Multiphase Flow in Porous Media: II. Pore-level Modeling

Abstract

Abstract The pores a phase occupies and the way those pores are interconnected are shown here to determine the macroscopic transport properties of that phase. Such transport properties are dispersivity, capacitance, relative phase. Such transport properties are dispersivity, capacitance, relative permeability, and capillary pressure. A pore-level, three-dimensional permeability, and capillary pressure. A pore-level, three-dimensional network model is presented in this paper which incorporates the structure of porous rock, pore-level fluid displacement mechanisms, and saturation history. The model calculates pore-level distribution of fluids, and then computes the steady-state transport properties of such distributions. The results are compared with experimentally obtained values and illustrate the nature of fluid flow and the mechanisms of mixing in strongly wetting rocks. Introduction Multiphase transport in porous media is characterized traditionally by means of several macroscopic transport properties such as relative permeability, capillary pressure and dispersivity. These properties have permeability, capillary pressure and dispersivity. These properties have been found experimentally to depend on parameters such as fluid saturations, saturation history, and fluid properties as well as pore space morphology. Thus the state of fluid distribution within the pores is important in determining the transport properties. This work deals with how the fluid distributions are created and in what way they affect the macroscopic transport properties. The pore space in most naturally occurring media is highly chaotic. But multiphase flow through it is not a random process. It is governed by continuum-level laws of mechanics such as the Navier-Stokes equation, continuity equation, diffusion equation and the boundary conditions at the fluid-fluid, solid-fluid interfaces and at solid-fluid-fluid contact lines. But the complex morphology of any naturally occurring porous medium defies implementation of a model that directly incorporates continuum laws to predict macroscopic transport properties. In flows where the force of capillarity is not negligible (appropriate for most flows encountered in oil recovery), it is possible to translate the continuum laws into pore- level laws, i.e. conditions for significant pore-level events. A pore- level model treats the pore space as an assemblage of pore segments and incorporates pore-level laws to calculate fluid distribution and macroscopic transport properties. Several pore-level models have been used in the past; they vary with respect to dimensionality, and connectedness of pore space, shape of pore segments and details of pore-level mechanisms used. The bundle-of-tubes models are the most widely used; Van Brakel gives an excellent review. These models are all too simplistic and lack the important network topology of real pore space. Several statistical methods have also been used for modelling single-phase and multi-phase transport in porous media. Use of effective medium theory to compute single-phase permeability illustrates the role of pore size distribution and connectivity. Physical-statistical models fro single-phase dispersion show the role of fluid flow in mechanical mixing. Application of percolation theory to multi-phase flow by Larson et al. illustrates the critical role of medium topology. Wilson and Gelhar have extended Haring and Greenkorn's model to calculate dispersion in the wetting phase in partially saturated media; but they had to make numerous assumptions regarding fluid distributions. Purely statistical methods are limited in the details of pore morphology and displacement physics they can incorporate. To date no satisfactory statistical model has been proposed for explaining mixing in multi-phase flow. Fatt was the first to use a multiply-connected pore space –– a two-dimensional network of cylindrical tubes in a direct computational model. Others have modified Fatt's original model in terms of connectivity, shape of pore segments and pore level physics. Ksenzhek and Lin and Slattery used three-dimensional networks.