We study transport of passive tracers by plane laminar flows with stagnation points. This setup serves as a simple model of transport in porous media. Close to stagnation points, the flow velocity is much lower than on the average. Many experimental data disclose that transport through porous media is slower than predictions of the standard advection-diffusion model. Commonly, in descriptions of flows

A theoretical analysis of a viscous flow in a corrugated curved channel enclosing a porous medium is carried out. The alignment of the corrugations of the outer and the inner curved walls is taken arbitrarily, and the corrugations are considered to be sinusoidal in nature with periodicity. The flow problem is described by Darcy–Brinkman model, derived in the curvilinear coordinates. The effects of

Chemical flooding has been implemented intensively for some years to enhance sweep efficiency in porous media. Low salinity water flooding (LSWF) is one such method that has become increasingly attractive. Historically, analytical solutions were developed for the flow equations for water flooding conditions, particularly for non-communicating strata. We extend these to chemical flooding, more generally

This paper presents the development of a model enabling the analysis of rarefied gas flow through highly heterogeneous porous media. To capture the characteristics associated with the global- and the local-scale topology of the permeable phase in a typical porous medium, the heterogeneous multi-scale method, which is a flexible framework for constructing two-scale models, was employed. The rapid spatial

We present a solute transport model, developed by employing a dynamic pore network modeling approach, to investigate dispersive solute transport behaviors in consolidated porous media. The model is capable of upscaling solute transport processes from pore to core, under two-phase fluid configurations. The governing equations of fluid flow, fluid displacement, and solute transport are solved at the

New and existing results of capillary rise experiments on five sandstones and a limestone differing in pore radius distribution were analyzed. Fitting of Lucas–Washburn equation (square of capillary rise height is linearly correlated with time and effective pore radius) showed that the effective pore radius notably smaller than the realistic pore radii in the rock needs to be used to reproduce the

Modeling coupled systems of free flow adjacent to a porous medium by means of fully resolved Navier–Stokes equations is limited by the immense computational cost and is thus only feasible for relatively small domains. Coupled, hybrid-dimensional models can be much more efficient by simplifying the porous domain, e.g., in terms of a pore-network model. In this work, we present a coupled pore-network/free-flow

During hydraulic fracturing, thousands of barrels of fluid are injected into the rock surrounding the created fractures. Observations show that later during flowback, only a small fraction of the injected fluid volume is produced back. In tight naturally fractured formations, this can be explained by the leading role of preexisting rock discontinuities in the transport of fluids in such rocks. In this

Anomalous moisture transport in cement-based materials is often reported in the literature, but the conventional single-porosity moisture transport models generally fail to provide accurate simulation results. Previous studies suggested that the anomalous moisture transport could be caused by different moisture transport velocity in large and small pores. Based on this concept, the present study proposes

Direct numerical simulations of flow on micro-computed tomography (micro-CT) images are extensively used in many disciplines of science and engineering. Recently, we have developed a pore-scale finite volume solver (PFVS) to directly solve for flow on micro-CT images and predict permeability of digital cores. The solver assigns a local conductivity to each voxel based on geometrical and topological

A new semi-analytical solution to the advection–dispersion–reaction equation for modelling solute transport in layered porous media is derived using the Laplace transform. Our solution approach involves introducing unknown functions representing the dispersive flux at the interfaces between adjacent layers, allowing the multilayer problem to be solved separately on each layer in the Laplace domain

A comprehensive experimental protocol is presented for the characterization of physico-chemical and morphological properties of absorbent hygiene products (AHPs), composite materials, mainly made of super absorbent polymer (SAP) granules blended with cellulose fibres (fluff). The protocol is based on a combination of experimental methods for the characterization of the material properties varying SAP/fluff

An analysis of spatial resolution is incorporated into an efficient model calibration approach with multi-scale data integration to examine the reliability of the estimated solution. The resolution is a measure of the degree of averaging of the local-scale (grid block) permeabilities during parameter estimation via inverse modeling. For a given set of data, it indicates the regions where our estimate

There are several key factors proposed in the literature responsible for oil mobilization and recovery by nanofluids as enhanced oil recovery agents. These factors include interfacial tension (IFT) reduction, wettability alteration, inhibition of fines migration, and flow profile control. However, there is not a general consensus on the relative contribution and importance of each factor. Moreover

Apparent liquid permeability (ALP) in ultra-confined permeable media is primarily governed by the pore confinement and fluid–rock interactions. A new ALP model is required to predict the interactive effect of the above two on the flow in mixed-wet, heterogeneous nanoporous media. This study derives an ALP model and integrates the compiled results from molecular dynamics (MD) simulations, scanning electron

The deposition characteristics of lead ions (Pb2+) in the presence of silicon powders (i.e., suspended particles, SPs) were investigated in water seepage in a long one-dimensional sand column experiment. The injected SPs possess a very wide particle-size distribution (PSD). The concentrations of deposited Pb2+ and SPs and the migration distance along the water flow direction were measured by sampling

Fluid permeability of solid foams is a crucial parameter to control transport phenomena in numerous engineering applications, such as heat exchangers or filters for example. Open-cell foams with monodisperse pore diameter ranging from 200 to 1000 µm and solid volume fraction ranging from 0.1 to 0.38 are produced and Darcy permeability is measured. The permeability divided by the square of the pore

In situ subsurface remediation has been widely used as an efficient means of cleaning up non-aqueous phase liquid (NAPL) from contaminated soils and aquifer. The use of tracer, surfactant and foam is often considered to keep track of the propagation of injected fluids in the medium, dissolve and mobilize contaminants trapped by capillary forces, and overcome the level of heterogeneity and improve displacement

The paper presents results of the modelling of heat transfer at film boiling of a liquid in a porous medium on a vertical heated wall bordering with the porous medium. Such processes are observed at cooling of high-temperature surfaces of heat pipes, microstructural radiators etc. Heating conditions at the wall were the constant wall temperature or heat flux. The outer boundary of the vapor film was

This paper presents an experimental and numerical investigation of the electrokinetic propagation of acid or base fronts through clayey soil. The experimental study included measuring the electric current, the mass of water extracted, and the advance of the acid and base fronts in synthetic sediment composed of 25% kaolinite and 75% silt. The results show that the flux rate remains constant over time

In this paper, we study the flow through a corrugated channel filled with a fluid-saturated sparsely packed porous medium. The porous medium flow is described by the Darcy–Lapwood–Brinkman system taking into account the Brinkman extension of the Darcy law and the flow inertia. We assume the periodicity of the roughness in the longitudinal direction and that the flow is governed by the prescribed pressure

The convective double-diffusive instability in a two-layer system consisting of a binary fluid layer overlaying a fluid-saturated porous layer is investigated numerically. The system moves periodically in a vertical direction under the conditions of gravity field. The layers are heated from below and oscillate with high frequency and small amplitude. The instability threshold for the convection onset

Cilia are hair-like structures that move in unison with the purpose of propelling fluid. They are found, for example, in the human bronchiole respiratory system and molluscs. Here, we validate a novel model of fluid flow due to the movement of cilia in a fixed computational domain. We consider two domains, a porous medium and a free-fluid domain and numerically solve the Stokes–Brinkman system of equations

The linear stability of buoyant parallel flow in a vertical porous layer with an annular cross section is investigated. The vertical cylindrical boundaries are kept at different uniform temperatures, and they are assumed to be impermeable. The emergence of linear instability by convection cells is excluded on the basis of a numerical solution of the linearised governing equations. This result extends

The onset of double-diffusive convection in an electrically conducting fluid-saturated porous layer is studied. The convective flow in the porous medium is induced by horizontal temperature and concentration gradients with net horizontal mass throughflow. The effect of magnetic field on the instability of convection is taken into consideration. The stability of the steady-state solution is investigated

A multi-dimensional, compressible fluid flow solver, valid in both channel and porous media, is derived by volume-averaging the Navier–Stokes equations. By selecting an appropriate average density/velocity pair, a continuous, stable solution is obtained for both pressure and velocity. The proposed model is validated by studying the pressure drop of two commonly used experimental setups to measure in-plane

The employment of 2D models to investigate the properties of 3D flows in porous media is ubiquitous in the literature. The limitations of such approaches are often overlooked. Here, we assess to which extent 2D flows in porous media are suitable representations of 3D flows. To this purpose, we compare representative elementary volume (REV) scales obtained by 2D and 3D numerical simulations of flow

Flow modelling challenges in fractured reservoirs have led to the development of many simulation methods. It is often unclear which method should be employed. High-resolution discrete fracture and matrix (DFM) studies on small-scale representative models allow us to identify dominant physical processes influencing flow. We propose a workflow that utilizes DFM studies to characterize subsurface flow

CO2 injection into oil reservoirs is widely accepted as an effective enhanced oil recovery and CO2 storage technique. While oil recovery and CO2 storage potential of this technique have been studied extensively at the core-scale, complex multiphase flow and fluid–fluid interactions at the pore scale during near-miscible CO2 injection have not, and this area needs more study. To address this, a unique

We investigate nonlinear stability in a model for thermal convection in a saturated porous material using Brinkman theory, taking into account viscous dissipation effects. There are (at least) two models for viscous dissipation available, and we include a derivation of one of these by assuming that the flow in the porous medium may be described by a theory for a mixture of an elastic solid and a linearly

This study aims at investigating non-Fickian temporal scaling of fast mixing processes using fractional advection dispersion equation (FADE) model in Indiana carbonate, multi-lognormal hydraulic conductivity field, self-affine fractures and cemented porous media, in which the fundamental solution of the FADE model is a standard symmetric Lévy stable distribution. The temporal scaling of the scalar

Exchange processes between a turbulent free flow and a porous media flow are sensitive to the flow dynamics in both flow regimes, as well as to the interface that separates them. Resolving these complex exchange processes across irregular interfaces is key in understanding many natural and engineered systems. With soil–water evaporation as the natural application of interest, the coupled behavior and

Electrokinetic and electroosmotic couplings can play important roles in water and ions transport in charged porous media. Electroosmosis is the phenomena explaining the water movement in a porous medium subjected to an electrical field. In this work, a new model is obtained through a new up-scaling procedure, considering the porous medium as a bundle of tortuous capillaries of fractal nature. From

The Bruggeman model is routinely employed to determine transport parameters in macroscale electrochemical models. Yet, it relies on both a simplified representation of the pore-scale structure and specific hypotheses on the transport dynamics at the pore scale. Furthermore, its inherent scalar nature prevents it from capturing the impact that pore-structure anisotropy has on transport. As a result

In the last decade, the interest towards fluids characterized by a complex rheology has increased in the scientific community. Physicochemical, rheological and fluid mechanical approaches are adopted to characterize the peculiarities of non-Newtonian fluids. These fluids show remarkable properties that can be exploited to improve remediation techniques or optimize industrial operations. While the existence

Foam has shown promising characteristics for soil remediation, especially as a blocking agent. In very permeable porous media, high groundwater velocity reduces the efficiency of in situ remediation by decreasing the contact time with contaminants. To use foam to reduce water velocity, this paper investigates its properties in very permeable porous media (> 4.10−10 m2). Alpha olefin sulfonate foam

The application of 3D technology for fabrication of artificial porous media samples improves porous media flow studies. The geometrical characteristics of a porous media pore channel: the channel shape, size, porosity, specific surface, expansion ratio, contraction ratio, and the tortuous pathway of the channel can be controlled through advanced additive manufacturing techniques (3D printing), computed

Reservoir simulation using high-fidelity fluid models is typically employed to study subsurface displacement processes that involve complex physics. Such processes are highly nonlinear and occur at the interplay of phase thermodynamics (phase stability and split) and rock/fluid interaction (relative-permeability). Due to its nonlinearity, relative-permeability is an important constitutive of the conservation

A general boundary-layer coordinate transformation was proposed in order to find the necessary conditions under which similarity solutions exist for free, forced and mixed convective Darcian flows subject to local thermal non-equilibrium. The aim of this study is to present the effects of local thermal non-equilibrium on the boundary-layer heat transfer in porous media, identifying each of the parameters

Foam reduces the gas mobility in porous media both by increasing the effective viscosity of the gas phase and by trapping a large portion of the gas in place. This reduction is directly related to the number density of lamellae in the gas phase. Therefore, understanding the pore-level events associated with lamella generation and destruction processes and investigating the trapped foam behavior are

The onset of Darcy–Bénard convection in an unlimited horizontal porous layer is studied theoretically. The thermomechanical boundary conditions of Dirichlet or Neumann type at the lower and upper plane are switched from one type to another, at certain values of the horizontal x-coordinate. A semi-infinite portion of the lower boundary is defined as thermally conducting and impermeable, while the remaining

Two-phase transport with simultaneous component adsorption and mechanical entrapment occurs in numerous suspension and nano-colloidal flows in porous media, including polymer flooding in oilfields. To the contrary of one-dimensional (1D) self-similar solution for polymer flooding that ignores the mechanical entrapment, accounting for this phenomenon breaks self-similarity. However, this non-self-similar

The diffusion kinetics may experience either standard or anomalous behavior. In a porous medium, a transport process may distinguish between the standard and anomalous diffusion. Herein, we perform an analysis of the diffusion concentration profiles in a hierarchically porous material using the standard and the time-fractional diffusion equations. It is shown that the mass transfer regime changes from

The present study deals with computational investigation of natural convection in a porous chamber having a copper finned heat sink and a thermally producing element of finite thickness and heat conductivity. The enclosure is cooled from the external vertical and upper horizontal walls, whilst the remaining borders are considered to be thermally insulated. Newtonian and heat-conducting liquid with

Effective and optimal hydrocarbon production from heterogeneous and anisotropic reservoirs is a developing challenge in the hydrocarbon industry. While experience leads us to intuitive decisions for the production of these heterogeneous and anisotropic reservoirs, there is a lack of information concerning how hydrocarbon and water production rate and cumulative production as well as water cut and water

In this study, we investigate the secondary sorption in an air-entrained Portland cement mortar that is purged with different gases—\(\hbox {CO}_{2}, \hbox {CH}_{4}\), or \(\hbox {N}_{2}\). By altering the gas phase present in the void space, we are able to evaluate how gas solubility influences the secondary sorption. The rate of water sorption in the presence of different gases in the entrained voids

One attractive aspect of CO2 sequestration in shale formations is the preferential adsorption of CO2 compared to methane, which may provide enhanced methane production as well as sequestration of carbon dioxide. In this work, a comprehensive theoretical model of CO2 migration at the pore scale is developed to study CO2 migration properties in organic-rich shale formations. The proposed model takes

Understanding the shear-flow-transport processes in rock fractures is one of major concerns for many geo-engineering practices, yet the effect of shear direction change on the flow and transport properties through rough-walled rock fractures has received little attention. In this study, a series of shear tests on artificial fractures with different surface roughness are conducted, in which the shear

The stability of natural convection in a vertical layer of heat-generating Darcy porous medium saturated with an Oldroyd-B fluid using a local thermal non-equilibrium (LTNE) model has been investigated numerically. The impermeable vertical walls of the porous layer are maintained at different uniform temperatures. As a consequence of LTNE model, two temperature equations representing the fluid and

In the original publication of the article, Table 2 was published incorrectly.

The dynamic responses of an anisotropic multilayered poroelastic half-space to a point load or a fluid source are studied based on Stroh formalism and Fourier transforms. Taking the boundary conditions and the continuity of the materials into consideration, the three-dimensional Green’s functions of generalized concentrated forces (force and fluid source) applied at the free surface, interface and

Capillary force and boundary layer effect are the main causes of non-Darcy flow in tight oil reservoir. This paper proposes a non-Darcy flow dynamics characterization method for low-speed water flooding in tight oil reservoirs. It applies constant-speed mercury injection and casting thin section experiments to quantitatively characterize the micro-pore throat structure parameters, and uses the visual

Multiphase flow in porous media is strongly influenced by the pore-scale arrangement of fluids. Reservoir-scale constitutive relationships capture these effects in a phenomenological way, relying only on fluid saturation to characterize the macroscopic behavior. Working toward a more rigorous framework, we make use of the fact that the momentary state of such a system is uniquely characterized by the

During waterflooding, spontaneous imbibition is a fundamental recovery mechanism in fractured reservoirs. A large number of numerical and experimental studies have been devoted to understand the interaction mechanism between the matrix and the fractures at the core scale under various boundary conditions. Little attention has been paid, however, to the effect of microfractures on pore-scale spontaneous

A macroscopic model that accounts for the effect of momentum dispersion on flows in porous media is proposed. The model is based on the pore scale prevalence hypothesis (PSPH). The effects of macroscopic velocity gradient on momentum transport are approximated using a Laplacian term. A local Reynolds number Red, which characterizes the strength of momentum dispersion, is introduced to calculate the

Bio-based materials, such as hemp concrete, have been widely recommended to reduce carbon emissions and energy consumption of buildings as a means of addressing current environmental problems. These materials may possess very interesting hygrothermal and acoustic performance. Hemp concrete is composed of hemp particles embedded in a binder that forms a very heterogeneous and porous component. The aim

Carbonate reservoirs are heterogeneous from pore scale to field scale. Waterflood in carbonate reservoirs often leaves behind a substantial amount of oil due to pore-scale and large-scale bypassing. Polymer flooding can improve sweep efficiency and oil production. Most EOR polymers cannot be transported through low-permeability (< 30 mD) rocks. Hydrophobically modified associative polymers (APs) associate

We investigate viscous fluid flows and concurrent fluid-driven deformations in porous media. The hydro-mechanically (H-M) coupled pore-network model (PNM) is developed, which combines the two-dimensional square-lattice PNM and block-spring model. The single-/two-phase flows into saturated deformable porous media are simulated through iterative two-way coupling method in H-M coupled PNM. A comparison

Numerous sessile drop and micro-computed tomography (micro-CT) studies have been conducted to quantify geologic carbon storage formation wettability by measuring static contact angles (θ); however, the influence of pore geometry remains unknown. In this work, six sandstones (Bandera Brown, Berea, Bentheimer, Mt. Simon, Navajo, and Nugget) are used to measure θ using the two aforementioned experimental

The arguments in Eqs. (16) and (18) have typographical errors in the original publication of the article.