setup program The Setup program installs PF MODEL any OCX control files and the default files from the installation disks to your hard drive Important You cannot simply copy files from the installation disks to your hard drive and run PF MODEL You must use the Setup program first This will decompress and install the files in the appropriate directories The following procedure will install PF MODEL on your hard drive e Insert disk 1 into drive A e Use the appropriate setup command for your operating environment For example in Windows 98 you would go to Add Remove Programs found in Control Panels You may also run the Setup program by double clicking on the Setup icon located on disk 1 in drive A e Follow the setup instructions on your screen Q 3 Running PF MODEL You are now ready to run the pneumatic fracturing computer model Go to the Start button and select the PF MODEL icon Q 4 Tutorial Please refer to Chapter 4 Step by Step Exampl
95. atic fracturing Pisciotta ef al 1991 and Schuring et aL 1991 Experience has shown that soils which are in the plastic range PL w LL can also be successfully fractured 29 However post fracture air flows in plastic soils may be retarded by moisture in the pores and fractures As the moisture content of a clay soil increases above the liquid limit w gt LL the soil exhibits a tendency to flow Although there has been little field experience with fracturing soils above the liquid limit laboratory studies have shown that fracture healing could be a problem Hall 1995 Relative Density Consistency This geotechnical property is only used to describe soil formations Relative density is applied to cohesionless soils e g sand while consistency is applied to cohesive soils e g clay The relative density consistency is usually obtained by the widely used standard penetration test or SPT ASTM D1586 84 which consists of driving a split spoon sampler into the ground by dropping a 140 Ib weight from a height of 30 in The sum of the blows required to drive the spoon is recorded and is used to compute the standard penetration resistance or N value Sowers and Sowers 1970 Table 2 4 on the following page shows a correlation between penetration resistance and relative density for cohesionless soils and a correlation between penetration resistance and consistency for cohesive soils Relative density consistency has two im
96. ating 60 100 M marginally recommended rating 45 60 N not recommended rating 0 40 n a not applicable unknown not provided to evaluator D Evaluator Results T B System Rating Result lt x lt lt lt lt X lt lt Z Z 6 lt lt 70 78 64 66 70 62 79 75 74 74 74 56 36 55 65 EIT Table J 3 Validation of Graphical Leakoff Method K K Using Bisection Model Engine Site Name K K R z R z b R b R b R Mead PF Model used in 2 cm sec cm sec actual MCad w single R z useage w full R z useage 5 E f s Frelinghuysen 1 2 65E 04 2 65E 04 0 0800 4 23 2 72E 04 2 72E 04 1 20 1 14 0 0543 4 231 0 0548 4 237 1 01 1 00 4 66E 04 4 66E 04 1 20 1 14 0 0211 4 231 0 0211 4 225 1 00 1 00 3 70E 04 3 70E 04 1 20 1 14 0 0322 4 231 0 0322 4 225 1 00 1 00 Frelinghuysen 2 2 72E 04 2 72 04 1 42 1 14 0 0345 8 531 0 0344 8 518 1 00 1 00 4 41 04 4 41 04 1 42 1 14 0 0370 8 531 0 0369 8 518 1 00 1 00 1 09E 03 1 09E 03 0 95 1 00 0 0075 5 713 0 0074 5 682 0 98 0 99 3 36E 04 3 36E 04 1 41 1 14 0 0239 11 786 0 0235 11 7235 0 98 0 99 4 37 04 4 37 04 1 43 1 14 0 0378 8 628 0 0373 8 591 0 99 1 00 2 93E 04 2 93E 04 1 31 1 14 0 0377 11 203 0 0388 11288 1 03 1 01 Frelinghuysen 3 8 47E 04 8 47E 04 0 70 0 71 0 0169 4 231 0 0172 4 249 1 00 1 00 2 10 2 00 0 0272 12 568 0 0274 12 587 1 01 1 00 1 60 2 00 0 0249 9 599 0 0251 9 612 1 01 1
97. bjective probability theory is used to perform site screening The example shows how various pieces of evidence 51 such as grain size overburden and plasticity result in a belief for the applicability of pneumatic fracturing 3 3 System Design Approach Over the years there has been extensive research in the field of pneumatically induced fractures and its controlling physical processes Recent efforts by Puppala 1998 have led to the development of a mathematical model that determines the radius of pneumatic fractures in soil and rock formations This section will present the background information leading to the final conclusions of that study regarding fracture propagation followed by a detailed discussion of PF Model s System Design algorithm 3 3 1 Physical Processes There are three physical processes that control pneumatically induced fractures They are pressure distribution leakoff and deflection These three processes are coupled to predict the radius of fracture propagation This section briefly discusses each of the three models Pressure Distribution Model A model has been developed at NJIT that defines the relationship between air flow and artificially induced fractures Nautiyal 1994 The model accounts for the pressure dissipation in a fracture which states that as radial distance increases from the injection well pressure head decreases within the fracture The solution is based on Poiseuille type flow between
98. c conductivity has been determined then it should be entered here Please refer to the help screen for further discussion about pneumatic conductivity Click the button DONE Now look at some of the other default values This will require using PF MODEL s Advanced functions Select ADVANCED from the Menu Bar Select INPUT PARAMETERS from the Advanced Menu The Input Parameter screen is shown in Figure 4 5 on the following page It lists the system and geotechnical parameters used by the System Design algorithm Take time to examine the values and become familiar with the terms Some of these should be obvious e g density of gas Young s modulus and formation density Others such as the Head Loss Factor require expert knowledge in the development and subsequent analysis of the Flownet Library 17 PNEUMATIC FRACTURING COMPUTER MODEL Click the button DONE The previous two screens Pneumatic Conductivity and Input Parameters are where most experts will make adjustments to fine tune a site changing conductivity modulus density etc as required Since everything looks in order it s time to find out the expected radius Select COMPONENTS from the Menu Bar Select SYSTEM DESIGN from the Components Menu Advent Figure 4 5 The Input Parameters Screen 18 PNEUMATIC FRACTURING COMPUTER MODEL You should now see the System Design screen as shown in Figure 4 6 below gou S p Q u
99. cal conversations Forward chaining acts as the control strategy of PF Model s expert system since the pneumatic fracturing process starts out with pieces of geological evidence proceeding toward a single conclusion i e the applicability of the pneumatic fracturing technology The probabilities that are required to determine pneumatic fracturing applicability ratings are stored in the knowledge base Table 3 3 on the following page shows the assigned probabilities in the knowledge base for permeability enhancement The probabilities for dry and liquid media injection are located in Appendix E The probabilities for the three different technology variants were established through discussions with pneumatic fracturing experts over a period of months The dominant consideration was past performance of pneumatic fracturing under a variety of geologic conditions Careful attention was given to the relative scale of probabilities between the various formations as well as the absolute scale which acknowledged the importance of a particular type of evidence It is noted that field reference data are limited and some probabilities are speculative based upon the inherent geotechnical properties of a particular formation Table 3 3 Assigned Permeability Enhancement Probabilities for the Site Screening Component of PF Model Formation Clay Clayey Sand Clayey Silt Silty Clay Silt Silty Sand Sand Sand amp Gravel Gravel Shale Siltston
100. ce Val frmKnowledgeBase txtLiquidMl Formation SandGravel Text End Select Case Gravel Select Case TechnologyFlag Case 1 Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation Gravel Text Case2 Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation Gravel Text Case3 Liquid Media Injection Evidence Val frmKnowledgeBase txtLiquidM Formation Gravel Text End Select Case Shale Siltstone Select Case TechnologyFlag Casel Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation Shale Text Case2 Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation Shale Text Case3 Liquid Media Injection Evidence Val frmKnowledgeBase txtLiquidMI Formation Shale Text End Select Case Sandstone Select Case TechnologyFlag 1 Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation Sandstone Text Case2 Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation Sandstone Text Case3 Liquid Media Injection Evidence Val frmKnowledgeBase txtLiquidMI Formation Sandstone Text End Select Case Limestone Dolomite Select Case TechnologyFlag Case 1 Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation Limestone Text Case2 Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation Limestone Text Case3 Liquid Media Injection Evidence Val frmKnowledgeBase txtLiquidMI Formation Limestone Text
101. companied with a numerical rating to reflect the level of belief in the recommendation The Site Screening component was evaluated using both system validation and user acceptance For system validation a panel of 5 experts subjectively rated 15 sites for each of the pneumatic fracturing variants and the results were compared with model recommendations The system agreed with the majority of expert opinions although some fine adjustments to the knowledge base were made as part of the validation process Perhaps the ultimate test of the expert system is user acceptance Therefore the program was designed with an interactive and user friendly graphical user interface 393 amp The GUI is menu driven with buttons dialogues pull down menus etc The program can also be command driven if desired In order to further assure user acceptance early versions were shown to potential users and feedback was solicited The final determination of acceptance though will not be known until after the program is released The System Design component was programmed traditionally and therefore consisted of structured algorithms The System Design component has two main algorithms the Fracture Prediction and Calibration Modes The Fracture Prediction Mode estimates the maximum aperture and radius for the pneumatic fracturing process The algorithm arrives at the solution by the 10 112 convergence of three physical proc
102. conductivity were selected The goal of the calibration was to reproduce in general average behavior of the actual site data Obviously data points for individual injections exhibited a certain amount of scatter Once the and K values for the given consistency of clayey silt were established the consistency level was changed i e from stiff to medium etc and the process was repeated Unfortunately large amounts of data were not available for each consistency It was therefore necessary to use trends from the literature to extrapolate the modulus to extreme cases In addition it was not felt that there was enough regressive information on K to warrant an adjustment Therefore in general a single value of K was used for each soil type 102 After PF Model was calibrated to clayey silt the other fine grained soil types i e clay clayey sand and silty clay were analyzed Although limited data were available for these soils the amount was not as large as for clayey silt Therefore the calibration was made on a relative basis In other words the expected trends between pneumatic conductivity and grain size were used The moduli were calibrated in a similar manner Table 4 7 Calibration of Default Values for Fine Grained Soils Defaults Predictions E K Z Q p b R psi cm sec scfm ipsi in Clay Unknown 2000 2 7x107 10 1500 21 0 23 16 5 Soft 500 2 7 107 10 1500 21 0 15 7 Medium 2000 2 7x10 10 1500 21 0 23
103. coupled with CASE STUDIES A presentation of various case studies PNEUMATIC FRACTURING COMPUTER MODEL ABOUT PF MODEL About PF MODEL HELP Describes how to access PF MODEL s help and explanation facility and if all else fails how to contact NJIT CEES for technical assistance 10 PNEUMATIC FRACTURING COMPUTER MODEL CHAPTER 4 STEP BY STEP EXAMPLE 4 0 General Overview The following example is deliberately simple to quickly get the first time user comfortable with using PF MODEL 4 1 Description of Problem Figure 4 1 shows a BTX plume that originated at the Little Bighorn Refinery and is migrating towards a nearby creek The contaminant originated from surface spills over an extended period of years Tank Farm Refinery f 74 E S e Tm Ww OCS Z BTX Plume P Direction of Ground J Water Flow zu n v EE 1 Crazy Horse Creek U Figure 4 1 Map showing location of BTX plume at Little Bighorn Refinery 11 PNEUMATIC FRACTURING COMPUTER MODEL In order to stop the plume migration it has been determined that the contaminants should be removed from the subsurface The subsurface profile consists of a 3 ft thick layer of miscellaneous granular fill and an underlying shale beginning at a depth of 19 ft A medium stiff clayey silt UCS CL lies between the fill and shale The water table varies seasonally from 6 to 15 f
104. ction gas etc This is the preferred method to modify the default parameters since it does not permanently change your default libraries EXPERT Expands to another drop down menu This option is only or an expert among the experts The three default libraries are accessed through this option and changes will become permanent if saved The libraries are e Flownet contains the flownet shape factors used for the Graphical Leakoff Methods e Knowledge Base Contains the heuristic probabilities based on subjective probability theory Bayes theory used by the inference engine of the Site Screening expert system e Default Contains the geotechnical and system defaults for the 14 geologic formation supported by PF MODEL It is not recommended that you permanently modify these libraries If you make a change or mistake and wish to return to the original libraries you will need to either reinstall PF MODEL from the original distribution disks or contact NJIT CEES for the master def files 3 3 1 6 BACKGROUND Menu From this menu item you can access some of the history and background information of the pneumatic fracturing technology and help for PF MODEL HISTORY Since 1987 when research began on the pneumatic fracturing technology a rich and colorful history has developed This option will guide you through the journey APPLICATIONS Discusses some of the more traditional applications pneumatic fracturing is
105. d Abramson 1990 will now be presented Let the frame of discernment be defined as an exhaustive set of mutually exclusive events Consider the simple case of four different competing events W X Y and Z Therefore has four different elements The number of possible hypotheses is 2 representing all possible subsets of or 16 elements In DST if the evidence shows that an event is disconfirmed it is equivalent to confirming the other events For example disconfirming W is equivalent to confirming X Y 7 or everything but W Let be a subset of in that the basic probability assigned to the set A is defined as m A This is the total belief of if the function m satisfies 1 The basic probability number of a null event is 0 m 0 2 The sum of the basic probability numbers for all subsets of is 1 opt A t 126 127 Let Bel A be the total amount of belief in A which can be expressed as Bel A SE m B Bel is called a belief function if the following conditions are satisfied 1 The belief in a null hypothesis is 0 Be 0 2 The belief in is 1 Bei 8 1 3 The sum of beliefs of and 4 must be less than or equal to 1 Bel A Bel A 1 As an example assume the basic probability assignments are m W 0 1 m X 0 2 0 3 m Z 0 4 and m W X 0 5 The belief Bel W m W3 or 0 1 shows that the Bel equals m for single eve
106. d be noted that due to the limitations of Mathcad only the final K z shape factor ratio is used for each iteration performed by Mathcad s equivalent PDF Subroutine as shown in the fourth column On the other hand PF Model has a full library of shape factors available for each iteration in the PDF Subroutine thus the true R z value is assigned during each iteration The results in the final column represent the ratio PF Model to Mathcad for both aperture and radius The estimated maximum aperture ratio varied 0 04 with the average being 1 01 while the radius ratio varied 0 01 with the average being 1 00 Validation results for the other graphical leakoff methods ie K and K 10K as well as the analytical leakoff method are contained in Appendix J Overall the results from Table 4 6 and Appendix J indicate that the Fracture Prediction Mode of PF Model accurately represents the mathematical model 4 3 2 Calibration of the System Design Component The System Design component was calibrated by referring to existing data The field data was based on the 6 sites comprised of 31 injections shown previously in Table 4 6 as Table 4 6 Validation of Graphical Leakoff Method 5K Using Bisection Model Engine Site Name K K oz Riz b R b R b R used in f Mcad PF Model i cm sec cm sec actual MCad w single R z useage w full R z usage z fi ft Frelinghuysen 1 9 35E 04 1 87E 04 0 0800 9 70E 0
107. d of many dividing or divorcing the BN of Figure C2 into 132 three separate networks has the effect of reducing the amount of specified distributions considerably Figure C 3 represents the BN that corresponds to Table 3 4 for plastic fine grained soils The four soils with clay minerals represent the four states in the node Soil Type The node Depth has been reduced to the three states that apply only to soils refer to Table 3 4 while Plasticity and Relative Density Consistency are still comprised of three states Results and Water Table remain the same each with only two states This represents a network with 432 distributions that need to be specified Density Consistency Figure C 3 A Bayesian Network for Plastic Fine Grained Soils Figure C 4 on the following page shows a BN for rocks The Rock Type consists of five states while the Depth consists of the three states that apply only to rock refer to Table 3 6 Fracture Frequency and Weathering each contain three states while Results and Water Table remain unchanged each containing two states This represents 540 distributions that need to be specified 133 Fracture Rock Type Figure C 4 Bayesian Network for Rocks Figure C 5 below shows the remaining BN for non plastic soils The Soil Type here consists of the four non clay soils while Depth Water Table Consolidation and Results remain unchanged The total number of distributions required are 1
108. d on the development of an expert system which generates technology recommendations This section provides an overview of current expert system technology and theory as well as the advantages and disadvantages 2 1 1 Introduction to Expert Systems Expert systems or knowledge based expert systems are computer programs that represent and use the knowledge of some human expert in order to solve problems or give advice within a narrowly defined field or domain Durkin 1994 This definition does not distinguish the difference between expert systems and conventional programs and techniques however Conventional programs can be interactive and contain rules of selection decision yet still not be an expert system Table 2 1 shows the important differences between expert systems and conventional programs Table 2 1 Differences Between Conventional Programs and Expert Systems Maher 1987 Conventional programs Expert systems Representation and use of data Representation and use of knowledge Knowledge and control integrated Knowledge and control separated Algorithmic repetitive process Heuristic inferential process Effective manipulation of data bases Effective manipulation of knowledge bases Oriented toward numerical processing Orientated toward symbolic processing 2 1 1 1 Origins of Expert Systems Early computers were originally high speed data processors Programs were written based on a prescribed algorithm to perform a series of
109. de used in programming PF Model as the entire code would be too extensive to list as part of this work The selected code is included for review of programming style and copyright protection purposes Floppy disks of PF Model can be obtained with a manual from the Center for Environmental Engineering and Science CEES located at the New Jersey Institute of Technology 138 Warren St Newark NJ 07102 The phone number is 973 596 2457 CHAPTER 4 VALIDATION AND CALIBRATION OF PF MODEL 4 1 Introduction In order for PF Model to be useful for consultants designers and researchers it must provide reasonable results Since PF Model has two different components Site Screening and System Design two distinctive evaluation methods will be used The approach for evaluating the Site Screening component was system validation and user acceptance Section 4 2 The System Design component was verified more traditionally i e validation and calibration Section 4 3 The results of each of these evaluation procedures will now be examined 4 2 Site Screening Since the Site Screening component is an expert system its evaluation differs greatly from conventional computer programs In conventional programs verification is the major concern since this determines if the program completely satisfies the initial conditions Adrion et al 1982 As discussed previously in Chapter 2 conventional programs have well defined algorithms and structures and th
110. depth FractureToughness Pi R_n 0 5 DENSITY Gas Exit Function FileError Divide by zero If Err Number 11 Then Msg The algorithm is dividing by zero This is most amp Chr 13 Msg Msg amp likely due to an incorrectly entered system input amp Chr 13 Msg Msg amp or geologic parameter Go back and check your amp Chr 13 Msg Msg amp entered data amp Chr 13 amp Chr 13 Msg Msg amp If the problem persists please make a amp Chr 13 Msg Msg amp note of the following information amp Chr 13 amp Chr 13 Msg Msg amp Error number amp Err Number amp Chr 13 Msg Msg amp Description amp Err Description amp Chr 13 Msg Msg amp Location amp Screen ActiveForm Name amp Chr 13 Msg Msg amp Procedure amp ProcName 198 MsgBox Msg Resume ErrorAbort Else Msg An untrapped error has occured Please make a amp Chr 13 Msg Msg amp note of the following information amp Chr 13 amp Chr 13 Msg Msg amp Error number amp Err Number amp Chr 13 Msg Msg amp Description amp Err Description amp Chr 13 Msg Msg amp Location amp Screen ActiveForm Name amp Chr 13 Msg Msg amp Procedure amp ProcName MsgBox Msg Resume ErrorAbort End If ErrorAbort Abort Yes End Function Private Function ApertureCalculation Abort ApertureFlag D depth K Modulus
111. e the algorithm steps the radius incrementally This process continues until the three controlling conditions elastic form pressure distribution and formation leakoff which correspond to the calculations of Steps 36 37 and 39 respectively are satisfied These three steps as well as the others that make up the PDF subroutine are discussed below 67 Y Step 33 Initialize discrete radius r Step 34 Calculate propagation pressure p Deflection Solver Calculate Step 36 aperture b Step 37 ES Increment r Step 41 Calculate pressure p Step 39 Leakoff Method Calculate flow res Do Step 42 Q flow b aperture p pressure Figure 3 7 The PDF Subroutine Pressure Deflection and Flow Step 33 Discretize the Fracture Radius The fracture radius is discretized into a number of segments equal to R rincy where rincer is defined as rincr 0 001 if R ry lt 1 ft 3 18 68 otherwise 0 1 3 19 Step 34 Calculate Propagation Pressure The pressure required to propagate fractures is given by Pprop Pm Pk 3 20 where is the maintenance pressure and is the pressure required to overcome fracture toughness A semi empirical relationship is available for estimating maintenance pressures in the saturated zone is given by King 1993 Pm a z B Zw x y a X Zw X y
112. e engine will access each probability from the knowledge base By examining the flow 48 Y Select Grain Size based on Soil Type Grained Soils Grained Soils Plasticity I Water Table Determine Rules to be Fired Applicability Rating Figure 3 4 Flow Chart Representing How Inference Engine Accesses Probabilities From Knowledge Base 49 chart it can be seen that the model obtains evidence and then proceeds toward a desired goal i e forward chaining Figure 3 4 also shows the step in the heuristic process where the inference engine determines the rules that are to be fired refer to the in the figure As pointed out previously in Chapter 2 the selection of the rule and the uncertainty theory used is the most important aspect of the inference engine and the discussion which follows will provide a clearer understanding of the implementational logic used In order to clarify the implementational logic or which rules are fired in the inference engine it is advantageous to change the terms and B of Equation 2 2 In subjective probability if we let p H be the prior probabilities of all possible hypotheses and p E H be the conditional probabilities for observing a piece of evidence given a hypothesis Equation 2 2 can be rewritten in terms of H and E This yields pOELH x p x x p H Initially the user will give the sys
113. e Depth Depth Depth Plasticity Relative Density Weathering Consistency Water table depth Fracture Frequency Water table depth Water table depth These geotechnical properties in turn were divided into qualifiers in order to quantify the geological evidence for analysis by the expert system This was done in 93 subsequent discussions with human experts Table 4 3 below shows how the geotechnical properties were qualified Table 4 3 Breakdown of Geotechnical Properties Into Qualifiers Formation Type Clay Clayey Sand Clayey Silt Silty Clay Silt Silty Sand Sand Sand amp Gravel Gravel Shale Siltstone Sandstone Limestone Dolomite Granite Gneiss Schist Basalt Depth for Rocks lt 4 ft 4 8 ft gt 8 ft Depth for Soils lt 6 ft 6 12 ft gt 12 ft Consistency Soft Medium Stiff Relative Density Loose Medium dense Dense Plasticity w lt PL PL lt lt LL w gt LL Fracture Frequency Widely jointed Medium jointed Closely jointed Weathering Slightly weathered Moderately weathered Heavily weathered Water Table Fracturing is above Fracturing is below Once the geotechnical properties were firmly established a system utility to access this information was developed for an early version of PF Model This utility was 94 subsequently evaluated by experts for ease of use understanding and visual aesthetics After some minor GUI modifications the final system utility wa
114. e Sandstone Limestone Dolomite Granite Gneiss Schist Basalt Depth 4 ft a 4 8 ft gt 8 ft SERTE 6 12ft gt Notes a applicable to rocks b applicable to fine grained soils 0 65 0 70 0 75 0 70 0 50 0 45 0 25 0 20 0 10 0 75 0 65 0 65 0 55 0 50 0 40 0 55 0 65 0 25 0 50 0 55 c applicable to coarse grained soils Plasticity lt PL PL lt w lt LL w gt LL Consistency b Soft Medium Stuff Relatiye Density Loose Medium dense Dense Weathering Slightly weathered Moderately weathered Heavily weathered Fracture Frequency Widely jointed Medium jointed Closely jointed Water Table Fracturing is above Fracturing is below 0 60 0 45 0 10 0 40 0 50 0 60 0 40 0 50 0 60 0 45 0 60 0 55 0 20 0 50 0 60 45 Note that for certain formation types some geotechnical properties may not be applicable as evidence For example if the formation is a silty sand the only applicable 46 geotechnical properties are depth for soils relative density and water table It is therefore the task of the inference engine to determine which probabilities are applicable and which rules are to be fired The rules to be fired can be categorized by their overall interactions Since some of the geotechnical properties listed in Table 3 3 apply to certain types of formations i e only clay soils exhibit plasticity while other pro
115. e to quickly get acquainted with PF MODEL s intuitive interface PNEUMATIC FRACTURING COMPUTER MODEL PF MODEL Version 3 0 An Integrated Modeling Environment and Expert System for Pneumatic Fracturing Developed and Written by Brian Sielski and John Schuring May 1999 NJIT CEES 138 Warren Street Room 220 Newark NJ 07102 tel 973 596 5849 fax 973 642 7170 TABLE OF CONTENTS Chapter Page GETTING STARTED inten ates ae erac tee p CORR UAR RAIN fp tat icu epus 1 LI BPESMODEL VetSIOBS doa eine at een 1 1 2 Required and Optional Hardware see emen PTT 1 t3 Iastaline PP MODE Do p kasupi enitn 2 14 User A ene tic iacit Ru puces s tr ritu orbe porta supa IUS 3 1 5 Runnin PE MODEBLD tcr euet epus Cher eau denies EE aa aa 3 2 THEORETICAL BACKGROUND hia Dr 4 3 LISUNCEPESMODEL ols ers ees toads gue a aa tau asda bio aureae 5 2 9 a asc aeu ap to merid b tas es Sate epp IO pep RUE arcade 5 Howto R n PEsSMODED u a as to ege tuae ensi 3 3 2 Hot Keys and Mouse Functions a italy dasa hence fL ONE uas 5 3 9 Screen Layout KI 3 5 Lhe Top Menu DE oscar u i aa Gan 6 6 mol b AILE MORBUS deat tasa utes amanaya
116. e 60 to 100 The technology is likely to be effective System Utilities Throughout the development of the Site Screening component human experts were consulted to determine the system utilities as well as their design This process was done over many months with different pneumatic fracturing experts The most important step in this process was to determine which geotechnical parameters influence the success of pneumatic fracturing After extensive discussion it was determined that the seven geotechnical properties detailed in Chapter 2 ie formation type depth plasticity etc have the greatest influence on the pneumatic 92 fracturing process Further discussions led to the following conclusions about these properties e formation type was the most important property to effect pneumatic fracturing and therefore should always be required as cipit data for the expert system e hierarchical order was established for the remaining geotechnical properties and the geotechnical properties are independent of each other The importance of formation type and the other geotechnical properties as applied to pneumatic fracturing was previously discussed in Chapter 2 The hierarchical order of the geotechnical properties is shown below in Table 4 2 and are grouped according to soil or rock type Table 4 2 Hierarchical Order of Geotechnical Properties Fine Grained Soils Coarse Grained Soils Rocks Soil type Soil type Rock typ
117. e Screening component of PF Model like most expert systems contains knowledge that evolves Therefore the way the pneumatic fracturing technology is viewed by experts may change over time This can be due to a number of factors including development of new equipment modifications of existing equipment change in work procedures and even new research results Conversely as the expert system is used deficiencies may also be discovered Therefore the validation of the expert system is a continuous process 4 2 2 User Acceptance of Site Screening Component This is perhaps the ultimate test of an expert system If the Site Screening component is not accepted by the end user the expert system will then be of little worth At this point a base of 50 or more users are expected including pneumatic fracturing vendors design 89 consultants and government regulators Of course the final determination of user acceptance will not be known until after the program is released to the public The major issues of user acceptance are e ease of use e presentation of results e clarity of explanations and e system utilities Ease of Use During the development of the technical features of PF Model an effort was made to present the program in an easy to use format since some users are reluctant to even try new software Throughout the programming of PF Model s interface the following features were incorporated to make it user friendly
118. e fracture wells Assume that a 25 ft well spacing is desired and that a 20 overlay of fracture influence radius will be implemented The required fracture radius is then 25 120215ft Therefore the system parameters must now be be modified to extend the fracture radius from 14 04 ft the previous result to 15 0 ft The default flow rate of 1500 scfm must now be increased to accomplish this Click on the OVERRIDE DEFAULT check box for Flow Rate A text field has now appeared next to each system parameter For the system flow rate 20 PNEUMATIC FRACTURING COMPUTER MODEL Enter the value 2500 scfm Click the button CALCULATE The estimated aperture is 0 864 in lt lt lt The estimated radius 15 15 7 ft lt lt lt Note you could also adjust Maintenance Pressure to obtain a larger fracture radius However we will retain the default Maintenance Pressure which is associated with the selected flow rate The chosen value of flow rate is apparently too high Now try a lower value Enter the value 2000 scfm Click the button CALCULATE The estimated aperture is 0 676 in lt lt lt The estimated radius is 15 16 ft lt lt lt You can continue with new values for system design but these are close enough That s because you ve used default values for conductivity and modulus It is estimated that the accuracy of the model when using the defaults is 25 More accurate results could be obtained by performing
119. e injection is performed at a pressure which exceeds the natural in situ stresses and at a flow rate which exceeds the permeability of the formation In soil formations pneumatic fracturing enhances the permeability of the formation by creating fracture networks while in rock formations the effect is the dilation and extension of existing discontinuities which improves the interconnection between existing fractures The immediate benefit is improved access to the subsurface contaminants so that liquids and vapors can be transported and extracted more rapidly Pneumatic fracturing is similar in concept to the hydraulic fracturing techniques used in the petroleum industry Gidley ef al 1989 The principal difference is that hydraulic fracturing uses water to create the fractures while pneumatic fracturing uses a gas usually air This is a significant and advantageous difference In using air as an injection fluid fracture propagation is more rapid due to the lower viscosity of air over water In addition air is less likely to remobilize and spread contaminants than water Pneumatic fracturing has been successfully demonstrated in the field at a number of contaminated sites Among these are U S EPA SITE Demonstrations at contaminated sites in Hillsborough New Jersey to enhance soil vapor extraction U S EPA 1993 and in Marcus Hook Pennsylvania to enhance in situ bioremediation U S EPA 1995 Pneumatic fracturing is now available commerci
120. e more specific thereby moving away from any marginal recommendations caused by the coupling technologies However the disadvantage of a more specific approach 1s that the recommendations 116 may become too complex and cause confusion for users that are just interested in the overall validity of the technology for a site Future versions of PF Model will need to address which of the two groups of users to accommodate vendors and experts or consultants and government agencies PF Model should be used in conjunction with field operations at the earliest possible date to assess its predictive ability as well as to obtain feedback on the graphical user interface Comments and suggestions should be complied and reviewed for possible inclusion into future versions of PF Model The Default Library should be updated to reflect any new site data as it becomes available At a minimum an annual review of sites should be undertaken to insure that the defaults provide reasonable results and updated accordingly Over the next two years the defaults for rocks and the coarse grained soils should receive the greatest effort as data available for default calibration of these formation types were limited during this study Currently there are two anisotropic conditions supported by PF Model K 5K and K 10K Other anisotropic conditions could be supported including instances for when K gt K so that a wider range of formation condi
121. e part of the expert system that contains the domain knowledge and heuristics of the expert In general it is the collection of knowledge in the form of rules procedures and facts The most typical way to represent the heuristics of the expert is to apply an IF THEN decision structure Georgeff 1983 The knowledge base also contains a high level of competence in the general knowledge about the behavior and interactions in the problem domain The scheme of the knowledge base is one of the most critical decisions in that it impacts the design of the inference engine the knowledge acquisition facility and overall efficiency of the system Stefik et al 1982 Working Memory The working memory is the component of the expert system that models the human s short term memory 1t contains the global data base used by the rules of the system facts both entered and inferred and the intermediate results that make up the current state of the problem Hunt 1986 Eventually the working memory expands as the expert system reasons about the current problem Information and data subsequently generated by the expert system in order to solve the problem are also stored When the problem is solved the working memory not only contains the solution but all the intermediate results as well Inference Engine Also known as the control structure or rule interpreter the inference engine 1s the part of the program that performs the reasoning 1t locates the re
122. e reached depths of 50 ft but there is no theoretical maximum depth limit As long as sufficient back pressure and flow can be delivered into the formation with higher capacity equipment fracturing can be propagated at greater depths 28 The minimum depth of injection is based on the ability of the formation to act as a seal during injection For example formations which are made of fill materials will tend to exhibit daylighting which means that the fractures will intersect the ground surface However formations such as rock will allow injections closer to the surface i e 3 ft with minimal amounts of daylighting Plasticity Another important property is plasticity A soil that can be remolded in the presence of some moisture without crumbling is said to be plastic Plasticity applies only to fine grained soils when clay minerals are present i e clay clayey silt clayey sand and silty clay Soil plasticity is measured using the Atterberg Limits Test ASTM D4318 93 which correlates soil moisture content with plastic behavior Descriptions of soil consistency in relationship to Atterberg Limits are presented in Table 2 3 Table 2 3 Description of Atterberg Limit Range Atterberg Limit Range Description w lt PL brittle PL lt w lt LL plastic w gt LL liquid Note PL plastic limit LL liquid limit and w moisture content It has generally been found that brittle soils w PL respond well to pneum
123. e the Soil Rock Type combo box with the soils and rocks cboType Addltem Clay cboType Addltem Clayey Sand cboType Addltem Clayey Silt cboType Addltem Silty Clay cboType Addltem Silt cboType Addltem Silty Sand cboType Addltem Sand cboType Addltem Sand and Gravel cboType AddItem Gravel cboType AddItem cboType Addltem Shale Siltstone cboType Addltem Sandstone cboType Addltem Limestone Dolomite cboType Additem Granite Gneiss Schist cboType AddItem Basalt Initialize the Weathering combo box cboWeathering AddItem Unknown cboWeathering Addltem Slightly weathered cboWeathering AddItem Moderately weathered cboWeathering Addltem Highly weathered Initialize the Fracture Frequency combo box cboFracFrequency AddItem Unknown cboFracFrequency Addltem Closely jointed cboFracFrequency Addltem Medium jointed cboFracFrequency Addltem Widely jointed Disable all the geologic system media property objects which will be enabled when the proper checkbox s is selected Call GeologicalPropertiesFalse Call SystemPropertiesFalse 210 End Sub Sub cboType Click Call the subroutine that turns on off the approriate data input parameters which are are not needed depending on the soil or rock type selected Call GeologicalPropertiesOnOff When a first time or new formation type is selected the Con Den should be unknown frmConDen optUnknown Value True Call EstablishForma
124. e tip are satisfied during the same segment of the subroutine This is repeated for each increment in radius Therefore when the fracture radius extends past 7 ft the processing time can become quite lengthy The steps involved in the subroutine are presented below Step 15 Engine Selection When control of the algorithm is passed to this subroutine it passes which model engine has been selected This step determines which subsequent logic to follow bisection or increasing If Bisection is selected the subroutine proceeds to Step 16 Otherwise the subroutine proceeds to Step 30 for the Increasing Engine Steps 16 through 19 Radius Initialization The initialization of the upper and lower bounds of the radius interval are chosen such that the actual radius lies within this interval From experience the lower limit RZ ow is chosen to be the well radius in most cases 0 25 ft For the upper limit RHigh a value of 200 ft is selected Next the value of R Miq is prepared which is R High R Low 3 3 15 64 three values are then passed as input to the PDF Subroutine which processes the values as a parallel operation in logic Step 20 PDF Subroutine The PDF or Pressure Deflection and Flow Subroutine is passed control with values of the radii determined in the Model Engine Subroutine The PDF Subroutine is discussed in Section 3 3 3 3 Step 21 Internal Storage of PDF Subroutine Results As control passes b
125. e txtDryMI Formation SiltyClay Text Case3 Liquid Media Injection Evidence Val frmKnowledgeBase txtLiquidMI Formation SiltyClay Text End Select Case Silt Select Case TechnologyFlag Case 1 Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation Silt Text Case Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation Silt Text Case3 Liquid Media Injection Evidence Val frmKnowledgeBase txtLiquidMI Formation Silt Text End Select Case Silty Sand Select Case TechnologyFlag 1 Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation SiltySand Text Case2 Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation SiltySand Text Case3 Liquid Media Injection Evidence Val frmKnowledgeBase txtLiquidMI Formation SiltySand Text End Select Case Sand Select Case TechnologyFlag Case Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation Sand Text Case2 Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation Sand Text Case3 Liquid Media Injection 203 Evidence Val frmKnowledgeBase txtLiquidMI Formation Sand Text End Select Case Sand and Gravel Select Case TechnologyFlag Case Permeability Enhancement Evidence Val frmKnowledgeBase txtK Formation SandGravel Text Case2 Dry Media Injection Evidence Val frmKnowledgeBase txtDryMI Formation SandGravel Text Case3 Liquid Media Injection Eviden
126. ely highly M Y y Y 65 Sandstone 10 16 n a n a n a widely slightly N Y Y N 43 Basalt 15 n a n a medium slightly M M M M 60 Sandstone 12 8 n a n a n a 227 M Y Y Y 76 Notes Evaluators are Dr J Schuring Patent Holder of PF B T Boland PF Design Engineer NJIT C B Sielski PF Research Assistant NJIT D J Liskowitz President ARS Technologies Inc E T King Sr Engineer McLaren Hart Environmental Engineering Corp Y recommended rating 60 100 M marginally recommended rating 45 60 N not recommended rating 0 45 n a not applicable L8 unknown not provided to evaluator 88 The system results in Tables 4 1 J 1 and J 2 show an agreement of 93 93 and 80 per cent respectively This represents an overall average of 89 per cent among the three pneumatic fracturing variants It should be noted that the subscripts shown for certain recommendations in Table 4 1 represent the original opinion of the expert are inevitable that evaluators would assess each recommendation differently Therefore evaluators were also asked to rate each site numerically i e from 1 to 10 In some instances it was apparent that the original recommendation was a gray area for the evaluator In these instances the relative weight of the rating further defined their opinion and was adjusted accordingly Although this may seem like an end to system validation that is not the case The Sit
127. erefore can be measured against some objective standard On the other hand an expert system is designed to answer questions heuristically for which there is no right or wrong answer That is there is no gold standard against which the performance of the expert system can be measured absolutely Gasching et al 1983 83 84 Because of the lack of an absolute standard the Site Screening component was evaluated using system validation and user acceptance Preece 1990 The evaluation methods are somewhat more relaxed than the stringent verification process that the System Design component has undergone see Section 4 3 System validation tries to determine if the system performs the intended task satisfactorily Hollinger 1989 User acceptance evaluates whether the system meets the needs of the user It is noted that the procedures of system validation and user acceptance are somewhat subjective and therefore make the evaluation of an expert system complex Durkin 1994 4 2 1 System Validation of Site Screening Component Since the Site Screening component models the decision making process of a human expert PF Model should obtain the same results as the expert Therefore the system validation of the Site Screening component involved the use of test cases The selected test cases were based on a blend of actual and hypothetical field experiences which varied in success During the validation procedure the site evidence was give
128. ers methods of solution expert system design etc used in PF MODEL the following two references are helpful Sielski B Development of a Computer Model and Expert System for Pneumatic Fracturing of Geologic Formations Ph D Dissertation Department of Civil and Environmental Engineering New Jersey Institute of Technology Newark NJ May 1999 Puppala S Fracture Propagation and Particulate Transport in Pneumatically Fractured Geologic Formations Ph D Dissertation Department of Civil and Environmental Engineering New Jersey Institute of Technology Newark NJ August 1998 PNEUMATIC FRACTURING COMPUTER MODEL CHAPTER 3 USING PF MODEL 3 0 General Overview PF MODEL fully exploits the graphical user interface GUI that is familiar to anyone that uses Windows type programs such as Microsoft s Word or Excel PF MODEL uses the same pull down menus buttons scroll bars etc that are familiar to most users today It should therefore be easy and intuitive to use PF MODEL 3 1 How to PF MODEL Refer to Chapter 1 Getting Started to run PF MODEL When the program starts an introductory screen will appear Select Go to move to the Data Input screen 3 2 Hot Keys and Mouse Functions As outlined in Section 1 2 a mouse is required to use PF MODEL This is the easiest and most efficient way to move about in PF MODEL However most menu items and buttons can be accessed using Hot Keys The Hot Key which correspond
129. esign Engineer NJIT C B Sielski PF Research Assistant NJIT D J Liskowitz President ARS Technologies Inc E T King Sr Engineer McLaren Hart Environmental Engineering Corp Y recommended rating 60 100 M marginally recommended rating 45 60 not recommended rating 0 45 n a not applicable 27 unknown not provided to evaluator TIT Table J 2 System Validation of Liquid Media Injection Variant Depth to Depth W T Relative Fracture Formation Type ft ft Consistency Plasticity Density Frequency Weathering Silty Clay 18 10 medium UT n a n a n a Clayey Silt 10 18 medium brittle n a n a n a Clay 8 4 soft plastic n a n a n a Silty Clay 12 10 medium liquid n a n a n a Clay 10 22 72 222 n a n a n a Clay 4 10 very stiff brittle n a n a n a Silty Sand 14 8 n a n a med dense n a n a Sand 24 10 n a n a dense n a n a Sand and Gravel 14 20 n a n a very dense n a n a Siltstone 20 12 n a n a n a closely slightly Shale 10 227 n a n a n a 222 202 Shale Siltstone 12 18 n a n a n a widely highly Sandstone 10 16 n a n a n a widely slightly Basalt 15 TN n a n a n a medium slightly Sandstone 12 8 n a n a n a 222 T Notes T Evaluators are Dr J Schuring Patent Holder of PF B T Boland PF Design Engineer NJIT C B Sielski PF Research Assistant NJIT D J Liskowitz President ARS Technologies Inc E T King Sr Engineer McLaren Hart Environmental Engineering Corp Y recommended r
130. esses that include pressure distribution leakoff and deflection The Calibration Mode determines the post fracture Young s modulus and pneumatic conductivity of a site that has already been fractured e a pilot test This algorithm regresses the modulus using the modified deflection equation then converges on the conductivity in an algorithm similar to the Fracture Prediction Mode The algorithm for the Fracture Prediction Mode of the System Design component has two solution methods bisection and increasing It also uses two methods to determine leakoff graphical and analytical Finally there are four deflection solvers to model overburden deflection These options are coded into three nested subroutines that allow the user to select any of the above methods to determine the aperture and radius The Calibration Mode uses the Bisection Engine due to processing speed considerations since the algorithm converges on two solutions in two separate intervals e the pneumatic conductivity and the corresponding residual flow rate that satisfies the conductivity in the current iteration of the subroutine The leakoff method used is the Analytical method since in virtually all instances the actual field results use the effective conductivity Kef However all four Deflection solvers are available in this mode 11 113 While calibrating the System Design algorithm a flaw was detected in the original pressure distribution mathematic
131. estone Dolomite Or cboType Text Granite Gneiss Schist Or cboType Text Basalt Then cmdConsDense Enabled False Else OCR is instead true i e a soil type cmdConsDense Enabled True End If End Sub Sub SystemPropertiesFalse This procedure is used to make all the objects in system design disabled i e false lbISystemProperties Enabled False IbIFlowRate Enabled False txtFlowRate Enabled False IbiMaintenancePressure Enabled False txtMaintenancePressure Enabled False IbIWellRadius Enabled False txtWellRadius Enabled False cmdPneumaticConductivity Enabled False IblOverride Enabled False chkOverrideFlow Enabled False chkOverridePressure Enabled False chkOverride WellRadius Enabled False IbiDefaultFlow Enabled False IbiDefaultPressure Enabled False IbIDefaultWellRadius Enabled False End Sub Sub SystemPropertiesTrue This procedure is used to make all the objects in system design enabled i e true IbISystemProperties Enabled True IbIFlowRate Enabled True txtFlowRate Enabled True IbIMaintenancePressure Enabled True 208 txtMaintenancePressure Enabled True IbIWellRadius Enabled True txtWellRadius Enabled True cmdPneumaticConductivity Enabled True IblOverride Enabled True chkOverrideFlow Enabled True chkOverridePressure Enabled True chkOverrideWellRadius Enabled True IbiDefaultFlow Enabled True IbIDefaultPressure Enabled True IbiDefau
132. etter understand the rating 15 PNEUMATIC FRACTURING COMPUTER MODEL Click the button Take time to read the recommendation ratings in the help box After reading the recommendation ratings it is obvious that this site s value of 76 is a good candidate for permeability enhancement Notice that there is still evidence that is not known In this instance it is plasticity Now check out if there can be any adverse effects due to plasticity The eight geotechnical labels on the upper right are also active objects By clicking on any of them a screen with qualifiers pops up To see the effects of plasticity Click on the label PLASTICITY Select the option w lt PL By this selection you are assuming that the clayey silt is in a brittle condition w lt PL Now check to see what effect this has on the technology recommendation Click on the button PERMEABILITY ENHANCEMENT A rating of 83 is given This is an excellent condition for pneumatic fracturing However let s look at one more condition where the plasticity is liquid w gt LL Click on the label PLASTICITY Select the option w gt LL Click on the button PERMEABILITY ENHANCEMENT A rating of 27 is given In this instance pneumatic fracturing is not likely to be effective for permeability enhancement without use of system variants e g proppants What this indicates is that more evidence is always desirable in order to have confidence in the recommendatio
133. ew York NY 1969 Lenat D The Nature of Heuristics Artificial Intelligence Vol 19 pp 189 249 1982 Levitt T Choosing Uncertainty Representations in Artificial Intelligence International Journal of Approximate Reasoning Vol 2 pp 217 232 1988 Maher M Expert Systems Components Expert Systems for Civil Engineers American Society of Civil Engineers 1987 Michie D Expert Systems in the Micro Electronic Age Edinburgh University Press Edinburgh Great Britain 1979 Microsoft Visual Basic Programmers Guide Microsoft Corporation 1997 Nautiyal D Fluid Flow Modeling for Pneumatically Fractured Formations M S Thesis Department of Civil and Environmental Engineering New Jersey Institute of Technology Newark NJ 1994 220 REFERENCES Continued Newell A and Simon H A Human Problem Solving Prentice Hall Englewood Cliffs NJ 1972 Ng K and Abramson B Uncertainty Management in Expert Systems IEEE Expert Vol 5 No 2 1990 Nilson R Proffer W and Duff R Modeling Gas driven Fractures Induced by Propellant Combustion Within a Borehole International Journal of Rock Mech Min Sci and Geomech Abstr Vol 22 No 1 pp 3 19 1985 Patterson D Introduction to Artificial Intelligence and Expert Systems Prentice Hall Englewood Cliffs NJ 1990 Pearl J Probabilistic Reasoning in Intelligent Systems Morgan Kaufmann Publishers San Mateo CA 1988 Perk
134. f the current study the use of BNs was investigated as a means to handle uncertainty in PF Model Preliminary studies showed that pneumatic fracturing can be modeled directly with a BN yet further investigation indicated that an influence diagram might be more appropriate It also appeared to be feasible to model pneumatic fracturing as a combination BN influence diagram The purpose of this appendix is to present what has been researched to date and to report on some of the difficulties of applying BNs to pneumatic fracturing Ultimately after several months of study it was decided to use subjective probability Appendix A 128 129 to handle uncertainty The study of BNs was nevertheless useful in identifying a causal dependency of the geologic properties e depth plasticity weathering etc on the success of pneumatic fracturing The use of BNs in future versions of PF Model is still considered possible C 2 Geologic Evidence The design of PF Model s expert system which is based on subjective probability theory was done in conjunction with research efforts in Bayesian networks Bayesian networks and subjective probability theory are related in many aspects since both are derived from Bayes theory the difference being the use of DAGs Influence diagrams in BNs Therefore most of the findings are shared between both models The base knowledge used in PF Model s expert system is applicable to the pneumatic fracturing BN a
135. ficial Intelligence Wiley amp Sons New York NY Vol 1 1987 Shortliffe E and Buchanan B Rule Based Expert Systems The MYCIN Experiments of the Stanford Heuristic Programming Project Addison Wesley Reading MA 1984 Shortliffe E Buchanan B and Feigenbaum E Knowledge Engineering for Medical Decision Making A Review of Computer Based Clinical Decision Aids Proc IEEE Piscataway NJ Vol 67 No 9 pp 1207 1224 1979 Sielski B Overview of Pneumatic Fracturing and the Computer Model Memorandum March 20 1998 Sowers and Sowers G F Introductory Soil Mechanics and Foundations Third Edition Macmillan Publishing Co Inc New York NY 1970 Spence D and Turcotte D Magma Driven Propagation of Cracks Journal of Geophysical Research 90 B1 pp 575 580 1985 Stallings W Fuzzy Set Theory versus Bayesian Statistics JEEE Trans Systems Man and Cybernetics Vol 7 No 3 pp 216 219 1977 Stefik M Aikins J Balzer R Benoit J Birnbaum L Hayes Roth F and Sacerdoti E The Organization of Expert Systems a Tutorial Artificial Intelligence Vol 18 pp 135 173 1982 Szolovits P and Pauker S Categorical and Probabilistic Reasoning in Medical Diagnosis Artificial Intelligence Vol 11 pp 115 144 1978 Tzvieli A Probabilistic Logic for Expert Systems in Fuzzy Expert Systems Kandel ed CRC Press Inc Boca Raton FL 1992 U S
136. future future PF Design and Operational Parameters Enhancement Predictions PF Applicability Figure 3 2 Top Level Flow Chart Showing the Model Components 3 1 1 Site Screening This component incorporates data collected from pneumatic fracturing projects to date and new data can be added as it becomes available The needed input data for a site screening analysis was previously discussed in Section 2 2 1 Geotechnical Properties They include formation type depth relative density consistency plasticity fracture 38 frequency weathering and water table depth These data are modeled as expert heuristic knowledge i e knowledge that cannot be quantified in PF Model s knowledge base To activate this model component the user must first enter any known or estimated geologic properties for a prospective site The program then compares the inputted information with the knowledge base Based upon the results of these comparisons a semi quantitative applicability rating will be assigned for the prospective site The programming methods to reach this decision will be based largely on expert systems 3 1 2 System Design The ability to initiate and propagate pneumatic fractures is a function of the geomechancial properties of the formation as well as the depth of overburden A model for predicting pneumatic fracture initiation and maintenance pressure has been developed at HSMRC by considering the geo
137. g in this kind of formation to date May 1999 Graphical leakoff method K 5K used 105 In view of the inherent assumption of the model and the lack of shallow data it was decided to calibrate the model for the specific range of 10 30 ft As future field data becomes available the calibration should be revisited This current limitation also makes it clear that an entirely new fracture propagation model that incorporates both bending and localized elastic compression needs to be developed 4 3 2 3 Calibration of Coarse Grained Soils Coarse grained soils behave somewhat differently than either fine grained soils or rocks when subjected to pneumatic fracturing Field observations to date show that surface heaves are minimal and it is difficult to determine precise propagation radii It is not known whether truly discrete fractures occur as they do in a cohesive formation Therefore the approach for calibrating coarse grained soil was to use pneumatic conductivity data and pneumatic conductivity trends found in literature Conductivity has a major influence on leakoff rate into the formation and thus largely determine the dimension of the fracture Similarly the moduli and moduli trends for coarse grained soils were taken from the literature but were also calibrated against the values used for fine grained soils The final default values for coarse grained soils are shown in Table 4 9 on the following page In general the deflections c
138. g on one extreme to probabilistic at the other Szolovits and Pauker 1978 The certainty factor approach is designed to handle these difficulties Obviously there were disadvantages with this method the most obvious brought out by Adams He found for example that some unstated assumptions made by certainty factors may not be valid Adams 1976 24 2 2 Site Screening Model Background An essential step in successful site remediation 1s selection of appropriate technologies Geotechnical properties play a major role in the decision process for in situ technologies like pneumatic fracturing This section discusses the various geotechnical properties which are considered in the Site Screening component of PF Model 2 2 1 Geotechnical Properties Years of experience and research with the pneumatic fracturing process have demonstrated that the success of the technology or its failure is dependent on a number of different geotechnical properties This has led to a hierarchical ranking of the geological properties After careful consideration and discussion with experts it has been determined that seven different factors can significantly affect the pneumatic fracturing process Sielski 1998 They are presented below in the order of perceived importance e Formation type e Depth e Plasticity soils e Relative Density Consistency soils e Fracture frequency rocks e Weathering rocks e Water table 25 Each of these will n
139. he dry unit weight y is 105 lb ft For all cases Poisson s ratio o is 0 40 For all cases fracture toughness is 0 0 141 Table D 3 Default Values for Rocks Used in PF Model v3 0 JU U UU L LLLLLLLLLLLLeweLLUUUUUUUUULULU ae GEOTECHNICAL PROPERTY DEFAULT post fracture Pneumatic Young s Conductivity Ku Modulus E Formation Type Fracture Frequency cm sec psi Shale Siltstone Unknown 1 1x10 6 000 Widely jointed NR N R Medium jointed 90 10 12 000 Closely jointed 1 1X 107 6 000 Sandstone Unknown 1 3X 10 8 000 Widely jointed N R N R Medium jointed 11 10 16 000 Closely jointed 1 3X 10 8 000 Limestone Dolomite Unknown 1 1x10 8 000 Widely jointed NR N R Medium jointed 9 0X 107 16 000 Closely jointed 1356107 8 000 Granite Gneiss Schist Unknown 1 1x10 10 000 Widely jointed N R N R Medium jointed 9 0 10 20 000 Closely jointed L1x10 10 000 Basalt Unknown 1 1x10 15 000 Widely jointed N R N R Medium jointed 9 0x 10 30 000 Closely jointed 1 310 15 000 Notes For all cases the dry unit weight y is 140 Ib ft For all cases Poisson s ratio v is 0 25 For all cases fracture toughness Kie is 0 0 N R Technology generally not recommended Value based on standard published rock properties only No experience with pneumatic fracturing in this kind of formation to date May 1999 APPENDIX E PROBABILITIES FOR PF MODEL S KNOWLEDG
140. he number of potential drops To account for pressure variation with respect to radial distance the length of the fracture is divided into n segments and then the number of flow tubes leaving each segment is counted The leakoff occurring in each segment can then be computed as D N f Oleak A K gas H Na J 8 8 hy n where ry is the well radius R is the final fracture radius and Hy is the total head driving the flow in the segment By further segmenting the radial fracture into concentric annular rings the formula for total leakoff in three dimensions can be derived as r R n Ny Oleak 25 AA alr 3 9 27 where rj is the inner radial distance and rj 4 is the outer radial distance of the annular ring The analytical method calculates leakoff by summing the lost flow from successive annular rings of the fracture surface This is given by r R Qleak gt TCR 2 alen 17 3 10 Fo Sry grad n where Kh gas and Ky gas are respectively the horizontal and vertical pneumatic conductivities of the formation pg is the driving pressure and xaq is the flowpath length along which the pressure is dissipated along the segment Deflection Model It is assumed that pneumatic fractures are due to overburden deflection which is a function of the pressure distribution within the fracture Canino 1997 A model to predict the overburden deflection was investig
141. hen applying pneumatic fracturing Table 1 PF Model s Knowledge Base Probabilities for Three Pneumatic Fracturing Variants Liquid Permeability Dry Media Media Enhancement Injection Injection Formation Clay 65 0 55 0 70 0 Clayey Sand 70 0 60 0 70 0 Clayey Silt 75 0 60 0 70 0 Silty Clay 70 0 60 0 70 0 Silt 50 0 75 0 70 0 Silty Sand 45 0 75 0 75 0 Sand 25 0 75 0 75 0 Sand and Gravel 20 0 65 0 65 0 Gravel 10 0 65 0 65 0 Shale Siltstone 75 0 65 0 65 0 Sandstone 65 0 60 0 60 0 Limestone Dolomite 65 0 55 0 55 0 Granite Gneiss Schist 55 0 55 0 55 0 Basalt 50 0 50 0 50 0 Depth For Soils lt 6 ft 25 0 40 0 30 0 6 12 ft 50 0 50 0 50 0 gt 12 ft 55 0 50 0 55 0 For Rocks lt 4 ft 40 0 40 0 40 0 4 8 ft 55 0 50 0 55 0 gt 8 ft 65 0 50 0 60 0 144 Table E 1 continued Consistency Soft 40 0 48 0 48 096 Medium 50 0 50 0 50 0 Stiff 60 0 52 0 52 0 Plasticity a w lt PL 60 0 55 0 55 0 PL lt w lt LL 45 0 55 0 50 0 gt 10 0 45 0 45 0 Relative Density Loose 40 0 60 0 60 0 Medium dense 50 0 55 0 55 0 Dense 60 0 50 0 50 0 Fracture Frequency Widely jointed 20 0 20 0 20 0 Medium jointed 50 0 48 0 50 0 Closely jointed 60 0 55 0 60 0 Weathering Slightly weathered 45 0 45 0 45 0 Moderately weathered 60 0 50 0 55 0 Heavily weathered 55 096 55 0 60 0 Water Table Fracturing is above 52 0
142. hen the discretized fracture radius is increased by Tiner given by 1 Fn liner 3 25 where r is the new segmental fracture radius rj is the segmental fracture radius for the current iteration and rjncy is the size of the incremental radius which was defined previously in Equations 3 18 and 3 19 Execution then passes back to Step 36 where the current values for residual flow and pressure are used as the input for the next segment about to be executed 73 Step 42 Output The values of residual flow aperture propagation radius and pressure are returned along with the process control back to the System Design Subroutine if the conditions of Step 40 are not satisfied Control is passed if and only if all three conditions are not satisfied which corresponds to the convergence of all three physical processes and indicates that the final propagation radius has been reached 3 4 Calibration Mode A Calibration Mode was implemented into PF Model to aid in analysis of field pilot tests during the site characterization phase of a project In this program mode actual field measurements of ground surface heave are input into PF Model to regress the actual post fracture Young s modulus and pneumatic conductivity for the formation being tested These values are then used directly in the System Design component to design full scale fracturing for the site As might be expected the accuracy of design predictions made after running the
143. his is because solution of a specific problem required quality knowledge within some narrow domain to successfully search for a solution Eventually the technology known as expert systems grew out of the AI branch of computer science Patterson 1990 In essence an expert system is an AI program with specialized problem solving expertise 2 1 1 2 Characteristics of Expert Systems The best way to introduce the concept of an expert system is to describe characteristics which are common to all expert systems These are listed and briefly discussed below Limited to Solvable Problems t may seem surprising but before the development of an expert system begins it must be determined if the problem is solvable An expert system will not work if there is no human expert available to obtain knowledge from New or novel research issues are therefore not candidates for expert systems programming Prerau 1985 Possesses Expert Knowledge An expert system must capture and encode the knowledge of a human expert including the expert s problem solving skills and his domain knowledge These skills or knowledge are not necessarily unique or brilliant rather they are known only by a few others Focuses Expertise Focusing the expertise should seem obvious but in fact programmers who have designed expert systems to encompass broad topics have achieved little success and failed Ham 1984 and Prerau 1985 Expert systems do not perform we
144. ies for handling uncertainty is presented in the following Subjective Probability Theory Subjective or Bayesian probability is used by most expert systems since it is favored by system developers Levitt 1988 and Tzvieli 1992 This is because a knowledge base stores human knowledge and facts and when representing an expert s knowledge it is usually viewed as subjective by the programmer Subjective probability is developed from the theory of partial belief called Bayesian theory after the English clergyman Thomas Bayes 1702 1761 The basic premise is that all degrees of belief should obey certain rules By attributing 4 as the degree of belief p given evidence B the famous formula of Bayes can be stated Pearl 1988 p B A x pC A p A B p B Q 1 For Bayes rule to handle the uncertainty found in expert systems it must be developed into a different form The mathematical extension of Bayes theorem which is detailed in Appendix yields the following basic equation for applying probability theory to expert systems p B A x p A ALB M 2 NARI pr r S PCS e 21 This states that the conditional probability of 4 given B can be obtained from the conditional probability of B given A For example consider an expert system where the rules are in the form If lt is true Then B will be observed with probability gt Clearly if is observed then the probab
145. ign and should only be considered if the program is to be rebuilt from the ground up 118 10 On some machines PF Model tends to run into an of Memory error This can 11 result from a number of factors including but not limited to the number of forms open the size of a form i e the Default Library or the size of a procedure One action taken to minimize the chance of this error was to unload default libraries not being accessed by the program Although this slowed down the access time between model components platform stability appears to have increased dramatically Other means to streamline and minimize the code should be investigated The most obvious would be to reduce the number of forms used in the design environment and break up long procedures into smaller ones In addition it was found that other programs can cause PF Model to crash For example some large memory programs continue to stay resident in memory even after the user terminates them These are termed terminate and stay resident programs It was found that if PF Model is run after exiting one of these programs there was insufficient memory to run PF Model During the design of the Site Screening component the effects of water table on the pneumatic fracturing process were not widely studied and therefore the probabilities for water table are based on expected results Further investigation of fracturing in the vadose and saturated zones sh
146. ility of event B is p But Equation 2 2 is also applicable in the case when is unknown and B is observed Equation 2 2 can then be used to compute the probability that is true as well Dempster Shafer Theory The Dempster Shafer theory was originally developed in the 1960s by Arthur Dempster Dempster 1967 and later extended by Glen Shafer Shafer 1976 in the 1970s The development of the theory was driven by the two difficulties Dempster and Shafer had with subjective probability theory These were the representation of ignorance and the idea that the subjective beliefs assigned to an event and its negation must sum to one Ng and Abramson 1990 In probability theory ignorance is represented by indifference or by uniform probabilities The problem believed here is that uniform probabilities seem to represent more information than is known Therefore you can attribute equal prior beliefs to either complete ignorance or equal belief in all hypotheses or events Also when new data or information does become available the original ignorance expressed in the prior belief may no longer be valid The mathematical development of the Dempster Shafer theory is outlined in Appendix B Shafer believed that evidence which partially favors a hypothesis should not be construed as also supporting its negation This contrasts with subjective 22 probability theory which states that once the probability of the occurrence is known the prob
147. ins T and Kern L Widths of Hydraulic Fractures Journal of Petroleum Technology No 13 pp 937 949 1961 Pisciotta T Pry D Schuring J Chan P and Chang J Enhancement of Volatile Organic Extraction in Soil at an Industrial Site Proceedings of FOCUS Conference on Eastern Regional Ground Water Issues National Water Well Association Portland ME October 1991 Pollard D Derivation and Evaluation of a Mechanical Model for Sheet Intrusions Tectonophysics No 19 pp 233 269 1973 Preece A Towards a Methodology for Evaluating Expert Systems Expert Systems Vol 7 No 4 pp 215 223 November 1990 Prerau D Selection of an Appropriate Domain for an Expert System AI Magazine pp 26 30 Summer 1985 Puppala S Fracture Propagation and Particulate Transport in Pneumatically Fractured Geologic Formations Ph D Dissertation Department of Civil and Environmental Engineering New Jersey Institute of Technology Newark NJ August 1998 Schuring J Valdis J and Chan P Pneumatic Fracturing of a Clay Formation to Enhance Removal of VOC s Proceedings Fourteenth Annual Madison Waste Conference University of Wisconsin Madison WI September 1991 221 REFERENCES Continued Shafer G Mathematical Theory of Evidence Princeton University Press Princeton NJ 1976 Shafer G The Art of Causal Conjecture The MIT Press Cambridge MA 1996 Shapiro S Encyclopedia of Arti
148. iquid media injections based on the geologic evidence that is known and subsequently entered as data The final phase of the study involves validation of the predictive aspects of the computer model especially those parts coded as an expert system Since 1989 a considerable amount of field data has been collected and was available to calibrate the propagation model Likewise for site screening calibration is based on actual past field demonstrations combined with heuristic reasoning In addition the model is run for hypothetical sites to push the envelope of the pneumatic fracturing technology in consultation with current experts in the field In summary the objectives of this research study are to 1 Investigate various probabilistic options available for an expert system 2 Design and code an expert system to make technology recommendations 3 Convert available analytical and numerical component models to computer code in order to make preliminary estimates of design parameters used in the technology 4 Establish an overall design and logic implementing a Windows format program 5 Include a User s Guide for design applications 6 Develop an interactive knowledge base containing the probabilities for pneumatic fracturing applications for previous and future site data and technology information 7 Develop a library of system and geotechnical defaults for PF Model to support the System Design component for estimating fract
149. ive This coincides best with how the pneumatic fracturing technology is viewed by others and therefore is appropriate to act as the control strategy in the inference engine In order to implement subjective probability into the model geotechnical parameters that affect pneumatic fracturing called the evidence were identified Further a hierarchy of importance among these pieces of evidence was established in order to 110 help quantify the final probabilities chosen in the knowledge base The geotechnical properties and their hierarchical order are e formation type depth e consistency relative density e plasticity e fracture frequency e weathering e water table Each of the geotechnical properties above were further divided into qualifiers After numerous discussions with experts in pneumatic fracturing a library of probabilistic defaults were established for each of the qualifiers in the knowledge base By quantifying this evidence the expert system was able to make technology recommendations with greater belief Probabilities were generated for the three main variant applications of pneumatic fracturing permeability enhancement dry media injection and liquid media injection The Site Screening component is designed to rate prospective sites according to three criteria pneumatic fracturing effective pneumatic fracturing marginally effective 111 and pneumatic fracturing not recommended The result is ac
150. junction with Mathcad Plus 6 0 a technical calculation program The second value is the 96 Table 4 4 Validation of Calibration Mode for Estimating Young s Modulus Site Name z Q P b R Ey per Ebr per EV Ebr MCad PF Model scfm psi ft psi Frelinghuysen 1 5 3 5 300 10 0 0792 4 2 3 37 5 1 01 3 5 300 10 0 0533 4 2 56 55 7 1 01 3 3 300 7 0 0208 4 2 86 85 3 1 01 3 5 300 8 0 0317 4 2 69 68 5 1 01 Frelinghuysen 2 a 6 715 13 0 0342 8 5 272 271 2 1 00 6 1227 14 0 0367 8 5 283 282 1 00 1157 15 0 0075 5 7 347 345 7 1 00 8 3 1500 18 0 0233 11 7 688 686 8 1 00 6 1500 17 0 0375 8 6 379 378 1 1 00 8 6 1339 17 0 0390 11 3 291 290 8 1 00 Frelinghuysen 3 a 6 857 15 0 0167 4 2 51 50 4 1 01 6 964 11 4 0 0275 12 6 1197 1195 6 1 00 6 1000 11 0 0250 9 6 449 448 5 1 00 9 943 16 5 0 0183 14 1 1149 1148 3 1 00 9 1114 14 7 0 0150 16 1 1890 1888 9 1 00 6 722 12 5 0 0275 11 7 1049 1047 5 1 00 8 3 984 17 0 0158 11 4 843 842 1 1 00 Tinker 8 1716 31 0 0417 19 5585 5582 3 1 00 19 1759 130 0 0125 30 8 39881 39874 8 1 00 8 1716 28 0 1000 23 4219 4217 8 1 00 Marcus Hook 6 1200 12 0 0500 16 2 1835 1834 1 1 00 6 1276 19 0 0500 15 8 3204 3202 1 1 00 6 1400 14 0 0700 15 1 1270 1269 4 1 00 Hillsborough 2 10 1500 21 0 000 27 9 7960 7958 5 1 00 12 1607 25 0 0258 294 8238 8236 2 1 00 14 1886 30 0 0317 27 7 4141 4140 3 1 00 Hillsborough 3 14 1029 28 0 0333 30 4683 4681 8 1 00 Newark 10 Th 375 0 0133 25 31135
151. known Or _ 201 frmSiteScreening blRelativeDensity Caption not applicable Then Call GetRelativeDensityEvidence TechnologyFlag EvidenceCounter El E2 E4 ES End If If Not frmSiteScreening Ib Weathering Caption Unknown Or _ frmSiteScreening b Weathering Caption not applicable Then Call GetWeatheringEvidence TechnologyFlag EvidenceCounter El E2 E4 E5 End If If Not frmSiteScreening lblFractureFrequency Caption Unknown Or _ frmSiteScreening lblFractureFrequency Caption not applicable Then Call GetFractureFrequencyEvidence TechnologyFlag EvidenceCounter El E2 E4 E5 End If If Not frmSiteScreening Ib WaterTable Caption Unknown Then Call GetWaterTableEvidence TechnologyFlag EvidenceCounter E1 E2 E4 ES End If Go to Subjective Probability Calculator Call SubjectiveProbability EvidenceCounter E1 E2 E3 E4 E5 Error code Exit Sub ErrorHandler Msg An untrapped error has occured Please make amp Chr 13 Msg Msg amp note of the following information amp Chr 13 amp Chr 13 Msg Msg amp Error number amp Err Number amp Chr 13 Msg Msg amp Description amp Err Description amp Chr 13 Msg Msg amp Location amp Screen ActiveForm Name amp Chr 13 Msg Msg amp Procedure amp ProcName MsgBox Msg End Sub Private Sub GetGeologyTypeEvidence TechnologyFlag EvidenceCounter El E2
152. ks are not formed by particle deposition and their existing discontinuities are mostly formed by thermal strain during cooling or tectonic movements Discontinuity patterns are less regular and it is likely that permeability and interconnectivity are more difficult to enhance It is noted that unlike sedimentary rocks experience with pneumatic fracturing of igneous and metamorphic rocks is very limited Overall when pneumatic fracturing is applied to a formation there are expected trends and predictable behaviors Fine grained soils and sedimentary rocks respond well to permeability enhancement by pneumatic fracturing In contrast coarse grained soils e g sand already have substantial permeability and pneumatic fracturing is not appropriate for permeability enhancement However media injection by the pneumatic fracturing process might still be recommended as an alternative technology variant for coarse grained soils In summary then it is texture and lithology that largely determine whether or not fractures will be formed and also how fluids will move through the formation Thus these are clearly the most important parameters in determining the applicability of pneumatic fracturing and they will be the dominant pieces of evidence in the probabilistic model Depth The depth of a formation is the second most important parameter in determining whether or not pneumatic fracturing will be successful Pneumatic fracturing projects to date hav
153. le directory application available for downloading PF Model could be then sent to a prospective user via e mail or downloaded from a web site An accompanying electronic manual for downloading would need to be developed The current manual could be used as a basis but the electronic manual would need to be reformatted for the many different possible text readers that may be encountered APPENDIX A SUBJECTIVE PROBABILITY THEORY Subjective or Bayesian probability is favored by expert system developers and is used in most expert systems Levitt 1988 and Tzvieli 1992 The main reason is that it allows the programmer to represent the human s expert knowledge in the program as subjective which it is Bayes Theorem which forms the basis of subjective probability theory will now be presented after Ng and Abramson 1990 Let be an event and let be the sample space The probability of event is p A where following three axioms must be satisfied 1 The probability of event A is positive or V A p A gt 0 2 The probability of the entire sample space is one or p Q 1 3 If k events A2 Ak are mutually exclusive then the probability that at least one of these events will occur is the sum of the individual probabilities k 4 JA20 Ap gt PCA Combining axioms 1 and 2 yields VAEQ 0 lt p A lt il A 1 121 122 Equation A 1 states that the probability of any event is between 0 a
154. lectrical Engineering The Pennsylvania State University University Park PA 1988 Major Civil Engineering Professional Background e Research Assistant Department of Civil Engineering 1997 1999 New Jersey Institute of Technology Newark NJ e Teaching Assistant Department of Civil Engineering 1994 1997 New Jersey Institute of Technology Newark NJ e Electrical Engineer 1988 1992 Kearfott Guidance amp Navigation Corp Wayne NJ Presentations and Publications Sielski B Schuring J Hall H Fernandez H and De Biasi V Pneumatic Fracturing Computer Model HSRC WERC Joint Conference on the Environment Albuquerque NM 21 23 May 1996 iv To My Loving Parents ACKNOWLEDGEMENT I owe a great debt of thanks to my dissertation advisor Dr John Schuring for his inspiration encouragement and guidance throughout this research His vision friendship and work ethic have guided me through this exciting journey and his unselfish kindness and compassion has set an example that will be with me for the remaining days of my life I also wish to thank Professors Paul Chan Edward Dauenheimer Robert Dresnack and John Ryon for serving as members of the committee and for their careful review and suggestions I am indebted to Tom Boland for his behind the scene efforts that enabled me to complete this research in a timely manner I would also like to thank him as well as Trevor King of McLaren Hart Environment
155. libration procedure as that previously described for clayey silt was performed for siltstone The modulus and conductivity were varied until a final set of parameters were selected Following the siltstone calibration the other rock formations were calibrated on a relative basis After completing the calibration for rock formations a range of standard cases was computed as shown in Table 4 8 on the following page Extreme cases for rock type fracture frequency flow rates and depth were examined to insure that unexpected behavior would not occur It is important to note that the data available for rock were limited to the depth range of 10 27 ft and therefore the calibration of PF Model was custom tailored to that range It was noticed that at depths shallower than 10 ft unrealistically high surface heaves i e apertures are predicted This was attributed to the fact that the fundamental mathematical model for the System Design component is in fact a bending deflection model i e it treats the formation as if it were a deep beam or plate Thus the equivalent depths of injection compared with soil is much greater on account of the higher stiffness 104 and modulus of rock Deep injections involve not just bending phenomena but also localized elastic compression above and below the fracture Table 4 8 Calibration of Default Values for Rocks Defaults Predictions E K z Q P b R psi cm sec ft scfm psi in
156. ll when tasked with problems outside their area of expertise just like humans An expert system can be successfully developed only when the scope of the problem is well defined Reasons Symbolically The knowledge used by an expert system can be expressed in symbolic terms rather than numerical terms Symbols can represent facts concepts and rules Problems are solved by manipulating symbols rather than by numeric processing i e conventional programs Reasons Heuristically Heuristics 1s the study or practice of procedures that are valuable but are incapable of proof Lenat 1982 A human expert possesses more than just public knowledge i e knowledge which is available in published literature A human expert 10 uses not only facts and theories to solve a problem but also considers past experiences Such knowledge gives the expert a practical understanding of the problem and allows the development of rules of thumb or heuristics to solve the problem To illustrate the difference between conventional programs that use algorithms and expert systems that often use heuristic techniques consider the example of a bicycle chain which keeps coming off while riding an indication of a stretched chain The conventional algorithm is a series of orders or calculations that are well structured 1 Measure the length of chain 2 Count the number of chain links U Compute link to length ratio EN If ratio gt 1
157. logic medium to be brittle elastic and overconsolidated King 1993 A model study describing fracture propagation behavior is also available Puppala 1998 These two studies form the basis of the fracture propagation component of PF Model Most often the System Design component will be used in a Fracture Prediction Mode which is activated when the user enters the system parameters and site geological properties The system parameters which influence fracture propagation are the injection flow rate and well radius The key geologic properties which must be input into PF Model to analyze fracture propagation are modulus of elasticity cohesion soil rock density and depth of overburden If the user is unable to determine these key parameters 39 or if they are unavailable the computer program provides default values For the system parameters the program defaults for flow rate and well radius are 1500 scfm and 0 25 in respectively although some flow rates may vary based on formation type i e typically 100 200 scfm higher in rock For the geotechnical properties the default values are based largely on a general textural description of the geologic materials at the site e g silty sand clayey silt shale etc For example if the site formation is sandstone but no tests were performed to determine the rock density the user could allow the computer program to use the default value in this instance 140 lb ft Default values for the 14
158. ls the associated logic of the Bisection and Increasing Model Engines which are selected by the user during the System Design Subroutine Figure 3 6 on the following page shows the logic of the Model Engine Subroutine The Bisection Model Engine Steps 16 through 28 is based on the method of bisections also known as binary chopping interval halving or Bolozano s method This method has the ability to substantially reduce the number of iterations and processing time required which is why this method is preferred and is the default engine for PF Model The method of bisections works by dividing the interval in half and then determining in which half the root resides The selected interval is halved again and the process repeats itself until the root converges to zero At this point the fracture radius has attained its maximum value Step 15 Bisection Method No Yes Step 16 Prepare as Input for PDF Rise Ruige and Riga i Step 17 v Step 18 Y Se 19 R Mid High R Low 62 Step 25 Run Calculate 96 Error Step 28 Error lt 0 1 Figure 3 6 The Model Engine Subroutine 63 The Increasing Model Engine Steps 20 30 through 32 is the alternative to the Bisection Engine The increasing method starts at the smallest radius ie the well radius and increases until the pressure and continuity conditions at the fractur
159. ltWellRadius Enabled True End Sub Sub GeologicalPropertiesTrue This procedure is used to make all the objects in geological properties enabled i e true IbIGeotechnicalProperties Enabled True IbIType Enabled True cboType Enabled True IbIFractureDepth Enabled True txtFractureDepth Enabled True IbIWaterDepth Enabled True txtWaterDepth Enabled True cmdPlasticityMoisture Enabled True cmdConsDense Enabled True IbIWeathering Enabled True cboWeathering Enabled True IbIFracFrequency Enabled True cboFracFrequency Enabled True Call GeologicalPropertiesOnOff End Sub Sub GeologicalPropertiesFalse This procedure is used to make all the objects in geological properties disable i e false IbIGeotechnicalProperties Enabled False IbIType Enabled False cboType Enabled False IbiFractureDepth Enabled False txtFractureDepth Enabled False IbIWaterDepth Enabled False txtWaterDepth Enabled False cmdPlasticity Moisture Enabled False cmdConsDense Enabled False lb Weathering Enabled False cboWeathering Enabled False 209 iblFracFrequency Enabled False cboFracFrequency Enabled False End Sub Sub Form_LoadQ Puts a date in the date field if this is a new file txtDate Date Puts blanks in system properties labels until defaults or overrides selected IbIDefaultFlow Caption IbIDefaultPressure Caption IbIDefaultWellRadius Caption Initializ
160. m the final probabilities of the BN of Figure C 7 were calculated It immediately became apparent that the output did not match field evidence or expert knowledge and expectations For example an expert in the field of pneumatic fracturing would expect the final results for a clay soil fracturing at a depth greater than 12 ft stiff consistency and w PL to be close to 90 per cent This is the best case for the success of fracturing The BN s Result was a success of 73 13 Each one of the states listed above was programmed in HUGIN with a belief of 90 or higher in success The discrepancy occurs due to the nature of multiplying fractions 0 90 x 0 90 0 81 0 81 x 0 90 0 729 etc Unfortunately this is not how the pneumatic fracturing expert thinks If all the best conditions are satisfied his confidence level of success would similarly exceed 90 In order to overcome the difficulty in perception it was proposed to scale the 73 13 upwards toward 90 This was found unsatisfactory as the scaling would not be linear especially if one considers the comparison to a worse case for this BN s success of pneumatic fracturing Naturally it is preferred to think of success on a 1 100 scale but in order to use a Bayesian Network or several BNs to model pneumatic fracturing it may be necessary to utilize a different evaluative scale 137 It is still preferable to have only one BN but due to the complexity of the interactions
161. mendation for the applicability of pneumatic fracturing can be made based on the final values of the hypotheses For this example the Site Screening component will determine if pneumatic fracturing is suitable for permeability enhancement at a particular site Three pieces of evidence grain size overburden and plasticity will be introduced showing how evidence effects the belief in hypotheses The site soil is a clayey silt where the soil moisture content is less than the plastic limit e w lt PL The depth of injection is 17 to 20 feet Past experience has shown that pneumatic fracturing would be beneficial for enhancing the permeability of this site Let two mutually exclusive and exhaustive hypotheses H and Z represent the effectiveness of pneumatic fracturing being applicable or not applicable respectively Prior probabilities p H and p H already assigned during the creation of the expert system s knowledge base are shown below 156 157 1 Fracturing applicable p H 0 50 2 Fracturing not applicable p H 0 50 The initial hypotheses are weighted equally because in all instances nothing is known about the site and each has an equal chance of occurring At this point in the analysis it would be trivial to continue to find the solution of H for the user is not concerned with pneumatic fracturing being not applicable Even if this value is desired by the user it is nothing more than the compleme
162. more easily accessed since the diffusive distances are shortened A one dimensional solution for a single discrete fracture is currently available Ding 1995 Work is underway to extend this to multiple fractures and this component can be added at a later date 3 2 Site Screening Approach The general approach to the site screening model was to implement an expert system that establishes the applicability of pneumatic fracturing for a particular site Figure 3 3 depicts a flow chart of the site screening model component in which the dotted box represents the tasks and actions performed by the expert system ze NK Input geologic evidence Working Memory Facts or evidence v Inference Engine Knowledge Base Hueristics and domain knowledge Obtain data from knowledge base Inference Engine Determine rules to be fired Inference Engine Make site comparison based on rules Pneumatic fracturing applicablitiy Figure 3 3 Flow Chart of Site Screening Component 44 The critical aspect of any expert system is the selection of which uncertainty theory to use which is strongly dependent on the problem domain and any existing conditions For reasons discussed in Chapter 2 it was determined that subjective probability theory is the most appropriate for PF Model since it has outperformed the other competing theories Wise and Henrion 1986 and experts were available for techni
163. n However the original recommendation rating of 76 is an indication that the site can support the technology Therefore you shall continue to develop the remedial plan and determine the expected maximum radius Select COMPONENT from the Menu Bar 16 PNEUMATIC FRACTURING COMPUTER MODEL Select the RETURN TO DATA INPUT from the Component Menu At this point the program begins to load the Flownet and Default libraries this will take a few seconds When completed the Data Input screen appears On the top right of the main screen in the frame titled Select component s for analysis Select the check box for SYSTEM DESIGN Note that more of the properties are now active But before proceeding just check the default values to make sure they re appropriate for your application Select the button PNEUMATIC CONDUCTIVITY Notice that the default value for the post fracture pneumatic conductivity is 0 00035 cm sec The default values for post fracture pneumatic conductivity have been carefully regressed from actual field measurements You should note that the value of this parameter will have a significant influence on the propagation radius of pneumatic fractures For this reason if you are using PF MODEL in the Fracture Prediction Mode as you are now is strongly advised that you use the default value However if a pilot test of pneumatic fracturing was performed at the site and the actual value of post fracture pneumati
164. n component of PF Model utilizes formation type and fracture frequency as qualifiers for determining the system and geotechnical default values of rocks formations While fracture frequency is certainly considered to have the greatest influence on fracture propagation the degree of weathering can significantly affect modulus and conductivity as well Therefore future version of 14 120 PF Model should consider incorporating formation type fracture frequency and weathering as default qualifiers for rock formations A User s Manual produced with sophisticated desktop publishing software will greatly enhance the aesthetics of the entire software package Currently the manual is produced with only a word processing program As an alternative the manual could be contracted out to a professional desktop publisher It is desirable to refine some sections of the manual For example Chapter 2 titled Theoretical Background should be developed for future inclusion Currently the reader is directed to other references which detail the theory behind the program e g subjective probability expert systems and System Design algorithms If a user wishes to alter the defaults or knowledge base an understanding of the theory is essential Thus the inclusion of theoretical background would be advantageous As an alternative to a hard copy distribution which requires three disks and a printed manual it is possible to create a sing
165. n the following section 3 3 3 System Design Algorithm The System Design algorithm is represented by three nested subroutines They are the System Design Model Engine and PDF Subroutines and are presented in the following three sections 3 3 3 1 System Design Subroutine This is the top level of the System Design algorithm The subroutine is shown in Figure 3 5 on the following page In this subroutine many of the initializations and preparations of data required in the later subroutines are carried out as detailed in the following discussion Step 1 Input Geotechnical amp System Properties Step 2 Bisection Model Engine selected Yes No s Step 3 Step 4 Intialize Bisection Intialize Increasing Model Engine Model Engine Step 5 Graphical Leakoff Method selected Step 7 Initialize Analytical Intialize Graphical Leakoff Method Leakoff Method Selection of Deflection Solver i Step 10 i Step 11 i Step 12 iri p DE d Circular Plan amp Log Circular Plan amp Anticlinal Plan amp Circular linc gt Linearly Taperine Pressure Uniform Pressure Uniform Pressure Pressure Step 13 Step 14 A rture Model Engine Ra Rd Subroutine Figure 3 5 The System Design Subroutine 58 Step 1 Input The geotechnical and system parameters required by the algorithm are entered first Certain ge
166. n to both the expert system and several expert evaluators and the results were compared It should be noted that when the evaluators agree with the system the results are viewed as correct otherwise they are wrong This approach assumes that the test case result is 10096 correct and that any different answer is incorrect This is not necessarily the case since the findings represent an expert opinion not a gold standard The system validation step was based on three major considerations They were 85 e test criterion e test cases and e Selection of evaluators Test Criterion The test criterion was selected to directly reflect the Site Screening component The applicability of pneumatic fracturing at the sites were rated using three categories technology recommended technology marginal and technology not recommended In addition three different variants of pneumatic fracturing were evaluated ie permeability enhancement dry media injection and liquid media injection Test Cases Likewise the selection of the test cases was based on the goal of the Site Screening component and original objective of the expert system The test cases were selected to be typical sites that one expects to encounter in remediation work It is believed that if the Site Screening component can make reliable recommendations 8096 of the time for typical sites the other more difficult sites can be handled by a human expert Fifteen differe
167. ncement MouseUp Button As Integer Shift As Integer X As Single Y As Single 7 If Button vbLeftButton Then Put an hourglass up to indicate the program is calculating Screen MousePointer vbHourglass Screen MousePointer 11 Set Flag 1 for Permeability Enhancement Probability Recommedations TechnologyFlag 1 Call AssignEvidence TechnologyFlag El E2 E3 E4 ES Screen MousePointer 0 sets the pointer back to the default End If If Button vbRightButton Then HELP_ITEM Permeability Enhancement Call Help HELP ITEM End If End Sub Public Sub AssignEvidence TechnologyFlag El E2 E3 E4 E5 Dim EvidenceCounter As Integer ProcName AssignEvidence On Error GoTo ErrorHandler EvidenceCounter 1 Call GetGeologyTypeEvidence TechnologyFlag EvidenceCounter El E2 E3 E4 E5 If Not frmSiteScreening lblDepth Caption Unknown Then Call GetDepthEvidence TechnologyFlag EvidenceCounter E1 E2 E3 E4 E5 End If If Not frmSiteScreening IblPlasticity Caption Unknown Or _ frmSiteScreening bIPlasticity Caption not applicable Then Call GetPlasticityEvidence TechnologyFlag EvidenceCounter E1 E2 E4 E5 End If If Not frmSiteScreening lbIConsistency Caption Unknown Or _ frmSiteScreening IblConsistency Caption not applicable Then Call GetConsistencyEvidence TechnologyFlag EvidenceCounter E1 E2 E3 E4 E5 End If If Not frmSiteScreening IbIRelativeDensity Caption Un
168. nd 1 A s complement 4 contains all the events in except A Since A and A are mutually exclusive and 4 UJ A Q axiom 3 yields P A p A A p Q A 2 This can be rewritten in order to compute p 4 from p 4 more easily as p A 1 3 Let B be another event The probability that will occur given that occurs is called the conditional probability of A given B or p A B The probability that and B will both occur is called the joint probability of A and B and is written as B By definition the conditional probability p 4 B is equal to the ratio of the joint probability p r B to the probability of B if B 15 nonzero This can be written as _ p A B HABI A 4 Similarly the conditional probability of B given is 123 p Br A BEDS 5 and thus P BOA p BA xp A A 6 Since joint probability is commutative p B p B r Therefore p Ar B p Br A p BA x p A A 7 Substituting equation A 7 into A 4 yields Bayes rule p B A x p A ALB p A B 8 which was previously stated in Chapter 2 as Equation 2 1 For Bayes rule to be useful for the uncertainty found in expert systems it must be developed further If the events and B are independent then by definition p A B p A and p B A p B 9 124 This is based on the premise that if the two events
169. ng process Starting with the original knowledge base the results of the expert system were compared to the results of the evaluators If the expert system agreed with the majority opinion for a selected site the system results were deemed satisfactory If the system differed with the majority opinion some fine tuning of the knowledge base was required to bring the expert system results into agreement The expert system was then reevaluated for each site to insure that the changes to the knowledge base did not alter the system results elsewhere This process was repeated unti the results in the tables were obtained Table 4 1 System Validation of Permeability Enhancement Variant Depth to _ Depth W T Relative Fracture Evaluator Results T System Formation Type ft ft Consistency Plasticity Density Frequency Weathering A B C D E Result Rating Silty Clay 18 10 medium TN n a n a n a Y Y M Y 72 Clayey Silt 10 18 medium brittle n a n a n a Y Y Y Y 83 Clay 8 4 soft plastic n a n a n a M Y M M 48 Silty Clay 12 10 medium liquid n a n a n a N M N N 23 Clay 10 27 77 n a n a n a Y Y M Y 65 Clay 4 10 very stiff brittle n a n a n a M M Y M 60 Silty Sand 14 8 n a n a med dense n a n a M N M M 48 Sand 24 10 n a n a dense n a n a N N N N 36 Sand and Gravel 14 20 n a n a very dense n a n a N N N N 33 Siltstone 20 12 n a n a n a closely slightly Y Y Y Y 86 Shale 10 n a n a 299 299 Y Yu Y Y 85 Shale Siltstone 12 18 n a n a n a wid
170. ng uncertainty 2 1 3 1 General Approaches In expert systems there are two main approaches to solve problems the derivation approach and the formation approach Maher 1987 The derivation approach starts at a known state and uses deductive logic to arrive at a known solution This approach is desirable if there are predefined solutions available in the knowledge base of the expert system This means that the expert system will provide a solution based on the specifications of the given problem If an inference network between the predefined solutions and the input data can be achieved the derivation approach can be implemented The other general approach is the formation approach which uses information about the known state to generate more information to form higher level solutions Information from the knowledge base is used in order to form a solution This method is 17 used when it is either impractical or impossible to store all the predefined solutions in the knowledge base The formation approach is implemented by identifying parts of the solution and then heuristics to combine them 2 1 3 2 Control Strategies Many strategies for solving problems guided by the knowledge contained in the knowledge base exist The three most common control strategies for choosing the next action given many alternative problem solving steps are presented next Forward Chaining An expert system uses a forward chaining strategy if it works from
171. ngle Dim PHI As Single Dim PRES n As Single Dim PRES next As Double Dim PRES prop As Single Dim Qleak As Single Dim Qres As Single Dim R incr As Single Dim R n As Single ProcName StarTrek Assign the procedure name for error handling On Error GoTo FileError R next RADIUSwell R_n RADIUSwell Determine to use either the default flow or user entered flow If frmDataInput chkOverrideFlow Value 1 Then Checked or on Qres Val frmDatalInput txtFlowRate Elself frmDatalnput chkOverrideFlow Value 0 Then Unchecked or off Qres Val frmDatalnput IbIDefaultFlow Caption End If Determines the value of the hydraulic conductivity that is used for the graphical flownet method If mnuLeakOffGraphicalKh Kv Checked True Or _ mnuLeakOffGraphicalKh 5Kv Checked True Or _ mnuLeakOffGraphicalKh 10Kv Checked True Then PneumaticConductivity Kv Kh 0 5 End If Determines the value of K which is used for the circular plate log distribution If mnuSolverLogDistribution Checked True Then K PRESdriv Log RADIUS RADIUSwell End If PRES 144 DENSITYGas converts psi to ft PRES prop PRESprop Abort Density DENSITYGas depth FractureToughness R n units ft Do While Qres gt 0 And R next lt RADIUS And PRES n gt PRES prop R incr 0 1 If RADIUS R n lt 1 Then R incr 0 001 End If R next R n R incr XX next n 2
172. ns The field data for these sites are presented in the tables throughout this section 95 It should be noted that PF Model will continue to be calibrated as future sites are further added to the data base 4 3 1 Validation of the System Design Component The System Design component was validated by comparing PF Model s predicted results with actual field results This approach confirms that PF Model represents the currently established fracture propagation mathematical models Since the System Design component has two modes of operation the Calibration Mode and the Fracture Prediction Mode two separate validations were done The results are presented in the following two sections 4 3 1 1 Validation of Calibration Mode As previously discussed the Calibration Mode regresses the post fracture Young s modulus and pneumatic conductivity from actual field data Therefore successful validation of the Calibration Mode will require agreement of these two geotechnical parameters with the results from the original mathematical model Table 4 4 on the following page shows the results for the validation of Young s modulus The first two columns summarize the site data The third column consists of two values The first is a back calculation of Young s modulus Ebe That is the observed field radius and aperture were used to back calculate the modulus for the given site The calculation of Ebc was performed using the mathematical model in con
173. nt of fracturing being applicable or 1 The first piece of evidence grain size is introduced in subjective probability as E In PF Model the expert system s inference engine accesses from the knowledge base the probability for a Clayey Silt and subsequently enters this value into the working memory The inference engine performs the same process for the remaining pieces of evidence till none remain Therefore in this example it will access two more probabilities one each for depth and plasticity Below are the probabilities for the three pieces of evidence accessed from the knowledge base and are the same as those listed in Table 3 3 e Clayey Silt 0 75 e Depth gt 12 ft 0 55 e Plasticity w lt PL 0 60 158 After the inference engine has determined how many pieces of evidence are available it will determine which rule will be fired to determine the applicability of pneumatic fracturing The posterior probability for the hypothesis is calculated using Equation 3 4 restated below P E H x p E x x p EH x p H Sa F 1 uu POEM x pE H x x p E H x p H where p Ej H 0 75 p E H5 0 25 p E2 Hj 0 55 p E2 H2 0 45 e p E3 H 0 60 p E3 H5 0 40 thus the rule to be fired and solved is H E E E 0 75x 0 55x 0 60x 0 50 ds 0 75 0 55x 0 60 x 0 50 0 25x 0 45x 0 40x 0 50 F 2 This states that for the site in
174. nt test cases were selected and are shown in Table 4 1 These cases include common geologic situations for pneumatic fracturing as well as more challenging geologic conditions Selection of Evaluators The selection of evaluators was also consistent with the original goal and objective of the Site Screening component A total of five evaluators were used 86 for system validation This included the two experts who were largely responsible for development of the PF Model program and whose knowledge the expert system reflects In addition three evaluators were selected from the remediation field who are considered to be the foremost experts in the relatively new process of pneumatic fracturing System Validation Results The results of the system validation are presented in Table 4 1 for the permeability enhancement variant and additional results for dry and liquid media variants are contained in Tables J 1 and J 2 of Appendix J respectively The first column in each table summarizes the available geotechnical evidence for the test cases The results of the five expert evaluators are presented in the second column Each evaluator was asked to rate each site as variant recommended Y variant marginally recommended M and variant not recommended N Finally the corresponding expert system result and technology rating for each case are shown in the last column These system results and ratings were determined through an iterative testi
175. nts But Bel W X m W m X m W X 0 1 0 2 0 5 0 8 where the Bel function is greater than or equal to m for sets that contain more than one element Although the Dempster Shafer theory can explicitly express ignorance the theory suffers from the use of unfamiliar terminology and lacks formal semantics Since the representation of all hypotheses in DST is the power set of all possible hypotheses a huge subset of probability assignments must be assigned by the expert It is not surprising that there are few expert systems built using DST Ng and Abramson 1990 APPENDIX C BAYESIAN NETWORKS APPLIED TO PF MODEL C 1 Background Bayesian networks BNs are used to model domains that contain some element of uncertainty A BN is a directed acyclic graph DAG where each node of the represents a random variable Each node has a conditional probability table for the states of the random variable it represents The conditional probability table contains the probabilities of the node being in a specific state given the state of its parents URL Hugin 1998 An extension of BNs is the concept of influence diagrams Influence diagrams are used in place of BNs when working with decision making This is not to say that a model for decision making can not be constructed with a pure BN An influence diagram is simply a BN with utility and decision nodes which are not explicitly covered in BNs URL Hugin 1998 As part o
176. o hard above below 70 0 55 0 52 0 55 0 79 1 70 0 50 0 52 0 55 0 75 5 70 0 55 0 52 0 45 0 71 7 70 0 50 0 52 0 45 0 67 4 70 0 30 0 50 0 55 0 48 0 50 0 52 0 55 0 45 0 70 0 55 0 50 0 55 0 77 7 70 0 50 0 50 0 55 0 74 0 70 0 55 0 50 0 45 0 70 0 70 0 50 0 50 0 45 0 65 6 Liquid Media Injection 70 096 55 0 48 0 55 0 76 3 70 0 50 0 48 0 55 0 72 5 70 0 55 0 48 0 45 0 68 3 70 0 50 0 48 0 45 0 63 8 154 Silty Clay Depth Consistency Water Table Probability 70 0 30 0 52 0 55 0 57 0 70 0 30 0 52 0 45 0 47 0 70 0 30 0 50 0 55 0 55 0 70 0 30 0 50 0 45 0 45 0 70 0 30 0 48 0 55 0 53 0 70 0 30 0 48 0 45 0 43 0 155 APPENDIX F SUBJECTIVE PROBABILITY SITE SCREENING EXAMPLE This appendix will demonstrate how subjective probability theory is used in the Site Screening component of PF Model In subjective probability theory when piece of evidence is introduced the hypothesis belief will change As succeeding pieces of evidence are introduced each hypotheses belief subsequently changes until no further evidence is available or given to the computer model At this point a recom
177. of Graphical Leakoff Method K 5K Using Bisection Mode EPDE au u pu Simiyun eU nte Sa a tuom tut Sp ads 100 4 7 Calibration of Default Values for Fine Grained Soils sss 102 4 8 Calibration of Default Values Tor Rocks cuatro dote entire Mates Ere nee 104 4 9 Calibration of Default Values for Coarse Grained Soils sss 106 D 1 Default Values for Plastic Fine Grained Soils Used in PF Model 3 0 139 D 2 Default Values for Coarse Grained Soils Used in PF Model v3 0 140 1 3 Default Values for Rocks Used in PF Model tt coetus ta bent 141 E 1 PF Model s Knowledge Base Probabilities for Three Pneumatic Eract nng Variants dec M Redi M taa aha tes 143 G 1 Shape Factors for Isotropic Condition K K Ademas att alan siot uda 161 G 2 Shape Factors for Anisotropic Condition K SK eee prn etaed dens 162 G3 Shape Factors for Anisotropic Condition K TOR aai ette dais 163 Il System Validation of Dry Media Injection Variant 212 J 2 System Validation of Liquid Media Injection 213 J 3 Validation of Graphical Leakoff Method K K Using Bisection Model ununi ME REN MN 214 xiii LIST OF TABLES Continued Table Page J 4 Validation of Graphical Leakoff Method K 10K Using Bisection Engine sau anu qasa aaa es DER imas mune eT Uu 215 J 5 Validation
178. of priori probabilities to geologic evidence 23 Other Theories Two other theories for dealing with uncertainty in expert systems are possibility theory and the certainty factor approach Possibility theory was developed by Zadeh 1978 due to the difficulties he had with using probability theory s representation of inexact or vague information It is based on his theory of fuzzy sets Possibility theory expresses vague terms such as very likely or probably with precision and accuracy If these terms were coded with probability their imprecision or fuzziness would be lost i e either the event occurred or it did not The advantage of possibility theory then is that events may be represented with shades of gray since human knowledge of facts is very rarely precise There are disadvantages with fuzziness however that are identified in Cheeseman 1986 Stallings 1977 Wise and Henrion 1986 and Giles 1982 The disadvantages include the difficulty of interpreting fuzzy quantifiers and the necessity of fuzzy theories altogether In the 1970s Shortliffe developed the certainty factor approach which he used in the later development of MYCIN a medical expert system for the diagnosis of infectious blood diseases Shortliffe and Buchanan 1984 Shortliffe felt that probability theory would not be appropriate Shortliffe et al 1979 for medical diagnosis since decisions can vary over a wide spectrum from categorical reasonin
179. of the geologic formations ie this applies only to that soil type a single BN be feasible only if modeling tricks are implemented without compromising the theory behind Bayesian networks There are other untouched areas of Bayesian networks that may provide some solutions For example actions intervening and non intervening utilities symbol transmission and causal independence should all be explored to help create a manageable BN APPENDIX D DEFAULT VALUES FOR GEOTECHNICAL PROPERTIES IN PF MODEL This appendix contains the default values used by PF Model version 3 0 The default values are broken up into three categories as shown in Tables D 1 to D 3 on the following pages The default values in Table D 1 are for plastic fine grained soils The default values are based on either the formation type or the formation type and the known consistency Table D 2 lists defaults for coarse grained soils based on formation type or formation type and relative density Finally Table D 3 shows the default values for rocks which is based on the formation type or the formation type and fracture frequency The calibration procedure is described in Chapter 4 138 139 Table D 1 Default Values for Plastic Fine Grained Soils Used in PF Model v3 0 i M V FV GEOTECHNICAL PROPERTY DEFAULT post fracture Pneumatic Young s Modulus Conductivity K ji E Formation Type Consistency cm sec psi Clay Unknown 2 7X10 2 0
180. ontains some degree of uncertainty for the success of the technology This can arise from the user s wish to protect himself legally or simply from the fact that site geology and geotechnical properties vary greatly over the same site Clarity of Explanations Many expert systems provide the user with explanations on the reasoning of the system ie Why does the system require the depth of injection Since it is expected that most users of PF Model will either be experts or designers with some geotechnical knowledge the reasoning of the expert system will normally be 9 apparent However should a user require more information an explanation can be easily accessed through PF Model s Help Function In the design of the Site Screening component it was considered critical to provide an explanation facility for interpretation of the numeric rating This is intended to provide a comfort level in the degree of belief by the expert system The recommendation rating is broken into three categories or ranges and each range has a corresponding recommendation that the rating falls in as detailed below 0 to 45 The technology is not recommended for traditional applications e 45 to 60 The technology is deemed to be marginally effective Although the technology may provide some degree of enhancement a cost to benefit analysis may be appropriate Also it is recommended that further evidence be acquired to refine the analysis
181. otechnical parameters are site specific and will be known beforehand if a site characterization has been performed Any unknown geotechnical parameters are assigned default values based on the selected geologic formation System parameters are based on the anticipated injection event and can always be entered as data although defaults will be assigned if required Table 3 7 summarizes these various inputs Table 3 7 Input Parameters for the System Design Subroutine System Properties usually known Geotechnical Properties usually known usually unknown Formation type Pneumatic conductivity Flow rate Depth Young s modulus Maintenance pressure Depth to water table Poisson s ratio Well radius Boring Log Data Formation density Note Can include information such as consistency density fracture frequency etc Steps 2 3 amp 4 Selection of Model Engine PF Model allows the user to select from two different types of model engines the Bisection Engine and the Increasing Engine In this step of the subroutine it is determined which model engine is to be used The subroutine then initializes the selected model engine for use Should the user not specify which model engine to run the Bisection Engine will 59 be used as the default The discussion of the two model engines is presented in the following section the Model Engine Subroutine Steps 5 6 amp 7 Selection of Leakoff Method n this step the
182. ould be carried out in order to more fully understand the effects of the water table on the different pneumatic fracturing variants This would increase belief in the technology recommendations 119 12 During calibration of the System Design component it was observed that PF Model does not accurately predict fracture dimensions for the extreme ranges of rock depths i e very shallow and very deep It is hypothesized that this may be due to the effects of modulus averaging For example some of the existing sites used in this study to calibrate rock had a significant thickness of soil overburden Since moduli for rock are much greater than that for soil it is clear that the current model is analyzing an effective modulus rather than the actual modulus for these cases Further investigation into the effect of this condition on model results is recommended and it may be appropriate to change the model to reflect actual soil and rock depths It is also important to note that high surface heaves at shallow depths can be attributed to the fact that the fundamental mathematical model is in fact a bending deflection model Deep injections involve not just bending phenomena but also localized elastic compression above and below the fracture This current limitation makes it clear that an entirely new fracture propagation model that incorporates both bending and localized elastic compression should be developed 13 Currently the System Desig
183. ow be discussed in the context of their importance to pneumatic fracturing Formation Type For soils texture is the most fundamental descriptor of the geomaterial The sizes of particles that make up soil vary over a wide range from clay size 0 075 mm all the way up to boulders gt 9 in Burmister 1970 A number of different classification systems have been developed to describe particle size within an engineering context Table 2 2 shows the more common classification systems including those developed by the U S Department of Agriculture USDA the American Association of State Highway and Transportation Officials AASHTO and the Unified Soil Classification System USCS developed by the U S Army Corps of Engineers In the United States the USCS is the most used Table 2 2 Particle Size Classifications Das 1994 Grain size mm Name Gravel Sand Silt Clay USDA gt 2 2 to 0 05 0 05 to 0 002 lt 0 002 AASHTO 76 2 to 2 2 to 0 075 0 075 to 0 002 lt 0 002 USCS 76 2 to 4 75 4 75 to 0 075 Fines i e silts and clays lt 0 075 The principal effect of soil texture on pneumatic fracturing is that it largely controls the permeability and porosity of the soil This is related to the basic principle 26 that a pneumatic fracture will continue to propagate only as long the fluid injection rate exceeds the ability of the soil pores to accept the fluid ie the permeability For example when air is injected into clay
184. p Err Description amp Chr 13 Msg Msg amp Location amp Screen ActiveForm Name amp Chr 13 Msg Msg amp Procedure amp ProcName MsgBox Msg End Sub Public Sub Increasing Abort ApertureFlag D Density DENSITYGas depth _ FractureToughness HeadLossDistance K Kh Kv MaintPres Modulus _ Poisson PRESdriv RADIUSwell next VISCOSITYGas XX Dim RADIUS As Single Dim RADincr As Single Dim Qtip As Single ProcName Increasing On Error GoTo ErrorHandler nitialize the variables RADIUS 1 RADincr 0 01 Qtip 1 Do While Qtip gt 0 RADIUS RADIUS RADincr Qtip StarTrek Abort ApertureFlag D Density DENSITYGas depth _ FractureToughness HeadLossDistance K Kh Kv MaintPres Modulus _ Poisson PRESdriv RADIUS RADIUSwell R next VISCOSITYGas XX If Abort Yes Then Exit Sub If RADIUS gt 100 Then infinite loops check txtEstimatedRadius Text ERROR Exit Do 193 End If Loop ApertureFlag 1 Turns on aperture at well calculation Call ShowResults Abort ApertureFlag D Density DENSITYGas depth FractureToughness _ HeadLossDistance K Kh Kv MaintPres Modulus Poisson PRESdriv _ RADIUS RADIUSwell R_next VISCOSITYGas XX Error Code Exit Sub ErrorHandler Msg An untrapped error has occured Please make a amp Chr 13 Msg Msg amp note of the following information amp Chr 13 amp Chr 13 Msg Msg amp Error number amp Err
185. per square foot plastic limit effective overburden pressure xvii Q Qleak Ores qu R D Yincr scfm Sec TM u wW zw reff t LIST OF SYMBOLS Continued injection flow rate air flow lost into formation residual flow in fracture unconfined compressive strength final fracture radius radius segmented radius well radius incremental radius standard cubic feet per minute second s time trademark velocity of fluid moisture content depth depth to water table or depth below surface effective unit weight dry unit weight xviii II S li 3 I lI I on l lt I LIST OFSYMBOLS Continued unit weight of water a coefficient dynamic viscosity of fluid ratio of a circle s circumference to its diameter silly density of fluid Poisson s ratio potential function sample space universal quantifier the start or end of a program flow represents any kind of processing function a decision or switching type function represents human readable data such as printed output data xix JLIOACLIE LIST OF SYMBOLS Continued represents a named process such as a subroutine or a module stored data identifier or connector data input by manual means such as with a keyboard represents modifications preparations or initializing a routine internal storage Bayesian Network belief node XX CHAPTER 1
186. perties had different states for the categorized formations ie the states of depth for soil and rock are different interpretation by the inference engine is difficult Therefore in order to minimize internal code processing time and logic the geologic formations are arranged into three different categories which are accessed separately by the inference engine These are shown in Tables 3 4 to 3 6 which follow Table 3 4 Geologic Properties that Apply to Fine Grained Soils Clay Clayey Sand Clayey Silt Silty Clay e Depth 6ft 6 12 ft gt 12 ft e Consistency soft medium stiff e Plasticity w lt PL lt lt 11 w gt LL e Water Table fracturing is above fracturing is below 47 Table 3 5 Geologic Properties that Apply to Coarse Grained Soils Silt Silty Sand Sand Sand amp Gravel Gravel e Depth lt 6 ft 6 12 ft gt 12 ft e Density loose medium dense dense e Water Table fracturing is above fracturing is below Table 3 6 Geologic Properties that Apply to Rocks Shale Siltstone Sandstone Limestone Dolomite Granite Gneiss Schist and Basalt e Depth lt 4 ft 4 8 ft gt 8 ft e Fracture Frequency widely jointed medium jointed closely jointed e Weathering slightly weathered moderately weathered heavily weathered e Water Table fracturing is above fracturing is below Figure 3 4 on the following page is a flow chart that shows how the inferenc
187. pneumatic fracturing should participate in the validation Since the inference engine and knowledge base are robust any annual validation should only be considered as fine tuning the model No additional programming will be needed Although the inference engine of the expert system uses subjective probability research in the area of Bayesian networks showed promise as an alternative and should be considered as a viable method to handle uncertainty Implementation of a BN would allow for more complex interactions between evidence and may allow for interdependence among evidence should such conditions in the technology exist An ActiveX control for Bayesian networks has recently been released from Hugin A S Denmark which would greatly assist in programming a new inference engine for the expert system By using the ActiveX control extensive redesign of the Site Screening component and PF Model can be avoided After many discussions with experts during the knowledge acquisition process of the Site Screening component it became clear that some felt that the three technology variants are too general For example Permeability Enhancement is normally coupled with different treatment technologies such as pump and treat or soil vapor extraction SVE It is possible that pump and treat might be recommended while SVE for the same site and parameters might be not recommended Thus these experts preferred that the technology variants b
188. pon reaching this step in the subroutine the post fracture values for Young s modulus E and effective pneumatic conductivity Key are returned These values represent an estimation of the actual field conditions Now instead 79 of using default values for E and Keff in the System Design component these values can be used 3 5 Program Language and Structure Several application development tools were available for development of PF Model and include Borland C Builder Borland Delphi IBM VisualAge C Microsoft Visual C and Microsoft Visual Basic Although these development tools can create powerful and robust applications many are aimed at different audiences For example Visual Basic is aimed at developers who are using Microsoft products exclusively These development tools each have different features and therefore exhibit different advantages over the others In the instance of Visual ge C it uses debugger and automatic memory manager and is specifically designed to improve programmer productivity through incremental compilation Even the degree of sophistication between two development tools aimed at the same audience can vary such as Delphi and Visual Basic Delphi uses Decision Cube components which help create local multidimensional data stores that can be summarized into cross tabulated views and graphs Although these cross tab queries can be created in Visual Basic Delphi s Decision Cube can more easily pivot
189. portant influences on the propagation of pneumatically induced fractures First it is an indication of the elastic modulus or stiffness of soil formations Loose or soft soil formations will usually exhibit localized deformation around the injection point resulting in modest propagation radii In contrast firm or stiff formations will deform less but influence radii will be larger 30 Table 2 4 Standard Penetration Test DERE niin m a Ee Relative Density of Consistency of Cohesionless Soils Cohesive Soils Penetration Penetration Resistance V Relative Resistance V blows ft Density blows ft Consistency 0 4 Very loose lt 2 Very soft 4 10 Loose 2 4 Soft 10 30 Medium dense 4 8 Medium 30 50 Dense 8 15 Suff gt 50 Very dense 15 30 Very Suff gt 30 Hard The second influence of relative density consistency on pneumatic fracturing is it may affect the direction of fracture propagation It is well known that in the hydraulic fracturing industry that fractures tend to propagate perpendicular to the direction of least principal stress Hubbert and Willis 1957 Therefore in formations where the least principal stress is vertical most pneumatically induced fractures occur in the horizontal plane Such behavior may be expected in soils that are at least of firm density or medium consistency Since most formations tend to be overconsolidated due to past geologic events and therefore more likely to be of firm density or medium con
190. primitive The system may then ask the user other questions which will cause possible firing of other rules These conclusions are then added to the working memory The entire process repeats until all subgoals and goals have been Saeed The information provided by the user and inferred by the system are stored in working memory With an understanding of the original goal this information determines if it is true or false Mixed Chaining The mixed chaining control strategy is when the system uses both forward chaining and backward chaining strategies The advantage of mixed chaining is that the user supplies only the relevant information needed to solve the problem If the initial hypothesis is wrong the system moves to the next assumption based on the current information This strategy operates with known facts and assigns a probability to the potential solutions or conclusions It then attempts to support the highest priority solution by creating subgoals and requesting additional information from the user if necessary If the conclusion is false the system takes the next highest priority solution and then attempts again to determine if the solution is true or false This process is repeated until the solution is true 2 1 3 3 Handling Uncertainty An expert system is required to reason with uncertain information so selecting an uncertainty theory to model the expert system becomes 20 important discussion of the more popular theor
191. pth of fracture FractureToughness Val frmInputParameters txtFractureToughness HeadLossFactor Val frmInputParameters txtHeadLossFactor Modulus Val frmInputParameters txtY oungsModulus 191 Poisson Val frmInputParameters txtPoissonsRatio Determine which well radius to use either default or user provided If frmDatalnput chkOverrideWellRadius Value 1 Then Checked or on RADIUSwell Val frmDatalnput txtWellRadius Elself frmDatalnput chkOverrideWellRadius Value 0 Then Unchecked or off RADIUSwell Val frmDatalnput IblDefaultWellRadius Caption End If VISCOSITYGas Val frmInputParameters txtV iscosityGas ApertureF lag 0 Turns off aperture at well calculation Determine which hydraulic conductivities to use If anisotropic conductivity is selected If frmPneumaticConductivity optKhKv True Then Kh Val frmPneumaticConductivity txtHorizontalConductivity Kv Val frmPneumaticConductivity txtVerticalConductivity If isotropic conductivity is selected Elself frmPneumaticConductivity optTotalConductivity True Then Kh Val frmPneumaticConductivity txt TotalConductivity Kv Kh Else use the default as an isotropic Else Kh Val frmPneumaticConductivity txtPneumaticDefault Kv Kh End If Calculation of driving pressure Determine which pressure to use either the default or user provided If frmDatalnput chkOverridePressure Value Then Checked or on MaintPres Val frmDa
192. quired knowledge and infers new knowledge from the base knowledge Armed with the control information it uses the knowledge base to match facts in the working memory When the 14 inference engine finds a match it will add the rule s condition to the working memory and continue to scan for other possible matches The inference engine must also have the capability to modify and expand the knowledge base to draw conclusions about the problem The search strategy used by the inference engine to develop the required knowledge or inference paradigm can be one of three fundamental types Bielawski and Lewand 1988 1 forward chaining which starts with known conditions and works toward a desired goal 2 backward chaining which starts from the desired goal and works backward toward supporting conditions or 3 mixed chaining which is a combination of both forward and backward chaining These search strategies for the inference engine will be further discussed in Section 2 1 3 Problem Solving Strategies Using Expert Systems Since the inference engine is detached from the knowledge base changes can be made to either component without necessarily having to alter the other For example one may be able to add information to the knowledge base or increase the performance of the inference engine without having to modify code elsewhere Clancey 1983 That is not to say that the inference engine is totally independent of the knowledge base
193. rk for Non Plasti6 Solils a d nd eae nt er dude cadet 133 Bayesian Network of Plastic Fine Grained Soils with Example of Divorced emnes cfe iae Dados ove DE Pr catu ge 134 Bayesian Network Modeling the Success of Pneumatic Fracturing for Plastic Fine Grained S018 sexi Asses ee cic de apa S id Ned 135 XV b bw C Cpnorm cm e g etal etc GUI LIST OF SYMBOLS aperture width ground heave at well cohesion idealized C for normal consolidation centimeter s copyright Young s modulus for example from the Latin exempli gratia and others from the Latin et alii and other things from the Latin ef cetera feet acceleration due to gravity graphical user interface total head that is from the Latin id esr inches conductivity fracture toughness effective pneumatic conductivity horizontal pneumatic conductivity vertical pneumatic conductivity xvi Ib lerad LL m mm N Nd Nf p Pd PF Pk Pm Pprop Pw pef psf PL Po LIST OF SYMBOLS Continued pound s flowpath length liquid limit meter s millimeter number of blow counts number of potential drops number of flow tubes pressure driving pressure pneumatic fracturing pressure required to overcome fracture toughness maintenance pressure propagation pressure pressure in well pounds per cubic foot pounds
194. s are the seven geotechnical properties discussed in Section 2 2 1 Geotechnical Properties The overall interactions discussed in Section 3 2 Site Screening Approach and corresponding Tables 3 4 3 5 and 3 6 were actually derived from the early research of BNs and therefore are applicable in this discussion These geotechnical properties and tables will not be repeated here but the reader is encouraged to review these two sections before proceeding since they are referenced frequently in the next section C 3 Approaches The initial approach for creating a BN for pneumatic fracturing was to use a converging connection Figure C 1 shows an example of a converging connection where the parents 130 of A are B through E The parents are said to be independent when nothing is known about A except what can be inferred from A s parents B E Evidence on one of the parents has no influence on the others Jensen 1996 Figure C 1 Converging Connection Figure C 2 on the following page shows the earliest version of the pneumatic fracturing BN The child Results has two states either yes pneumatic fracturing successful or no not successful The parent Formation has 13 states i e each geologic formation type clay silt shale etc The parent Depth has six states Three of these states though apply only to nine soil types while the remaining three depths apply only to the five rock types as discussed in Sections 2 2
195. s coded Finally it was decided to create a system utility that would give users access to the knowledge base This approach allows the expert system to be updated as the technology evolves and also permits licensed technology vendors to create a knowledge base with their own proprietary data It should be noted that if the knowledge base is modified and multiple experts are not consulted the expert system may in effect become insular and therefore would not truly represent the consensus of expert opinion for the technology 4 3 System Design As opposed to the heuristic structure of the previous section the System Design component is programmed with structured algorithms Therefore validation and calibration of this component is relatively straight forward The validation step confirms that the model is reasonably representative of the pneumatic fracturing process while the calibration step establishes the necessary coefficients and default values to insure proper functioning of the model PF Model was subjected to both these procedures Currently with over 40 sites pneumatically fractured to date a reasonable data base exists for validation and calibration purposes The sites selected for validation and calibration were previously screened Puppala 1998 to insure that sites of only acceptable data quality were used in the evaluation process Six different sites were selected three involving soil formations and three involving rock formatio
196. s experience and expert knowledge It also contains an extensive default library which is calibrated to previous site data PF Model allows potential users to add proprietary data generated by future projects into the knowledge base and default library A nominal amount of format detailing is incorporated for user convenience The program has two principal 35 36 Mathematical Modeling Field Prototype and Research Demos Commercial Availability Y Laboratory Bench Scale Figure 3 1 Conceptualization of the Technology Transfer Process components Site Screening and System Design Figure 3 2 on the following page is a top level flow chart showing the model component s interactions and outputs The dashed lines in Figure 3 2 represent areas of future research This section will introduce these model components Discussion of the design approach for Site Screening and System Design are detailed in Sections 3 2 and 3 3 respectively The Calibration Mode Section 3 4 follows The chapter will conclude with a description of the program language and structure Section 3 5 37 Input Geologic Data Propagation nenta ontaminant System Design Sup E LA E Site Screening F l Injection I Transport 1 ite Screening Fracture Liquid and I Analysis 1 l 1 Solid
197. s to any particular menu item or button is identified by an underscore under a letter The Hot Key is activated by simultaneously pressing the lt Alt gt key and the Hot Key ie the underscored letter In most screens the tab key can be used to move from one field or button to another field or button 3 3 Screen Layout The graphical user interface consists of two parts the Main Screen and the Menu Bar PNEUMATIC FRACTURING COMPUTER MODEL 3 3 1 The Top Menu Bar The top menu bar gives access to the following six options FILE Select or create a data set print save or exit PF MODEL COMPONENT Select an active component to move to LEAKOFF Select the method of leakoff used by the model DEFLECTION Allows the user to select from four bending deflection solvers modeled in the program ADVANCED Allows access to the more advanced functions of PF MODEL Only the more experienced user should access these functions BACKGROUND Provides background and general information including help The desired option is selected and executed by either clicking the left mouse button while positioned over the option or by using the appropriate Hot Key All of the above menus are drop down menus where more options are displayed These option can be accessed by continuing to use the mouse or the Hot Keys The menus are described further in the following sections 3 3 1 1 FILE Menu When you choose the F
198. sistency horizontal fractures are most often expected when the pneumatic fracturing process is applied It follows that in formations of loose density or soft consistency fractures will tend to propagate in the vertical plane Although the standard penetration test is a valuable method of soil investigation it should only be used as a guide for relative density consistency since results are always 31 approximate Lambe and Whitman 1969 Therefore caution must be applied when applying this piece of evidence in the probabilistic model In general the standard penetration test is considered more reliable for cohesionless soils than cohesive soils Fracture Frequency Discontinuities or fractures occur naturally in rock formations originating from thermal and tectonic stresses as well as unloading of overburden materials Various types of discontinuities are encountered including cracks joints faults and shear zones Bates and Jackson 1984 In general rock formations of the same lithology develop a somewhat similar discontinuity geometry For example basalt commonly exhibits vertical columnar joints while shale exhibits bedding joints Research over the last 10 years has shown that the principal effect that pneumatic fracturing has on rock formations is that it dilates existing discontinuities Thus rocks with fairly frequent fractures will respond best Conversely formations with only a few widely spaced fractures are not good
199. ski The objective of this study was the development of a new computer program called PF Model to analyze pneumatic fracturing of geologic formations Pneumatic fracturing is an in situ remediation process that involves injecting high pressure gas into soil or rock matrices to enhance permeability as well as to introduce liquid and solid amendments PF Model has two principal components 1 Site Screening which heuristically evaluates sites with regard to process applicability and 2 System Design which uses the numerical solution of a coupled algorithm to generate preliminary design parameters Designed as an expert system the Site Screening component is a high performance computer program capable of simulating human expertise within a narrow domain The reasoning process is controlled by the inference engine which uses subjective probability theory based on Bayes theorem to handle uncertainty The expert system also contains an extensive knowledge base of geotechnical data related to field performance of pneumatic fracturing The hierarchical order of importance established for the geotechnical properties was formation type depth consistency relative density plasticity fracture frequency weathering and depth of water table The expert system was validated by a panel of five experts who rated selected sites on the applicability of the three main variants of pneumatic fracturing Overall PF Model demonstrated better than an 80 agreemen
200. soils the natural permeability of the formation can not accept the air quick enough and discrete fractures are created in the formation Conversely in a coarse soil formation such as sand which has a relatively high permeability the effect of pneumatic fracturing is very different Although there may be some local fracturing around the borehole for the most part the sand is able to accept the injected air In this instance the main effect is rapid aeration as air passes through interstitial pore spaces In cases where soils have a marginal permeability it becomes difficult to predict the effect pneumatic fracturing will have In this instance more evidence about the soil formation is required In rocks the lithology acts as the fundamental descriptor type color mineral composition and grain size are all lithologic characteristics Boggs 1987 The principal effect of rock lithology on pneumatic fracturing is that it largely controls discontinuities and interconnectivity For example consider a sedimentary rock such as shale or sandstone Sedimentary rocks are formed by particle deposition and are characterized by their distinctive layers This layering also known as stratification imparts numerous and regular discontinuities which dilate during pneumatic fracturing A certain amount of dilation is permanent leading to substantial increases in permeability and interconnectivity 27 On the other hand igneous and metamorphic roc
201. t The maximum depth of the BTX plume is 15 ft Figure 4 2 shows a profile view DC RE ns ums m zn p rant rem y E E 3f _ Misc Granular Fill water table varies Medium Stiff Clayey Silt with season 56 15 ft bottom extent of plume 19 ft wmm ia S i i WERE ag Ba Tae gp a a a el sane M Shale A TAE ee zs RTL MEE o rSf Figure 4 2 Cross sectional view of BTX plume A preliminary investigation is undertaken to develop a remedial plan in order to e determine if the pneumatic fracturing technology is applicable at the Little Bighorn Refinery and e ifit is increase the permeability of the clayey silt so that vapor extraction may be applied You are to use PF MODEL to Determine if this site is applicable for the pneumatic fracturing technology If it 1s estimate the maximum expected radius of fracture extent Determine system requirements pressure and flow to effect permeability enhancement to a design goal of wells spaced at 15 ft oN 12 PNEUMATIC FRACTURING COMPUTER MODEL 4 2 Generation of Data Set Start PF MODEL by clicking on the PF MODEL icon located in your Start Menu of the Windows task bar After the introductory screen you are now viewing the Data Input screen Figure 4 3 Take time to view this screen and even explore some of the options available from the Menu Bar such as the Background Menu note that man
202. t with the expert panel The System Design component was programmed with structured algorithms to accomplish two main functions 1 to estimate fracture aperture and radius Fracture Prediction Mode and 2 to calibrate post fracture Young s modulus and pneumatic conductivity Calibration Mode The Fracture Prediction Mode uses numerical analysis to converge on a solution by considering the three coupled physical processes that affect fracture propagation pressure distribution leakoff and deflection The Calibration Mode regresses modulus using a modified deflection equation and then converges on the conductivity in a method similar to the Fracture Prediction Mode The System Design component was validated and calibrated for each of the 14 different geologic formation types supported by the program Validation was done by comparing the results of PF Model to the original mathematical model For the calibration process default values for flow rate density Poisson s ratio modulus and pneumatic conductivity were established by regression until the model simulated in general actual site behavior PF Model was programmed in Visual Basic 5 0 and features a menu driven GUI Three extensive default libraries are provided probabilistic knowledge base flownet shape factors and geotechnical defaults Users can conveniently access and modify the default libraries to reflect evolving trends and knowledge Recommendations for future study are incl
203. talnput txtMaintenancePressure ElseIf frmDataInput chkOverridePressure Value 0 Then Unchekced or off MaintPres Val frmDatalnput lbIDefaultPressure Caption End If PRESdriv MaintPres Density depth 144 units in psi Calculation of head loss distance HeadLossDistance HeadLossFactor depth units in feet Determines the value of D which is used for the circular plate log distribution If mnuSolverLogDistribution Checked True Then D Modulus depth 3 12 1 Poisson 2 End If If mnuAdvancedEnginelncreasing Checked True Then Call Increasing Abort ApertureFlag D Density DENSITYGas depth _ FractureToughness HeadLossDistance K Kh Kv MaintPres Modulus _ Poisson PRESdriv RADIUSwell R next VISCOSITYGas XX Else 192 Call Bisection Abort ApertureFlag D Density DENSITYGas depth _ FractureToughness HeadLossDistance K Kh Kv MaintPres Modulus _ Poisson PRESdriv RADIUSwell R next VISCOSITYGas XX End If Screen MousePointer 0 Sets mouse pointer back to default End If If Button vbRightButton Then HELP ITEM System Design Calculation Call Help HELP ITEM End If Error Code Exit Sub ErrorHandler Msg An untrapped error has occured Please make a amp Chr 13 Msg Msg amp note of the following information amp Chr 13 amp Chr 13 Msg Msg amp Error number amp Err Number amp Chr 13 Msg Msg amp Description am
204. tem information about characteristics of the site 7 e the evidence The posterior possibility p H E E is computed for all hypotheses from the supplied evidence E and stored probabilities The Site Screening component of PF Model has two hypotheses pneumatic fracturing is applicable and pneumatic fracturing is not applicable There is also the possibility that numerous pieces of evidence are available In order to account for both multiple hypotheses and multiple pieces of evidence Equation 3 1 can be generalized in a 50 manner proposed by Ng and Abramson 1990 This is accomplished by first considering a single piece of evidence with multiple mutually exclusive and exhaustive hypotheses The relation becomes pCE H x p H 22 P E H x p H p H E For multiple evidence and multiple mutually exclusive and exhaustive hypotheses the following is obtained p H WI DEIN EU p E E Eyl Hy x p H 3 3 In order to simplify Equation 3 3 conditional independence can be assumed among the pieces of geological evidence given the hypothesis Therefore p 3 4 pay PCE A x pE p H This is the general equation used by the inference engine in determining the applicability of pneumatic fracturing in the Site Screening component Appendix F contains an illustrative example of how su
205. these descriptors to consistency is shown in Table 3 1 In PF Model this table functions as an interactive system utility where the user selects the appropriate descriptor and then PF Model uses the corresponding consistency Table 3 1 Guide to Consistency and Strength of Clay Soils Estimated Unconfined SPT Compressive Penetration Strength q Consistency blows ft Field Identification Guide tons ft Very soft lt 2 Extruded between fingers when lt 0 25 squeezed Soft 2 4 Molded by slight finger pressure 0 25 0 5 Medium 4 8 Molded by strong finger pressure 0 5 1 0 Stiff 8 15 Readily indented by thumb but 1 0 2 0 penetrated only with great effort Very stiff 15 30 Readily indented by thumbnail 2 0 4 0 Hard gt 30 Indented with difficulty by gt 4 0 thumbnail 41 Another descriptor related to consistency but not as definitive is the overconsolidation ratio OCR Some users may prefer to describe soil by OCR in lieu of the descriptors mentioned above Therefore the guide shown in Table 3 2 which related consistency to OCR is also incorporated into PF Model but as a subsequent interactive utility to Table 3 1 Table 3 2 Approximate Relationship Between Consistency Consolidation and OCR Typical Consolidation Consistency Description Typical Value of OCR Very soft to soft Normally consolidated OCR 1 Medium to stiff Slightly overconsolidated OCR 5 Very stiff to hard Heavily overconsolidated OCR
206. tical method and graphical method The analytical method calculates leakoff by summing the lost flow from successive annular rings of the fracture surface The graphical method modifies Darcy s law to account for pressure variation with respect to radial distance in three dimensions ANALYTICAL Use the Analytical method to find the solution This leakoff method uses an effective conductivity GRAPHICAL Use the Graphical or flownet method to find the solution The graphical method expands to another drop down menu It allows for the use of isotropic as well as anisotropic conditions The default leakoff method for PF MODEL is K 5K PNEUMATIC FRACTURING COMPUTER MODEL h sm AAA M Q M M X M AA P 9 3 3 1 4 DEFLECTION Menu It is assumed that pneumatic fractures cause deflection of the overburden in a manner similar to a thick plate in bending The DEFLECTION menu provides four optional deflection models with different combinations of pressure distribution and formation geometry LOG DISTRIBUTION CIRCULAR PLAN This is the default selection of PF MODEL which uses a logarithmic pressure distribution acting on a circular plate to predict a tapering fracture It is always recommended that this Deflection Solver be used The other three Deflection Solvers are included for research purposes CONSTANT PRESSURE CIRCULAR PLAN Selects a const
207. tionDefaults Call CalculatePressure Call Establish WellRadiusDefaults End Sub APPENDIX J TABLES USED IN VALIDATION AND CALIBRATION OF PF MODEL Both the Site Screening and System Design components of PF Model underwent extensive validation and calibration procedures This appendix contains the remaining tables of this evaluation as discussed previously in Chapter 4 Validation and Calibration 211 Table J 1 System Validation of Dry Media Injection Variant Depth to Depth W T Relative Fracture Evaluator Results T System Formation Type ft ft Consistency Plasticity Density Frequency Weathering A B C D E Result Rating Silty Clay 18 10 medium 77 n a n a n a M M 55 Clayey Silt 10 18 medium brittle n a n a n a Y Y 69 Clay 8 4 soft plastic n a n a n a M M 53 Silty Clay 12 10 medium liquid n a n a n a M M 50 Clay 10 55 Clay 4 10 very stiff brittle n a n a n a M M 57 Silty Sand 14 8 n a n a med dense n a n a Y Y 75 Sand 24 10 n a n a dense n a n a b Y 71 Sand and Gravel 14 20 n a n a very dense n a n a Y Y 69 Siltstone 20 12 n a n a n a closely slightly Y Y 60 Shale 10 n a n a n a 222 222 M Y 65 Shale Siltstone 12 18 n a n a n a widely highly M N 4 Sandstone 10 16 n a n a n a widely slightly N N 27 Basalt 15 TEE n a n a n a medium slightly N N 43 Sandstone 12 8 n a n a n a i M 55 Notes t Evaluators are Dr J Schuring Patent Holder of PF B T Boland PF D
208. tions may have been needed to arrive at a conclusion Backward Chaining Backward chaining involves reasoning from a conclusion or hypothesis backing through the rules in search of the facts which support or discount that hypothesis This type of control strategy can be advantageous since some problems begin naturally by forming a hypothesis and then seeing if it can be proven I believe the chain just fell off my bike This strategy also focuses on the given goal asking questions that relate only to its solution It searches the knowledge base that is relevant only to the current problem as opposed to forward chaining which attempts to infer everything possible from all available information The primary disadvantage of backward chaining is that it will follow a given line of reasoning even if the goal is dropped and switches to a different one Durkin 1994 Backward chaining operates by collecting the set of rules that contain the solution in the THEN part These rules are called goal rules rules that can be proven if one of these goal rules fires The goal rule will only fire if its premises are satisfied These premises are in turn supported by other rules which requires the inference engine to prove them as well These are termed subgoals The system then searches its rules 19 recursively to validate both the subgoals and the original goal Eventually a premise is reached that is not supported by any of the system s rules ie a
209. tions are available to the user Any new anisotropic conditions will of course require the development of corresponding flownet shape factors 117 7 To expand the usefulness of the program two additional components Supplemental Media Injection and Contaminant Transport should be added when research is completed in these areas 8 Visual Basic 6 0 has recently been released Although PF Model was written in Visual Basic 5 0 there is no need to update the program However when Visual Basic 7 0 is released it is highly recommended that the code interface and functionality of PF Model be carefully evaluated in order to determine if an upgrade is advantageous No release date has yet been announced for Visual Basic 7 0 9 The running of PF Model as a multiple document interface MDI should be investigated Currently PF Model is a single document interface SDI A SDI allows for only a single document to be open the current document must be closed in order to open another For example the WordPad application that is distributed with Microsoft Windows is a SDI Examples of MDIs are applications such as Microsoft Excel and Microsoft Word for Windows In these applications multiple documents can be displayed at the same time where each document is displayed in its own window A survey of some sort should be undertaken regarding a SDI MDI design for the program The conversion of PF Model to a MDI would require an extensive redes
210. uded in the work DEVELOPMENT OF A COMPUTER MODEL AND EXPERT SYSTEM FOR PNEUMATIC FRACTURING OF GEOLOGIC FORMATIONS by Brian Michael Sielski A Dissertation Submitted to the Faculty of New Jersey Institute of Technology in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Department of Civil and Environmental Engineering May 1999 Copyright O 1999 by Brian Michael Sielski ALL RIGHTS RESERVED APPROVAL PAGE DEVELOPMENT OF A COMPUTER MODEL AND EXPERT SYSTEM FOR PNEUMATIC FRACTURING OF GEOLOGIC FORMATIONS Brian Michael Sielski Dr John R Schuring Dissertation Advisor Date Professor of Civil and Environmental Engineering NJIT Dr Paul C Chan Committee Member Date Professor of Civil and Environmental Engineering NJIT Edward G Dauenheimer Committee Member Date Professor of Civil and Environmental Engineering NJIT Dr Robert Dresnack Committee Member Date Professor of Civil and Environmental Engineering NJIT Dr John W Ryon Committee Member Date Professor of Computer and Information Science NJIT BIOGRAPHICAL SKETCH Author Brian Michael Sielski Degree Doctor of Philosophy Date May 1999 Graduate and Undergraduate Education e Doctor of Philosophy in Civil Engineering New Jersey Institute of Technology Newark NJ 1999 e Master of Science in Environmental Engineering New Jersey Institute of Technology Newark NJ 1994 e Bachelor of Science in E
211. ult values instead Step 2 Regress Modulus Deflection of the overburden can be modeled by assuming the bending of an elastic circular plate that 15 clamped at its edges with a logarithmically varying load In this step the Young s modulus for the formation is calculated by manipulating Equation 3 11 into a more useful form Based on 75 Step 1 Regress Young s Modulus Y Step 3 Prepare as input K Kaige and Rusia 5 Step 4 Step 6 Step 5 Step 10 Step 11 RK ov V e QR GS R K 0 Y a Step 13 K K K High Pid Low Step 14 Calculate Error Step 15 Error lt 0 1 Pneumatic Conductivity Figure 3 8 The Calibration Subroutine 76 the maximum measured radius R and the maximum measured ground heave at the well by it is possible to solve for Young s modulus as follows R 2 12 1 0 Pm 2 E 3 26 gt 3 26 In b Z 7 w Steps 3 through 6 The initialization of the upper and lower bounds of the post fracture pneumatic conductivity interval are chosen such that the actual conductivity lies within this interval The lower limit KZ gw is chosen to be zero For the upper limit KHigh a value of 100 ft day is selected Next the value of KMid is prepared which is K High Krow 3 27 three values are then passed as input to the Composite
212. ure and log pressure 2 NE 1 IOkR 8k 16 256D PE Au RE m p 64D 32D 2 4 _ 572 2 4 pf circular plan fracture b 3pa v rg 28292 R and uniform pressure 16 Ez EU WI p1 anticlinal plan fracture ps paQt v 2825 R and uniform pressure 2Ez P by circular plan fracture and tb linearly tapering pressure cr rrr NEST wc z Pd Ez 3 1 JR Notes k Dz cad a 2 1 0 16Ez Inr Fw The choice of Deflection Solver has a significant effect on the estimated fracture radius Regressive analyses have shown that the equation for bending of a circular plate fixed at its edges best approximates field results Canino 1997 Therefore the circular plan fracture and log pressure distribution will be the default selection in PF Model 61 Step 13 Model Engine Subroutine At this point in the System Design Subroutine control is passed to the Model Engine Subroutine which is discussed in the following section Step 14 System Design Output When control is passed back from the Model Engine Subroutine the final output is then presented to the user The fracture radius and aperture that satisfy the flow and pressure conditions are presented in numerical form while aperture width residual flow and pressure distributions within the fracture as a function of radial distance are presented in graphical form 3 3 3 2 Model Engine Subroutine This subroutine contro
213. ure radius and aperture This dissertation will begin with a summary of expert systems site screening and propagation model backgrounds Chapter 2 This will be followed by a discussion of the approach for the different model components and how they are coded and or theorized Chapter 3 Next the model will be field validated and calibrated with data from previous sites and discussion with experts Chapter 4 Finally conclusions and recommendations for future study are presented Chapter 5 The User s Guide for PF Model is included in Appendix H CHAPTER 2 BACKGROUND INFORMATION This chapter will provide the reader with appropriate background information used in programming the computer model First since some components of the computer model are in part based on expert systems an introduction to expert systems is presented Second the parameters or geologic evidence required for successful application of the site screening model will be described Finally the analytical model used in solving fracture propagation and associated research will be discussed 2 1 Expert Systems The overall objective of the study is to capture the available knowledge of the pneumatic fracturing process thus allowing distribution of this expertise on a wider scale PF Model encompasses both a heuristic model i e the Site Screening component and an analytical model i e the System Design component The Site Screening component is base
214. vergence algorithm consists of thousands of iterations any difference in significant figures is compounded as the algorithm propagates thereby creating the higher variation 4 3 1 2 Validation of Fracture Prediction Mode The Fracture Prediction Mode estimates the maximum fracture radius and aperture upon inputting geological and operational data Therefore in a manner similar to the Calibration Mode successful validation requires agreement between PF Model and the original mathematical model 98 Table 4 5 Validation of Calibration Mode for Estimating Pneumatic Conductivity Site Name z Q P b R m per Kr per PF Model scfm psi cm sec Frelinghuysen 1 a 3 5 300 10 0 0792 4 2 6 70e 4 6 76e 4 0 99 3 5 300 10 0 0533 4 2 6 70e 4 6 86e 4 0 98 3 5 300 7 0 0208 4 2 1 28e 3 1 25 3 1 02 3 9 300 8 0 0317 4 2 9 36e 4 9 71e 4 0 96 Frelinghuysen 2 6 715 13 0 0342 8 5 6 24e 4 6 11e 4 1 02 1227 14 0 0367 8 5 1 00 3 9 43e 4 1 06 6 1157 15 0 0075 5 7 2 46e 3 2 61e 3 0 94 8 3 1500 18 0 0233 11 7 7 10e 4 7 16e 4 0 99 6 1500 17 0 0375 8 6 8 50e 4 8 55e 4 0 99 8 6 1339 17 0 0390 11 3 7 40e 4 7 49e 4 0 99 Frelinghuysen 3 6 857 15 0 0167 42 2 64e 3 2 65e 3 1 00 6 964 114 00275 126 484e4 4 80 4 1 01 6 1000 11 0 0250 9 6 9 44e 4 9 26e 4 1 02 9 943 16 5 0 0183 14 1 3 96e 4 4 15e 4 0 95 9 1114 14 7 0 0150 16 1 5 04e 4 5 06e 4 1 00 6 722 12 5 0 0275 11 7 3 50e 4 3 54e 4 0 99 8 3 98
215. was available you would enter that data instead For the depth of fracturing we ll select an average depth for the plume Enter the value of 10 ft Next enter the depth of the water table It is known that the water table varies from 6 to 15 ft Assume that the work is to be done in August and therefore the water table is likely to be at its lowest level Enter the value of 15 ft Other evidence is also available The clayey silt is of medium stiff consistency Therefore Click the button CONSISTENCY amp RELATIVE DENSITY Select the option MEDIUM TO STIFF Click the button DONE This is all the data and site evidence that is available Now proceed to the Site Screening component and see if the pneumatic fracturing technology is going to be applicable 14 PNEUMATIC FRACTURING COMPUTER MODEL Select COMPONENT from the Menu Bar Select SITE SCREENING from the Component Menu At this point the program begins to load the knowledge base library When the library is loaded the Site Screening screen appears Figure 4 4 Figure 4 4 The Site Screening Screen Notice in the top right of the main screen there are eight geotechnical properties The site information that you entered in the Data Input screen should be reflected here If everything looks right Click on the button PERMEABILITY ENHANCEMENT A technology recommendation rating of 76 is given Right now this value may not have any significant meaning To b
216. y of the options are not active yet Take time to fill out the project name date and your name if you haven t already in Dinta Input Figure 4 3 The Data Input Screen After becoming familiar with the Data Input screen you are now ready to enter the known Little Bighorn Refinery site data You first want to determine if pneumatic fracturing can be used for permeability enhancement at this site On the top right of the main screen find the frame that says Select component s for analysis and Select the check box for SITE SCREENING 13 PNEUMATIC FRACTURING COMPUTER MODEL Note that some of the Geotechnical Properties are now activated and ready for data entry If you have any questions or need help on a particular item you can get help by placing the pointer over the item and RIGHT CLICK the mouse For example put the mouse pointer over the text Soil Rock Type Right Click the label SOIL ROCK TYPE Now you can get a quick hint or more help on the geologic types supported by PF MODEL Throughout PF MODEL you can obtain help by right clicking other buttons labels and graphs Click the button DONE You ll now select the soil type by scrolling down the Soil Rock Type drop down box Select CLAYEY SILT Although not visible to you at this time PF MODEL has already selected geotechnical and system default values based on the soil type you have selected If actual field data from the Little Bighorn Refinery

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