Modeling of hydraulic fracture closure on proppants with proppant settling

The placement of proppants in a hydraulic fracture is governed by slurry flow, proppant transport and settlement. The proppant distribution can significantly affect the conductivity of the hydraulic fracture, and hence will impact the productivity of hydraulic fractured wells. Past studies have investigated fracture closure on proppants by envisioning hydraulic fractures as two parallel plates with uniformly distributed proppants. However, in reality, hydraulically induced fractures are wider in the middle and narrower near the fracture edges. In addition, a proppant dune is likely to be accumulated at the bottom of the fracture because of proppant settling. As a result, fracture closure on proppants is controlled by both fracture geometry and the distribution of proppant in the fracture. This is a dynamic process where fracture geometry and the proppant pack will evolve as a function of pressure, and the associated surface contact problem is notoriously challenging to solve because of its non-linear and nonlocal nature. In this study, we proposed a general approach to model hydraulic fracture closure. The residual fracture width profile for both propped and un-propped sections can be obtained at different drawdown pressures for rocks with different clay content. The maximum stress acting on proppants can be calculated to guide the selection of proppants with appropriate strength. Most importantly, the effect of stress concentration and stress amplification can be quantified when a proppant dune or bank is formed. We also show that the traditional method of estimating the maximum stress on a proppant pack is an underestimation.