Calculating equivalent permeability: a review
Tóm tắt
Từ khóa
Tài liệu tham khảo
Ababou, R., Random porous media flow on large 3-D grids: numerics, performance and application to homogenization. In IMA Volumes in Mathematics and its Applications, “Environmental Studies: Mathematical, Computational and Statistical Analysis”, ed. M.F. Wheeler. Springer-Verlag, New York Publishers, 1995, pp. 1–25.
Ababou, R., McLaughlin, D., Gelhar, L.W. & Tompson, A.F.B., Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media. Trans. Porous Media, 4(6) (December 1989).
Abramovich, 1995, Effective permeability of log-normal isotropic random media, J. Phys. A: Math. gen., 28, 693, 10.1088/0305-4470/28/3/022
Anderson, M.P., Characterization of geological heterogeneity. In Second George Kovac's Colloquium, Paris, 1995, UNESCO.
Anguy, 1995, The local change of scale method for modelling flow in natural porous media (1): Numerical tools., Adv. Water Res., 17, 337, 10.1016/0309-1708(94)90010-8
Auriault, 1991, Heterogeneous medium. Is an equivalent macroscopic description possible?, Int. J. Engng Sci, 29, 785, 10.1016/0020-7225(91)90001-J
Bachu, S. & Cuthiell, D., Effects of core-scale heterogeneity on steady state and transient fluid flow in porous media: Numerical analysis. Water Resour. Res., 26(5) (May 1990) 863–874.
Beckie, 1994, The universal structure of the groundwater flow equations, Water Resour. Res., 30, 1407, 10.1029/93WR03413
Begg, 1989, Assigning effective values to simulation grid-block parameters for heterogeneous reservoirs, SPE Reservoir Engineering, 4, 455, 10.2118/16754-PA
Begg, S.H. & King, P.R., Modelling the effects of shales on reservoir performance: Calculation of effective vertical permeability. SPE 13529 (1985), Society of Petroleum Engineers.
Bensoussan, A., Lions, J.L. & Papanicolaou, G., Asymptomatic Analysis for Period Structures. North-Holland, Amsterdam, 1978.
Berkowitz, 1993, Percolation theory and its application to groundwater hydrology, Water Resour. Res., 29, 775, 10.1029/92WR02707
Bøe, 1994, Analysis of an upscaling method based on conservation of dissipation, Trans. Porous Media., 17, 77, 10.1007/BF00624051
Bourgeat, 1988, Eléments de comparaison entre la méthode d'homogénéisation et la méthode de prise de moyenne avec fermeture, C. R. Acad. Sci. Paris, 306, 463
Bourgeat, 1995, Effective model of two-phase flow in a porous medium made of different rock types, Applicable Analysis, 58, 1, 10.1080/00036819508840360
Cardwell, 1945, Average permeabilities of heterogeneous oil sands, Trans. Am. Inst. Mining. Met. Pet. Eng., 34
Crapiste, 1986, A general closure scheme for the method of volume averaging, Chem. Engng Sci., 41, 227, 10.1016/0009-2509(86)87003-8
Dagan, 1979, Models of groundwater flow in statistically homogeneous porous formations, Water Resour. Res., 15, 47, 10.1029/WR015i001p00047
Dagan, 1993, High-order correction of effective permeability of heterogeneous isotropic formations of log-normal conductivity distribution, Trans. Porous Media, 12, 279, 10.1007/BF00624462
de Gennes, 1976, La percolation: un concept unificateur, La Recherche, 7, 919
de Marsily, 1993, Quelques méthodes d'approche de la variabilité spatiale des reservoirs souterrains, Hydrogéologie, 4, 259
de Marsily, 1994, Quelques réflexions sur l'utilisation des modèles en hydrologie, Revue des Sciences de l'Eau, 7, 219, 10.7202/705198ar
de Wit, A., Correlation structure dependence of the effective permeability of heterogeneous porous media. Submitted to Phys. Fluids (1995).
Desbarats, 1987, Numerical estimation of effective permeability in sand-shale formations, Water Resour. Res., 23, 273, 10.1029/WR023i002p00273
Desbarats, 1992, Spatial averaging of hydraulic conductivity in three-dimensional heterogeneous porous media, Math. Geol., 24, 249, 10.1007/BF00893749
Deutsch, 1989, Calculating effective absolute permeability in sandstone/shale sequences, SPE Form. Eval., 4, 343, 10.2118/17264-PA
Duquerroix, J.-P.L., Lemouzy, P., Nœtinger, B. & Kruel-Romeu, R., Influence of the permeability anisotropy ratio on large-scale properties of heterogeneous reservoirs. 68th Annual Tech. Conf. and Exhb. of the SPE, Houston SPE 26648, 1993, 29–40.
Durlofsky, 1991, Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media, Water Resour. Res., 27, 699, 10.1029/91WR00107
Durlofsky, 1992, Representation of grid block permeability in course scale models of randomly heterogeneous porous media, Water Resour. Res., 28, 1791, 10.1029/92WR00541
Durlofsky, 1994, Accuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities, Water Resour. Res., 30, 965, 10.1029/94WR00061
Durlofsky, L.J., Jones, R.C. & Miliken, W.J., A new method for the scale up of displacement processes in heterogeneous reservoirs. In Thomassen, [103].
Dykaar, 1992, Determination of the effective hydraulic conductivity for heterogeneous porous media using a numerical spectral approach, Water Resour. Res., 28, 1155, 10.1029/91WR03084
Dykaar, 1992, Determination of the effective hydraulic conductivity for heterogeneous porous media using a numerical spectral approach, Water Resour. Res., 28, 1167, 10.1029/91WR03083
Ene, 1991, Estimations du tenseur de perméabilitié, C. R. Acad. Sci. Paris, 312, 1269
Ene, H.I. & Polis̆evski, D., Thermal Flow in Porous Media. D. Rediel Publishing Company, Dordrecht, Holland, 1987.
Espedal, M.S. & Sævareid, O., Upscaling of permeability based on wavelet representation. In Thomassen, [103].
Fayers, 1992, A review of current trends in petroleum reservoir description and assessment of the impacts on oil recovery, Adv. Water Resour., 15, 341, 10.1016/0309-1708(92)90002-J
Fenton, 1993, Statistics of block conductivity through a simple bounded stochastic medium, Water Resour. Res., 29, 1825, 10.1029/93WR00412
Gallouët, T. & Guérillot, D., Averaged heterogeneous porous media by minimization of the error on the flow rate. In Thomassen, [103].
Garcia, M.H., Journel, A.G. & Aziz, K., An automatic grid generation and adjustment method for modeling reservoir heterogeneities. Tech. rep., Stanford Center for Reservoir Forecasting Report 3, 1990.
Gautier, Y. & Nœtinger, B., Preferential flow-paths detection for heterogeneous reservoirs using a new renormalization technique. In Thomassen, [103].
Gelhar, L.W., Stochastic Subsurface Hydrology. Prentice-Hall, Englewood Cliffs, New Jersey, 1993.
Gelhar, 1983, Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res., 19, 161, 10.1029/WR019i001p00161
Gómez-Hernández, J.J., A stochastic approach to the simulation of block conductivity fields conditioned upon data measured at a smaller scale, PhD thesis, Stanford University, March 1991.
Gómez-Hernández, J.J. & Journel, A.G., Stochastic characterization of grid-block permeabilities: from point values to block tensors. In 2nd European Conference on the Mathematics of Oil Recovery, Paris, 1990, eds. D. Guèrillot and O. Guillon. Édition Technip, pp. 83–90.
Guèlot, D., Rudkiewicz, J.L., Ravenne, C., Renard, G. & Galli, A., An integrated model for computer aided reservoir description: from outcrop study to fluid flow simulations. Revue de l'IFP, 45(1) (1990).
Gutjahr, 1978, Stochastic analysis of spatial variability in suvsurface flows 2: Evaluation and application, Water Resour. Res., 14, 953, 10.1029/WR014i005p00953
Guyon, 1984, Application de la percolation à la physique des milieux poreux, Annales des Mines, 5–6, 17
Haldorsen, M.H., Simulator Parameter Assignment and the Problem of Scale in Reservoir Engineering, eds. L.W. Lake and H.B. Caroll. Academic Press, Orlando, 1986, 293–340.
Haldorsen, M.H. & Lake, L.W., A new approach to shale management in field scale simulation models. SPE 10976 (1982) Society of Petroleum Engineers.
Harvey, 1995, Mapping hydraulic conductivity: Sequential conditioning with measurements of solute arrival time, hydraulic head, and local conductivity, Water Resour. Res., 31, 1615, 10.1029/95WR00547
Hinrichsen, 1993, A fast algorithm for estimating large-scale permeabilities of correlated anisotropic media, Trans. Porous Media, 12, 55, 10.1007/BF00616362
Holden, L. & Lia, O., A tensor estimator for the homogenization of absolute permeability. Trans. Porous Media, 8(1) (May 1992) 37–46.
Indelman, 1994, A higher-order approximation to effective conductivity in media of anisotropic random structure, Water Resour. Res., 30, 1857, 10.1029/94WR00077
Indelman, P. & Dagan, G., Upscaling of heterogeneous formations: General approach and application to isotropic media. Trans. Porous Media, 12(2) (August 1993) 61–183.
Journel, A.G., Deutsch, C.V. & Desbarats, A.J., Power averaging for block effective permeability. SPE 15128 (1986) Society of Petroleum Engineers.
Journel, A.G. & Gómez-Hernandez, J.J., Stochastic imaging of the Wilmington clastic sequence. SPE Form. Eval. SPE 19857 (March 1993) 33–40.
Kadanoff, 1966, Scaling laws for Ising models near Tc, Physics, 2, 263, 10.1103/PhysicsPhysiqueFizika.2.263
Kasap, E. & Lake, L.W., An analytical method to calculate the effective permeability tensor of a grid block and its application in an outcrop study. SPE Symp. on Reservoir Simulation, Houston SPE 18434 (Feb 1989).
King, 1987, The use of field theoretic methods for the study of flow in heterogeneous porous medium, J. Phys. A: Math. Gen., 20, 3935, 10.1088/0305-4470/20/12/038
King, 1989, The use of renormalization for calculating effective permeability, Trans. Porous Media, 4, 37, 10.1007/BF00134741
Kitanidis, P.K., Effective hydraulic conductivity for gradually varying flow. Water Resour. Res. 26(1) (June 1990) 1197–1208.
Kitanidis, P.K., Groundwater flow in heterogeneous formations. In Second George Kovac's Colloquium, Paris, 1995, UNESCO.
Kolterman, 1992, Paleoclimatic signature in terrestial flood deposits, Science, 256, 1775, 10.1126/science.256.5065.1775
Kruel-Romeu, R., Écoulement en milieu hétérogène: prise de moyenne de perméabilite en régimes permanent et transitoire, PhD thesis, Universitý of Paris VI, June 1994.
Kruel-Romeu, 1995, Calculation of internodal transmissibilities in finite difference models of flow in heterogeneous media, Water Resour. Res., 31, 943, 10.1029/94WR02422
Lachassagne, P., Estimation des perméabilités moyennes dans les milieux poreux fortement non-uniformes étudiés sous l'angle stochastique — Application aux essais de débit en aquifère captif, PhD thesis, Paris School of Mines, November 1989.
Landau, L.D. & Lifshitz, E.M., Electrodynamics of Continuous Media. Pergamon, Oxford, 1960.
Le Loc'h, G. Étude de la composition des perméabilités par des méthodes variationelles, PhD thesis, Paris School of Mines, November 1987.
Lemouzy, P., Calcul de la perméabilité absolute effective. Paris, IFP (note interne, RF40 no. 2685) (1991).
Long, 1982, Porous media equivalents for networks of discontinuous fractures, Water Resour. Res., 18, 645, 10.1029/WR018i003p00645
Malick, K.M. & Hewett, T.A., Boundary effects in the successive upscaling of absolute permeability. Tech. Rep. 8th Annual Meeting, Stanford Center for Reservoir Forecasting, May 1995.
Martin, J.H. & Cooper, J.A., An integrated approach to the modeling of permeability barrier distribution in a sedimentologically complex reservoir. In 59th Annual Technical Conference, Houston, Texas, September 1984, Soc. of Pet. Eng.
Matheron, G., Eléments pour une Théorie des Milieux Poreux. Masson, Paris, 1967.
Matheron, G., Composition des perméabilités en milieu poreux hétérogène: Critique de la règle de pondération géométrique. Revue de l'IFP, 23 (February 1968) 201–218.
Matheron, G., Quelques inégalités pour la perméabilité effective d'un milieu poreux hétérogène. In Cahiers de Géostatistique, Fascicule 3. Paris School of Mines, 25–26 May, 1993.
Matheron, G., Beucher, H., Fouquet, C.D., Galli, A., Guérillot, D. & Ravenne, C., Conditional simulation of the geometry of fluvio-deltaic reservoirs. 62nd Annual Tech. Conf. and Exhb. of the SPE, SPE 16753 (September 1987) 591–599.
Mei, 1989, Mechanics of heterogeneous porous media with several spatial scales, Proc. R. Soc. Lond. A, 246, 391, 10.1098/rspa.1989.0132
Neuman, S.P., Generalized scaling of permeabilities: validation and effect of support scale. Geophys. Res. Lett., 21(5) (March 1994) 349–352.
Neuman, 1993, Prediction of steady state flow in nonuniform geologic media by conditional moments: exact nonlocal formalism, effective conductivities and weak approximation, Water Resour. Res., 29, 341, 10.1029/92WR02062
Njifenjou, A., Eléments finis mixtes hybrides duaux et homogénéisation des paramètres pétrophysiques — Application à l'étude numérique d'écoulement en milieu poreux, PhD thesis, University of Paris VI, Mars 1993.
Njifenjou, 1994, Expression en termes d'énergie pour la perméabilité absolute effective, Revue de l'IFP, 49, 345, 10.2516/ogst:1994020
Nœtinger, 1994, The effective permeability of a heterogeneous porous medium, Trans. Porous Media, 15, 99, 10.1007/BF00625512
Nœtinger, B. & Jacquin, C., Experimental tests of a simple permeability composition. SPE 22841 (1991) 253–260.
Norris, R.J. & Lewis, J.J.M., The geological modeling of effective permeability in complex heterolitic facies. SPE 22692 (1991), 359–374.
Pickup, 1994, Permeability tensors for sedimentary structures, Math. Geol., 26, 227, 10.1007/BF02082765
Pickup, G.E., Jensen, J.L., Ringrose, P.S. & Sorbie, K.S., A method for calculating permeability tensors using perturbed boundary conditions. In 3rd European Conf. on the Mathematics of Oil Recovery, Delft, June 1992.
Poley, A.D., Effective permeability and dispersion in locally heterogeneous aquifers. Water Resour. Res., 24(11) (November 1988) 1921–1926.
Quintard, 1987, Ecoulement monophasique en milieu poreux: effets des hétérogénéités locales, J. Mec. Theor. Appl., 6, 691
Quintard, 1994, Convection, dispersion, and interfacial transport of contaminants: Homogeneous porous media, Adv. Water Res., 17, 221, 10.1016/0309-1708(94)90002-7
RamaRao, 1995, Pilot point methodology for automated calibration of an ensemble of conditionally simulated transmissivity fields:, Water Resour. Res., 31, 475, 10.1029/94WR02258
Roth, C., Contribution de la géostatisque à la résolution du problème inverse en hydrogéologie, PhD thesis, Paris School of Mines, 1995.
Rubin, Y. & Gómez-Hernández, J., A stochastic approach to the problem of upscaling of conductivity in disordered media: Theory and unconditional numerical simulations. Water Resour. Res. 22(4) (April 1990).
Rubinstein, 1989, Flow in random porous media: mathematical formulation, variational principles, and rigorous bounds, J. Fluid Mech., 206, 25, 10.1017/S0022112089002211
Saucier, 1992, Scaling of the effective permeability in multifractal porous media, J. Phys. A: Math. Gen., 191, 289
Sànchez-Vila, 1995, A synthesis of approaches to upscaling of hydraulic conductivities, Water Resour. Res., 31, 867, 10.1029/94WR02754
Sykes, 1964, Exact critical percolation probabilities for site and bond problems in two dimensions, J. Math Phys., 5, 1117, 10.1063/1.1704215
Tetzlaf, D.M. & Harbaugh, J.W., Simulating Clastic Sedimentation. Van Nostrand Reinhold, New-York, 1989.
Thomassen, P.R., ed., 4th European Conference on the Mathematics of Oil Recovery, Røros, Norway, June 1994.
Tran, T., Addressing the missing scale: Direct simulation of effective modeling cel permeability. Tech. Rep. 8th annual meeting, Stanford Center for Reservoir Forecasting, May 1995.
Tran, T. & Journel, A., Automatic generation of corner-point-geometry flow simulation grids from detailed geostatistical descriptions. Tech. Rep. 8th annual meeting, Stanford Center for Reservoir Forecasting, May 1995.
Vanmarcke, E., Random Fields. MIT Press, Cambridge, MA, 1984.
Wen, 1996, Upscaling hydraulic conductivities in heterogeneous media: An overview, J. Hydrol., 183, ix, xxxii
White, C.D. & Horne, R.N., Computing Absolute Transmissibility in the Presence of Fine-scale Heterogeneity, SPE 16011, pp. 209–220.
Wiener, 1912, Abhandlungen der mathematisch, Physischen Klasse der Königlichen Sächsischen Gesellschaft der Wissenschaften, 32, 509
Yamada, T., A dissipation based coarse grid system and its application to the scale-up of two-phase problems. Tech. Rep. 8th annual meeting, Stanford Center for Reservoir Forecasting, 1995.