On study of relative phase permeabilities for anisotropic media

A. Kh. Pergament ; P. Yu. Tomin

Matematičeskoe modelirovanie, Tome 23 (2011) no. 5, pp. 3-15.

Résumé

In the paper study of properties of relative phase permeabilities for media with anisotropic filtration properties is carried out using numerical-analytical method. The anisotropy may be related to fracturing caused by brittle crushing. The analysis of relations between phase and absolute permeability tensors is made in assumption of capillary equilibrium. Samples of relative phase permeability functions are obtained for media with orthotropic and monocline symmetry of filtration properties. The influence of connectivity property on the functions is shown, and the saturation dependence of direction of principal axes for phase permeability tensor is investigated. Thereby the misalignment of phase and absolute permeability tensors is shown. The results qualitatively coincide with experimental data.

Détail

Keywords: anisotropy, fractured media, multiphase flows, relative phase permeability.

Bibliographie

[1] L. Lonergan, R. J. H. Jolly, K. Rawnsley, D. J. Sanderson, Fractured Reservoirs, Geological Society, London, 2007

[2] G. I. Barenblatt, Yu. P. Zheltov, I. N. Kochina Ob osnovnykh predstavleniyakh teorii filtratsii odnorodnykh zhidkostei v treschinovatykh porodakh, Prikladnaya matematika i mekhanika, 24:5 (1960), 852–864

[3] J. E. Warren, P. E. Root, “The behavior of naturally fractured reservoirs”, Soc. Petrol. Eng. Journal, 3 (1963), 245–255

[4] P. van Lingen, J.-M. Daniel, L. Cosentino, M. Sengul, Single Medium Simulation of Reservoirs with Conductive Faults and Fractures, SPE Middle East Oil Show (Bahrain, 17–20 March 2001), SPE, paper 68165

[5] N. M. Dmitriev, V. M. Maksimov, “Modeli filtratsii flyuidov v anizotropnykh treschinovato-poristykh sredakh”, Doklady Akademii nauk, 416:3 (2007), 338–340 | Zbl

[6] N. M. Dmitriev, V. M. Maksimov, “Opredelyayuschie uravneniya dvukhfaznoi filtratsii v anizotropnykh poristykh sredakh”, Izv. RAN. MZhG, 1998, no. 2, 87–94 | MR | Zbl

[7] M. N. Dmitriev, N. M. Dmitriev, V. V. Maslennikov, “K predstavleniyu funktsii otnositelnykh fazovykh pronitsaemostei dlya anizotropnykh poristykh sred”, Izv. RAN. MZhG, 2005, no. 3, 118–125 | MR | Zbl

[8] M. N. Dmitriev, N. M. Dmitriev, V. M. Maksimov, D. Yu. Semiglasov, “Effekty anizotropii pri dvukhfaznykh filtratsionnykh techeniyakh”, Izv. RAN. MZhG, 2010, no. 3, 140–146

[9] M. B. Moranville, D. P. Kessler, R. A. Greenkorn, “Directional Disperson Coefficients in Anisotropic Porous Media”, Ind. Eng. Chem. Fundamen., 16:3 (1977), 327–332 | DOI

[10] L. G. Fel, J. Bear, “Principal Axes and Values of the Dispersion Coefficient in the 2D Axially Symmetric Porous Medium”, Continuous Media with Microstructure, 2010, 351–355

[11] J. Bear, L. G. Fel, Y. Zimmels, “Effects of Material Symmetry on the Coefficients of Transport in Anisotropic Porous Media”, Transp. Porous Med., 82 (2010), 347–361 | DOI | MR

[12] L. Fel, J. Bear, “Dispersion and Dispersivity Tensors in Saturated Porous Media with Uniaxial Symmetry”, Transp. Porous Med., 85 (2010), 259–268 | DOI | MR

[13] J. Bear, C. Braester, P. C. Menier, “Effective and Relative Permeabilities of Anisotropic Porous Media”, Transport Porous Media, 2 (1987), 301–316

[14] P. S. Ringrose, J. L. Jensen, K. S. Sorbie, The Use of Geology in the Interpretation of Core-Scale Relative Permeability Data, SPE 69th Annual Technical Conference and Exhibition (New Orleans, LA, USA, 25–28 September 1994), SPE, paper 28448

[15] G. E. Pickup, D. Carruthers, Effective Flow Parameters for 3D Reservoir Simulation, European 3D Reservoir Modelling Conference (Stavanger, Norway, 16–17 April 1996), SPE, paper 35495

[16] A. F. Grachev, Sh. A. Mukhamediev, “O treschinovatosti kamennougolnykh izvestnyakov Moskovskoi sineklizy”, Fizika Zemli, 2000, no. 1, 61–77

[17] A. F. Grachev, Sh. A. Mukhamediev, “Treschinovatost gornykh porod i otsenka napryazhenii in situ v obnazheniyakh, podverzhennykh vozdeistviyu vzryvov”, Fizika Zemli, 2000, no. 2, 34–43

[18] G. I. Barenblatt, V. M. Entov, V. M. Ryzhik, Dvizhenie zhidkostei i gazov v prirodnykh plastakh, Nedra, M., 1984

[19] L. J. Durlofsky, “Upscaling and Gridding of Fine Scale Geological Models for Flow Simulation”, 8th International Forum on Reservoir Simulation, Italy, 2005

[20] T. Corey, C. H. Rathjens, “Effect of Stratification on Relative Permeability”, J. Pet. Tech., 8:12, December (1956), 69–71

[21] M. M. Honarpour, A. S. Cullick, Naji Saad, Influence of Small-Scale Rock Laminations on Core Plug Oil/Water Relative Permeability and Capillary Pressure, University of Tulsa Centennial Petroleum Engineering Symposium (Tulsa, OK, USA, 29–31 August 1994), SPE, paper 27968

[22] M. M. Honarpour, A. S. Cullick, N. Saad, N. V. Humphreys, Effect of Rock Heterogeneity on Relative Permeability: Implications for Scale-up, SPE Asia Pacific Oil and Gas Conference (Kuala Lumpur, Malaysia, 20–22 March 1995), SPE, paper 29311

[23] P. W. M. Corbet, P. S. Ringrose, J. L. Jensen, K. S. Sorbie, Laminated Clastic Reservoirs: The Interplay of Capillary Pressure and Sedimentary Architecture, SPE 67th Annual Technical Conference and Exhibition (Washington, DC, October 4–7 1992), SPE, paper 24699

[24] N. Saad, A. S. Cullick, M. M. Honarpour, Effective Relative Permeability in Scale-Up and Simulation, SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium (Denver, CO, USA, 20–22 March 1995), SPE, paper 29592

[25] T. F. M. Kortekaas, Water/Oil Displacement Characteristics in Crossbedded Reservoir Zones, SPE Annual Technical Conference and Exhibition (San Francisco, 5–8 October 1983), SPE, paper 12112

[26] R. D. Kanevskaya, M. I. Shviller, “Osobennosti filtratsii nesmeshivayuschikhsya zhidkostei v poristykh sredakh s anizotropnymi fazovymi pronitsaemostyami”, Izv. RAN. MZhG, 1992, no. 5, 91–100 | MR | Zbl

[27] V. S. V. Rajan, Discussion of The Origins of Anisotropy, SPE, paper 18394; Journal of Petroleum Technology, 40 (1988), 905

[28] L. I. Sedov, Mekhanika sploshnoi sredy, v. 1, Nauka, M., 1970

[29] X. H. Wen, L. J. Durlofsky, M. G. Edwards, “Use of Border Regions for Improved Permeability Upscaling”, Mathematical Geology, 35:5 (2003), 521–547 | DOI

[30] V. P. Myasnikov, M. Yu. Zaslavskii, A. Kh. Pergament. Algoritmy osredneniya i metod opornykh operatorov v zadachakh porouprugosti, Doklady Akademii nauk, 397:5 (2004), 622–626

[31] M. Yu. Zaslavskii, A. Kh. Pergament, “Algoritmy osredneniya i metod opornykh operatorov v ellipticheskikh zadachakh s razryvnymi koeffitsientami”, ZhVM i MF, 45:9 (2005), 1594–1605 | MR | Zbl

[32] A. Kh. Pergament, V. A. Semiletov, M. Yu. Zaslavsky, “Multiscale Averaging Algorithms for Flow Modeling in Heterogeneous Reservoir”, Proceedings of 10th European Conference on the Mathematics of Oil Recovery, 2006, P014

[33] M. Yu. Zaslavskii, “Ob algoritme osredneniya dlya resheniya ellipticheskikh zadach s razryvnymi koeffitsientami”, Doklady Akademii nauk, 419:2 (2007), 197–202 | MR

[34] A. Kh. Pergament, V. A. Semiletov, P. Yu. Tomin, “O nekotorykh mnogomasshtabnykh algoritmakh sektornogo modelirovaniya v zadachakh mnogofaznoi filtratsii”, Matematicheskoe modelirovanie, 22:11 (2010), 3–17 | Zbl

[35] T. J. Lassetter, J. R. Waggoner, L. W. Lake, “Reservoir Heterogeneities and their Influence on Ultimate Recovery”, Reservoir Characterization, Academic Press, 1986, 545

[36] S. G. Rassokhin, “Vliyanie anizotropii poristoi sredy na protsessy filtratsii uglevodorodov”, Aktualnye problemy osvoeniya, razrabotki i ekspluatatsii mestorozhdenii prirodnogo gaza, VNIGAZ, M., 2003, 74–83

[37] S. G. Rassokhin, “Otnositelnye fazovye pronitsaemosti pri filtratsii uglevodorodov v gidrofilnom i gidrofobnom kerne”, Aktualnye problemy osvoeniya, razrabotki i ekspluatatsii mestorozhdenii prirodnogo gaza, VNIGAZ, M., 2003, 50–64