Phase-Field Simulation of Hydraulic Fracturing by CO2, Water and Nitrogen in 2D and Comparison With Laboratory Data

Hydraulic fracturing of tight subsurface formations has mainly been conducted using water. Waterless hydraulic fracturing by CO2 may have advantages over fracturing by water. The challenge has been numerical simulation of the process. In this work, we conduct a comprehensive study on 2D hydraulic fracturing simulation by water, CO2, and nitrogen. The simulations are based on the phase-field; the results are compared with the lab data. We first present advances in simulation of fluid exchange between the fractures and the rock matrix. The conventional nodal-based finite element method may give rise to unphysical negative pressure around the tip and fracture notch. We demonstrate that the mixed hybrid finite element method gives non-negative pressure distribution. Next, we examine the effect of inertial term on fracture configuration and observe branching by CO2 under dynamic formulation with a low critical energy release rate. Lastly, we find from our simulations that in shale rocks, the critical energy release rate is the lowest for CO2, followed by nitrogen, and then water. Consequently, CO2 provides the highest fracture surface area and fracture intensity. In a sandstone sample we find nitrogen has a lower energy release rate than water. As a result, the fracture surface area is higher for nitrogen than water. Our simulation results confirm that the phase-field method may incorporate fluid-rock surface free energy without the need for various parameter adjustments.