Understanding transport and retention mechanisms in porous media is essential in environmental and industrial processes such as subsurface contamination, water filtration and polymer flooding in oil reservoirs. In this article, new averaged equations for colloid transport and retention in porous media are obtained based on the master equation. In addition, new boundary conditions are discussed and

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

Abstract The electrical conductivity of porous dielectric materials saturated with water is usually determined by the bulk water conduction. However, the unsaturated state can be affected by a water film covering the unsaturated grain surface. Thus far, a few studies have been conducted on the study of the electrical conductivity with respect to water film covering the grain surface. In this study

To better understand the CO2 sequestration and enhanced shale gas recovery, it is of great significance to study the adsorption characteristics of CO2 and CH4 in different types of shale. In this study, the mineral composition, pore structure and CH4 and CO2 adsorption isothermals of marine and continental shale samples were determined, an adsorption model was proposed to describe the adsorption behaviors

Countercurrent spontaneous imbibition (SI) is an important flow mechanism for oil recovery in fractured reservoirs during waterflooding. SI plays a key role in the mobilization of oil in the matrix because it facilitates water infiltration by capillarity even when the matrix permeability is low, which limits fluid transport by advection. However, the modeling of SI in fractured media under dynamic

Three-phase flow in porous media is encountered in many applications including subsurface carbon dioxide storage, enhanced oil recovery, groundwater remediation and the design of microfluidic devices. However, the pore-scale physics that controls three-phase flow under capillary dominated conditions is still not fully understood. Recent advances in three-dimensional pore-scale imaging have provided

Fluid mechanics simulation of steady state flow in complex geometries has many applications, from the micro-scale (cell membranes, filters, rocks) to macro-scale (groundwater, hydrocarbon reservoirs, and geothermal) and beyond. Direct simulation of steady state flow in such porous media requires significant computational resources to solve within reasonable timeframes. This study outlines an integrated

A more thorough understanding of the properties of bulk material structures in solid–liquid separation processes is essential to understand better and optimize industrially established processes, such as cake filtration, whose process outcome is mainly dependent on the properties of the bulk material structure. Here, changes of bulk properties like porosity and permeability can originate from local

We present numerical simulations of post-Darcy flow in thin porous medium: one consisting of staggered arrangements of circular cylinders and one random distribution of cylinders bounded between walls. The simulations span a range of Reynolds numbers, 40 to 4000, where the pressure drop varies nonlinearly with the average velocity, covering nonlinear laminar flow to the fully turbulent regime. The

CO\(_\text {2}\) injection for enhanced oil recovery (CO\(_\text {2}\)-EOR) or for storage in depleted oil and gas reservoirs can be a means for disposing of anthropogenic CO\(_\text {2}\) emissions to mitigate climate change. Fluid flow and mixing of CO\(_\text {2}\) and hydrocarbons in such systems are governed by the underlying physics and thermodynamics. Gravity effects such as gravity override

Leveraging high-fidelity lattice Boltzmann simulations combined with analytical modeling, we establish a comprehensive micro-scale description of immiscible two-phase fluid displacement occurring during favorable and unfavorable displacement conditions in a heterogeneous porous medium under a wide range of wettability. The emergence of corner-flow events is found to promote a compact displacement pattern

The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use

The effects of periodicity assumptions on the macroscopic properties of packed porous beds are evaluated using a cascaded Lattice-Boltzmann method model. The porous bed is modelled as cubic and staggered packings of mono-radii circular obstructions where the bed porosity is varied by altering the circle radii. The results for the macroscopic properties are validated using previously published results

Porous media characterization is crucial to engineering projects where the pore shape has impact on performance gains. Membrane filters, sportswear fabrics, and tertiary oil recovery are a few examples. Kozeny–Carman (K–C) models are one of the most frequently used to understand, for instance, the relation between porosity, permeability, and other small-scale parameters. However, they have limitations

We investigate and classify possible analytical solutions for a simplified version of the foam bubble population model, by varying injection conditions and kinetic foam generation parameter. We prove that the behavior of the analytical solutions changes at the transition between two regions, similar to rarefaction-shock solutions for the Buckley-Leverett equation. In one region (region I), the solutions

This paper concerns a method and a test set-up to measure the permeability of plates of metal foams and sets of wire meshes used to control flows in fluid filters and other flow systems designed to yield constant velocity distributions over large cross sections of flows. The method is based on permeability considerations using the Ergun equation to describe the pressure losses of packages of mono-dispersed

Acoustic properties of dry or saturated porous media can be studied numerically by a combined use of lattice spring models and lattice Boltzmann models. The methodology is briefly described and it is systematically applied to a series of Fontainebleau sandstones whether they are dry or saturated with incompressible or compressible fluids. The velocities of compression and shear waves, as well as their

Compositional simulation is typically used to study subsurface displacement processes that involve complex physics. Such processes are highly nonlinear and they occur at the interplay of phase thermodynamics (phase stability and split) and rock/fluid interaction (relative permeability). To better characterize the convergence failures of compositional nonlinear solvers, we study the analytical and discrete

The establishment of the representative elementary volume (REV) in studies of porous media is crucial for linking microscopic structure and pore-scale fluid configurations to macroscopic flow processes. We present analysis of the REV of porosity, specific interfacial area, and topological measures (Betti numbers and the Euler characteristic) for an air–water–Bentheimer sandstone system imaged using

A screen composed of in-plane thin strips is embedded in a porous medium. The screen is either normal or parallel to the applied pressure gradient which forces a flow through the anisotropic porous medium. The principal axes of anisotropy are assumed to be aligned with that of the screen. The governing equation is fourth order and cannot be factored as in the isotropic case. The solutions are found

Gaseous flow through ultra-tight porous media, e.g. shale and some high-performance insulation materials, is often rarefied, invalidating an analysis by the continuum flow theory. Such rarefied flows can be accurately described by the kinetic theory of gases which utilizes the Boltzmann equation and its simplified kinetic models. While discrete velocity methods have been successful in directly solving

Nanoscale spontaneous imbibition is a common process in nanoporous soil and unconventional reservoirs. Due to the complexity of these natural nanoporous media, the relevant spontaneous imbibition dynamics are still unclear. Thus, this paper studies spontaneous imbibition dynamics of liquids into a nanoporous carbon scaffold (NCS, with controllable wettability and pore geometry). The effects of evaporation

Pore-scale finite-volume continuum models of electrokinetic processes are used to predict the Debye lengths, velocity, and potential profiles for two-dimensional arrays of circles, ellipses and squares with different orientations. The pore-scale continuum model solves the coupled Navier–Stokes, Poisson, and Nernst–Planck equations to characterize the electro-osmotic pressure and streaming potentials

Solutal convection in a horizontal layer filled with porous media with horizontal seepage of a mixture is investigated considering the solute immobilization and clogging. A flow through porous media is modelled within the standard Darcy–Boussinesq model, and the immobilization process is described by the mobile/immobile media (MIM) approach. To describe the clogging process, the present model takes

Capillary dominated flow or imbibition—whether spontaneous or forced—is an important physical phenomena in understanding the behavior of naturally fractured water-driven reservoirs (NFR’s). When the water flows through the fractures, it imbibes into the matrix and pushes the oil out of the pores due to the difference in the capillary pressure. In this paper, we focus on modeling and quantifying the

Fine-migration-induced permeability damage in geological reservoirs is a critical problem in several environmental and energy operations. This study presents a novel numerical model aimed at predicting the hydro-mechanical response of a saturated porous formation containing fines to injection-induced fluid flow. The proposed model contains two novel components: incorporation of spatiotemporal fluid

Inherent pore structure of rocks has a significant impact on the acid–rock interaction during the acidizing process. In this study, a new pore-scale reactive transport model applying Darcy–Brinkmann–Stokes method has been developed based on the open-source computational fluid dynamics platform, OpenFOAM, and validated with experimental results. By solving the mass balance equation and advection–diffusion

A correction to this paper has been published: https://doi.org/10.1007/s11242-021-01569-3

To improve the understanding of gas transport processes in tight rocks (e.g., shales), systematic flow tests with different gases were conducted on artificial micro- to nanoporous analogue materials. Due to the rigidity of these systems, fluid-dynamic effects could be studied at elevated pressures without interference of poro-elastic effects. Flow tests with narrow capillaries did not reveal any viscosity

The long-standing question on the adequate description of multiphase flow in porous media may be ultimately decided based on the ability to estimate model parameters with sufficient accuracy that make the models distinguishable. Since the most-common Darcy scale multiphase flow models all use a somewhat phenomenological relative permeability or resistance factor formulation, the key question is what

Abstract Most analyses of fluid flow in porous media are conducted under the assumption that the permeability is constant. In some “stress-sensitive” rock formations, however, the variation of permeability with pore fluid pressure is sufficiently large that it needs to be accounted for in the analysis. Accounting for the variation of permeability with pore pressure renders the pressure diffusion equation

While several studies have linked network and in-fracture scale properties to conservative transport behavior in subsurface fractured media, studies on reactive transport cases remain relatively underdeveloped. In this study, we explore the behavior of an irreversible kinetic reaction during the interaction of two solute plumes, one consisting of species A and the other species B. When the plumes converge

Pore bulk modulus in continuum apparent permeability models was generally treated as an independent parameter or deduced from the Betti-Maxwell reciprocal theorem neglecting the sorption effect, which is not appropriate for the unconventional reservoirs with strong gas sorption. In this work, pore bulk modulus was firstly derived from the Betti-Maxwell theorem with the consideration of the gas sorption

This study develops a new numerical model adopting a generic relation between the nonaqueous phase liquid (NAPL) mass and aqueous-phase NAPL concentration to simulate the relationship between NAPL contaminant mass discharge and contaminant mass reduction in the source zone, which plays a critical role to assist with site management decisions on contaminated zone remediation. The model can accommodate

In this paper, we introduce an estimation of the random Klinkenberg slip coefficient in the apparent permeability model using a chaos decomposition technique. The apparent permeability expression (Klinkenberg model) is used to describe natural gas transport in low-permeability media. In this process, the Klinkenberg factor is considered as a random parameter that depends on two random variables. The

Although gas drainage technology has greatly developed, gas concentration and utilization rates are still very low, resulting in substantial quantities of low concentration gas emissions in coal mine. To study the roles of suction pressure on gas drainage, a mathematical model is developed in this study for coupled gas migration and coal deformation based on a dual-porosity medium. The simulation results

The object of this study is to investigate the question of convective movement of a reacting solute in a viscous incompressible occupying a plane layer in a saturated bidisperse porous material. Among the characteristics of a bidisperse porous medium are pores, called macropores, but porosity in the solid skeleton, known as microporosity, arises where there are cracks or fissures in that skeleton.

The deformation of coal during the injection of sorptive gases can be classified into two types: deformation due to the pore pressure and the swelling deformation of the coal matrix induced by adsorption. These types of deformation have not been investigated separately in the previous researches. The main reason is that measuring the radial strain of the coal core directly and accurately is extremely

Natural convection heat transfer in a rectangular cavity filled with a saturated porous medium with variable permeability is investigated analytically and numerically. The side walls of the cavity are heated and cooled by constant heat fluxes, while the horizontal walls are adiabatic. The governing parameters for the problem are thermal Rayleigh number, R, the aspect ratio of the cavity, A, and the

X-ray micro-computed tomography (\(\mu\)CT) can produce realistic 3D-images of the pore structure of a material. Extracting its geometry enables the computation of effective properties of the material—such as the permeability (k) and the hydrodynamic dispersion coefficient (\(D_h\))—, through the solutions of the Stokes equation (SE) and Advection-Diffusion equation (ADE), respectively. In this study

Enzymatically induced calcite precipitation (EICP) is an engineering technology that allows for targeted reduction of porosity in a porous medium by precipitation of calcium carbonates. This might be employed for reducing permeability in order to seal flow paths or for soil stabilization. This study investigates the growth of calcium-carbonate crystals in a micro-fluidic EICP setup and relies on experimental

Hydraulic fracturing causes water to invade reservoir rock. This invaded water is called a water block as it lowers the effective permeability of the rock to oil. Field and laboratory results show that the water block is temporary. We hypothesize that (a) the clearing is caused by capillary-dominated advection of water, and (b) the clearing takes place when the water saturation drops at the fracture

We model hydrothermal convection using a partial differential equation formed by Darcy velocity and temperature—the velocity formulation. Using the Elder problem as a benchmark, we found that the velocity formulation is a valid model of hydrothermal convection. By performing simulations with Rayleigh numbers in the non-oscillatory regime, we show that multiple quasi-steady-state solutions can be one

Liquid drainage within foam is generally described by the foam drainage equation which admits travelling wave solutions. Meanwhile, Richards’ equation has been used to describe liquid flow in unsaturated soil. Travelling wave solutions for Richards equation are also available using soil material property functions which have been developed by Van Genuchten. In order to compare and contrast these solutions

Multiphase fluid flow in porous media is important to a wide variety of processes of fundamental scientific and practical importance. Developing a model for the pore space of porous media represents the first step for simulating such flows. With rapid increase in the computation power and advances in instrumentation and imaging processes, it has become feasible to carry out simulation of multiphase

Abstract The interaction between the fluid flow and the deformable porous media is crucial in the applications of adsorption/absorption. The immersed boundary coupled lattice Boltzmann method is used in this study. The spring constant k of porous skeleton is introduced to consider the deformation effects. Subsequently, the evolutions of deformation of porous skeleton and hydrodynamic characteristics

Conventional concepts for transport in porous media assume that the heterogeneous distribution of hydraulic conductivities is the source for the contaminant temporal and spatial heavy tail. This tailing, known as anomalous or non-Fickian transport, can be captured by the β parameter in the continuous-time random walk framework. This study shows that with the increase in spatial correlation length between

Polymer solutions are often described as viscoelastic fluids, whose rheological behavior dynamically evolves according to the flow shear rate due to successive contractions and relaxations of inner deformable components. Contrary to shear-thickening and shear-thinning fluids, viscoelastic fluids can undergo an increase in the normal stress-differences even in simple geometries, leading to counterintuitive

A thermodynamically consistent phase field model that accounts for initial stress state is proposed in this paper to simulate the gas migration process in saturated bentonite. The energy contribution due to the fracturing process is included in Coussy’s thermodynamic framework for unsaturated porous media. The possible effect of the interfaces between different phases on the driving force functional

This review paper proposes a critical overview of experimental techniques and innovative experimental methods to observe and deeply understand the migration of water inside wood and biosourced materials. The state of the art of the knowledge of water transfer phenomena are first presented, namely liquid and bound water migration, together with shrinkage/swelling. Then, the papers presenting the 3D

In the original publication of the article, the Electronic Supplementary Material was missed.

Abstract Many non-Newtonian fluids, including polymers, exhibit both shear-thinning and viscoelastic rheological properties. A lattice Boltzmann (LB) model is developed for simulation of the flow of thinning–elastic fluids through porous media. This model applies the Oldroyd-B constitutive equation and the Carreau model, respectively, to account for the viscoelastic and shear-thinning behaviors of

The multiphase flow transport properties find ubiquitous applications in partially saturated granular media, particularly in the vadose zone due to alternate drying and wetting cycles. The spatial heterogeneity in the degree of saturation at the pore scale has a significant impact on the transport properties of the porous materials. In the present work, three-dimensional (3D) computed tomography (CT)

The boundary layer thickness and influence in the single-phase flow in the tight reservoirs have been widely measured. The influence of boundary layer on the oil migration into originally water-saturated tight reservoirs has been theoretically deduced but has not been experimentally validated. In this work, the existence of boundary layer in tight reservoir oil migration is investigated by comparing

A spectrum of environmental, industrial, and biomedical processes depends on solute plume spreading in laminar flows within porous media. The literature includes a number of approaches to model solute movement in this context, but fewer techniques are reported to measure it experimentally. To address this gap, this study describes novel experimental methods that permit measurement of solute plume spreading

The stability of the waterfront in a heterogeneous porous medium and in the absence of gravity effects is controlled by capillary and viscous forces. Under oil-wet conditions, waterflood is a drainage process and the displacement front advances in zones with larger pores where capillary forces are lower, and the rate of displacement is higher compared to zones with smaller pores. Hence, in a waterflood

Darcy’s law (which states that a fluid flow rate is directly proportional to the pressure gradient) is shown to be accurate in a rather narrow range of flow velocities. Numerous studies show that at low pressure gradients gas slippage effect occurs, which gives overestimated flow rates compared to Darcy’s law. At higher flow rates, Darcy’s law is usually replaced by the Forchheimer equation which accounts

Uncertainty quantification and sensitivity analysis are crucial tools in the development and evaluation of mathematical models. In enhanced oil recovery, the co-injection of foam in porous media has been investigated through laboratory experiments and mathematical models as a promising technique for improving sweep efficiency. In this work, we study two mathematical models of foam flow in porous media

Wettability alteration has been recognized as the dominant mechanism of ion-tuned waterflooding, where the ionic composition of injecting brine is modified to improve oil recovery. Yet mechanisms of ion-tuned wettability have not been fully understood, and there are ongoing debates over the effectiveness and relative contribution of each mechanism. In this paper, ion-tuned wettability in variable oil-brine-rock