A Cut-Cell Polyhedral Finite Element Model for Coupled Fluid Flow and Mechanics in Fractured Reservoirs

Abstract

Mechanical deformation induced by injection and withdrawal of fluids from the subsurface can significantly alter the flow paths in naturally fractured reservoirs. Modeling coupled fluid flow and mechanical deformation in fractured reservoirs relies on either sophisticated gridding techniques or enhancing the variables (degrees of freedom) that represent the physics to describe the behavior of fractured formation accurately. The objective of this study is to develop a spatial discretization scheme that cuts the “matrix” grid with fracture planes and utilizes traditional formulations for fluid flow and geomechanics.

The flow model uses the standard low-order finite volume method with the compartmental embedded discrete fracture model (cEDFM). Due to the presence of nonstandard polyhedra in the grid after cutting/splitting, we use numerical harmonic shape functions within a polyhedral finite element (PFE) formulation for mechanical deformation. To enforce fracture-contact constraints, we use a penalty approach.

We provide a series of comparisons between the approach that uses conforming unstructured grids and an unstructured discrete fracture model (uDFM) with the new cut-cell PFE formulation. The manuscript validates and compares both methods for linear elastic, single-fracture slip, and Mandel’s problems with tetrahedral, Cartesian, and perpendicular-bisectional (PBI) grids. Finally, the paper presents a fully coupled 3D simulation with multiple inclined intersecting faults activated in shear by fluid injection, which caused an increase in effective reservoir permeability.

Our approach allows for great reduction in the complexity of the (gridded) model construction while retaining the solution accuracy together with great savings in the computational cost compared with uDFM. The flexibility of our model with respect to the types of grid polyhedra allows us to eliminate mesh artifacts in the solution of the transport equations typically observed when using tetrahedral grids and two-point flux approximation.