Algebraic Dynamic Multilevel (ADM) Method For Simulations Of Multiphase Flow With An Adaptive Saturation Interpolator

Matteo Cusini, Hadi Hajibeygi

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

4 Citations (Scopus)

Abstract

An Algebraic Dynamic Multilevel (ADM) method for simulations of multiphase flow in heterogeneous porous media with an adaptive enriched multiscale formulation for saturation unknowns is presented. ADM maps the fine-scale fully-implicit (FIM) discrete system of equations to a dynamic multilevel system, the resolution of which is defined based on the location of the fluid fronts. The map between the dynamic multilevel resolutions is performed algebraically by sequences of restriction and prolongation operators. While finite-volume restriction operators are necessary to ensure mass conservation at all levels, different interpolation strategies can be considered for each main unknown (e.g., pressure and saturation). For pressure, the multiscale basis functions are used to accurately capture the effect of fine-scale heterogeneities at all levels. In previous works, all other unknowns (e.g., saturation) were interpolated with piece-wise constant functions. Hence, the multiscale nature of saturation equation was not fully exploited. Here, an adaptive interpolation strategy, thus a multiscale transport formulation, is employed for the saturation unknowns that allows to preserve most details of the fine-scale saturation distribution even in regions where a coarser resolution is employed. In regions where the ratio between the coarse and the fine-scale saturation updates is detected to be constant throughout the time-dependent simulation, such ratio is stored and employed as interpolator for subsequent time-steps in which a coarser resolution is employed. Numerical results are presented to study the accuracy and efficiency of the method and the advantages of such interpolation strategy for test cases including challenging non-linear physics, i.e. gravitational and capillary effects.       
Original languageEnglish
Title of host publication16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018
EditorsD. Gunasekera
PublisherEAGE
Number of pages11
ISBN (Print)9789462822603
DOIs
Publication statusPublished - 2018
Event16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018: 3–6 September 2018, Barcelona, Spain - Barcelona, Spain
Duration: 3 Sep 20186 Sep 2018
Conference number: 16
https://events.eage.org/en/2018/ecmorxvi

Conference

Conference16th European Conference on the Mathematics of Oil Recovery, ECMOR 2018
Abbreviated titleECMOR 2018
CountrySpain
CityBarcelona
Period3/09/186/09/18
Internet address

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