Fracture closure and proppant settling are two fully coupled processes during both shut-in and production. Proppant distribution greatly affects the residual fracture width and conductivity evolution, whereas fracture closure might limit proppant settling and force the proppant to crush or embed into the rock. Modeling fracture closure with proppant settling and embedment is challenging because of the multiple coupled physical processes involved, large time-scale differences, and extreme nonlinearity in the coupling of the processes. Conventional fracture-closure models either use simplified analytical estimates of the stress-dependent permeability of the reservoir or explicitly calculate the fracture width using empirical relationships, without considering the effect of fluid leakoff and dynamic changes in the proppant distribution in the fracture. In this work, we use a novel fully implicitly coupled fracturing/reservoir simulator to study fracture closure and proppant-settling/embedment processes during shut-in and production. This simulator implicitly couples the reservoir (rock deformation and porous flow), fracture (fracturing-fluid flow, proppant transport), and wellbore (slurry distribution, production) domains. During shut-in, a modified Barton-Bandis (Bandis et al. 1983) formula is used to describe the nonlinear relationship between the contact force and the residual fracture aperture considering the dynamic proppant spatial distribution and rock heterogeneity. During production, fracture conductivity is evaluated according to proppant distribution and further fracture closure caused by proppant crushing and embedment. A Newton-Raphson method is applied to solve the coupled system of equations.

Results from the simulations clearly show that typical periods of shut-in after fracturing lead to the formation of proppant banks at the bottom of the fracture in low-permeability, low-leakoff formations. This can lead to near-wellbore tortuosity and poor connectivity between the wellbore and the hydraulic-fracture network. Stress-dependent permeability, likely induced by induced unpropped fractures, is shown to be essential to obtain reasonable values of leakoff and to history match production trends. Proppant embedment is shown to be an important factor controlling production-decline rates in clay-rich shales.