The prediction of the first fluidized path of a yield-stress fluid in complex porous media is a challenging yet an important task to understand the fundamentals of fluid flow in several industrial and biological processes. In most cases, the conditions that open this first path are known either through experiments or expensive computations. Here, we present a simple network model to predict the first open channel for a yield-stress fluid in a complex porous medium. For porous media made of non-overlapping disks, we find that the pressure drop required to open the first channel for given yield stress depends on both the relative disks size to the macroscopic length of the system and the packing fraction. We also report the statistics on the arc-length of the first open path. Finally, we discuss the implication of our results on the design of porous media used in energy storage applications.
Yield-stress is a problematic and controversial non-Newtonian flow phenomenon. In this article, we investigate the flow of yield-stress substances through porous media within the framework of pore-scale network modeling. We also investigate the validity of the Minimum Threshold Path (MTP) algorithms to predict the pressure yield point of a network depicting random or regular porous media. Percolation theory as a basis for predicting the yield point of a network is briefly presented and assessed. In the course of this study, a yield-stress flow simulation model alongside several numerical algor…
In this work, we study the role of viscoelastic instability in the mechanical dispersion of fluid flow through porous media at high Peclet numbers. Using microfluidic experiments and numerical simulations, we show that viscoelastic instability in flow through a hexagonally ordered (staggered) medium strongly enhances dispersion transverse to the mean flow direction with increasing Weissenberg number (Wi). In contrast, preferential flow paths can quench the elastic instability in disordered media, which has two important consequences for transport: First, the lack of chaotic velocity fluctuatio…
A numerical model was developed for flows involving an interface between a homogenous fluid and a porous medium. The numerical model is based on the finite volume method with body-fitted and multi-block grids. The Darcy-Forchheimer extended model is used to govern the flow in the porous medium region. At its interface, a shear stress jump was imposed, together with a continuity of normal stress. Furthermore, the effect of the jump condition on the diffusive flux is considered, additional to that on the convective part which has been usually considered. Numerical results of three flow configura…
Shear stress is an important physical factor that regulates proliferation, migration and morphogenesis. In particular, the homeostasis of blood vessels is dependent on shear stress. To mimic this process ex vivo, efforts have been made to seed scaffolds with vascular and other cell types in the presence of growth factors and under pulsatile flow conditions. However, the resulting bioreactors lack information on shear stress and flow distributions within the scaffold. Consequently, it is difficult to interpret the effects of shear stress on cell function. Such knowledge would enable researchers…
In the above paper the authors treat the natural convection boundary layer flow in a Darcy-Brinkman-Forchheimer porous medium. In the energy equation the radiation effect has been taken into account. A two-parameter perturbation method is used for the solution of the equations. The first order results are presented in tables and figures. This is an interesting work but there are some weak points which are presented below:
In this paper, we address the issue of threshold yield pressure of yield-stress materials in rigid networks of interconnected conduits and porous structures subject to a pressure gradient. We compare the results as obtained dynamically from solving the pressure field to those obtained statically from tracing the path of the minimum sum of threshold yield pressures of the individual conduits by using the threshold path algorithms. We refute criticisms directed recently to our previous findings that the pressure field solution generally produces a higher threshold yield pressure than the one obt…
Porous materials are used in many fields, including energy industry, agriculture, medical industry, etc. The generation of digital porous media facilitates the fabrication of real porous media and the analysis of their properties. The past random digital porous media generation methods are unable to generate a porous medium with a specific permeability. A new method is proposed in the present study, which can generate the random packed isotropic porous media with specific porosity and permeability. Firstly, the process of generating the random packed isotropic porous media is detailed. Secondl…
We generalize a theory of Biot for a porous solid based on nonlinear elasticity theory to incorporate temperature effects. Acceleration waves are studied in detail in the fully nonlinear theory. The wavespeeds are found explicitly and the amplitudes are then determined. The possibility of shock formation is discussed.
Immiscible fluid-fluid displacement in porous media is of great importance in many engineering applications, such as enhanced oil recovery, agricultural irrigation, and geologic CO2 storage. Fingering phenomena, induced by the interface instability, are commonly encountered during displacement processes and somehow detrimental since such hydrodynamic instabilities can significantly reduce displacement efficiency. In this study, we report a possible adjustment in pore geometry which aims to suppress the capillary fingering in porous media with hierarchical structures. Through pore-scale simulat…
It is well-known that wettability exerts fundamental control over multiphase flow in porous media, which has been extensively studied in uniform-wet porous media. In contrast, multiphase flow in porous media with heterogeneous wettability (i.e., mixed-wet) is less well-understood, despite its common occurrence. Here, we study the displacement of silicone oil by water in a mostly oil-wet porous media patterned with discrete water-wet clusters that have precisely controlled wettability. Surprisingly, the macroscopic displacement pattern varies dramatically depending on the details of wettability…
In this paper we show the global well-posedness of solutions to a three-dimensional magnetohydrodynamical (MHD) model in porous media. Compared to the classical MHD equations, our system involves a nonlinear damping term in the momentum equations due to the "Brinkman-Forcheimer-extended-Darcy" law of flow in porous media.
Comment on "Scalings of Rayleigh-Taylor Instability at Large Viscosity Contrasts in Porous Media" (N. Sabet, H. Hassanzadeh, A. De Wit, and J. Abedi (2021) Phys. Rev. Lett. 126:094501).
We present a numerical study on the dynamics of imbibition fronts in porous media using a pipe network model. This model quantitatively reproduces the anomalous scaling behavior found in imbibition experiments [Phys. Rev. E {\bf 52}, 5166 (1995)]. Using simple scaling arguments, we derive a new identity among the scaling exponents in agreement with the experimental results.
The injection and in-situ generation of foam in porous media successfully control gas mobility and improve the fluids' sweep efficiency inside porous media. Mathematical models describing this problem use two phases, foamed gas and fluid, and usually have a term for foam generation and destruction. Moreover, the non-Newtonian foam behavior is frequently modeled using the Hirasaki and Lawson's formula for foamed gas viscosity. In this paper, we detail how the traveling wave analysis can be used to estimate the propagation profiles and velocity for a range of non-Newtonian foam models in porous …
In this letter, we show that pore-scale diffusiophoresis of colloidal particles along local salt gradients manifests in the macroscopic dispersion of particles in a porous medium. Despite is transient character, this microscopic phenomenon controls large-scale particle transport by altering their partitioning between transmitting and dead-end pores. It determines the distribution of residence and arrival times in the medium. Depending on the diffusiophoretic mobility, particles can be mobilized from or trapped in dead-end pores, which provides a means for the controlled manipulation of particl…
Topology optimization offers optimal material layouts, enabling automation in the design of devices. Given the recent advances in computer technology and additive manufacturing, topology optimization is increasingly being used to design complex porous structures, for example, microfluidic devices. For the flow of fluids in such miniature-sized porous structures, viscous shearing stress will be significant. But the Darcy model -- the most popular mathematical model describing the flow of a single-phase incompressible fluid in rigid porous media -- neglects the internal friction arising from vis…
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 lattice Boltzmann method has been successfully applied for the simulation of flow through porous media in the creeping regime. Its technical properties, namely discretization, straightforward implementation and parallelization, are responsible for its popularity. However, flow through porous media is not restricted to near zero Reynolds numbers since inertial effects play a role in numerous natural and industrial processes. In this paper we investigate the capability of the lattice Boltzmann method to correctly describe flow in porous media at moderate Reynolds numbers. The selection of th…
The flow of a gas through porous medium is considered in the case of pressure dependent permeability. Approximate self-similar solutions of the boundary-value problems are found.
We study the displacement of three immiscible Stokes fluids with constant viscosities in a porous medium. The middle-layer fluid is contained in a bounded region. We give an analysis of the linear stability of this process. This stability problem has no solution (in general).
We compute the fluid flow time-correlation functions of incompressible, immiscible two-phase flow in porous media using a 2D network model. Given a properly chosen representative elementary volume, the flow rate distributions are Gaussian and the integrals of time correlation functions of the flows are found to converge to a finite value. The integrated cross-correlations become symmetric, obeying Onsager's reciprocal relations. These findings support the proposal of a non-equilibrium thermodynamic description for two-phase flow in porous media.
The study of flow of non-Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield-stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality …
Convection heat transfer in porous media is a universal phenomenon in nature, and it is also frequently encountered in scientific and engineering fields. An in-depth understanding of the fundamental mechanism of convection heat transfer in porous media requires efficient and powerful numerical tools. In this paper, a cascaded lattice Boltzmann (CLB) method for convection heat transfer in porous media at the representative elementary volume (REV) scale is presented. In the CLB method, the flow field is solved by an isothermal CLB model with the D2Q9 lattice based on the generalized non-Darcy mo…
The coefficients of dispersion, D_{ij}, and the dispersivity, a_{ijkl}, appear in the expression for the flux of a solute in saturated flow through porous media. We present a detailed analysis of these tensors in an axially symmetric porous medium and show that in such a medium, the dispersivity is governed by 6 independent moduli. We present also the constraints that have to be satisfied by these moduli. We also show that at least two independent experiments are required in order to obtain the values of these coefficients for any three-dimensional porous medium domain.
Steady laminar flows through porous media spontaneously generate Lagrangian chaos at pore scale, with qualitative implications for a range of transport, reactive and biological processes. The characterization and understanding of mixing dynamics in these opaque environments is an outstanding challenge. We address this issue by developing a novel technique based upon high-resolution imaging of the scalar signature produced by push-pull flows through porous media samples. Owing to the rapid decorrelation of particle trajectories in chaotic flows, the scalar image measured outside the porous mate…
We study reactive transport in a stressed porous media, where dissolution of the solid matrix causes two simultaneous, competing effects: pore enlargement (chemical deformation), and pore compaction due to mechanical weakening. A novel, mechanistic pore-scale model simulates flooding of a sample under fixed confining stress, showing that increasing stress inhibits permeability enhancement, increasing the injected volume required to reach a certain permeability, in agreement with recent experiments. We explain this behavior by stress concentration downstream, in the less dissolved (hence stiffe…
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…
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…
In this paper, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is developed for simulating incompressible axisymmetric thermal flows in porous media at the representative elementary volume (REV) scale. In the model, a D2Q9 MRT-LB equation is proposed to solve the flow field in addition to the D2Q5 LB equation for the temperature field. The source terms of the model are simple and contain no velocity and temperature gradient terms. The generalized axisymmetric Navier-Stokes equations for axisymmetric flows in porous media are correctly recovered from the MRT-LB model through the C…
In this work we show the application of Sailfish to the study of fluid dynamics in porous media. Sailfish is an open-source software based on the lattice-Boltzmann method. This application of computational fluid dynamics is of particular interest to the oil and gas industry and the subject could be a starting point for an undergraduate or graduate student in physics or engineering. We built artificial samples of porous media with different porosities and used Sailfish to simulate the fluid flow through in order to calculate permeability and tortuosity. We also present a simple way to obtain th…
We analyze spreading of a density front in the Küntz-Lavallée model of porous media. In contrast to previous studies, where unusual properties of the front were attributed to anomalous diffusion, we find that the front evolution is controlled by normal diffusion and hydrodynamic flow, the latter being responsible for apparent enhancement of the front propagation speed. Our finding suggests that results of several recent experiments on porous media, where anomalous diffusion was reported based on the density front propagation analysis, should be reconsidered to verify the role of a fluid flow.
Multiparticle collision dynamics (MPCD) is a relatively new algorithm of fluid flow simulations that has been applied mostly to flows around simple objects. One might ask how it behaves in more complex flows. Therefore, we extend MPCD to simulate transport in porous media. For this, a particle-level drag force is introduced into the original algorithm. The force hinders the flow, which results in global resistance to flow and decrease of permeability. The extended algorithm is validated in the flow through a porous channel and compared with an analytical solution. Some basic properties of the …
We demonstrate through numerical simulations and a mean field calculation that immiscible two-phase flow in a porous medium behaves effectively as a Bingham viscoplastic fluid. This leads to a generalized Darcy equation where the volumetric flow rate depends quadratically on an excess pressure difference in the range of flow rates where the capillary forces compete with the viscous forces. At higher rates, the flow is Newtonian.
Immiscible fluids flowing at high capillary numbers in porous media may be characterized by an effective viscosity. We demonstrate that the effective viscosity is well described by the Lichtenecker-Rother equation. The exponent $α$ in this equation takes either the value 1 or 0.6 in two- and 0.5 in three-dimensional systems depending on the pore geometry. Our arguments are based on analytical and numerical methods.
Upscaling the effect of heterogeneities in porous media is crucial for macroscopic flow predictions, with widespread applications in energy and environmental settings. In this study, we derive expressions for the upscaled flow properties of a porous medium with a vertical heterogeneity, using a combination of asymptotic analysis and numerical simulations. Then, we use these upscaled expressions to describe the dynamic flooding of an aquifer, where the classic Buckley-Leverett formulation is modified to account for heterogeneities. In particular, we show that heterogeneities can modify flooding…
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…
The problem of steady mixed convection boundary-layer flow on a cooled vertical permeable circular cylinder embedded in a fluid-saturated porous medium is studied. Here, we evaluate the flow and heat transfer characteristics numerically for various values of the governing parameters and demonstrate the existence of dual solutions beyond a critical point.
This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a known velocity covariance function. In the hierarchical model, we represent (random) concentration in terms of its cross-sectional average and a variation function. We derive a one-dimensional stochastic advection-dispersion-type equation for the average concentration and a stochastic Poisson equation for the variation function, as well as expressions for the e…
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.
In this paper, a double multiple-relaxation-time lattice Boltzmann model is developed for simulating transient solid-liquid phase change problems in porous media at the representative elementary volume scale. The model uses two different multiple-relaxation-time lattice Boltzmann equations, one for the flow field and the other for the temperature field with nonlinear latent heat source term. The model is based on the generalized non-Darcy formulation, and the solid-liquid phase change interface is traced through the liquid fraction which is determined by the enthalpy method. The model is valid…
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 problem of the flow trough a porous media is formulated in terms of a pressure equation, based on arguments of volume conservation which state the mechanical equilibrium between the solid and the fluid phases. In the resulting governing equations, the conservation of mass is replaced by a transport-diffusion equation for the pressure field. When the deformation of the solid matrix is negligible, the pressure equation can be approximated by a non-linear diffusion equation. The behavior of the system of equations is tested under an oscillatory pressure gradient.
Permeability estimation of porous media from direct solving Navier--Stokes equation has a wide spectrum of applications in petroleum industry. In this paper, we utilize a pressure-correction projection algorithm in conjunction with the interior penalty discontinuous Galerkin scheme for space discretization to build an incompressible Navier--Stokes simulator and to use this simulator to calculate permeability of real rock sample. The proposed method is accurate, numerically robust, and exhibits the potential for tackling realistic problems.
We develop and validate a new model to study simultaneous erosion and deposition in three-dimensional porous media. We study the changes of the porous structure induced by the deposition and erosion of matter on the solid surface and find that when both processes are active, channelization in the porous structure always occurs. The channels can be stable or only temporary depending mainly on the driving mechanism. Whereas a fluid driven by a constant pressure drop in general does not form steady channels, imposing a constant flux always produces stable channels within the porous structure. Fur…
