Reservoir Modeling for Flow Simulation by Use of Surfaces, Adaptive Unstructured Meshes, and an Overlapping-Control-Volume Finite-Element Method
- Matthew Jackson (Imperial College) | James Percival (Imperial College) | Peyman Mostaghimi (Imperial College) | Brendan Tollit (Imperial College) | Dimitrios. Pavlidis (Imperial College) | Christopher Pain (Imperial College) | Jefferson Gomes (Imperial College) | Ahmed H. Elsheikh (Imperial College) | Pablo Salinas (Imperial College) | Ann Muggeridge (Imperial College) | Martin Blunt (Imperial College)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- May 2015
- Document Type
- Journal Paper
- 115 - 132
- 2015.Society of Petroleum Engineers
- reservoir, novel, modelling, simulation
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- 624 since 2007
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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 multiscale geologic heterogeneity and the prediction of flow through that heterogeneity. The research builds on more than 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.
Geologic heterogeneities, whether structural, stratigraphic, sedimentologic, or diagenetic in origin, are represented as discrete volumes bounded by surfaces, without reference to a predefined grid. Petrophysical properties are uniform within the geologically defined rock volumes, rather than within grid cells. The resulting model is discretized for flow simulation by use of an unstructured, tetrahedral mesh that honors the architecture of the surfaces. This approach allows heterogeneity over multiple length-scales to be explicitly captured by use of fewer cells than conventional cornerpoint or unstructured grids.
Multiphase flow is simulated by use of 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 Darcyforce balances on unstructured meshes and thus accurately calculates pressure, velocity, and saturation fields throughout the domain. Computational costs are reduced through dynamic adaptivemesh optimization and efficient parallelization. Within each rock volume, the mesh coarsens and refines to capture key flow processes during a simulation, and also preserves the surface-based representation of geologic heterogeneity. Computational effort is thus focused on regions of the model where it is most required.
After validating the approach against a set of benchmark problems, we demonstrate its capabilities by use of a number of test models that capture aspects of geologic heterogeneity that are difficult or impossible to simulate conventionally, without introducing unacceptably large numbers of cells or highly nonorthogonal grids with associated numerical errors. Our approach preserves key flow features associated with realistic geologic 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.
|File Size||1 MB||Number of Pages||18|