Application of M3GM in a Petroleum Reservoir Simulation

Document Type: Research Paper

Authors

K. N. Toosi University, Civil department

Abstract

Reservoir formations exhibit a wide range of heterogeneity from micro to macro scales. A simulation that involves all of these data is highly time consuming or almost impossible; hence, a new method is needed to meet the computational cost. Moreover, the deformations of the reservoir are important not only to protect the uppermost equipment but also to simulate fluid pattern and petroleum production strategy. In this regard, multiscale multiphysic mixed geomechanical model (M3GM) is recently developed. However, applications of petroleum reservoirs through gas or water injection in the depleted reservoir are in concern. In the present paper, a multiscale finite volume framework and a finite element method are employed to simulate fluid flow and rock deformation respectively. The interactions of solid and fluid phases are instated through the M3GM framework. Then, its application in the petroleum reservoir through injection process is validated. The numerical results are compared with the fine scale simulations and reasonable agreement with high computational efficiency is obtained.

Keywords


REFERENCES

Aarnes J. E., “On the Use of a Mixed Multiscale Finite Element Method for Greater Flexibility and Increased Speed or Improved Accuracy in Reservoir Simulation,” Multiscale Model Simul., 2004, 2, 421-439.

Arbogast T., “Implementation of a Locally Conservative Numerical Sub-grid Upscaling Scheme for Two-phase Darcy Flow,” Comput. Geosci., 2002, 6, 453-481.

Durlofsky L. J., “Numerical Calculation of Equivalent Grid Block Permeability Tensors for Heterogeneous Porous Media,” Water Resource Research, 1991, 27, 699-708.

Durlofsky L. J., “Upscaling of Geocellular Models for Reservoir Flow Simulation: A Review of Recent Progress,” International Forum on Reservoir Simulation. Buhl/Baden-Baden, Germany, 2003, 1-58.

Farmer C. L., “Upscaling: A review,” Int. J. Numer. Meth Fluids, 2002, 40, 63-78.

Chen Z. and Hou T. Y., “A mixed multiscale finite element method for elliptic problems with oscillating coefficients,” Math. Comput., 2002, 72, 541–576.

Efendiev Y., Ginting V., Hou T. Y., and Ewing R., “Accurate Multiscale Finite Element Methods for Two-phase Flow Simulations,” J. Comp. Phys., 2006, 220, 155–174.

Hajibeygi H. and Jenny P., “Multiscale Finite-volume Method for Parabolic Problems Arising from Compressible Multiphase Flow in Porous Media,” Computational Physics, 2009, 228, 5129-5147.

Sadrnejad S. A., Ghasemzadeh H., and Taheri E., “Multiscale Multiphysic Mixed Geomechanical Model in Deformable Porous Media,” Journal for Multiscale Computational Engineering, 2014, 12(6), 529-547.

Taheri E., “Multiscale Modeling of Oil Transport in Deformable Porous Media,” Ph.D. Thesis, K. N. Toosi University of Technology, 2015.

Lewis R. W. and Schrefler B. A., “Finite Element Method in the Static and Dynamics Deformation and Consolidation of Porous Media,” (2nd Ed.) England, Wiley, 1998.

Bruno M. S. “Subsidence-induced Well Failure,” In SPE (Chevron Oil Field Research, Society of Petroleum Engineers), SPE 20058-PA, 1992.

Rhett D. W. and Revisited E., “A New Model of Ekofisk Reservoir Geomechanical Behavior,” In SPE/ISRM Rock Mechanics in Petroleum Engineering, (Trondheim, Norway 1998), 1990.

Carbognin L., Gatto P., Mozzi G., and Gambolati G., “Land subsidence of Ravenna and its similarities with the Venice case. Proceedings of the Engineering Foundation Conference on Evaluation and Prediction of Subsidence,” New York: ASCE, 1978, 254-266.

Lewis R. W. and Sukirman Y., “Finite Element Modelling for Simulating the Surface Subsidence above a Compacting Hydrocarbon Reservoir,” Int. J. Analytic. Numer. Meth. Geomech., 1993, 18, 619-639.

Li X. and Zienkiewicz O. C., “Multiphase Flow in Deforming Porous Media and Finite Element Solutions,” Computers & Structures, 1992, 45(2), 211-227.

Minkoff S. E., Stone C. M., Bryant S., Peszynska M., et al., “Coupled Fluid Flow and Geomechanical Deformation Modeling,” Journal of Petroleum Science and Engineering, 2003, 38, 37-56.

Phillips P. J. and Wheeler M. F. “A Coupling of Mixed and Continuous Galerkin Finite Element Methods for Poroelasticity I: the Continuous in Time Case,” Comput. Geosci., 2007, 11, 131-144.

Phillips P. J. and Wheeler M. F., “A Coupling of Mixed and Continuous Galerkin Finite Element Methods for Poroelasticity II: The Discrete-in-time Case,” Comput. Geosci., 2007, 11, 145-158.

Settari A. and Walters D. A., “Advances in Coupled Geomechanical and Reservoir Modeling With Applications to Reservoir Compaction,” SPE Reservoir Simulation Symposium, Houston, Texas, 1999.

Settari A. and Mourits F. M., “Coupling of Geomechanics and Reservoir Simulation Models. Proc. Of the 8th Int. Conf. on Computer Methods and Advances in Geomechanics,” Morgantown, West Virginia, 1994, 2097-2158.

Dean R. H., Gai X., Stone C. M., and Minkoff S. E., “A Comparison of Techniques for Coupling Porous Flow and Geomechanics,” In SPE Reservoir Simulation Symposium (Houston 2003), SPE 79709, 2003.

Gutierrez M. and Lewis R. W. “The Role of Geomechanics in Reservoir Smulation,” In Proceedings of the SPE/ISRME; ROCK198, (SPE paper 47392) (Trondheim, Norway, 1998.

Gutierrez M., Lewis R. W., and Masters I. “Petroleum Reservoir Simulation Coupling Fluid and Geomechanics,” SPE Reservoir Evaluation & Engineering, 2001, 4, 164-171.

Wan J., Durlofsky L. J., Hughes T. J. R., and Aziz K. “Stabilized Finite Element Methods for Coupled Geomechanics Reservoir Flow simulations,” In SPE Res Simul Sym (SPE 79694) (Houston 2003).

Jeannin L., Mainguy M., Masson R., and Gilbert S. V. “Accelerating the Convergence of Coupled Geomechanical-reservoir Simulations,” Int. J. Numer. Anal. Meth. Geomech., 2007, 31, 1163–1181.

Prevost J. H. “Partitioned Solution Procedure for Simultaneous Integration of Coupled-field Problems,” Commun. Numer. Meth. Engng., 1997, 13, 239-247.

Wheeler M. F. and Gai X., “Iteratively Coupled Mixed and Galerkin Finite Element Methods for Poroelasticity,” Numer Meth for PDEs, 2007, 23, 785–797.

Kim J., Tchelepi H. A., and Juanes R., “Rigorous Coupling of Geomechanics and Multiphase Flow with Strong Capillarity,” SPE Journal, 2013, 1123-1139.

Aarnes J. E., Kippe V., Lie K. A., and Rustad A. B. “Modelling of Multiscale Structures in Flow Simulations for Petroleum Reservoirs in Geometrical Modeling,” Numerical Simulation and Optimization Applied Mathematics at SINTEF. Springer, Verlag, 2007.

Sadrnejad S. A., Ghasemzadeh H., and Taheri E., “Multiscale Advance Features in Modeling Oil Transport in Porous Media,” In 21st Annual International Conference on Mechanical Engineering-ISME, Tehran, Iran, 2013.

Wen X. H., Durlofsky L. J., and Edwards M. G., “Use of Border Regions for Improved Permeability Upscaling,” Mathematical Geology, 2003, 35, 521-547.

Jenny P., Lee S. H., and Tchelepi H. A., “Multi-scale Finite-volume Method for Elliptic Problems in Subsurface Flow Simulation,” Computational Physics, 2003, 187, 47-67.

Jenny P., Lee S. H., and Tchelepi H. A. “Adaptive Fully Implicit Multi-scale Finite-volume Method for Multi-phase Flow and Transport in Heterogeneous Porous Media,” Journal of Computational Physics, 2006, 217, 627-641.

Lee S. H., Wolfsteiner C., and Tchelep H. A., “Multiscale Finite-volume Formulation for Multiphase Flow in Porous Media: Black Oil Formulation of Compressible, Three-phase Flow with Gravity,” Computational Geoscience, 2008, 12, 351-366.

King M. J., MacDonald D. G., Todd S. P., and Leung, H., “Application of Novel Upscaling Approaches to the Magnus and Andrew Reservoirs,” SPE European Petroleum Conference. The Hague, The Netherlands, SPE 50643, 1998.

Chen Y., Durlofsky L. J., Gerritsen M., and Wen X. H., “A Coupled Local–global Upscaling Approach for Simulating Flow in Highly Heterogeneous Formations,” Advances in Water Resources, 2003, 26, 1041-1060.

Wen X. H., Durlofsky L. J., and Edwards M. G., “Upscaling of Channel Systems in Two Dimensions Using Flow-based Grids,” Transport in Porous Media, 2003, 51, 343–366.

Peszy´nska M., Wheeler M. F., and Yotov I., “Mortar upscaling for multiphase flow in porous media,” Comput. Geosci., 2002, 6, 73-100.

Christie M. and Blunt M. , “Tenth SPE Comparative Solution Project: a Comparison of Upscaling Techniques,” SPE Reserv. Evaluat. Eng., 2001, 4, 308–317.

Durlofsky L. J. “Upscaling of Geocellular Models for Reservoir Flow Simulation: A Review of Recent Progress,” In International Forum on Reservoir Simulation (Buhl/Baden-Baden), Germany, 2003, 1-58.

Jenny P., Lee S. H., and Tchelepi. H. A., “Adaptive Multiscale Finite-Volume Method For Multiphase Flow And Transport In Porous Media,” Multiscale Model. Simul., 2004, 3, 50-64.

Lee S. H., Wolfsteiner C., and Tchelep H. A., “Multiscale Finite-volume Formulation for Multiphase Flow in Porous Media: Black Oil Formulation of Compressible, Three-phase Flow with Gravity,” Computational Geoscience, 2008, 12, 351-366.

Jenny P. and Lunati I. “Modeling Complex Wells with the Multi-scale Finite-volume Method,” Journal of Computational Physics, 2009, 228, 687–702.

Lee S. H., Zhou H., and Tchelepi H. A. “Adaptive Multiscale Finite-volume Method for Nonlinear Multiphase Transport in Heterogeneous Formations,” Journal of Computational Physics, 2009, 228, 9036–9058.

Lunati I. and Jenny P., “Multiscale Finite-volume Method for Density-driven Flow in Porous Media,” Computational Geoscience, 2008, 12, 337-350.

Hajibeygi H., Bonfigli G., Hesse M. A., and Jenny P., “Iterative Multiscale Finite-volume Method,” Journal of Computational Physic, 2008, 227, 8604–8621.

Hajibeygi H. and Jenny P. “Adaptive Iterative Multiscale Fnite Volume Method,” J. Comput. Phys., 2011, 230, 628–643.

Aarnes J. E. and Efendiev Y. “Mixed Multiscale Finite Element for Stochastic Porous Media Flows,” SIAM Sci. Comp., 2008, 30, 2319–2339.

Efendiev Y., Ginting V., Hou T. Y., and Ewing R. “Accurate Multiscale Finite Element Methods for Two-phase Flow Simulations,” J. Comp. Phys., 2006, 220, 155–174.

Efendiev Y., Hou T. Y., and Wu X. H., “Convergence of a Nonconforming Multiscale Finite Element Method,” SIAM J. Numer. Anal., 2000, 37, 888–910.

Hou T. Y., Wu X. H., and Cai Z. “Convergence of a Multiscale Finite Element Method for Elliptic Problems With Rapidly Oscillating Coefficients,” Math. Comput., 1999, 68, 913–943.

Efendiev Y. and Hou T. Y. “Multiscale Finite Element Methods Theory and Applications,” Series: Surveys and Tutorials in the Applied Mathematical Sciences, Springer, 2009.

Lunati I. and Jenny P., “Treating Highly Anisotropic Subsurface Flow With The Multiscale Finite-Volume Method,” Multiscale Model. Simul., 2007, 6, 308-318.

Samier P., Quettier L., and Thiele M. “Applications of Streamline Simulations to Reservoir Studies,” SPE Res. Eval. & Eng., SPE-78883-PA, 2002, 5(4): 324–332.

Baker R. O., Kuppe F., and Chug S., et al., “Full-Field Modeling Using Streamline-Based Simulation: 4 Case Studies,” Presented at the SPE Reservoir Simulation Symposium, SPE-66405-MS, Houston, Texas, 2001.

White I. R. and Lewis R. W., “The Numerical Simulation of Multiphase Flow Through a Porous Medium and its Application to Reservoir Engineering,” Applied Mathematical Modelling, 1981, 5(3), 165–172.

Geiger S., Roberts S., Mattha S. K., Zoppou C., et al., “Combining Finite Element and Finite Volume Methods for Efficient Multiphase Flow Simulations in Highly Heterogeneous and Structurally Complex Geologic Media,” Geofluids, 2004, 4, 284–299.