A dynamic network model for two‐phase immiscible flow

A dynamic pore‐scale network model is formulated for two‐phase immiscible flow. Interfaces are tracked through the pore throats using a modified Poiseuille equation, whereas special displacement rules are used at the pore bodies. The model allows interfaces to move over several pore‐lengths within a time step. Initial computational results are presented for a drainage experiment to demonstrate some of the features of the model.

[1]  J. Brakel Pore space models for transport phenomena in porous media review and evaluation with special emphasis on capillary liquid transport , 1975 .

[2]  F. Dullien Porous Media: Fluid Transport and Pore Structure , 1979 .

[3]  Alkiviades C. Payatakes,et al.  Network simulation of steady-state two-phase flow in consolidated porous media , 1996 .

[4]  Norman R. Morrow,et al.  Interfacial Phenomena in Petroleum Recovery , 1990 .

[5]  Madalena M. Dias,et al.  Network models for two-phase flow in porous media Part 1. Immiscible microdisplacement of non-wetting fluids , 1986, Journal of Fluid Mechanics.

[6]  Salin,et al.  Invasion percolation in a hydrostatic or permeability gradient: Experiments and simulations. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  V. Dussan Immiscible liquid displacement in a capillary tube: The moving contact line , 1977 .

[8]  Michael A. Celia,et al.  Recent advances in pore scale models for multiphase flow in porous media , 1995 .

[9]  William G. Gray,et al.  General conservation equations for multi-phase systems: 1. Averaging procedure , 1979 .

[10]  Martin J. Blunt,et al.  Relative permeabilities from two- and three-dimensional pore-scale network modelling , 1991 .

[11]  William G. Gray,et al.  Macroscale continuum mechanics for multiphase porous-media flow including phases, interfaces, common lines and common points , 1998 .

[12]  Cesar Zarcone,et al.  Numerical models and experiments on immiscible displacements in porous media , 1988, Journal of Fluid Mechanics.

[13]  Madalena M. Dias,et al.  Network models for two-phase flow in porous media Part 2. Motion of oil ganglia , 1986, Journal of Fluid Mechanics.

[14]  William G. Gray,et al.  Thermodynamic basis of capillary pressure in porous media , 1993 .

[15]  L. Scriven,et al.  Capillary dispersion in porous media at low wetting phase saturations , 1989 .

[16]  T. J. Lasseter,et al.  Two-phase flow in random network models of porous media , 1985 .

[17]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[18]  E. W. Washburn The Dynamics of Capillary Flow , 1921 .

[19]  T. Matsuura,et al.  Viscous and capillary pressures during drainage: Network simulations and experiments , 1997 .

[20]  Michael A. Celia,et al.  A Functional Relationship Between Capillary Pressure, Saturation, and Interfacial Area as Revealed by a Pore‐Scale Network Model , 1996 .

[21]  L. Scriven,et al.  Hydrodynamic Model of Steady Movement of a Solid / Liquid / Fluid Contact Line , 1971 .

[22]  William G. Gray,et al.  Unsaturated Flow Theory Including Interfacial Phenomena , 1991 .

[23]  Joel Koplik,et al.  Creeping flow in two-dimensional networks , 1982, Journal of Fluid Mechanics.

[24]  William G. Gray,et al.  Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries , 1990 .

[25]  G. Constantinides,et al.  A theoretical model of collision and coalescence of ganglia in porous media , 1991 .