Algebraic dynamic multilevel (ADM) method for fully implicit simulations of multiphase flow in porous media

Cusini, Matteo; Kruijsdijk, C.P.J.W. van; Hajibeygi, Hadi

doi:10.1016/j.jcp.2016.03.007

Cited by 52 publications

(35 citation statements)

References 21 publications

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“…However, the idea of the MS data assimilation can be extended to seamlessly address data available at multiple scales, or even consider one, or multiple MS grid resolution(s) for assimilation purposes only and different one(s) for the forward simulation. To this end, multilevel multiscale strategies (Cusini et al, 2016) could be applied. Following the same multilevel multiscale strategy, data acquired at different scales (e.g.…”

Section: Discussionmentioning

confidence: 99%

A Multiscale Method For Data Assimilation

Moraes

Hajibeygi

2018

Proceedings

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In data assimilation problems, various types of data are naturally linked to different spatial resolutions (e.g. seismic and electromagnetic data), and these scales are usually not coincident to the subsurface simulation model scale. Alternatives like down/upscaling of the data and/or the simulation model can be used, but with potential loss of important information. To address this issue, a novel Multiscale (MS) data assimilation method is introduced. The overall idea of the method is to keep uncertain parameters and observed data at their original representation scale, avoiding down/upscaling of any quantity. The method relies on a recently developed mathematical framework to compute adjoint gradients via a MS strategy. The fine-scale uncertain parameters are directly updated and the MS grid is constructed in a resolution that meets the observed data resolution. The advantages of the technique are demonstrated in the assimilation of data represented at a coarser scale than the simulation model. The misfit objective function is constructed to keep the MS nature of the problem. The regularization term is represented at the simulation model (fine) scale, whereas the data misfit term is represented at the observed data (coarse) scale. The performance of the method is demonstrated in synthetic models and compared to down/upscaling strategies. The experiments show that the MS strategy provides advantages 1) on the computational side -expensive operations are only performed at the coarse scale; 2) with respect to accuracy -the matched uncertain parameter distribution is closer to the "truth"; and 3) in the optimization performance -faster convergence behaviour due to faster gradient computation. In conclusion, the newly developed method is capable of providing superior results when compared to strategies that rely on the up/downscaling of the response/observed data, addressing the scale dissimilarity via a robust, consistent MS strategy.

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Section: Discussionmentioning

confidence: 99%

A Multiscale Method For Data Assimilation

Moraes

Hajibeygi

2018

Proceedings

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“…2). A more detailed description of the sequence of prolongation and restriction operators can be found in Cusini et al (2016). …”

Section: Algebraic Dynamic Multilevel (Adm) Methodsmentioning

confidence: 99%

“…Recently, an Algebraic Dynamic Multilevel (ADM) method (Cusini et al, 2016) was proposed for multiphase flow in heterogeneous porous media. The ADM extended the applicability of multiscale methods in the sense that it was employed to FIM systems, where all unknowns crossed multiple scales.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Dynamic Multilevel (ADM) Method for Immiscible Multiphase Flow in Heterogeneous Porous Media with Capillarity

Cusini¹,

Kruijsdijk²,

Hajibeygi³

2016

Proceedings

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SUMMARYAn algebraic dynamic multilevel method (ADM) is developed for fully-implicit (FIM) simulations of multiphase flow in heterogeneous porous media with strong non-linear physics. The fine-scale resolution is defined based on the heterogeneous geological one. Then, ADM constructs a space-time adaptive FIM system on a dynamically defined multilevel nested grid. The multilevel resolution is defined using an error estimate criterion, aiming to minimize the accuracy-cost trade-off. ADM is algebraically described by employing sequences of adaptive multilevel restriction and prolongation operators. Finite-volume conservative restriction operators are considered whereas different choices for prolongation operators are employed for different unknowns. The ADM method is applied to challenging heterogeneous test cases with strong nonlinear heterogeneous capillary effects. It is illustrated that ADM provides accurate solution by employing only a fraction of the total number of fine-scale grid cells. ADM is an important advancement for multiscale methods because it solves for all coupled unknowns (here, both pressure and saturation) simultaneously on arbitrary adaptive multilevel grids. At the same time, it is a significant step forward in the application of dynamic local grid refinement techniques to heterogeneous formations without relying on upscaled coarse-scale quantities.

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“…On the other hand, the pressure and saturation blocks of the prolongation operator, (P p ) i i−1 and (P S ) i i−1 are different [20] as different interpolation rules are used for each variable. In this work (P S )…”

Section: Solution Strategymentioning

confidence: 99%

“…On the other hand, DLGR techniques adapt the grid resolution throughout the time-dependent simulation to employ a high-resolution grid where necessary (i.e., the advancing saturation front), and are, therefore, transport-oriented methods. The Algebraic Dynamic Multilevel (ADM) method [20] has been introduced to address the multi-scale multilevel coexistence of the pressure (elliptic or parabolic) and transport (hyperbolic) unknowns, at the same time, within both fully implicit (FIM) and sequential (implicit and explicit) simulation frameworks. ADM develops a dynamic multilevel system for all unknowns, through an algebraic formulation, where the resolutions are connected through sets of basis functions.…”

Section: Introductionmentioning

confidence: 99%