Transport Property Estimation of Non-Uniform Porous Media

Document Type : Research Article


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

2 Petroleum Research Center, Petroleum University of Technology, Tehran, I.R. IRAN

3 Department of Chemical and Petroleum Engineering, Kansas University, Kansas , U.S.A.


In this work a glass micromodel which its grains and pores are non-uniform in size, shape and distribution is considered as porous medium. A two-dimensional random network model of micromodel with non-uniform pores has been constructed. The non-uniformity of porous model is achieved by assigning parametric distribution functions to pores throat and pores length, which was measured using image analysis technique. Statically derived expressions have been used for prediction of macroscopic properties of porous model including: dispersion coefficients, permeability-porosity ratio and capillary pressure. The results confirmed that predicted transport properties are in good agreement with the available experimental data.


Main Subjects

[1] Man, H. N., Jing, X. D., Pore Network Modeling of Electrical Resistivity and Capillary Pressure Characteristics, Transp. Porous Media, 41, 263, (2000).
[2] Dullien, F.A.L., “Porous Media: Fluid Transport and Pore Structure”, 2nd Edition, Academic Press, New York, (1992).         
[3] Scheidegger, A.E., Statistical Hydrodynamics in Porous Media, J. Appl. Phys., 25(8), 994, (1954).
[4] De Josselin de Jong, G., Longitudinal and Transverse Diffusion in Granular Deposits, Trans. American Geophys. Union, 39, 67, (1958).
[5] Saffman, P.G., A Theory of Dispersion in a Porous Medium, J. Fluid Mech., 6(3), 321, (1959).
[6] Greenkorn, R.A., Kessler, D.P., Dispersion in Heterogeneous, Non-Uniform Anisotropic Porous Media, in "Flow through Porous Media", American Chem. Soc., Washigton, D.C., (1970).
[7] Sahimi, M., Flow Phenomena in Rocks: From Continuum Models to Fractals, Percolation, Cellular Automata, and Simulating Annealing, Rev. Mod. Phys., 65, 1393, (1993).
[8] Holt, R.M., Fjaer, E., Torsaeter, O., Bakke, S., Petrophysical Laboratory Measurements  for Basin and Reservoir Evaluation, Mar. Pet. Geol., 13(4), 383, (1996).
[9]  Patzek, T. W., Verification of a Complete Pore Network Simulator of Drainage and Imbibition, Soc. Petrol. Eng. J., 6, 144, (2001).
[10] Piri, M., Blunt, M. J., Three-Dimensional Mixed-Wet Random Pore-Scale Network Modeling of Two- and Three-Phase Flow in Porous Media, I: Model Description, Phys. Rev. E, 71, 026301(2005).
[11] Buckley, J.,  Multiphase  Displacement  in  Micro-models, in "Interfacial Phenomena in Petroleum Technology", Edited by N. Morrow, Marcel Decker, New York, (1991).
[12] Sahimi, M., Hughes, B.D., Scriven, L.E., Davis, H.T., Dispersion in Flow through Porous Media, I: One-Phase Flow, Chem. Eng. Sci. 41, 2103, (1986).
[13] Bruderer, C., Bernabe, Y., Network Modeling of Dispersion: Transition from Taylor Dispersion in Homogeneous Networks to Mechanical Dispersion in Very Heterogeneous Ones, Water Resour. Res., 37, 897, (2001).
[14] Lowe,  C. P.,  Frenkel,  D.,  Do  Hydrodynamic Dispersion Coefficients Exist?, Phys. Rev. Lett., 77, 4552, (1996).
[15] Souto, H. P. A., Moyne, C., Dispersion in Two-Dimensional Periodic Porous Media, Part II:Dispersion Tensor, Phys. Fluids 9, 2253, (1997).
[16] Huseby, O., Thovert, J.F., Adler, P.M., Dispersion in Three-Dimensional Fracture Networks, Phys. Fluids, 13, 594, (2001).
[17] Wolfsberg,  A. V.,  Freyberg,  D. L.,  Efficient Simulation of Single Species and Multispecies Transport in Groundwater with Local Adaptive Grid Refinement, Water Resour. Res., 30 (11), 2979, (1994).
[18] Tompson,  A. F. B.,  Gelhar,  L. W.,  Numerical Simulation of Solute Transport in 3D, Randomly Heterogeneous Porous Media, Water Resour. Res., 26(10), 2541, (1990).
[19] LaBolle,  E.  M.,  Fogg,  G.  E., Tompson,  A. F. B., Random-Walk Simulation of Transport in Heterogeneous Porous Media: Local Mass Conservation Problem and Implementation Methods, Water Resour. Res., 32(3), 583, (1996).
[20] Ghazanfari, M. H.,  Rashtchian,  D.,  Kharrat, R., Voussughi, S., Capillary Pressure Estimation of Porous Media Using Statistical Pore Size Function, Chem. Eng. Tech., 30, 862, (2007).
[21] Marle, C.M., "Multiphase Flow in Porous Media":, Gulf Publishing, Houston, (1981).
[22] Andrew, L.Z., Aimar, P., Meireles, M., Pimbely, J.M., Belfort, G., Use of the Log-Normal Density Function to Analyze Membrane Pore Size Distribution: Functional Forms and Discrepancies, J. Mem. Sci., 91, 293, (1994)
[23] Ghazanfari, M.H., Prediction of Multiphase Flow Properties in Porous Media Using Micromodel Experiments and Pore-Scale Modeling, PhD. Thesis, Sharif University of Technology, Tehran (2008).
[24] McKellar, M.., Wardlaw , N., A Method of Making Two-Dimensional Glass Micromodels of Pore Systems, J. Can. Pet. Technol., 21, 39, (1982).
[25] Bear, J, Bachmat, Y., "Introduction to Modeling of Transport Phenomena in Porous Media", Kluwer Academic Publishers, Dordrecht, (1990).
[26] Bear, J., "Dynamics of Fluids in Porous Media", Elsevier, New York , (1975).
[27] Ghazanfari M.H., Kharrat, R., Rachtchian, D. and Vossoughi S., Statistical Model of Dispersion in 2-D Glass Micromodel, SPE 113343, IOR2008, Tusla, (2008).
[28] Ghazanfari, M. H.,  Rashtchian,  D.,  Kharrat, R., Vossoughi, S., Khodabakhsh, M., Unsteady State Relative Permeability and Capillary Pressure Estimation of Porous Media, XVI International CMWR Conf., Denmark, (2006).