Multiscale gradient computation for multiphase flow in porous media

R. Moraes, J. R.P. Rodrigues, H. Hajibeygi, J. D. Jansen

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

5 Citations (Scopus)
25 Downloads (Pure)


A multiscale gradient computation method for multiphase flow in heterogeneous porous media is developed. The method constructs multiscale primal and dual coarse grids, imposed on the given fine-scale computational grid. Local multiscale basis functions are computed on (dual-) coarse blocks, constructing an accurate map (prolongation operator) between coarse- and fine-scale systems. While the expensive operations involved in computing the gradients are performed at the coarse scale, sensitivities with respect to uncertain parameters (e.g., grid block permeabilities) are expressed in the fine scale via the partial derivatives of the prolongation operator. Hence, the method allows for updating of the geological model, rather than the dynamic model only, avoiding upscaling and the inevitable loss of information. The formulation and implementation are based on automatic differentiation (AD), allowing for convenient extensions to complex physics. An IMPES coupling strategy for flow and transport is followed, in the forward simulation. The flow equation is computed using a multiscale finite volume (MSFV) formulation and the transport equation is computed at the fine scale, after reconstruction of mass conservative velocity field. To assess the performance of the method, a synthetic multiphase flow test case is considered. The multiscale gradients are compared against those obtained from a fine-scale reference strategy. Apart from its computational efficiency, the benefits of the method include flexibility to accommodate variables expressed at different scales, specially in multiscale data assimilation and reservoir management studies.

Original languageEnglish
Title of host publicationSociety of Petroleum Engineers - SPE Reservoir Simulation Conference 2017
PublisherSociety of Petroleum Engineers
Number of pages14
ISBN (Print)9781510838864
Publication statusPublished - 1 Jan 2017
EventSPE Reservoir Simulation Conference 2017 - Montgomery, United States
Duration: 20 Feb 201722 Feb 2017


ConferenceSPE Reservoir Simulation Conference 2017
Country/TerritoryUnited States

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


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