Reservoir Modeling for Flow Simulation Using Surfaces, Adaptive Unstructured Meshes, and Control-Volume-Finite-Element Methods

Abstract

We present new approaches to reservoir modelling and flow simulation that dispose of the pillar-grid concept that has persisted since reservoir simulation began. This results in significant improvements to the representation of multi-scale geological heterogeneity and the prediction of flow through that heterogeneity. The research builds on 20+ years of development of innovative numerical methods in ocean modelling, refined and modified to deal with the unique challenges associated with reservoir simulation.

Geological heterogeneities, whether structural, stratigraphic, sedimentologic or diagenetic in origin, are represented as discrete volumes bounded by surfaces, without reference to a pre-defined grid. Petrophysical properties are uniform within the geologically-defined rock volumes, rather than within grid-cells. The resulting model is discretized for flow simulation using an unstructured, tetrahedral mesh that honors the architecture of the surfaces. This approach allows heterogeneity over multiple length-scales to be explicitly captured using fewer cells than conventional corner-point or unstructured grids.

Multiphase flow is simulated using a novel mixed finite element formulation centered on a new family of tetrahedral element types, P_N(DG)-P_N+1, which has a discontinuous N^th-order polynomial representation for velocity and a continuous (order N+1) representation for pressure. This method exactly represents Darcy force balances on unstructured meshes and thus accurately calculates pressure, velocity and saturation fields throughout the domain. Computational costs are reduced through (i) automatic mesh adaptivity in time and space and (ii)  efficient parallelization . Within each rock volume, the mesh coarsens and refines to capture key flow processes, whilst preserving the surface-based representation of geological heterogeneity. Computational effort is thus focussed on regions of the model where it is most required.

Having validated the approach against a set of benchmark problems, we demonstrate its capabilities using geologically complex test models that are difficult or impossible to simulate conventionally, without introducing unacceptably large numbers of cells or highly non-orthogonal grids with associated numerical errors. The new approach preserves key flow features associated with realistic geological features that are usually lost. The approach can also capture near wellbore flow features such as coning, changes in surface geometry across multiple stochastic realisations, and geomechanical models with fracture propagation, opening and closing.