  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.
