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An enhanced local pressure model for three-dimensional simulation of hydraulic fracturing

Optimizing the hydraulic fracturing process requires understanding on the fracture process in relation with the poro-mechanical properties of the rock formation. Numerical simulations of this process can be of assistance in achieving this requirement. In order to correctly model crack growth due to fracking, the following three key
ingredients need to be taken into account: (i) the exchange of fluid between the fracture and the rock formation (ii) the fluid flow in the fracture and (iii) the changing spatial configuration due to fracture propagation, i.e. the creation of a crack surface [1].


The two-dimensional enhanced local pressure model has been developed for hydraulic fracturing simulations [2]. In this model, which can be considered as an extension of the partition of unity based representations, the pressure in the fracture is described by an additional set of degrees of freedom. The pressure gradient due to fluid leakage near the fracture surface is reconstructed analytically, based on Terzaghi’s consolidation solution. With this numerical formulation we ensure that all externally applied fluid flow goes exclusively in the fracture and avoid the necessity to use a fine mesh near the fracture to capture the pressure gradient. Bulk poroelasticity is based on Biot Theory. The fracture process is governed by a cohesive traction separation law.


In this paper we will present the extension of the enhanced local pressure model to simulation hydraulic fracture in 3 dimensions, which is essential to the study realistic fracking phenomena. The position of the fracture surface will be represented and updated by two evolving level
set functions [3]. The performance of the model will be demonstrated by the analysis of the nucleation and the propagation of fracture planes near pressurised boreholes.


[1] J. Adachi, E. Siebrits, A. Peirce and J. Desroches (2007) Computer simulation of hydraulic fractures. International Journal of Rock Mechanics and Mining Sciences, 44(5),
739–757.

[2] E.W. Remij, J.J.C. Remmers, J.M. Huyghe and D.M.J. Smeulders. The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials. Submitted to Computer Methods in Applied Mechanics and Engineering.

[3] N. Moës, A. Gravouil and T. Belutschko (2002) Nonplanar 3D crack growth by the exetended finite element and level sets - Part I: Mechanical model. International Journal for Numerical Methods in Engineering, 53(11), 2549–2568.

Author(s):

Ernst Remij    
Eindhoven University of Technology
Netherlands

Joris Remmers    
Eindhoven University of Technology
Netherlands

Jacques Huyghe    
Eindhoven University of Technology
Netherlands

David Smeulders    
Eindhoven University of Technology
Netherlands