Abstract
A model of consecutive placements of two different immiscible fluids, possessing different densities and rheological properties, into an expanding fracture is presented. Hydraulic fracturing technology, based on such a fluid placement, is expected to allow better fracture shape control. Mathematically, the problem is reduced to solving a two-dimensional second-order nonlinear partial differential equation describing pressure distribution in a semiellipsoid domain with moving boundaries. The level set method is used to track the interface between the fluids in time. Numerical examples of the placement of power-law fluids are presented, and the accuracy of the computations is investigated.
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