Integrated simulation of three-dimensional hydraulic fracture propagation and Lagrangian proppant transport in multilayered reservoirs

Abstract

The numerical simulation of hydraulic fractures is a critical yet challenging computational problem due to its multi-physics nature. This paper develops an integrated hydraulic fracturing simulator by coupling a planar three-dimensional (PL3D) fracture propagation model with an efficient Eulerian–Lagrangian (E–L) proppant transport model. The fracture propagation model uses the finite volume method (FVM) and displacement discontinuity method (DDM) to solve the fluid flow and rock deformation, respectively. For proppant transport, we develop a pseudo-3D multiphase particle-in-cell (P3D MP-PIC) model, in which the fluid flow is addressed by FVM as a continuum, but the particles are tracked in a Lagrangian fashion as discrete phases. In contrast to Eulerian–Eulerian (E–E) proppant transport models, the P3D MP-PIC can efficiently deal with multi-modal particle simulations (i.e., particles of different sizes or materials) and avoid the problem of numerical diffusion. The fracture propagation and proppant transport models are validated by analytical solutions and laboratory experiments. We adopt a one-way coupling strategy to consider the effect of complex fracture propagation and fluid leak-off on slurry transport, in which the dynamic fracture geometry and fluid leak-off is first computed via the fracture propagation model, followed by the fully coupled fluid–particle simulation using the P3D MP-PIC. The integrated model can simulate the fracturing treatments in multilayered reservoirs with varying confining stresses at an industrial field scale. The simulation results can improve the prediction of effective/propped fracture geometries and better the fracturing designs.