A Tracing Algorithm for Flow Diagnostics on Fully Unstructured Grids With Multipoint Flux Approximation
- Zhao Zhang (Heriot-Watt University) | Sebastian Geiger (Heriot-Watt University) | Margaret Rood (Imperial College London) | Carl Jacquemyn (Imperial College London) | Matthew Jackson (Imperial College London) | Gary Hampson (Imperial College London) | Felipe Moura De Carvalho (University of Calgary) | Clarissa Coda Marques Machado Silva (University of Calgary) | Julio Daniel Machado Silva (University of Calgary) | Mario Costa Sousa (University of Calgary)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2017
- Document Type
- Journal Paper
- 1,946 - 1,962
- 2017.Society of Petroleum Engineers
- unstructured grids, porous media, flow diagnostics, control volume finite element method, advective transport
- 3 in the last 30 days
- 218 since 2007
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Flow diagnostics is a common way to rank and cluster ensembles of reservoir models depending on their approximate dynamic behavior before beginning full-physics reservoir simulation. Traditionally, they have been performed on corner-point grids inherent to geocellular models. The rapid-reservoir-modeling (RRM) concept aims at fast and intuitive prototyping of geologically realistic reservoir models. In RRM, complex reservoir heterogeneities are modeled as discrete volumes bounded by surfaces that are sketched in real time. The resulting reservoir models are discretized by use of fully unstructured tetrahedral meshes where the grid conforms to the reservoir geometry, hence preserving the original geological structures that have been modeled.
This paper presents a computationally efficient work flow for flow diagnostics on fully unstructured grids. The control-volume finite-element method (CVFEM) is used to solve the elliptic pressure equation. The flux field is a multipoint flux approximation (MPFA). A new tracing algorithm is developed on a reduced monotone acyclic graph for the hyperbolic transport equations of time of flight (TOF) and tracer distributions. An optimal reordering technique is used to deal with each control volume locally such that the hyperbolic equations can be computed in an efficient node-by-node manner. This reordering algorithm scales linearly with the number of unknowns.
The results of these computations allow us to estimate swept-reservoir volumes, injector/producer pairs, well-allocation factors, flow capacity, storage capacity, and dynamic Lorenz coefficients, which all help approximate the dynamic reservoir behavior. The total central-processing-unit (CPU) time, including grid generation and flow diagnostics, is typically a few seconds for meshes with O (100,000) unknowns. Such fast calculations provide, for the first time, real-time feedback in the dynamic reservoir behavior while models are prototyped.
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