SPE Introduction The injection of carbon dioxide (CO 2 ), a greenhouse gas (GHG), in coalbeds is probably one of the more attractive

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1 SPE Numerical Simulator Comparison Study for Enhanced Coalbed Methane Recovery Processes, Part I: Pure Carbon Dioxide Injection David H.-S. Law, SPE, Alberta Research Council (ARC) Inc., L.G.H. (Bert) van der Meer, SPE, TNO-NITG and W.D. (Bill) Gunter, SPE, Alberta Research Council (ARC) Inc. Copyright 2002, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the SPE Gas Technology Symposium held in Calgary, Alberta, Canada, 30 April 2 May This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box , Richardson, TX , U.S.A., fax Abstract The injection of carbon dioxide (CO 2 ) in deep, unmineable coalbeds can enhance the recovery of coalbed methane (CBM) and at the same time it is a very attractive option for geologic CO 2 storage as CO 2 is strongly adsorbed onto the coal. Existing CBM numerical simulators which are developed for the primary CBM recovery process, have many important features such as: (1) a dual porosity system; (2) Darcy flow in the natural fracture system; (3) pure gas diffusion and adsorption in the primary porosity system; and (4) coal shrinkage due to gas desorption; taken into consideration. However, process mechanisms become more complex with CO 2 injection. Additional features such as: (1) coal swelling due to CO 2 adsorption on coal; (2) mixed gas adsorption; (3) mixed gas diffusion; and (4) non-isothermal effect for gas injection; have to be considered. This paper describes the first part of a comparison study between numerical simulators for enhanced coalbed methane (ECBM) recovery with pure CO 2 injection. The problems selected for comparison are intended to exercise many of the features of CBM simulators that are of practical and theoretical interest and to identify areas of improvement for modeling of the ECBM process. The first problem set deals with a single well test with CO 2 injection and the second problem set deals with ECBM recovery process with CO 2 injection in an inverted five-spot pattern. Introduction The injection of carbon dioxide (CO 2 ), a greenhouse gas (GHG), in coalbeds is probably one of the more attractive options of all underground CO 2 storage possibilities: the CO 2 is stored and at the same time the recovery of coalbed methane (CBM) is enhanced. 1 The revenue of methane (CH 4 ) production can offset the expenditures of the storage operation. 2,3 Coalbeds are characterized by their dual porosity: they contain both primary (micropore and mesopore) and secondary (macropore and natural fracture) porosity systems. The primary porosity system contains the vast majority of the gas-in-place volume while the secondary porosity system provides the conduit for mass transfer to the wellbore. Primary porosity gas storage is dominated by adsorption. The primary porosity system is relatively impermeable due to the small pore size. Mass transfer for each gas molecular species is dominated by diffusion that is driven by the concentration gradient. Flow through the secondary porosity system is dominated by Darcy flow that relates flow rate to permeability and pressure gradient. The conventional primary CBM recovery process begins with a production well that is often stimulated by hydraulic fracturing to connect the wellbore to the coal natural fracture system via an induced fracture. When the pressure in the well is reduced by opening the well on the surface or by pumping water from the well, the pressure in the induced fracture is reduced which in turn reduces the pressure in the coal natural fracture system. Gas and water begin moving through the natural and induced fractures in the direction of decreasing pressure. When the natural fracture system pressure drops, gas molecules desorb from the primary-secondary porosity interface and are released into the secondary porosity system. As a result, the adsorbed gas concentration in the primary porosity system near the natural fractures is reduced. This reduction creates a concentration gradient that results in mass transfer by diffusion through the micro and mesoporosity. Adsorbed gas continues to be released as the pressure is reduced. When CO 2 (which is more strongly adsorbable than CH 4 ) is injected into the coal natural fracture system during the ECBM recovery process, it is preferentially adsorbed into the primary porosity system. Upon adsorption, the CO 2 drives

2 2 DAVID H.-S. LAW, L.G.H. (BERT) VAN DER MEER AND W.D. (BILL) GUNTER SPE CH 4 from the primary porosity into the secondary porosity system. The secondary porosity pressure is increased due to CO 2 injection and the CH 4 flows to production wells. The CO 2 is stored in-situ and is not produced unless the injected gas front reaches the production wells. The process, in general, is terminated at CO 2 breakthrough. A full understanding of all the complex mechanisms involved in the enhanced coalbed methane recovery process with CO 2 injection (CO 2 -ECBM) is essential to have more confidence in the numerical modeling of the process. The objective of this study of comparison of numerical simulators is to provide the incentive to improve existing CBM simulators for capability and performance assessment of the CO 2 -ECBM recovery process. Decription of CBM Simulators Existing commercial and research CBM simulators are developed, in general, to model primary CBM recovery process taken into account of many important features such as: dual porosity nature of coalbed; Darcy flow of gas and water (i.e., multiphase flow) in the natural fracture system in coal; diffusion of a single gas component (i.e., pure gas) from the coal matrix to the natural fracture system; adsorption/desorption of a single gas component (i.e., pure gas) at the coal surface; and coal matrix shrinkage due to gas desorption. However, Law et al. 4,5 have suggested that in order for a CBM simulator to correctly model the more complicated mechanisms involved in the CO 2 -ECBM recovery process, it has to be improved, taking into account many additional features such as: coal matrix swelling due to CO 2 adsorption on the coal surface; compaction/dilation of the natural fracture system due to stresses; diffusion of multiple gas components (i.e., mixed gas) between the coal matrix and the natural fracture system; adsorption/desorption of multiple gas components (i.e., mixed gas) at the coal surface; non-isothermal adsorption due to difference in temperatures between the coalbed and the injected CO 2 ; and water movement between the coal matrix and the natural fracture system. Five CBM simulators have participated in the comparison study: (1) GEM, Computer Modelling Group (CMG) Ltd., Calgary, Alberta, Canada; (2) ECLIPSE, Schlumberger GeoQuest, Abingdon, Oxon, United Kingdom; (3) COMET 2, Advanced Resources International (ARI), Arlington, Virginia, U.S.A.; (4) SIMED II, Commonwealth Scientific and Industrial Research Organization (CSIRO), Kinnoull Grove, Syndal, Victoria, Australia and the Netherlands Institute of Applied Geoscience TNO, Utrecht, The Netherlands; and (5) GCOMP, BP, Houston, Texas, U.S.A.. These simulators except GCOMP are all commercial in nature. The numerical simulators, GEM and SIMED II, are compositional simulators with additional features for CBM modeling. Due to nature of these simulators, GEM and SIMED II are capable to handle multiple (i.e., 3 or more) gas components. On the other hand, the numerical simulators, ECLIPSE (CBM model) and COMET 2, are black oil simulators with additional features for CBM modeling and only capable to handle two gas components (e.g., CH 4 and CO 2 only). The newly developed COMET 3 by ARI can handle three gas components. This feature is essential in modeling ECBM recovery processes with flue gas (i.e., a mixture of CO 2 and nitrogen (N 2 )) injection. The numerical simulator, GCOMP, is a compositional simulator converted to model the CBM recovery process based on the approach suggested by Seidle and Arri. 6 With the assumption that the diffusion of gases from the primary porosity system into the natural fracture system of the coal is instantaneous, a single porosity approach can be used instead of the dual porosity approach. This approach allows many conventional oil and gas compositional simulators to model CBM recovery processes. A summary of the CBM features, which some have been in existence for several years and others are recently developed, in the five aforementioned simulators is given in Table 1. Although dual porosity approach can be used in GCOMP, single porosity approach is recommended by BP for CBM modeling. Therefore, GCOMP is incapable to handle mixed gas diffusion in this case. On the other hand, ECLIPSE does not incorpate the extended Langmuir isotherm theory 7,8 in the CBM model. However, it has a feature (i.e., relative adsorption for each gas component) to allow the simulator to take into account the non-ideal adsorption behaviour of a two-gas mixture. Approach The approach used in this comparison study, in general, follows those used by a series of SPE comparison studies The authors organize and manage the simulator comparison study; facilitate the development and selection of appropriate test problems; distribute them to identified software developers with commercial CBM simulators and other interested groups of scientists and engineers who want to participate in this exercise; and solicit, collect, reconcile, and document solutions. Development and selection of sample test problems is made on the basis of major mechanisms expected to occur in the CO 2 -ECBM recovery process, taking into account the existing simulation capabilities and future needs. The test

3 NUMERICAL SIMULATOR COMPARISON STUDY FOR ENHANCED COALBED METHANE SPE RECOVERY PROCESSES, PART I: PURE CARBON DIOXIDE INJECTION 3 problems do not necessary represent real field situations. The initial two sets of test problems emphasize the comparison of the performance of CBM simulators, which may only have the features to model the primary CBM recovery process. At a later stage, two more sets of test problems will be developed that address more complicated process mechanisms. At this stage, improvement on some of the existing CBM simulators by incorporating the additional features for CO 2 -ECBM recovery process is necessary. Finally, performance of CBM simulators will be compared for their capability to history match field test data collected by the ARC through performing micro-pilot tests 19 by CO 2 injection into coal seams in Alberta, Canada. 20 The first two sets of test problems have been assembled, which are intended to initiate the study. ARC and TNO have been working very closely with various software developers to compare their CBM simulators and identify/recommend areas of improvement. In fact, most of the numerical runs using GEM, ECLIPSE, SIMED II and GCOMP in this comparison study are conducted in ARC and TNO with the help of the software developers to ensure that the final results are the best representatives of their simulators. Alternatively, participants such as ARI chose to model and study the test problems using their own CBM simulator, COMET 2, with frequent communication with ARC. Descriptions of Test Problem Sets The first problem set deals with a single well test (i.e., micropilot test ) with pure CO 2 injection (see Figure 1) and the second problem set deals with CO 2 -ECBM recovery process in an inverted five-spot pattern (see Figure 2). These two problem sets compare the basic features of the CBM simulators, which allow most simulators to participate in this stage of the study. Darcy flow of gas and water in the natural fracture system in coal; adsorption/desorption of two different gas components (i.e., CH 4 + CO 2 ) at the coal surface; instantaneously gas flow (i.e., diffusion) between the coal matrix and the natural fracture system; no coal matrix shrinkage/swelling due to gas desorption/adsorption; no compaction/dilation of natural fracture system due to stresses; and no non-isothermal adsorption due to difference in temperatures between the coalbed and the injected CO 2. A complete description of the two problem sets as offered to the participants is given in Appendixes A, B and C. The coalbed characteristics are the same for both problem sets. Results All participants are asked to provide the initial gas-in-place (IGIP) (i.e., the adsorbed and the free gas amounts of CH 4 in the coalbed) in their simulation as the first screen of errors in input entry. A list of the initial gas-in-place for both problem sets 1 and 2 for the five CBM simulators is given in Table 2. Since the coalbeds considered in the simulation for problem sets 1 and 2 are 160 acres and ¼ of 2.5 acres, respectively, the IGIP for problem set 1 is 256 times that for problem set 2. It is found that there is good agreement within a few percent error between different simulators. All participants are also asked to ensure their simulations mimick instantaneously gas diffusion between the coal matrix and the natural fracture system for the test problems in this study. Furthermore, five-point diffenering scheme is recommended for the 5-spot pattern simulation in problem set 2, mainly because the more complex nine-point differencing scheme cannot be handled by the dual porosity approach used in some CBM simulators. Problem Set 1. Figure 3 shows a comparison of well bottomhole pressure as a function of time indicating the four operating stages of the single well test: (1) CO 2 injection stage; (2) pressure falloff stage; (3) gas production stage; and (4) pressure buildup stage. Figures 4 and 5 show comparisons of CH 4 /CO 2 production rates and production gas compositions for CH 4 /CO 2 as functions of time, respectively. During the gas production stage, the injected CO 2 near the well is produced first with high rate. But CO 2 production rate declines rapidly as CO 2 around the well is depleted which corresponds to the decline of the production CO 2 composition. On the other hand, CH 4 production rate remains rather constant throughout the gas production stage. Problem Set 2. Figure 6 shows comparisons of CH 4 production rates for the primary CBM and CO 2 -ECBM recovery processes as functions of time indicating the enhancement of CH 4 production due to CO 2 injection. In general, the enhancement of CH 4 production remains until CO 2 breakthough occurs at the producer after approximately 60 days. It is appropriate to mention that due to the presence of an initial gas saturation of 0.408, the typical negative decline in CH 4 production rate in primary CBM recovery process due to pumped-off of water is not observed in this case. Figures 7 and 8 show comparisons of injection bottomhole pressure and CO 2 /total gas production rates as functions of time, respectively. It is found that all simulators predict an initial decline of total gas production rate (i.e., mainly CH 4 production rate) at the beginning of CO 2 injection. This period of declined gas production rate is short (i.e., 2 to 3 days) and mainly due to relative permeability effects. Shortly after CO 2 injection, mobile water in the coalbed is displaced towards the producer that redcues the gas relative permeability around the producer. After majority of the mobile water is produced, the gas relative permeability around the producer increases which corresponds to the increase in CH 4 production rate. The CH 4 production rate reaches a maximum value after approximately 8 days. Under the condition of constant CO 2 injection rate,

4 4 DAVID H.-S. LAW, L.G.H. (BERT) VAN DER MEER AND W.D. (BILL) GUNTER SPE injection bottom-hole pressure declines initially as mobile water is being displaced around the injector and gas injectivity increases. After the decline, the injection bottom-hole remains rather constant until CO 2 breaks through at the producer after approximately 60 days, then the injection pressure gradually increases. It is because after CO 2 breakthrough, the injected CO 2 channels through towards the producer with only very little being adsorbed at the coal surface (i.e., acting as a weakly adsorbable gas). In general, under the condition of constant injection rate, injection pressure for a weakly adsorbable gas (e.g., N 2 ) is higher than that for a strongly adsorbable gas (e.g., CO 2 ). Figure 9 shows a comparison of production gas compositions for CH 4 /CO 2 as a function of time. After CO 2 breakthrough occurs at the producer after approximately 60 days production, CH 4 composition decreases sharply as the production rate of CO 2 increases. This indicates great sweep efficiency in the 5-spot pattern for CO 2 injection, as there is little CH 4 left to produce. Figure 10 shows a comparison of CO 2 distribution as the CO 2 mole fraction in the gas phase in the natural fracture system after 30, 60 and 90 days. This information is not provided by GCOMP. The contour plots represent a ¼ of the 5-spot pattern with injector located at the upper left-hand corner and the producer located at the lower right-hand corner. The CO 2 distribution confirms the good sweep efficiency with CO 2 injection. All well data presented are on a full-well basis and pattern results are for the full 5-spot pattern consisting of four onequarter producers and one full injector (see Figure 2). Discussions In general, there is very good agreement between the results from the different CBM simulators. The differences between the predictions from different simulators may result for a variety of reasons: possible different initialization procedure (e.g, initial gasin-place); possible different dual porosity approach in the simulators; handling of wells (e.g., ¼ well in 5-spot pattern); tolerance on the convergence of iterations; and selection of numerical control parameters. One may anticipate good agreement between the results from different simulators due to the simplicity of the two problem sets. While good agreement does not ensure validity of any of the results, however, a lack of agreement does give cause for some concern for the capability of the simulators to handle not only the primary CBM recovery process but also the more complex ECBM recovery processes. Based on the results of this comparison study, the authors believe that confidence has been established for all participated simulators. The first two simple problem sets can serve as baseline for different CBM simulators when they participate in the comparison of more complex test problems in the later stage of this study. Proposed Test Problem Sets Comparison study on more complex test problems is ongoing. Problem Set 3. Problem set 3 is an enhancement of problem set 2 by taking into account the effect of gas desorption time (or gas diffusion rate) between the coal matrix and the natural fracture system. In order to participate, it is necessary for the CBM simulator to have the additional features of: (1) dual porosity approach; and (2) mixed gas diffusion. Problem Set 4. Problem set 4 is an enhancement of problem set 2 by taking into account the effect of permeability and porosity changes under stress according to the Palmer and Mansoori theory. 21 In order to participate, it is necessary for the CBM simulator to have the additional features of: (1) stress dependent permeability and porosity; and (2) coal shrinkage. Problem Set 5. Problem set 5 is history matching of field test data provided by the ARC. The authors believed that in order to successfully history match the field data, it is necessary for the CBM simulator to have the additional features of: (1) dual porosity approach; (2) mixed gas diffusion; (3) stress dependent permeability and porosity; and (4) coal shrinkage/swelling. It will be a good opportunity to identify the areas needing improvement and validate the CBM simulator. Acknowledgements This study was supported by the University of California Ernest Orlando Lawrence Berkeley National Laboratory (LBNL) under the Contract LBNL No as part of the GEO-SEQ Project funded by the National Energy Technology Laboratory (NETL) of the U.S. Department of Energy (DOE). The authors would like to thank the following people for their helpful discussions and/or participation in this study: GEM Peter Sammon, Computer Modelling Group (CMG) Ltd., Calgary, Alberta, Canada Long Nghiem, Computer Modelling Group (CMG) Ltd., Calgary, Alberta, Canada Mohamed Hassam, Computer Modelling Group (CMG) Ltd., Calgary, Alberta, Canada ECLIPSE Jim Bennett, Schlumber GeoQuest, Abingdon, Oxon, U.K. Sridhar Srinivassen, Schlumber GeoQuest, Calgary, Alberta, Canada Tim Hower, Malkewicz Hueni Associates, Denver, Colorado, U.S.A.

5 NUMERICAL SIMULATOR COMPARISON STUDY FOR ENHANCED COALBED METHANE SPE RECOVERY PROCESSES, PART I: PURE CARBON DIOXIDE INJECTION 5 COMET 2 Larry Pekot, Advanced Resources International (ARI), Arlington, Virginia, U.S.A. Scott Reeves, Advanced Resources International (ARI), Houston, Texas, U.S.A. SIMED II Xavior Choi, Commonwealth Scientific and Industrial Research Organization (CSIRO), Kinnoull Grove, Syndal, Victoria, Australia GCOMP John Mansoori, BP, Houston, Texas, U.S.A. Mel Miner, Marlet Consulting, Calgary, Alberta, U.S.A. Nomenclature G s = gas storage capacity, m 3 /kg G sl = dry, ash-free Langmuir storage capacity, m 3 /kg G si = multicomponent storage capacity of component i, in-situ basis, m 3 /kg G sli = single component Langmuir storage capacity of component i, dry, ash-free basis, m 3 /kg nc = number of components p = pressure, kpa p L = Langmuir pressure, kpa p Li or p Lj = single component Langmuir pressure of component i or j, kpa w a = ash content, weight fraction w we = equilibrium moisture content, weight fraction y i or y j = mole fraction of component i or j in the free gas (vapor) phase Metric Conversion Factors C 1.8 C +32 = F km (10 2 ) = acre kg/m (10-2 ) = lb/ft 3 kpa = psia m = ft m 3 /d (10 1 ) = scf/d m 3 /kg (10 4 ) = scf/ton References 1. Gunter, W.D., Gentzis, T., Rottenfusser, B.A. and Richardson, R.J.H.: Deep Coalbed Methane in Alberta, Canada: A Fuel Resource with The Potential of Zero Greenhouse Gas Emissions, Energy Convers. Mgmt, Volume 38, Suppl., (1997) S217-S Wong, S., Gunter, W.D. and Mavor, M.J.: Economics of CO 2 Sequestration in Coalbed Methane Reservoirs, Proceedings of SPE/CERI Gas Technology Symposium 2000, Paper SPE 59785, Calgary, Alberta, Canada, April 3-5, (2000) Wong, S., Gunter, W.D., Law, D.H.-S. and Mavor, M.J.: Flue Gas Injection and CO 2 Sequestration in Coalbed Methane Reservoirs, Economic Considerations, presented at The 5 th International Conference on Greenhouse Gas Control Technologies (GHGT-5), Cairns, Australia, (2000) August Law, D.H.-S., van der Meer, L.G.H. and Gunter, W.D.: Modelling of Carbon Dioxide Sequestration in Coalbeds: A Numerical Challenge, presented at The 5 th International Conference on Greenhouse Gas Control Technologies (GHGT- 5), Cairns, Australia, (2000) August Law, D.H.-S., van der Meer, L.G.H. and Gunter, W.D.: Comparison of Numerical Simulators for Greenhouse Gas Storage in Coalbeds, Part I: Pure Carbon Dioxide Injection, presented at The 1 st National Conference on Carbon Sequestration, Washington, D.C., U.S.A., (2001) May Seidle, J.P. and Arri, L.E.: Use of Conventional Reservoir Models for Coalbed Methane Simulation, Paper CIM/SPE , presented at The Canadian Institute of Mining (CIM)/ Society of Petroleum Engineers (SPE) International Technical Meeting, Calgary, Alberta, Canada, (1990) June Langmuir, I.: The Adsorption of Gases on Plane Surface of Glass, Mica and Platinum, Journal of the American Chemical Society, Volume 40, (1918) Arri, L.E., Yee, D., Morgan, W.D. and Jeansonne, N.W.: Modeling Coalbed Methane Production with Binary Gas Sorption, Paper SPE 24363, presented at The SPE Rocky Mountain Regional Meeting, Casper, Wyoming, U.S.A., (1992), May Odeh, A.S.: Comparison of Solutions to a Three-Dimensional Black Oil Reservoir Simulation Problem, JPT, Volume 33, (1981) Weinstein, H.G., Chappelear, J.E. and Nolen, J.S.: Second Comparative Solution Project: A Three-Phase Coning Study, JPT, Volume 38, (1986) Kenyon, D.E. and Behie, G.A.: Third SPE Comparative Solution Project: Gas Cycling of Retrograde Condensate Reservoirs, JPT, Volume 39, (1987) Aziz, K., Ramesh, A.B. and Woo, P.T.: Fourth SPE Comparative Solution Project: Comparison of Steam Injection Simulators, JPT, Volume 39, (1987) Killough, J.E. and Cossack, C.: Fifth SPE Comparative Solution Project: Evaluation of Miscible Flood Simulators, Paper SPE 16000, presented at the 9 th SPE Symposium on Reservoir Simulation, San Antonio, Texas, U.S.A., (1987) February Frioozabadi, A. and Thomas, K.: Sixth SPE Comparative Solution Project: Dual Porosity Simulators, JPT, Volume 42 (1990) Nghiem L., Collins D. A. and Sharma R.: Seventh SPE Comparative Solution Project: Modelling of Horizontal Wells in Reservoir Simulation, Paper SPE 21221, presented at the 11 th SPE Symposium on Reservoir Simulation, Anaheim, California, U.S.A., (1991) February Quandalle P.: Eighth SPE Comparative Solution Project: Gridding Techniques in Reservoir Simulation, Paper SPE 25263, presented at the 12 th SPE Symposium on Reservoir Simulation, New Orlean, Louisiana, U.S.A., (1993) February 28-March Killough, J.E.: Ninth SPE Comparative Solution Project: A Reexamination of Black-Oil Simulation, Paper SPE 29110, presented at the 13 th SPE Symposium on Reservoir Simulation, San Antonio, Texas, U.S.A., (1995) February Christie, M.A. and Blunt, M.J.: Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques, Paper SPE 66599, presented at the SPE Reservoir Simulation Symposium, Houston, Texas, U.S.A., (2001) February Puri, R., Voltz, R. and Duhrkopf, D.: A Micro-Pilot Approach to Coalbed Methane Reservoir Assessment, Proceedings of

6 6 DAVID H.-S. LAW, L.G.H. (BERT) VAN DER MEER AND W.D. (BILL) GUNTER SPE Intergas 95, University of Alabama/Tuscaloosa, Paper 9556, Tuscaloosa, Alabama, U.S.A., (1995) May 15-19, Wong, S. and Gunter, W.D.: Testing CO 2 Enhanced Coalbed Methane Recovery, Greenhouse Issues, IEA Greenhouse Gas R&D Programme, Volume 45, (November 1999) Gash, B.W., Measurement of Rock Properties in Coal for Coalbed Methane Production, Paper SPE 22909, presented at The 66 th SPE Annual Technical Conference and Exhibition, Dallas, Texas, U.S.A., (1991) October Palmer, I. And Mansoori, J.: How Permeability Depends on Stress and Pore Pressure in Coalbeds: A New Model, Paper SPE 36737, presented at 1996 SPE Annual Technical Conference and Exhibition, Denver, Colorado, U.S.A., (1996) October 6-9. Appendix A Coalbed Characteristics The problem sets have as many common features as possible (e.g., coalbed characteristics, well radius, etc.). Coalbed Properties Coal seam thickness = 9 m [ ft] Top of coal seam = m [ ft] Absolute permeability of natural fracture = 3.65 md Porosity of natural fracture system = Effective coalbed compressibility = 1.45 x 10-7 /kpa [1 x 10-6 /psia] Initial Reservoir Conditions Temperature = 45ºC [113ºF] Pressure (assumed uniform from top to bottom) = 7650 kpa [ psia] Gas saturation = (100% CH 4 ) Water saturation = Water Properties at 45ºC (113ºF) Density = 990 kg/m 3 [61.8 lb/ft 3 ] Viscosity = cp Compressibility = 5.8 x 10-7 /kpa [4 x 10-6 /psia] Pure Gas Adsorption Isotherms at 45ºC (113ºF) Average in-situ coal density = 1434 kg/m 3 [89.5 lb/ft 3 ] Average in-situ moisture content (by wt.), w we = Average in-situ ash content (by wt.), w a = The dry, ash-free isotherm parameters shown in Table A-1 will be used to estimate the in-situ storage capacity as a function of pressure, ash content, and in-situ moisture content using the Langmuir relationship: 7 G s p = GsL[ 1 ( wa + wwe )] A-1 p + p where: G s G sl w a w we p p L L gas storage capacity dry, ash-free Langmuir storage capacity ash content, weight fraction equilibrium moisture content, weight fraction pressure Langmuir pressure The individual component isotherm parameters are used to compute storage capacity when multiple gas species are present. The computation is based upon extended Langmuir isotherm theory. 8 The extended Langmuir isotherm relationship is listed as following: pyi pli G si = GsLi [ 1 ( wa + wwe )] A-2 nc y j 1 + p p j= 1 where: G si multicomponent storage capacity of component i, in-situ basis G sli single component Langmuir storage capacity of component i, dry, ash-free basis p Li or p Lj single component Langmuir pressure of component i or j y i or y j mole fraction of component i or j in the free gas (vapor) phase nc number of components p pressure of the free gas phase Relative Permeability Data The relative permeability relationship shown in Table A-2 is based upon the relationship published by Gash. 21 No effect of temperature or hysteresis on the relative permeability is considered and the capillary pressures are assumed to be zero. Appendix B Problem Set 1 Problem 1: Single well CO 2 injection test Grid System Cylindrical (r-θ-z) grid system: (see Figure 1) Area = 160 acres Radius = 454 m [1,489.5 ft] r-direction: see Table B-1 θ-direction: θ = 360º z-direction: z = 9 m [29.5 ft] Operating Conditions Well location: (i = 1, j = 1, k = 1) Well radius (2 7/8 well): m Well skin factor = 0 Lj [ ft] 15-day CO 2 injection period (0 15 days): CO 2 injection rate (full well) = 28, sm 3 /d [1 x 10 6 scf/d] Maximum bottom-hole pressure = 15,000 kpa [2,175.6 psia] 45-day shut-in period (15 60 days) Well shut-in for pressure falloff

7 NUMERICAL SIMULATOR COMPARISON STUDY FOR ENHANCED COALBED METHANE SPE RECOVERY PROCESSES, PART I: PURE CARBON DIOXIDE INJECTION 7 60-day production period ( days) Maximum gas production rate (full well) = 100,000 m 3 /d [ x 10 6 scf/d] Minimum bottom-hole pressure = 275 kpa [ psia] 62.5-day shut-in period ( days) Well shut-in for pressure buildup Appendix C Problem Set 2 Problem 2: 5-spot CO 2 -ECBM recovery process Grid System Rectangular (x-y-z) grid system: (see Figure 2) Area = ¼ of a 2.5 acres pattern Pattern half width = m [165 ft] x and y-directions: see Table C-1 z-direction: z = 9 m [29.5 ft] Operating Conditions Well locations: Injection well: (i = 1, j = 1, k = 1) Production well: (i = 11, j = 11,k = 1) Well radius (2 7/8 well): m [ ft] Well skin factor = day continuous CO 2 injection/production period ( days): CO 2 injection rate (full well) = 28, sm 3 /d [1 x 10 6 scf/d] Maximum bottom-hole pressure = 15,000 kpa [2,175.6 psia] Maximum gas production rate (full well) = 100,000 m 3 /d [ x 10 6 scf/d] Minimum bottom-hole pressure = 275 kpa [ psia] Problem 2P: 5-spot primary CBM recovery process Grid System Same as Problem 2 Operating Conditions Well locations: Production well: (i = 11, j = 11,k = 1) Well radius (2 7/8 well): m [ ft] Well skin factor = day continuous gas production period ( days): Maximum gas production rate (full well) = 100,000 m 3 /d [ x 10 6 scf/d] Minimum bottom-hole pressure = 275 kpa [ psia]

8 8 David H.-S., L.G.H. (Bert) van der Meer and W.D. (Bill) Gunter SPE Table 1: Features for modeling coalbed methane (CBM) recovery processes CBM Simulators GEM ECLIPSE COMET SIMED II GCOMP Mutliple Gas Components (3 or more: CH 4, CO 2 & N 2) Dual Porosity Approach Mixed Gas Diffusion (Different Diffusion Rates) Mixed Gas Adsorption (Extended Langmuir Model) Stress Dependent Permeability and Porosity Coal Shrinkage/Swelling Table 2: Initial gas-in-place for problem sets 1 and 2 CBM Simulators GEM ECLIPSE COMET 2 SIMED II GCOMP Problem Set 1 Initial gas-in-place (sm 3 ) 160-acres x x x x x10 7 Problem Set 2 Initial gas-in-place (sm 3 ) ¼ 2.5 acres 5-Spot Pattern x x x x x10 5 Table A-1: Dry, ash-free Langmuir isotherm parameters Methane Carbon Dioxide Nitrogen Langmuir Pressure, P L Dry, Ash-Free Langmuir Volume, G sl kpa psia kpa psia kpa psia 4, , ,241 3,951 m 3 /kg scf/ton m 3 /kg scf/ton m 3 /kg scf/ton Table A-2: Relative permeability relationship Water Saturation S w Rel. Perm. to Water k rw Rel. Perm. to Gas k rg Water Saturation S w Rel. Perm. to Water k rw Rel. Perm. to Gas k rg

9 NUMERICAL SIMULATOR COMPARISON STUDY FOR ENHANCED COALBED METHANE SPE RECOVERY PROCESSES, PART I: PURE CARBON DIOXIDE INJECTION 9 Table B-1: Radial grid system used for Problem Set 1 r r i (m) (ft) (m) (ft) Table C-1: Rectangular grid system used for Problem Set 2 x or y x or y i or j (m) (ft) (m) (ft)

10 10 DAVID H.-S. LAW, L.G.H. (BERT) VAN DER MEER AND W.D. (BILL) GUNTER SPE x 1 Grid System 9 m 454 m Figure 1: Schematic diagram of radial grid system used in problem set 1 P P 1/4 of 2.5-acre 5-Spot Pattern 11 x 11 Grid System I I P P m P Figure 2: Schematic diagram of rectangular grid system used in problem set 2

11 NUMERICAL SIMULATOR COMPARISON STUDY FOR ENHANCED COALBED METHANE SPE RECOVERY PROCESSES, PART I: PURE CARBON DIOXIDE INJECTION 11 CO 2 Injection Pressure Falloff Pressure Buildup Gas Production Figure 3: Problem set 1 well bottom-hole pressure CO 2 CH 4 Figure 4: Problem set 1 CH 4 and CO 2 production rates

12 12 DAVID H.-S. LAW, L.G.H. (BERT) VAN DER MEER AND W.D. (BILL) GUNTER SPE CO 2 CH 4 Figure 5: Problem set 1 Production gas compositions for CH 4 and CO 2 CO 2 Injection Primary Figure 6: Problem set 2 CH 4 proudction rate for primary CBM and CO 2-ECBM recovery processes for full 5-spot pattern

13 NUMERICAL SIMULATOR COMPARISON STUDY FOR ENHANCED COALBED METHANE SPE RECOVERY PROCESSES, PART I: PURE CARBON DIOXIDE INJECTION 13 Figure 7: Problem set 2 Injection bottom-hole pressure Total CO 2 Figure 8: Problem set 2 CO 2 and total gas production rates for full 5-spot pattern

14 14 DAVID H.-S. LAW, L.G.H. (BERT) VAN DER MEER AND W.D. (BILL) GUNTER SPE CH 4 CO 2 Figure 9: Problem set 2 Production gas compositions for CH 4 and CO 2 CO 2 Mole Fraction in Gas Phase in Fracture CO 2 30 days 60 days 90 days GEM ECLIPSE COMET2 SIMED II Figure 10: Problem set 2 CO 2 distributions as CO 2 mole fraction in gas phase in natural fracture system