Algebraic Multiscale Framework for Fractured Reservoir Simulation

Abstract

Despite welcome increases in the adoption of renewable energy sources, oil and natural gas are likely to remain the main ingredient in the global energy diet for the decades to come. Therefore, the efficient exploitation of existing suburface reserves is essential for the well-being of society. This has stimulated recent developments in computer models able to provide critical insight into the evolution of the flow of water, gas and hydrocarbons through rock pores. Any such endeavour, however, has to tackle a number of challenges, including the considerable size of the domain, the highly heterogeneous spatial distribution of geological properties, as well as the intrinsic uncertainty and limitations associated with field data acquisition. In addition, the naturally-formed or artificially induced networks of fractures, present in the rock, require special treatment, due to their complex geometry and crucial impact on fluid flow patterns.
From a numerical point of view, a reservoir simulator’s operation entails the solution of a series linear systems, as dictated by the spatial and temporal discretization of the governing equations. The difficulty lies in the properties of these systems, which are large, ill-conditioned and often have an irregular sparsity pattern. Therefore, a brute-force approach, where the solutions are directly computed at the original fine-scale resolution, is often an impractically expensive venture, despite recent advances in parallel computing hardware. On the other hand, switching to a coarser resolution to obtain faster results, runs the risk of omitting important features of the flow, which is especially true in the case of fractured porous media.
This thesis describes an algebraic multiscale approach for fractured reservoir simulation. Its purpose is to offer a middle-ground, by delivering results at the
original resolution, while solving the equations on the coarse-scale. This is made possible by the so-called basis functions – a set of locally-supported cross-scale interpolators, conforming to the heterogeneities in the domain. The novelty of the work lies in the extension of these methods to capture the effect of fractures. Importantly, this is done in fully algebraic fashion, i.e. without making any assumptions regarding geometry or conductivity properties.
In order to elicit the generality of the proposed approach, a series of sensitivity studies are conducted on a proof-of-concept implementation. The results, which include both CPU times and convergence behaviour, are discussed and compared to those obtained using an industrial-grade AMG package. They serve as benchmarks, recommending the inclusion of multiscale methods in next-generation commercial reservoir simulators.