20121119
We study the fluidstructure interaction encountered in hydraulic fracturing, a technique used by the oil and gas industry. Simulating this process needs to take into account the interaction between a fracturing solid and the fluid flow in the crack. In particular, with the possible presence of a fluid lag, the evolving fluid front inside the crack and the crack front (crack tip if in 2D) are constrained by a KuhnTucker complementarity condition, which is analogous to the case of contact mechanics. Bruteforce methods to keep track of both fronts usually require the use of a costly predictioncorrection scheme. In this presentation, we formulate this coupled problem in which the KuhnTucker condition is accommodated through a variational inequality with respect to the liquid pressure. The resulted numerical methods (finite element method or displacement discontinuity method for the solid): (a) allow modeling the evolution of both fronts with a resolution consistent with the mesh size, (b) eliminate the need of explicitly tracking the fluid front, and (c) eliminate the need of switching boundary conditions along different parts of the crack front. All of these lead to substantial saving in computational cost. Numerical examples with a nonpropagating fracture are used to verify the proposed methods, for future generalization to propagating fractures.
Category: CE SeminarTechnische Universität Darmstadt
Graduate School CE
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D64293 Darmstadt

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