Network models for two-phase flow in porous media Part 1. Immiscible microdisplacement of non-wetting fluids

A theoretical simulator of immiscible displacement of a non-wetting fluid by a wetting one in a random porous medium is developed. The porous medium is modelled as a network of randomly sized unit cells of the constricted-tube type. Under creeping-flow conditions the problem is reduced to a system of linear equations, the solution of which gives the instantaneous pressures at the nodes and the corresponding flowrates through the unit cells. The pattern and rate of the displacement are obtained by assuming quasi-static flow and taking small time increments. The porous medium adopted for the simulations is a sandpack with porosity 0.395 and grain sizes in the range from 74 to 148 μrn. The effects of the capillary number, Ca , and the viscosity ratio, κ = μ o /μ w , are studied. The results confirm the importance of the capillary number for displacement, but they also show that for moderate and high Ca values the role of κ is pivotal. When the viscosity ratio is favourable (κ 10 −5 , and becomes excellent as Ca → 10 −3 . On the other hand, when the viscosity ratio is unfavourable (κ > 1), the microdisplacement efficiency begins to improve only for Ca values larger than, say, 5 × 10 −4 , and is substantially inferior to that achieved with κ < 1 and the same Ca value. In addition to the residual saturation of the non-wetting fluid, the simulator predicts the time required for the displacement, the pattern of the transition zone, the size distribution of the entrapped ganglia, and the acceptance fraction as functions of Ca , κ, and the porous-medium geometry.