Validation and Application of a Three-Dimensional Model for Simulating Proppant Transport and Fracture Conductivity

Hydraulically fractured well productivity greatly depends on fracture conductivity, which itself is dictated by proppant transport and placement. To guide engineering design and evaluate performance of proppant placement, a full understanding of the underlying physics and robust numerical models are needed. This paper introduces a continuum approach for simulating the transport of multiple fluids and proppant particles within hydraulic fractures. To achieve computational efficiency, this proppant model is developed based on the assumption of multi-component single phase flow and captures proppant settling, hindering effects, proppant-bed erosion and transport. Inter-particle stresses and collisions are not numerically calculated but represented through empirical correlations to include the effects of particle clustering and hindered settling. This model couples the fluid phase and particle phase through the slip velocity, which is governed by particle settling, particle–particle interaction and fluid-particle drag forces. The presented proppant model is validated by comparing numerical results with experimental data. With the calibrated simulation, the modeling capabilities on fracturing treatment design are demonstrated through sensitivity analysis and field-scale applications. Moreover, based on proppant placement and deformation, a generic model is applied to forecast fracture conductivity in different scenarios. As illustrated in this study, this coupled three-dimensional model is capable of simulating proppant placement and fracture conductivity under various operational conditions. This model can be broadly applied to improve fracturing design in various formations, including tight sandstone, shale, coal bed methane and carbonate reservoirs.