Improved Simulation of Subsurface Flow in Heterogeneous Reservoirs Using a Fully Discontinuous Control-Volume-Finite-Element Method, Implicit Timestepping and Dynamic Unstructured Mesh Optimization

Abstract:

We present a new, high-order, control-volume-finite-element (CVFE) method with discontinuous representation for pressure and velocity to simulate multiphase flow in heterogeneous porous media. Time is discretized using an adaptive, fully implicit method. Heterogeneous geologic features are represented as volumes bounded by surfaces. Within these volumes, termed geologic domains, the material properties are constant. A given model typically contains numerous such geologic domains. Our approach conserves mass and does not require the use of CVs that span domain boundaries. Computational efficiency is increased by use of dynamic mesh optimization, in which an unstructured mesh adapts in space and time to key solution fields, such as pressure, velocity or saturation, whilst preserving the geometry of the geologic domains. Up-, cross- or down-scaling of material properties during mesh optimization is not required, as the properties are uniform within each geologic domain. We demonstrate that the approach, amongst other features, accurately preserves sharp saturation changes associated with high aspect ratio geologic domains such as fractures and mudstones, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than an equivalent fine, fixed mesh and conventional CVFE methods. The use of implicit time integration allows the method to efficiently converge using highly anisotropic meshes without having to reduce the time-step. The work is significant for two key reasons. First, it resolves a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media, in which CVs span boundaries between domains of contrasting material properties. Second, it reduces computational cost/increases solution accuracy through the use of dynamic mesh optimization and time-stepping with large Courant number.