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The co-transport of contaminants by soil colloids can generate substantial environmental risk in the subsurface, and this behavior is greatly affected by the particle size of soil colloids. A variable charge bulk soil was separated into four soil particle size fractions (i.e., 10–1, 1–0.45, 0.45–0.2 and

Understanding the transport behavior of N-doped graphene (NG) in porous media is critical to assess its environmental impact. In this work, sand column experiments were conducted to compare the transport and retention of NG and graphene oxide (GO) and to investigate the effects of temperature (4 and 25 °C), solution ionic strength (1 and 5 mM) and sand grain size (0.3–0.4 and 0.5–0.6 mm) on the transport and retention of NG in saturated porous media. The retention of NG in the column was larger than GO. The transport of NG was sensitive to solution ionic strength, and it was more mobile under lower ionic strength. The transport of NG increased with the increasing of sand grain size, and the results can be expounded by the colloid filtration theory. The transport of NG was larger at the lower temperature tested because of the reduction of repulsively electrostatic forces between sand and NG as temperature increased. Advection-dispersion equation was applied to simulate the transport and retention of GO and NG in saturated porous media and model simulations fitted the experimental data very well. Findings of this study are of great importance for exploring the transport and fate of NG in the natural environment.

The transient stress distribution is obtained for a saturated porous medium containing an array of equally distributed collinear cracks when each crack is opened by suddenly applied internal pressure. The integral and Laplace transforms are employed to reduce the mixed boundary-value problem to solving the Fredholm integral equation. The influence of pore fluid and the size of the crack with respect to the distance between the neighbouring cracks on the dynamic stress intensity factor are investigated. Numerical results are presented and compared with the corresponding values of the dry medium.

Xanthan gum (XG) was utilized to rheologically modify the reduced graphene oxide based nanoscale zero valent iron (nZVI/rGO) in the study, to enhance the stabilization and transportation of the remediation materials in-situ. The results demonstrated that the saturated adsorption capacity of XG on nZVI/rGO (CAds XG/CnZVI/rGO) was 0.133, and when CFree XG/CnZVI/rGO was over 0.072, XG-nZVI/rGO was rheologically modified, manifesting high charged density (

We consider a Darcy problem for saturated porous media written in dual formulation in presence of a fully immersed inclusion. The lowest order virtual element method is employed to derive the discrete approximation. In the present work we study the effect of cells with cuts on the numerical solution, able to geometrically handle in a more natural way the inclusion tips. The numerical results show the validity of the proposed approach.

Recent laboratory studies have shown the injection of colloidal Mg(OH)2 could provide an effective and low cost alternative as a long term pH buffering system. In this study, Mg(OH)2 was modified by Tween 80 and SDS and the modified suspension had the properties of high stability, small particle size (the average particle diameter D50 was smaller than 1 μm) and negative charge (zeta potential = −14.26 mV at pH = 10.54). All of these properties demonstrated that colloidal Mg(OH)2 may have satisfactory transport performance in porous media. However, colloidal Mg(OH)2 is heterogeneous colloids with a high concentration, the transport performance in porous media is significantly different from homogeneous colloids, and the model simulation is relatively complex. To solve these problems, method of calculus combined with colloid filtration theory (CFT), T-E equation and modified Maxwell theory was used to simulate the transport performance of high concentration of Mg(OH)2 colloids. Results indicated that the observed experimental results matched well with the model simulations. Hydrodynamic force, DLVO attractive force and colloid diffusion are the major factors controlling the migration of colloidal Mg(OH)2 in porous media and could quantitatively describe the influence of injection velocity, porous media size and ionic strength on colloidal Mg(OH)2 transport properties by model calculation.

Porosity is an important variable in consolidation theory. However, porosity information is missing in Biot’s model when the solid constituent of the porous media is assumed to be compressible. This paper develops a macro–microscopic coupled consolidation model in order to track the evolution of the porosity for saturated porous media with compressible constituents. The proposed model exploits a u − e v sr − p form with the aim to incorporate the coupled behavior between the macroscopic and microscopic volumetric compressibility. Subsequently, a specific study on the analytical solutions for the case of a linear-loaded one-dimensional consolidation problem based on the proposed model is presented. Two examples are shown in order to demonstrate how to apply the proposed model. The proposed model paves the way to study the consolidation problem with porosity-dependent coefficients for saturated porous media with compressible constituents.

High-pressure tunnels with reinforced concrete lining have been extensively utilized in project practice. This study aims at developing a complete hydro-mechanical numerical model of high-pressure tunnels with emphasis on the interaction between lining and rock mass. In the model, a fully hydro-mechanical coupled formulation for saturated porous media is first established. A virtual element approach is proposed and combined with the master–slave contact algorithm to consider the interaction between lining and rock mass under hydro-mechanical coupling. A simple elastic-damage model is proposed to model the mechanical behaviour of the reinforced concrete lining. Moreover, the evolution formulations of the cracking and permeability of the reinforced concrete lining are derived based on China’s specifications. The proposed numerical model is first verified by simulating two examples that have analytical solutions. Then, the case study of an actual high-pressure tunnel is carried out. The whole water infilling process is numerically simulated and the obtained results are compared with the measured field data. The consistence between them further verifies the present numerical model. Consequently, some primary design-related parameters are investigated numerically with the present numerical model, and the results can be considered as general guide rules for the design of high-pressure tunnels.

The mechanism of the effect of stresses on wave propagation in a fluid-saturated porous media has not been well understood. The goal of this paper is to fill this gap. First we formulated the general equations of motion in a homogeneously pre-stressed fluid-saturated medium and use them to derive explicit expressions of velocity dependence on stresses. Equations for fast and slow longitudinal waves allow substantial simplifications. The feasibility of fast longitudinal wave simplification is verified by comparison with experimental data available in literature.

In August 2019, this journal published the paper “A cell model of effective thermal conductivity for saturated porous media” (Zhu, 2019), which develops and validates a new analytical prediction model for the thermal conductivities of saturated porous materials. This critique reveals that the model is conceptually and practically flawed, by on the one hand showing that it may result in thermal conductivities outside of the series and parallel limits and by on the other hand exposing its poor performance for dry porous media contrary to Zhu's positive outcomes. Given that these flaws, if known to the author and/or reviewers, would (probably) have led them to a “not fit for publication” evaluation, the discusser suggests an official retraction of (Zhu, 2019).

The combination of ball milling technology and biochar materials provides new prospects for environmentally friendly and sustainable environmental pollution control technologies, but comes with opportunities and risks. In this study, column experiments were used to evaluate the environmental behavior of ball‑milled biochar (BMBC). The results of the column experiments showed that BMBC transport increased with a high flow velocity, large medium size, high pH, and low ionic strength. Owing to the strong adsorption of Cd2+ by BMBC, the presence of BMBC in the medium led to a decrease in effluent Cd2+. The presence of Cd2+ in the solution slightly inhibited the transport of BMBC. The transport of Cd2+ was facilitated by BMBC due to the high affinity. Therefore, attention should be paid to favorable conditions for BMBC transport. This study provides a perspective to assess the behavior of BMBC in the environment and whether its interaction with Cd2+ will introduce new environmental hazards.

Influence of granular size and groundwater flow rate on transport of Pseudomonas migulae AN-1 in saturated porous media was non-invasively and visually investigated with a novel imaging technique based on our previously established green fluorescent protein-tagging approach. AN-1 was transported faster than water was. The finer the media were, the greater the enhancement of bacterial velocity was. Mass recovery (MR) increased, while deposition rate coefficient (Kc) decreased, with increasing granular size. Similar and linear trends of MR and Kc, respectively, were quantitatively observed with increasing water flow rate. The images revealed that the initial shape of bacterial plume after injection was a narrow strip along the injection well and an ellipsoid in the lower part of the injection well in medium and coarse sand, respectively. Bacterial plume migrated horizontally in medium sand, but shifted slightly downward in coarse sand. Under similar conditions, the fluorescent area carrying AN-1 in medium sand was larger than that carrying AN-1 in coarse sand during the same period. The visualisation method of this study captured both the movement of free-state and retained bacteria that adhered to sediments. A continuous biological zone composed of planktonic and retained AN-1 was observed. These findings are significant for actual bioremediation.

For a fully-coupled Darcy–Stokes system describing the exchange of fluid and stress balance across the interface between a saturated porous medium and an open very narrow channel, the limiting problem is characterized as the width of the channel converges to zero. It is proven that the limit problem is a fully-coupled system of Darcy flow in the porous medium with Brinkman flow in tangential coordinates of the lower dimensional interface.

The objective of this study is to understand the effect of heterogeneous layer on the migration of gaseous and dissolved CO2 in the saturated porous media and to figure out which parameter is most sensitive to detect CO2 leakage in this system. A set of lab experiments were conducted using 2-D sand tank with various sensors. To investigate the migration characteristics of leaked CO2 around the heterogeneous layer, 2-D numerical simulations were carried out with a model which reflects on the experimental condition. The experiments and modelling results suggested that there is the effect of layer, which has slightly different properties compared with adjacent medium, on CO2 migration even though the difference is quite small in geological scale. These results will be helpful for designing the MMV plan for successful leakage monitoring on the GCS site.

Laboratory batch sorption and sand column experiments were conducted to examine the effects of temperature (6 and 24°C) on the retention and transport of GO in water-saturated porous media with different combination of solution ionic strength (IS, 1 and 10mM), sand type (natural and acid-cleaned), and grain size (coarse and fine). Although results from batch sorption experiment showed that temperature affected the sorption of GO onto the sand grains at the low IS, the interactions between GO and the sand were relatively weak, which did make the temperature effect prominent. When the IS was 1mM, experimental temperature showed little effect on GO retention and transport regardless of the medium properties. GO was highly mobile in the sand columns with mass recovery rates ranged from 77.3% to 92.4%. When the IS increased to 10mM, temperature showed notable effects on GO retention and transport in saturated porous media. For all the combinations of sand type and grain size, the higher the temperature was, the less mobile GO particles were. The effects of temperature on GO retention and transport in saturated porous media were further verified though simulations from an advection-dispersion-reaction model.

Continuum porous media theories, extended by a diffusive phase-field modeling (PFM) approach, introduce a convenient and efficient tool to the simulation of hydraulic fracture in fluid-saturated heterogeneous materials. In this, hydraulic- or tension-induced fracture occurs in the solid phase. This leads to permanent local changes in the permeability, the volume fractions of the constituents as well as the interstitial-fluid flow. In this work, the mechanical behaviors of the multi-field, multi-phase problem of saturated porous media, such as the pore-fluid flow and the solid-skeleton deformation, are described using the macroscopic Theory of Porous Media (TPM). To account for crack nucleation and propagation in the sense of brittle fracture, the energy-minimization-based PFM procedure is applied, which approximates the sharp edges of the crack by a diffusive transition zone using an auxiliary phase-field variable. Furthermore, the PFM can be implemented in usual continuum finite element packages, allowing for a robust solution of initial-boundary-value problems (IBVP). For the purpose of validation and comparison, simulations of a two-dimensional IBVP of hydraulic fracture are introduced at the end of this research paper.

An edge-based smoothed point interpolation method is adopted for coupled hydro-mechanical analysis of saturated porous media with elasto-plastic behaviour. A novel approach for the evaluation of the coupling matrix of the porous media is adopted. Stress integration is performed using the substepping method, and the modified Newton-Raphson approach is utilised to address the nonlinearities arising from the elasto-plastic constitutive model used in the formulation. Numerical examples are studied and the results are compared with analytical solutions and those obtained from the conventional finite element method (FEM) to evaluate the performance of the proposed model.

A two-and-a-half-dimensional (2.5-D) coupled finite element–boundary element (FE–BE) model is presented to simulate the three-dimensional dynamic interaction between saturated soils and structures with longitudinally invariant geometries. A regularized 2.5-D boundary integral equation for saturated porous media is derived that avoids the evaluation of singular traction integrals. The 2.5-D coupled FE–BE model is established by using the continuity conditions on the soil–structure interface. The developed model is verified through comparison with an existing semi-analytical method. Two case studies of a tunnel embedded in a poroelastic half-space and the efficiency of a vibration isolating screen are presented.

Numerical modeling of reservoirs with low permeability or under undrained conditions often suffers from spurious fluid pressure oscillations due to the improper construction of approximation spaces. To address this issue, a fully coupled, stabilized meshfree formulation is developed based on a fluid pressure projection method, in which an additional stabilization term is added to the variational equation to correct the deficiency of the equal-order u – p reproducing kernel approximation. The projection scheme is formulated under the framework of the stabilized conforming nodal integration which enables a significant enhancement of the computational efficiency and accuracy, and the spurious low-energy modes of nodal integration are also eliminated. The effectiveness of the proposed stabilized meshfree formulation is demonstrated by solving several benchmark problems.

Accurately predicting the fate and transport of nano-TiO2 in porous media is critical to assess its environmental impact. This study was designed to understand the effects of gain size and structural heterogeneity under different ionic strength (IS) on the fate and transport of nano-TiO2 in saturated porous media. In the columns packed homogenously with sand of different grain sizes (920, 550, 390, and 275μm), the transport of nano-TiO2 decreased when the IS increased from 0.1 to 1 or 10mM. For all the three IS conditions, the retention of the nano-TiO2 particles in the columns increased when the gain size decreased, and the mobility of the nano-TiO2 was the lowest in the sand at size of 275μm with recovery rates of 0.30% to 1.72%. The mass recovery rates of TiO2 in other homogeneous columns were higher and ranged from 0.37% to 59.9%. Structural heterogeneity created two flow domains for the retention and transport of nano-TiO2 particles in the saturated porous media. The fast-flow domain dominated the flow and transport processes of the nano-TiO2 in the heterogeneous columns under the tested conditions. As a result, the transport of nano-TiO2 in the heterogeneous porous media was faster and higher than that in the homogeneous columns under similar experimental conditions. Because of the dominance of the fast-flow domain, the recovery rates of the nano-TiO2 in the heterogeneous columns were similar and ranged from 59.8% to 66.9%. These results reflected the importance of preferential flow to the fate and transport of nano-TiO2 particle in porous media. Simulations from a two-domain model matched the experimental breakthrough curves very well.

General finite element software has unique advantages in solving complicated engineering problems, which has been widely applied in the dynamic analysis of single-phase media. However, the commonly used software does not provide a saturated porous two-phase element that can be adopted for dynamic analysis. In this paper, a user-defined element for dynamic analysis of saturated porous media is developed in the general finite element software ABAQUS. The user-defined element takes the displacements of solid skeleton and pore fluid as the basic unknown-variables, and adopts the implicit time integration scheme. By combining it with the equivalent linear method, the nonlinear dynamic analysis of saturated soil can also be realized. The correctness of the user-defined element is verified by solving four numerical examples.

In establishing the numerical model to simulate the saturated soil-structure interaction subjected to dynamic loadings, the absorbing boundary conditions are usually applied to simulate the wave propagation in the field. In this study, a type of viscous boundary in conjunction with the domain reduction method (DRM) is proposed as an advanced absorbing boundary. The performance of this advanced absorbing boundary is examined by comparing the seismic responses of rectangular tunnel modeled with different boundary conditions in FLAC3D. The numerical results suggest that the advanced absorbing boundary has advantages over the other types of boundaries in minimizing the wave reflection at the numerical boundaries. Furthermore, the proposed advanced absorbing boundary is also employed for the seismic investigation of clay-pile systems, the results of which compare favorably well with the corresponding seismic centrifuge test results. The numerical analysis results indicate that the advanced absorbing boundary proposed in this study can be effectively employed for the efficient dynamic analysis of structures founded on the saturated porous media.

The pore structure and unfrozen water film have a significant influence on the frost heave of saturated porous media. The freezing process and frost heaving characteristics of saturated sandstones have been studied in this research by theoretical and experimental approaches. A developed micromechanical model has been proposed, considering the distribution function of pore size, the effect of unfrozen water film, and the interfacial free energy. The distribution of pore size in sandstone can well satisfy a dual-pore structure model, including the thin pores and coarse pores. Besides, four typical thickness functions are used to investigate the influence of the thickness of unfrozen water film on the disjoining pressure and frost heaving strains. The exponential equation suggested by Fagerlund (1973) may be better to quantify the thickness of this film by comparing with the experimental results. In addition, the frost heaving strains are also very close to the experimental values if ignoring the unfrozen water film. This calculation results may give the reasons why a satisfactory results can also be obtained with the absence of the unfrozen water film in the previous models. This study provides a better understanding of the frost heaving mechanism of saturated porous materials.

Understanding subsurface transport of per- and polyfluoroalkyl substances (PFASs) is of critical importance for the benign use and risk management of PFASs. As one of the most commonly found PFASs, perfluorooctanoic acid (PFOA) is used as a representative PFAS and water-saturated column experiments were conducted to investigate the effect of Al/Fe oxyhydroxide coating and ionic strength on its transport at an environmentally relevant PFOA concentration (6.8 μg L−1). Our results showed a clear increase in PFOA retardation in Al/Fe oxyhydroxide coated sand (retardation factor: Al: 1.87–5.58, Fe: 1.28–4.05) than those in uncoated sand (1.00–1.05), due to the stronger electrostatic attraction between anionic PFOA and Al/Fe oxyhydroxide coated sand surface. Notably, Al oxyhydroxide have a more profound effect on PFOA retention and retardation than Fe oxyhydroxide. Besides, higher ionic strength significantly inhabited PFOA retention and retardation in positively charged sand, and the considerable retention of PFOA (∼90%) in deionized water than those in 1.5 mM and 30.0 mM NaCl (

As emerging contaminants of global concern, nanoplastics are significantly potential carriers of hydrophobic organic compounds in aquatic and soil environment. However, little is known about the interactions between the transports of nanoplastics and organic contaminants in porous media. In this study, the cotransport of naphthalene with polystyrene nanoplastics (PSNP) in saturated sand columns as influenced by the PSNP/naphthalene ratio and ionic strength (IS) was investigated. The presence of PSNP dramatically enhanced the mobility of naphthalene at low IS (0.5 mM), but such effect was prohibited at high IS (5 mM and 50 mM). The mobility of PSNP in the sand column was higher when it was solely exist in the pore-water than that when in the presence of naphthalene, because of the charge-shielding effect. This work showed that the coexistence of PSNP and naphthalene would influence the mobility of each other in the saturated porous media, which highly related to their concentration ratio and IS levels.

The transport of colloid in saturated porous media is of great significance for the assessment of environmental risk and bioremediation. However, coupled effects of high pH and chemical heterogeneity on colloid retention and release in saturated porous media remain unclear. We studied colloid transports in acid treated/untreated glass beads under various high pH values and ionic strength (IS) conditions to elucidate the effect of high pH and chemical heterogeneity. Chemical impurities promote the colloid to attach to the primary minimum. Increasing environmental pH of solutions would weaken the colloidal retention capacity. Once pH increases to 11, almost no colloid retention occurs no matter chemical impurities exist or not. Adsorbed colloids in the primary minimum can be detached at high pH environments (from 10 to 12). Despite the final similar environmental pH (from 10 to 12), different amounts of colloids are reserved at the ends of the attaching processes and eluting processes. Effects of chemical impurities on colloid retention are negligible when pH = 10 or higher. At the same time, colloid release in high pH solution is also related to disabled chemical impurities. Although previous studies show no obvious rule about colloid release with changing pH (from 6.8–10), our results demonstrate significant coupled effects of high pH and chemical heterogeneity on colloid retention and release in saturated porous media. We also found that straining might be underestimated. Our results improve the understanding about the role of pH in colloid transport processes.

We propose and analyze a model of coupled heat transport and water flow in variably saturated porous media under conditions of freezing and thawing. Solution of the model provides temperature, liquid water content and ice content in porous media as a function of space and time. We employ the Rothe method to construct systems of approximate solutions for which the existence and regularity are proved. Numerical scheme is based on specific semi-implicit discretization in time, which preserve the pseudo-monotone structure of the discrete problem. Numerical results are compared with experimental data reported in the literature. The model satisfactorily predicts characteristic phenomena in porous media under frost actions such as water movement toward freezing fronts and the presence of liquid water in frozen regions.

Antibiotic ciprofloxacin (CIP) is immobile in the subsurface but it has been frequently detected in the aquatic system. Therefore it is important to investigate the factors impacting CIP's mobilization in aquifer. Laboratory columns packed with sand were used to test colloid-facilitated CIP transport by 1) using kaolinite or montmorillonite to mobilize presorbed-CIP in a column or 2) co-transporting with CIP by pre-mixing them before transport. The Langmuir model showed that CIP sorption by montmorillonite (23 g kg − 1 ) was 100 times more effective than sand or kaolinite. Even with strong CIP complexation ability to Fe/Al coating on sand surface, montmorillonite promoted CIP transport, but not kaolinite. All presorbed-CIP by sand was mobilized by montmorillonite after 3 pore volumes through co-transporting of CIP with montmorillonite. The majority of CIP was fixed onto the montmorillonite interlayer but still showed inhibition of bacteria growth. Our results suggested that montmorillonite with high CIP sorption ability can act as a carrier to enhance CIP's mobility in aquifer.

Low-molecular-weight organic acids (LMWOAs) are ubiquitous in the aquatic environment and consequently may affect the heavy metal transport in aquifer systems. In this study, the influences of LMWOAs on the transport of Cd2+ under different pH conditions in saturated porous media were evaluated. For this, three LMWOAs such as acetic acid, tartaric acid, and citric acid were employed. A two-site nonequilibrium transport model was applied to simulate the transport data. Under acidic conditions (pH 5.0), the results indicated that LMWOAs inhibited the transport of Cd2+ even at the low concentrations of organic acids (i.e., 0.05 and 0.1 mM). The inhibition effects might be attributed to the complexation role of the sand surface-bound organic acids and also electrostatic interaction. Meanwhile, the inhibition effects of LMWOAs on Cd2+ transport in the following order of citric acid > tartaric acid > acetic acid, which was also in agreement with the decreasing complex stability constants between Cd2+ and LMWOAs. This order may be dependent on their molecular structures (i.e., amount and type of functional groups) and complexing strength. Interestingly, when the LMWOA concentrations 0.5 mM, tartaric acid and citric acid still inhibited Cd2+ transport, while acetic acid slightly enhanced the Cd2+ mobility due to its weaker complexing strength. However, under neutral conditions (pH 7.0), LMWOAs generally enhanced the transport of Cd2+. The transport-enhancement of LMWOAs was ascribed to the formation of stable aqueous non-adsorbing Cd–organic acid complexes. In addition, citric acid could obviously inhibit the transport of Cd2+ under competitive transport conditions (i.e., with competing cations), which is mainly due to different complex affinities of citric acid to Pb2+ and Cd2+. These findings demonstrate that LMWOAs may inhibit or facilitate Cd2+ transport under different environmental conditions. Thus, environmental assessment concerning the transport of heavy metals should consider the roles of organic acids.

Based on the u – U formulation of Biot equation and the assumption of zero permeability coefficient, a viscous-spring transmitting boundary which is frequency independent is derived to simulate the cylindrical elastic wave propagation in unbounded saturated porous media. By this viscous-spring boundary the effective stress and pore fluid pressure on the truncated boundary of the numerical model are replaced by a set of spring, dashpot and mass elements, and its simplified form is also given. A u – U formulation FEA program is compiled and the proposed transmitting boundaries are incorporated therein. Numerical examples show that the proposed viscous-spring boundary and its simplified form can provide accurate results for cylindrical elastic wave propagation problems with low or intermediate values of permeability or frequency content. For general two dimensional wave propagation problems, spuriously reflected waves can be greatly suppressed and acceptable accuracy can still be achieved by placing the simplified boundary at relatively large distance from the wave source.

This article examines the unsteady, pressure driven flow of a non-Newtonian fluid with reacting species in a parallel plate channel filled with a homogeneous, isotropic and saturated porous medium. A differential type third grade constitute equation is employed to model the non-Newtonian character of the fluid. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi-implicit finite difference scheme. Graphical results are presented and discussed qualitatively and quantitatively with respect to various parameters embedded in the problem.

Based on the plasticity, damage and seepage theory of equivalent continuum media, a fully coupled seepage-elastoplasticity-damage model for saturated porous media is proposed, which could reproduce the evolution of tensile and compressive damage, plasticity, porosity, permeability, and observed spatial distribution of pore pressure of the surrounding rock. This presented method is validated by the in-place testing data of the water conveyance tunnel project under the Yellow River, which is part of the South–North Water Diversion Project in China, and can be used as a reference for safety monitoring of similar hydraulic tunnel.

CO 2 injection in brine-saturated Bentheimer sandstone was studied experimentally to visualize and quantify salt precipitation in porous rock caused by evaporation of water into injected gaseous phase CO 2 . Gas and solid-salt saturation profiles were captured by μ-CT (micro computed tomography) and the pressure drop over the core was monitored continuously. The experimental results were compared with numerical simulations using the TOUGH2 reservoir simulator with the equation of state module ECO2N, and a numerical code that we have developed with an alternative approach on evaporation. Using the equilibrium phase partitioning model in TOUGH2, simulation results predict injectivity decline due to an accumulation of precipitated salt near the core inlet. This is in contradiction to our experimental observations, in which neither salt accumulation nor injectivity impairment was noticed. It appears that at near well injection velocities, local equilibrium phase partitioning used in the simulator overestimates evaporation of water into the CO 2 gaseous phase. On the other hand, satisfying results were obtained from our model which uses a kinetic formulation for the evaporation. No injectivity impairment was found which is compatible with the experimental results.

Storage of CO2 in depleted natural gas reservoirs is considered an attractive option to mitigate climate change concerns of CO2 from sources such as thermal power plants. In this regard, a number of depleted gas reservoirs located in Northern Alberta, Canada have been identified as potential sites for CO2 storage at temperature and pressure conditions at which CO2 forms gas hydrate crystals in the presence of water. This offers the possibility of storing more CO2 than what can be normally stored as a gas at the same conditions. The injection of CO2 in a bed of silica sand partially saturated with water (wet sand) at pressure and temperature conditions similar to those in a typical depleted gas reservoir in Northern Alberta was investigated in this work. The CO2 gas was injected into the simulated reservoir under the gas cap mode and the spiral tube mode procedure. Through the pressure drop measurements the CO2 gas consumption was determined and also the amount of water converted to hydrate was calculated. The results indicate that 39–47% of water formed hydrate in the gas cap mode gas injection experiments and 51–55% in the spiral tube mode injection experiments. Hydrate saturation reached 0.11–0.15 after 24 h for each gas injection mode. Finally, the capacity of the laboratory reservoir to store CO2 in various forms was determined.

Microbubbles are one solution to the channeling problem in the displacement process through porous media. However, applications of microbubbles to geological carbon sequestration (GCS) is scarcely reported. In this work, we injected supercritical CO2 (scCO2) into brine-saturated sandstone and mapped the displacement process by medical computed tomography (CT). The injections were performed by two methods: an analog of a regular drainage process and a special injection module incorporating microbubble injection. The microbubble injection increased the scCO2 saturation, which corresponds to the sweep efficiency, by alleviating the channeling effect. We then investigated the microbubble injection in numerical simulations and gained insights into the injection mechanism. Both injection processes were reasonably produced by assigning the sub-core permeability approximation with the porosity−capillary pressure approach ( ϕ - P c ). Based on these results, we attributed the macroscale effects of microbubble injection to the lowered entry capillary pressure.

Summary The removal of nonaqueous phase liquids (NAPLs) from contaminated soils by means of fresh water injection through a rejection well can be treated as a fully coupled problem involving the NAPL dissolution, radial aqueous-phase-liquid flow and dissolved NAPL transport through solute advection and diffusion/dispersion. The governing equations of this coupled problem can be mathematically described by a set of simultaneous partial differential equations with variable coefficients. In the case of the NAPL dissolution ratio (which is defined as the ratio of the equilibrium concentration of the dissolved NAPL to the density of the NAPL) approaching zero, analytical solutions for the NAPL dissolution problem associated with radial aqueous-phase-liquid flow have been derived in this paper. As a direct application example, the derived analytical solutions are used to investigate the fundamental behaviours of the NAPL dissolution problems associated with radial aqueous-phase-liquid flow in the fluid-saturated porous media. The related analytical results have demonstrated that three key factors, namely the dimensionless comprehensive number (which is known as the Zhao number and can be used to represent the overall hydrodynamic characteristic of a NAPL dissolution system), the initial saturation of the residual NAPL and the dimensionless injection well radius, can have significant effects on the dimensionless NAPL dissolution front propagation speed, the dimensionless NAPL dissolution front location and dimensionless breakthrough time of the NAPL dissolution front in the NAPL dissolution system associated with radial aqueous-phase-liquid flow.

Saturated sand-packed column experiments were conducted to investigate the influence of physicochemical factors on the transport and retention of surfactant stabilized silver nanoparticles (AgNPs). The normalized concentration in breakthrough curves (BTCs) of AgNPs increased with a decrease in solution ionic strength (IS), and an increase in water velocity, sand grain size, and input concentration (Co). In contrast to conventional filtration theory, retention profiles (RPs) for AgNPs exhibited uniform, nonmonotonic, or hyperexponential shapes that were sensitive to physicochemical conditions. The experimental BTCs and RPs with uniform or hyperexponential shape were well described using a numerical model that considers time- and depth-dependent retention. The simulated maximum retained concentration on the solid phase (Smax) and the retention rate coefficient (k1) increased with IS and as the grain size and/or Co decreased. The RPs were more hyperexponential in finer textured sand and at lower Co because of their higher values of Smax. Conversely, RPs were nonmonotonic or uniform at higher Co and in coarser sand that had lower values of Smax, and tended to exhibit higher peak concentrations in the RPs at lower velocities and at higher solution IS. These observations indicate that uniform and nonmonotonic RPs occurred under conditions when Smax was approaching filled conditions. Nonmonotonic RPs had peak concentrations at greater distances in the presence of excess amounts of surfactant, suggesting that competition between AgNPs and surfactant diminished Smax close to the column inlet. The sensitivity of the nonmonotonic RPs to IS and velocity in coarser textured sand indicates that AgNPs were partially interacting in a secondary minimum. However, elimination of the secondary minimum only produced recovery of a small portion (

This paper reports on the formulation and implementation of the displacement and stress models of the hybrid-Trefftz finite elements for elastostatic problems defined on saturated porous media. The supporting mathematical model is the (u-w) formulation of the Biot theory of porous media. The hybrid-Trefftz models are derived from the corresponding (pure) hybrid models by selecting the domain trial functions from the free-field solutions of the governing Navier equation. The resulting elements are highly robust and convergent, as they embody the physical characteristics of the modelled problem. Moreover, all coefficients present in the solving system are defined by boundary integral expressions.

We consider a saturated porous medium of Darcy type with an exothermic reaction occurring on the domain boundary. In this model the reaction is the main driving force behind convection and we establish continuous dependence of the solution on the reaction terms.

The present paper is focused on the analysis of heat and mass transfer in boundary-layer free convection over an inclined flat plate embedded in a fluid saturated porous medium in the presence of thermophoresis. The governing equations are transformed into a set of coupled differential equations, which are solved numerically using the local non-similarity method. A comparison between the results given by this method and the local similarity method is also presented. For various values of the problem parameters, graphs of thermophoretic wall velocity, Nusselt number and concentration profiles in the boundary layer are presented. Variation of the dimensional thermophoretic wall velocity along the plate for different angles of inclination are presented in a physical relevant case.

The effects of hydrodynamic and thermal heterogeneity, for the case of variation in both the horizontal and vertical directions, on the onset of convection in a horizontal layer of a saturated porous medium uniformly heated from below, with horizontal throughflow, are studied analytically for the case of weak heterogeneity. It is found that the horizontal throughflow has no effect on the stability of the longitudinal modes but it does affect the stability of the transverse modes. When the permeability decreases in the direction of the throughflow the transverse modes are stabilized (and so the longitudinal ones are favored). When the permeability increases in the direction of the throughflow a small amount of throughflow may destabilize the transverse modes and so destabilize the layer as a whole.

A general approach is proposed for defining the macroscopic free energy density function (and its complement, the free enthalpy) of a saturated porous medium submitted to finite deformations under non-isothermal conditions, in the case of compressible fluid and solid constituents. Reference is made to an elementary volume treated as an ‘open system’, moving with the solid skeleton. The proposed free energy depends on the generalised strains (namely an appropriate measure of the strain of the solid skeleton and the variation in fluid mass content) and the absolute temperatures of the solid and fluid phases (which are assumed to differ from each other for the sake of generality). This macroscopic energy proves to be a potential for the generalised stresses (namely the associated measure of the total stress and the free enthalpy of the pore fluid per unit mass) and the entropies of the solid and fluid phases. In contrast with mixture theories, the resulting free energy is not the simple sum of the free energies of the single constituents. Two simplified cases are examined in detail, i.e. the semilinear theory (originally proposed for isothermal conditions and extended here to non-isothermal problems) and the linear theory. The proposed approach paves the way to the consistent non-isothermal-hyperelastic-plastic modelling of saturated porous media with a compressible fluid and solid constituents.

This article examines the thermal effects in an unsteady flow of a pressure driven, reactive, variable viscosity, third-grade fluid through a porous saturated medium with asymmetrical convective boundary conditions. We assume that exothermic chemical reactions take place within the flow system and that the asymmetric convective heat exchange with the ambient at the surfaces follow Newton’s law of cooling. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi-implicit finite difference scheme. Graphical results are presented and discussed qualitatively and quantitatively with respect to various parameters embedded in the problem.

In this paper, a model of the generalized thermoviscoelasticity for a saturated porous media is used. Taking the rheological properties of the volume into consideration, it is developed on the basis of the thermo-hydro-elastodynamic model proposed by the authors. The formulation is applied to the generalized porous thermoviscoelasticity theories: coupling theory, Lord–Shulman theory and Green–Lindsay theory. The general characteristic equations for arbitrary coordinate system are derived using a semi-analytical approach in the Laplace domain. Exact solutions of the saturated porous thermoviscoelastic media, with a cylindrical cavity that is subjected to a time dependent thermal load, are obtained in the absence of heat sources. Numerical results are illustrated graphically employing numerical method for inverting the Laplace transform. Comparisons are made with the results predicted by these theories and the classical theory. In addition, the influence of rheological parameters on the thermoviscoelastic property is analyzed.

A rigorous treatment of the thermal expansion coefficient of the solid skeleton for saturated homogeneous porous media is presented. It is shown that the overall thermal expansion coefficient of a porous medium is equal to the thermal expansion coefficient of the solid constituent. It is also shown that the size of the pores and porosity has no influence on the thermal expansion coefficient of a porous medium, and the void ratio is independent of the thermal expansion of the solid skeleton in the elastic region of the material response. In addition, non-isothermal constitutive relations for saturated porous media are presented, and a closed form solution for the heating-induced pore pressure is derived. The validity of the theoretical assertions is examined through a targeted program of laboratory testing as well as data from the literature.

In recent years the industrial applications of porous materials has shown a growing relevance. Most of the technological thermal processes in porous media involve time-dependent thermal conditions. Therefore, the temperature at each point of the material also changes in time. In order to correctly carry out the technological process, it becomes necessary to know the temperature distribution inside the material. This is a problem of heat conduction in a fluid saturated porous media subject to a lack of local thermal equilibrium (LTNE). The purpose of this paper is to elucidate the several causes of LTNE, even in steady or quasi steady heat transfer processes in saturated porous media, and to evaluate the influence of structural characteristic of porous media and the presence of surfactant in the saturating liquid phase.

This study fundamentally investigated the swelling and distribution of benzene-light nonaqueous phase liquid (LNAPL) in porous media while cosolvent was flushed to the benzene-partially saturated system. Furthermore, the effects of simultaneous injection of cosolvent and air on the LNAPL behavior were visualized and thus quantified within a two-dimensional transparent porous medium. Partitioning types of alcohols affected dissolution of benzene entrapped in porous media. Tert-butanol (TBA) and 1-propanol floods apparently increased the LNAPL area, while a 70% ethanol flood reduced the LNAPL area by dissolution. Airflow facilitates mobilization of the swollen LNAPL by TBA and 1-propanol, while it facilitates dissolution of non-swollen LNAPL by ethanol. Therefore, LNAPL behavior during cosolvent flooding would be determined by partitioning type of alcohols and the presence of airflow.