Permeability Estimation of Regular Porous Structures: A Benchmark for Comparison of Methods

Wagner, Anne; Eggenweiler, Elissa; Weinhardt, Felix; Trivedi, Zubin; Krach, David; Lohrmann, Christoph; Jain, Kartik; Karadimitriou, Nikolaos; Bringedal, Carina; Voland, Paul; Holm, Christian; Class, Holger; Steeb, Holger; Rybak, Iryna

doi:10.1007/s11242-021-01586-2

Cited by 31 publications

(26 citation statements)

References 49 publications

(62 reference statements)

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“…Through the definition of 𝐽 𝑆 , the formulation in Equation (36) becomes 𝑛 𝑆 = 𝑛 𝑆 0𝑆 𝐽 −1 𝑆 . With linearization, the relationship yields the following:…”

Section: Appendix A: Unified Unsaturated/saturated Porous Media Conti...mentioning

confidence: 99%

“…34,35 where an idealized micro-geometry of the pore network was considered. To estimate the permeability of a benchmark periodic porous structure, Wagner et al 36 compared in an upscaling study the results of the Kozeny-Carman equation, various homogenization methods, pore-scale simulations (including LBM), and pore-scale experiments. In their work, they concluded that the homogenization and pore-scale models provided accurate permeability results, whereby the Kozeny-Carman relation did not provide acceptable permeability results and the pore-scale experiments yielded underestimated values.…”

Section: Introductionmentioning

confidence: 99%

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A multiscale LBM–TPM–PFM approach for modeling of multiphase fluid flow in fractured porous media

Chaaban

Heider

Markert

2022

Num Anal Meth Geomechanics

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In this paper, we present a reliable micro-to-macroscale framework to model multiphase fluid flow through fractured porous media. This is based on utilizing the capabilities of the lattice Boltzmann method (LBM) within the phase-field modeling (PFM) of fractures in multiphase porous media. In this, we propose new physically motivated phase-field-dependent relationships for the residual saturation, the intrinsic as well as relative permeabilities. In addition, an anisotropic, phase-field-dependent intrinsic permeability tensor for the fractured porous domains is formulated, which relies on the single-and multiphasic LBM flow simulations. Based on these results, new relationships for the variation of the macroscopic theory of porous media (TPM)-PFM model parameters in the transition zone are proposed. Whereby, a multiscale concept for the coupling between the multiphasic flow through the crack on one hand and the porous ambient, on the other hand, is achieved. The hybrid model is numerically applied on a real microgeometry of fractured porous media, extracted via X-ray microcomputed tomography data of fractured Berea Sandstone. Moreover, the model is utilized for the calculation of the fluid leak-off from the crack to the intact zones. Additionally, the effects of the depth of the transition zone and the orientation of the crack channels on the amount of leakage flow rates are studied. The outcomes of the numerical model proved the reliability of the multiscale model to simulate multiphasic fluid flow through fractured porous media.

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“…Through the definition of 𝐽 𝑆 , the formulation in Equation (36) becomes 𝑛 𝑆 = 𝑛 𝑆 0𝑆 𝐽 −1 𝑆 . With linearization, the relationship yields the following:…”

Section: Appendix A: Unified Unsaturated/saturated Porous Media Conti...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A multiscale LBM–TPM–PFM approach for modeling of multiphase fluid flow in fractured porous media

Chaaban

Heider

Markert

2022

Num Anal Meth Geomechanics

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“…In terms of permeability prediction, the labeling process of geological specimens is connected to the computation of 3D stationary flow fields of a single-phase fluid within the pore space. For permeability prediction under regular geometries, a broader set of methods is available as described and compared in [9].…”

Section: Introductionmentioning

confidence: 99%

“…More precisely, our forward simulation is based on a distributed-parallel Stokes solver utilizing the finite element library MFEM [20]. As studied in [9] for simple cylindrical obstacles, such DNS approaches (in this case FEM) deliver results comparable to LBM. However, our implementation successfully alleviates the drawback of an impractically large number of iterations to obtain the desired accuracy on complex geometries.…”

Section: Introductionmentioning

confidence: 99%

Estimating permeability of 3D micro-CT images by physics-informed CNNs based on DNS

Gärttner¹,

Alpak²,

Meier³

et al. 2021

Preprint

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In recent years, convolutional neural networks (CNNs) have experienced an increasing interest for their ability to perform fast approximation of effective hydrodynamic parameters in porous media research and applications. This paper presents a novel methodology for permeability prediction from micro-CT scans of geological rock samples. The training data set for CNNs dedicated to permeability prediction consists of permeability labels that are typically generated by classical lattice Boltzmann methods (LBM) that simulate the flow through the pore space of the segmented image data. We instead perform direct numerical simulation (DNS) by solving the stationary Stokes equation in an efficient and distributedparallel manner. As such, we circumvent the convergence issues of LBM that frequently are observed on complex pore geometries, and therefore, improve on the generality and accuracy of our training data set.Using the DNS-computed permeabilities, a physics-informed CNN (PhyCNN) is trained by additionally providing a tailored characteristic quantity of the pore space. More precisely, by exploiting the connection to flow problems on a graph representation of the pore space, additional information about confined structures is provided to the network in terms of the maximum flow value, which is the key innovative component of our workflow. As a result, unprecedented prediction accuracy and robustness are observed for a variety of sandstone samples from archetypal rock formations.

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“…Kozeny-Carman, or determined by means of numerical upscaling techniques, e.g. [27,55,64] and references therein. However, the permeability is uncertain in general.…”

mentioning

confidence: 99%

Global sensitivity analysis using multi-resolution polynomial chaos expansion for coupled Stokes-Darcy flow problems

Kroeker,

Oladyshkin,

Rybak

2022

Preprint

Self Cite

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Determination of relevant model parameters is crucial for accurate mathematical modelling and efficient numerical simulation of a wide spectrum of applications in geosciences. The conventional method of choice is the global sensitivity analysis (GSA). Unfortunately, at least the classical Monte-Carlo based GSA requires a high number of model runs. Response surfaces based techniques, e.g. arbitrary Polynomial Chaos (aPC) expansion, can reduce computational effort, however, they suffer from the Gibbs phenomena and high hardware requirements for higher accuracy. We introduce GSA for arbitrary Multi-Resolution Polynomial Chaos (aMR-PC) which is a localized aPC based data-driven polynomial discretization. The aMR-PC allows to reduce the Gibbs phenomena by construction and to achieve higher accuracy by means of localization also for lower polynomial degrees. We apply these techniques to perform the sensitivity analysis for the Stokes-Darcy problem which describes fluid flow in coupled free-flow and porous-medium systems. We consider the Stokes equations in the free-flow region, Darcy's law in the porous-medium domain and the classical interface conditions across the fluid-porous interface including the conservation of mass, the balance of normal forces and the Beavers-Joseph condition for the tangential velocity. This coupled problem formulation contains four uncertain parameters: the exact location of the interface, the permeability, the Beavers-Joseph slip coefficient and the uncertainty in the boundary conditions. We carry out the sensitivity analysis of the coupled model with respect to these parameters using the Sobol indexes on the aMR-PC expansion and conduct the corresponding numerical simulations.

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Permeability Estimation of Regular Porous Structures: A Benchmark for Comparison of Methods

Cited by 31 publications

References 49 publications

A multiscale LBM–TPM–PFM approach for modeling of multiphase fluid flow in fractured porous media

A multiscale LBM–TPM–PFM approach for modeling of multiphase fluid flow in fractured porous media

Estimating permeability of 3D micro-CT images by physics-informed CNNs based on DNS

Global sensitivity analysis using multi-resolution polynomial chaos expansion for coupled Stokes-Darcy flow problems

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