Two-Phase Flow in Random Network Models of Porous Media

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Abstract
To explore how the microscopic geometry of a pore space affects the macroscopic characteristics of fluid flow in porous media, we have used approximate solutions of the Navier-Stokes equations to calculate the flow of two fluids in random networks. The model pore space consists of an array of pores of variable radius connected to a random number of nearest neighbors by throats of variable length and radius. The various size and connectedness distributions may be arbitrarily assigned, as are the wetting characteristics of the two fluids in the pore space. The fluids are assumed to be incompressible, immiscible, Newtonian, and of equal viscosity. In the calculation, we use Stokes flow results for the motion of the individual fluids and incorporate microscopic capillary force by using the Washburn approximation. At any time, the problem is mathematically identical to a random electrical network of resistors, batteries, and diodes. From the numerical solution of the latter, we compute the fluid velocities and saturation rates of change and use a discrete timestepping procedure to follow the subsequent motion. The scale of the computation has restricted us so far to networks of hundreds of pores in two dimensions (2D). Within these limitations, we discuss the dependence of residual oil saturations and interface shapes on network geometry and flow conditions.