Application of Operator-Splitting Technique in Numerical Simulation of Gas-Hydrate Reservoirs
- Amir Shahbazi (Computer Modelling Group Ltd.) | Mehran Pooladi-Darvish (Fekete Associates Inc. (Acquired by IHS))
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- July 2013
- Document Type
- Journal Paper
- 1,067 - 1,079
- 2013. Society of Petroleum Engineers
- 5.9.1 Gas hydrates, 5.5 Reservoir Simulation
- 1 in the last 30 days
- 227 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
Modeling of hydrate reservoirs has revealed large time-scale discrepancies between the mechanisms involved. Compared with the fluid- and heat-flow terms,the time scale of the kinetics term is orders of magnitude smaller, especially when the intrinsic reaction rate is large. Previous studies have shown that simulation of hydrates may require very small timesteps to ensure convergence.Further investigations have shown that, for sharp decomposition cases in which dissociation occurs in a narrow region, nonphysical oscillation becomes a simulation issue, unless very small timesteps are chosen. A 3D numerical model incorporating heat and fluid flow with kinetics of decomposition and reformation of hydrates has been developed. In this paper, a methodology forthe use of larger timesteps is proposed without loss of accuracy. The focus ofthis work is on the decoupling of the reaction and flow operators. The decoupling, or so-called operator splitting, allows selection of different timesteps for the different mechanisms. The success of the splitting methodology in saving computational time is demonstrated for two cases. The first case shows oscillatory solutions, and the application of operator splitting allows for an oscillation-free solution at a smaller run time. In the second case, a problem with a range of reaction constants is studied. Obtaining a stable solution without operator splitting requires adjusting the overall timestep, such that the problem with the faster reaction requires very small timesteps. The application of operator splitting in this case allows for a stable solution with much larger timesteps. The contribution of this work is developing a methodology to improve the computational-time of large-scale simulations of gas-hydrate reservoirs without loss of accuracy.
|File Size||1 MB||Number of Pages||14|
Aavatsmark, I., Barkve, T., and Mannseth, T. 1997. Control VolumeDis¬cretization Methods for 3D Quadrilateral Grids in Inhomogeneous,Anisotropic Reservoirs. Paper SPE 38000 presented at the 14th SPE Symposium onReservoir Simulation, Dallas, Texas, 8-11 June. http://dx.doi.org/10.2118/38000-PA.
Abou-Kassem, J. H. and Aziz, K. 1985. Handling of Phase Change in ThermalSimulation. J Pet Tech 37 (9): 1661-1663. http://dx.doi.org/10.2118/13015-PA.
Anderson B. J, Kurihara M., White M. D., et al. 2011. Regional Long-TermProduction Modeling from a Single Well Test, Mount Elbert Gas HydrateStratigraphic Test Well, Alaska North Slope. Marine Pet. Geol. 28 (2): 493-501. http://dx.doi.org/10.1016/j.marpetgeo.2010.01.015.
Brooks, R. H. and Corey, A. T. 1964. Hydraulic Properties of Porous Media.Hydrology Papers, Vol. 3. Fort Collins, Colorado: Colorado StateUniversity.
Cao, H. 2002. Development of Techniques for General Purpose Simulators. PhDdissertation, Stanford University, Stanford, California (June 2002).
Clarke, M. A. and Bishnoi, P. R. 2001. Measuring and Modelling the Rate ofDecomposition of Gas Hydrates Formed from Mixtures of Methane and Ethane.Chem. Eng. Sci. 56 (16): 4715-4724. http://dx.doi.org/10.1016/S0009-2509(01)00135-X.
Coats, K. H., Thomas, L. K., and Pierson, R. G. 1995. Compositional andBlack-Oil Reservoir Simulation. Paper SPE 29111 presented at the SPE ReservoirSimulation Symposium, San Antonio, Texas, 12-15 February. http://dx.doi.org/10.2118/29111-MS.
Computer Modeling Group Ltd. 2007. CMG STARS. Calgary, Alberta, Canada.
Douglas, J. and Rachford, H. H. 1956. On the Numerical Solution of HeatConduction Problems in Two or Three Space Variables. Trans. Am. Math.Soc. 82 (2): 421-439.
Glowinski, R. and Tallec, P. L. 1989. Augmented Lagrangian andOperator-Splitting Methods in Nonlinear Mechanics. Studies in Applied andNumerical Mathematics. Philadelphia: Society for Industrial and AppliedMathematics.
Kamath, V. A. and Holder, G. D. 1987. Dissociation Heat TransferCharacteristics of Methane Hydrates. AIChE J. 33 (2):347-350. http://dx.doi.org/10.1002/aic.690330228.
Kim, H. C., Bishnoi, P. R., Heidemann, R. A., et al. 1987. Kinetics ofMethane Hydrate Decomposition. Chem. Eng. Sci. 42 (7):1645-1653. http://dx.doi.org/10.1016/0009-2509(87)80169-0.
Kurihara, M., H. Ouchi, T. Inoue, T., et al. 2005. Mallik 5L-38 Gas HydrateThermal-Production Test through Numerical Simulation. In Scienti?c Resultsfrom the Mallik 2002 Gas Hydrate Production Research Well Program, MackenzieDelta, Northwest Territories, Canada, ed. S.R. Dallimore, T.S. Collett,A.E. Taylor. Bulletin 585. Ottawa, ON, Canada: Geological Survey of Canada.
Lake, L.W. 1989. Enhanced Oil Recovery. Upper Saddle River, New Jer¬sey:Prentice-Hall Inc.
Li, G., Moridis, G.J., Zhang, K. et al. 2010. Evaluation of Gas ProductionPotential from Marine Gas Hydrate Deposits in Shenhu Area of South China Sea.Energ Fuel 24 (11): 6018-6033. http://dx.doi.org/10.1021/ef100930m.
Li, G., Moridis, G.J., Zhang, K. et al. 2011. The Use of Huff and PuffMethod in a Single Horizontal Well in Gas Production from Marine Gas HydrateDeposits in the Shenhu Area of South China Sea. J Pet Sci Eng 77 (1): 49-68. http://dx.doi.org/10.1016/j.petrol.2011.02.009.
Masuda, Y. S., Naganawa, S., Ando, S. et al. 1997. Numerical Calculation ofGas Hydrate Production Performance from Reservoirs Containing Natural GasHydrates. SPE Asia Paci?c Oil and Gas Conference, Kuala Lumpur, Malaysia, 14-16April.
Masuda. Y., Kurihara, M., Ohuchi, H., and Sato, T. 2002. A ?eld-scalesimulation study on gas productivity of formations containing gas hydrates.,Proceeding of the 4th International Conference on Gas Hydrates, Yokohama,Japan, 19-23 May.
Moridis, G. J., Kowalsky, M. B., Pruess, K. 2005. HydrateResSim UsersManual: A Numerical Simulator for Modeling the Behavior of Hydrates in GeologicMedia. Contract No. DE-AC03-76SF00098. Berkeley, California: Department ofEnergy, Lawrence Berkeley National Laboratory.
Moridis, G. J. and Reagan, M. T. 2007. Strategies for Gas Production fromOceanic Class 3 Hydrate Accumulation. Paper OTC-18865 presented at 2007Offshore Technology Conference, Houston, Texas, April 30-May 3. http://dx.doi.org/10.4043/18865-MS.
Moridis, G. J., Kowalsky, M. B., Pruess, K. 2008. TOUGH HYDRATE v1.0 User'sManual: A Code for the Simulation of System Behavior in Hydrate-BearingGeologic Media. Report LBNL-00149E. Berkeley, California: Lawrence BerkeleyNational Laboratory.
Moridis, G.J., Silpngarmlert, S., Reagan, M.T. et al. 2011. Gas Productionfrom a Cold, Stratigraphically Bounded Gas Hydrate Deposit at the Mount ElbertGas Hydrate Stratigraphic Test Well, Alaska North Slope: Implications ofUncertainties. Marine Pet. Geol. 28 (2): 517-34. http://dx.doi.org/10.1016/j.marpetgeo.2010.01.005.
Parker, J.C., Lenhard, R.J., and Kuppusamy, T. 1987. A Parametric Model forConstitutive Properties Governing Multiphase Flow in Porous Media. WaterResources Research 23 (4), 618-624.
Pooladi-Darvish, M., and Hong, H. 2011. Use of MDT Results Over a HydrateInterval at Mt. Elbert for Long-term Production Forecast: Implications ofUncertainties. Marine Pet. Geol. 28 (2): 535-545. http://dx.doi.org/10.1016/j.marpetgeo.2010.01.006.
Peaceman, D. W. 1978. Interpretation of Well-Block Pressures in NumericalReservoir Simulation. SPE J. 18 (3): 183-194. http://dx.doi.org/10.2118/6893-PA.
Peaceman, D. W. and Rachford Jr., H. H. 1955. The Numerical Solution ofParabolic and Elliptic Differential Equations. J. Soc. Indust. Appl.Math. 3 (1): 28-41. http://dx.doi.org/10.2307/2098834.
Reagan, M. T. and G. J. Moridis. 2009. Large-Scale Simulation of Meth¬aneHydrate Dissociation along the West Spitsbergen Margin. Geophys. Res.Lett. 36: L23612. http://dx.doi.org/10.1029/2009GL041332.
Shahbazi, A. 2010. Mathematical Modeling of Gas Production from Time-steps.PhD dissertation, University of Calgary, Calgary, Alberta, Canada (March2010).
Shahbazi, A. and Pooladi-Darvish, M. 2009. Ice Formation during Gas HydrateDecomposition. Paper presented at the 8th World Congress of ChemicalEngineering, 23-27 August 2009, Montreal, Quebec, Canada.
Shahbazi, A. and Pooladi-Darvish, M. 2010. Behavior of Depressurization inType III Hydrate Reservoirs. Paper SPE 137047 presented at the CanadianUnconventional Resources and International Petroleum Conference, Calgary,Alberta, Canada, 19-21 October. http://dx.doi.org/10.2118/137047-MS.
Strang, G. 1968. On the Construction and Comparison of Difference Schemes.SIAM Journal on Numerical Analysis 5 (3): 506-517. http://dx.doi.org/10.1137/0705041.
Sun, X. and Mohanty, K. K. 2005. Simulation of Methane Hydrate Reser¬voirs.Paper SPE 93015 presented at the 2005 SPE Reservoir Simulation Symposium,Houston, Texas, January 31-February 6. http://dx.doi.org/10.2118/93015-MS.
Sun, X. and Mohanty K. K. 2006. Kinetic Simulation of Methane HydrateFormation and Dissociation in Porous Media. Chem Eng Sci 61(11): 3476-3495. http://dx.doi.org/10.1016/j.ces.2005.12.017.
Uddin, M., Coombe, D. A., Law, D. A., et al. 2006. Numerical Studies ofGas-Hydrates Formation and Decomposition in a Geological Reservoir. Paper SPE100460 presented at SPE Gas Technology Symposium, Calgary, Alberta, Canada,15-17 May. http://dx.doi.org/10.2118/100460-MS.
Van Genuchten, M.T. 1980. A closed-form equation for predicting thehy¬draulic conductivity of unsaturated soils. Soil Science Society ofAmerica Journal 44: 892-898.
Verma, S. and Aziz, K. 1997. A Control Volume Scheme for Flexible Grids inReservoir Simulation. Paper SPE 37999 presented at SPE Reservoir SimulationSymposium, Dallas, Texas, 8-11 June. http://dx.doi.org/10.2118/37999-MS.
White, M. D. and Oostrom, M. 2006. STOMP Subsurface Transport Over MultiplePhase: User's Guide PNNL-15782 (UC-2010). Richland, Washington: Paci?cNorthwest National Laboratory.
Yanenko, N. N. 1971. Splitting Methods for Partial Differential Equations.IFIP Congress (2): 1206-1213.
Zatsepina, O., Hong, H., and Pooladi-Darvish, M. 2008. Behavior of GasPro¬duction from Type III Hydrate Reservoirs. 6th International Conference onGas Hydrates, 6-10 July 2008, Vancouver, British Columbia, Canada.