Upscaled equations for two-phase flow in highly heterogeneous porous media: Varying permeability and porosity

Ghosh, Tufan; Bringedal, Carina; Helmig, Rainer; Sekhar, G. P. Raja

doi:10.1016/j.advwatres.2020.103716

Cited by 7 publications

(2 citation statements)

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“…In addition, macroscopic interfaces could be captured by the model. Considering stratified heterogeneous media, Ghosh et al (2020) studied twophase flow in a porous column with varying porosity and permeability in a periodic manner. The resulting flow equations were derived using the homogenization technique and the model predictions were validated by direct numerical simulations at the pore-scale finding good agreement.…”

Section: Coupled Phenomena and Multiphase Flow In Porous Mediamentioning

confidence: 99%

Editorial: Recent developments in upscaling and characterization of flow and transport in porous media

Lasseux

Valdés‐Parada

Wood

2021

Advances in Water Resources

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Le et al. (2020) studied the flow and transport problem of CO 2 -enhanced coalbed methane recovery also by means of the homogenization technique. They considered a multiscale model that incorporated two levels of porosity that correspond to nanopores and the cleat network. This work includes a set of numerical simulations showing that the cleat permeability decreases significantly near the injection well because of the high injection pressure. In addition, Sharmin et al. (2020) considered two-phase (or unsaturated) incompressible flow in a thin, but long, single pore (a thin strip) with a stratified distribution of the two phases and derived an effective model starting from the Navier-Stokes equations. The upscaled model was obtained using the asymptotic homogenization method. It encompasses different regimes associated to the values of the capillary number and viscosity ratio. It also accounts for surface tension variations (Marangoni effects) which may result from the transport of a solute in one of the two phases. The upscaled model was compared to direct numerical simulations of the 2D pore-scale model. Finally, Airiau and Bottaro (2020) used the adjoint homogenization method to shed new light on the derivation of upscaled models for steady and creeping flow of a shear-thinning fluid in homogeneous porous media. These authors derived a Darcy-like model, where the components of the effective permeability tensor were obtained from the solution of an associated boundary-value problem in a periodic unit cell. Due to the dependence of the viscosity on the pore-scale flow, a coupled solution approach was used that translated into a strong anisotropy of the permeability tensor, even in isotropic geometries.Not all the works corresponding to this research topic used the homogenization method to carry out their analysis. For example, Cotta et al. (2020) studied flow and transport in fractured porous media using the generalized integral transform technique to derive analytical and numerical-analytical solutions. A salient feature of this work is the treatment of multiporosity cases, by means of a single integral transformation process. This approach is illustrated with two examples in fractured media and unsaturated soils. In addition, Angot et al. ( 2020) used an asymptotic analysis to study single-phase inertial flow in the fluidporous boundary. They show that the total inertial work exerted by the fluid over the solid is always positive. Non-equilibrium modeling for transport in homogeneous and heterogeneous porous mediaThis research subject comprises stochastic modeling and upscaling of transport processes. Engdahl and Bolster (2020) proposed to use a

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Section: Coupled Phenomena and Multiphase Flow In Porous Mediamentioning

confidence: 99%

Editorial: Recent developments in upscaling and characterization of flow and transport in porous media

Lasseux

Valdés‐Parada

Wood

2021

Advances in Water Resources

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“…Scientists and engineers have been trying to model physical phenomena occurring in nature for centuries, one of which is the transport of a quantity in space and time through natural media. A few examples include: subsurface fluid flow modeling (e.g., Ghosh et al., 2020; T. Koch et al., 2021), climate modeling (e.g., IPCC, 2013; Marchuk, 1974), and diffusion‐reaction modeling (e.g., Turing, 1952; Wei & Winter, 2017). Of course, contaminant transport and attenuation in water resources research also falls into this problem class.…”

Section: Introductionmentioning

confidence: 99%

Learning Groundwater Contaminant Diffusion‐Sorption Processes With a Finite Volume Neural Network

Praditia

Karlbauer

Otte

et al. 2022

Water Resources Research

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Improved understanding of complex hydrosystem processes is key to advance water resources research. Nevertheless, the conventional way of modeling these processes suffers from a high conceptual uncertainty, due to almost ubiquitous simplifying assumptions used in model parameterizations/closures. Machine learning (ML) models are considered as a potential alternative, but their generalization abilities remain limited. For example, they normally fail to predict accurately across different boundary conditions. Moreover, as a black box, they do not add to our process understanding or to discover improved parameterizations/closures. To tackle this issue, we propose the hybrid modeling framework FINN (finite volume neural network). It merges existing numerical methods for partial differential equations (PDEs) with the learning abilities of artificial neural networks (ANNs). FINN is applied on discrete control volumes and learns components of the investigated system equations, such as numerical stencils, model parameters, and arbitrary closure/constitutive relations. Consequently, FINN yields highly interpretable results. We demonstrate FINN's potential on a diffusion‐sorption problem in clay. Results on numerically generated data show that FINN outperforms other ML models when tested under modified boundary conditions, and that it can successfully differentiate between the usual, known sorption isotherms. Moreover, we also equip FINN with uncertainty quantification methods to lay open the total uncertainty of scientific learning, and then apply it to a laboratory experiment. The results show that FINN performs better than calibrated PDE‐based models as it is able to flexibly learn and model sorption isotherms without being restricted to choose among available parametric models.

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Numerical investigation of spontaneous imbibition in an anisotropic reservoir

Ghosh

Gujjala

Deb

et al. 2022

Geomech. Geophys. Geo-energ. Geo-resour.

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Upscaled equations for two-phase flow in highly heterogeneous porous media: Varying permeability and porosity

Cited by 7 publications

References 48 publications

Editorial: Recent developments in upscaling and characterization of flow and transport in porous media

Editorial: Recent developments in upscaling and characterization of flow and transport in porous media

Learning Groundwater Contaminant Diffusion‐Sorption Processes With a Finite Volume Neural Network

Numerical investigation of spontaneous imbibition in an anisotropic reservoir

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