Numerical methods for hydraulic fracture propagation: A review of recent trends

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

“…Mass conservation is a difficult issue when using mesh adaptivity as stated in Lecampion et al, and therefore, it was verified for the examples presented in this manuscript. The biggest errors at a propagation step are 0.06 % for the penny‐shaped problem, 0.08 % for the planar elliptical problem, and 0.009 % for the leak‐off verification problem.…”

“…These schemes produce very accurate solutions even for coarse meshes. However, it is still unclear how to extend the algorithm to nonplanar 3‐D fractures with mixed mode loading …”

Model‐Based Evaluation of Methods for Maximizing Efficiency and Effectiveness of Hydraulic Fracture Stimulation of Horizontal Wells

“…Additionally, it is important to note that the leak‐off coefficient C L is coupled with the fluid viscosity, that is, higher viscosity leads to lower leak‐off. Neglecting any accumulation of particulate/polymer on the fracture comprising a low‐permeability “filter cake,” and further assuming that the fluid injected to the fracture is not too dissimilar in viscosity to the native fluid in the reservoir, the viscosity and leak‐off rate are coupled via Carter's leak‐off parameter (Carter, ; Lecampion et al, ). where k is the rock permeability, c r is the reservoir compressibility, combining the reservoir fluid and pore compressibility, ϕ is the rock porosity, σ o is the in situ stress, and p o is the reservoir pressure.…”

“…As an illustrative example, we show that injection volume can vary significantly depending upon both the nominal regime (location in the plots in Figure as defined by Φ and τ in equations and , respectively) and the fracture spacing. Specifically, we contrast uniformly spaced and a particular nonuniform spacing, which is inspired from prior work (Cheng & Bunger, ; Cheng & Bunger, , b; Lecampion et al, ), demonstrating that some nonuniform spacing configurations can balance the impact of stress shadow acting on the fractures, thereby leading to more uniform fracture growth. This parametric study entails varying viscosity and characteristic leak‐off parameter C L 0 , keeping all other quantities unchanged with practically relevant values given by until a fracture surface area of 100,000 m 2 is achieved.…”

“…To summarize, the model requires simultaneous solution of 6 N equations corresponding to the following physical laws: Volume balance , where in our ROM we adopt a weak form wherein volume balance is assured globally but not at every location. Additionally, volume balance must account for fluid loss to the formation and here we follow the widely used Carter's method to describe the history‐dependent leak‐off under the assumptions that the hydraulic fracture velocity greatly exceeds the characteristic fluid diffusion velocity in the rock and that the transient fluid net pressure (difference between fluid pressure and in situ stress in the rock) is much smaller than the difference between the in situ stress and the undisturbed pore pressure in the reservoir rock (Carter, ; Lecampion et al, ). Laminar fluid flow describing a Newtonian fluid flowing within the fracture according to the classical Poiseuille law. In our ROM we avoid discretization by assuming a functional form that is consistent with known inlet and tip asymptotic behavior, which are the two locations where energy is predominantly dissipated. Crack propagation imposing a condition for crack extension according to linear elastic fracture mechanics.…”