An XFEM Model for Hydraulic Fracturing in Partially Saturated Rocks

¹ Department of Earth Science and Engineering, Imperial College, London, United Kingdom
² School of Civil and Environmental Engineering, University of New South Wales, Sydney, Australia

^a Corresponding author: s.salimzadeh@imperial.ac.uk

Abstract

Hydraulic fracturing is a complex multi-physics phenomenon. Numerous analytical and numerical models of hydraulic fracturing processes have been proposed. Analytical solutions commonly are able to model the growth of a single hydraulic fracture into an initially intact, homogeneous rock mass. Numerical models are able to analyse complex problems such as multiple hydraulic fractures and fracturing in heterogeneous media. However, majority of available models are restricted to single-phase flow through fracture and permeable porous rock. This is not compatible with actual field conditions where the injected fluid does not have similar properties as the host fluid. In this study we present a fully coupled hydro-poroelastic model which incorporates two fluids i.e. fracturing fluid and host fluid. Flow through fracture is defined based on lubrication assumption, while flow through matrix is defined as Darcy flow. The fracture discontinuity in the mechanical model is captured using eXtended Finite Element Method (XFEM) while the fracture propagation criterion is defined through cohesive fracture model. The discontinuous matrix fluid velocity across fracture is modelled using leak-off loading which couples fracture flow and matrix flow. The proposed model has been discretised using standard Galerkin method, implemented in Matlab and verified against several published solutions. Multiple hydraulic fracturing simulations are performed to show the model robustness and to illustrate how problem parameters such as injection rate and rock permeability affect the hydraulic fracturing variables i.e. injection pressure, fracture aperture and fracture length. The results show the impact of partial saturation on leak-off and the fact that single-phase models may underestimate the leak-off.