Upscaling of unstable miscible displacements and multiphase flows using multiresolution wavelet transformation

SPE Reservoir Simulation Symposium, Proceedings

Volumn , Issue , 2005, Pages 387-401

  Sahimi, M ^a   Rasaei, R ^a,b   Ebrahimi, F ^a,c   Haghighi, M ^b  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b UNIVERSITY OF TEHRAN   (Iran)

^c U of Birjand   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; COMPUTER SIMULATION; MECHANICAL PERMEABILITY; PETROLEUM RESERVOIRS; PROBLEM SOLVING; WAVELET TRANSFORMS;

GEOLOGICAL MODELS; RESERVOIR SIMULATIONS; TOTAL VARIATION DIMINISHING (TVD); WAVELET TRANSFORMATIONS;

MULTIPHASE FLOW;

EID: 22244449372     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2523/93320-ms     Document Type: Conference Paper

References (88)

1. M. Sahimi, Flow and Transport in Porous Media and Fractured Rocks, Second Revised and Expanded Edition (Wiley-VCH, Weinheim, Germany, 2005).
2. Coats K.H., Dempsey J.R., and Henderson J.H., "The use of vertical equilibrium in two dimensional simulation of three- dimensional reservoir performance", SPE 2797 (1971).
3. Hearn C.L., "Simulation of stratified waterflooding by pseudo relative permeability curves", JPT 23, 805 (1971).
4. Jacks H.H., Smith O.J.E., and Mattax C.C., "The modeling of a three-dimensional reservoir by a two-dimensional reservoir simulator-the use of dynamic pseudo functions", SPE 4071 (1973).
5. Starley G.P., "A material balance method for driving interblock water/oil pseudofimctions for coarse grid reservoir simulation", SPE 15621 (1988).
6. Emmanuel A.S., and Cook G.W., Pseudo-relative permeability for well modeling, SPE 4731 (1974).
7. Kyte J.R., and Berry D.W.," New pseudo functions to control numerical dispersion", SPE 5105 (1975).
8. Lasseter T.J., Waggoner J.R., and Lake L.W., Reservoir heterogeneities and their influence on ultimate recovery, in Reservoir Characterization, edited by L.W. Lake and H.B. Carroll (Academic Press, Orlando, 1986).
9. Kossack C.A., Aasen J.O., and Opdal S.T., "Scaling-up laboratory permeabilities and rock heterogeneities with pseudo functions for field simulations", SPE 18436 (1989).
10. Stone H.L., "Rigorous black oil pseudo functions", SPE 21207 (1991).
11. Hewett T.A., and Berhens R.A., Scaling laws in reservoir simulation and their use in a hybrid finite difference/streamtube approach to simulating the effects of permeability heterogeneity, in Reservoir Characterization II, edited by L.W. Lake, H.B.Carroll, and T.C. Wesson (Academic Press, San Diego, 1991).
12. Beier R.A., "Pseudo relative permeabilities from fractal distributions", SPE 24371 (1992).
13. Pickup G.E., and Sorbie K.S., "Development and application of a new two-phase scaleup method based on tensor permeabilities", SPE 28586 (1994).
14. Lohne A., Virnovsky G., and Durlofsky L.J., "Two-stage upscaling of two-phase flow: from core to simulation scale", SPE 89422 (2004).
15. Ciammetti G., Ringrose P.S., Good T.R., Lewis J.M.L., and Sorbie K.S., "Waterflood recovery and fluid flow upscaling in a shallow Marian and Fluvial sandstone sequence"e, SPE 30783 (1995).
16. Stephen K.D., Clark J.D., and Pickup G.E., "Modeling and flow simulations of a North Sea Turbidite reservoir: sensitivities and upscaling", SPE 78292 (2002).
17. Barker J.W., and Thibeau S., "A critical review of the use of pseudo relative permeabilities for upscaling", SPE 35491 (1996).
18. Barker J.W., and Dupouy P., An analysis of dynamic pseudo relative permeabilities methods, Proceedings of the Fifth European Conference on the Mathematics of Oil Recovery, Leoben, Austria (1996).
19. Ram\'e M., and Killough J.E., "A new approach to the simulation of flows in highly heterogeneous porous media", SPE 21247 (1991).
20. Verdiere S., Guerillot D., and Thomas J.M., Dual mesh method for multiphase flows in heterogeneous reservoirs, Proceedings of Fifth European Conference on the Mathematics of Oil Recovery, Leoben, Austria (1996).
21. Gautier Y., Blunt M.J., and Christie M.A., "Nested griding and streamline-based simulation for fast reservoir performance prediction", Comput. Geosci. 3, 295 (1999).
22. Guedes S.S., and Schiozer D.J., "An implicit treatment of upscaling in numerical reservoir simulation", SPE 51937 (1999).
23. Hermitte T., and Gu\'erillot, D., "A more accurate numerical scheme for locally refined meshes in heterogeneous reservoirs", SPE 25261 (1995).
24. Arbogast T., and Bryant S. L., "Numerical subgrid upscaling for waterflood simulations", SPE 66375 (2001).
25. Hou T.Y., and Wu X.H., "A multiscale finite element method for elliptic problems in composite materials and porous media", J. Comput. Phys. 134, 169 (1997).
26. Hou T.Y., Wu X.H., and Cai X.," Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients", Math. Comput. 227, 913 (1999).
27. Audigane P., and Blunt M.J., "Dual mesh method in upscaling", SPE 79681 (2003).
28. Audigane P., and Blunt M.J., "Dual mesh method for upscaling in waterflood simulation", Trans. Porous Media 55, 71 (2004).
29. Durlofsky L.J., Jones R.C., and Milliken W.J., "A non-uniform coarsening approach for the scale up of displacement processes in heterogeneous porous media", Adv. Water Resour., 20, 5-6, 335- 47 (1997).
30. Muggeridge A.H., Generation of effective relative permeabilities from detailed simulation of flow in heterogeneous porous media, in Reservoir Characterization II, edited by L.W. Lake, H.B.Carroll, and T.C. Wesson (Academic Press, San Diego, 1991).
31. Bourgeat A., "Homogenized behavior of two-phase flows in naturally fractured reservoirs with uniform fractures distribution", Comp. Meth. Appl. Mech. Eng. 47, 205 (1984).
32. Saez A.E., Otero C.J., and Rusinek I., "The effective homogeneous behavior of heterogeneous porous media", Trans. Porous Media 4, 213 (1989).
33. Durlofsky L.J., "Numerical calculations of equivalent grid block permeability tensors for heterogeneous porous media", Water Resour. Res. 27, 699 (1991).
34. Amaziane B., Bourgeat A., and Koebbe J., "Numerical simulation and homogenization of two-phase flow in heterogeneous porous media", Trans. Porous Media 6, 519 (1991).
35. Amaziane B., "Global behavior of compressible three-phase flow in heterogeneous porous media", Trans. Porous Media 10, 43 (1993).
36. Chappelear A. and Hirasaki G.J., "A model of oil-water coning for two dimensional areal reservoir simulation", SPE 4980 (1976).
37. Woods A.C., and Khurana A.K., "Pseudofunctions for water coning in a three dimensional reservoir simulation", SPE 5525 (1977).
38. King P.R., Snyder D.E., Obut T.S., and Perkins R.L., "A case study of the full-field simulation of a reservoir containing bottomwater", SPE 21203 (1991).
39. Durlosfky L.J., Milliken W.J., and Bemath A., "Scaleup in the near-well region", SPE 61855 (2000).
40. Verma S., and Aziz K., Two and three dimensional flexible grids for reservoir simulation, Proceedings of the Fifth European Conference on the Mathematics of Oil Recovery, Leoben, Austria (1996).
41. Wallstorm T.C., Hou S., and Durlofsky L.J., "Application of a new two-phase upscaling technique to realistic reservoir cross sections", SPE 51939 (1999).
42. Castellini A., Edwards M.G., and Durlofsky L.J., Flow based modules for grid generation in two and three dimensions, Proceedings of Seventh European Conference on the Mathematics of Oil Recovery, Baveno, Lago Maggiore, Italy (2000).
43. Garcia M.H., Journel A.G., and Aziz K., "An automatic grid generation and adjustment method for modeling reservoir heterogeneity", SPE 21471 (1992).
44. Li D., Lake A.S., and Lake L.W., "Global scale-up of reservoir model permeability with local grid refinement", SPE (1995).
45. Li D., and Beckner B., "Optimal uplayering for scaleup of multimillion-cell geologic models", SPE 62927 (2000).
46. Younis R.M., and Caers J., A method for reservoir scale-up by static-based non-uniform gridding, Stanford Center for Reservoir Forecasting Annual Report (2001).
47. Younis R.M., and Caers J., A method for static-base upgridding, Proceedings of the Eighth European Conference on the Mathematics of Oil Recovery, Freiberg, Germany (2002).
48. Daubechies I., "Orthonormal basis of compactly supported wavelets", Commun. Pure Appl. Math. 41, 901 (1988).
49. Daubechies I., Ten Lecture on Wavelets (SIAM, Philadelphia, 1992).
50. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P., Numerical Recipes, 2nd ed. (Cambridge University Press, London, 1992).
51. Moridis G.J., Nikolaou M., and You Y., "The use of wavelet transforms in the solution of two-phase flow problems", SPE 29144 (1996).
52. Mehrabi A.R., and Sahimi M., "Coarsening of heterogeneous media: Application of wavelets", Phys. Rev. Lett. 79, 4385 (1997).
53. Ebrahimi F., and Sahimi M., "Multiresolution wavelet coarsening and analysis of transport in heterogeneous porous media", Physica A 316, 160 (2002).
54. Sahimi M., Heidarinasab A., and Dabir B., "Computer simulation of conduction in heterogeneous materials: application of wavelet transformations", Chem. Eng. Sci. 59, 4291 (2004).
55. Kikani J., and He M., "Multiresolution analysis of long-term pressure transient data using wavelet methods", SPE 48996 (1998).
56. Athichanagorn S., Horne R.N., and Kikani J., "Processing and interpretation of long-term data acquired from permanent pressure gages", SPE 56419 (1999).
57. Soliman M.Y., Ansah J., Stephenson S., and Mandal B., "Application of wavelet transform to analysis of pressure transient data", SPE Paper 71571, New Orleans, Louisiana (2001).
58. Ebrahimi F., Scale-up of Heterogeneous Porous Media and Flow and Transport therein Using Wavelet Transformation, Ph.D. Thesis, Ferdowsi University of Mashhad, Iran (2002).
59. Brewer K.E., and Wheatcraft S.W., Including multi-scale information in the characterization of hydraulic conductivity distributions, in Wavelets in Geophysics, edited by P. Kumar, E. F. Georgiou, and C.K. Chui, (Academic Press, San Diego, 1994), p. 213.
60. Panda M.N., Mosher C., and Chopra A.K., "Application of wavelet transforms to reservoir data analysis and scaling", SPE 3656 (1996).
61. Mehrabi A.R., Rassamdana H., and Sahimi M., "Characterization of long-range correlation in complex distributions and profiles", Phys. Rev. E 56, 712 (1997).
62. Lu P., and Horne R.N., "A multiresolution approach to reservoir parameter estimation using wavelet analysis", SPE Paper 62985, Dallas, Texas (2000).
63. Sahimi M., and Hashemi M., "Wavelet identification of the spatial distribution of fractures", Geophys. Res. Lett. 28, 611 (2001).
64. Heidarinasab A., Dabir B., and Sahimi M., "Multiresolution wavelet-based simulation of transport and photochemical reactions in the atmosphere", Atmos. Envir. 38, 6381 (2004).
65. Sahimi M., "Large-scale porous and wavelet transformations", Comput. Sci. Eng. 5 (No. 4), 75 (2003).
66. Chu L., Schatzinger R.A., and Tham M.K., "Application of wavelet analysis to upscaling of rock properties", SPE Paper 36517, Denver, Colorado (1996).
67. Hewett T.A., "Fractal distributiona of reservoir heterogeneity and their influence on fluid transport", SPE Paper 15386, New Orleans, Louisiana (1986).
68. Hewett T.A., and Behrens R.A., "Conditional simulation of reservoir heterogeneity with fractals", SPE Formation Eval. 5, 217 (1990).
69. Araktingi U.G., and Orr F.M., "Viscous fingering in heterogeneous porous media", SPE Paper 18095, Houston, Texas (1988).
70. King M.J., and Scher H., "Geometric dispersion and unstable flow in porous media", Phys. Rev. A 41, 874 (1990).
71. Koval E.J., "A method for predicting the performance of unstable miscible displacement in heterogeneous media", Soc. Pet. Eng. J. 3, 145 (1963).
72. Ebrahimi F., and Sahimi M., "Multiresolution wavelet scale up of unstable miscible displacements in flow through heterogeneous porous media", Transp.Porous Media 57, 75 (2004).
73. Settari A., and Aziz K., "Treatment of nonlinear terms in the numerical solution of partial differential solutions for multiphase flow in porous media", Int. J. Multiphase Flow 1, 817-44 (1975).
74. Thomas C.W., Principles of Hydrocarbon Reservoir Simulation (International Human Resources Development Corporation, Boston, 1982).
75. Harten A., "On a class of highly accurate convective modeling procedure based on quadratic upstream interpolation", Comput. Methods Appl. Mech. Eng. 19, 59 (1979).
76. Harten A., and Osher S., "Uniformly high-order accurate non-oscillatory schemes", SIAM. J. Numer. Anal., 24, 279-309 (1987).
77. Yee H.C., and Harten A., "Implicit TVD schemes for hyperbolic conservative laws in curvilinear coordinates", AIAA J. 25, 266 (1987).
78. Rubin B., and Blunt M.J., "Higher order implicit flux limiting schemes for black oil simulation", SPE 21222 (1991).
79. Wolcott D.S., Kazemi H., and Dean R.H., "A practical method for minimizing the grid orientation effect in reservoir simulation", SPE 36723 (1996).
80. Wattenbarger R.C., Aziz K., and Orr J.F.M., "High-throughput TVD-based simulation of tracer flow", SPE 29097 (1997).
81. Peddibhotla S., Gupta A.D., and Xue G., "Multiphase streamline modeling in three-dimensions: further generalizations and a field application", SPE 38003 (1997).
82. Sammon P.H., Kurihara M., and Liang J., "Applying high-resolution numerical schemes in reservoirs described by complex corner-point grids", SPE 66344 (2001).
83. Thiele M., and Edwards M.G., "Physically based higher order Godunov schemes for compositional simulation", SPE 66403 (2001).
84. Shrivastava V.K., Nghiem L.X., and Moore R.G., "A novel approach for incorporating physical dispersion in miscible displacement", SPE 77724 (2002).
85. Mallison B., Gerritsen M., Jessen K., and Orr J.F.M., "High order upwind schemes for two-phase multicomponent flow", SPE 79671 (2003).
86. van Leer B., "Towards the ultimate conservative difference scheme, V. A second order sequal to Godunov's method", J. Comp. Phys. 32, 101 (1979).
87. Sweby P.K., High resolution TVD schemes using flux limiters, Lectures in Applied Mathematics 22, 289 (1985).
88. Roe P.L., Some contribution to the modeling of discontinuous flows, Lectures in Applied Mathematics 22, 163 (1985).