The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials

In this paper, we present an enhanced local pressure model for modelling fluid pressure driven fractures in porous saturated materials. Using the partition-of-unity property of finite element shape functions, we describe the displacement and pressure fields across the fracture as a strong discontinuity. We enhance the pressure in the fracture by including an additional degree of freedom. The pressure gradient due to fluid leakage near the fracture surface is reconstructed based on Terzaghi’s consolidation solution. With this numerical formulation we ensure that all fluid flow goes exclusively in the fracture and it is not necessary to use a dense mesh near the fracture to capture the pressure gradient. Fluid flow in the rock formation is described by Darcy’s law. The fracture process is governed by a cohesive traction separation law. The performance of the numerical model for fluid driven fractures is shown in three numerical examples

Numerical modelling of hydraulic fracturing

In this paper we present a numerical model for hydraulic fracturing purposes. The rock formation is modelled as a poroelastic material based on Biot’s Theory. A fracture is represented in a discrete manner using the eXtended Finite Element Method (X-FEM). The fluid flow is governed by a local mass balance. This means that there is an equilibrium between the opening of the fracture, the tangential fluid flow, and the fluid leakage. The mass balance in the fracture is solved with a separate equation by including an additional degree of freedom for the pressure in the fracture. The fracture can grow in arbitrary directions by using an average stress criterion. We show a result of hydraulic fracture propagation for a 2D circular borehole. The fracture direction is consistent with the expected direction

The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials

In this paper, we present an enhanced local pressure model for modelling fluid pressure driven fractures in porous saturated materials. Using the partition-of-unity property of finite element shape functions, we describe the displacement and pressure fields across the fracture as a strong discontinuity. We enhance the pressure in the fracture by including an additional degree of freedom. The pressure gradient due to fluid leakage near the fracture surface is reconstructed based on Terzaghi’s consolidation solution. With this numerical formulation we ensure that all fluid flow goes exclusively in the fracture and it is not necessary to use a dense mesh near the fracture to capture the pressure gradient. Fluid flow in the rock formation is described by Darcy’s law. The fracture process is governed by a cohesive traction separation law. The performance of the numerical model for fluid driven fractures is shown in three numerical examples

On the numerical simulation of crack interaction in hydraulic fracturing

In this paper, we apply the enhanced local pressure (ELP) model to study crack interaction in hydraulic fracturing. The method is based on the extended finite element method (X-FEM) where the pressure and the displacement fields are assumed to be discontinuous over the fracture exploiting the partition of unity property of finite element shape functions. The material is fully saturated and Darcy’s law describes the fluid flow in the material. The fracture process is described by a cohesive traction-separation law, whereas the pressure in the fracture is included by an additional degree of freedom. Interaction of a hydraulic fracture with a natural fracture is considered by assuming multiple discontinuities in the domain. The model is able to capture several processes, such as fracture arrest on the natural fracture, or hydraulic fractures that cross the natural fracture. Fluid is able to flow from the hydraulic fracture into the natural fracture. Two numerical criteria are implemented to determine whether or not the fracture is crossing or if fluid diversion occurs. Computational results showing the performance of the model and the effectiveness of the two criteria are presented. The influence of the angle between a hydraulic fracture and a natural fracture on the interaction behaviour is compared with experimental results and theoretical data

A partition of unity based model for hydraulic fracturing

In this contribution we present a partition of unity based model for the simulation of hydraulic fracturing processes. Bulk poroelasticity is based on the Biot theory. The pressure in the fracture is included as an additional degree of freedom. A Fracture can grow in arbitrary directions by using the Camacho Ortiz fracture criterion with a cohesive zone formulation. The performance of the numerical model is addressed by considering fracture propagation from a 2D borehole. The initial stress field is validated with Kirsch's analytical solution. The results from the numerical model indicate that preferred direction of a hydraulic fracture is in the direction of the highest confining stress. In future works this model will include the nucleation of fractures and can be applied to more complex hydraulic fracturing situations

A partition of unity-based model for crack nucleation and propagation in porous media, including orthotropic materials

In this paper, we present a general partition of unity-based cohesive zone model for fracture propagation and nucleation in saturated porous materials. We consider both two-dimensional isotropic and orthotropic media based on the general Biot theory. Fluid flow from the bulk formation into the fracture is accounted for. The fracture propagation is based on an average stress approach. This approach is adjusted to be directionally depended for orthotropic materials. The accuracy of the continuous part of the model is addressed by performing Mandel’s problem for isotropic and orthotropic materials. The performance of the model is investigated with a propagating fracture in an orthotropic material and by considering fracture nucleation and propagation in an isotropic mixed-mode fracture problem. In the latter example we also investigated the influence of the bulk permeability on the numerical results

A partition of unity-based model for crack nucleation and propagation in porous media, including orthotropic materials

In this paper, we present a general partition of unity-based cohesive zone model for fracture propagation and nucleation in saturated porous materials. We consider both two-dimensional isotropic and orthotropic media based on the general Biot theory. Fluid flow from the bulk formation into the fracture is accounted for. The fracture propagation is based on an average stress approach. This approach is adjusted to be directionally depended for orthotropic materials. The accuracy of the continuous part of the model is addressed by performing Mandel’s problem for isotropic and orthotropic materials. The performance of the model is investigated with a propagating fracture in an orthotropic material and by considering fracture nucleation and propagation in an isotropic mixed-mode fracture problem. In the latter example we also investigated the influence of the bulk permeability on the numerical results

Nucleation and mixed mode crack propagation in a porous material

Understanding crack propagation in hydraulic fracturing for purposes of enhanced oil recovery, gas recovery or geothermal applications demands advanced numerical techniques able to handle multiple fracturing in 3D media. The Partition of Unity Method (PUM) formulation in a 2D poro-elastic media is used to model fracture propagation and nucleation. Biot theory is used for the bulk poroelasticity. The cohesive zone formulation with a Camacho-Ortiz fracture criterion is able to handle mixed mode fracture in arbitrary directions. Fluid flow from the formation into the crack and vice versa are accounted for, as well as fluid flow in the bulk material. The influence of the permeability on fracture nucleation and propagation velocity are investigated in a mixed mode fracture simulation. Fracture nucleation and propagation velocity increase with a higher permeability. The crack path is also found to be dependent on the permeability