A finite element model for three dimensional hydraulic fracturing

Philippe R.B. Devloo, Paulo Dore Fernandes, Sônia M. Gomes, Cedric Marcelo Augusto Ayala Bravo and Renato Gomes Damas

Mathematics and Computers in Simulation (MATCOM), 2006, vol. 73, issue 1, 142-155

Abstract: This paper is devoted to the development of a model for the numerical simulation of hydraulic fracturing processes with 3d fracture propagation. It takes into account the efects of fluid flow inside the fracture, fluid leak-off through fracture walls and elastic response of the surrounding porous media. Finite element techniques are adopted for the discretization of the conservation law of fluid flow and the singular integral equation relating the traction and the fracture opening. The discrete model for the singular integral equation is implemented using a stencil matrix structure allowing an efficient implementation of the fluid–structure interaction problem. Newton’s method combined with GMRES linear solver are used to solve the resulting nonlinear set of equations. An algorithm for fracture propagation is proposed which is based on the balance of the amount of fluid transported to a certain point with the amount of fluid that could be lost by leak-off. To illustrate the feasibility of the model, we present simulation results for typical operational parameters.

Keywords: Hydraulic fracturing; Finite elements; Boundary elements; Petroleum recovery (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:73:y:2006:i:1:p:142-155

DOI: 10.1016/j.matcom.2006.06.020

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