Sulfur deposition in sour gas reservoirs: laboratory and simulation study Sulfur deposition in sour gas reservoirs: laboratory and simulation study

Sulfur deposition in sour gas reservoirs: laboratory and simulation study

  • 期刊名字:石油科学(英文版)
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  • 论文作者:Guo Xiao,Du Zhimin,Yang Xuefen
  • 作者单位:State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation
  • 更新时间:2020-09-15
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论文简介

Pet. Sci.(2009)6:405414DOI10.1007/s1218200900624Sulfur deposition in sour gas reservoirslaboratory and simulation studyGuo Xiao, Du Zhimin, Yang Xuefeng, Zhang Yong and Fu DekuiState Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University,Chengdu, Sichuan 610500, ChinaAbstract: Sulfur deposition in the formation, induced by a reduction in the solubility of the sulfur in thegas phase, may significantly reduce the inflow performance of sour gas wells and some wells in sour gasreservoirs have even become completely plugged with deposited sulfur within several months. Accurateprediction and effective management of sulfur deposition are crucial to the economic viability of sour gasreservoirsIn this paper, a dynamic flow experiment was carried out to investigate formation damage resultingfrom sulfur deposition using an improved experimental method. The core sample was extracted from theproducing interval of the LG2 well, LG gas field in the Sichuan Basin. The experimental temperaturewas 26C and the initial pressure was 19 MPa, The displacement pressure continuously decreased from19 to 10 MPa, and the depletion process lasted 15 days. Then the core was removed and dried. The coremass and core permeability were measured before and after experiments. Experimental results indicatedhat the core mass increased from 48.372 g before experiment to 48. 386 g afterwards, while thepermeability reduced from 0.726 to 0.608 md during the experiment. Then the core was analyzed with ascanning electron microscope(SEM) and energy-dispersive X-ray mapping. The deposition pattern andmicro-distribution of elemental sulfur was observed and the deposited elemental sulfur distributed as afilm around the pore surfaceIn addition, a preliminary three-dimensional, multi-component model was developed to evaluatethe effect of sulfur deposition on production performance, and the effect of production rate on sulfurdeposition was also investigated. Simulation results indicated that the stable production time would beshortened and the gas production rate would be decreased once sulfur deposited in the formation. Theincrease in deposited sulfur at high flow rates may be attributed to a bigger pressure drop than that atlow gas flow rates. Gas production rate has a severe effect on sulfur saturation in the grid of producingwell located in sourervoir. The work suggests sulfur deposition should be considered to correctlypredict production performance and gas production rate should be optimized in order to control or retarsulfur deposition during the development of sour gas reservoir.Key words: Sour gas reservoir, sulfur deposition, experiment, numerical simulation, formation damage1 Introductionelemental sulfur and h,sMany studies were focused on sulfur production anElemental sulfur is often present in appreciable quantities or deposition in gas/oil wellbore holes, especially of gasin sour gas under reservoir conditions( Brunner and Woll, reservoirs(Brunner and Woll, 1980; Hyne,1968;Roberts1980, Brunner et al, 1988). Reduction in pressure and 1997). The problem of elemental sulfur deposition has beentemperature generally reduces the solubility of sulfur in sour mainly covered in the areas of chemical engineering, gasgas. Once the reservoir fluid has reached a sulfur-saturated processing, and chemical analysis(Sung and Johnson, 1989;state, further reduction in pressure and temperature will Flowers, 1990; Aitani, 1993). The proposed treatments werecause sulfur to deposit. On the other hand, the sulfur in the chemical separation(Beskov et al, 1989)or biological andgas phase also reacts to form a hydrogen polysulfide species microbial treatments(GEk, 1994; Rutenberg et al,(Hyne and Derdall, 1980: Hyne, 1983 ). Since high pressure 1999). On the other hand, limited research has been devotedand temperature favor polysulfide formation, deposition to sul中国煤化工 rvoir rocks. Kuo andof elemental sulfur occurs when changes in pressure and Colsmathematical model oftemperature alter the decomposition of polysulfide to a solC Gedi and its influenceon fluid flow. The model considered elemental sulfur asCorrespondingauthor.email:guoxiao@swpu.edu.cnsome of the dissolved sulfur precipitates from the solutionReceived May 6, 2009as a result of depletion of reservoir pressure. The resultsPet. Sci.(2009)6:405414of the study showed a rapid buildup of solid sulfur around safety. In the experiment process, safety must be ensurethe well and significant deposition near the outer boundary because H2S is hypertoxic. (2) Few experimental methodsof the reservoir. Roberts (1997) have used a conventional for reference. Reduction in pressure and temperatureblack-oil reservoir simulator to model sulfur depositional generally reduces the solubility of sulfur in sour gas. Onceprocesses and described significant flow impairment induced the reservoir fuid has reached a sulfur-saturated state, furtherby sulfur deposition for a history match of the Waterton reduction in pressure and temperature will cause sulfurfield case. Lately, Du et al (2006)have presented a new gas- to deposit. The requirement for experiment equipment ofliquid-solid coupling model for fractured carbonate gas high sulfur gas reservoirs is much stricter than for liquidreservoirs with a high H2S-content, accounting for sulfur experiment equipment under the same conditions. (3)Longerdeposition, phase behavior variation, geochemical rock- experimental period. Variation of temperature and pressurewater-gas interactions and adsorption. They compared the run can result in elemental sulfur deposition. However, forresults with the Roberts'calculation results in the literature the special reservoirs, it maybe take a long time to make(Roberts, 1997)and analyzed the reason for the differences it happen. (4) Experimental results are uncertain. Becauseof the development indexes between these two models. of the limit of research period, the core experiment canHyne(1968) presented a survey of more than 100 producing not infinitely extend time, which could make the results ofwells in Canada and Europe about field operations of sour experiment different from actual state. For these four reasons,gas production. The survey focused on sulfur deposition at it is very difficult to evaluate the elemental sulfur depositedthe bottom of producing wells and showed that high bottom in the core from high sulfur gas reservoirs. Therefore, as therehole and wellhead temperature and low wellhead pressure were no ready-made experimental methods used for referenceprovide favorable conditions for sulfur deposition in well conditions, we have independently designed an experimentaltubing. Al-Awadhy et al ( 1998)performed the first study to process and assembled relevant experimental componentsinvestigate sulfur deposition in carbonate oil reservoirs. They Aiming at these key technological difficulties during gasconducted a single experiment and developed a numerical production in high temperature high pressure high HrS-cO2model describing the phenomena. Abou-Kassem(2000) gas reservoirs, on the basis of improved experimental testingstudied numerically and experimentally the deposition of method and process, formation damage resulting from sulfurelemental sulfur in porous media using gas and oil flow deposition has been conducted by using experimental andsystems. The results indicated the existence of permeability numerical simulation methodsdamage due to elemental sulfur deposition. Shedid and Zekri( 2002)conducted a detailed experimental study using a wide 2.1 Deposited sulfur in core samplesrange of applied flow rates, different initial concentrations of An experimental set up consists of a core holder, asulfur, and different rock permeability values. The results of measuring pump, a sample preparation, a container, athe study stressed the severity of the problem associated with corrosion proof pressure gauge, a voltage regulator, asulfur deposition for different fiow rates and under different confining pressure pump a back pressure valve, a backinitial sulfur concentrations of the crude oil. Shedid and pressure pump, a gas flow meter, and a ventilated fume hood,Zekri(2004)carried out ten dynamic flow experiments underas shown in Fig. Idifferent flow rates, using different crude oils of different The gas samples from TD5-1 well were flooded throughsulfur and asphaltene concentrations, to investigate the the actual cores to test the elemental sulfur deposition.Theimultaneous deposition of sulfur and asphaltene in porous composition of well head gas sample of X gas reservoir ismedia. Experimental results indicated that the increase in listed in Table 1. The scanning electron microscope(SEM)simultaneous sulfur and asphaltene concentrations in the was used to evaluate the sulfur deposited along the actualflowing oil could increase and accelerate the permeability coresdamage in carbonate reservoirsIn this paper, a dynamic flow experiment was carrieout to investigate formation damage resulting from sulfurdeposition using an improved experimental method. InTable 1 x gas reservoir fluid compositionaddition, a preliminary three-dimensional, multi-componentmodel was developed to evaluate the influences of sulfurMole fractieComponentdeposition on production performance. The effect ofproduction rate on sulfur deposition was also investigatedN20.50002 Experimental investigation of sulfurHS6.8600deposition2.7600Up to now, many experiments for modeling sulfur中国煤化工8600deposition in cores from oil reservoirs have been conductedCNMHGwhile few experiments have been made for high sulfur gas02100reservoirs globally. There are four main reasons for limited00200experiments of high sulfur gas reservoirs. (1) High risk forPet. Sci(2009)6:405414DesulfurizerFIg. 1 Schematic diagram of experimental set up for sulfur deposition- Measuring pump; 2-Sample preparation; 3-Container; 4,5-Corrosion proof pressure gauge; 6-VolLage regulator: 7-Core holder8-Confining pressure pump; 9-Back pressure valve; 10-Back pressure pump; 11-Gas flow meter; 12-Ventilated fume hoodX N Hand operated valve⑧2.2 Experimental resultsA set of dynamic flow experiments were carried outto investigate formation damage resulting from sulfurdeposition. The core sample from LG2 well was used, theexperimental temperature was 26C and the initial pressurewas 19 MPa. The confining pressure was kept as constantas 12 MPa. As the whole experimental process was in thestage of depletion, the displacement pressure decreasedcontinuously from 19 to 10 MPa, and the depletion processlasted 15 days. Then the core was removed and dried, thecore mass and core permeability were measured beforeand after the flow experiment. The result indicated thatthe core mass increased from 48.372 to 48.386 g, whilethe core permeability reduced from 0.726 to 0.608 md, asshown in Table 2. Then the core was analyzed by scanningelectron microscope(SEM)and energy spectrum. The(a)Backscattered-electron imagedeposition pattem and micro-distribution of elemental sulfurwas observed and the deposited elemental sulfur filmilydistributed around the pore surface, as shown in Fig. 2.Table 2 Variations in the core mass and core permeabilitybefore and after the flow experimentDre massBefore the experiment4837248.386increment00140.ll8中国煤化工Rate of change,%002916.253CNMHGmapFIg. 2 Distribution of sulfur in a polished section cut from theexperimental core after sulfur depositioPet. Sc(20096:4054143 Simulation investigation of sulfur equation.depositionIt is assumed that the solubility of elemental sulfur in thegas is Cri, and the density is Pe at the time of f, in a cell, while3. 1 Assumptionsthe solubility of elemental sulfur is Ca and the density is peat the time of t,, and that the temperature does not change inTo simplify the coupled gas-liquid-solid flow the time interval between t, and t2, the separated-out massmathematical model and be convenient to solve it, the of elemental sulfur for a unit of volume y be expressed asollowing assumptions were made.follows2) Fluid flow obeys Darcys law relative to the sulfur solid△M=△x△y△p6s(Cn-C2)phase fowSubstituting Eq. (4)into Eq (5)gives the model to3)Porosity and permeability are changed with pressure calculate separated-out mass of elemental sulfur:4)Media deformation is considered and the deformationis smallM()5)The solubility of the sulfur in the gas phase wasturated at initial time3. 4 Calculation of migration velocity of sulfur3.2 Differential equationsparticle in the gas mixtureThe differential equations governing the flow of water,Neglecting the clashes that may happen amonggas,and sulfur solid components in porous media can be particles in the gas mixture, it can be assumed thatwritten in the abbreviated formparticles have the same velocity in the same cell. Thus, bymeans of the method of particle dynamics, the calculationof migration velocity of sulfur particle in gas mixture is asfollowsVp叫sa61+exp(naI+exp(4/vabu, va/1-exp(4tvab) VL1-exp(4ryab//VA vP+(u,)=a(s,C,+C S,+S, )9+9(2)072VP可A621,9z(m2)bp apaxwhere K is permeability, 10um; p is pressure, MPa; o isporosity; P is the density of gas, g/cm; P, is the density where p is the density of the mixture of gas phase and solidof sulfur, g/cm; S, is the gas saturation; S, is the sulfur phase, ke/m; Cp is the resistance coefficient; r is the particlesaturation; u, is the migration velocity of sulfur particles, cm/ radius, m; Vp is the particle volume, m; mp is the particleS;Pg is the gas viscosity, uPas; t is time, s; 4s is source/sink mass, kgterm for gas, m/d; q, is source/sink term for elment sulfurm/d;v, is the volume of per unit, m; C, is the elemental 3.5 Calculation of deposition velocity of sulfursulfur solubility in gas mixture, g/m; C, is the suspended particle in gas mixturesulfur particle concentration in gas mixture, g/m; Zg is the The resistances to gas and solid in the course of migrationmole fraction of m component in gas phasein the conduit are related to gas/solid ratio, gas velocity,3.3 Calculation of the separated-out mass of velocity of suspended particles, diameter and shape ofelemental sulfurconduit, and gas velocity, so the energy loss caused by theresistances can be categorized into two types: energy lossA simple correlation developed by Chrastil (1982)for caused by friction between gas and conduit wall, and energypredicting the solubility of solids in a high pressure fluid was loss caused by clash and friction both between particles andused to evaluate the desired solubility-pressure relationships: between particle and gasC=p exp=+B(4) followVL凵中国煤化工0u:200CNMHGThe above equation has been used extensively to correlateohubility data for the design of supercritical fluid extraction "gprocesses(Sung and Johnson, 1989). The separated-outmass of elemental sulfur was calculated in light of the abovePet. sc.(2009)6:405414where d is the pipe diameter, m; ume is the velocity of gas permeability of pore space containing pluggable pathways;phase and solid phase, m/s; An is the gas friction coefficient; Kmpo is the initial permeability of pore space containingam is the solid friction coefficient; o is the porositynonpluggable pathyEq. (8)is the critical gas flow velocity with suspendedparticles. If gas flow velocity is less than the critical gas flow 4 Computer modelvelocity with suspended particles, suspended particles will beBased on the above mentioned mathematical models, apreliminary three-dimensional, multi-component, three-phase3.6 Sulfur adsorption model(gas- water-solid)flow numerical reservoir simulator wasdeveloped. A detail numerical model was listed in AppendixAdsorption of sulfur can be considered to take place A. The program code was written in Visual Basic and thefrom the monomer phase. Sulfur adsorption formula can be computing flow diagram is presented in Fig3expressed as:m, ",Data input and initializatioS+(m,/m2)xwhere n, is the solid adsorption quantity; m, is the mCalculation of phase state of fluidnumber of sulfur particle per unit mass in absorption layer; xis the mass fraction of solid phase in mixture in continuouspressurephase; S is the selectivity factor; m is the mass number of gasper unit mass in absorption layer; g is the mass fraction ofSolving pressure increment and buildup ofre in continuous ph3.7 Formation damage modelCalculation of velocity field of gas phaseSulfur deposition can induce a reduction in formaticorosity and permeability and the depositional rateaccelerated rapidly as the rock permeability decreasesIt is assumed that the volume of deposited-sulfur isinvariable while the pressure is changing. So the porositydamage model is as followsrate to carry parteφ=如-△φ=o-x100%No depositionwhere V, is the volume of deposited elemental sulfur; o is theJudging doposition of painitial porosity; V is the pore volumeThe permeability damage model presented here is basedCalculation of deposited mason the theory developed by Gruesbeck and Collins(Hyne,1968)who originally developed the theory to describeentrainment and deposition of fines in porous media. TheyCalculation of absorbedsuggested hypothetical division of the porous medium intopluggable and nonpluggable pathways. This involves theCalculation of saturatonuationrepresentation of the porous medium into two continuousbranches formed in such a way that one is of smaller poresalculation of composition ofthat can be eventually plugged completely. On the other hand,the nonpluggable pathways cannot be completely pluggedbecause as the pore throat diameter is reduced due to solid[ agrm no-tominitm d matin hine-deposition, the local speed becomes high enough to entraindeposits out of the pore spaces. Thus, permeability damagemodel is as followsExamination of time nerveK=/,kpo expl-ap/m Kno(1+ Be,End simtwhere K is the permeability, 10um; f is the fraction of pore中国煤化工 or calculationspace containing pluggable pathways; /np is the fraction ofre space containing nonpluggable pathways; a and B are4.1EHCNMHGelemental sulfurphenomenological constants to be specified; e is the volumeof fines deposited per unit initial pore volume, cm /cmUnder reservoir conditions, the solubility of sulfur insubscript p represents pluggable pathways; Kpo is the initial the gas phase was 0.94 g/m, and the initial sulfur content410Pet Sci(2009)6:405414in gas phase was 0.75 g/m. Therefore, sulfur in gas phaseTable 4 Reservoir fluid compositionwas undersaturated under reservoir conditions. With gasproduction, reduction in pressure and temperature will causeMole fractionsulfur to deposit. Solubility of sulfur in the gas phase reachesthe critical saturation state when the reservoir pressure00100decreases to 17. 4 MPa, as shown in Fig. 4. Gas volume inthe core under reservoir pressure of 17.4 MPa was 0.022030.1900munder reservoir conditions, while gas volume in the core0.0290under reservoir pressure of 10 MPa was 0.01969 munderreservoir conditions0.7600In light of Eq ( 5)or Eq. (6), the mass of elemental sulfur0.0060deposited in the dynamic flow experiment was evaluated tobe 0.014 g. The values of deposited sulfur predicted by the0.0050model were in good accordance with experimental resultsThe effects of sulfur deposition on the stableproduction time, cumulative production, and reservoirpressure were simulated, as shown in Figs. 5, 6, and 7These results indicated that the stable production times与=(174,0.75would be shortened and the gas production rate wouldbe decreased once sulfur deposited in the formationSulfur deposition could further cause a decrease inreservoir pressure. The effect of production rate on04sulfur deposition was investigated, as shown in Fig. 8he increase in deposited sulfur at high flow rates may beattributed to a greater pressure drop than at low gas flowrates. Sulfur deposition was not made worse by controlling101214161820SuLfur deposeFig. 4 The solubility of sulfur in the gas phase with pressure at304.2 Simulation of sulfur depositionThe gas-liquid-solid coupling model presented by du000ooodet al (2006) was used to evaluate the influences of sulfurdeposition on stable production time, cumulative production,and reservoir pressure. The effect of production rate on sulfurdeposition was also investigated. The parameters of the testcases are shown in Table 3 and Table 4Time, dTable 3 Reservoir propertiesFig. 5 The effect of sulfur deposition on gas production rateParametersValuc12}。 SuMur deposition consideredReservoir temperature, CInitial pressure,o。o。。。。Pay thickness, mPorosityH中国煤化工CNMHGPermeability, xIom0.726Time, dGrid dimension11x11×1FIg. 6 The effect of sulfur deposition on cumulative production of gasPet. Sci(2009)6:405414decreased once sulfur deposited in the formation4)The increase in deposited sulfur at high flow rates mayo SuMur deposition oonsideredbe attributed to a bigger pressure drop than that at low gasflow rates. Gas production rate has a severe effect on sulfursaturation in the grid of producing wells located in sour gas000000000oooreservoirs.5)The work suggests sulfur deposition should beconsidered to correctly predict production performance andgas production rate should be optimized in order to control orretard sulfur deposition during the development of sour gasreservoirAcknowledgmentsThis work was supported by the National High TechnologyFig. 7 The effect of sulfur deposition on reservoir pressureResearch and Development Program of China (863Program)(No. 2007AA06Z209)and the National NaturalScience Foundation of China(No. 50974104, 50774062 and50474039). Technical support of State Key Laboratory of Oiland gas Reservoir Geology and Exploitation we are workingis also gratefully acknowledgedReferencesAbou-Kassem J H. Experimental and numerical modeling of sulfur0-q3.5x10mplugging in carbonate reservoirs. Journal of Petroleum Science andEngincering2000.26(14):91-103Aitani A M. Sour natural gas drying. Hydrocarbon Processing. 1993(4):67-73Al-Awadhy F, Kocabas l, Abou-Kassem J H, et al. Experimental andnumerical modeling of sulfur plugging in carbonate oil reservoir. AbuDhabi International Petroleum Exhibition and Conference held inTime, dAbu Dhabi, U.A. November 11-14, 1998(SPE paper 49498)Beskov V S, Kandybin Al and Furmer Y V Modeling of the processFig. 8 The effect of the gas flow rate on sulfur depositionof the removal of sulfur on zinc oxide absorbents in ammoniaproduction. Russ. Chem. Ind. 1989. 21(3): 87-93the production flow rate of gas. The work suggests sulfur Brunner E, Place Jr M C and Woll W H. Sulfur solubility in sour gasPT.1988.40(12):1587-1592deposition should be considered to correctly predict Brunner E and Woll W H Solubility of sulfur in hydrogen sulfide andproduction performance during the development of sour gassour gases. Soc. Pet. Eng J. 1980. 20(5): 377-384reservoirsChrastil J, Solubility of solids and liquids in supercritical gas. J. Phys5 ConclusionsDu Z M, Guo X, Zhang Y, et al. Gas-liquid-solid coupled flow modellingin fractured carbonate gas reservoir with high H2S-content. SPE the1)Dynamic flow experiments were carried out toFirst International Oil Conference and Exhibition held in Cancun,investigate formation damage resulting from sulfur deposition Mexico, 31 August-2 September, 2006(SPE paper 103946)on the basis of improved experimental method. Experimental Flowers D G. Use of permeation devices in the analysis of sulfur gasesresults indicated that the core mass increased from 48.372 to by gas chromatography. Ind. Eng. Chem. Res. 1990. 29(7): 156548.386g, while the core permeability reduced from 0. 726 mD1568before the experiment to 0.608 mD afterwards.Gasiorek J Microbial removal of sulfur dioxide from a gas stream. Fuel2)A polished section from thecore wasexamined byProcessing Technolgy. 1994. 40(2-3): 129-138a scanning electron microscope equipped with an energy Hyne J B Study aids prediction of sulfur deposition in sour-gas wells.Oil and Gas Journal. 1968. 25(11): 107-113micro-distribution of elemental sulfur was observed and the Hyne J B. Controlling sulfur deposition in sour gas wells. World Oildeposited elemental sulfur was distributed as a film on theHyne J B and Derdall G. Sulfur deposition in reservoirs and production3)A preliminary three-dimensional, multi-component中国煤化工 nnual Gas Conditioningmodel was developed to evaluate the influences of sulfurCNMHGdeposition on production performance and the effect of Kuo Cstuay of fluid flow accompaniedproduction rate on sulfur deposition was also investigated. by solid precipitation in porous media. AICHE JournaL. 1966. 12(5)Simulation results indicated that the stable production timewould be shortened and the gas production rate would be Roberts B E. The effect of sulfur deposition on gaswell inflowPet. Sci. (2009)6performance. SPE Reservoir Engineering. 1997. 12(2): 118-123(SPE Shedid S A and Zekri A Y. Formation damage due to simultaneouspaper36707(1996)sulfur and asphaltene deposition. SPE International SymposiumRuitenberg R, Dijkman H and Buisman C JN. Biologically removingand Exhibition on Formation Damage Control held in Lafayettsulfur from dilate gas flows. J. Miner. Met. Mater. 1999. 51(5): 45-49 Louisiana, February 18-20, 2004(SPE paper 86553)Shedid S A and Zekri A. An experimental approach of elemental sulfur Sung N J and Johnson S J. Determination of the total amount of sulfur indeposition in carbonate oil reservoirs. Joumal of Petroleum Science petroleum fraction by capillary gas chromatography in combinationand Technology.2002.20(56):507-523of cold trapping, a total sulfur analyzer. J. Chromatography A. 1989.468(12)345-348Appendix aFinite-difference equationThe differential equations governing the flow of gas, sulfur and non-sulfur components in a porous medium can be writtenin the abbreviated form(3/、PgAxVp+v()=(+C+)+(A-1)KP,L8VI2(m=1,2,3,)PgThe numerical solution of partial differential equations by finite differences involves replacing the partial derivatives byfinite difference quotients. Then, instead of obtaining a continuous solution, an approximate solution was obtained at a discreteset of grid blocks or points at discrete timesIn expanded form, the differential equations( Eq (A-1))areor gasKP+KF-P"|+1K)-四K)Hg(5(ek P--Pr"_(, poPgFor sulfur componentK+[篇-+ge-e]+是[e-][(S C,+C; s,+S, )o]"-[(S.,+C;S,+S,)p]For non-sulfur comr+I nM+I中国煤化工CNMHG/AyP1-Pn1.(2k),是Pet. Sci(2009)6405414By multiplying Ar Ay Az, Eqs. (A-2),(A-3)and(A-4)can be written asP K(%,e(P:-P")+兮(4),(;-P")+()AxAz,p, KPm"-pm\△x△y/(2(SA2)-(s)+ qg匀y△zkK1-PAy, AzK(P1-Pr")Ar, Ay, KP-l-P(r:-r")Ay△[:-u]+△x△[-:]+x/[-(S, C,+C; S,+s)o-[(SC,+C Sg+s )p]+9△y△(卫KZ(P-PpgAx, az,p kZEHg(F-P")+a△xAy(K2(冬几,(e计-F)+4244y, p kz(r1-Pr")sP2)-(o2)△+q128Each of the transmissibility terms is divided into two parts. i.e, one is the geometric factor and the other is the fluidityDefficientAy△Ax△zAr 4Kf,=Ay, 4z,, f=Ax 4zt, f=Ax, Ay,The final form of the difference equation for gas isF(24)(m#-Pr")+F1(2)2-P")+F1(2P)+中国煤化工F(4)4(r#-P)+F:(4)4(-r)+CNMHGPet. Sci(2009)6:405414Similarly, the difference equation for elemental sulfur isF(2):(m1-P")+F1(2D1(P=1-P")+F1()1(Pr#-P")+FA4)(-PNy2(:计-+1(4)4(r1-r")+f(-x)+(-)+(x-)SC,+C; S,+s, )o-[S.,+ S+5, )o.qand the difference equation for non-sulfur components isF(421)(-P)+F1(42):(P-P")+F(42)(P#-P)+F(4z):(PH-P")+F1(4242):(-F")+F21(42):(F-F")p(2)-o22)+q(Edited by Sun Yanhua)中国煤化工CNMHG

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