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

Abstract

We present a dual network model to simulate coupled single-phase flow and energy transport in porous media including conditions under which local thermal equilibrium cannot be assumed. The models target applications such as the simulation of catalytic reactors, micro-fluidic experiments, or micro-cooling devices. The new technique is based on a recently developed algorithm that extracts both the pore space and the solid grain matrix of a porous medium from CT images into an interconnected network representation. We simulate coupled heat and mass transfer in these networks simultaneously, allowing naturally to model scenarios with heterogeneous temperature distributions in both void space and solid matrix. The model is compared with 3D conjugate heat transfer simulations for both conduction- and convection-dominated scenarios. It is shown to reproduce effective thermal conductivities over a wide range of fluid to solid thermal conductivity ratios with a single parameter set. Morevoer, it captures local thermal nonequilibrium effects in a micro-cooling device scenario.

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

“…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.…”

“…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.…”

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

“…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.…”

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

“…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.…”

“…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.…”