Computational Analysis of Proppant Transport and Screen-Out in Natural and Induced Fractures

Abstract

Abstract Predicting the pressure drop (or, equivalently, the effective permeability) across a fracture due to proppant injection is integral to the design of hydraulic fracturing treatments. This theoretical study investigates the relationship between permeability and proppant solid volume fraction, φ, for synthetic rough fractures via direct numerical simulation. For high aperture widths, it is found that permeability decreases in accordance with the cubic law with viscosity adjusted to that of a suspension. This is commensurate with what is currently employed in commercial hydraulic fracturing simulators. Moreover, permeability decreases with increasing fracture roughness. In narrow fractures, however, the permeability deviates further due to arching and localised clogging. However, screen-out, or complete fracture clogging, does not occur instantaneously. Instead, fracture permeability decreases as a continuous function of increasing φ, with gradually-increasing arching and localised clogging. The current binary criteria used by hydraulic fracturing simulators, which model a discontinuous jump in permeability at some φ, are therefore not reflective of the reality of particle transport in rough fractures because they grossly under-predict the permeability. Instead of the existing apparent viscosity and binary screen-out models, the permeability decline curves which are presented in this work should be incorporated into simulators as corrections to the cubic-law fracture permeability.