Dossier: Upscaling of Fluid Flow in Oil Reservoirs
Open Access
Issue
Oil & Gas Science and Technology - Rev. IFP
Volume 59, Number 2, March-April 2004
Dossier: Upscaling of Fluid Flow in Oil Reservoirs
Page(s) 119 - 139
DOI https://doi.org/10.2516/ogst:2004010
Published online 01 December 2006
  • Ababou, R. (1994) Solutions of Stochastic Groundwater Flow by Infinite Series, and Convergence of the One-dimensional Expansion. Stochastic. Hydrology and Hydraulics, 8, 139-155. [CrossRef]
  • Ahmadi, A., Labastie, A. and Quintard, M. (1993) Large Scale Properties for Flow Through a Stratified Medium Various Approaches. SPE RE, August, 214-220.
  • Ahmadi, A. and Quintard, M. (1996) Large Scale Properties for Two Phase Flow in Random Porous Media. Journal of Hydrology, 183, 69-99. [CrossRef]
  • Ahmadi, A. and Nœtinger, B. (1994) A Practical and Operational Method for the Calculation of Effective Dispersion Coefficients in Heterogeneous Porous Media. ECMOR IV, 4th European Conference on the Mathematics of Oil Recovery, Röros, Norway, 7-10 June.
  • Alabert, F.G. (1989) Constraining Description of Randomly Heterogeneous Reservoirs to Pressure Test Data: A Monte-Carlo Study. Paper 19600, SPE 64th Ann. Tech. Conf. and Exh. San Antonio, 207-221.
  • Arbogast, T. and Bryant, S.L. (2001) Numerical Subgrid Upscaling for Waterflood Simulations. SPE No. 66375, SPE Reservoir Simulation Symposium, Houston, 11-14 February.
  • Artus, V., Nœtinger, B. and Ricard, L. Dynamics of the Water Oil Front for Two-Phase, Immiscible Flow in Heterogeneous Porous Media. 1 Stratified Media. To be published in Transport in Porous Media.
  • Artus, V. and Nœtinger, B. (2002) Macrodispersion Approach for Upscaling of Two-Phase, Immiscible Flow in Heterogeneous Porous Media. ECMOR VIII, Freiberg, Germany, 3-6 Sept.
  • Avellaneda, M. (1996) Homogenization and Renormlization, the Mathematics of Multiple Scale Random Media and Turbulent Diffusion. Lectures in Applied Mathematics, 31, 251-268. [MathSciNet]
  • Blanc, G., Guérillot, D., Rahon, D. and Roggero, F. (1996) Building Geostatistical Models Constrained by Dynamic Data-A Posteriori Constraint. SPE 35478, European 3D Reservoir Modeling Conference, Stavanger, Norway, 19-33.
  • Blanc, G., Nœtinger, B., Piacentino, L. and Helios Reservoir Group (1996) Contribution of the Pressure Moments to the Interpretation of Numerical Simulation of Well Tests. ECMOR V - 5th European Conference on the Mathematics of Oil Recovery, Mining University Leoben, Austria, 3-6 Sept.
  • Bourgeat, M., Quintard, M. and Whitaker, S. (1988) Éléments de comparaison entre la méthode d’homogéneisation et la prise de moyenne avec fermeture. C.R. Acad. Sci., Paris, 306 2, 463-466.
  • Boyer, S. and Mari, J.L. (1994) Sismique et diagraphie, Éditions Technip, Paris.
  • Cardwell, W.T. and Parsons, R.L. (1945) Average Permeabilities of Heterogeneous Oil Sands Trans. American Inst. Min. Pet. Eng., 160, 34-42.
  • Cherblanc, F. (1999) Étude du transport miscible en milieu poreux hétérogènes: prise en compte du non-équilibre. Thèse, université Bordeaux 1.
  • Christakos, G.,Miller, C.T. and Oliver, D.S. (1993) Stochastic Perturbation Analysis of Groundwater Flow. Spatially Variable Soils, Semi Infinite Domains and Large Fluctuations. Stoch. Hydrol. and Hydrauli., 7, 3, 213-239. [CrossRef]
  • Christakos, G.,Hristopulos, D.T. and Miller, C.T. (1995) Stochastic Diagrammatic Analysis of Groundwater Flow in Heterogeneous Porous Media. Water Resources Research, 31, 7, 1687-1703. [CrossRef]
  • Cushman, J.H. (1984) On Unifying the Concepts of Scale, Instrumentation, and Stochastics in the Development of Multiphase Theory. Water Resources Research, 20, 11, 1668-1676. [CrossRef]
  • Cushman, J.H. and Ginn, T.R. (1993) Non Local Dispersion in Porous Media with Continuously Evolving Scale of Heterogeneity. Transport in Porous Media, 13, 1, 123-138. [CrossRef]
  • Dagan, G. (1989) Flow and Transport in Porous Formations Springer Verlag, Berlin.
  • Daviau, F. (1986) Interpr賡tion des essais de puits, Éditions Technip, Paris.
  • Deutsch, C.V. and Journel, A.G. (1992) Geostatistical Software Library and User's Guide, Oxford University Press.
  • Ding, D.Y. and Urgelli, D. (1997) Upscaling of Transmissibility for Field Scale Flow Simulation in Heterogeneous Media. SPE 38016 - Reservoir Simulation, 14th Symposium of the Society of Petroleum Engineers, Dallas, June 8-11, Proceedings, 311-312.
  • Duquerroix, J.P., Lemouzy, P., Nœtinger, B. and Romeu, R.K. (1993) Influence of the Permeability Anisotropy Ratio on the Large Scale Properties of Heterogeneous Reservoirs. SPE 26648, 68th Annual Tech. Conf. and Exhb. of the SPE, Houston, 29-40.
  • Durlovsk, L.J. (1991) Numerical Calculation of Equivalent Grid Block Permeability Tensors for Heterogeneous Porous Media. Water Resour. Res., 27, 699-708. [CrossRef] [MathSciNet]
  • Eschard, R., Doligez, B.D., Rahon, D., Ravenne, C. and Leloch, G. (1991) A New Approach for Reservoirs Description and Simulation Using Geostatistical Methods. Advances in Reservoir Technology, Characterization Modeling and Management.
  • Feitosa, G.S., Chu, L., Thompson, L.G. and Reynolds, A.C. (1993) Determination of Permeability Distribution From Well Test Pressure Data, SPE 26 407.
  • Furtado, F., Glimm, J., Lindquist, B. and Pereira, F. (1990) Multiple Length Scale Calculus of Mixing Length Growth in Tracer Floods. Kovaritch ed, Proceedings of the Emerging Technologies Conference, Houston TX, Institute for Improve Oil Recovery, 251-259.
  • Galli, A., Guérillot, D., Ravenne, C. and Heresim-Group (1990) Combining Geology, Geostatistics and Multiphase Fluid Flow for 3D Reservoir Studies. ECMOR II - 2nd European Conference on the Mathematics of Oil Recovery, Proceedings, Arles, Sep. 11-14, D. Guérillot, O. Guillon eds., 11-19.
  • Gautier, Y. and Nœtinger, B. (1997) Preferential Flow-Paths Detection for Heterogeneous Reservoirs Using a New Renormalization Technique. Transport in Porous Media, 26, 1-23. [CrossRef]
  • Gautier, Y. and Nœtinger, B. (1998) Determination of Geostatistical Parameters Using Well-Test Data. SPE 73rd ATCE, 27-30, New Orleans, USA.
  • Gautier, Y.,Blunt, M.J. and Christie, M.A. (1999) Nested Gridding and Streamline-Based Simulation for Fast Reservoir Performance Prediction. Computational Geosciences, 3, 295-320. [CrossRef]
  • Gelhar, W. (1993) Stochastic Subsurface Hydrology, Prentice Hall.
  • Germano, M. (1992) Turbulence: the Filtering Approach. J. Fluid Mech., 238, 325-336. [NASA ADS] [CrossRef]
  • Glimm, J.,Lindquist, B.,Pereira, F. and Peirls, R. (1992) The Multifractal Hypothesis and Anomalous Diffusion. Math. App. Comput., 11, 2, 189-207. [MathSciNet]
  • Goldenfeld, N. (1992) Lectures on Phase Transitions and the Renormalization Group, Frontiers in Physics, Addison Wesley.
  • Gomez-Hernandez, J. (1990) A Stochastic Approach to the Simulation of Block Conductivity Fields Conditioned upon Data Measured at a Smaller Scale, PhD, Stanford University.
  • Gorell, S., and Basset, R. (2001) Trends in Reservoir Simulation: Big Models, Scalable models? Will you please make up your mind? SPE 71 596, ATCE, New Orleans.
  • Gavalas, G.R. and Shah, P.C. (1976) Reservoir History Matching by Bayesian Estimation. Soc. Pet. Eng. J., 16, 6, 337-350. [CrossRef]
  • Granjeon, D. (1997) Modélisation stratigraphique déterministe - Conception et applications d'un modèle diffusif 3D multilithologique. PhD Dissertation, Mémoires Geosciences Rennes, France.
  • Granjeon, D., Joseph, P. and Doligez, B. (1998). Using a 3D Stratigraphic Model to Optimise Reservoir Description. Hart's Petroleum Engineer International, November, 51-58.
  • Guérillot, D.,Rudkiewicz, J.L.,Ravenne, C.,Renard, G. and Galli, A. (1989) An Integrated Model for Computer Aided Reservoir, Description: from Outcrop Study to Fluid Flow Simulations. Improved Oil Recovery. 5th European Symposium, Proceedings, Budapest, April 25-27, 651-660.
  • Guérillot, D.R.,Lemouzy, P. and Ravenne, C. (1991) How Reservoir Characterization can help to Improve Production Forecasts. Improved Oil Recovery. 6th European Symposium, Proceedings, Stavanger, May 21-23, 3-12.
  • Guérillot, D.R. and Verdière, S. (1995) Different Pressure Grids for Reservoir Simulation in Heterogeneous Reservoirs. SPE 29148, SPE Symposium on Reservoir Simulation, San Antonio.
  • Haas, A. and Nœtinger, B. (1996) Stochastic Reservoir Modelling Constrained by Well Test Permeabilities. Fifth International Geostatistics Congress, 22-27 Sept., Wollongong, Australia.
  • Haas, A. and Nœtinger, B. (1995) 3D Permeability Averaging for Stochastic Reservoir Modelling Constrained by Well Tests, Reservoir Description Forum. The Heriot-Watt and Stanford University, 10-14 Sept., Puebles Hydro, UK.
  • Horne, R.N. (1990) Modern Well Test Analysis, Petroway. Hou, T.Y. and Wu, X.H. (1997) A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media. J. Comput. Phys., 134, 169-189.
  • Hou, T.Y.,Wu, X.H. and Cai, X. (1999) Convergence of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients. Math. Comput., 227, 913-943. [CrossRef] [MathSciNet]
  • Hu, L.Y.,Blanc, G. and Nœtinger, B. (2001) Gradual Deformation and Iterative Calibration of Sequential Stochastic Simulations. Math. Geol., 33, 475-489. [CrossRef]
  • Hu, L.Y., Blanc, G. and Nœtinger, B. (1996) Estimation of Lithofacies Proportions Using Well and Well-Test Data. SPE 36571, Annual Technical Conference and Exhibition, 6-9 October, Denver, USA.
  • Hu, L.Y., Le Ravalec, M., Blanc, G. Corre, B., Haas, A., Nœtinger, B. and Roggero, F. (1999) Reducing Uncertainties in Production Forecasts by Constraining Geological Modeling Using Dynamic Data. SPE 56703, 74th Annual Technical Conference and Exhibition, 3-6 Oct., Houston, USA.
  • Hu, L.Y., Blanc G. and Nœtinger, B. (1998) Estimation of Lithofacies Proportions by Use of Well and Well-Test Data. SPE Reservoir Evaluation and Engineering, February.
  • Indelman, P. and Abramovich, B. (1994) A Higher Order Approximation to Effective Conductivity in Media of Anisotropic Random Structure. Water Resources Research, 30, 6, 1857-1864. [CrossRef]
  • Indelman, P. and Abramovich, B. (1995) Effective Permittivity of Log Normal Isotropic Random Media. J. Phys A: Math Gen., 28, 693-700. [CrossRef]
  • Indelman, P. (1996) Averaging of Unsteady Flows in Heterogeneous Media of Stationary Conductivity. J. Fluid. Mech., 310, 39-61. [CrossRef]
  • Jaekel, U. and Vereecken, H. (1997) Renormalization Group Analysis of Macrodispersion in a Directed Random Flow. Water Resources Research, 33, 10, 2287-2299. [CrossRef]
  • Jikov, V.V., Kozlov, S.M. and Oleinik, O.A. (1994) Homogenization of Differential Operators, Springer Verlag.
  • King, P. (1987) The Use of Field Theoretic Methods for the Study of Flow in Heterogeneous Porous Medium. J. Phys. A. Math. Gen., 20, 3935-3947. [CrossRef]
  • King, P. (1989) The Use of Renormalisation for Calculating Effective Permeability. Transport in Porous Media, 4, 37-58. [CrossRef]
  • Koslov, S.M. (1993) Central Limit Theorem for Multiscaled Permeability. Porous Media Meeting, Birkhauser, 19-33.
  • Kretz, V., Le Ravalec, M. and Roggero, F. (2002) An Integrated Reservoir Characterization Study Matching Production Data and 4D seismic. SPE - Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, San Antonio, 29 Sep.-2 Oct.
  • Lachassagne, P. (1989) Estimation des perméabilités moyennes dans les milieux poreux fortement non uniformes étudiés sous l’angle stochastique. Application aux essais de débit en aquifère captif. Thèse de doctorat, École des mines de Paris.
  • Landau, L.D. and Lifschitz, E.M. (1960) Electrodynamics of Continuous Media, Oxford, Pergamon.
  • Langlo, P. and Espedal (1994) Macrodispersion for Two-Phase, Immiscible Flow in Porous Media. Advances in Water Resources, 17, 217-316.
  • Lenormand, R. and Thiele, M. (1996) Determining Flow Equations from Stochastic Properties of a Permeability Field: the MHD model. SPE Journal, 179-190.
  • Lesieur, M. and Métais, O. (1996) New Trends in Large Eddy Simulations of Turbulence. Ann. Rev. of Fluid Mech., 28, 45-82. [CrossRef]
  • Mallet, J.L. (1997) Discrete Modeling for Natural Objects. Journal of Math. Geology, 29, 2, 199-219. [CrossRef] [MathSciNet]
  • Marle, C.M. (1981) Multiphase Flow in Porous Media, Éditions Technip, Paris.
  • Marle, C.M.,Simandoux, P.,Pacsirszky, J. and Gaulier, C. (1967) Étude du déplacement de fluides miscibles en milieu poreux stratifié. Revue de l’Institut Français du Pétrole, 22, 272-294.
  • Matheron, G. (1970) La théorie des variables régionalisées et ses applications. Les Cahiers du Centre de morphologie mathématique de Fontainebleau, Fascicule 5.
  • Matheron, G. (1967) Éléments pour une théorie des milieux poreux, Masson, Paris.
  • de Marsily, G. (1981) Hydrogéologie quantitative, Masson, Paris.
  • Matheron, G. (1967) Composition des perméabilités en milieu poreux hétérogène : méthode de Schwydler et règles de pondération Revue de l’Institut Français du Pétrole, 22, 3, 443-466.
  • Neuman, S.P. and Orr, S. (1993) Prediction of Steady State Flow in Nonuniform Geologic Media by Conditional Moments: Exact non Local Formalism, Effective Conductivities and Weak Approximation. Water Resources Research, 29, 2, 341-364. [CrossRef]
  • Nœtinger, B., Artus, V. and Ricard, L. Dynamics of the Water Oil Front for Two-Phase, Immiscible Flow in Heterogeneous Porous Media. 2 Isotropic Media, to be published in Transport in Porous Media.
  • Nœtinger, B. (2000) Computing the Effective Permeability of Log-Normal Permeability Fields Using Renormalization Methods. C.R. Acad. des sciences, Sciences de la Terre et des plan糥s, 331, 353-357.
  • Nœtinger, B. and Gautier, Y. (1998) Use of the Fourier-Laplace Transformation and of Diagrammatical Methods to Interpret Pumping Tests in Heterogeneous Reservoirs. Advances in Water Resources, 21, 581-590. [CrossRef]
  • Nœtinger, B. (1994) The Effective Permeability of a Heterogeneous Porous Medium. Transport in Porous Media, 15, 99-127. [CrossRef]
  • Nœtinger, B. and Artus, V. (2002) About Macrodispersion in Immiscible Diphasic Flows in Heterogeneous Porous Media: a Lagrangian Point of View. Second Symposium on Computational Modelling of Multiscale Phenomena, Petropolis, Brazil, 5-9 August.
  • Nœtinger, B. (1993) A Pressure Moment Approach for Helping Pressure-Transient Analysis in Complex Heterogeneous Reservoirs. SPE 26466, 68th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, 3-6 Oct., Houston, USA.
  • Nœtinger, B. and Haas, A. (1996) Permeability Averaging for Well-Tests in 3D Stochastic Reservoir Models. SPE 36653, Annual Technical Conference and Exhibition, 6-9 October, Denver, USA.
  • Nœtinger, B. and Jacquin, C. (1991) Experimental Tests of a Simple Permeability Composition Formula. SPE 22841, 66th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, 6-9 Oct., Dallas, USA.
  • Oliver, D.S. (1989) The Averaging Process in Permeability Estimation from Well Test Data. SPE 19845, SPE 64th Ann. Tech. Conf. and Exh.
  • Oliver, D.S., He, N. and Reynolds, A.C. (1996) Conditioning Permeability to Well Test Data. 5th ECMOR Conf. Proc. Leoben, 259-268.
  • Pianelo, L.,Guérillot, D. and Gallouët, T. (2000) Inversion simultanée des données sismiques et des données de production. Oil & Gas Science and Technology - Revue de l'IFP, 55, 3, 235-248. [CrossRef] [EDP Sciences]
  • Pianelo, L., Guérillot, D., Gallouët T. (2000) Coupled Inversion of Permeability and Acoustical Impedance an Outstanding Data Integration. ECMOR VII - 7th European Conference on the Mathematics of Oil Recovery, Baveno, Proceedings, Paper M-16, Sep. 5-8.
  • Quintard, M. and Whitaker, S. (1994) Transport in Ordered an Disordered Porous Media ii: Generalized Volume Averaging. Transport in Porous Media, 14, 179-206. [CrossRef]
  • Le Ravalec, M., Hu, L.Y. and Nœtinger, B. (2001) Stochastic Reservoir Modeling Constrained to Dynamic Data: Local Calibration and Inference of Structural Parameters. SPE 68883, SPE Journal.
  • Le Ravalec, M., Hu, L.Y. and Nœtinger, B. (1999) Stochastic Reservoir Model Constrained to Dynamic Data: Local Calibration and Inference of the Structural Parameters. SPE 56556, 74th Annual Technical Conference and Exhibition, 3-6 Oct., Houston, USA.
  • Le Ravalec, M., Hu, L.Y. and Nœtinger, B. (2000) The FFT Moving Average (FFT-MA) Method: an Efficient Tool for Generating and Conditioning Gaussian Simulations. Math. Geol. 32, 6.
  • Romeu, R.K. and Nœtinger, B. (1995) Calculation of Internodal Transmissibilities in Finite-Difference Models of Flow in Heteregeneous Media. Water Resources Research, April, 31, N4, 943-959.
  • Romeu, R.K., Lara, A.Q., Nœtinger, B. and Renard, G. (1996) Well Testing in Heterogeneous Media: a General Method to Calculate the Permeability Weighting Function. Four Latin American and Caribbean Petroleum Engineering Conference, 23-26 April, Port-of-Spain, Trinidad and Tobago.
  • Rubin, Y. and Dagan, G. (1988) Stochastic Analysis of Boundaries Effects on Head Spatial Variability in Heterogeneous Aquifers 1 Constant Head Boundary. Water Resources Research, 24, 10, 1689-1697. [CrossRef]
  • Ramé, M. and Killough, J.E. (1991) A New Approach to the Simulation of Flows in Highly Heterogeneous Porous Media. SPE 21247, SPE Symposium on Reservoir Simulation, Anaheim.
  • Renard, Ph. and de Marsily, G. (1997) Calculating Equivalent Permeability: a Review. Advances in Water Resources, 20, 5-6, 253-378. [CrossRef]
  • Saffman, P.G. and Taylor, G. (1958) The Penetration of a Fluid into a Porous Medium or Hele Shaw cell Containing a More Viscous Fluid. Proc. Royal Society of London, A245, 312-329. [CrossRef] [MathSciNet]
  • Schaaf, T., Mezghani, M. and Chavent, G. (2002) Direct Conditioning of Fine-Scale Facies Models to Dynamic Data by Combining the Gradual Deformation and Numerical Upscaling Techniques. Proc. 8th European Conference on the Mathematics of Oil Recovery, Freiberg, Germany.
  • Stauffer, D. (1985) Introduction to Percolation Theory, Taylor and Francis, London and Philadelphia.
  • Stepanayants, Y.A. and Teodorovitch, E.V. (2003) Effective Hydraulic Conductivity of a Randomly Heterogeneous Porous Medium. Water Resour. Res., 39, 3, 1065.
  • Tarantola, A. (1987) Inverse Problem Theory, Elsevier.
  • Urgelli, D. (1998) Upscaling of Transmissibility Applied to Corner Point Geometry. Paper SPE 52063, SPE - Society of Petroleum Engineers European Petroleum Conference, The Hague, Oct. 20-22.
  • Verdière, S. and Guérillot, D. (1996) Dual Mesh Method for Multiphase Flows in Heterogeneous Media. 5th European Conference on the Mathematics of Oil Recovery, Leoben, Austria, September 3-6.
  • Warren, J.E. and Price, H.S. (1961) Flow in Heterogeneous Porous Media. SPE Journal, 1, 153-169. [CrossRef]
  • de Witt, A. (1995) Correlation Structure Dependance of the Effective Permeability of Heterogeneous Porous Media. Physics of Fluids, 7, 11, 2553-2562. [CrossRef]
  • Zhang, Q. (1992) A Multiple Scale Theory of the Anomalous Mixing Length Growth for Tracer Flow in Heterogeneous Porous Media. J. Stat. Phys., 505, 485-501. [CrossRef]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.