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Microcomputer Simulation of the Transient Flow of Real Gas through

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12. 1965 considered the combined effects of turbulence wellbore storage and skin damage Matthews 1961 presented an early comprehensive paper on pressure buildup analysis and later Matthews and Russell 1967 published an SPE monograph on well testing concentrating mainly on liquid flow Until 1960 most gas flow studies concerned ideal gas Carter et al 1962 1963a 1963b and later Russell et al 1966 solved real gas flow problems and presented approximate methods for correcting ideal gas solutions to include real gas properties An important step was taken by Al Hussainy et al 1966a 1966b who introduced the real gas pseudo pressure concept Following Wattenbarger 1967 Fligelman 1981 used this concept to investigate short term drawdown tests where the exterior boundary does not influence the flow behavior at the well Fligelman s program solves a non linear partial differential equation that resulted from the consideration of various parameters simultaneously or not This work considered a constant rate inner boundary for the infinite reservoir case Couri 1987 used Fligelman s approach to verify classical correlations in the gas engineering literature that did not consider the effects of wellbore storage skin and turbulent flow simultaneously Couri also considered only drawdown cases 1 2 Turbulent Flow Turbulent flow causes an extra pressure drop at the well which can be mistaken for well damage Forchheimer 1901 added a
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19. and Jenkins R Unsteady Flow of Gas Through Porous Media One Dimensional Case Proceedings 1st U S Nat Cong Appl Mech 1952 763 Aronofsky J S Jenkins R A Simplified Analysis of Unsteady Real Gas Flow Trans AIME 1954 201 149 Bruce G H Peaceman D W and Rachford H H Jr Calculations of Unsteady State Gas Flow Through Porous Media Trans AIME 1953 198 79 Carter R D Solutions of Unsteady State Radial Gas Flow Trans AIME 1962 225 549 Carter R D Supplemental Appendix to Determination of Stabilized Gas Well Performance from Short Flow Tests ADI Doc No 7471 Library of Congress Washington D C 1963a Carter R D Miller S C and Riley H G Determination of Stabilized Gas Well Performance from a Short Flow Test Trans AIME 1963b 228 651 Cornell D and Katz D L Flow of Gases Through Consolidated Porous Media Ind and Eng Chem 1953 45 No 2 145 Couri F R Effect of Stress Sensitive Permeability Skin and Wellbore Storage on High Velocity Flow in Gas Well Test Master s Thesis Stanford University California 1987 Cullender M H and Smith R V Practical Solution of Gas Flow Equations for Wells and Pipelines with Large Temperature Gradient Trans AIME 1956 207 281 Dranchuck P Ma Pee R A ane Ronin D B Computer Calculations of Natural elation Institute of Petroletim ege Series No RSE i Earlougher R C Jr and Kers
20. constant pressure a radius must be provided in feet In the case of infinite acting an entry such as zero 0 should be made 7 DAMAGED ZONE RADIUS This field concerns a cylindrical zone around the wellbore altered by the drilling process which has a permeability different from the reservoir A damaged zone radius in feet is required If there is no damage a radius of zero 0 is required 8 WELL RADIUS A value in feet is required 9 WELL DEPTH This value is required to compute the gas properties table in order to compute wellbore storage A value in feet is required 10 THICKNESS The reservoir is modeled as a constant thickness circular layer A value in feet is required 11 POROSITY Enter fractional porosity between 0 01 and 0 8 12 GAS GRAVITY The specific gravity of the gas compared to air at standard conditions is required 13 14 The concentration of the gas impurities N2 CO2 and H2S should be entered as fractions Values should therefore be between zero and 1 0 15 TYPE OF GAS This information is required in order to select the proper Standing 1977 correlation RGF performs a test on the first letters of the information provided The user is encouraged to write as many letters as possible in the field box California The program checks on CAL Condensate The program checks on CON 16 RESERVOIR TEMPERATURE A temperature value in degrees Fahrenheit is required The simulated flow by RGF i
21. pb 19W T schux Tdu 7 up 41 20x duyoos 1 adun 000T 7 x1p3 1 owy3 7 au 3 p01d 3 1 apaq 0000001 P3033e T MT Je T PInaU T pequrad quyodu lt pequyad quyodu Mezdx ent oz pue 91 peas 005 17 7 OT op 91 37un pujaoz 0 paquj xd gzu podu ea Preta 0085 LT 83TIA l 3Tun pupae zpd3ewz 9pd3 que 4 LT pees 2783042 SILI uz 1 peoz GQuepeuz duap juz 1 pesz upewa wp juz 1 PERI KUT ews ATTIN y LT PEBI mia euz adux juz 41 pees esdxeuz Idx Juiz 1 pear xzjewz KIJZ I pe 3 peuz PAI Le LU peer KEEN REH DNR IS31un pupasz Q000T 23e1nu ODOT aduxnu OT upnu 000T saIdnu QQ0T Gu 3nu 8300 plepi Dupio3s e WPIA H 3rpua usunp pozd este 1 1np pozdj usy3 nq 03 2 1 ad41 uo 08 03 iz 1 ad 2 31 002 fuump Tsa1d duxoos du ST anp inp uouioo BIA Qj JBJOLAEYUD 1005 Teax 005 Teaj uolsu urp Thu p TPOI 1005 PASUA 905 e8ny10p 005 XIP 1008 393 005 dunaux p jea 1005 wp 005 dwep 1005 adun 005 e1dx 905 outa p T B02 3 0 4 8 p TEGI 3197 wy ipb qsaad exupp puyoe p3033 6043 JIeAU02 GUT JNOJQNE a TI pua umy IT TN EH uquf uezedwodeied a xeuf u puf oezadj mered 202481 eut JNOJGNS KAAL TTT OUT E SPEVEOREEEEVERE EEE SE SESE ED EE TEER SEPESSEEOREEEEEERERUOESESHOEES DOO EHO D pas uan ey ulul xeul 0000T o
22. which was a time consuming task was to follow these directions Plot fit with the log log graph first Plot fit next with the combination log log and derivative graph Check the coherence of the solution with a semi log plot like MDH AUTOMATE or a similar well test program was helpful in finding estimated values of permeability and skin effect before starting with RGF 49 The case studied was the following Flowrate of 10 000 Mcf D for 1 000 hours or 42 days Infinite acting case no external boundary Damaged region of three feet around the wellbore Wellbore radius of 0 333 feet Pay zone of 15 feet Wellbore Depth of 20 000 feet We considered a wellbore volume of 10 000 cubic feet The porosity was 15 the gas gravity 0 9 and the reservoir temperature 375 F The initial reservoir pressure before the start of the flow was 8 000 psia Part of the synthetic field data produced by RGF is presented in table 5 1 AUTOMATE gives the following solution for this test Permeability k 12 mD 3 Total skin 4 4 5 5 A manual plot fit is a time consuming task but experience will allow a user to anticipate how to change permeability and skin effect to affect the position of the plots on the screen of REAL GAS FLOW The fastest way to perform a manual fit is to perform a sensitivity analysis with one parameter at a time permeability first then skin effect then permeability again and so on 50 A SIA EE 80 O 00
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24. 11 1468 Hubbert M Darcy s Law and the Field Equations of Flow of Underground Fluids Trans AIME 1956 207 222 Hurst W Establishment of the Skin Effects and its Impediment to Fluid Flow into a Wellbore Pet Eng Oct 1953 25 B 6 Jenkins R and Aronofsky J S Unsteady Radial Flow of Gas Through Porous Media LAppl Mech ASME June 1953 20 No 2 210 Katz D L and Coats K H Underground Storage of Fluids Ann Harbor Ulrich s Books Inc 1968 Katz D L Cornell D Kobayashi R Poettman F H Vary J A Elenbaas J R and Weinaug C F Handbook of Natural Gas Engineering New York McGraw Hill Book Co Inc 1959 Lee A L Gonzales M H and Eakin B E The Viscosity of Natural Gases J Pet Tech August 1966 997 Matthews C S Analysis of Pressure Buildup and Flow Test Data J Pet Tech Sept 1961 862 Matthews C S and Russell D G Pressure Buildup and Flow Tests in Wells Soc Pet Eng Monograph Series 1967 1 62 Meunier D Kabir C S and Wittmann M J Gas Well Test Analysis Use of Normalized Pressure and Time Functions SPE Formation Evaluation Dec 1987 629 Ramey H J Jr Non Darcy Flow and Wellbore Storage Effects in Pressure Buildup and Drawdown of Gas Wells J Pet Tech Feb 1965 223 Ramey H J Jr Short time Well Test Data Interpretation in Presence of Skin Effect and Wellbore Storage J Pet Tech Ja
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28. C programs FRAN C FRAN H FRAN MAP FRAN L FRAN DLG FRAN RC FRAN DEF FILEMGR C FILEMGR H INPUT H SCOPE H SCOPE DLG in this order 88 UF qur OdH AEJQID IEJNR 3 3uy quy 3u 34313au0 uy xogsn3e3583epdp 3uy 9NOT GNMH au yisnqeqsog 2 poa saxyaezg ide IR O Ze IPYD UINOLIXINIOD 12849 qu suiegdnias Zi J849 Quy 3417118390399 huji squyocquay 3 GNMH SJUTOJKEJQ pyjoa su ods 241 Ja 1N ena 2 Quy JUI IXONPEBU proa eT T4ELEGPEOY Out aNNH 3011 queweTgqnduypeay lana JuUT eTTAJNdu peoy GNMH AoputMeserg Zut ana qul JuowaTJJNdUTeJ IN Y GNNH JUT GTTAJNdUTEJT IM Zut 347 wt INH X0TLIXON 3 erqnop erquop Quy qui JNMH SOTEDSKEJG erqnop 4 1849 JEOTJJEWIOJ POA XxeHj09 pros 830704038919 ZapoMat TA 33E0TJXENA 2QeOTAUTHA LJROTIXPIO SJEOTJUTWA fasnopbo rds sesnondolax 3103 T9QFIXENA Zo ltagetvews oz TeqetuyHa KOZI ieqeTujwX fu SINOU ouj3 aA AeP JOW 0381 ROTA OBISTTEJOJAJEU uZvQI QL RA BINSSEJd opnesd ssajuojsudWiG 08 81 22909411 i sinoy emp3 sa Tsd jinss j4 OBJSTIEJPJAINSSAXG 0W J su luo gusurp sa du ss Tuojsueulq gt O8 sIl1 3 qss luolsu ulq 4 3 I119P 3 e310p AI sa exnesaid opnasda 08 STIEJOGIGUIOH 4 sInoy ewy sa ernesesd opnesd og eT reques ne fs 83104 owg BITep Sa du e310da 08 e1pe39da 190007 s3n0y eur ezpop sa du r31
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30. MAIN FILE This is the filename under which the input parameters will be saved with the addition of the extension MAI Any character can be used except periods or spaces with a maximum of eight characters 3 RATE DATA FILE Requirements are the same as for the main file name The user should give the name of the file they previously created under a DOS editor and saved with an extension FLO Example NAME FLO The rate data file must be saved or copied in the working directory as well as all other relevant input files in order for the simulator to run 27 4 TYPE OF TEST In the future Buildup test or multirate test could be added to REAL GAS FLOW In the present version only drawdown and injection tests can be run The user should therefore write INJECTION or DRAWDOWN getting as many letters in the box as possible A drawdown is defined as a flowing period where at time zero the pressure is constant and identical at all points throughout the reservoir 5 OUTER BOUNDARY Three options exist The program checks only the first two letters of the input but as many letters can be used as will fit in the box Infinite Acting The program checks on IN No Flow The program checks on NO with The condition for the infinite outer boundary is lim m p m p t gt 0 4 1 If a no flow condition is imposed at the outer boundary oan 0 t gt 0 4 2 r 6 BOUNDARY RADIUS If the outer boundary condition is no flow or
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38. of a time pressure file allowing the user to compare field test data with the computed results from a simulation More is presented on this feature in Section 4 4 1 If field data is to be used the data file must be created by the user with an editor under DOS before starting the program As with other data files the field data file should be saved in the working directory with the extension PRS Example NAME PRS In the parameter input window the file name should be provided without the extension If field data will not be used a space blank should be entered in the field box in order to save and leave the input parameter screen 24 AUTOMATE TYPE CURVE Creates user made type curves to be used with the AUTOMATE II Computer Aided Well Test Analysis package It is possible to build a library of type curves in order to match field data or to run a non linear regression The requirements for this field are Enter 0 if the user doesn t want a type curve to be saved from the simulated results Enter 1 for a standard ppp versus tp type curve where the estimated parameters in AUTOMATE will be k the permeability and the porosity Enter 2 for a storage type curve PpD Versus tp Cp where the estimated parameter in AUTOMATE will be k the permeability and C the storage factor 30 More on this utility will be found in Section 4 6 Special Features 4 3 2 Flow Rate File Some conventions must be adopted 1 Time zero is the time at w
39. performed by selecting DIGITIZED TYPE CURVES from the list of available models 4 6 2 2 Creating One Type Curve As presented in section 4 3 1 3 three entries related to a type curve can be made in the main file before a simulation is run 0 if no type curve is desired 1 for a standard ppp versus tp plot 2 for a storage PpD versus tp Cp plot In all cases both the pseudopressure and the derivative curves will be provided If a simulation is run from TEST1 MAI the type curve file will be TEST1 MSG Additionally the curves will be marked by their respective value of CD e42s at their end Cp being defined in Eq 2 16 Again for one type curve only a user does not need to know the content of the type curve file NAME MSG But plotting field data against a unique type curve is 43 definitely not enough to analyze a test fully It nevertheless gives a user a good idea of how the field and the simulated data compare 4 6 2 3 Building a Library of Type Curves This task is more difficult since it requires a user to paste type curve files together Therefore a good knowledge and understanding of the content of these files is required See the AUTOMATE manual The physical task of putting files together is simple and not time consuming It must be done in DOS Figure 4 13 shows a simple library of five type curves The type curve data file for this particular pair of curves is presented in Table 4 3 and should be studied Figu
40. push of a button To get a list of the graphs press on PLOT MENU to get the screen shown in Fig 4 6 The Horner plot and the line source solution are not accessible but have been placed in the menu for future development Log Log Plot Log Log Derivative Plot Cartesian Plot Horner Plot Dimensionless Semi Log Plot Pressure History Plot Line Source Solution Plot Rate History Plot 4 5 1 Plot Menu 1 Miller Dyes Hutchinson Semi log plot of pseudopressure in psia versus time in hours 2 Log log Log log plot of log Amp in psia versus log At in hours 3 Log log derivative Log log plot of Atlog 0mp dAt in psia versus log At in hours 33 For the computed data from the simulator the derivative is a simple forward first degree finite difference calculation with no attention to noise reduction 4 Cartesian Cartesian graph of normalized pseudopressure in psia versus time in hours The normalized pseudopressure for this plot is p Hizi P PAP Po ana uz 4 5 This is an excellent way to express the pseudopressure because a unit of pressure is obtained This expression was introduced by Meunier et al 1987 and is also presented in Horne 1990 5 Horner Not accessible 6 Dimensionless Semi log plot of dimensionless pseudopressure versus dimensionless time tp 106 The dimensionless variables are described by Eqs 2 13 and 2 14 7 Pr ssur history Cartesian plot of pressure in psia versus time i
41. radius ft universal gas constant real skin effect 57 t time hrs T formation temperature R T average wellbore flowing temperature R Ts standard temperature R Tpe pseudocritical temperature R Tr reduced temperature dimensionless TI corrected critical temperature R u macroscopic gas velocity Vwb wellbore volume cu ft z real gas law deviation factor C diffusivity parameter B turbulence parameter md 1 Y specific gas gravity to air Darcy s law correction factor for damaged region radial Darcy s law correction factor v dimensionless logarithm ratio u p pressure dependent gas viscosity cp porosity fraction p p pressure dependent gas density lb cu ft Subscripts 1 damaged around the well D dimensionless e external 58 gas initial distance r from the wellbore center standard condition sandface wellbore 59 References Agarwal R G Al Hussainy R and Ramey H J Jr An Investigation of Wellbore Storage and Skin Effect in Unsteady Liquid Flow I Analytical Treatment Soc Pet Eng J Sept 1970 279 Al Hussainy R Ramey H J Jr and Crawford P B The Flow of Real Gases Through Porous Media L Pet Tech May 1966a 624 Al Hussainy R and Ramey H J Jr Application of Real Gas Flow Theory to Well Testing and Deliverability Forecasting J Pet Tech May 1966b 637 Aronofsky J S
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43. title main file rate data file pe of test outer bounda boundary radius damaged zone radius title of test to run main input file name rate data file name drawdown or injection defines external bounda external radius pay zone thickness well depth thickness relative gravity to air fraction gas impurities fractions letters CO2 H2S psia _ skin damage average in reservoir mD consider or not field data file name of file if applicable Automate type curve create or not code 0 1 or 2 Table 4 2 Summary of Main Input Data File reservoir temperature well head temperature wellbore volume initial reservoir pressure skin factor permeabilit Unit expected e O gt O To fill up a file the mouse must be used to move from one field to another clicking into the box of the field to enter next The order in which the fields are entered is irrelevant Only the title is optional All other fields are required Both lower case and upper case can be used when creating a file as long as the user is consistent For instance both drawdown and DRAWDOWN would be accepted as type of test but Drawdown would be rejected The program uses only oil field units To save a main file that has just been created the user should press the OK button The file will be saved in the active directory again this is the directory shown when clicking on OPEN in the parameter input window or on OUTPUT in the main m
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45. well and so on More on the different files used by REAL GAS FLOW is presented in Section 4 2 3 After having made a backup copy of the disk provided and copied all files and especially RGF EXE and FRANC EXE in the working directory REAL GAS FLOW must be set up into program manager Using the mouse click on WINDOWS SET UP inside the MAIN folder of program manager then click on OPTIONS and select SET UP APPLICATIONS Select the hard disk on which the working directory is located and then run the search by clicking OK This can take a few minutes depending on the number of applications on the disk After the search select RGF EXE on the left window in the dialog box click on ADD and then OK RGF will be added with its recognizable icon as a window application At this point of course it can be moved into any group 15 4 1 3 Starting Up REAL GAS FLOW can be started from the program manager window by double clicking on its icon At this point the main menu will fill the entire screen REAL GAS FLOW can also be started under the DOS environment by going into the working directory and typing the command WIN RGF 4 1 4 A Quick Guide to REAL GAS FLOW Before learning more about the program users will familiarize themselves with REAL GAS FLOW RGF by using a first example The following example files have been provided on the disk GUIDE MAI and GUIDE FLO The following instructions should be followed Start the program Click
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47. 01 0 001 0 0044 79 0012 _ IL 792 0025 793 00 788 0082 788 os 7460 oos mo JA 064 685 14 64 O 35 64 6n 639 824 eto 108 2065 IE 63 _ 35 59 58 j 53 AA a 6 59 E _ 542 AA 2246 5865 Table 5 1 Pressure History for Synthetic Field Data 51 After a significant trial and error period we were able to obtain the following match in Fig 5 1 The data in discrete points is the field data The simulated data a continuous line was obtained by entering into RGF s input parameter window all the information given before in addition to an estimated permeability of 17 mD and a skin of factor of 3 Figure 5 1 Plot Fitting Field Data and Simulated Data by Trial and Error Log Log Plot 52 Even though the log log graph shows the best match after a trial and error period of an hour and a half the semilog plot shows some divergence at late times E Keeser 3 RS POZZO Se Sree pe Ee O A Pseudo pressure vs time hours Figure 5 2 Plot Fitting Field Data and Simulated Data by Trial and Error Semi Log Plot The values that were used in order to create the set of data with RGF in the first place were Permeability 17 5 mD Skin damage 2 8 53 Our trial and error plot fit was within 3 of the correct solution for the permeability and 7 for the skin In this particular case we were persistent enough to get ve
48. 06 51 7y 11 1y A 3 Tpc 187 330yg 71 5y A 4 If the gas contains impurities corrections are made using Wichert and Aziz 1972 e 120 yc0 yu s 120 yco YH s l t s3 yy 5 A 5 Pe ee Pole O A 6 T yH s l yg s e ste A 7 The reduced pressure and temperature are p P A 8 Ppc TR T za A9 r Tp A 9 The reduced density is computed iteratively using Newton s method Then the z factor is estimated using the Dranchuck et al 1974 procedure f p KAL k_ r p 7 A 10 where f pr ap bp cp dp ep3 1 fp2 exp fp2 g A 11 f pr 6ap gt 3bp 2cp d ep2 3 fp2 3 2fp2 exp fp2 A 12 where a 0 06423 b 0 5353T 0 6123 c 0 3151Ty 1 0467 0 5783 T d Tr e 0 6816 T f 0 6845 g 0 27p p 0 27pr T and 0 27pr e A 13 Prlr 65 Gas compressibility is computed from 1 Cg SAKO 5 A 14 I br pepe a x where dz __1 Lac 2bp cp 2ep 1 fp p4 expl fp A 15 Opr Geh d S The viscosity is computed using the Lee et al 1966 procedure which is approximate for sour gases since the density is corrected for impurities K 10 y Hg K exp Xp A 16 where _ 9 4 0 02M T 209 19M T X 3 5 2 40 01M T y 2 4 0 2X p z p The final table concerns the term used to calculate changing wellbore olp z p storage as defined in Eqs 2 9 and 2 16 This task is performed by the s
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71. MICROCOMPUTER SIMULATION OF THE TRANSIENT FLOW OF REAL GAS THROUGH POROUS MEDIA A THESIS SUBMITTED TO THE DEPARTMENT OF PETROLEUM ENGINEERING AND COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF ENGINEER By Francois Joseph Groff June 1992 I certify that I have read this thesis and that in my opinion it is fully adequate in scope and in quality as partial fulfillment for the degree of Engineer He d ey Jr Principal Advisor I certify that I have read this thesis and that in my opinion it is fully adequate in scope and in quality as partial fulfillment for the degree of Engineer soos 4 A IN Hoa Roland N Horne Approved for the University Committee on Graduate Studies KT enen SE Dedicated to My mother Alice My father Robert My friends Genevieve Norman and Adegboyega In some way you all made this work possible Acknowledgments I would like to express my gratitude to Dr Henry Ramey Jr for his suggestions and guidance during this study His profound kindness has made this work possible I also thank Dr Roland Horne for serving on the committee for this thesis I finally extend my gratitude to Jean Cook from the Stanford Geothermal Program and to the Department of Petroleum Engineering at Stanford for their support and encouragement This work was supported by the Stanford Geothermal Program SGP under Department of Energ
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79. RASE button can be used at any moment if the user wishes to clear the screen The top title inside the screen heading reads REAL GAS FLOW when the program is first started This heading will change throughout the use of the program to include the title of a graph when a plot is made and the name of the output file that is being graphed 4 2 3 File Types All files used by REAL GAS FLOW are ASCII files All the files related to the same simulation will have the same name and will differ only by the three digit extension Some files are created by the program while others must be created by a user 19 4 2 3 1 Files Created by a User Let s suppose we are working on a well test design named TEST1 We must create a file TEST1 FLO containing the rate history using an editor The details for all input files will be found in Section 4 3 Setting Up the Data If we wish to compare the computed data from the simulation with field data we must provide the program with a pressure history file named TEST1 PRS 4 2 3 2 Files Created by REAL GAS FLOW The first file that RGF will create is the main parameter input file called by clicking the INPUT button in the main menu bar This parameter file is saved by RGF under TEST1 MAI The most important file containing graphic information from the simulation data produced by the program is TEST1 ACT for all data related to the active well This file is the largest one used by the program and will require on t
80. T SUTI oT Eg rep CAM TT KUTI ESET 9607 3 DOT CYT OMT 3 FATT 0073 DOT 2Z10p SF ATT Swap LOTT OTIS TI Sy 3 Bot t ep 042037 TRay fATT 1837 Teayo NUTT z 142035 TEA Yu TI z uoqq 1 1031 QS OP PEST ET EPO TER ESVEESEE SEES ER EERE Z SEER A AAA evereeveeees BAINO GATIFAJIBD BANGWOD sevevevere PEPE CERES SE AA CES EO ECEREEEEORESE SESE REED EDEEEROEEEEDY 8NnUT JUOJ 1 T uoqq Teaf 7 TEA uoqp T j Ob op WA AA AAA AA AA AA AA LUTTE eesecesvesroevevenvess TRAX OJUJ BAL sS3QAU v v PRESETS ER IZZZA ZI CE A A A A A AA AALT enuy yuos Jipue 11 eu j a2u010 01 je 105 Teal T uoqr uoq usya 1270 39 17 8473 boq 9DuBI07 01 Dot sqe Z 1 U T Polujid Juqodu j OE op pequyad Jurodu ew ye aoueiaj HI ov DE D 87 Appendix D Source Code of C Program for User Interface RGF EXE is a copy of FRAN EXE which is described here FRAN EXE is built by using the NMK command under Windows SDK The maintenance file called FRAN contains the following instructions all fran exe fran res fran rc fran h filemgr h input h scope h re r fran rc fran obj fran c fran h filemgr h input h scope h cl c AM Gsw Od Zipe W3 fran c filemgr obj filemgr c fran h filemgr h input h scope h cl c AM Gsw Od Zipe W3 filemgr c fran exe fran obj filemgr obj fran def link fran 1 re K fran res fran exe fran res re fran res This appendix presents the source code of the following
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89. c THW GWG W ARG TWA ALTEA W AWO Td ANG S3 W 41130 W AHD VLIL 1 N CSL 4 IW Le V131 7 TR V R VNVS T THA L13qs V131 S3 N TIA V131 Z THW V UWA ITA Nies 17 LAW V 3IdN3 DE OL 09 NAHL og 35 H 3I TIA IEA IICIN IN IU rr rara rare rro rar CR DYA a WAA AAA AAA EO RHEE EINER EINER rr EVE Tel IZI uwv9 2 CHIL LT NUJLoTWATV 3 OTGJUeWL3L IW 1 TT3G V131 YILIK 1 V Z UBLIWG 2 10 T g 2 d UT ad 12 dtd ya 1 ALTA 42 AWG AWA Z SETAQ e Z AWAWDs VLIL 1 LEI CHUIL OZ 0 1 CH83L OT oz OL 09 GLG S3 1 AM Oe ELO e TdV3TW S4 20039 WLIL 1 4 7 ARG E GWO Z GLT3Q 1 1 dde 2 dna 1 AAt 0e EI y TAWATW Nde Z VLIL I 1 PWBAL JIONI DI 04 OD Nani 0 OS dO GNW T D3 JILSN JI 004 Z Z LAG WEL TW 1 LTSq V131 Z t teg L n T v 81 lt fe Quy 1 old 2 verevseeyasersesv NADO P1QEJ Y S BUFJNOJ NS BLULessss2 3 00011 243189 4 MOOT GeAsta 0007114232 21qe37 uoumoo t0001 100534 0001 qdw 10001 quad 1qe3 UOWNOD d bal baz td zz cos uoyq ung ps eT OUCRFERESELESEOERE SESE EE EE ER EE SEES SEES UEEU EE EE EE REET ES ERED HED SRORERTEESEPERUSOSEUTESESE DERE EPO SESE SESE EERE rr rr rr rr pue EK E tr 2098 pa T T Woeza J1R TI 3 200874 Goxoos KE JuT z sqe lt JIeEdTI Rwy 7 old
90. ch K M Analysis of Short Time Transient Test Data by Type Curve Matching J Pet Tech 1974 793 Eilerts C K Integration of Partial Differential Equation for Transient Linear Flow of Gas Condensate Fluids in Porous Structures Trans AIME 1964 231 291 Eilerts C K Sumner E F and Potts N L Integration of Partial Differential Equation for Transient Linear Flow of Gas Condensate Fluids in Porous Structures Trans AIME 1965 234 141 Firoozabadi A and Katz D L An Analysis of High Velocity Gas Flow Through Porous Media J Pet Tech Feb 1979 211 Fligelman H Drawdown and Interference Test Analysis for Gas Wells with Wellbore Storage Damage and Non Laminar Flow Effects Ph D Dissertation Stanford University California 1981 Fligelman H Cinco Ley H Ramey H J Jr Braester C and Couri F Pressure Drawdown Test Analysis of a Gas Well Application of New Correlations SPE Formation Evaluation Sept 1989 406 Forchheimer P H Wasserbewegung durch Boden z Ver Deutsch Ing 1901 45 1781 61 Hegeman S Hallford D L and Joseph J A Well Test Analysis with Changing Wellbore Storage paper 21829 presented at the SPE Rocky Mountain Regional Meeting Denver CO Apr 15 17 1991 Horne R N lodez ach Petroway Inc Palo Alto 1990 Houpeurt A On the Flow of Gases in Porous Media Revue de l Institut Francais du Petrole 1959 XIV No
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92. directly from RGF to either a postscript file or to a printer is possible and easy Clicking on the PRINT button in the main menu bar will print the content of the plotting box on the screen PRINT doesn t send a hard copy of the screen to the printing device Therefore it does not print the input parameter window that displays main files for instance PRINT sends a graph to the printer the same way the graph was sent to the screen Therefore only the last plotted curve will be printed To print a superposition of curves when comparing field and synthetic data for instance or to print a hard copy of the screen a Windows accessory called CLIPBOARD must be used 4 7 2 Printing with CLIPBOARD The CLIPBOARD utility is embedded into Windows CLIPBOARD does not need to be opened or activated in order to be used as long as it is present in the Windows directory To produce a hard copy of any screen press the PRINTSCREEN button on the keyboard sometime PTSCR The screen is stored into the CLIPBOARD It can be pasted into any of the following programs MS Word Excel or PowerPoint using the EDIT menu At this point it can be sent to a printer 4 8 Leaving REAL GAS FLOW RGF can be exited at any time by double clicking on the upper left square button Two relevant issues when leaving the program are Saving important files and cleaning the working directory 47 All files created by RGF are automatically saved in the working directory After u
93. do this select the output file then select one plot in the PLOT MENU press GRAPH select the second plot in the plot menu and press GRAPH again The screen should display a graph similar to Fig 4 9 001 1E 02 1E 01 1E 00 1E 01 1E 02 1000 Figure 4 9 Typical Graph of Both Log Log and Derivative Plots RGF s ability to superpose plots from different output files is useful in order to compare results in the case of a sensitivity ana ysis An unlimited number of plots can be superposed so as to see the influence of one parameter on well test results If two runs were made with two different skin factors s 2 and s 10 the output files would be SKIN2 ACT and SKIN10 ACT Let s assume we wish to see a log log plot for both files First select skin2 act with the OUTPUT button then select log log plot in the 37 PLOT MENU and click on GRAPH The first plot is now on the screen Using the OUTPUT button again select skin10 act click on GRAPH again and the second plot appears See Fig 4 10 There is no need to go to PLOT MENU since RGF kept in memory that the last selection was LOG LOG This can be done repeatedly if more than two plots are desired Superposing plots for comparison is meaningful only if the scales are the same This is almost always the case when a sensitivity analysis is performed On the other hand two very different well tests would not be comparable because the plot scales could be different Real Gas Flow Log Lag D
94. e test we intend designing Clicking on the INPUT button provides a window or dialog box where the 17 characteristics of the well and the reservoir the gas properties and the flow considered must be defined At this point we can decide if we wish to compare field data with the computed data produced by the program and also whether computed results should be stored as a future custom type curve for the AUTOMATE well test interpretation software Instead of inputting a new set of parameters from scratch an old test can be called and opened This can be done to verify parameters from old tests or to modify a parameter from a previously run test design in order to perform a sensitivity analysis Once the list of input parameters is filled it can be automatically saved by simply clicking on an OK button Furthermore a control device reminds one that we cannot move on and save the input file if a critical parameter has been accidentally omitted The second task is to run the simulator by clicking on the RUN button in the main menu bar Windows 3 0 will open a DOS window and perform the calculations Run time will vary from computer to computer depending on the processor During computation a message is displayed in the DOS window giving information on the status of the simulation The simulator also prepares field data files if any so they can be displayed on the screen and compared with computed data Finally the simulator will save the r
95. e the same in order to run a simulation If some parameters have been omitted intentionally or accidentally pressing OK will produce an error message CANCEL Closes the parameter input window without saving any file and goes back to the main menu bar 4 3 1 1 Opening an Old Main File A main file can be opened in order to be displayed for changes or to run a simulation A user can display any main file on the template on the screen by clicking OPEN in the parameter input window The new OPEN window will display all files in the active directory To limit the list to the main files only the user can type mai in the text box instead of and then click on OPEN or by hitting the ENTER or RETURN key on the keyboard Only mai files will be displayed in the list box If there are more choices than can fit the list box scroll bars are provided so that the mouse can be used to move up and down the list Changing the active directory will show a weakness of the Windows environment the user must possess a slight knowledge of the DOS environment One alternative to Change Directory is to type the entire path for the new directory inside the text box For example if the present active directory is as in Fig 4 3 D we francois newtest mai a user can type in the text box D we john doe mai to have access to this set of files SE Main file E EE Initial SE Rate data file Open File Name Outer boundary Boundary Files in d we
96. ee T a p z p Zar ho Dimensionless distance r Ip Tw Dimensionless diffusivity _ H p cg P P W g pi 2 13 2 14 2 15 2 16 2 17 2 18 2 7 Resulting Equations After substitution and rearrangement the various flow equations and conditions are In the undamaged zone 13 dm p tp k dm rp tp 10 p Qp Mp Ip tp SS orp Se ec In the damaged zone 1 d dom Tp t k AM p pt Las SE Mp tp tp ER p Initial condition mp rp 0 0 At the interface between damaged and undamaged zones Siki a ep ADD 10 2 19 2 20 2 21 2 22 The inner boundary condition is a p z p o p z p _ d mp tp kifo ampGp tp _ A pl Zeil Cp a L m i Ce Bee 2 23 o p z p The outer boundary conditions are For the infinite acting case lim Mp 1p tp Mp tp 0 2 24 For the no flow condition omp Top tp 0 2 25 D 2 8 Comments on the Finite Difference Simulation The equations described were transformed into a finite difference form by Fligelman 1981 Although a time weighting factor can be used with simulation all runs are made with a fully implicit scheme The simulation runs with a dynamic time step In order to study early time flow accurately without wasting computing time after the transient period the incremental time step is always taken as 10 of the lowest time value inside a log cycle Another i
97. enu bar We cannot overemphasize the point that in order to run the simulation the main file must be in the working directory The working directory is the directory that contains RGF EXE Saving a main file will add the extension MAI to whatever was entered in the main file field If the user wishes to call a test TEST123 RGF will automatically save the main file as TEST123 MAI If a file TEST123 MAI already exists in the directory RGF will write over it If the user presses CANCEL instead of OK the parameter input window will disappear and all parameters currently entered will be erased from the screen without being saved Also RGF cannot be minimized upper right arrow on window applications while the parameter input window is on the screen Finally we should be aware that under the Windows configuration all characters do not require the same space on the screen For instance an m will require more than three times the space of an i On the average eight characters should fit in each field box but a box that can accept fourteen i characters will accept only four m or seven a characters When choosing names for the different data files remember that DOS requires that spaces or periods are excluded as characters 4 3 1 3 Detailed Description of Each Field 1 TITLE This field is optional and can contain any type of character It is useful to a user in order to remember specific runs dates or well locations 2
98. epth ft 10000 i Nu Thickness ft see Porosity fr A Prodjobs distance ft ee SE SE Figure 4 4 Example of File for Sensitivity Analysis with k 10mD Title Sensitivityanalysis Main file Gas gravity 9 DE lal Rate data flle H25 ffr o Skin factor Type ot test mee nh ermeability mD Outer boundary N2 fr o tot fyin radius ft Temperature F Well radius ft bar Field data file E Well depth ftg ooon Paez fogg oe care bin Jo volume Porosity fr 1 Prodjobs distance ft EO RE EE ERE TEES ze 2222 NME ZE end Example of File for Sensitivity Analysis with k 100mD z Figure 4 5 Once an old file is displayed inside the parameter input window clicking on OK will save the displayed file in the active directory and if and only if the active directory is also the working directory that contains RGF will the simulator be able to run This is an area where caution is required because distraction can lead to running the simulator with an unwanted input file 4 3 1 2 Creating a New Main File In order to run a new simulation a main file must be created The well test can be designed by trial and error and RGF permits one to perform sensitivity analysis in an easy fashion Table 4 2 is a practical summary of the 24 fields required to complete the file 25 Name of Field Meaning
99. erivative Plot Output file demo aaa time hours 001 0102 1 01 1E 00 10 01 10002 1000 Figure 4 10 Superposition of Log Log Plots From Two Different Output Files 4 5 2 3 Using the Cursor Utility Once a plot is on the screen clicking once with the mouse anywhere inside of the plot area will draw a cursor Whenever the mouse is clicked the cursor will reposition itself at the very tip of the arrow Holding the left button of the mouse down the cursor can be dragged on the screen 38 As soon as the cursor appears on the screen the x and y coordinates of the intersection between the cursor and the plotted curve are printed on the upper right side of the screen For example on Fig 4 11 the cursor shows the maximum of the derivative curve at delta mp 30 03 psia2 cp and time 0 23 hours 2 55 Real Gas Flow Lag Log Derivative Plot Output file demo aaa RSE 9 Cur X 0 238881 Delta mp vs delta time hours Cur Y 30 0331 Figure 4 11 Using the Cursor Utility to Pick Points on a Graph This cursor allows a user to compute the slopes of straight lines in a rapid fashion When more than one curve is plotted at the same time the cursor will show coordinates relevant to the last curve plotted on the screen It is therefore important to remember which one that was 39 4 6 Special Features This section describes two features available with RGF First the procedure to compare field data and com
100. ess wal Rate data gie ment Skin factor _ Initial Type of test ees mas permeability mD Outer boundary N2 fi _ Turbulence yin Boundary California or BEE Perm f PJ yn radius ft condensate gas Damaged zone Reservoir I radius ft Temperature F Own perm file Well radius fg __ Wellhead Flelddatame Well depth ft ees Kate avons ss EES curve bin eweg Thickness ft eege volume Porosity fr EG Prodjobs distance ft Figure 4 2 Input Parameter Window to Create and Display Main Input Files There are 24 parameters that should be considered plus a title that is optional There are three action buttons in the dialog box OK CANCEL and OPEN 21 OPEN Opens a second dialog box displaying the content of a selected directory This directory will be refered to as the active directory Selecting a main file with the extension MAI in this second window will display it in the parameter input window OK Accepts the parameter presently displayed in the dialog box as input data for the next run of the simulator These parameters could be freshly entered or could come from an old file with the use of the OPEN button OK will validate the display and make the dialog box disappear The parameter file will be saved automatically in memory inside the active directory OK will save all files in the active directory Therefore the active directory and the working directory should b
101. esults in a custom type curve for AUTOMATE if required and additional messages will appear on the screen for this purpose The next logical step is to view the result of the simulation Clicking OUTPUT in the main menu Bar gives access through a dialog box to the content of any directory on the hard disk or any floppy disk An output file from the last simulation or any old simulation can be loaded by selecting the desired file in the appropriate directory and clicking OPEN in the dialog box A set of messages informs us that the computer is loading the file and when this task is completed By clicking PLOT MENU on the main menu bar we have a choice of different plots ranging from a simple rate history plot to straight line analysis or log log plots Graphs can be plotted on the screen superposed or erased by using the two remaining buttons in the main menu bar 18 4 2 2 Main Menu Bar The use of the six main buttons on top of the screen when the program is started was explained briefly in the previous chapter A quick summary follows INPUT Calls a dialog box that allows one to design a new well test or call an old one RUN Run the FORTRAN simulator in a DOS window OUTPUT Allows user to select output files in any direction in order to create graphs on the screen PLOT MENU Present a list of nine different graphs GRAPH Execute the plotting of data on the screen ERASE Clears the screen leaving only the main menu Bar The E
102. francois newtest deg ft J amaged zone SB S n radius ft erm file Well radius ft data file ve Thickness ft Porosity fr Prodjobs distance ft 8 Figure 4 3 OPEN Window to Access Files on Disks An alternative is to type in the text box D N mai and use the mouse to select the successive subdirectories by double clicking on them Once a user is in the desired directory the quickest way to select a file is to double click on its name Old main files can be used to run the simulator if old result files have been lost or erased However the most useful aspect of displaying old main files is to be able to perform sensitivity analysis This can be done by displaying an old main file changing one input parameter permeability for instance and saving the new input file under a name that is slightly different from the previous one Figures 4 4 and 4 5 show two main files using the same rate data file The two files differ only by the value of permeability 10 and 100 and by their name 23 Ge Parameter Input Title Sensitivity analysis Rate data file masia Skin factor 3 peon fame CR nitt Outer boundary N2 9 0 Turbulence yin yes Boundary California or _ 2 5 radius ft o condensate gas Perm 1 P yin amaged zone Reservolr R radius ft Boz Temperature F 255 m perm file ege Well radius ft Wellhead Field data file EZ Temperature F Well d
103. g Log Derivative Plot Output file demo act 30 001 1E 02 1E 01 1E 00 1E 01 1E 02 1000 Figure 4 12 Superposition of Field and Synthetic Data 4 6 2 Creating Type Curves The following procedure is based on the use of the AUTOMATE Well Test Analysis package but similar software that uses user installable type curves could have been used A useful complement to this section is the AUTOMATE II user manual any version and especially Appendix D User installed type curves 42 4 6 2 1 Background AUTOMATE allows a user to enter their own type curves for plotting and or matching To do so the type curve must be digitized in a standard format file This is the task that Real Gas Flow will perform The name of this file must be included in the message file DIGITIZE MSG that is inside the AUTOMATE working directory Modifying DIGITIZE MSG can be achieved under DOS with any editor The format for the type curve input data file must be rigorously observed This requires no action by the user since RGF will write the entire file The correct format is nevertheless presented in detail in the AUTOMATE manual in case the user decides to make custom changes In addition to the digitized type curve AUTOMATE requires a minimum of 12 parameters related to the scales and legends of the plots To use the installed type curves CUSTOM CURVES must be selected inside the AUTOMATE menu followed by DIGITIZED TYPE CURVES An automated match can also be
104. ge in wellbore storage Hegeman et al 1991 presented an analytical model in Laplace space representing increasing or decreasing wellbore storage during well testing for a variety of well reservoir models They investigated exponential and error function time dependence to represent changing wellbore storage and considered buildup tests to demonstrate utility of their results We consider details of Fligelman s 1981 model in the next section 2 Mathematical Model A schematic of a radial flow model is shown in Fig 2 1 Wellbore Sealed upper Boundary z ircular Damaged sa RE rior Zone Boundary Sealed lower Boundary Figure 2 1 Radial Flow Model The assumptions made by Fligelman 1981 were 1 Horizontal radial flow no gravity effects 2 Isotropic rock properties 3 Gas saturation at 100 of pore volume 4 Isothermal flow 5 Constant porosity value 6 Newtonian fluid behavior 7 No Klinkenberg effect 2 1 Turbulence Effect High velocity non Darcy effects were represented by the Forchheimer equation transformed into a modified Darcy s law form by Swift and Kiel 1962 k op 2 1 u p or Hr 6 is a radial Darcy s law correction factor that is equal to unity for laminar flow and less than unity for turbulent flow EE 8 1 Bp p urk u p 2 2 B is the Katz et al 1959 1968 turbulence parameter e23 83 B DE 2 3 In the computer program the
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108. he average 10 to 20 Kbytes of memory depending on the duration of the test Finally if a file TEST1 PRS was provided by a user in order to compare computed and field data a new file TEST1 FLD will be created by RGF containing graphic information related to the field data Also if RGF is asked to generate a custom type curve to be used with AUTOMATE a file TEST1 MSG will be created containing the type curve as well as other relevant information At all times when RGF is used an internal file INPUT FIL requiring 10 bytes of memory will appear on the working directory This file is very small and can be ignored or deleted by a user because it will be recreated as needed by the program For each test design there will be between four and eight files on the working directory depending on the different options selected 20 4 3 Setting Up the Data In order to create the rate history file a user will require an editor under DOS that saves data in ascii format The same goes for the field pressure history file if needed The main data file TEST1 MAD presented in detail in the next chapter does not require the use of an editor since it is created by RGF 4 3 1 Main Data File After starting REAL GAS FLOW a user should press the INPUT button in the main menu bar This action produces a dialog box on the screen with the heading Parameter Input as in Fig 4 2 ep RealGasFlow Es Parameter input Main file se Gas gravity res pr
109. hich the well starts flowing 2 All time data are in hours The flow rates will be in Mcf D It is mandatory to have a flow rate data point at time zero since we need to specify at what time the well started to flow A typical flow rate data file for a constant rate drawdown test is 0 0 5000 500 end This means that the well flows at 5000 Mcf D from time zero for 500 hours If the user is familiar with AUTOMATE the same drawdown on AUTOMATE would have a rate data file like 0 0 5000 RGF requires one more line in order to tell the simulator when to stop This means that any rate data file already created for AUTOMATE can be used by adding a second line containing a time and end or stop instead of a rate Notice the free format for the data file The data can appear in any column in any format provided that there are only two numbers a time and a flow rate on each line It is important to provide RGF with a final line that specifies when to stop computing To find an easier way to modify data files under Windows without having to go back to the DOS environment please refer to Section 4 9 Computing Aides 31 4 4 Running the Simulation Clicking on RUN in the main menu bar will run the simulator The main issue is what case is being run A second point concerns the various messages on the screen during the simulation 4 4 1 Running the Right Case There should be no uncertainty as long as the user gives special attention t
110. ht 0000 97 000001 0009 8 0009 9 0007 e 0009 0000 2 0006 9 0084 9 0029 0 009b 0 000E 0 00910 ss AA qda WAA ajj SUH TOS wosg easay eddy 45 lt line 1 to 12 gt lt line 13 to n 13 gt lt next lines gt lt next n lines gt lt last lines gt Under DOS a short program is required to read the data points from each individual type curve file and to rewrite them as in the AUTOMATE manual All other 12 parameters Data points for the curves tp PpDl ppD2 etc All curves must have the same number of points and share the same time values Parameters related to the curve labels Data point for the derivative curves They must have the same number of points as the PpD Curves Parameters related to derivative curve labels parameters were edited manually when needed Going into AUTOMATE field data can be plotted with the library of type curves by performing a manual match with the type curve command after selecting digitized type curves A nonlinear regression can also be run with any library of type curves using the automatch function of AUTOMATE The result can be displayed with the function plot match 4 7 Printing There are two ways to print from RGF It is possible to print a graph of the data using the PRINT button provided by RGF or a hard copy of the entire screen can be made at any time using the CLIPBOARD utility of Windows 4 7 1 Printing Directly Printing
111. ic memory requirements for REAL GAS FLOW as long as Windows is installed REAL GAS FLOW can also be run from a floppy disk drive but this practice is not recommended because of disk access time 4 1 2 Setting Up REAL GAS FLOW is provided on a disk with a group of example files The executable files are RGF EXE and FRANC EXE All other files on the disk are not required to run the program but are provided to give the user a better understanding of the program by looking at old synthetic gas well tests RGF EXE and FRANC EXE must be copied into the working directory and remain there at all times To avoid building huge directories it is recommended that sub directories be created with old tests Old synthetic data can be retrieved and processed by REAL GAS FLOW independently of their location on the hard disk or any floppy disk To install the program and the examples in a directory called RGF 1 Insert the RGF floppy disk in drive A 2 Go into the disk or directory where RGF is to be created 3 Type mkdir RGF 4 Type cd RGF 5 Type copy A Files for REAL GAS FLOW have been named in a way that makes it easy for a user to organize the working directory When we design a new well test a name for the test must be defined for example EXAMPLE All data files related to the test EXAMPLE will differ only by their three character extensions EXAMPLE FLR is the flow rate history file EXAMPLE ACT is the pressure history file at the active
112. iles and can cancel the search by pressing CANCEL with the mouse 35 Pressing OPEN after having selected an output file with the mouse will load the data into the graphics subroutine and will trigger two messages that require the approval of the user by clicking on OK with the mouse The two messages are About to read amp convert data points This may require a few seconds to process and Completed reading of output file The screen will then go back to the initial main menu bar RGF is now ready to graph results IMPORTANT INPUT and OUTPUT show the same active directory If output files are selected in a directory different from the working directory the user should make certain that the next time a main file is created it is saved in the working directory 4 5 2 2 Plotting the Data Once an output file has been selected select a specific plot by clicking on the plot menu and clicking on the GRAPH button as in Fig 4 8 The ERASE key erases everything on the screen except the main menu bar It can be used to view different graphs in sequence It is also possible to superpose two or more graphs on the same screen Real Gas Flow Log Log Plot Output file take JAA 1E 02 1E 01 001 1E 02 1E 01 1E 00 1E 01 1E 02 1000 Figure 4 8 Typical Log Log Plot with REAL GAS FLOW 36 Since different plots have different scales only the log log plot and the log log derivative plot are meaningful to display together To
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114. mportant point is the selection of the radial space coordinates In order to cover the entire reservoir while focusing on the near well effects a logarithmic scale was used with the following transformation ya BD 2 26 Intep At early time the outer reservoir radius is very small When the pseudopressure at the outer limit is affected by production v is doubled which means that the external radius is squared This provides a large number of points near the wellbore where pressure gradients are large and fewer mesh points further from the well We consider programming in the next section 12 3 Programming Language and Development Features The code was developed on a personal computer The numerical model written in FORTRAN reads the input parameters computes the gas properties solves the gas flow equations and computes the results in a pixel format ready to be graphed The interface program that manages the screen and the windows with the use of the mouse and graphic tools such as push on buttons and pull down menus is written in C language and compiled with the Windows software development kit This program performs the acquisition of the main input parameters calls the FORTRAN simulator through a shell command opens and reads ASCII files containing the results of the simulation plots graphs on the screen and sends plots to the printer The choice of FORTRAN was straightforward because Fligelman s 1981 program used by Cou
115. n 1970 97 Russell D C Goodrich J H Perry G E and Bruskotter J F Methods for Predicting Gas Well Performance Trans AIME 1966 237 99 Smith R V Unsteady State Gas Flow into Gas Wells Trans AIME 1961 222 1151 SPE reprint Bth Een SCH Swift G W and Kiel O G The Prediction of Performance Including the Effect of Non Darcy Flow Trans AIME 1962 225 791 Tek M R Coats K H and Katz D L The Effect of Turbulence on the Flow of Natural Gases Through Porous Reservoirs Trans AIME 1962 225 799 Van Everdingen A F The Skin Effect and its Influence on the Productive Capacity of a Well Trans AIME 1953 198 171 Van Everdingen A F and Hurst W The Application of the Laplace Transformation to Flow Problems in Reservoir Problems Trans AIME 1949 186 305 Wattenbarger R A Effects of Turbulence Wellbore Damage Wellbore Storage and Vertical Fractures on Gas Well Testing Ph D Dissertation Stanford University Stanford California 1967 Wichert E and Aziz K Calculating Z s for Sour Gases Hydrocarbon Processing May 1972 51 63 Appendix A Computation of Gas Properties The pseudocritical pressure Ppc in psia and temperature Tpc in degrees Rankine are determined from the gas gravity using the Standing correlations For California gases ppc 677 15yg 37 572 A 1 Tpc 168 325g 12 5yg A 2 For Condensate gases ppc 7
116. n additional term to Darcy s law to include the increased pressure drop According to Hubbert 1956 and Houpert 1959 what is referred to as a non Darcy component does not correspond to the classical ideas of turbulent flow but is caused by convective accelerations of fluid particles in passing through the pore space Most experiments indicate that true turbulence occurs at Reynolds number values at least one order of magnitude higher than the Reynolds number values at which deviation from Darcy s law for laminar flow is observed All experiments have confirmed the general applicability of the Forchheimer type of flow equation Turbulence factors for the Forchheimer expression were determined by Cornell and Katz 1953 Katz and Coats 1968 presented a correlation of the turbulence coefficient as a function of permeability for the consolidated sandstones dolomites and limestones Additional experiments by Firoozabadi and Katz 1979 showed differences in slopes between correlations for consolidated media and unconsolidated media 1 3 Wellbore Storage The effect of wellbore storage was considered by Van Everdingen and Hurst 1949 and termed the annulus unloading effect It was further investigated by Ramey 1965 1970 Agarwal et al 1970 presented a storage and skin type curve Others presented several other type curves thereafter See Earlougher and Kersch 1974 Ramey and Agarwal 1972 presented an analytical solution for a step chan
117. n hours 8 Line source solution Not accessible 9 Rate history Cartesian plot of rate in Mcf Dversus time in hours 4 5 2 Overview Any output file containing results from simulation can be opened to create graphs on the screen The following two sections describe how to open an output file and plot the data on the screen A third section introduces the use of a cursor to pick points on a graph 4 5 2 1 Opening an Output File RGF treats files from the current simulation and those run in the past in the same manner To select a file for plotting go to the main menu bar and press the OUTPUT button An OPEN window similar to that for input files appears on the screen as in Fig 4 7 The pressure response data at the active well for a simulation where the main file was EXAMPLE MAI will be found in the file EXAMPLE ACT RGF created this file in the working directory at the end of a simulation Using the file manager utility of Windows 3 0 a user can move the output files with an extension ACT to different directories or sub directories for storage JE Open File Name Eilesin diwetfrancoisinewtest SER EE Figure 4 7 OPEN Window to Access Output Files Stored on Disks To open a file the procedure is the same as for opening a main file It can be easier to view the available files by typing ACT in the text box instead of The user can move up or down in the tree of directories and change disk drive to search for old f
118. nput Data File Table 4 3 Data File for Library of Type Curves Generated by RGF Table 5 1 Pressure History for Synthetic Field Data page 14 26 45 51 List of Figures Fig 2 1 Radial Flow Model Fig 4 1 Main Structure of REAL GAS FLOW Fig 4 2 Input Parameter Window to Create and Display Main Input Files Fig 4 3 OPEN Window to Access Files on Disks Fig 4 4 Example of File for Sensitivity Analysis with k 10mD Fig 4 5 Example of File for Sensitivity Analysis with k 100mD Fig 4 6 Choice of Available Plots for Viewing Results Fig 4 7 OPEN Window to Access Output Files Stored on Disks Fig 4 8 Typical Log Log Plot with REAL GAS FLOW Fig 4 9 Typical Graph of Both Log Log and Derivative Plots Fig 4 10 Superposition of Log Log Plots from Two Different Output Files Fig 4 11 Using the Cursor Utility to Pick Points on a Graph Fig 4 12 Superposition of Field and Synthetic Data Fig 4 13 Example of Combination of Five Type Curves to Build a Library Fig 5 1 Plot Fitting Field Data and Simulated Data by Trial and Error Log Log Plot Fig 5 2 Plot Fitting Field Data and Simulated Data by Trial and Error Semi Log Plot Fig 5 3 Non Linear Regression Fit of Synthetic Field Data on Generated Type Curves 0 p z p Fig A 1 Wellbore derivative Vs Bottom Hole Pressure for y 0 9 a p z p page 17 21 23 24 25 33 35 36 37 38 39 42 52 53 55 68 1 Introduction This section prese
119. nts the purpose of this study and previous studies The initial objective of early studies was to investigate pressure dependent wellbore storage for high drawdown gas wells The project described in this report is primarily concerned with improving gas well test analysis by providing an interactive graphic driven software usable by all engineers The main goals are to investigate the effects of wellbore storage skin and high velocity flow on real gas transient pressure response during drawdown or injection tests Drawdown tests are performed on gas wells to determine the flow capacity kh of the formation the condition of the wellbore and high velocity flow parameters Eilerts 1964 and Eilerts et al 1965 solved real gas flow for both linear and radial reservoirs with inclusion of real gas properties and turbulence Smith 1961 observed that the skin effect for gas wells often appeared to depend upon flowrate Tek et al 1962 and Swift and Kiel 1962 presented a fundamental basis for this observation high velocity flow could cause a pseudo skin effect in the damaged region near a gas well The language used when describing the mechanism that consumes energy at more than a linear rate with velocity is not consistent in the literature The term used in flow equations generally known as also has been given various names Ramey 1965 and Agarwal et al 1970 defined high velocity flow as non Darcy flow which can be treated as a flow rate de
120. o the next few steps 1 Make sure that the main data file is created and saved in the working directory This is always the case if the active directory and the working directory are identical 2 Be aware that the main file that will feed the simulator is the last one that was OK ed before pressing RUN 3 Make certain that all files required for a specific simulation to run are available in the working directory 4 Double check values and units in the main data file before saving it by pressing OK 4 4 2 During the Simulation MS Windows 3 0 runs the simulator in a DOS window The window will display periodically what fraction of the computation has been completed A simulation ends by informing the user that Everything went fine and that Data are now being stored for graphics If all data files have been set accordingly the only error message that might appear on the screen is to inform the user that with the parameters provided convergence toward a solution is not possible Mistakes made while editing the input data files can end the simulation prematurely In this case the final message will not appear on the screen This is a sign for the user to double check input files beginning with their location in the proper directory Once a simulation is completed the screen returns to the main menu which appears when RGF is first started 32 45 Plotting Results Nine different graphs can be obtained from the results by the
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122. of the effects of changing turbulence factor and changing wellbore storage on gas well tests The program also can be used in order to design well tests It has also been shown that this software can be an interpretation tool by plot fitting real data in a trial and error approach The program will allow a user to work in combination with other software programs that perform non linear regression on type curves Finally this program can be tailored to work on other specific applications such as the problem of adsorption in geothermal engineering Further improvements could also be provided to the software in order to consider a large variety of well tests such as buildup multirate and interference tests 56 Nomenclature Cg ki m p gl Pi Psc Ppn Ppc Pe dsc dsf dwb Ti Te Tw dimensionless wellbore storage gas compressibility psi formation thickness ft formation permeability md damaged annular region permeability md molecular weight 1b mole real gas potential psi2 cp pressure psia average wellbore flowing pressure psia initial formation pressure psia standard pressure psia normalized pseudopressure psia pseudocritical pressure psia corrected critical pressure psia reduced pressure dimensionless gas production rate Mcf D sandface gas flow rate Mcf D wellbore rate Mcf D radial distance from wellbore center ft damaged annular region radius ft external radius ft wellbore
123. on INPUT in the main menu bar Click on OPEN inside of the new window Select GUIDE MAI in the working directory and press OK The main parameter input file is now displayed Click on OK at the bottom of the window Click on RUN in the main menu bar The simulator is now running in a DOS window for a few minutes Click on OUTPUT in the main menu bar Select GUIDE ACT in the working directory Click on OK in both messages on the screen Click on PLOT MENU in the main menu bar Select Log Log plot Click on GRAPH in the main menu bar The results of the simulation are now displayed Click on ERASE in the main menu bar The user should now have a basic understanding of the software capabilities 16 4 2 Overview This section provides an overview of REAL GAS FLOW The methodology followed by the program is presented the main menu bar is introduced and a description of the files used during a simulation is provided 4 2 1 Methodology After starting RGF the main menu bar appears on the screen The process is self explanatory Figure 4 1 shows the arrangement of the major components of REAL GAS FLOW Call old Input Prepare Field data file files Parameters for comparison Create type curve for AUTOMATE Plot and Erase Choice of plots Run Simulation Open Results files for plotting Figure 4 1 Main Structure of REAL GAS FLOW The first task is to input all the parameters which are relevant to th
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126. pendent skin effect Firoozabadi and Katz 1979 argued that the term non Darcy flow was not specifically descriptive The same was said for defining Darcy flow for low velocities and an inertia regime for higher velocities since the inertia effects are always present Firoozabadi and Katz proposed to adopt the term high velocity flow to describe the condition where neglecting Bpv calculates less pressure drop than would occur and velocity coefficient to describe B instead of turbulent factor or inertial coefficient Fligelman et al 1989 adopted the term non Darcy flow effect defined as a pseudo skin Dqsc that is not simply an additional term as are the other skin factor components Although high velocity flow was studied in this paper we will refer to this effect as turbulence for convenience Wellbore storage skin effects and high velocity flow were considered in a numerical solution for transient gas well test analysis for one dimensional flow by Fligelman 1981 This solution is the starting point for this project The effect of high velocity flow near a wellbore can be detrimental to the producing capacity of a gas well The calculation of formation conductivity for cases of high flow rates using conventional semilog graphing yields values which are lower than the true formation conductivity Turbulence effects if not properly identified can be mistaken for formation damage and can lead to serious errors in the interp
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128. puted data is presented The remaining sections introduce the generation of type curves for use with other well test analysis programs such as AUTOMATE 4 6 1 Using Field Data An overview of the process of comparing field data and computed data from a simulation follows A user creates a data file of time and pressure data from field measurements in the working directory This data file will have a name and an extension PRS The name will be listed in the main file RGF will read NAME PRS and convert it into a graphic file NAME FLD ready to be graphed FLD for field It is important to declare the name of the field data file in the main file each time a run is made in order for RGF to check that all data will be plotted with the same scale 4 6 1 1 Setting Up the Field Data A pressure file must be arranged in pairs of numbers one pair per line with time in hours and a pressure in psia Again free format is used We require that the file contains no more than 500 lines in order to limit computing and plotting time A typical part of a file for a drawdown would look like 0 01 4507 0 05 4505 0 1 4490 0 2 4485 0 8 4480 10 4473 10 4460 100 4450 For users familiar with AUTOMATE the same pressure files can be used for both programs However RGF does not require a pressure point at time zero A user should be certain to input an accurate initial pressure value in the main file before the simulation Writing the pressure file it is
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130. re 4 13 Example of Combination of Five Type Curves to Build a Library A type curve file with derivative values has the following structure 44 LEzS O 3z6 0 Lien FER o LX NZ tezs o ects o DON UNI KA Ta Wa 0150 LC LN ierg DN 862670 250 662570 06250 STES O 665 0 Ki toso 12150 etso ISO DON 1166 0 615670 LZ 08 6 0 416570 1oz9 0 12696 988 0 D sen osro t 06911 o8iE i 0916 T DAAT KEN onir osse t 0961 Gidi 02917 UNI LUKA WA o6cb T 6 8L 0 4043 0 US OM LOOS LR 06610 085 PT 015 Pt 0069 yt Sone PT gses o ters o 18 6 0 HG CR HACK 30550 Zeep 1rs 0 erso LXO L NU L kE 9 S6150 LOOK teo s0rs 0 501570 6 ye 0 DO SLIS 0 618570 6956 0 4296 0 995 0 sesso ris o 43160 lees o 226570 b09 0 tere 1953 0 ZEE O 11 0670 Donat 02281 09 07 nogaz KX oto6 z 0s9z 0959 KAN 0 9E b 014 6 DE 08cr E 01963 Gast E oses t voza o GR 9 95 0 tizko OTA CIN 002547 0089 81 ote et 1 00 5 0 09 50 LR 6iZ6 0 80C5 0 secs gets 8 E6 0 fre ses o eats o sses o sasta eses O T9 S O Z teo sres o 6555 0 2850 S6050 Z re o 9165 0 z2s6 0 UN 08550 ON sz9s 0 00950 tbLS O Tres o 946570 bozs 0 0999 0 teos o ovet t osiE t ozivit 0099 T 0686 1 05917 olen Drag 00175 0159 00Z9 E osete Dat E ot l ETA KW Zong o Tees o 1955 0 rzo teez o LAN
131. retation Using a constant wellbore storage model to analyze well test data exhibiting changing storage may lead to large errors in the estimation of the skin damage In the case of a drawdown with storage when plotted on a log log graph of the real gas pseudo pressure versus time a shifting of the conventional graph from one dimensionless wellbore storage constant to a greater value might occur As these cases would involve a high pressure drop of several thousands psi it was believed that changing wellbore storage was responsible for this behavior This led to Fligelman s 1981 mathematical model wherein wellbore storage is treated rigorously In a similar model developed by Wattenbarger 1967 wellbore storage was not treated accurately A modern interactive tool for investigating these important effects was needed The objective of this project was to provide a numerical simulation for the isothermal and horizontal flow of real gas from a well through a homogeneous and isotropic formation on a personal computer under a graphic environment It is assumed that the gas flow in the formation is properly represented by a Forchheimer 1901 type equation The wellbore boundary condition is a specified surface flow rate The exterior boundary condition is either constant pressure no flow across the boundary or infinite acting A major concern was to provide others involved in research activities and students with a software package as easy to
132. ri 1987 was written in FORTRAN for a mainframe computer The C programming language has had a large impact on the computing world in the last seven years It allows programmers to write code for both very simple tasks and very sophisticated applications It allows modular program design with an extensive set of instructions and capabilities Finally many of the programming features of Windows were designed with the C language in mind The choice of Windows was also straightforward since this program has become a standard desktop tool for most corporations Windows is a graphic based multitasking windowing environment that runs under MS DOS Applications written for Windows have a consistent appearance and command structure that makes new Windows programs easy to use In order to write programs for Windows the software development kit provides an abundance of built in subroutines that allow easy implementation of pop up menus scroll bars dialog boxes icons and many other features of a user friendly graphical interface The next section presents a user manual for the program 4 User Manual for REAL GAS FLOW This user manual is arranged in the order of the operations a user is most likely to perform Section 4 1 describes how to initiate the program Section 4 2 presents an overview of REAL GAS FLOW Section 4 3 describes how to arrange the input data Section 4 4 explains how to run the simulation Section 4 5 describes how to plot the result
133. ry close to the solution by the method of trial and error A process to accelerate the fit or confirm it is to bracket the values of s and k build a library of type curves covering this range as presented in Section 4 6 2 and use AUTOMATE to perform a nonlinear regression of the field data onto the type curves For instance for values of skin between 0 and 5 and values of permeability between 10 and 20 AUTOMATE will perform an automatic match as on Fig 5 3 Keeping track of each type curve displayed and knowing its corresponding parameters the best interpolation can be read directly on the screen SIAMA 2dA payessuayH uo LEA PSY 9n tnu S JO IJ uotss 318 3 WUT Ce 311 ao a2 OTxT IPT Ba 0001 00T OT T To To D a H V H T u R OT 00T MOTA SE Teddy WOAIJ GAIN Sd IL 55 6 Conclusions An interactive software program that simulates the flow of real gas through porous media has been prepared It runs under a graphic environment and allows a user to compare sets of data perform sensitivity analysis and display field data The easy access to data and quick display of graphs on the screen should reduce time waste caused by having such a program on a mainframe computer with access via terminal Both the installation and the use of the program are easy A main menu bar controls the major actions Creating input files or plotting data from old well tests is a matter of seconds This program will allow investigation
134. s Section 4 6 presents special features available with the program Finally Section 4 7 presents two alternatives for printing Section 4 8 pinpoints a few details relevant to leaving the application and Section 4 9 introduces two computing aids with Windows 4 1 Installation The hardware configuration is presented and followed by a guide to set up and start the program 4 1 1 Configuration REAL GAS FLOW was designed to run on any IBM PC or compatible with a processor 286 or higher 386 486 16 Mhz or more A math coprocessor 8087 or higher 287 387 is not required but recommended because of the matrix manipulation during the simulation 2 MB of RAM is enough to use the application even though Windows is commonly used with 4 MB Table 4 1 shows simulation time for a drawdown test run on different configurations of computers Run time is sensitive to both processor type and frequency The well was flowed for 1000 hours or 40 days All computers were equipped with math coprocessors 286 6Mhz 386 16Mhz 486 25Mhz Darcy Flow______ amins Lampe mins NonDarcy Flow Il2mins 7mins_ mins Table 4 1 Simulation Time on Various Computers REAL GAS FLOW is a Window application and Windows 3 0 or later is required and so is a mouse All actions during the program execution are triggered by using the left button on the mouse Finally a graphics adapter monitor either color or monochrome is required 14 There is no specif
135. s isothermal The temperature value is used both in the flow equations and to generate the gas properties table 17 WELLHEAD TEMPERATURE As for the reservoir temperature a degree Fahrenheit value is required This parameter is used to compute the temperature gradient in the well The temperature is required to compute wellbore storage 18 WELLBORE VOLUME The wellbore volume between the pay zone and the surface is required in cubic feet This value is used to compute wellbore storage and therefore the inner boundary condition As presented in Eq 2 16 the dimensionless wellbore storage is y 7 p z p LT a p z p BA D 4 3 ki 2nrzh CH 29 19 INITIAL RESERVOIR PRESSURE This is the pressure in psia at any point in the reservoir before the flowing period 20 SKIN FACTOR This value is dimensionless and reflects the formation damage around the well If k is the permeability in the reservoir and k the permeability in the damaged region the skin factor s is defined in Eq 2 5 aig ch fn 4 4 1 Tw 21 PERMEABILITY This is the constant permeability in mD of the homogeneous reservoir 22 TURBULENCE A yes or no answer is required here RGF checks only the first letter and looks for a y or an n in either upper or lower case YES means that turbulence effects will be included by RGF in the Forchheimer equation NO means that the flow will follow Darcy s law 23 FIELD DATA FILE This field asks for the name
136. sing RGF it is recommended to save batches of test results under related names in specific directories or subdirectories Remember that when reusung old tests the main input files as for the flow rate files and field data files must be put back into the working directory Before leaving the working directory one should remove unnecessary old input and output files All files AAA and INPUT FIL which are temporary files for RGF can be removed also 4 9 Computing Aids It is recommended to open a FILE MANAGER window in RGF s background in order to copy files between directories and sub directories This is an easy way to insure that all files needed are in the working directory before running a simulation NOTEPAD one of the Windows accessories can be used as an editor All NOTEPAD files are also text files The objective is to have easy access under Windows to files with the following extension FLO Flow rate files PRS Pressure files for field data MSG Type curve data files in order to edit them To do so a user must start the FILE MANAGER go into the Windows directory and double click on the file win ini A file called NOTEPAD WIN INI will appear In the extensions section the following lines should be inserted flo notepad exe flo msg notepad exe msg prs notepad prs prs If win ini is saved and the computer rebooted any files with the extensions specified will be accessible for editing as text files
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142. ual for REAL GAS FLOW 4 1 Installation 4 1 1 Configuration 4 1 2 Setting Up 4 1 3 Starting Up 4 1 4 A Quick Guide to REAL GAS FLOW 4 2 Overview 4 2 1 Methodology 4 2 2 Main Menu Bar 4 2 3 File Types 4 2 3 1 Files Created by a User 4 2 3 2 Files Created by REAL GAS FLOW 4 3 Setting Up the Data 4 3 1 Main Data File 4 3 1 1 Opening an Old Main File 4 3 1 2 Creating a New Main File 4 3 1 3 Detailed Description of Each Field 4 3 2 Flow Rate File 4 4 Running the Simulation Page Y y ra M ka OO 00 3 zl IN UA no 4 4 1 Running the Right Case 4 4 2 During the Simulation 4 5 Plotting Results 4 5 1 Plot Menu 4 5 2 Overview 4 5 2 1 Opening an Output File 4 5 2 2 Plotting the Data 4 5 2 3 Using the Cursor Utility 4 6 Special Features 4 6 1 Using Field Data 4 6 1 1 Setting Up the Field Data 4 6 1 2 Plotting Field Data 4 6 2 Creating Type Curves 4 6 2 1 Background 4 6 2 2 Creating One Type Curve 4 6 2 3 Building a Library of Type Curves 4 7 Printing 4 7 1 Printing Directly 4 7 2 Printing with CLIPBOARD 4 8 Leaving REAL GAS FLOW 4 9 Computing Aids 5 Using RGF as a Well Test Interpretation Tool 6 Conclusions Nomenclature References Appendix A Computation of Gas Properties Appendix B Flow Chart of Fortran Code Appendix C Source Code of Fortran Program for Flow Simulation Appendix D Source Code of C Program for User Interface List of Tables Table 4 1 Simulation Time on Various Computers Table 4 2 Summary of Main I
143. ubroutine WELLPRO based on the Cullender and Smith 1956 method to compute the static bottom hole pressure using H 0 01875y H a A 17 D where H is the length of the section along which the integration is performed and Pt and P are the wellhead and bottomhole pressure values respectively The total length of the well was divided into three equal sections The right hand side of Eq A 17 was integrated using a third order numerical method Using the top pressure of the lowest section as the bottom pressure of the next section the procedure was repeated until the wellhead was reached An average value of P z was obtained by calculating P z at various depths A range of sandface pressure values at the well from 500 to 9000 psia was chosen and the appropriate values of P z were calculated A spline function was used to cover the entire range of bottom hole pressures from 500 to 9000 psia Figure al p z A 1 shows the behavior of the term fe as a function of the bottom hole pressure p Z p for a wellhead temperature of 75 F a temperature gradient of 20 F per 1000 Ft a gas gravity of 0 9 and three different values of well depth 3000 9000 and 15000 Ft 67 z 6 0 3A 103 mss iq oH wonog s A Cons ARLA nq AOM T V Zu pisd d 0008 0009 O00b 0002 33 000T 4 doS 00 INITAVED TUNLVAIANAL AJUNLVYAdNAL GVAHKTTAM 33 0006 H w w rin o oi vg o o mee kg ki 33 000 H Appendi
144. under FILE MANAGER The next section shows an example of the use of RGF as a tool for well test analysis 48 5 Using RGF as a Well Test Interpretation Tool A major application of the software is to design well tests Another application is to have an interactive tool with which sensitivity analysis can be performed But RGF can also be used as a tool for interpreting field test data especially when software based on traditional models shows poor confidence limits For a high velocity and high pressure drop well test changing wellbore storage changing turbulence coefficient or a combination can cause a poor interpretation Another cause of poor interpretation may result from a poor estimation of the initial pressure in the reservoir before the start of flow In this example an associate created a set of synthetic field data with RGF and submitted a pressure history file a rate data file and some additional data concerning the reservoir and the well completion to an associate the analyst This should simulate the analysis of a field test where permeability and skin would be the unknowns The objective was to determine whether an analyst could find the permeability and skin by plot fitting the synthetic field data and a succession of data simulated by trial and error with the help of RGF to find a satisfactory match REAL GAS FLOW offers a variety of graphs to choose from Experience showed that a satisfactory way to perform the match
145. use as possible in order to produce future results and or design well tests The software can also be used in future studies of other systems as in geothermal engineering for instance Specific goals for the program were to allow a user to compare synthetic well tests with each other compare field data and synthetic data create libraries of type curves from synthetic well tests obtain graphic representation of synthetic data as soon as the simulation is over and finally have easy access to past data 1 1 Previous Work Van Everdingen and Hurst 1949 published analytical solutions to the diffusivity equation for radial systems Many solutions were available as Laplace transform inversion integrals and could not be expressed in term of elementary functions The first ideal gas flow solutions were published by Aronofsky and Jenkins 1952 and Jenkins and Aronofsky 1953 They introduced computer techniques to solve non linear gas flow equations followed by Bruce et al 1953 Cornell and Katz 1953 graphically integrated the differential equation for ideal gases and included the effects of turbulence Van Everdingen 1953 and Hurst 1953 introduced the skin effect later generalized by Wattenbarger 1967 by including a damaged annular region adjacent to the well Smith 1961 studied the effect of flow rate on drawdown testing and Swift and Kiel 1962 and Tek et al 1962 explained Smith s results as due to transient turbulent flow Ramey
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147. velocity u for the Forchheimer equation is calculated through an iterative method k RT k or 28p p i let eent u 2 4 2 2 Formation Damage We assume an annular damaged region around the well with an altered permeability kj and radius rq s E h i Ga ki of course many combinations of rj and kj can provide the same skin effect s 2 3 Initial Condition The initial condition is that the pressure throughout the circular system at time zero is equal to a constant p pi t 0 ry Sr Sr 2 6 Or in term of pseudopressure m p m py t 0 Ty ST STe 2 7 2 4 Inner Boundary Condition We assume a constant surface production rate In this case a material balance on the wellbore leads to dsc dwb dsf 2 8 in which Zo Tev c T_L z p 1 u p 9m p 25 and Toc om p sf ek r 2 10 PeT ar r r 2 5 Outer Boundary Condition The outer boundary is circular The condition for the infinite outer boundary is lim _ m p m p t gt 0 2 11 If a no flow condition is imposed at the outer boundary Sm pl gen 2 12 dr I L 2 6 Dimensionless Quantities The partial differential equation describing flow was transformed into a dimensionless form using Dimensionless time k tp T nF dur lee re Dimensionless pseudo pressure for constant mass rate Iy p m p ie TP R p Dimensionless rate _ dscPscl AD HT m p Dimensionless wellbore storage mE p
148. very important not to leave blank lines at the end of the file as RGF will read them as pairs of zeros When a pressure file has been provided to compare field and computed data a message appears in the DOS window at the end of the simulation telling the user that the field data is being converted in order to be plotted 4 6 1 2 Plotting Field Data All field data files to be plotted will have an extension FLD These files can be handled the same way as the output files from a simulation To select a file go to OUTPUT and make the selection in the working directory Then use PLOT MENU GRAPH and ERASE the same way as for all other files For instance field data and simulated data can be superposed as on Fig 4 12 Unlike simulated data that is graphed in blue as a continuous function field data will be shown in green or red in large points as a discrete function A second difference with the way field data is handled by RGF lies in the computation of the derivative As presented in Horne 1990 in order to reduce the noise in the shape of this derivative only data points that are separated by at least 0 2 of a log cycle are used rather than points that are immediately adjacent The derivative can be written as a ot i lnt i n ti ti k APi j A ln ti jti j t AP Inti ft JAP 4 6 In ti j ti In ti j ti k In ti ti In t t k In ti ti_k ln ti j ti k 41 Int 1nt 20 2 Int Intj_ 20 2 Dest Gas Flow Lo
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150. x B Flow Chart of Fortran Code Start Get name of main file Read input fil Create and Open all files Subroutines gaspro Creation of gas properties tables zfacgt viscosity wellpro Compute initial values in tD 0 NSTEP 0 tD tD dtD New time step iter iter 1 New iteration Calculate Gama coefficient Sub tine G at each point ubroutine Gamaco Calculate Turbulence coef Subroutine Deltc for each blo Set up matrix coeffiecients Subroutine Matcof Solve matrix equation by Thomas Algorythm Subroutine Thomas 69 No No onvergen New iteration eached Yes Yes Storage of Data for plots and type curves is time gt Yes total flowing time 2 No No is outer boundary felt Yes Squaring Re Rw Rearrangement of matrix New log cycle o dimensioless time 2 Yes Set up new time step New time step Dubroutine Setdt New time step 70 No convergence Subroutine Ticartes Tilog Subroutine Trancar Tranlog Set up pressure and time alues into pixel form Subroutine Convert Subroutine Convert Create type curve file 71 Appendix C Source Code of Fortran Program for Flow Simulation 72 apoye gt d D LO 30 3 Y 2URIJ o SL03080 D LLJ 15103080 wezDo1d O JUEIJ SIDILBO 3 0UE1J S3DUNOS 73 S IL D oe 038 109d M
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152. y contract No DE F607 901D12934 and by the Schlumberger Corporation through the Schlumberger Fellowship for Earth Sciences at Stanford This support is gratefully acknowledged iv Abstract An interactive program that lets users study the flow of real gas through porous media under a graphic environment has been presented The program treats high velocity flow accurately so that it is not mistaken for formation damage A rigorous treatment of wellbore storage is also a major departure from traditional well test models A mathematical model written by Fligelman in 1981 is the foundation of this project The program presented here with its graphic capabilities places results at the user s fingertips This program can be used in research activities to perform sensitivity analysis It can also be used as a working tool for well test design or well test interpretation Finally it can be used as an educational tool for all the tasks just mentioned Table of Contents Dedication Acknowledgment Abstract Table of Contents List of Tables List of Figures 1 Introduction 1 1 Previous Work 1 2 Turbulent Flow 1 3 Wellbore Storage 2 Mathematical Model 2 1 Turbulence Effect 2 2 Formation Damage 2 3 Initial Condition 2 4 Inner Boundary Condition 2 5 Outer Boundary Condition 2 6 Dimensionless Quantities 2 7 Resulting Equations 2 8 Comments on the Finite Difference Simulation 3 Programing Language and Development Features 4 User Man

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