A New Approach for Constructing Pore Network Model of Two Phase Flow in Porous Media

Document Type : Research Article


Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, I.R. IRAN


Development of pore network models for real porous media requires a detailed understanding of physical processes occurring on the microscopic scale and a complete description of porous media morphology. In this study, the microstructure of porous media has been represented by three dimensional networks of interconnected pores and throats which are designed by an object oriented approach. Afterwards, the connectivity of the system has been optimized by an optimization algorithm. To validate the methodology, a network of a carbonate sample is constructed. In this model, the geometrical characteristics of the pores and throats, such as their shapes, effective radii and lengths, are selected from the image analysis of SEM picture and statistical distribution methods based on the mercury injection test results. Then the constructed network is further tuned according to laboratory measured porosity, absolute permeability and capillary pressure. Having built a flexible and detailed model, its prediction of relative permeability and saturation variation along a core plug are compared with experimental data for both drainage and imbibition phenomena. This comparison shows good matches for almost all experimentally measured data.


Main Subjects

1]  Fatt, I., The Network Model of Porous Media, I.Capillary Pressure Characteristics, Trans. AZME, 207, 144 (1956a).
[2]  Fatt, I., The Network Model of Porous Media, II. Dynamic Properties of a Single Size Tube Network, Trans. AIME, 207, 160 (1956b).
[3]  Fatt, I., The Network Model of Porous Media, III. Dynamic Properties of Networks with Tube Radius Distribution, Trans. AlME, 207, 164 (1956c).
[4]  Blunt, M., King, M. J. and Scher, H. Simulation and Theory of Two-Phase Flow in Porous Media, Physical Review A, 46(12), 7680 (1992).
[5] Vizika, O., Avraam, D.G. and Payatakes, A.C., On the Role of the Viscosity Ratio During Low-Capillary Number Forced Imbibition in Porous Media, J. Coil. lnt. Sci., 165, 386 (1994).
[6] Bryant, S.L., Mellor, D.W., Cade, C.A., Physically Representative Network Models of Transport in Porous Media, AIChE J., 39, 387 (1993).
[7]  Hughes, R.G., Blunt M.J. Pore Scale Modeling of Rate Effects in Imbibition, Transport in Porous Media, 40, 295 (2000).
[8] Blunt, M. J., Constraints on Contact Angles for Multiple Phases in Thermodynamic Equilibrium, Journal of Colloid and Interface Science, 239, 281 (2001).
[9] Jackson, M. D., Valvatne, P. H. and Blunt, M. J., Prediction of Wettability Variation and its Impact on Flow Using Pore- to Reservoir-Scale Simulations, Journal of Petroleum Science and Engineering, 39, 231 (2003).
[10] Kovscek, A.R., Wong, H. and Radke, C.J., A Pore Level Scenario for the Development of Mixed Wettability in Oil Reservoirs, AICHE J., 39, 1072 (1993).
[11] Man, H.N. and Jing, X.D., Pore Network Modeling of Electrical Resistivity and Capillary Pressure Characteristics, Advances in Water Resources, 41, 263 (2000).
[12] Blunt, M., Effects of Heterogeneity and Wetting on Relative Permeability Using Pore Level Modeling, Society of Petroleum Engineers Journal, 2, 70 (1997).
[13] Blunt, M. J., “Flow in Porous Media-Pore-network Models and Multiphase Flow, Current Opinion in Colloid and Interface Science, 6(3), 197 (2001).
[14] Valvatne, P. H. and Blunt, M. J., “Predictive Pore-Scale Network Modeling,” SPE844550, Proceedings of the SPE Annual Meeting, Denver, Colorado, 5-8 October (2003).
[15] Okabe, H. and Blunt, M. J., Multiple-Point Statistics to Generate Geologically Realistic Pore-Scale Representations, Proceedings of the Society of Core Analysts’ Annual Meeting, SCA2003-A33, 22-25 September, PAU, FRANCE (2003).
[16] Vogel,  H. J.  and  Roth, K., A New Approach for Determining Effective Soil Hydraulic Functions, European Journal of Soil Science, 49(4), 547 (1997).
[17] Øren,  P.  and  Bakke,  S.,  Process   Based Recons-truction of Sandstones and Prediction of Transport Properties, Transport in Porous Media, 46, 311 (2002).
[18] Øren, P.E. and Pinczewski, W.V., Fluid Distribution and Pore-Scale Displacement Mechanisms in Drainage Dominated Three-Phase Flow, Transport in Porous Media, 20, 105 (1995).
[19] Nguyen, V.H., Sheppard, A.P., Knackstedt, M.A., Pinczewski, W.V., A Dynamic Network Model for Imbibition, Paper SPE 90365, Presented at eh 2004 SPE International Petroleum Conference in Mexico Held in Puebla, Mexico,8-9 November (2004).
[20] Piri, M. and Blunt, M. J., “Pore-Scale Modeling of Three-Phase Flow in Mixed-Wet systems,” SPE 77726, Proceedings of the SPE Annual Meeting, San Antonio, Texas, 29 September-2 October (2002).
[21] Lopez, X. P., Valvatne, P. H. and Blunt, M. J., Predictive Network Modeling of Single-Phase Non-Newtonian Flow in Porous Media, Journal of Colloid and Interface Science, 264(1), 256 (2003).
[22] Valvatne, P., Piri, M. Lopez, X. and Blunt, M. J., “Predictive Pore-Scale Modeling of Single and Multiphase Flow,” Proceedings of the ESF Workshop on Multiphase Flow Porous Media,Delft, June (2003).
[23] Dixit, AB., McDougall, SR., Sorbie, KS., A Pore-Level Investigation of Relative-Permeability Hysteresis in Water-Wet Systems, SPE J, 3,115 (1998).
[24] Lowry, MI, Miller, CT, Pore-Scale Modeling of Nonwetting-Phase Residual in Porous Media, Water Resources Res., 31(3), 455 (1995).
[25] Adler,  P.M.,  Jacquin,  C.G,  Thovert,  J.F.,  The Formation Factor of Reconstructed Porous Media, Water Resources Res., 28, 15716 (1992).
[26] Blunt, M.J., Jackson, M.D, Piri, M., Valvatne, P.H. Detailed Physics, Predictive Capabilities and Macroscopic Consequences for Pore-network Models of Multi-phase Flow Advances in Water Resources, 25, 1069 (2002).
[27] Blunt, M.J, Effects of Heterogeneity and Wetting on Relative Permeability using Pore Level Modeling, SPE J., 2, 70 (1997).
[28] Schwarz, B. C. E., Devinny, J. S. and Tsotsis, T. T., A Biofilter Network Model Importance of the Pore Structure and Other Large-Scale Heterogeneities, Chemical Engineering Science, 56(2), 475 (2001).
[29] Wilkinson, D, Willimsen, J., Invasion Percolation: A New Form of Percolation Theory, J. Phys. A,
16, 3365 (1983).
[30] Mark  A.  Knackstedt,  Adrian  P.  Sheppard,  and Sahimi, M., Pore Network Modeling of Two-Phase Flow in Porous Rock, The Effect of Correlated Heterogeneity, Advances in Water Resources, 24, 257 (2001).
[31] Blunt, M.J. and Scher, H., Pore-Level Modeling of Wetting, Phys. Rev., E52, 6387 (1995).
[32] Sahimi, M.,  Flow  Phenomena  in  Rocks,  from Continuum Models to Fractals, Percolation, Cellular Automata and Simulated Annealing, Rev. Mod. Phys., 65, 1393 (1993).
[33] Heiba, AA, Sahimi, M, Scriven LE, Davis HT. Percolation Theory of Two-Phase Relative Permeability, SPE Paper 11015, (1982).
[34] Kantzas, A, Chatzis, I., Network Simulation of Relative Permeability Curves Using a Bond Correlated-Site Percolation Model of Pore Structure, Chem. Eng Commun., 69, 191 (1988).
[35] Al-Gharbi, M. S. and Blunt, M. J., “A 2D Dynamic Pore Network Model for Modeling Primary Drainage,” Proceedings of the ESF Workshop on Multiphase Flow in Porous Media,Delft, June (2003).
[36] Hoshen J, Kopelman R. Percolation and Cluster Size, Phys. Rev. B, 14, 3438 (1976).
[37] Singiresu S. Rao, “Engineering Optimization: Theory and Practice”, 3rd Edition, Wiley-Interscience, (1996).
[38] Brown, G. O., (2002). Henry Darcy and the Making of a Law, Water Resources Research, 38(7) doi: 10.1029/2001WR000727. (Reviews the process of Darcy's discovery).
[39] Patzek, T. W. and Silin, D. B., Shape Factor and Hydraulic Conductance in Noncircular Capillaries, I.One-Phase Creeping Flow, Journal of Colloid and Interface Science, 236(2), 295 (2001).
[40] Fenwick, D. H. and Blunt, M. J. Three-Dimensional Modeling of Three Phases Imbibition and Drainage, Advances in Water Resources, 21(2), 121 (1998).
[41] Øren, P.E., Bakke, S. and Arntzen, O. J., Extending Predictive Capabilities to Network Models, SPE Journal, 3(4), 324, (……..).
[42] Mogensen, K. and Stenby, E.H. A Dynamic Pore-Scale Model of Imbibition, Paper SPE 39658, Presented at the 1998 SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma, 19-22 April (1998).
[43] Ransohoff, T.C. and Radke, C.J., Laminar Flow of a Wetting Liquid along the Corners of a Predominantly Gas-Occupied Noncircular Pore, J. Coil. Int. Sci., 121, 392 (1988).
[44] Blair, P, M, Calculation of Oil Displacement by Countercurrent Water Imbibition, Sot. Pet. Eng. J., 195 (1964).
[45] Grham, J. W. and Richardson, J. G., Theory and Application of Imbibition Phenomena in Recovery of Oil, Transactions of the AIME, 216, 377 (1959).
[46] Lenormand, R. Marconi, C., “Role of Roughness and Edges During Imbibition in Square Capillaries," Paper SPE 13264 in Proceedings of the  59th SPE Annual Technical Conference and Exhibition,Houston,TX, September (1984).
[47] Pickell, J.J., Swanson, B.F. and Hickmann, W.B. Application of Air-Mercury and Oil-Air Capillary Pressure Data in the Study of Pore Structure and Fluid Distribution, SPE J., 6, 55 (1966).
[48] Roof, J.G., Snap-Off of Oil Droplets in Water-Wet Pores, Society Petroleum Engineering Journal, 10, 85 (1970).
[49] Oak, M.J., Three-Phase Relative Permeability of Water-WetBerea, Paper SPE 20183, Proceedings of the SPE.
[50] Effects of Spatially Heterogeneous Porosity on Matrix Diffusion as Investigated by X-ray Absorption Imaging, J. Contam. Hydrol., 42, 285 (…….).
[51] Lenormand,  R.,  “Pattern  Growth  and  Fluid Displacements through Porous Media”, Physical, A, 140, 114 (1986).
[52] Hilbert, M. and Miller, C.T.: Pore-morphology-Based Simulation of Drainage in TotallyWetting Porous Media, Advances in Water Resources, 24, 243 (2001).