Abstract
Even though hydraulic fracturing is a common and well adopted well stimulation method in petroleum industry, there are still open scientific questions in the area, mainly due to complexity of the phenomena involved in the process. In this paper, we particularly address the problem of fracture closure and productivity in situations, when proppant distribution inside the fracture is strongly heterogeneous. This can happen, for instance, during pulsed injection, in which a pulse of clean fluid is alternated with a pulse of slurry with proppant. Such a combination leads to Saffman-Taylor instability and, consequendy, to spatially heterogeneous distribution of proppant. To address the problem, a coupled hydraulic fracturing and proppant transport model is utilized to simulate proppant placement in a fracture. After that, a three-dimensional finite element model is used to compute fracture closure and fluid inflow or productivity. Several numerical examples with various pumping schedules are presented to better understand the influence of proppant heterogeneity on fracture closure and the resulting production. In addition, to get insights about the observed behavior, an analytical model for fracture closure between two proppant pillars is presented. The model provides a single dimensionless parameter that quantifies the degree of fracture closure between the pillars of proppant. Numerical results are analyzed and discussed in relation to this dimensionless number.
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