GeoChemFoam is an open-source OpenFOAM-based numerical modelling toolbox that includes a range of custom packages to solve complex flow processes including multiphase transport with interface transfer, single-phase flow in multiscale porous media, and reactive transport with mineral dissolution. In this paper, we present GeoChemFoam's novel numerical model for simulation of conjugate heat transfer in micro-CT images of porous media. GeoChemFoam uses the micro-continuum approach to describe the fluid-solid interface using the volume fraction of fluid and solid in each computational cell. The velocity field is solved using Brinkman's equation with permeability calculated using the Kozeny-Carman equation which results in a near-zero permeability in the solid phase. Conjugate heat transfer is then solved with heat convection where the velocity is non-zero, and the thermal conductivity is calculated as the harmonic average of phase conductivity weighted by the phase volume fraction. Our model is validated by comparison with the standard two-medium approach for a simple 2D geometry. We then simulate conjugate heat transfer and calculate heat transfer coefficients for different flow regimes and injected fluid analogous to injection into a geothermal reservoir in a micro-CT image of Bentheimer sandstone and perform a sensitivity analysis in a porous heat exchanger with a random sphere packing.
We present the novel numerical model GeoChemFoam, a multiphase reactive transport solver for simulations on complex pore geometries, including microfluidic devices and micro-CT images. The geochemical model includes bulk and surface equilibrium reactions. Multiphase flow is solved using the Volume-Of-Fluid method and the transport of species is solved using the Continuous Species Transfer method. The reactive transport equations are solved using a sequential Operator Splitting method, with the transport step solved using our OpenFOAM-based Computational Fluid Dynamics toolbox, and the reaction…
We present a novel time-stepping method, called Operator Splitting with Capillary Relaxation (OSCAR), for efficient Volume-Of-Fluid simulations of capillary-dominated two-phase flow. OSCAR uses operator splitting methods to separate the viscous drag and the surface tension forces. Different time-steps are used for the viscous drag steps, controlled by the injection velocity, and for the capillary relaxation steps, controlled by the velocity of capillary waves. Although OSCAR induces an additional numerical error of order 0 in time resulting from the splitting, it is well suited for simulations…
Fluid flow through intricate confining geometries often exhibits complex behaviors, certainly in porous materials, e.g. in groundwater flows or the operation of filtration devices and porous catalysts. However, it has remained extremely challenging to measure 3D flow fields in such micrometer-scale geometries. Here, we introduce a new 3D velocimetry approach for optically opaque porous materials, based on time-resolved X-ray micro-computed tomography (micro-CT). We imaged the movement of X-ray tracing micro-particles in creeping flows through the pores of a sandpack and a porous filter, using …
The flow of micropolar fluid through a membrane modeled as a swarm of solid cylindrical particles with porous layer using the cell model technique is considered. The flow is directed perpendicular to the axis of the cylinders. Boundary value problem involves traditional conditions of velocities and stresses continuity, no-stress and no-couple stress / no-spin condition on hypothetical cell surface. The problem was solved analytically. The influence of micropolar and porous medium parameters on hydrodynamic permeability of a membrane has been studied.
The present paper considers the flow of micropolar fluid through a membrane modeled as a swarm of solid cylindrical particles with porous layer using the cell model technique. Traditional boundary conditions on hypothetical cell surface were added with an additional condition: the no spin condition / no couple stress condition. Expressions for velocity and microrotation vector components have been obtained analytically. Effect of various parameters such as particle volume fraction, permeability parameter, micropolarity number etc. on hydrodynamic permeability of membrane has been discussed.
Microchannel with porous wall has various microfluidic applications including iontophoresis, diagnostic devices, etc. In order to have an efficient and better design of such devices, exact quantification of velocity field in the microchannel needs to be established. In the present study, an analytical solution of velocity field in a microchannel with porous wall was obtained for a Newtonian fluid in case of a combined electroosmotic and pressure driven flow using perturbation technique. The velocity profile was reduced to well known solutions for three asymptotic cases, namely, purely electroo…
Pore structures and gas transport properties in porous separators for polymer electrolyte fuel cells are evaluated both experimentally and through simulations. In the experiments, the gas permeabilities of two porous samples, a conventional sample and one with low electrical resistivity, are measured by a capillary flow porometer, and the pore size distributions are evaluated with mercury porosimetry. Local pore structures are directly observed with micro X-ray computed tomography (CT). In the simulations, the effective diffusion coefficients of oxygen and the air permeability in porous sample…
New insight into the contribution of the microscale vortex evolution towards convection heat transfer in porous media is presented in this paper. The objective is to determine how the microscale vortices influence convection heat transfer in turbulent flow inside porous media. The microscale temperature distribution is analyzed using flow visualization in 2D using streamlines and in 3D using Q structures. The pertinent observations are supplemented with the comparison of surface skin friction and heat transfer using: (1) surface skin friction lines and (2) joint PDF of pressure and skin fricti…
This study refutes the premise that the distribution of flow speeds in complex porous media can be described by a simple function such as a normal or exponential variation. In many complex porous media, including those relevant for subsurface storage and recovery applications, a separation of scales exists between larger inter-granular pores and micro-porosity inside the grains, leading to different flow signatures that need to be described by multimodal functions with distinct flow field characteristics. We demonstrate this finding by devising a novel methodology to simulate fluid flow in car…
The flow of viscoelastic fluids in porous media is encountered in many practical applications, such as in the enhanced oil recovery process or in the groundwater remediation. Once the flow rate exceeds a critical value in such flows, an elastic instability with fluctuating flow field is observed, which ultimately transits to a more chaotic and turbulence-like flow structure as the flow rate further increases. In a recent study, it has been experimentally shown that this chaotic flow behaviour of viscoelastic fluids can be suppressed by increasing the geometric disorder in a model porous media …
We investigate how a filter media microstructure influences filtration performance. We derive a theory that generalizes classical multiscale models for regular structures to account for filter media with more realistic microstructures, comprising random microstructures with polydisperse unidirectional fibres. Our multiscale model accounts for the fluid flow and contaminant transport at the microscale (over which the media structure is fully resolved) and allows us to obtain macroscopic properties such as the effective permeability, diffusivity, and fibre surface area. As the fibres grow due to…
Displacement experiments carried out in microfluidic porous media analogs show that reduced surface tension leads to a more stable displacement, opposite to the process in Hele-Shaw cells where surface tension stabilizes the displacement of a more viscous fluid by a less viscous fluid. In addition, geometry of porous media is observed to play an important role. Three random microfluidic porous media analogs were made to study water-oil drainage dynamics, featuring a pattern of randomly connected channels with a uniform width, a pattern with Gaussian channel width distribution, and a pattern wi…
We present the visual analysis of our novel parameter study of porous media experiments, focusing on gaining a better understanding of drainage processes on the micro-scale. We analyze the temporal evolution of extracted characteristic values, and discuss how to directly compare experiments that exhibit processes at different temporal scales due to varying boundary and physical conditions. To enable spatio-temporal analysis, we introduce a new abstract visual representation showing which paths through the porous media were occupied to what extent, e.g., allowing for classification into viscous…
We present a numerical study of nonlinear electrokinetic transport in porous media, focusing on the role of heterogeneity in a porous microstructure on ion concentration polarization and over-limiting current. For simplicity, the porous medium is modeled as a network of long, thin charged cylindrical pores, each governed by one-dimensional effective transport equations. For weak surface conduction, when sufficiently large potential is applied, we demonstrate that electrokinetic transport in a porous network can be dominated by electroconvection via internally induced flow loops, which is not p…
Liquid bridges are commonly encountered in nature and the liquid transfer induced by their rupture are widely used in various industrial applications. In this work, with the focus on the porous tip, we studied the impacts of capillary effects on the liquid transfer induced by the rupture through numerical simulations. To depict the capillary effects of a porous tip, a time scale ratio, R_T, is proposed to compare the competing mechanisms of spontaneous imbibitiona and external drag. In terms of R_T, we then develop a theoretical model for estimating the liquid retention ratio considering the g…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scales to systematically upscale a novel problem involving cells of varying area to obtain effective contin…
Given their capability of spreading active chemical species and collecting electricity, porous media made of carbon fibers are extensively used as diffusion layers in energy storage systems, such as redox flow batteries. In spite of this, the dispersion dynamics of species inside porous media is still not well understood and often lends itself to different interpretations. Actually, the microscopic design of efficient porous media which can potentially and effectively improve the performances of flow batteries, is a still open challenge. The present study aims to investigate the effect of fibr…
Mineral dissolution in porous media coupled with single- or multi-phase flows is pervasive in natural and engineering systems including carbon capture and sequestration (CCS) and acid stimulation in reservoir engineering. Dissolution of minerals occurs as chemicals in the solid phase is transformed into ions in the aqueous phase, effectively modifying the physical, hydrological and geochemical properties of the solid matrix, and thus leading to the strong coupling between local dissolution rate and pore-scale flow. However, our fundamental understanding of this coupling effect at the pore leve…
The electrolyte (comprising of solute ions and solvents) flow-through the porous media is frequently encountered in nature or in many engineering applications, such as the electrochemical systems, manufacturing of composites, geothermal engineering, soil pollution. In this study, we provide a new general theory for the electrochemical flows-through porous media. We use static method and set up two representative elementary volumes (REVs). One is the macroscopic REV of the mixture of the porous media and the electrolyte, while the other is the microscopic REV in the electrolyte fluid. The estab…
The focus of this paper is to systematically study the influence of solid obstacle surface roughness in porous media on the microscale flow physics and report its effect on macroscale drag and Nusselt number. The Reynolds averaged flow field is numerically simulated for a flow through a periodic porous medium consisting of an in-line arrangement of square cylinders with square roughness particles on the cylinder surface. Two flow regimes are identified with respect to the surface roughness particle height: fine and coarse roughness regimes. The effect of the roughness particles in the fine rou…
The relationship between the microstructure of a porous medium and the observed flow distribution is still a puzzle. We resolve it with an analytical model, where the local correlations between adjacent pores, which determine the distribution of flows propagated from one pore downstream, predict the flow distribution. Numerical simulations of a two-dimensional porous medium verify the model and clearly show the transition of flow distributions from $δ$-function-like via Gaussians to exponential with increasing disorder. Comparison to experimental data further verifies our numerical approach.
Velocity distribution functions link the micro- and macro-level theories of fluid flow through porous media. Here we study them for the fluid absolute velocity and its longitudinal and lateral components relative to the macroscopic flow direction in a model of a random porous medium. We claim that all distributions follow the power exponential law controlled by an exponent $γ$ and a shift parameter $u_0$ and examine how these parameters depend on the porosity. We find that $γ$ has a universal value $1/2$ at the percolation threshold and grows with the porosity, but never exceeds 2.
An open-sourced multiphase Darcy-Brinkman approach is proposed to simulate two-phase flow in hybrid systems containing both solid-free regions and porous matrices. This micro-continuum model is rooted in elementary physics and volume averaging principles, where a unique set of partial differential equations is used to represent flow in both regions and scales. The crux of the proposed model is that it tends asymptotically towards the Navier-Stokes volume-of-fluid approach in solid-free regions and towards the multiphase Darcy equations in porous regions. Unlike existing multiscale multiphase s…
Experimental two-phase invasion percolation flow patterns were observed in hydrophobic micro-porous networks designed to model fuel cell specific porous media. In order to mimic the operational conditions encountered in the porous electrodes of polymer electrolyte membrane fuel cells (PEMFCs), micro-porous networks were fabricated with corresponding microchannel size distributions. The inlet channels were invaded homogeneously with flow rates corresponding to fuel cell current densities of 1.0 to 0.1 A/cm2 (Ca 10e-7-10e-8). A variety of fractal breakthrough patterns were observed and analyzed …
We extend the two-scale expansion approach of periodic homogenization to include time scales and thus can tackle the full instationary Navier-Stokes-Cahn-Hilliard model at the pore scale as microscale. Time scale separation allows us to keep microscale dynamics, responsible e.g. for hysteresis, and arrive at a numerically tractable micro-macro model including coupled generalized Darcy's laws.
Natural porous systems, such as soil, membranes, and biological tissues comprise disordered structures characterized by dead-end pores connected to a network of percolating channels. The release and dispersion of particles, solutes, and microorganisms from such features is key for a broad range of environmental and medical applications including soil remediation, drug delivery and filtration. Yet, the role of microscopic structure and flow for the dispersion of particles and solutes in such disordered systems has been only poorly understood, in part due to the stagnant and opaque nature of the…
Pore network modelling has traditionally been used to study displacement processes in idealized porous media related to geological flows, with applications ranging from groundwater hydrology to enhanced oil recovery. Very recently, pore network modelling has been applied to model the gas diffusion layer (GDL) of a polymer electrolyte membrane (PEM) fuel cell. Discrete pore network models have the potential to elucidate transport phenomena in the GDL with high computational efficiency, in contrast to continuum or molecular dynamics modelling that require extensive computational resources. Howev…
The problem of diffusion in a porous medium with a spatially varying porosity is considered. The particular microstructure analyzed comprises a collection of impenetrable spheres, though the methods developed are general. Two different approaches for calculating the effective diffusion coefficient as a function of the microstructure are presented. The first is a deterministic approach based on the method of multiple scales; the second is a stochastic approach for small volume fraction of spheres based on matched asymptotic expansions. We compare the two approaches, and we show good agreement b…
Droplet wicking and evaporation in porous nanochannels is experimentally studied on a heated surface at temperatures ranging from 35oC to 90oC. The fabricated geometry consists of cross-connected nanochannels of height 728 nm with micropores of diameter 2 um present at every channel intersection; the pores allow water from a droplet placed on the top surface to wick into the channels. Droplet volume is also varied and a total of 16 experimental cases are conducted. Wicking characteristics such as wicked distance, capillary pressure, viscous resistance and propagation coefficient are obtained a…
Models that describe two-fluid flow in porous media suffer from a widely-recognized problem that the constitutive relationships used to predict capillary pressure as a function of the fluid saturation are non-unique, thus requiring a hysteretic description. As an alternative to the traditional perspec- tive, we consider a geometrical description of the capillary pressure, which relates the average mean curvature, the fluid saturation, the interfacial area between fluids, and the Euler characteristic. The state equation is formulated using notions from algebraic topology and cast in terms of me…
CNN-powered micro- to macro-scale flow modeling in deformable porous media
Institute of Mechanics and Computational Mechanics (IBNM), Leibniz University Hannover（莱布尼茨汉诺威大学力学与计算力学研究所（IBNM））；Institute of Applied Mechanics, University of Stuttgart（斯图加特大学应用力学研究所）；Institute of General Mechanics, RWTH Aachen University（亚琛工业大学普通力学研究所）
Solute dispersion in magnetically influenced multiphase flow through a porous tube: axial transport and microrotational effects
Cooch Behar Panchanan Barma University（古奇比哈尔潘查南·巴尔马大学）；SRM Institute of Science and Technology（SRM科学技术研究所）；University of Galway（高威大学）；Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校）
