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

We present new approaches to reservoir modeling 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 geophysical fluid mechanics, 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, PN(DG)-PN+1, which has a discontinuous N-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 focused 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 a number of test models which capture aspects of geological heterogeneity that are difficult or impossible to simulate conventionally, without introducing unacceptably large numbers of cells or highly non-orthogonal grids with associated numerical errors. Our approach preserves key flow features associated with realistic geological features that are typically lost. The approach may also be used to capture near wellbore flow features such as coning, changes in surface geometry across multiple stochastic realizations and, in future applications, geomechanical models with fracture propagation, opening and closing. Introduction Reservoir modelling and flow simulation have become ubiquitous in the hydrocarbon industry over the past 20 years and the development of flow simulation models now follows a widely accepted workflow that is surprisingly similar across companies and academic institutions, regardless of the software tools used (e.g. Bryant and Flint, 1993): 1. The reservoir volume is defined by surfaces representing the top and base of the reservoir and surfaces representing key reservoir bounding faults. 2. Additional faults within the reservoir are represented by additional surfaces, across which the top and base surfaces may be offset. 3. The reservoir is subdivided into geologically defined zones by one or more surfaces, which may be offset across the fault surfaces. These surfaces may be interpreted from seismic data, or correlated between wells, in which case the topography of the surfaces may be dictated by the top and/or base reservoir surfaces. Conventional reservoir models may contain 10s to 100s of these surfaces.