The Effects of Isolated Permeability Interferences on the Sweep Efficiency and Conductivity of a Five-Spot Network

Abstract The results of an experimental and theoretical study of the effects of rectilinear impermeable barriers and highly permeable channels on the sweep efficiency and conductivity of a five-spot network are presented. The study was carried out using Hele-Shaw and conductive sheet analogs for both normal and inverted flood patterns. A functional relationship was developed which provides quantitative prediction of the above parameters; i.e., sweep efficiency and conductivity, for the nonhomogeneous system. To evaluate this, it is necessary only to measure the interference modulus of the obstacle using a simple expression. The results indicate that impermeable barriers, with an interference modulus greater than zero, always cause a decrease in the conductivity and the sweep efficiency of the pattern. On the other hand, permeability channels do not have a significant effect on these parameters, unless they are located along the streamlines. The study also discusses a method of formulating the difference equations pertaining to the two-dimensional Laplacian in a system containing rectilinear barriers. In addition, a technique is described for tracing the progress of a free surface, using marked particles, in a stream containing discontinuities such as those occurring at the extremities of barriers. The above computational scheme was used in a digital computer program to simulate results of the Hele-Shaw analog. The computed values of sweep efficiency were in good agreement with the experimental values. INTRODUCTION At the present time waterflooding remains the most widely used technique for the secondary recovery of oil. Among the numerous factors that affect the performance of a waterflood, the areal sweep efficiency constitutes one of the most critical parameters. It is a function only of the geometric distribution of the wells for a homogeneous medium and unit mobility ratio. Geological considerations, however, such as the presence of sealing faults or solution channels in the rock matrix, would generally exert an adverse effect on the areal sweep efficiency of a waterflood network. Surprisingly little information is presently available1-3 on the quantitative implications of such permeability interferences. It was the object of this investigation to consider the presence of rectilinear, impermeable and highly permeable interferences in an otherwise homogeneous five-spot pattern, and to analyze their effects on the resulting sweep efficiency and pattern conductivity. The experimental phase of the study was conducted using two different models: the Hele-Shaw flow cell and the field plotter. For experimental convenience, the geometric boundaries of the five-spot were assumed to constitute streamlines even in the case where the interference was asymmetrically placed with respect to a repeated five-spot pattern. A second object of the study was to develop a computational scheme for numerically calculating the pressure distribution in a five-spot flow pattern containing rectilinear, impermeable barriers, and to use this distribution to compute the sweep efficiency. EXPERIMENTAL PROCEDURE HELE-SHAW ANALOG The Hele-Shaw analog was used both as a visual model and for determining the sweep efficiency for systems involving impermeable barriers. The physical limitations of this model as a means of experimentally studying the motion of a fluid in porous medium have been adequately discussed elsewhere.2,7 Likewise, it can be easily verified that the analogy remain s valid when a portion of the region between the plates contains an obstacle of the same thickness as the distance between the plates.4 HELE-SHAW ANALOG The Hele-Shaw analog was used both as a visual model and for determining the sweep efficiency for systems involving impermeable barriers. The physical limitations of this model as a means of experimentally studying the motion of a fluid in porous medium have been adequately discussed elsewhere.2,7 Likewise, it can be easily verified that the analogy remain s valid when a portion of the region between the plates contains an obstacle of the same thickness as the distance between the plates.4