A new and consistent well model for one-phase flow in anisotropic porous media using a distributed source model

Koch, Timo; Helmig, Rainer; Schneider, Martin

doi:10.1016/j.jcp.2020.109369

Cited by 7 publications

(7 citation statements)

References 27 publications

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“…When these are placed close together in the same FV cell, we find ourselves in Case 2.1 , and Assumption 2 in Section 2.6 breaks down. In this case, models that don’t integrate an analytical description of interactions among sources [ 37 , 72 ] fail to capture the source to sink interactions. With increasing separation distance d between the source and sink, Assumption 2 is recovered but, depending on the size of , the deviation from Assumption 1 may increase ( Case 1.3 ).…”

Section: Results: Error Estimationmentioning

confidence: 99%

Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma

Pastor-Alonso,

Berg,

Boyer

et al. 2024

PLoS Comput Biol

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Recent progresses in intravital imaging have enabled highly-resolved measurements of periarteriolar oxygen gradients (POGs) within the brain parenchyma. POGs are increasingly used as proxies to estimate the local baseline oxygen consumption, which is a hallmark of cell activity. However, the oxygen profile around a given arteriole arises from an interplay between oxygen consumption and delivery, not only by this arteriole but also by distant capillaries. Integrating such interactions across scales while accounting for the complex architecture of the microvascular network remains a challenge from a modelling perspective. This limits our ability to interpret the experimental oxygen maps and constitutes a key bottleneck toward the inverse determination of metabolic rates of oxygen. We revisit the problem of parenchymal oxygen transport and metabolism and introduce a simple, conservative, accurate and scalable direct numerical method going beyond canonical Krogh-type models and their associated geometrical simplifications. We focus on a two-dimensional formulation, and introduce the concepts needed to combine an operator-splitting and a Green’s function approach. Oxygen concentration is decomposed into a slowly-varying contribution, discretized by Finite Volumes over a coarse cartesian grid, and a rapidly-varying contribution, approximated analytically in grid-cells surrounding each vessel. Starting with simple test cases, we thoroughly analyze the resulting errors by comparison with highly-resolved simulations of the original transport problem, showing considerable improvement of the computational-cost/accuracy balance compared to previous work. We then demonstrate the model ability to flexibly generate synthetic data reproducing the spatial dynamics of oxygen in the brain parenchyma, with sub-grid resolution. Based on these synthetic data, we show that capillaries distant from the arteriole cannot be overlooked when interpreting POGs, thus reconciling recent measurements of POGs across cortical layers with the fundamental idea that variations of vascular density within the depth of the cortex may reveal underlying differences in neuronal organization and metabolic load.

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Section: Results: Error Estimationmentioning

confidence: 99%

Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma

Pastor-Alonso,

Berg,

Boyer

et al. 2024

PLoS Comput Biol

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“…We have shown that the reconstruction significantly reduces the discretization error. Another approach is the Peaceman well model known in reservoir engineering [27,36,37]. Peaceman devises a reconstruction method eliminating discretization errors for one specific discretization scheme, and with some assumptions on the structure of the mesh and the orientation of the well tube.…”

Section: Summary and Final Remarksmentioning

confidence: 99%

Nonlinear mixed-dimension model for embedded tubular networks with application to root water uptake

Koch,

Wu,

Schneider

2021

Preprint

Self Cite

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We present a numerical scheme for the solution of nonlinear mixed-dimensional PDEs describing coupled processes in embedded tubular network system in exchange with a bulk domain. Such problems arise in various biological and technical applications such as in the modeling of root-water uptake, heat exchangers, or geothermal wells. The nonlinearity appears in form of solution-dependent parameters such as pressure-dependent permeability or temperature-dependent thermal conductivity. We derive and analyse a numerical scheme based on distributing the bulk-network coupling source term by a smoothing kernel with local support. By the use of local analytical solutions, interface unknowns and fluxes at the bulk-network interface can be accurately reconstructed from coarsely resolved numerical solutions in the bulk domain. Numerical examples give confidence in the robustness of the method and show the results in comparison to previously published methods. The new method outperforms these existing methods in accuracy and efficiency. In a root water uptake scenario, we accurately estimate the transpiration rate using only a few thousand 3D mesh cells and a structured cube grid whereas other state-of-the-art numerical schemes require millions of cells and local grid refinement to reach comparable accuracy.

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“…Introducing the Joukowski function , defines the transform as follows where z = x + i y and w = u + i v = M e iθ , and based on Euler formula, we can get …”

Section: Mathematical Model Of Multiregion Coupling Flowmentioning

confidence: 99%

“…43,44 An analytic function is introduced which transforms from the elliptic domain to circular domain (Figure 5), and the original problem is solved by using the inverse transformation. Introducing the Joukowski function 45,46 defines the transform as follows…”

Section: Mathematical Model Of Multiregionmentioning

confidence: 99%

Study on Pressure Propagation in Tight Oil Reservoirs with Stimulated Reservoir Volume Development

Zhu

Liu

Li³

et al. 2021

ACS Omega

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The stimulated reservoir volume fracturing development in tight oil reservoirs is characterized by multiscale flow of the reservoir matrix, fracture network, and hydraulic fracture. Therefore, the flow field structure is extremely complex. Multiscale flow characteristics have been revealed through the systematical experiments including the threshold pressure gradient and the stress sensitivity. Based on the theory of elliptical flow, a comprehensive and practical mathematical model of multiregion coupling flow is established to characterize the multiscale flow, and the pressure distribution equation is derived. The calculation method of moving boundary is established to simulate the dynamic supply boundary and the dynamic pressure distribution by using the steady-state sequential replacement method. The characteristics of multiscale flow, multistage development state, and stress sensitivity are considered, especially the different stress sensitivity characteristics in different regions. Finally, the pressure propagation in tight reservoirs is clarified and the influence of matrix permeability, stress sensitivity characteristics, and drawdown pressure on the distance at the dynamic supply boundary are revealed. The research results provide theoretical basis for the development effect evaluation.

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A new and consistent well model for one-phase flow in anisotropic porous media using a distributed source model

Cited by 7 publications

References 27 publications

Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma

Modeling oxygen transport in the brain: An efficient coarse-grid approach to capture perivascular gradients in the parenchyma

Nonlinear mixed-dimension model for embedded tubular networks with application to root water uptake

Study on Pressure Propagation in Tight Oil Reservoirs with Stimulated Reservoir Volume Development

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