NUMERICAL SIMULATION OF THREE-DIMENSIONAL INTERSECTING/NONPLANAR FAULTS IN RESERVOIR-GEOMECHANICAL MODELS USING THE EXTENDED FINITE ELEMENT METHOD

This presentation proposes a numerical method for simulating nonplanar/intersecting faults in the three-dimensional reservoir and geomechanical models. The approach is based on the extended finite element method (X-FEM), in which the discretizing mesh does not need to conform to the geometry of the faults. The focus of the presentation is on modeling faults with complex geometries such as curved or nonplanar faults, or intersection of multiple faults.

Faults are geological entities with thicknesses (of the order cm) several orders of magnitude smaller than the grid blocks (of the order 10 m) typically used to discretize reservoir and/or over-under-burden geological formations. Introducing faults in a complex reservoir and/or geomechanical mesh therefore poses significant meshing difficulties for conventional FEMs. Using the X-FEM, we overcome this problem by introducing faults in the mesh without meshing them explicitly. We consider the strong-coupling of solid displacement and fluid pressure in a three-dimensional poro-mechanical (reservoir-geomechanical) model. For the geomechanics, the fault is treated as an internal displacement discontinuity that allows slipping to occur using a Mohr-Coulomb type criterion. For the reservoir, the fault is either a) an internal fluid flow conduit that allows fluid flow in the fault as well as to enter/leave the fault, or is b) a barrier to flow (sealing fault). For internal fluid flow conduits, the continuous fluid pressure approximation admits a discontinuity in its normal derivative across the fault, whereas for a sealing fault, the pressure approximation is discontinuous across the fault.

Additional significant challenges arise when the faults are nonplanar or intersecting. In the X-FEM, when a fault cuts through a finite element, that element needs to be partitioned with respect to the fault plane for the purpose of numerical integration. When multiple faults cut through an element, we propose a special procedure for element partitioning based on a recursive algorithm. A tree data structure in conjunction with a linked list is implemented and geometric predicates and intersection routines are utilized.