2012
DOI: 10.1137/110836201
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A Multiscale Method Coupling Network and Continuum Models in Porous Media I: Steady-State Single Phase Flow

Abstract: We propose a numerical multiscale method for coupling a conservation law for mass at the continuum scale with a discrete network model that describes the microscale flow in a porous medium. In this work we focus on coupling pressure equations. Evaluating pressure from a detailed network model over a large physical domain is typically computationally very expensive. We assume that over the same physical domain there exists an effective mass conservation equation at the continuum scale which could have been solv… Show more

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Cited by 39 publications
(20 citation statements)
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References 50 publications
(77 reference statements)
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“…Incorporation of multiscale electrochemical phenomena has not been widely attempted in a PN modeling framework as it poses severe computational difficulties due to the need for incorporating partial-differential relationships. There have been limited efforts at building a robust electrochemical transport simulation that takes advantage of both modeling techniques [25,26].…”
Section: Coupled Continuum and Pore-network Modelsmentioning
confidence: 99%
“…Incorporation of multiscale electrochemical phenomena has not been widely attempted in a PN modeling framework as it poses severe computational difficulties due to the need for incorporating partial-differential relationships. There have been limited efforts at building a robust electrochemical transport simulation that takes advantage of both modeling techniques [25,26].…”
Section: Coupled Continuum and Pore-network Modelsmentioning
confidence: 99%
“…For instance, possible capillary condensation effects upon transport (induced as the local chemical potential reaches a specific value for a given pore size or scale) cannot be described using homogenization techniques in which a single density or pressure equation is used for a given type (therefore not accounting for possible adsorption changes induced by transport). It is worth mentioning that many works in the literature use hybrid models, which employ pore scale and continuum descriptions of the same phenomenon in different regions of a computational domain [34][35][36][37]. A number of other upscaling approaches have been reviewed in Refs.…”
Section: A State Of the Artmentioning
confidence: 99%
“…It is also noteworthy, that the approach seems to be a special case of the Global Jacobian methods of Ganis et al (2012) and Mehmani and Balhoff (2014). Chu et al (2012) proposed an approach based on the heterogeneous multiscale method (HMM), in which macroscopic conservation equations are written assuming unavailability of constitutive fl ow equations (e.g., Darcy's law) at the macro scale. The missing data were instead supplied from locally sampled pore-network simulations across the domain.…”
Section: Hybrid Modelingmentioning
confidence: 99%