A Non-Local Model for Fluid-Structure Interaction with Applications in Hydraulic Fracturing

Abstract

Modeling important engineering problems related to flow-induced damage (in the context of hydraulic fracturing among others) depends critically on characterizing the interaction of porous media and interstitial fluid flow. This work presents a new formulation for incorporating the effects of pore pressure in a non-local representation of solid mechanics. The result is a framework for modeling fluid-structure interaction problems with the discontinuity capturing advantages of an integral-based formulation. A number of numerical examples are used to show that the proposed formulation can be applied to measure the effect of leak-off during hydraulic fracturing as well as modeling consolidation of fluid-saturated rock and surface subsidence caused by fluid extraction from a geologic reservoir. The formulation incorporates the effect of pore pressure in the constitutive description of the porous material in a way that is appropriate for nonlinear materials, easily implemented in existing codes, straightforward in its evaluation (no history dependence), and justifiable from first principles. A mixture theory approach is used (deviating only slightly where necessary) to motivate an alteration to the peridynamic pressure term based on the fluid pore pressure. The resulting formulation has a number of similarities to the effective stress principle developed by Terzaghi and Biot and close correspondence is shown between the proposed method and the classical effective stress principle.

Keywords:

• Hydraulic Fracturing
• Non-local Numerical Methods
• Mixture Theory
• Constitutive Modeling
• Subsidence
• Rock Consolidation
• Effective Stress Principle

Acknowledgments

This work was supported by the Institute for Structural Engineering (ISE) at Stellenbosch University. Their support is gratefully acknowledged.