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Jonas Eskilsson 2008-08-20

1. Pipe 1 old 82 Pipe 1 new 4 Pipe 2 old Bq Pipe 2 new p amp Pipe 3 old e Pipe 3 new T g 2 a Pipe section Figure 12 Pressure along the pipes for resulting flows in old and new program It deserves to once again be pointed out that in the determination of the actual flow through the pipes during part two of the draining the stagnation enthalpy corresponding to the initial pressure of part one is used As an example this causes the initial flow rate of pipe 2 in RB7 to be merely 26 9 kg s compared to the 31 4 kg s predicted by the new program If the stagnation enthalpy corresponding to the initial pressure of part two is used instead the old program predicts a flow of 32 5 kg s which is much closer to the value of the new program The documents of this facility show that none of the flows above that were calculated with the old program were used when designing the pipe system The tank pressure used in the calculation of the flow through pipe 2 was actually 5 0MPa instead of the known 6 27MPa This mismatch will under predict the flow through the pipe and hence the total draining time in this case also will deviate from the preferred 600 seconds As a reminder it can be pointed out that the time earlier calculated by the new program was 441 seconds The main reason however is still the different use of stagnation enthalpy even if the under predicted flow in pipe 2 also contributes An overview o
2. oe 96 pe L 3 Plug flow Stratified flow Wavy flow Slug flow Figure 3 The different flow patterns for adiabatic flow in horizontal pipes 2 In bubbly flow the gas is moving as isolated bubbles in the liquid and as the fraction of gas increases the result is plug flow with large plugs of air Stratified flow can only truly exist if 10 Jonas Eskilsson Emergency Draining of Recovery Boilers the gas and liquid is moving with the same velocity since the forces between the surfaces then will equal each other In all other cases the forces causes waves on the surface of the liquid small waves in wavy flow and large ones that reach the ceiling in slug flow When the fraction of gas is further increased and the flow velocity is high annular flow will dominate and the liquid only exist in a film along the wall 2 To determine what type of flow that exists in a certain application one can use photographs or use one of the numerous flow regime charts that have been developed over the years The chats predict the type of flow at a certain point depending on the density viscosity and mass flux of gas and liquid Figure 4 shows an example of what a flow regime chart may look like A problem with using a chart is that the result is only true for the point being examined and the flow pattern will in many cases change as the pressure decreases down stream BE vm V773 zs H EH mae Hy mil ioe cope SS ie D NEN NI
3. There is no theoretical literature on how these matters should be treated and approximations for this paper are addressed in Chapter 7 2 2 and Chapter 7 2 3 respectively 4 4 2 Drift Flux Model The drift flux model as the homogenous model relies on calculating properties for a mixture and therefore also requires thermal and mechanical equilibrium Interestingly it allows for the phases to travel at different velocities This is done by introducing a drift velocity which models the relative speed of one phase compared to the other So far this model has unfortunately only shown successful results for bubbly flow and plug flow 5 It will not be further investigated in this report 4 4 3 Separate Flow Model In separated flow the gas and liquid are treated as two separate flows which are not bound by the conditions of thermal equilibrium and equal speed Fewer simplifications can be made and eq 12 eq 14 well models the pressure gradient 6 Unfortunately there are very few analytical models for calculating the frictional part of the pressure gradient there are a few ones existing for bubbly flow but not for the annular flow that might be expected in this application Therefore the calculations of the frictional pressure gradient in all separated models depend on empirical correlations and diagrams most commonly by presenting values of the so called two phase multiplier Using the whole mass flow as either gas or liquid depending on the do
4. An energy balance between the inlet and outlet is used to see what quality would satisfy the energy equation eq 46 which is evaluated with media data corresponding to the calculated outlet pressure As long as this quality is not equal to the exit quality assumed when calculating the pressure the exit quality is increased and the calculation repeated 2 C 2 hy hj 9h 70h ies Eu 9 81 z 2 0 eq 46 h enthalpy of liquid per mass unit hyap enthalpy of vaporization per mass unit c velocity of fluid z height above reference level Index 1 Inlet Index 2 Outlet The output data from one pipe section is used as input to the next Using this approach enough information is available to determine how the pressure varies with the length of a pipe Since the pipe system that is to be evaluated consists of many connected pipes the flow will also be subject to singular pressure drops at the entrance to a new pipe The knowledge of these pressure drops for two phase flows is still limited and needs further investigation 7 This study uses equation 47 which according to tests in Lufkin can be used with acceptable results 13 2 Ap lt zF eq 47 The value of z is dependent on how the pipes are connected and can be estimated from general guidelines of singularities F is the two phase multiplier and defined as F 1 0 V V 1 eq 48 This approach directly determines the pressure after a singularity but to continue the
5. Ein energy entering the system Eout energy leaving the system E change in internal kinetic and potential energy inside the system Since energy can enter and leave a system by heat work or mass flow eq 27 can be written as Q W 9 m0 Q Ws me M e M e eq 28 out Qin Heat transfer to the control volume Qou Heat transfer from the control volume Win Work done on the system Wou Work done by the system Min Mass entering the control volume Mour Mass leaving the control volume in The energy of a entering fluid stream per mass unit o The energy of a leaving fluid stream per mass unit m Mass inside the control volume before n Mass inside the control volume after e Energy per mass unit of fluid inside system before e Energy per mass unit of fluid inside system after The energy of a flowing fluid per mass unit is the sum of its enthalpy h kinetic energy Ke and potential energy Pot 0 h Ke Pot eq 29 The system is stationary and thus its change in kinetic and potential energy is zero The energy inside the system per mass unit e is then only the internal energy u Also no work is done on or by the system and no mass is entering the control volume This reduces eq 28 to 19 Jonas Eskilsson Emergency Draining of Recovery Boilers Q Q Mou a Ke Pot m u mg eq 30 u Internal energy before per unit mass w Internal energy after per unit mass In re
6. Model bn dp eot esee cae Dee eta capa a ae eee 21 3 22 ETICHON PACIOE n etie bee oca alt on dde fet tese ad cele andes aati cede Gendt 23 7 2 0 Determination OF the Quality oon eet tipo decuit cet AS 26 7 2 4 Flow Determination and Pressure Drop eese enne 27 oop Forces at the Pipe Outlets noce aed edge Beh a RN 27 S Results oes tent oc a sae tt eee ea e a a cana oe de et cU c Mc ies 29 Salt Restle Tank usc asctse let ils n 29 5 2 Result Pipe Syste ernn tach aah cutee pe d iquh tede Gaston deco tub cas te put us 30 8 3 Result Combination of Programs eee scavseecsesauncssenedeesscascoessbunacecssndevestsaesnacdevent 31 9 DISCHSSIOlE dapi Soto thea reno e taal due cobe ct ach Rot Godelier aces a eter choad odes 33 9 1 Thoughts Concerning the Validity of the Program eee 33 9 2 Comparison of Model to Old PrOgf almb ssssesssssrrssrrrsrrrsrrrsrrrrrrrrrsrrr enne enne 34 DO LARISA stoppt utpidiemtieiriubis memi cts addu eii aues ut Mi diu a 34 y E834 Nm 36 i AS OM CISION repr 39 Acknowledgements rne meth Tore denen u ecd To d bU tenu me ci Hiat See B NaN SEN 40 Loo Foi Ho Nd CRN a cet cae a te est eL Ded LM E AL M pde ES DATE c OU 41 App ndix 1 lb sut deseos ee iust necne sn Ay eR oed ELA sa en 42 Appendix 2 RB32 o m dod ci E M E 43 Appendix 3 Comparing of Pipe Pressures eee esc ed ei d eria es Sete 44 Appendix 4 Propram D6SliE Hino eedem bu epe
7. calculation the quality at this point must also be known Eq 49 provides the necessary expression 3 1 Qe 0 eq 49 vap 26 Jonas Eskilsson Emergency Draining of Recovery Boilers Since the pressure after the entrance drop is know the enthalpy of the liquid and enthalpy of vaporization is easily evaluated from steam tables The actual enthalpy of the fluid h is calculated by noting that since there are no heat losses from the pipe the decrease in enthalpy along the pipe is the result of increased velocity 13 In equation 50 the actual enthalpy has been replaced by the initial enthalpy the enthalpy of saturated water in the tank minus the kinetic energy of the fluid at this point 1 c o h h M 2 vap h eq 50 In eq 51 the velocity of the fluid has been expressed in terms of quality mass flux and specific volumes of the gas and the liquid This gives animplicit expression for the quality which is recalculated with different values of quality until a satisfactory match is obtained G V 1 V jog p UR ME vap h eq 51 7 2 4 Flow Determination and Pressure Drop The output in terms of pressure and quality from one pipe is used as input to the next This means that for a given mass flow the pressure along the whole pipe system can be determined If liquid is drained from the tank to the atmosphere the resulting flow will be the flow that yield an outlet pressure equal the atmospheric pres
8. constrained by an upper section there is no guarantee that the outlet pressure will equal the critical pressure An example of this is illustrated in table 2 where the pressure along a fictional pipe and the critical pressure is compared Table 2 Ppipe MPa 7 24 7 21 7 18 359 3 24 3 18 1 62 Pcrit MPa 1 19 1 19 1 19 3 37 0 76 0 76 0 76 Pressure along a pipe with a sudden decrease in diameter in the fourth section A mass flow low enough not to fall below the critical pressure in section four it will not reach the critical pressure at the outlet Since it is assumed that the outlet pressure is equal to the critical pressure or Phack if it happens to be higher when determining the force onthe pipe this is important to keep in mind Which section that places the constraint on the flow is indicated by the pressure matrix in the output file If this section is not the last one it is highly recommended to re construct the design of the pipe system Pressure gradients in choked flow are a complicated matter and all calculations in this paper should be doubted when choking occurs The output file for the example above would show the number four in the cell corresponding to the last not valid mass flow indicating that the choking occurred in that section If a larger diameter was chosen the critical pressure would instead occur in the end of the last section and all calculations would be much more reliable While on the subject of critical pressure it is
9. of the cases the error was lower than 8 which must be considered relatively low 8 There is a good chance the error would have been even lower if a better method for determining the friction factor had been used Many different studies for providing values of two phase multipliers for separated flow have been conducted Unfortunately it is difficult to be sure which correlations give the most accurate results Also all correlations for annular flow that have shown decent accuracy are missing algebraic expression and therefore solely rely on diagrams These have to be converted to computer code if they are to be used in this application Bergles 7 expresses the opinion that the Martinelli Nelson correlation seems to be better than the homogenous for low mass velocities G lt 1300kg nrs but in other cases the homogenous model might be a better option One of the shortcomings of Martinelli Nelson is that it does not account for the surface tension between the phases even though at high pressures it could prove to be very important Whalley 5 states The homogenous model can give very satisfactory results for the void fraction and the overall pressure gradient However at low pressures the results can be inaccurate More precisely he recommends the homogenous model as long as the density ratio between the liquid and the gas is lower than ten which corresponds to a pressure above 120bar and the mass flux is above 2000kg n s The correl
10. or Pmot the calculations are terminated Input from Pressure after each pipe section Stagnation enthalpy for the current volume element Pipe data for the section being evaluated Critical pressure for this section Start pressure for each section Start quality for each section Assumed mass flow Output to Pressure after each pipe section Pressure after each section Quality after each section Indication of if critical pressure was reached in this section Quality at P Calculates quality at a given pressure using an energy balance It is used to account for singular pressure drops in a pipe Input from Pipepressure Stagnation enthalpy for the volume element being drained Specific volume for gas and liquid Enthalpy of liquid Enthalpy of vaporisation Mass flux Output to Pipepressure Quality Energy The program Pipepressure uses the Matlab function fzero to find the quality at the end of a step that satisfies the energy equation This file simply contains this expression Mediedata Calculates enthalpy and specific volume for liquid and gas at a given pressure under saturated conditions It uses the subprograms ep1H20 epvH20 eqtH20 vplH20 vpvH20 and vx2 How they interact has not been looked into since the function is a part of the previously used program Mediedata 1s used by pipepressure and endpressurepartl 51 Appendix 5 User Manual Make sure the following has been decided for each p
11. that each volume element would take the same time to drain Figure 11 shows that this is not entirely true but since the losses are small compared to the total energy content the assumption should still be acceptable The calculated forces on the pipe outlets is greatest at the beginning of the draining when the flow is at its peak and since the program uses the mean pressure of the first volume element to estimate the flow used in eq 53 one should expect slightly higher forces than those calculated Tests show that this increase is of the order 0 5 1 9 2 Comparison of Model to Old Program By comparing results to real cases it has been confirmed that the old Matlab program give acceptable results and it would be preferred if results of the new program did not greatly differ from the old ones The draining of the recovery boilers in RB2 and RB7 will serve as examples when the results are compared In RB2 the old program was used to calculate the draining time for an existing boiler with a pipe system in place In RB7 it was instead used to simulate how the pipe system should be constructed in order to complete the first part of the draining in 600 seconds When the old program is used these purposes call for widely different approaches As time is anoutput from the new program it should be much easier to use and both facilities can be handled in the same way In RB2 the time output is the final result In RB7 a pipe system is chosen the total time
12. two phase integral and void fractions estimated by Martinelli and Nelson to a large data bank in Cambridge England He suggested slightly different values of these factors and presented it in tabular form They are not presented here but can be viewed in Convective Boiling and Condensation by Collier Another common way to evaluate the void fraction is by comparing the slip SI and mass fraction Also in this field extensive studies containing large quantities of data have been conducted One of the most accurate is Chisholm s study from 1973 eq 25 which is a simple relationship that provides the least standard deviation of the studies compared It should be noted that the standard deviation still is of the order 25 Once the quality has been determined the void fraction is calculated by using eq 26 7 Sl ofra eq 25 G s ee eq 26 1 0 p q 16 Jonas Eskilsson Emergency Draining of Recovery Boilers 5 Problem Description A program to solve the problem at hand must have access to some general information about the pressure vessel In all calculations the pressure vessel will be considered a tank with unspecified geometry and the parameters that may be used as input are The total volume of the tank The volume of liquid before the draining The volume of liquid after the draining The initial pressure inside the tank In the beginning of the draining process it is necessary to remove liquid more quickly than in th
13. urs Do dass RN gs s r Defend casein las pers annans 48 Appendix 5 User Manila scettr aloe IRIS Ee ues Fel Bokm rket r inte definierat Jonas Eskilsson Emergency Draining of Recovery Boilers Outline of Master Thesis Project Chapter 1 Introduction Presents an introduction of how this project can contribute to the develop ment of safe means for the pulp and paper industry to meet environmental and economic concerns Chapter 2 Background Contains general information about the employer and the assignment Chapter 3 Aim of the Master Thesis Project The aim of this Master Thesis Project is presented Chapter 4 Theory The treatment of two phase flows greatly differs from single phase flows and this chapter gives an introduction of the recovery boiler how two phase flows are categorised and how equations for pressure drops in pipes for two phase flows can be derived Chapter 5 Problem Description Contains detailed information about the actual problem along with a discussion of what simplifications can be justified and special phenomenon that the solution must pay attention to Chapter 6 Strategy Armed with the information from Chapter 5 an algorithm to solve the assignment is suggested Chapter 7 Execution Contains discussions concerning what pressure models can be used and what information still needs to be provided Subjects that need further investigation are presented with an analysis of how the calculations needed f
14. worth mentioning that Bergles 7 suggest the use of a homogenous model instead of the slip model developed by Moody which for practical reasons both the new and old program uses to 33 Jonas Eskilsson Emergency Draining of Recovery Boilers predict the critical pressure According to him the slip model tend to over predict the possible flow before choking occurs The pressure difference between the tank pressure and the pipe outlet will force a certain mass flow through the pipes Since the calculations of pressure gradients are dependant on that the mass flow is known one must assume a flow and check if the correct outlet pressure is reached This means that the calculated pressures along the pipe will only be correct if in fact the mass flow assumed is exactly correct If this is not the case the pressure gradient will not be correctly evaluated which will result in incorrect pressures along the pipe Test runs show that these pressures seem to be extremely sensitive to which mass flow is used and only a mass flow very close to the correct value will yield pressures close to reality Unfortunately calculation speed is a major concern and should the pipe pressures for some reason be needed the parameter flow accurancy in the input file can be decreased This will give better pressure accuracy but also further increase the calculation time Finally it should be noted that in order to estimate the heat losses from the tank an assumption was made
15. 01 7 5114 4 2158 4 5202 4 0268 4 3582 1 7645 1 8612 41 3 41 36 9 6843 9 6843 8 9824 8 9317 8 1581 8 0828 7 95 7 9028 7 5558 7 5487 TATI TAT 7 338 7 3484 4 2667 4 4896 40731 4326 1 7802 1 7421 41 2 40 81 8 6944 8 6944 8 1306 8 2854 8 4033 8 4738 8 0438 8 1364 5 7771 5 9158 4377 4 5413 4 1868 4 3728 1 5784 17 37 368 1 2 3 4 5 Old program calc paper 6 Mold z 37 5 Mnew 35 5 1 2 3 f 5 6 j 7 amp 8 9 10 1 2 RBS pipe2 3 Mold 41 2 4 Knew 40 81 5 amp 7 8 9 amp 10 H 1 2 3 4 5 m rew amp The old flow for this pipe is over predicted because it does mot 7 take inta account that the prilical pressure at ending of section 8 two has been passed If pipe 2 is idend in new program a higher flow might be possible Pressure MPa Pressure MPa RB8 pipe1 Mold z 41 3 Mnew 41 36 RB8 pipeconv Mold 37 0 Mnew 36 80 o ol res Pipe1 RB2 lt Pcrit 3 2421 Flow RB7 pipe 1 Flow RB pipe 2 RB pipe 3 Flow 5 4898 5 4898 5 3883 5 4212 3 1483 3 4083 3 1432 3 1142 1 239 1 189 68 61 05 7 4874 7 4874 7 3819 7 3848 6 9711 6 979 6 8648 6 8846 6 7913 6 8185 6 6282 6 6677 6 4682 6 5223 6 2711 6 3359 5 7957 5 846 5 2456 5 3121 5 1463 5 2225 1 5188 1 5017 39 38 58 7 4874 7 4874 7 36 7 3869 7 176 7 2239 6 9661 7 0183 5 3918 5 5387 406004 4 553 3 2675 3 3984 1 4321 1 3
16. 1 01 Bergles Collier Delhaye Hewitt and Mayinger Two Phase Flow and Heat Transfer in the Power and Process Industries Hemisphere Publishing Corporation New York 1981 Durst Tsiklauri and Afgan TwoPhase momentum heat and masstranfer in chemical process and energy engineering systems McGraw Hill 1979 Cengel and Boles Thermodynamics An Engineering Approach 2 edition McGraw Hill 1994 Crowe Sommerfeld and Tsuji Multiphase Flows with Droplets and Particles CRC Press Boston 1998 Streeter Wylie Bedforg Fluid Mechanics 9 edition McGraw Hill 1998 Hutcherson Henry and Wollersheim Two Phase Vessel Blowdown of an Initially Saturated Liquid Article in Journal of Heat Transfer Vol 105 November 1983 Lufkin Recovery Boiler test runs and calculations 4 Appendix 1 RB7 Appendix 2 RB2 43 Appendix 3 Comparing of Pipe Pressures Pipe 2 RB2 Pstart Pipe 3 RB2 Pipe 3 RB2 RB1 fallpipe T 0 5 4917 5 4917 5 2934 5 3237 5 1623 52111 4 9752 5 046 4 7281 4 55 1 7337 1 7094 36 35 34 3 8516 3 8516 3 6508 3 7469 3 5202 3 6782 3 3489 3 5714 3 1353 3 4208 0 97 1 2054 20 275 4 0082 4 0082 3 986 3 9878 3 914 3 9143 Aaron Cc Oc BON n OOC N 0 C0 CO Oh 4 QN Pipe 2 RB2 Mold 57 Mnew 55 1 Pipe3 RB2 Mold 36 0 Mnew 35 3 7 Pipe 3 RB2 second part Mold 20 0 Mnew 27 5 45 4 LO i 3 bu 1 os o RB1 fallpipe T 0 Mold 9 7 M
17. 706 36 6 35 18 6 605 7 1874 6 4015 7 3111 5 1571 6 036 4 8382 5 711 4 1226 5 2755 4 326 5 1806 3 9114 4 7421 3 7864 4 6163 1 2796 1 6264 14 17 87 Un E b b N OCOANDAKRWN cow Gi R Ne in e WN el RB2 Pipe1 Mold 68 Mnew 261 05 Pressure MPa e N WwW e oO o e N w gt o o RB7 pipe 2 Mold 36 6 Mnew 35 18 Pressure MPa So NS BS hh og C e R o e a The initial pressure dees not equal tank pressure 7 The real flow on old model should be higher 8 8 Pressure MPa Pressure MPa aS N 0 amp Qo C RB7 pipe 1 Mold 39 Mnew 38 58 8 T5 7 9 old 6 5 anew 6 55 5 0 2 4 6 8 10 12 14 RB7 pipe 3 Mold 14 7 Mnew 17 87 o chd i new 2 4 B 8 1D 47 Appendix 4 Program Design The main program consists of ten different files Main first part of drainingprogram Endpressurepart1 Sum_of_pipeflows_part1 Calculate flow Pressure after each pipe section PC2 Pipepressure Quality at P Energy Input data Empty output and Mediedata n addition to these six more files Ep1n2o Epvh2o Eqth20o Vplh2o Vpvh2o and Vx2 are used by Mediedata and Pc2 and are copied from the old program Figure 13 illustrates how the main functions interact with each other Pressure after each pipesection Figure 13 Schematic overview of the program 48 Main first part of drainingprogram This is the con
18. Emergency Rapid Drain System Jonas Eskilsson February 20 2008 Master s Thesis in Energy Technology 30 credits Supervisor at TFE Britt Andersson Examiner Ronny Ostin Umea University Department of TFE Sweden Jonas Eskilsson Emergency Draining of Recovery Boilers Tomningssystem f r Sodapannor Sammanfattning Metso Power r ett v rldsledande f retag med spetskunskap inom konstruktion och service av sodapannor Genom att atervinna kemikalier och generera elektricitet fran restprodukter skapar sodapannan de n dv ndiga f ruts ttningarna for pappersindustrin att m ta de st ndigt kande milj kraven fr n dagens samh lle F r att undvika en explosion m ste pannorna vara utrustade med ett s kerhetssystem som kan tappa av vattnet ur tryckk rlet vid en eventuell olycka Syftet med det h r examensarbetet r att designa ett Matlab program som ber knar t mningstiden och de resulterande krafterna som uppst r f r ett s dant system Det utvecklade programmet anv nder en homogen modell f r att approximera tryckgradienter f r tv fasfl den Andra modeller har unders kts och utv rderats i j mf relse med experimentellt uppm tta trycks nkningar men uppvisar inga f rb ttringar i noggrannhet Resultaten j mf rs med ber kningar fr n ett tidigare anv nt program och uppvisar likheter i bland annat t mningstid f r den f rsta delen av processen Krafterna p r rmynningarna ber knas till cirka 25 st rre n vad tid
19. FEET TT EST Pe N 5 LI 1 S L2 gules Figure 4 Flow regime chart by Scott 1963 2 4 3 Theoretical Deriving of the Pressure Drop in a Pipe By deriving general expressions for the pressure gradient that are valid for all types of flows it is later possible to choose a flow model that fits the situation at hand Different models calls for different simplifications which affect the expressions derived The choice of model mainly depends on the need for accuracy available data and computer power Below the pressure gradient for flow in an inclined pipe is derived by using the law of momentum conversation The type of flow does not affect the resulting equations and stratified flow is used as an example to illustrate the problem 11 Jonas Eskilsson Emergency Draining of Recovery Boilers Figure 5 Momentum and forces for acting on a fluid flowing in an inclined pipe 2 The change of momentum and the force acting on the fluid in the positive x direction can be expressed as M 6M cug dug M 6M Mu du M gu M u eq and SOP 6F F Sup SP gsin 00x eq 2 where index L represents liquid and index G gas 3 Also S cross sectional area m u speed m s M mass kg F force N P pressure Pa g gravitation constant m s density kg m In eq 1 the first two terms represents the momentum leaving the control volume and the last term the momentum entering i
20. Pa 2 85 3 61 5 89 3 09 5 28 Comparison of ending pressure for the new program and documented cases No documented data exist for the second part of RB2 and RB5 If no losses are included in the calculations the predicted end pressures will be slightly higher than those presented here By approximating the losses as discussed in Chapter 7 1 the end pressures seem to well match documented cases The first part of draining the tank in RB7 will be used as an example of how the pressure in the tank varies illustrated in figure 7 The input data used in the analysis are can be found in Appendix 1 Q o 3 o L4 o a 40 Removed liquid m3 Figure 7 Pressure in the tank as a function of removed liquid 29 Jonas Eskilsson Emergency Draining of Recovery Boilers The approach to determine the tank pressure described in Chapter 7 1 also generates data of how much liquid must actually be drained This volume is not equal to the volume shown in figure 7 which rather illustrates the total volume that must be removed as viewed from the initial conditions During the process of emptying the tank the density will change and liquid will evaporate which means that all liquid that must be removed does not have to be drained The mass that must in fact leave the tank through the pipes for each volume element is shown in figure 8 6 Volume element Figure 8 Mass that is to be passed through the draining p
21. a number of factors important to design of draining systems Jonas Eskilsson Emergency Draining of Recovery Boilers Table of Content MAURO VU CEO ase ae Geode ecd seal ees io eds Tessa etum 6 2 BAC cuis EAM 7 2L BRIDIoye Essa Ceca doter nbi ue cites E E a EER A S da atoms Irene 7 PAN NIT 23 1 180 21 ERT eL 7 3 Alm OF the M ster Thesis PIBIeCEu 5 oss oes eae atte oe an sa dixic bue endis Ie ERE 8 PE SENG OLY MERETUR I 9 4 1 The RecOVery BOotllet a editt Ro OPE sned ADI SOS c ied synd deres ske RAR antares 9 4 2 Flow du ide T sissi sr 10 4 3 Theoretical Deriving of the Pressure Drop in a Pipe seen 11 4 4 Models for Pressure Drop ite eee ert p MR RR HARE Sen RR HN HERE e Rn aea Qu Ie eade de eue vae 14 4 4 1 Homogenous Model ssssmessrrssrrssrrrerrressressrerrrrrsrrr e essem eae URS Neh ee sa TN Le Pone Pea ren or 14 4 4 2 Drift Flux Model aei ipeo eerte iced s Used Sueca Lordi eee 15 4 4 3 Separate Flow Model eer ert a ae SN SU RR S ence eda Rx Er Fe Ree de eb ue 15 5 Problem Description 2e eats poeta nas aed tates aad ok a eee tosta ed ees 17 6 SIR irt VANESSA T stoapad T S NS NEN Fel Bokm rket r inte definierat fien DD S 19 7 1 Discharge of the Tank oos au eee epe Fel Bokm rket r inte definierat 7T 2 Pressure Prop tila Pipe Sy5te unen sd des dine rst t ee Be a ads 21 1 2 Clhoosmeg a
22. a product of pressure and area and pressure can be divided into a static and a dynamic part the net force for one pipe can be calculated according to eq 52 11 FSF S P TE auc Frar S eq 52 tot static 27 Jonas Eskilsson Emergency Draining of Recovery Boilers Poack is the back pressure meaning the pressure at the point where the fluid is being drained to often atmospheric and S is the cross section area of the pipe outlet The static pressure is the pressure calculated by the program and a dimension analysis show that the dynamic pressure can be expressed as wu spur POM V dynamic 2 ES 2 2 eq 53 where V is the specific volume of the fluid 28 Jonas Eskilsson Emergency Draining of Recovery Boilers 8 Result 8 1 Result Tank Table 1 show the initial and final pressures in the tank according to documented cases and this model for both part 1 and part 2 of the draining The names represent real facilities containing recovery boilers where the tank pressure after the draining has been evaluated with the old program As previously discussed the losses from the tank have been chosen to produce final pressures similar to documented data Table 1 Part 1 RB1 RB2 RB3 RB4 RB5 RB6 RB7 Pstart MPa 4 02 5 5 5 1 8 28 4 52 4 2 7 5 Pend new MPa 3 25 448 4 12 6 89 3 83 3 71 6 28 Pend doc MPa 3 21 454 4 16 6 9 3 87 3 68 6 31 Part 2 Pstart MPa 3 21 4 12 7 05 3 71 6 28 Pend new MPa 2 79 3 56 5 9 3 09 5 28 Pend doc M
23. ach volume element resulting in a series of pressures during the draining The mean value for each volume element is then used as tank pressure by the other files Input from Main first part of drainingprogram Pressure before the draining of a volume element Liquid volume before draining of a volume element Liquid volume after draining of a volume element Number of volume elements Total volume of tank Output to Main first part of drainingprogram Pressure after draining of a volume element Mass which have left the control volume for each volume element Mass that have been vaporized for each volume element Sum of pipeflows part1 Defines the number of pipes so that its subprograms can be used for both part one and two of the process It calls the function Calculate flow and passes relevant information on to it Input fromMain first part of drainingprogram Average pressure for a volume element O utput tO Main first part of drainingprogram Flow for each pipe 49 Calculate_flow The pipe current design is loaded and the Pressure after each pipe section file is run for different flows until the flow has stabilized itself Forces on the pipe outlets and critical pressures are calculated in send to the excel file for results Input from Sum_of_pipeflows Average pressure for the current volume element Information of which pipe it is Input from Input data xls Design of the pipe system Output
24. ality there is no input of heat to the system but the term will still serve a purpose in this calculation The idea is that if the pressure after the removal of the liquid was known the heat supplied to reach this pressure could be calculated This is possible since the internal energy and enthalpy for gas and liquid can be evaluated from steam tables under saturated conditions One can be sure that in order to keep the pressure constant heat must be added because of the energy needed to convert liquid to steam By carefully decreasing the assumed final pressure and repeatedly doing so until eq 30 shows that no heat needs to be transferred to the system the correct pressure can be estimated The calculations below show how the terms in eq 30 can be evaluated for an assumed end pressure The total mass inside the control volume is the sum of the gas and liquid masses Since the total volume initial and ending liquid volume and the initial and final pressures are known or assumed the masses before and after the draining can be calculated with eq 31 eq 32 The pressures are used to determine specific volume internal energy and enthalpy from steam tables V tot Y V eq 31 iq liq gas M m m eq 32 y v Viig Volume occupied by the fluid V Specific volume of the fluid Veas Volume occupied by the gas V Specific volume of the gas The enthalpy per mass unit for the liquid used in eq 30 will be the average enthalpy
25. aluate the Reynolds number one must know the viscosity of the liquid since Re Gd u eq 43 where p is the viscosity The viscosity is mainly a function of temperature and therefore the temperature in the pipe has been assumed to equal the saturation temperature at the current pressure A regression of tabular values for liquid water has been made and is presented in figure 6 24 Jonas Eskilsson Emergency Draining of Recovery Boilers 0 0003 0 00025 0 0002 0 00015 a E o gt D o o 2 gt 0 0001 0 00005 5 Psat MPa Figure 6 Regression of tabular values for viscosity of liquid water This concludes the task of calculating the parameters needed to evaluate the frictional pressure gradient It is the approach that will be used in this study but in case of future changes an alternative way of approximating the viscosity is outlined below This will affect the value of the friction factor and could prove more correct 3 Frictional Pressure Prop Using a Mean Viscosity The mean viscosity can be used in evaluating Reynolds number and then the friction factor can be calculated as for one phase flow One way to express the viscosity is eq 44 but many other suggestions have been made too 1 0 LL Es eq 44 U M This may present a better method than the one outlined above as it predicts the correct viscosity when the quality is both zero and one There is however no guarantee tha
26. art of the draining process before attempting to use the program Starting pressure Liquid volume before draining Liquid volume after draining Total tank volume Number of pipes used during each part of the draining Back pressure The name including xls and location of the file where the result from each part of the draining should be stored Design of the pipe system to be evaluated including length angle of elevation diameter roughness and singular resistance of each pipe section All of the above parameters are to be specified in the file Input Data xls which must be saved in the same catalogue as the rest of the program files Never change anything but the actual parameter values in this sheet as this might cause the program to read values from the wrong cell Also note that if e g four pipes are used the data for these must be specified as the first four pipes in the input file Data for pipes remaining from an earlier test can remain in the input file as long as the number of pipes used in the current test is specified It is worth to once again point out that changing anything but the numerical values in the input file can cause the program to crash If one of the pipe sections does not have a length but only a singular resistance it is necessary to enter it as a short length i e 0 01m instead of zero This way the singularity will still be accounted for Finally make sure to enter a zero in the Length c
27. ations presented by Lockhart Martinelli Nelson and Thom does not account for the influence of mass flow Experiments by Muscettola in 1963 indicate that all these correlations are mostly valid for mass fluxes of 500 1000kg sm This shortcoming has been addressed by correlations suggested by Baroczy and Friedel 7 The Baroczy correlations unfortunately have drawbacks that will later be discussed The Friedel correlation is one of the most recent models developed and in fact much of the literature used in this study is too old to include this model The prediction of pressure drop by the Friedel correlation seems to give quite good results when compared to experimental data 6 A study by Idsinga 1977 used 3460 experimental steam water pressure losses ranging from 17 to 103 bars with a steam quality from subcooled to superheated It compared 18 existing correlations for determining the pressure drop in two phase flow Overall the homogenous model delivered the most accurate results For the special range of the quality being below 0 6 and the mass flow below 2700 kg m s the Baroczy correlation best modelled the measured 22 Jonas Eskilsson Emergency Draining of Recovery Boilers pressure drop 7 Unfortunately this model relies on diagrams and only has data for the two phase multiplier based on a mass flux of 1356kg m s Therefore it needs extensive interpolation of existing diagrams in order to be of use for other mass flows This is possi
28. ble but would require time consuming work to be done To account for the effect of mass flux Streeter 11 instead suggests the use of the Friedel correlation as earlier mentioned As a final note it is important to highlight the fact that even the best empirical methods for the calculation of two phase pressure gradients give errors of the order of 40 5 Because of the uncertainty of the methods for separated flow outlined above this project will determine pressure gradients from the homo genous model Should this not give reliable result the pressure drop part of the program can be redesigned 7 2 2 Friction Factor To be able to use the homogenous model the friction factor and the change of quality along the pipe must be known First the problem with determining the friction factor will be addressed This may represent the biggest uncertainties of this model and other commercial programs too and time invested in improving this step could be well spent There are numerous ideas presented in this field by among others Whalley Streeter Collier Cengel and Bergles Unfortunately few conclusions have been confirmed even though much focus has been paid to the subject When comparing different models it is important to keep in mind that some authors use the Fanning definition of the friction factor while others use the Darcy definition One is simply a multiple of the other but should the wrong one be used it obviously greatly affects the result T
29. calculated and if this is not close to 600 seconds changes should made to the pipe design 9 2 1 RB2 Test runs using the input data for RB2 specified in Appendix 2 predicts that the initial flow through the pipes will be 61 1kg s 55 1kg s and 35 3kg s respectively The total time is estimated to 334 seconds but it should be kept in mind that the losses in the program are based on the fact that the draining will take 600 seconds The error in the result will therefore be greater the more it deviates from this value The mean flow to empty the pressure vessel in 600 seconds with the use of the old program is calculated to 75kg s When the actual flows through the pipes are calculated and added it 34 Jonas Eskilsson Emergency Draining of Recovery Boilers yields a total initial flow of 161kg s more than twice the recommended flow see results in table 3 Table 3 Actual Calculated tank Known tank pressure Old program flow kg s pressure MPa MPa Pipe 1 initial 68 5 4898 5 5 Pipe 2 initial 57 5 4841 5 5 Pipe 3 initial 36 5 4917 5 5 Shows the initial mass flows through each pipe for RB2 part 1 as calculated by the old program The good matches between the pressure used in the calculations and the known initial tank pressure indicate that the flows are quite accurate The documented calculations for this facility are summarized in table 4 They incorrectly assume that the mass that must be drained is the product of the change in liquid
30. corresponding to the initial and final pressures If a known fraction of steam would exit with the liquid it could easily be accounted for by adjusting the enthalpy according to thermodynamical relations Examinations of test results show that this is seldom the case Lufkin study The amount of mass leaving the system is equal to the total change of mass inside the system m m m eq 33 The total internal energy of the system is the product of internal energy and mass in this case calculated as the sum contributions done by the liquid and the gas mij ju mu t MU eq 34 20 Jonas Eskilsson Emergency Draining of Recovery Boilers The potential energy per unit mass of the exiting fluid is neglected and the kinetic energy is approximated by eq 35 using an exit velocity c of 6m s This value depends on the construction and diameter of the exit hole but tests show that the contributions of kinetic energy to the total exiting energy are as small as 0 1 0 2 percent and further analysis are not needed Ke Ye eq 35 There is no really good way to approximate the heat transfer from the system In reality the losses would depend on the size of the pressure vessel the pressure inside it the surface temperature and its material Since some of these quantities will vary in time it would be a difficult transient problem to solve Instead the following approximations have been made The time t needed to drain each volume element b
31. e end For this reason the draining should be split into two parts where each part can use a different number of draining pipes To decrease the risk of uncontrollable vaporisation and avoid too much thermal stress on the pressure vessel it has been agreed that each part should take about ten minutes to complete In reality the liquid is drained from the downcommers which are subject to some static pressure This means that the fluid may be slightly sub cooled instead of saturated at the pipe entrance but as the pressure will quickly decrease this will be ignored Since a mix of vapour and liquid co exist in the tank it will be assumed that they are in equilibrium and each phase is saturated This makes it possible to use enthalpy internal energy specific volume enthalpy of vaporisation and temperature corresponding to the saturation pressure It must however be kept in mind that liquid will turn into steam as the pressure decreases a phenomena referred to as flashing and since the specific volume of vapour is greater than that of liquid the mixture must accelerate in order to not violate the law of mass conversation According to physical laws the velocity can not exceed the speed of sound and when the flow is limited by this constraint it is commonly referred to as choked flow Choking is definitely a limiting factor in this application and must be taken into account during the calculations When the calculations are finished the program must pr
32. e used to determine the time needed to drain a certain volume element By adding the time for each volume element the total time is calculated Since the number of pipes used during the first part of the draining may not be the same as in the second part the program will be split in two as mentioned in Chapter 5 Each will calculate the time needed to drain the volume specified as input data Changes will have to be made to the pipe system if either one of them greatly differs from ten minutes 18 Jonas Eskilsson Emergency Draining of Recovery Boilers 7 Execution 7 1 Discharge of the Tank When water is drained from the tank the pressure inside it will decrease Since the water is saturated it will immediately start boiling and a certain amount is vaporized This process requires energy and the temperature inside the system will therefore decrease When equilibrium is reached and the system once again is saturated the boiling will stop but the pressure at this point will be lower than the initial one In case of an accident the important thing is to empty the tank of liquid which means that the removed volume can be viewed as the sum of the liquid exiting the tank and the amount turned into steam The end pressure inside the tank canbe calculated using a thermodynamical approach For systems with unsteady flow rates the energy balance over a control volume in this case the tank can be expressed as 9 E E AE eq 27 System
33. ell to the right of the last section this tells the program to stop when the pressure after the last section has been evaluated Should the pressures along the pipes be of interest the parameter flow_accurancy should be decreased to 0 01kg s or less The default value is 0 05kg s which works fine for most applications but it does not calculate the pressures along the pipe very precisely The program is started by choosing the correct directory in Matlab and typing part1 This initiates a calculation process that depending on the computer used will take about an hour to complete The result is stored in the file specified in the input data This file contains one sheet per pipe with the following information Flows tested by the program Indication of if the critical pressure was reached for the flow tried and in that case in which section this occurred Pressure at the end of every pipe section for all valid mass flows Critical pressure in every pipe section for the last valid flow Force at the pipe outlet In addition sheet I includes information for each volume element about Mean pressure in the tank Combined mass that has been drained through the pipes 52 Mass evaporated which thus did not have to be drained Time to drain the volume element Flow through each pipe To start the second part of the draining one must open the input file and change Starting pressure using the end pressure fro
34. elonging to the same part of the draining process is equal The total time for one part is 600 seconds A constant value 800kW for part one and 950kW for part two is chosen for a tank volume of 126m This ensures that the results match documented data of the final pressure and the losses noted during a draining test The losses are weighted in relation to the total volume of the tank This yields eq 36 and eq 37 for the first and second part of the draining respectively 800kW Ly eq 36 Qon TT q 950kW f eq 37 Q ou 126 tot q This provides all properties necessary to evaluate eq 30 As previously discussed the process of assuming a final pressure is repeated until the calculation shows that no heat needs to be added to the system With the method above the final pressure in the tank could easily be calculated That would however not be quite satisfactory Using the average pressure to calculate the flow in the pipe system would cause considerable error Instead the total volume is divided into smaller volume elements For each element a final pressure is assumed and the heat calculation continued until the correct end pressure of this element is reached This pressure serve as input data to the next volume element and the process is complete when the end pressures of all the volume elements have been determined The mean pressure for each element is used as input to the program that calculates the flow through the pipe syst
35. em 7 2 Pressure Prop in a Pipe System 7 2 1 Choosing a Model As the liquid flows along the pipe the pressure will decrease The large pressure difference between the internal pressure in the tank and the outlet pressure combined with the fact that the liquid is close to saturated will quickly initiate intensive boiling and fast vaporisation 21 Jonas Eskilsson Emergency Draining of Recovery Boilers These circumstances imply annular flow and validate the choice for a model fitting this flow 10 Should the drainage be done from the economiser of the recovery boiler instead the liquid will not be saturated and thus the regime where annular flow occur would be shorter It must however still be considered relatively short due to the large total pressure drop and the same model could be used Since the homogenous model uses average quantities of the mixture and depend on thermal equilibrium between the phases it requires that one phase is well dispersed into the other The later ensures that the momentum and energy transfers are quick enough for equilibrium to be established The model is most applicable if no great changes in flow pattern occur along the pipe and thermal non equilibrium would not greatly influence the flow pattern 7 Experiments with flows in high pressure steam tubes by Whitcutt and Chojnowski in 1973 compared measured results to the results predicted by the homogenous model using a single phase friction factor In 95
36. eved by using the inner diameter di and the shear stress at the wall eq 18 The later is a function of the density speed and friction factor f according to eq 19 I 18 d d d 4 t l 2 oA 2u f r puf eq 19 In analogy with the previous derivation of the general pressure gradient eq 17 can now be divided into three components and written in terms of mass flux mass fraction and void fraction 2 AF dP ldF 2fpw 2fG V eq 20 dx J S dx d d dP du aV dP SEGE Red AR ted yy 21 gedood deea E 14 Jonas Eskilsson Emergency Draining of Recovery Boilers dP g sinO SET 2 eq 22 dx idm Y Since the mass fraction of gas and therefore mean specific volume will change along the pipe the pressure drop due to acceleration is quite complicated It is an implicit function and in the expression for the total pressure gradient it must be rearranged to arrive at an explicit expression eq 23 xay dn dP If the properties above are evaluated at a known pressure and considered constant for a short length the pressure gradient for this section can be calculated Multiplying the result with the length considered and subtracting it from the initial pressure will yield the starting pressure for the next section However there are two major problems left to solve for this to be a usable method The friction factor must be calculated The rate of quality change over the section considered must be known
37. f the forces present at the outlet from the pipes is shown in table 6 The values calculated in the old program seem to be about 80 of those predicted by the new Both models have arrived at the same conclusion of how the force should be calculated and hence the differences are due to how the properties used are approximated The far most likely parameter to differ is the specific volume since the programs use different models to calculate it Table 6 RB7 pipe 1 RB7 pipe 2 RB7 pipe 3 Force new program 10 96 10 08 5 06 Force old program 8 54 7 92 3 19 Forces acting on the pipe outlets in RB7 37 Jonas Eskilsson Emergency Draining of Recovery Boilers The relatively greater difference in pipe 3 is because the tank pressure used in the calculation by the old program never reached the known tank pressure of 7 SMPa as was previously illustrated by figure 12 and table 5 38 Jonas Eskilsson Emergency Draining of Recovery Boilers 10 Conclusion By using a homogenous model the program developed can well simulate two phase flow and calculate the pressure drop in a pipe system for saturated and unsaturated water In combination with calculating the pressure inside a pressure vessel as a function of the removed liquid this allows the draining time to be determined The program predicts similar results to the previously used program the main difference being a quicker draining time during the second part of the process As the program presents
38. here are several ways to estimate the friction factor and three of them will be further discussed 1 Constant Value of the Friction Factor This is the simplest and also the most incorrect way to treat the frictional pressure drop It is best used for a first estimate and in that case a value 0 005 for the friction factor in high pressure boilers and annular flow may be used 12 2 Friction Factor Equal to One Phase Flow The frictional pressure gradient can be evaluated using a friction factor corresponding to if the whole flow in the pipe was considered to be one phase One must of course decide if it is appropriate to use liquid or gas as the reference flow the choice most likely depending on the quality of the flow If the whole flow is considered liquid the frictional pressure gradient can be expressed as 2f GV E EYE eq 38 LO dx d l where index LO denotes Liquid overall 11 This equation is derived the same way as eq 20 but uses only the specific volume of the liquid instead of an average value The ratio of the actual pressure gradient to the liquid overall pressure gradient is aP dP _ De IM I IV eq 39 dx jJ dx Jio d d fioV 23 Jonas Eskilsson Emergency Draining of Recovery Boilers By assuming that the friction factor for the two phase flow equals the friction factor for the liquid phase the frictional pressure drop can be written dx V dx Jio Using this approach the first ter
39. hipped biomass used in the pulp production is cooked in a boiler To separate lignin and hemi cellulose from cellulose and also recover important chemicals the pulp is passed through a washer Afterwards the washing fluid contains chemicals and waste which after it has been steam dried to 65 80 dry substance is burned in the recovery boiler Figure 1 shows a general flow sheet for a pulp mill and how the recovery boiler is integrated in the fibre line Cooking amp Delignification leaching Recovery Nem Boiler Tu Power boiler Effluent treatment White liquor filter reen liquor filter Figure 1 Flow sheet for a pulp mill Metso slideshow By burning the organic waste and utilizing the heating value steam for the drying process is provided The excess steam is expanded in a turbine in order to produce electricity During the combustion sodium carbonate Na2CO3 and due to less oxygen than needed for complete combustion sodium sulphide Na25S is formed Because of the high temperature in the combustion chamber these compounds melts and are passed through the burning bed to the dissolving tank The use of burned chalk CaO helps solving the sodium carbonate and both sodium hydroxide NaOH and calcium carbonate CaCO3 are formed the later being a solid substance commonly referred to as mesa 1 Left in the liquid are sodium sulphide and sodium hydroxide which are used in the digesting of the pulp The add
40. igare har antagits Jonas Eskilsson 2008 02 20 Examensarbete i Energiteknik 30 po ng Handledare pa TFE Britt Andersson Examinator Ronny Ostin Jonas Eskilsson Emergency Draining of Recovery Boilers Abstract Metso Power possesses world leading competence in the design and service of recovery boilers an important and widely used unit in the pulp and paper mills of today By recovering chemicals and producing electricity from waste products the recovery boiler greatly improves the possibility for the paper industry to meet environmental demands To avoid an explosion in case of an accident the boilers must be equipped with an emergency system that can drain a two phase water mixture from the pressure vessel This Master of Thesis deals with the designing of a Matlab computer program that calculates the draining time and the resulting forces for such a system The program developed uses a homogenous model to approximate pressure gradients for two phase flows the choice being based on research of existing correlations in combination with their proven accuracy Results are compared to a program previously used among other things predicting a similar time for the first half of the draining but a shorter time for the second part The forces at the pipe outlets are estimated to be about 25 higher than those previously calculated This paper provides information to gain a good understanding of how two phase flows can be treated and used to predict
41. ing of secondary air above the bed provides extra oxygen and ensures complete combustion and thereby maximum steam production of the organic compounds By using the procedure outlined above a minimum of chemicals is consumed steam for drying is provided and electricity produced 1 A simplified overview of the process is given by figure 2 Jonas Eskilsson Emergency Draining of Recovery Boilers Chemicals Water Preparation of boiling fluid Steam Drying Chemical Recovery 5 em Steam Ele ctricity I E I es Ja I Figure 2 Overview of recovery part of the pulp process 1 4 2 Flow Patterns The phenomena of a liquid flowing together with a gas greatly complicate the analysis compared to the case of single phase flow To accurately describe a certain flow one must know the momentary flow pattern and adjust it if pressure drops causes it to change further down streams Flow patterns in horizontal pipes are divided into bubbly flow plug flow stratified flow wavy flow slug flow and annular flow 2 Figure 3 illustrates what the gas and fluid profile for the different flow patters may look like Each type calls for simplifications which causes different pressure drops velocity distributions and heat transfer To predict the correct behaviour of a certain flow it is therefore very important to choose an appropriate model o o oS e 00 o9 o9 9 b b o is 8 a CJ Bubbly flow o lt
42. ipes of RB7 for each volume element of part 1 8 2 Result Pipe System The result from the pipe pressure calculations will also be illustrated by the exampl of RB7 part 1 Figure 9 shows how the pressures varies along each pipe for the initial mass flows A linear decrease in pressure over each pipe section has been assumed The outlet pressure varies among the pipes due to the difference in mass flow and pipe diameter 30 Jonas Eskilsson Emergency Draining of Recovery Boilers s Pipe 1 M 38 58kg s Pipe 2 M 35 18kg s e Pipe 3 M 17 87kg s f Q o E 3 o o o o 6 8 Pipe section Figure 9 Pressures for initial mass flows along the pipe 1 2 and 3 for RB7 Part I Appendix 3 contains more results of how the pressure varies with pipe length for the calculated mass flows They are compared to the results generated by the old program to make sure that the calculations yield similar results 8 3 Result Combination of Programs By combining the two programs described it is possible to calculate the constantly changing mass flow during the whole process and the time needed to drain each volume element The mean pressure for each volume element is sent to the pipe program which determines the flow rate through each pipe during the draining of this volume element Figure 10 shows how the flows varies during the draining of RB7 Part 1 3l Jonas Eskilsson Emergency Draining of Recover
43. m in eq 27 can be substituted by eq 40 This leaves only the evaluation of the friction factor for liquid overall flow which is normally done by using the Moody chart This is a well known and widely used graphical correlation connecting Reynolds number Re to the friction factor for different pipes Since the friction factor in the program must be evaluated many times over eq 41 presented by Colebrook where e is the roughness of the pipe will instead form the base of calculation e d n 2 51 e 1 4 Foarcy a 3 7 Re 4 parey The value of the Fanning friction factor is a quarter of the Darcy factor and is used in all calculations in this project The Colebrook equation is implicit and instead of using an iterative process which might prove more accurate an approximate equation presented by Haaland in 1983 will be used 1 11 l 1 8 log cid pee eq 42 pm 3 7 Re According to Cengel 3 the results obtained from eq 42 are within two percent of those given by the Colebrook equation Carefully determining the friction factor from the Moody chart for each section would be slightly better but this is in this case not very practical As long as the steam quality is reasonably low this way of determining the frictional pressure drop seems quite good Should the quality rise above fifty percent it would be better to use a gas overall model The program developed will use the above model for estimating the friction factor To ev
44. m the first part Liquid start volume Liquid end volume Other parameters that may be different for this draining The actual calculation is started by typing part2 in Matlab This part will take about the same time as the first part to complete Make sure the file name specified in input data is not the same as the one used for the first part This will cause the results for that part to be overwritten If the time calculated for part 1 or part 2 differs from 600 seconds it is recommended to re design the pipe system and repeat the calculations 53 54
45. minating the multiplier is the estimated constant that the pressure gradient due to friction for one phase flow is to be multiplied by in order to give the pressure gradient for the two phase flow being examined 7 15 Jonas Eskilsson Emergency Draining of Recovery Boilers dx f dx f liquid f Two phase multiplier The first thoughts concerning the evaluation of two phase multipliers were presented by Lockhart and Martinelli in 1949 and were based on the idea that each phase of the flow occupies a certain space Standard pressure gradient equations were used separately on each flow and thus the interaction between the phases was ignored The study yielded values ofthe two phase multiplier for four different flow regimes and were graphically presented By only considering the turbulent flow regime Martinelli and Nelson further developed the correlations making it valid for boiling and condensation applications as well 8 One of the parameters that must be evaluated to use the two phase model is the integral of the two phase multiplier over the length of the pipe Marinelli and Nelson chose to present this as a numerical value depending on the pressure and quality Void fractions whichalso must be known to evaluate the pressure drop were estimated by interpolating pressure curves in a quite complicated way and were presented in a diagram as a function of pressure and quality 7 In 1964 Thom concluded a study which compared the values of the
46. nder great stress and avoiding this is a primary concern in the construction of recovery boilers In order to prevent such an accident the boilers are equipped with a safety system which drains the water If it is drained too quickly the pressure vessel is placed under much thermal stress while a slow drainage is dangerous due to the issues earlier discussed This paper deals with how the drainage time of a pressure vessel consisting of water and steam can be calculated and thus designed in order to meet the demands placed upon it Jonas Eskilsson Emergency Draining of Recovery Boilers 2 Background 2 1 Employer Metso Power builds install and service recovery boilers that are to be a part of existing or planned paper mills Boilers are sold separately or together with whole pulp mills in co operation with Metso Paper Metso Power with main operations in Finland Sweden USA and Brazil employs 1500 people worldwide The base for this Master of Science project has been in the office at Lindholmen Gothenburg 2 2 Assignment The agreement between suppliers users and insurance companies states that the system must be possible to drain in about twenty minutes This is a compromise between reducing the risk of explosions due to uncontrollable vaporisation and the thermal stress placed on the pressure vessel This reveals a need for a program that calculates the draining time for existing systems and that also can be used in the design of new one
47. necting part of the program this file calculates the total time for the first part of the draining process After the calculation the flow through each pipe the time and the mean tank pressure for all volume elements are send to an excel file and presented to the user Also the force on the pipe outlets the end pressure and end volume will be included in this file The Microsoft Excel worksheet Input Data xls is used as an input file to the program Here the user will present values for the parameters Total volume of tank Initial pressure Liquid volume at the start of part 1 Liquid volume at the end of part 1 Directory and name of file where the results should be stored Backpressure Number of pipes These values are then read by Main first part of drainingprogram which will create a copy of Empty output which contains only text and store it in the directory chosen by the user It will divide the volume that is to be removed from the tank into a number of volume elements and pass their data on to endpressurepart1 At the end of the calculation process the file receives information from Sum o pipeflows part1 of the flow through each pipe and can then calculate the time needed to drain each volume element Endpressurepart1 Calculates what the pressure inside the tank will be after a volume element has been emptied which is done by change in density vaporisation and draining The main program calls the function for e
48. new 9 56 45 4 35 H 3 5 i 2 15 t 0 o 44 RB1 fallpipe T 10 Flow RB1 fallpipe T 20 Flow RB1 np T G Flow RB1 np T 10 Flow 3 2032 3 2032 3 1918 3 1885 3 1292 3 1242 3 1179 3 1159 3 1135 3 1128 3 0208 3 0463 2 973 2 9875 2 956 2 9665 0 79 0 843 83 847 2 7761 2 7761 2 7677 2 7643 2 711 2 7044 2 7006 2 6971 2 0978 2 6945 2 0175 2 6394 2 5813 2 5911 2 5682 2 5737 0 682 0 7099 7 57 7 397 4 024 4 024 3 8037 3 864 3 3993 3 4725 3 3438 3 4443 3 1652 3 2634 3 1013 3 2025 1 096 1 0785 39 37 9 32 32 3 036 3 08 201 2 79 2 68 2 77 2 54 2 03 25 2 58 0 87 0 86 335 32 6 O0 001 C NN o 00 R6 nFKN O Ob o NA F 001 amp Wry RB1 fallpipe T 20 Mold 7 57 Mnew 7 37 Pressure MPa RB1 fallpipe T 10 Mold 8 3 Mnew 8 17 Pressure MPa f MN Ld al 2 wn MN wn we amp n a RB1 new pipe T 0 Mold z 39 0 Mnew 37 9 old 1i t new 0 0 1 2 3 4 5 6 rd 8 RB1 new pipe T 10 Mold 33 5 Mnew 32 6 e old l new D t 1 2 3 4 L B 7 8 Pressure MPa N w gt a ON Own amp AN e tn Pressure MPa S D on hw un Uu wn a wn 45 Old calc Paper Flow RB8 pipe1 Flow RB8 pipe2 Flows RBB pipeconv Flow 9 53 9 53 8 81 8 89 821 8 31 6 65 7 01 33 341 0 83 1 62 Aa 355 9 6963 9 6963 9 0071 9 1357 8 1931 8 2755 7 9916 8 0948 7 7328 7 8562 7 6597 7 7875 7 36
49. nother part of the program is consulted to calculate the initial tank pressure using a specific mass flow If either the resulting pressure does not match the initial tank pressure or the flow used does not match the desired flow the draining time will not equal 600 seconds How long it will be is not estimated The desired flows tank pressure and pipe flows are summarized in table 5 Table 5 Desired Actual Calculated tank Known tank Old program flow kg s flow kg s pressure MPa Pressure MPa Pipe 1 initial 30 5 39 7 487 7 5 Pipe 2 initial 36 3 36 3 7 474 7 5 Pipe 3 initial 14 7 14 7 6 605 7 5 In reality the actual flow through a pipe will be the flow that causes the calculated tank pressure to equal the known tank pressure As shown here this flow is often not the desired one It can easily be seen that pipe 1 has not been very well designed Calculating from the outlet a flow of 39kg s is necessary to reach the tank pressure at 7 5MPa The desired flow is only 30 5kg s hence the pipe is oversized In pipe 3 the flow used to calculate the pressure in the tank equals the desired flow but the calculated pressure is below the known tank pressure This is clearly seen in figure 12 where the pressures along the pipes are shown for both the old and the new program This means that the actual flow for pipe 3 in the old model should in fact be a bit higher than table 5 suggests 36 Jonas Eskilsson Emergency Draining of Recovery Boilers
50. or the suggested algorithm will be addressed Chapter 8 Result Results from the program parts developed are presented and combined to calculate the time for the whole draining process Chapter 9 Discussion A discussion highlights points that may influence the validity of the program and results are compared to the formerly used program By using existing facilities the differences between the programs are analysed Chapter 10 Conclusion The most important conclusions are summarized Jonas Eskilsson Emergency Draining of Recovery Boilers 1 Introduction The pulping industry is one of largest in the world an enormous quantity of wood is turned into paper each year From an ecological and economic point of view it is of great importance to use all means possible to minimize the stress placed on the environment By attaching a recovery boiler to the pulp mill one can reduce the amounts of chemicals used and at the same time utilize the heating value of the waste products The constant improvement of units such as this provides the means necessary to combine the pulp industry witha society where energy supply and environmental issues are major concerns In the recovery boiler waste products are burned produc ing steam of high temperature and pressure Should there for some reason be a leakage of liquid from the water system into the furnace a rapid expansion due to water vaporising would occur This would place the material of the furnace u
51. ovide the following The pressure inside the tank as a function of removed liquid The initial mass flow through each pipe used The time for each part the draining The force that the pipe outlet will be subject to 17 Jonas Eskilsson Emergency Draining of Recovery Boilers 6 Strategy The strategy for finding the time needed to empty the tank is to 1 Calculate the pressure inside the tank as a function of how large volume that has been removed either by vaporization draining or change in density Calculate the pressure drop in the pipe system as a function of the flow This step requires information regarding material and construction of the pipe system and must also pay respect to choked flow and flashing To avoid some of the problems associated with transient flow the volume of fluid that needs to be removed will be split up into a number of volume elements During the draining of one volume element the pressure inside the tank will be viewed as constant being the mean of the initial and ending pressures for the current volume element This makes it possible to treat the flow during the drainage of one volume element as constant 3 The correct flow rate for one volume element can be calculated by comparing the pressure difference between the tank and the pipe exit to the pressure drop over the pipe system calculated in point 2 The correct mass flowis the flow that causes equal pressure differences This flow can then b
52. ppendix 2 which uses a different model This suggests that the model used for the pressure gradient is reasonably well designed AS earlier discussed the total volume liquid that must be removed is divided into a certain number of volume elements For each element the end pressure is calculated by determining the heat that must be supplied to reach an assumed pressure An error is associated with each calculation and the more volume elements used the greater the error will be Using small steps when assuming the end pressure will increase the accuracy but at the expense of calculation time One must also keep in mind that the whole point of using a large number of volume elements was to be able to assume short periods of constant pressure inside the tank The more elements used the more valid this assumption will be thus a large number of elements is preferred from this point of view Because of the reasons stated it is important to carefully consider the number of volume elements and how the expression for the assumed pressure should be written It will always be a compromise between time accuracy of the tank pressure program and accuracy of the pipe system program The default value of number of volume elements is ten for each part of the process and the method of pressure assumption can be viewed in Appendix 4 file pipepressure The program does not allow flows that result in that the critical pressure is reached If the flow is choked and hence
53. qe Me OM eq 13 dx jJ dx a 1 a dP a l a mE g sin 0 eq 14 X stat Vo V 13 Jonas Eskilsson Emergency Draining of Recovery Boilers 4 4 Models for Pressure Drop All the models discussed below are treating the flow with a uniform velocity profile meaning that the velocities in the centre and at the boundary are the same Since the fluid at the boundary is stationary this is not true but the averaging of speed over the cross section greatly simplifies the calculations and seems to produce acceptable errors 2 4 4 1 Homogenous Model Instead of treating the flow as two fluids a homogenous approach models the flow as one fluid with properties that are a mixture of the two flows The properties are weighted in relation to the quality of the mixture This approach has two major requirements that the two fluids are in thermal and mechanical equilibrium and that they have the same velocity When these simplifications are made a less complicated expression for the momentum can be derived The mean specific volume and the product of cross section area and mean density can be expressed as V oV 1 9 V eq 15 Sp Sc pa S p eq 16 By using the above equations combined with the fact that the velocities are equal the pressure equation eq 3 can be written as dE LS Go o and eq 17 dx S dx dx Before further analysis is made the pressure gradient due to friction must be expressed in terms of known quantities This is achi
54. s The program currently used has many flaws and was originally constructed for a HP calculator and later implemented in Matlab It lacks references and relies on extensive research which is not well documented the program designer is retired and can not be consulted with this problem This makes the train of thought very difficult to follow and since the results obtained rely on that a program match can be found further discussed in Chapter 9 2 their accuracy is limited To remedy this a new program must be developed which can better deal with the complicated nature of two phase flow and is adjusted to the technology and computer abilities of today Jonas Eskilsson Emergency Draining of Recovery Boilers 3 Aim of the Master Thesis Project This study focus on developing a new algorithm for handling the nature of two phase flow in pipe systems and predict the drainage time of the water inside the pressure vessel The program developed will in a user friendly way illustrate how the pressure inside the recovery boiler varies with removed liquid and present the mass flow through each pipe as a function of time The program must be able to handle either saturated or unsaturated water entering the pipes its condition depending on where in the recovery boiler it is to be drained from Jonas Eskilsson Emergency Draining of Recovery Boilers 4 Theory 4 1 The Recovery Boiler In order to break the chemical bindings and extract cellulose fibres the c
55. sure or the critical pressure for this flow If very large pipes are used the critical pressure will be below the atmospheric pressure and the whole pressure potential of the tank can be used to maximize the flow Often this is not very practical and the flow is instead restricted by the critical pressure The program developed uses a method of interval decreasing to determine the accurate flow If the flow tried causes choking at some point the program tries a mass flow equal to the mean of the last tried flow and the last flow that did not cause choking instead This process is continued until the difference between the current flow and the flow used in the last successful calculation is satisfactory small It should be noted that only when the resulting outlet pressure is exactly equal to the critical pressure or the back pressure whichever is highest the pressures along the pipe will be correct This is further discussed in Chapter 9 1 Since the speed of the program is a primary concern it does not iterate until a precise match between outlet pressure and critical pressure is found but only until the mass flow has stabilized Should the pressures along the pipe system be needed the default conditions concerning when to end the iteration must be changed 7 2 5 Forces at the Pipe Outlets The mass leaving the pipe system will cause forces on the pipe structure and from an engineering point of view these forces are important to know Since force is
56. t The forces acting between the two phases have been left out in eq 2 since they cancel each other The net force acting on the fluid equals its change of momentum and the above equations can be set equal and rearranged to create an expression of the pressure drop along the x axis In equation 3 the second order derivatives have been neglected which according to Holland is acceptable in almost all cases 4 dP ldF ld peie yino gs M M dx S dx dx ne ut S 12 Jonas Eskilsson Emergency Draining of Recovery Boilers The three components of the right hand side of equation 3 will from here on be referred to as the pressure gradient due to friction acceleration and static head dP dP dP dP St pep eq 4 a n en When calculating pressure drops along pipes it is more convenient to express the momentum and acceleration term with the help of the mass flux G void fraction a and the mass fraction of gas These are defined as So Q e 5 S q S 1 0 eq 6 S q Mg W e 7 M q 1 0 u 8 a e M q M G eq 9 5 q These equations make it possible to express the velocity of the fluid in terms of its specific volume V M V GV ug 25 eq 10 as a u M We SUOG eq 11 1 0 S l a Finally the definitions used above and the expression for the velocity are substituted into the pressure equations which yields dP 1dF T dx J S dx 1 2 AA d ge we
57. t the value of Reynolds number and friction factor will be correctly estimated a fact that many reports have pointed out and caused Dukler to evaluate the mean viscosity in a different manner 7 It is difficult to predict how much the choice of model will affect the result in this application but it might be worth more attention The Reynolds number calculated by the mean viscosity can be used in eq 42 as with model number two used in a connection with the Blasius equation being valid only for smooth pipes The later approach makes it possible to calculate the frictional pressure drop directly with eq 45 which will not be derived here and in that way avoid the error introduced by eq 41 and its simplification eq 42 1 4 V V dP dP 1 0 8 Ile 1 lu u eq 45 dx f dx Jio V KH 25 Jonas Eskilsson Emergency Draining of Recovery Boilers It should be pointed out that the old program used an expression of Churchill that originates from the Colebrook equation This study has found no validation of this expression 7 2 3 Determination of the Quality By assuming that no vaporisation occurs along a pipe the pressure gradient at the entrance can be calculated using eq 23 Since the water is saturated and the outlet pressure is lower than the inlet pressure a certain amount of steam will in fact form Hence the pressure at the outlet will in fact be slightly higher than the pressure that was calculated using the pressure gradient above
58. the old program in combination with man made calculations which as discussed above are not entirely correct A similar comparison is made for the second part of the process The old program indicates that the flow through pipe 3 should be 32kg s for the draining to be completed in 10 minutes Based on the existing pipe system the initial flow through this pipe is calculated to 20kg s No 35 Jonas Eskilsson Emergency Draining of Recovery Boilers other pipes are being used during this draining By using the same method as outlined above the total time is calculated to 1004 seconds The time calculated by the new program is 754 seconds which is a lot shorter than what was previously assumed The main reason for this is that the old program uses the stagnation enthalpy corresponding to the starting pressure of the first draining while the new program continuously evaluate it for each volume element This fundamental difference exits throughout all the facilities compared and is the single greatest cause to that the programs does not deliver equal draining times 9 2 2 RB7 This calculation is a much more complicated procedure using the old program The basic idea is to first use the program to decide what the initial and ending flows should be in order to empty the pressure vessel in 600 seconds Data for how the boiler is constructed is then used to calculate how the flow should be distributed among the three pipes When this is established a
59. the total time as output instead of relying on calculations by the user to find a match between subprograms the manual error introduced is significantly less than before 39 Jonas Eskilsson Emergency Draining of Recovery Boilers Acknowledgements I would like to give thanks to Anders Littorin and Anders Fransson Anders Littorin who has been my supervisor has spent a lot of time discussing and encouraging my work and for this I am grateful In cases where neither he nor I have had answers Anders Fransson has been consulted and provided me with guidelines and motivation I would also like to especially thank Maria Henriksson for her great understanding of my needs and ambitions outside of work Without this I would have had no motivation to work She has also provided technical support on various subjects which I have no previous knowledge of 40 Jonas Eskilsson Emergency Draining of Recovery Boilers References 10 11 12 13 Sveriges skogsindustrif rbund Luftf rbr nning Br derna Hanssons Boktryckeri AB 1981 Tong and Tang Boiling Heat Transfer and Two Phase Flow Taylor amp Francis London 1997 Cengel Turner and Cimbala ThermalFluid Science 3 edition McGraw Hill 2007 Holland Fluid flow for chemical engineers London 1995 Whalley Two Phase Flow and Heat Transfer Oxford University Press New York 1996 Dennis R Liles Two Phase Flow http library lanl gov cgi bin getfile 03 02 pdf Viewed 2007 1
60. to Sum o pipeflows Resulting flow for current pipe and volume element Pressure after each pipe section The function calculates the pressure after each section of the pipe for the flow assumed For each section Pipepressure and PC2 are called Input from Pc2 Critical pressure for each pipe section Input from Ca1culate Flow Assumed mass flow Pipe design Average pressure for a volume element O utput to calculate_Flow Pressure after each pipe section Quality after each pipe section Critical pressure at the same points An indication of if critical pressure was reached and in that case in which section Force at end of a pipe section PC2 Determines the critical pressure for a given mass flow and pipe section It uses the subprograms eplH20 epvH20 eqtH20 vplH20 vpvH20 and vx2 How they interact has not been looked into since the function is a part of the previously used program Input from Pressure_after_each pipe_section Mass flux for the section being evaluated Stagnation enthalpy for current tank pressure Output to Pressure after each pipe section Critical pressure for the current mass flow and pipe section 50 Pipepressure Calculates pressure and quality for a given mass flow in a number of steps along the pipe section Handles both singular pressure drops and pressure gradients due to friction static head and acceleration If the pressure for the given mass flow falls below the critical
61. volume and the density at the initial pressure The time needed for the draining is assumed to be equal to the quotient of the mass and initial flow Table 4 Pressure 5 5 Mpa Density 768 kg m3 Drained Volume 65 m3 Mass 49920 kg Draining flow 161 kg s Time 310 s Documented calculations of RB2 part I This approach uses a number of simplifications The mass calculated above is the total change in liquid mass All of this mass must not be drained a certain amount will vaporize and thus present no danger Also neglected is the change in density for the liquid when the pressure is lowered This means that the remaining mass after the draining does not quite occupy the whole space assumed The later neglecting does not however have any significant impact on the result The flow used to calculate the time is the initial flow and will decrease slightly during the draining In addition to the errors above there also seems to be an error in the flow rate calculation for pipe 1 According to Appendix 3 the pressure inside the pipe system will sink below the critical pressure for a flow of 68kg s This means choking will occur and to deliver this flow one of the pipe sections will have to be changed The new program does not allow critical flow and therefore only an initial mass flow of 61kg s The total time according to the new program for part 1 was as mentioned calculated to 334 seconds which can be compared to the 310 seconds predicted by
62. y Boilers Flow kg s Figure 10 Flow rate for pipe I 2 and 3 during draining of RB7 Part I The mass that must leave the tank during the draining of one volume element calculated in the tank program is divided with the mass flow to calculate the time needed to empty a volume element The draining times for RB7 part 1 are presented in figure 11 The total time for the whole process is the sum of the times for each volume element 6 Volume element Figure 11 Time to drain each volume element The total time is calculated to 546 seconds Simulations for the second part of the draining in RB7 using only two pipes estimate the time to 441 seconds This corresponds to a total time of 16 minutes and 27 seconds which is several minutes faster than recommended The forces acting on the pipe outlets from RB7 at the maximum flow rates are 10 9kN 10 1KN and 5 0kN respectively 32 Jonas Eskilsson Emergency Draining of Recovery Boilers 9 Discussion 9 1 Thoughts Concerning the Validity of the Program The discussion in Chapter 7 2 clearly states that the choice of model can greatly affect the evaluation of the pressure gradient for pipe flows Since this is a major part of the final program it is important to keep in mind when evaluating the results Having pointed this out it should be noted that the pressures along the pipes and the corresponding mass flows very well match those obtained with the old program see A

Jonas Eskilsson 2008-08-20

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