Abstract
A mathematical reservoir model is presented to simulate the propagation of waterflood-induced hydraulic fractures in a symmetry element of a waterflood pattern. The model consists of a conventional single-phase reservoir simulator coupled with an analytical fracture model.The model is capable of simulating fracture propagation as a function of (1) injection and propagation as a function of (1) injection and production rates or pressures, (2) reservoir and fluid production rates or pressures, (2) reservoir and fluid properties, and (3) formation-fracturing pressures. properties, and (3) formation-fracturing pressures. Examples are given that clearly illustrate the characteristics of hydraulic-fracture growth. The key variables are injection rate and voidage/replacement ratio. Fractures can be contained by restricting the injection rate and by imposing a voidage/ replacement ratio equal to or less than 1.The modeling technique presented here also may be applied to other fracturing problems, particularly in cases where leakoff is significant and, thus, should be taken into account rigorously.
Introduction
Injection pressures in water-injection wells often exceed the formation-fracturing pressures, either unintentionally or by design. Although this leads to improved injectivity, it might jeopardize the flooding efficiency of waterfloods; induced hydraulic fractures can grow to be very long, thereby adversly affecting areal sweep efficiency.At present, quantitative information on the propagation of waterflood-induced hydraulic propagation of waterflood-induced hydraulic fractures is scarce. Theories of hydraulic fracturing do exist but are geared to controlled fracture-stimulation techniques. In these techniques the induced fractures and propagation times are relatively short and fluid losses are kept low by using additives in the fracture fluids. Waterflood-induced fractures, on the other hand, may grow for many years and are characterized by high fluid losses.In this paper a mathematical model for simulating hydraulic fracture growth under waterflood conditions is presented. The model is capable of calculating fracture propagation in a two-dimensional symmetry element of a unit mobility ratio waterflood containing one injector and one or more producers. With this model, fracture growth can be investigated as a function of (1) injection rates and production rates or pressures, (2) reservoir and fluid properties, and (3) formation-fracturing pressures. pressures. Several examples are given that clearly illustrate the general growth characteristics of waterflood-induced hydraulic fractures.The model presented is relatively simple in scope and is certainly open to improvements. Yet in its present form it is already a valuable diagnostic and present form it is already a valuable diagnostic and predictive tool that can be used to manage fractured predictive tool that can be used to manage fractured waterfloods better.
Physical Model Physical Model Fig. 1 depicts the physical model we wish to simulate. It consists of (1) a symmetry element of a waterflood reservoir containing injection and production wells, and (2) a fracture extending from an injection well in a chosen direction.In this model the reservoir has a uniform or slightly varying thickness that is small relative to the areal dimensions. The mobility ratio of the waterflood is M = 1.0. In this system fluid flow in the reservoir can be approximated by the equation for two-dimensional single-phase compressible flow.
SPEJ
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The dyad symmetry element is the molecular target for c-fos induction and inhibition during K 562 differentiation along mutually exclusive lineages
