Phase Field Model of Hydraulic Fracturing in Poroelastic Media: Fracture Propagation, Arrest, and Branching Under Fluid Injection and Extraction

Abstract

The simulation of fluid‐driven fracture propagation in a porous medium is a major computational challenge, with applications in geosciences and engineering. The two main families of modeling approaches are those models that represent fractures as explicit discontinuities and solve the moving boundary problem and those that represent fractures as thin damaged zones, solving a continuum problem throughout. The latter family includes the so‐called phase field models. Continuum approaches to fracture face validation and verification challenges, in particular grid convergence, well posedness, and physical relevance in practical scenarios. Here we propose a new quasi‐static phase field formulation. The approach fully couples fluid flow in the fracture with deformation and flow in the porous medium, discretizes flow in the fracture on a lower‐dimension manifold, and employs the fluid flux between the fracture and the porous solid as coupling variable. We present a numerical assessment of the model by studying the propagation of a fracture in the quarter five‐spot configuration. We study the interplay between injection flow rate and rock properties and elucidate fracture propagation patterns under the leak‐off toughness dominated regime as a function of injection rate, initial fracture length, and poromechanical properties. For the considered injection scenario, we show that the final fracture length depends on the injection rate, and three distinct patterns are observed. We also rationalize the system response using dimensional analysis to collapse the model results. Finally, we propose some simplifications that alleviate the computational cost of the simulations without significant loss of accuracy.

Improved algorithms for generalized finite element simulations of three‐dimensional hydraulic fracture propagation

“…With phase field, fracture nucleation, propagation, and bifurcation can be simulated without the need for remeshing. However, very small element sizes are necessary close to the entire fracture surface, and defining the fracture opening from the smeared field can be challenging …”

Theoretical, numerical, and experimental analysis of effective extraction radius of coalbed methane boreholes by a gas seepage model based on defined criteria

“…At present, gas predrainage along coal seam boreholes is mainly used in China, which is also an effective method for coal seam gas recovery and gas disaster prevention and control in coal mines, as shown in Figure . The effective extraction radius of borehole is an important parameter for this method, which is used for the determination of borehole spacing in gas extraction . If the gas extraction borehole spacing is too large, there will be extraction blind zones formed between extraction boreholes, bringing extremely large potential accidents to production in coal mines.…”

“…It is undeniable that numerical simulation has become an important method to study the effective extraction radius. Researchers have established mathematical models to describe the laws of gas flow in coal seams around boreholes and have used the CFD software for numerical simulation to obtain the effective extraction radius of boreholes along coal seams …”

“…The effective extraction radius of borehole is an important parameter for this method, which is used for the determination of borehole spacing in gas extraction. 23,24 If the gas extraction borehole spacing is too large, there will be extraction blind zones formed between extraction boreholes, bringing extremely large potential accidents to production in coal mines. If the gas extraction borehole spacing is too small, the gas extraction rate and gas extraction volume may be increased to a certain extent, but this will increase the borehole construction workload, resulting in an increase in the gas extraction cost.…”

“…Researchers have established mathematical models to describe the laws of gas flow in coal seams around boreholes and have used the CFD software for numerical simulation to obtain the effective extraction radius of boreholes along coal seams. 12,23,30,35,36 Among the gas extraction test methods, the gas pressure method, 26,30 gas content method, 37 and gas tracer method 38 are three common methods for measuring the effective extraction radius. The gas tracer method has low reliability, and thus, it cannot be used to analyze the degree of influence and obtain the effective extraction radius accurately.…”