A robust finite element‐finite volume strategy for viscosity‐dominated hydraulic fracture propagation using an asymptotic tip enrichment

Jin, Tao; White, Joshua A.; Settgast, Randolph R.

doi:10.1002/nag.3416

“…where subscripts 𝑖 and 𝐴 represent the direction and the node number, respectively. Following the standard finite element procedure, linearizing the first part 𝑅 (1) solid (𝒖) with respect to the displacement field provides:…”

Section: Consistent Linearization and Initializationmentioning

confidence: 99%

“…Many geological processes and geotechnical engineering applications can be modeled as fracture propagation in porous media that are driven by pressurized fluid. Developing robust numerical methods to accurately simulate these processes can provide better understandings about many natural phenomena, such as magmatic system, 1,2 and improve existing engineering techniques, such as hydraulic fracturing [3][4][5][6] and geothermal energy harvesting. 7 The fracture propagation in geological systems driven by injected fluid involves two different physical processes.…”

Section: Introductionmentioning

confidence: 99%

“…In order to overcome the numerical difficulties caused by the fluid pressure singularity, a numerical technique based on the asymptotic solutions was proposed to enrich the treatment of the fluid volume near the fracture tip. 1 This enrichment strategy was implemented within a finite element-finite volume coupled computational framework. 3 Despite its successes in standard benchmark problems, such as the KGD and the penny-shape problems, and in field-scale simulations of hydraulic fracturing, the aforementioned enrichment technique suffers the following two limitations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A consistent linearization scheme for KGD problems using fracture tip asymptotic solutions

Jin

¹

2023

Num Anal Meth Geomechanics

Self Cite

0

View full text Add to dashboard Cite

Recently, a fluid volume enrichment strategy based on the asymptotic solutions near the crack tip was proposed for fluid‐driven fracture propagation problems. Despite its successes in various benchmark and field‐scale problems of hydraulic fracturing simulations, the aforementioned enrichment strategy has the following limitations. First, the tightly coupled solid‐fluid nonlinear system cannot be consistently linearized due to the fast marching method applied to solve the Eikonal equation for fracture tracking. As a result, an approximated Jacobian had to be deployed for the Newton‐Raphson iterations. This is particularly troublesome when the fracture front propagates into newly fractured cells, since a large number of nonlinear iterations are required for convergence because of the inconsistent linearization. Second, the existing method only focused on the viscosity‐dominated fracture propagation regime. Even though the extension of the method to the toughness‐dominated regime could be relatively straightforward, it is not immediately clear how to apply the enrichment technique to the transition regime. This work is dedicated to address the above two limitations. Specifically, a unified fracture propagation criterion is proposed, which not only works for the viscosity‐dominated regime, but also for the toughness‐dominated regime and the transition regime in between. The techniques to consistently linearize the coupled solid‐fluid system and properly initialize the primary unknowns are demonstrated, which result in the significant reduction of required number of nonlinear iterations for convergence. The proposed technique is demonstrated in the context of the Khristianovic‐Geertsma‐de Klerk (KGD) problems due to its relative simplicity.

show abstract

“…As explained in Settgast et al (2017), this is necessary to preserve the stability of the scheme when new crack segments are added. The recent work by Jin et al (2022) proposes a method for removing this parameter by employing partially fractured elements. The incorporation of similar modifications in the context of the multi-resolution scheme is the subject of future work.…”

Section: Viscosity Dominated Kgd Problemmentioning

confidence: 99%

A multi-resolution approach to hydraulic fracture simulation

Costa

¹

,

Cusini

²

,

Jin

³

et al. 2022

View full text Add to dashboard Cite

We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack representation in a global domain to a phase-field representation in a local subdomain near the crack tip. The multi-resolution approach addresses issues such as the computational expense of accurate hydraulic fracture simulations and the difficulties associated with reconstructing crack apertures from diffuse fracture representations. In the global domain, a coupled system of equations for displacements and pressures is considered. The crack geometry is assumed to be fixed and the displacement field is enriched with discontinuous functions. Around the crack tips in the local subdomains, phase-field sub-problems are instantiated on the fly to propagate fractures in arbitrary, mesh independent directions. The governing equations and fields in the global and local domains are approximated using a combination of finite-volume and finite element discretizations. The efficacy of the method is illustrated through various benchmark problems in hydraulic fracturing, as well as a new study of fluid-driven crack growth around a stiff inclusion.

show abstract

“…As explained in [7], this is necessary to preserve the stability of the scheme when new crack segments are added. The recent work by Jin et al [50] proposes a method for removing this parameter by employing partially fractured elements. The incorporation of similar modifications in the context of the multi-resolution scheme is the subject of future work.…”

Section: Viscosity Dominated Kgd Problemmentioning

confidence: 99%

A Multi-Resolution Approach to Hydraulic Fracture Simulation

Costa¹,

Cusini²,

Jin³

et al. 2022

Preprint

Self Cite

0

View full text Add to dashboard Cite

We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack representation in a global domain to a phase-field representation in a local subdomain near the crack tip. The multi-resolution approach addresses issues such as the computational expense of accurate hydraulic fracture simulations and the difficulties associated with reconstructing crack apertures from diffuse fracture representations. In the global domain, a coupled system of equations for displacements and pressures is considered. The crack geometry is assumed to be fixed and the displacement field is enriched with discontinuous functions. Around the crack tips in the local subdomains, phase-field sub-problems are instantiated on the fly to propagate fractures in arbitrary, mesh independent directions. The governing equations and fields in the global and local domains are approximated using a combination of finite-volume and finite element discretizations. The efficacy of the method is illustrated through various benchmark problems in hydraulic fracturing, as well as a new study of fluid-driven crack growth around a stiff inclusion.

show abstract

A robust finite element‐finite volume strategy for viscosity‐dominated hydraulic fracture propagation using an asymptotic tip enrichment

Cited by 4 publications

References 85 publications

A consistent linearization scheme for KGD problems using fracture tip asymptotic solutions

A consistent linearization scheme for KGD problems using fracture tip asymptotic solutions

A multi-resolution approach to hydraulic fracture simulation

A Multi-Resolution Approach to Hydraulic Fracture Simulation

Contact Info

Product

Resources

About