### Prediction Of Two-Phase Relative Permeability In Porqus Media Based On Network Modeling Of Lattice Gas Automata

#### Abstract

The displacement of one fluid by another is controlled by the geometry of the pore space. The relative hydrodynamic conductance of each fluid at a given saturation is the relative permeability, while the pressure difference between the phases is the capillary pressure. These two functions determine the macroscopic fluid flow behavior in hydrocarbon reservoir over the scale of centimeters to kilometers.

At the pore seale fluids reside in intergranular space of typical sedimentary rocks. The rock type and fluid properties are likely to change drastically through the reservoir, the only sample of rock come from drilling wells, which represents a tiny fraction of the total volume in a reservoir. Furthermore, relative permeability measurements on these samples are difficult and time consuming. To quantify and control uncertainty in recovery estimations, it is necessary to have some theoretical understanding of transport properties. Such understanding would enable us to predict the sensitivity of relative permeability to geological factors such rosity, and the nature of the fluids. This work is a pre- liminary step in this direction. A more important result from this work is that we are now able to quantify the change in the relative permeability to those geological factors.

In this paper a pore structure and displacements mechanisms to model two-phase flow in porous media were constructed using lattice gas automata. The void space of the media is represented as a network of large spaces (pores) connected by narrower throats. The aggregation of cell pore volumes is used to calculate the porosity of the network and the fluid saturation when different cells are occupied by different fluids. By judicious choices for the distribution of pore and throat sizes of the network it is possible to predict relative permeability. For predicting the absolute and relative permeability, it is assumed that the viscous pressure drops occur across the throats.#### Keywords

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Blunt, MJ, King, MJ, and Scher, H., 1992: "Simulation and Theory of Two-phase Flow in Porous Media", Physical Review A, 46, p.7680 - 7699.

Blunt, MJ , and Scher, H., 1995: "Pore-level Modeling of Wetting". Physical Review A, 46, p.7680 - 2. 7699.

Blunt, MJ, 1997: "Physically Based Network Modeling of Multiphase Flow in Intermediate-Wet Porous Media", Journal of Petroleum Science and Engineering , 14, p.1 - 14.

Boghosian, BM, and Coveney, PV, 2000: "A Particulate Basis for an Immiscible Lattice-Gas Model", Computer Physics Communications, 129, p.46 - 55.

Collins , RE, 1976 : Flow of Fluids through Porous Material, PennWell Books, Tulsa-Oklahoma.: PennWell Publishing Co., p.3 - 26; and 139- 149.

Dullien, FAL, 1992: Porous Media: Fluids Transport and Pore Structure, New York.: Aca- demic Press, Inc.

Frisch, U., Hasslacher, B., and Pomeau, Y. , 1986: "Lattice-Gas Automata for the Navier-Stokes Equation", Physical Review Letters, 56, p.1505 - 1508.

Frisch, U., d' HumiÃ¨res, D., Hasslacher, B., Lallemand , P., and Pomeau, Y., 1987: "Lattice Gas Hydrodynamics in Two and Three Dimensions", Complex Systems, 1, p.649 - 707.

Kadanoff, LP, McNamara, GR, and Zanetti, G., 1989: "From Automata to Fluid Flow: Comparison of Simulation and Theory", Physical Review A, 40, p.4527-4541.

Kharabaf, H., and Yortsos, Y. C., 1996 : "A Pore-Network Model for Foam Formation and Propagation in Porous Media", SPE Annual Technical Conference and Exhibition. Denver, p.779 - 790.

Koponen, A., Kataja, M., and Timonen, J., 1997: "Permeability and Porosity of Porous Media", Physical Review E, 56, p.3319 - 3325 .

Kristanto, D, and Awang, M., 2001: "Determina- tion of the Permeability and Porosity of Porous Media by Lattice Gas Automata Method", MSTC01- B-82, Malaysian Science and Technology Congress (MSTC) 2001, Melaka, Malaysia, 8-10 October.

Kristanto, D, and Awang, M., 2002: "Simulation of Two-phase Reservoir Fluids Separation by Immis- cible Lattice Gas Automata", 4ASTC-A-13, 4th Asian Science and Technology Congress (4ASTC) 9. 2002, Kuala Lumpur, Malaysia, 25-27 April.

Kristanto, D, and Awang, M., 2003 : "Lattice Gas Automata Simulations to Determine the Macroscopic Properties of a Porous Medium", Advanced Tech- nology Congress (ATC) 2003 in the Conference on Advances Theoretical Sciences (CATS), Putrajaya - Kuala Lumpur, Malaysia, 20-21 May.

Kristanto, D, and Awang, M., 2003: "Estimation of Surface Tension for Two Immiscible Fluids Using Lattice Gas Automata", SPE 84892, Society of Petroleum Engineers International on Improved Oil Recovery Conference in Asia Pacific (SPE- IIORC), Kuala Lumpur, Malaysia, 20-21 October.

Larson, RG, Davis, HT, and Scriven, LE, 1981 "Displacement of Residual Nonwetting Fluid from Porous Media", Chemical Engineering Science, 36, p.75 - 85.

Oren, PE, and Pinczewski, WV, 1995: "Fluid Distribution and Pore-Scale Displacement Mechanisms in Drainage Dominated Threephase Flow", Transport in Porous Media, 20, p.105 - 133.

Rege, SD, and Fogler, HS, 1987 : "Network Modeling for Straining Dominated Particle Entrapment in Porous Media", Chemical Engineering Science, 42, p. 1553-1564.

Rothman, DH, 1988: "Cellular-automaton Fluids: A Model for Flow in Porous Media", Geophysics, 53, p.509 - 518.

Rothman, DH, and Keller, JM, 1988 : "Immiscible Cellular-Automaton Fluids", Journal of Statistical Physics, 52, p.1119 - 1127.

Rothman, DH, and Zaleski, S., 1997: Lattice Gas Cellular Automata: Simple Models of Complex Hydrodynamics, London, UK. : Cambridge University Press, p.12 - 60; 151 - 165; and 203 - 232.

Sheng, P., and Zhou, MY, 1988 : "Dynamic Permeability in Porous Media", Physical Review Letters, 61, p.1591 - 1594.

Sandrea, R., and Nielsen, R., 1994 : Dynamics of Petroleum Reservoirs Under Gas Injection, Houston, Texas.: Gulf Publishing Company, p.58-92.

Wolfram, S., 1986 : "Cellular Automaton Fluids 1: Basic Theory", Journal of Statistical Physics, 45, p.471 - 529.

Zaleski, S., and Appert, C., 1990: "Lattice Gas with a Liquid-Gas Transition", Physical Review Letters, 64, p.1 - 4.

DOI: https://doi.org/10.29017/SCOG.27.1.874

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