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Biot’s theory of poroelasticity describes seismic waves propagating through fluid-saturated porous media, so-called two-phase media. The classic Biot’s theory of poroelasticity considers the wave dissipation mechanism as being the friction of relative motion between the fluid in the pores and the solid rock skeleton. However, within the seismic frequency band, the friction has a major influence only on the slow P-wave and an insignificant influence on the fast P-wave. To represent the intrinsic viscoelasticity of the solid skeleton, we incorporate a generalized viscoelastic wave equation into Biot’s theory for the fluid-saturated porous media. The generalized equation that unifies the pure elastic and viscoelastic cases is constituted by a single viscoelastic parameter, presented as the fractional order of the wavefield derivative in the compact form of the wave equation. The generalized equation that includes the viscoelasticity appropriately describes the dissipation characteristics of the fast P-wave. Plane-wave analysis and numerical solutions of our wave equation reveal that (1) the viscoelasticity in the solid skeleton causes the energy attenuation on the fast P-wave and the slow P-wave at the same order of magnitude and (2) the generalized viscoelastic wave equation effectively describes the dissipation effect of the waves propagating through the fluid-saturated porous media.

In a comparison of modified nanoscale zero-valent iron (NZVI), bare NZVI used to remediate deep contaminated groundwater source areas has more advantages. However, the influence of injected bare NZVI deposition on the permeability of aquifer remains unclear, together with which are still the key factors of engineering cost and contamination removal. Hence, this study sought to assess a method of measuring hydraulic conductivity with a constant head device and to examine the permeability loss mechanism of NZVI injected into different saturated porous media, using column tests. The results showed that it was feasible to determine hydraulic conductivity by the constant head device. The permeability loss caused by NZVI injection increased with a decrease in the grain size of the porous media, and was determined by the amount and distribution of NZVI deposition. The NZVI distribution area had a good linear correlation with dispersivity of the porous media. Additionally, although surface clogging occurred in all porous media, the amount of NZVI deposition at the injection point was largest in fine sand, so that its permeability loss was the most; this was more likely to cause hydraulic fracturing and expand the area of the contaminant source zone. These results have implications for NZVI field injection for successful groundwater remediation.

Comments to K.M. Pervaiz Fathima, Ren\'e de Borst, Implications of single or multiple pressure degrees of freedom at fracture in fluid saturated porous media, Engineering Fracture Mechanics, 213 (2019), 1-20.

This article deals with the behavior of reflection/transmission phenomena on the propagation of SH waves in a corrugated fluid-saturated porous layer sandwiched between heterogeneous viscoelastic a...

We examined how injection/suction impacts the flow characteristics for mixed convection across a vertical cone saturated porous medium in the presence of double dispersion and chemical reaction effects. We perform suitable transformations to convert the nonlinear system of partial differential expressions into a system of non-dimensional form and received dimensionless equations solved numerically by the bivariate Chebyshev spectral collocation quasi-linearization method. We explain the outcomes of the flow characteristics over various variables through diagrams and numerical benchmarks. We also establish precision verification of the chosen numerical technique through a comparison with prior published computations and found to be in great assent. The residual analysis section also illustrated which unblocks convergence of the present results.

The characteristics of P-wave reflection coefficients can be dependent on the properties of the interface separating the two dissimilar poroelastic media. To evaluate the influence of the interface condition, we have developed a general theoretical formulation of seismic reflection and transmission of waves at arbitrary incidence angles in fluid-saturated porous media. The formulation is derived based on the quasistatic Biot’s theory and incorporates a more general boundary condition for fluid pressure. Simple analytic expressions are obtained for reflection and transmission coefficients at normal incidence. The equations incorporate an interfacial impedance that can be used to effectively characterize the interface condition. Based on the new formulation, we study the coupled effects of dynamic fluid flow and the interface condition on the reflection and transmission coefficients. Two pertinent reflection scenarios in exploration geophysics are considered in the numerical analysis, i.e., a gas-water contact and a free fluid overlying a gas-saturated medium. We examine the corresponding P-wave reflection coefficient resulting from different interface conditions such as imperfect hydraulic contact, capillary pressure, and open- and sealed-pore interfaces. Our results reveal that the interface condition can affect the frequency dependence and amplitude-versus-angle signatures of the reflection coefficient.

A theoretical investigation has been made for a radiating and chemically reacting viscous-fluid of a conducting gas over a vertical porous surface immerse in a saturated porous medium for the impact of magnetic drag-force, buoyancy forces and thermal-diffusion (Soret) order under oscillatory suction and heat absorption. The analytical solutions have been derived for the physical variables related to the governing equations under the appropriate boundary conditions. It is found that the velocity profiles increase with the increasing values of Soret number (S0) and higher Soret number (S0 = 5) shows the large temperature difference. It is noticed that increasing radiation parameter (R) elevated the velocity profiles near the plate. In the effects of Soret number (S0) the velocity profiles are an increasing function for both the cases of M = 0 and M = 10. The validity and accuracy of the flow model is presented and found suitable to proceed the work. In this study, the findings would be useful in many practical areas such as diffusion operations, which involved molecular diffusion of species with molar concentration.

This study deals with review of different improvements done in the formulation of the governing equations to simulate accurate solute transport in saturated porous media over the years. The traditional advection-dispersion equation (ADE) model is the simplest lumped model founded on the assumptions of Fick’s law of diffusion. But it typically underestimates the breakthrough concentration in leading and/or tailing region due to non-fickian transport. It is modified into mobile-immobile model (MIM) considering the medium having micropores with stagnant water pockets but allowing solute exchange by diffusion between mobile and immobile zone which is quantified by mass transfer coefficient. Multi-process non-equilibrium (MPNE) model further simulates for a system with both physical and chemical non-equilibrium by assuming instantaneous and rate-limited sorption in advective and non-advective domains. Using the concept of dual permeability, slow fast transport (SFT) model divides the liquid phase in the domain into three zones i.e. fast, slow and immobile. Here chemical interaction between the fluid and soil matrix takes place only in slow and immobile zones. Non-fickian solute transport does not follow Brownian motion rules so a random variable is required to explain it. Hence continuous time random walk (CTRW) model is used where solute transport is characterized by joint probability variable. Special case of CTRW with solute having considerable probability of moving long distances and follow power law gives Fractional advection-dispersion equation (FADE) model. These models varying from relatively simple to more complex formulations and assumptions are discussed here highlighting the merits and demerits of each.

Current work involves entropy generation studies within nine porous containers involving identical area for Prm = 155 (engine oil), Dam=10−5−10−2 at Ram=106. The entropy generation maps for lesser ...

Water suspension with heat transport into unsaturated-saturated porous media is analyzed. The numerical modeling includes the infiltration of silt. Moreover, the heat energy of suspension is exchanged with the heat energy of the matrix. The deposited silt influence the porosity and hydraulic permeability. The flow model is based on Richard's type equation and empirical van Genuchten - Mualem model describing capillarity driving force and saturation-pressure relation governing the flow in unsaturated part of porous media. The developed numerical method is usable for solving inverse problems determining some model parameters. The numerical method is based on flexible time discretization and a finite volume method in space variables. The nonlinearity in the flow part of the model is solved by iterative linearization based on the idea in Celia et all. The correctness of the numerical approximation is justified also by a different numerical approximation based on space discretization leading to the reduction of the whole system to the solution of ordinary differential equations. But this method requires significantly more computation time. This is not suitable for solving inverse problems. The used method is justified in numerical experiments solving the direct problem.

Carbon nanotubes (CNTs) are widely used and may pose potential environmental risks to soil and groundwater systems. Therefore, it is important to improve current understanding of the fate and transport of CNTs in porous media. In this study, the transport behavior of multi-walled carbon nanotubes (MWCNTs) with different surface modifications were examined in water-saturated sand columns under different pH (5 and 7) and ionic strength (0.1, 1, and 5 mM) conditions. COOH-MWCNTs have the strongest mobility among the five types of MWCNTs, followed by pristine MWCNTs. NH2-MWCNTs, Cu-MWCNTs, and Fe-MWCNTs have the weaker mobility. The transport of five types of MWCNTs decreased with the increase of ionic strength, while increased with the increase of pH value. The results suggested that the transport of MWCNTs can be affected by the electrostatic attraction between the functional groups on the surface of MWCNTs and quartz sand. Moreover, the pH and ionic strength of the solution also played an important role in enhancing the transport of MWCNTs, which have great significance for evaluating the transport and fate of MWCNTs in natural environment.

Based on Biot’s model for saturated porous media, the governing equation of fluid-saturated porous rectangular plates is presented, in which the compressibility of solid particles and fluid and the viscosity of pore fluid is taken into account. A series solution is given for simply-supported fluid-saturated porous plates. The accuracy of the solution is validated by degenerating the fluid-saturated porous rectangular plates into single-phase solid rectangular plates. As a numerical example, the free vibration characteristic and the dynamic response under harmonic loads are analysed. The influence of surface infiltration conditions, porosity, pore fluid permeability coefficient and loading frequency on the free vibration frequency is discussed.

The material point method (MPM) has been increasingly used to simulate coupled hydro-mechanical problems involving large deformations. However, when addressing saturated porous media with an almost incompressible liquid phase, the classic explicit MPM with low-order interpolation functions is not stable if no further stabilization approach is used. In this study, a solid-velocity–liquid-velocity-based hydro-mechanical governing formulation is adopted to construct a two-phase single-point explicit generalized interpolation material point (GIMP) method. To stabilize this set of formulation, the XPIC(m) (extended PIC of order m) method is extended to erase null space noise and damp high-frequency waves in both solid and liquid phases; additionally, a cell-based averaging approach is adopted to solve locking issues and smooth stress field variables. Several numerical examples have been presented to demonstrate the capabilities of the stabilized coupled GIMP method in simulating coupled hydro-mechanical problems involving dynamic effects and large deformations.

Natural convection in an inclined cavity filled with saturated porous media has been investigated. A time-dependent solution using a spectral weighted residual method is determined. Preparing the g...

Weakly nonlinear stability analysis has been performed using the finite amplitude Ginzburg-Landau model. The layer is oscillating vertically in sinusoidal manner. Using the finite amplitude analysis heat mass/transfer is quantified in the system. The disturbances of the flow are expanded in power series of small parameter. In addition to the modulation, the effect of throughflow is discussed on heat/mass transfer in the system. The values of viscoelastic parameters are considered in this paper are λ1 > λ2 and Γ < 1 to validate the problem. The time relaxation parameter λ1 has destabilizing effect, while the time retardation parameter λ2 has stabilizing effect on the system. The effects of amplitude and frequency of modulation on heat/mass transports have been analyzed and depicted graphically. The studies establish that the heat/mass transports can be controlled effectively by g-jitter and throughflow. Further, it is found that better results may obtain for an oscillatory mode of convection.

Numerical calculations in DHI FEFLOW software environment were used to assess the effect of variably saturated zone parameters on capillary barrier formation. The sensitivity of the model to these parameters was analyzed, and the conditions of barrier degeneracy were given.

In this paper we have investigated the effect of throughflow on thermal convection in a viscoelastic fluid saturated porous media. The governing equations are modelled in the presence of throughflow. These equations are made dimensionless and the obtained nonlinear problem solved numerically. There are two types of throughflow effects on thermal instability inflow and outflow investigated by finite amplitude analysis. This finite amplitude equation is obtained using the complex Ginzburg-Landau amplitude equation (CGLE) for a weak nonlinear oscillatory convection. The heat transport analysis is given by complex Ginzburg-Landau amplitude equation (CGLE). The numerical results indicate that due to the non-uniform throughflow there is instability at the bottom plate and influence the heat transfer in the system. The vertical throughflow is having both stable and unstable modes depending on flow direction. The nature of viscoelastic fluid is having both effects either stabilize or destabilize. Further, it is found that the nonlinear throughflow effects have dual role on heat transport. The solutions of the present problem are obtained numerically by using Runge-Kutta fourth order method.

Transport of environmental pollutants in groundwater systems can be greatly influenced by colloids. In this study, the cotransport of Pb2+ and silica (SiO2) colloids at different Pb2+ concentrations was systematically investigated by batch adsorption and saturated sand column experiments. Results showed that SiO2 colloids had low adsorption capacity for Pb2+ (less than 1% of the input) compared with sands. In saturated porous media, SiO2 colloids showed a high mobility; however, with the increase of Pb2+ concentration in the sand column, the mobility of SiO2 colloids gradually decreased. Notably, SiO2 colloids could facilitate Pb2+ transport, although they did not serve as effective carriers of Pb2+. Under the condition of low Pb2+ concentration, SiO2 colloids promoted the Pb2+ transport mainly through the way of “transport channel,” while changing the porosity of the medium and masking medium adsorption sites were the main mechanisms of SiO2 colloid–facilitated Pb2+ transport under the condition of high Pb2+ concentration. The discovery of this non-adsorption effect of colloids would improve our understanding of colloid-facilitated Pb2+ transport in saturated porous media, which provided new insights into the role of colloids, especially colloids with weak Pb2+ adsorption capacity, in Pb2+ occurrence and transport in soil-groundwater systems.

The stability of nanofluid flow in a vertical channel packed with a porous medium is examined for the local thermal nonequilibrium state of the fluid, particle, and solid–matrix phases. The effects of Brownian motion along with thermophoresis are incorporated in the nanofluid model. The Darcy–Brinkman model for the flow in a porous medium and three-field model, each representing the fluid, particle, and solid–matrix phases separately, for the temperature is used. A normal mode analysis is used to obtain the eigenvalue problem for the perturbed state, which is then solved using the Chebyshev spectral collocation technique. The critical Rayleigh number and corresponding wavenumber are presented graphically for the effect of different local thermal nonequilibrium parameters. It is noticed that the influence of local thermal nonequilibrium (LTNE) parameters on convective instability is significant.

This paper investigates the influence of the variation in the groundwater table on ground vibrations from underground tunnels by an analytical model. The saturated porous medium is used to model the soil layer under the groundwater table, and the dry single-phase medium is applied to simulate the soil above the groundwater table. The transfer matrix method and wave transformation are applied to derive the solution for a tunnel in a dry/saturated layered half-space. Ground vibrations from a tunnel in a three-layered half-space are computed by using the proposed model. The numerical results demonstrate that the vibration levels increase as the groundwater table drops. The displacement field is similar to that of a saturated half-space when the groundwater table is above the tunnel, while it is similar to that of a dry single-phase half-space as the groundwater table is under the tunnel.

When applying equal-order monolithic schemes for the solution of incompressible fluid saturated porous media dynamics, the resulting pressure field often exhibit spurious oscillations. This is in part due to violation of the inf-sup restriction. Although the mixed order monolithic scheme such as Taylor–Hood element scheme can circumvent this problem and yet use a mixed order monolithic scheme, a reduction of accuracy of both displacements and pressures may happen when the porous media permeability is small. In this paper, we present a new equal-order monolithic scheme that can accurately handle a broader range of permeabilities. We consider the u-p and u-v-p formulations from the theory of porous media (u:solid displacement, v:liquid velocity, p:liquid pressure) for fully saturated materials. We name the new scheme as the fractional steps correction method. Results show that this scheme succeeds in solving both formulations quite well with a spatial discretisation based on either the finite difference or the finite element method.

This paper analytically investigates the dynamic interaction of two neighboring tunnels in the saturated soil. The twin tunnels are simulated using the Flugge shell theory, and the surrounding soil is modelled by the Biot’s theory. The solution for cylindrical waves in saturated porous media is derived by applying the potential decomposition. The addition theorem is subsequently introduced to translate cylindrical waves, thereby satisfying the boundary conditions at the interfaces between the twin tunnels and saturated soil. Numerical examples are presented to analyze soil vibrations under different loading conditions calculated by different tunnel models. The neighboring tunnels have strong dynamic interaction, resulting in the insertion gain up to ± 20 dB. It is recommended to account for the interaction between neighboring tunnels when calculating the vibrations from underground railways.

To figure out the influence of different factors on the diffusion of carbon dioxide (CO2) in oil-saturated porous media, an experimental method using a multifunctional core displacement instrument ...

Summary This paper presents SH wave scattering by a frozen porous inclusion embedded in fluid-saturated porous media. We propose two computational methods, wave function expansion (WFE) and boundary element method (BEM), for wave scattering analyses. In WFE formulation, the components of displacement and stress are expressed by the superposition of the Bessel functions. The unknown coefficients in the expression are obtained via boundary conditions. On the other hand, in BEM formulation, boundary values of the frozen porous media are expressed by generalized displacement and traction. The generalized displacement consists of displacement components of the solid skeleton and the ice matrix, and the generalized traction is composed of the traction components of the two solid phases. Several numerical examples provide the validity of the proposed methods and the properties of the scattered waves. The discussion of the scattering properties focuses on the effects of ice saturation parameter, frequency of harmonic incident wave, the incident angle of the harmonic wave and the shape of the inclusion.

A porous medium saturated with water-ZnO nanofluid is used for thermoregulation by natural convection of a cubic electronic component contained in a tilted hemispherical cavity. The ratio between t...

This paper deals with the inverse problems of wells' location and transmissivity estimation in a saturated porous media. Wells are considered as circular holes and the heterogeneous domain is divid...

Knowledge of particle deposition and transport in saturated porous media is of significant importance for various engineered applications and environmental concerns. Surface physical and chemical h...

International audience; Understanding streaming potential generation in porous media is of high interest for hydrological and reservoir studies as it allows to relate water fluxes to measurable electrical potential distributions. This streaming potential generation results from an electrokinetic coupling due to the presence of an electrical double layer developing at the interface between minerals and pore water. Therefore, the pore sizes of the porous medium are expected to play an important role in the streaming potential generation. In this work we use 2‐D pore network simulations to study the effect of the pore size distribution upon this electrokinetic mechanism. Our simulations allow a detailed study of the influence of a large range of permeabilities (from 10−16 to 10−10 m2) for different ionic concentrations (from 10−4 to 1 mol/L). We then use and compare two different approaches that have been used over the last decades to model and interpret the streaming potential generation: the classical coupling coefficient or the effective excess charge density, which has been defined recently. Our results show that the four pore size distributions tested in the present work have a restricted influence on the coupling coefficient for ionic concentration smaller than 10−3 mol/L while it completely drives the behavior of the effective excess charge density over orders of magnitude. Then, we use these simulation results to test an analytical model based on a fractal pore size distributions. This model predicts well the effective excess charge density for all pore size distributions under the thin double layer assumption.

An understanding of nanobubble (NB) migration in porous media is needed for potential environmental applications. The solution chemistry is well known to be a critical factor in determining interactions of other colloids and nanoparticles with surfaces. However, little quantitative research has examined the influence of solution chemistry on NB transport. One-dimensional column experiments were therefore conducted to investigate the transport, retention, and release of NBs in glass beads under different solution chemistry conditions. NB concentrations in the effluent were reduced with an increase in ionic strength (IS) or a decrease in pH due to a reduction in the repulsive force between the glass surface and NBs, especially when the solution contained Ca2+ as compared to Na+ and for larger NBs. This result was somewhat surprising because electrostatic and van der Waals interactions for NBs were both repulsive on a homogeneous glass bead surface. NB retention on the surface was explained by ubiquitous nan...