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 production rates or pressures, (2) reservoir and fluid 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.
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Hagoort et al. (1980) studied this question.
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