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 Nth-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.