This paper presents the coupled model of a hydraulic fracturing and proppant transport. The former is described in terms of enhanced pseudo-3D model that considers height growth across two symmetric stress barriers, while the latter is given by two-dimensional transport model, stemming from the solution of an elliptical equation for fluid pressure and advection equation for the proppant transport. These two sub-modules are solved numerically using implicit time integration in hydraulic part and explicit time stepping in the transport part. In addition to that, interpolation is used to couple the two models with different grids. Results of several numerical simulations are presented for different configurations to demonstrate the interplay between these two modules. In particular, the developed coupled scheme allows us to study phenomena associated with complex fluid flow within the fracture, such as for the case of Saffman-Taylor instability.

中文翻译：

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用于水力压裂的增强型伪 3D 模型与支撑剂输送模型的耦合

本文介绍了水力压裂和支撑剂输送的耦合模型。前者用增强的伪 3D 模型描述，该模型考虑了两个对称应力屏障的高度增长，而后者由二维输运模型给出，源于流体压力的椭圆方程和对流方程的解。支撑剂运输。这两个子模块使用水力部分的隐式时间积分和运输部分的显式时间步长进行数值求解。除此之外，插值用于将两个模型与不同的网格耦合。给出了不同配置的几个数值模拟结果，以证明这两个模块之间的相互作用。特别是，