Abstract
Using the numerical techniques shown in this paper it is possible to compute the simultaneous dynamical behavior of multiple fluid-fluid interfaces in two dimensions. Hence, fluid-fluid interface models of several oil recovery processes can be constructed which allow prediction of the effect of fluid flow in two dimensions on the behavior of these processes while taking into account various physical effects, such as saturation gradients, phase changes and thermal stimulation. Techniques for constructing fluid-fluid interface approximations for several oil recovery processes are reviewed. The validity of these techniques is established by comparison to experimental results. The availability of a computer program for computing the behavior of multiple fluid-fluid interface problems makes the use of potentiometric models uneconomic. The results indicate the areal sweep efficiencies obtained from potentiometric model studies at high mobility ratios may be somewhat optimistic. The results also indicate that the areal sweep efficiency curves obtained at high viscosity ratios mu2/mu1 greater than 2–4 using miscible fluids in porous media are misleading and that considerable care must be taken in defining the mobility ratio for a displacement process, especially for miscible fluids.
Introduction
Many of the methods used to estimate areal sweep efficiency assume that the oil recovery process can be represented by one or more fluid-fluid interfaces. When the mobilities of the displaced and displacing phases are assumed equal, this quantity can be computed using analytical mathematical methods. For non-unit mobility ratio, experimental methods based upon the fluid-fluid interface concept include potentiometric and electrolytic blotter models. Scaled models of porous media have also been used to study this problem. Fay and Prats and Aronofsky used numerical techniques to compute breakthrough sweep efficiency, but neither of these studies were extended beyond breakthrough. Numerical techniques which have been developed for solving a general fluid-fluid interface problem are presented in a companion paper. These techniques have been incorporated into a program for a large-scale digital computer which can treat simultaneously the dynamical behavior of as many as six fluid-fluid interfaces. Thus it is possible to simulate the behavior of several oil recovery processes taking into account such effects as saturation gradients. Techniques for representing several oil recovery processes by fluid-fluid interfaces are presented. Processes considered are conventional water flooding with and without a mobile gas phase, hot water flooding, miscible flooding and enriched gas drive. Other processes, whose effects could he studied by this technique, but are not considered in detail here, are underground combustion and steam injection processes and various slug processes such as gas-water injection and alcohol-solvent processes. Theoretical results obtained with single interfaces for mobility ratios of 0.25, 1, 2, 4, 8, 16, 32 and 64 in a repeated five-spot are compared to experimental results for this geometrical configuration obtained using miscible fluids and conductive analogs. Predicted recovery curves for water flooding in a repeated five-spot are compared to experimental results reported in the literature. Example calculations are shown for a conventional water flood in the presence of a free gas phase and for a hot-water flood.
MATHEMATICAL PRELIMINARIES
We assume that the rock matrix is homogeneous with constant thickness, absolute permeability and porosity. The fluids are incompressible. We also neglect the effects of gravity.
SPEJ
P. 171ˆ
Numerical Method for Fuel Distribution Downstream of the Emulsifying Channel Injector
