A (Dual) Network Model for Heat Transfer in Porous Media

Koch, Timo; Weishaupt, Kilian; Müller, Johannes; Helmig, Rainer

doi:10.1007/s11242-021-01602-5

Cited by 18 publications

(13 citation statements)

References 66 publications

(84 reference statements)

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“…However, studies and modeling on thermal disequilibrium between fluid and solid phases have gained interests lately (Karani and Huber 2017 ; Koch et al. 2021 ). If we consider a heat tracer test where we create a breakthrough curve like those in Fig.…”

Section: Discussionmentioning

confidence: 99%

“…Usually, such an energy conservation model of heat tracer tests assumes thermal equilibrium between the fluid and the porous solid, T f = T s , (Shook 2001;Anderson 2005;Saar 2011). However, studies and modeling on thermal disequilibrium between fluid and solid phases have gained interests lately (Karani and Huber 2017;Koch et al 2021). If we consider a heat tracer test where we create a breakthrough curve like those in Fig.…”

Section: Limitations and Outlookmentioning

confidence: 99%

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Relating Darcy-Scale Chemical Reaction Order to Pore-Scale Spatial Heterogeneity

et al. 2022

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Due to spatial scaling effects, there is a discrepancy in mineral dissolution rates measured at different spatial scales. Many reasons for this spatial scaling effect can be given. We investigate one such reason, i.e., how pore-scale spatial heterogeneity in porous media affects overall mineral dissolution rates. Using the bundle-of-tubes model as an analogy for porous media, we show that the Darcy-scale reaction order increases as the statistical similarity between the pore sizes and the effective-surface-area ratio of the porous sample decreases. The analytical results quantify mineral spatial heterogeneity using the Darcy-scale reaction order and give a mechanistic explanation to the usage of reaction order in Darcy-scale modeling. The relation is used as a constitutive relation of reactive transport at the Darcy scale. We test the constitutive relation by simulating flow-through experiments. The proposed constitutive relation is able to model the solute breakthrough curve of the simulations. Our results imply that we can infer mineral spatial heterogeneity of a porous media using measured solute concentration over time in a flow-through dissolution experiment.

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Section: Discussionmentioning

confidence: 99%

Section: Limitations and Outlookmentioning

confidence: 99%

Relating Darcy-Scale Chemical Reaction Order to Pore-Scale Spatial Heterogeneity

et al. 2022

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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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“…It is important to highlight that with the network method it would be possible to model other problems similar to the one presented here and that have been recently studied by other authors. Thus, Koch et al [34] present a very similar network model that includes the possibility of considering different fluid and solid phase temperatures. However, this situation of thermal non-equilibrium at the local level is typical of phenomena associated with chemical reactions, evaporation or heat/cold injections (among others) which do not occur in the groundwater flow scenarios that we address in this work.…”

Section: Introductionmentioning

confidence: 99%

“…However, this situation of thermal non-equilibrium at the local level is typical of phenomena associated with chemical reactions, evaporation or heat/cold injections (among others) which do not occur in the groundwater flow scenarios that we address in this work. On the other hand, Koch et al [34] use an integral approximation procedure, a different numerical technique than the one used here. In another recent work, Matias et al [35] address porous media that change over time due to swelling and erosion processes.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Heat Transport Problems in Porous Media Coupled with Water Flow Using the Network Method

2021

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In the present work, a network model for the numerical resolution of the heat transport problem in porous media coupled with a water flow is presented. Starting from the governing equations, both for 1D and 2D geometries, an equivalent electrical circuit is obtained after their spatial discretization, so that each term or addend of the differential equation is represented by an electrical device: voltage source, capacitor, resistor or voltage-controlled current source. To make this possible, it is necessary to establish an analogy between the real physical variables of the problem and the electrical ones, that is: temperature of the medium and voltage at the nodes of the network model. The resolution of the electrical circuit, by means of the different circuit resolution codes available today, provides, in a fast, simple and precise way, the exact solution of the temperature field in the medium, which is usually represented by abaci with temperature-depth profiles. At the end of the article, a series of applications allow, on the one hand, to verify the precision of the numerical tool by comparison with existing analytical solutions and, on the other, to show the power of calculation and representation of solutions of the network models presented, both for problems in 1D domains, typical of scenarios with vertical flows, and for 2D scenarios with regional flow.

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A (Dual) Network Model for Heat Transfer in Porous Media

Cited by 18 publications

References 66 publications

Relating Darcy-Scale Chemical Reaction Order to Pore-Scale Spatial Heterogeneity

Relating Darcy-Scale Chemical Reaction Order to Pore-Scale Spatial Heterogeneity

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

Numerical Simulation of Heat Transport Problems in Porous Media Coupled with Water Flow Using the Network Method

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