Reservoir Engineering – Laboratory Research - Laboratory Studies of Five-Spot Waterflood Performance

A program of scaled flow model experiments has been undertaken to study the performance of five-spot water floods. The modeling procedures are discussed and the construction and operation of the flow models are described. The tests were specifically designed to investigate the effects of injection rate and of oil-to-water viscosity ratio on oil recovery. The areal sweep of five-spot water floods was also studied, and direct comparisons between five-spot and linear flooding behavior have been established to permir better utilizatfon of core analysis results for purposes of field waterflood evaluations. INTRODUCTION For a long time reservoir engineering procedures have been confined to the consideration of idealized, one-dimensional or linear systems.11* However, direct application of the linear waterflood mechanism to the evaluation of actual field performance is justifiable only for the purposes of rough approximation. To obtain a realistic analysis of field behavior, it is necessary to account for reservoir geometry and well distribution, and to take into consideration the configuration of the flow of fluids between injection and producing wells. In the past it has been attempted to account for the complex nature of the fluid movement in the reservoir by associating each well pattern with a certain "sweep-efficiency constant", e.g., a sweep efficiency of 72 per cent for the conventional five-spot pattern.' More recently, methods of waterflood evaluation have been improved by the introduction of variable sweep-efficiency factors, defining the areal coverage as a function of cumulative water injection and viscosity or "mobility" ' ratio.""' These variable sweep-efficiency factors, derived from miscible fluid displacement experiments, require the assumption of piston-like displacement of oil by water. This implies that only one fluid, either oil or water, is moving at any one point of the reservoir ht any moment. Such an assumption, however, is incompatible with the bulk of the experimental evidence and also theoretical considerations which indicate that usually in the area invaded by water, both oil and water are flowing in varying proportions, in accordance with the relative permeability characteristics of the porous medium. Another recent approach toward the evaluation of five-spot flooding behavior involves correlations of the areal sweep efficiency (observed in immiscible fluid experiments) with a "mobility ratio," based on the consideration of the "average" relative permeability to the displacing fluid. Combination of these correlations with a modification of the Buckley-Leverett frontal-drive equation leads to a computational procedure for predicting the recovery performance of areal water floods. While of considerable interest, this approach has no complete theoretical justification and, therefore, does not entirely clarify the features of five-spot water floods. Rigorous, theoretical treatment of waterflood behavior in two- or three-dimensional systems as encountered in the reservoir, including proper consideration of relative permeability and capillary-pressure functions, is as yet beyond the scope of analytical or computational methods. The, behavior of such water floods can, however, be studied by means of scaled flow model ekperiments, which is the approach followed in these investigations. The flow model experiments described in this paper simulate a uniform, horizontal formation of constant thickness with fully penetrating wells. The system under consideration is entirely liquid saturated and not influenced by compressibility effects, which is representative of the situation achieved after gas fill-up under practical conditions. Gravity segregation effects are assumed to be negligible, which implies a relatively thin reservoir formation and/or low vertical permeability. THEORETICAL CONSIDERATIONS For a flow system of uniform thickness with no appreciable effects of gravity segregation, the analysis of water-oil displacement can be confined to a two-dimensional treatment based on the consideration of a "slice" of unit thickness. Referring to previously established derivations," the displacement of oil by water in such a system can be described by the following, dimen-sionless equations: