Porous Media Systems Research Articles

Characterization on Temporal Evolution of Porosity, Permeability, and Reactive Specific Surface Based on Fractal Model During Mineral Dissolution

AbstractAccurately understanding the temporal changes in hydrological properties induced by mineral dissolution is of great importance for characterization on reactive transport system in porous media. A theoretical model for characterizing the temporal evolution of rock porosity, permeability, and reactive specific surface during mineral dissolution under two different scenarios is developed with introduction of fractal dimensions of porous media. In the first scenario, dissolution rate is assumed as a linear function of temporal pore size, and changes in fractal dimensions are closely related to the time. The second scenario allows for the constant fractal dimension and an inverse relation between dissolution rate and time. The proposed model is fully verified with some published literatures, and most of results show the excellent/good fit with experimental/simulated data. The validation of the proposed model is also briefly discussed, mainly affected by reactive transport regimes.

Microscale modeling of nondilute flow and transport in porous medium systems.

Nondilute transport occurs routinely in porous medium systems. Experimental observations have revealed effects that seemingly depend upon density, viscosity, velocity, and chemical activity. Macroscale models based upon averaged behavior over many pores have been relied upon to describe such systems to date, which require parametrization of important physical phenomena in material coefficients. To advance fundamental understanding of these complex systems, we examine nondilute transport from a fundamental microscale, or pore-scale, continuum modeling perspective. We approximate the solution of a model based upon the variable-density Navier-Stokes equations and a nondilute species transport equation. Known dependencies of the densities, viscosities, chemical activity, and diffusion for a salt solution on chemical composition are included in the model. Microscale model solutions are averaged to the macroscale and compared with extant experimental observations. Investigation of the effects of various physical phenomena on the microscale velocity distribution and the observed macroscale dispersion are considered using dimensional analysis and constrained simulations. Simulation results are used to explain observed experimental results in light of underlying mechanisms. Conditions under which the various physicochemical effects investigated are important are revealed.

Colloid retention and mobilization mechanisms under different physicochemical conditions in porous media: A micromodel study

Clear understanding of pore-scale mechanisms that control transport and retention of colloids in porous media at different physicochemical conditions is critical to improve design and efficient cleanup methodologies of filter beds. The objective of this work was to investigate the impact of hydrophobicity, solution ionic strength, and pH on colloid retention mechanisms in single-phase and two-phase flow in porous media systems. A series of experiments were conducted using a geometrically representative micromodel. Hydrophilic and hydrophobic colloids were dispersed in water at different solution ionic strength and pH conditions. Findings indicate that hydrophilic colloids exhibit high filtration efficiency as the colloids interact attractively with other colloids and solid-water-interface irrespective of the solution chemistry. However, for hydrophobic colloids, changes in solution chemistry significantly increase colloid retention where the colloid interaction become attractive with the increase in ionic strength and decrease in pH values. Colloids attached to the collector surfaces mobilized by the strong capillary forces induced by the moving gas-water interface and transported along with the interface. However, hydrophilic colloids redeposited on gas-water-solid interfaces or thin water films because of their greater capillary potential. Therefore, greater filtration efficiency is achieved with the hydrophilic colloids compared to the hydrophobic colloids for which the efficiency can be improved by changing the solution chemistry. Moreover, the removal efficiency by the moving gas-water interface was observed to be more for hydrophobic colloids compared to hydrophilic colloids for which the efficiency can be improved by lowering the ionic strength or increasing the pH value. This study indicates that the coupled effects of solution chemistry and colloid hydrophobicity should be taken into account while investigating efficient filtration and cleaning practices for the filter beds.

Modeling cross model non-Newtonian fluid flow in porous media

Fluids exhibiting non-Newtonian rheologies are used in a range of applications, including hydraulic fracturing, enhanced oil recovery, remediation, and industrial processes. Hydraulic fracturing in particular has received attention from environmental scientists, policy-makers, and the general public due in part to concerns about the possibility of contamination of groundwater resources by the complex and potentially harmful fluids used in the process. The non-Newtonian nature of many hydraulic fracturing fluids complicates the prediction of their movement, and precludes use of most traditional flow and transport models. To improve understanding of the flow of such fluids in porous media, a series of column experiments was conducted and a pore-scale lattice Boltzmann model (LBM) was developed, verified, and used to simulate analogous systems. Flow experiments were conducted with guar gum solutions of varying concentration and three porous media systems. The LBM was developed for transient, three-dimensional porous medium systems and included a shear rate-dependent dynamic viscosity based on the Cross rheological model. The LBM was verified using a semi-analytical solution for Cross model fluid flow, OpenFOAM simulations, and grid resolution inter-comparisons between two different solution approaches. Simulations were performed on synthetic porous medium systems produced with a sphere packing algorithm to approximate the properties of the experimental systems. The simulations were in good agreement with the experimental results, particularly for systems that exhibited the greatest non-Newtonian character. The modeling approach developed in this work provides a valuable tool for investigating relationships between pore-scale fluid flow and macroscale variables of interest for simulating movement of non-Newtonian fluids at larger scales.

Mass transfer during transient condensate vaporization: Experimental and modeling study

The gas condensate reservoirs, which are a major source of energy, usually experience an unwanted phenomenon called liquid drop-out. Gas injection as a proven effective remedy is generally employed to diminish the liquid loss. The condensate recovery by gas injection is typically estimated by assuming local equilibrium. This assumption is not valid in porous media when the limited contact area, high velocity, and low residence time are involved, particularly in near-wellbore region. In this study, we attempt to calculate mass transfer coefficient of the gas condensate systems in porous media at the transient state. Hence, a number of experiments are performed where the tests include three injection gases (CO2, N2, and CH4), three liquid types as condensate components (C5, C6, and C7), and three mean grain sizes (150–300 μm) within a wide range of gas velocity (0.00472–0.0283 cm/s). The experiments are modeled numerically and analytically based on the effluent concentrations. The obtained mass transfer coefficients are then employed to introduce new models such that Sherwood number (Sh) is correlated to Peclet (Pe) and Schmidt (Sc) numbers, and other physical/operational parameters. Based on a systematic sensitivity analysis as well as the modeling results, both analytical and numerical modeling approaches are promising and viable. The statistical parameters are calculated to be 97.13% (R2) and 0.0044 (mean squared error or MSE) for the analytical method, and 97.33% (R2) and 0.00303 (MSE) for the numerical solution, confirming the accuracy and reliability of the employed models. The mass transfer coefficients are then fitted well using three correlations with R2 values of 95.29%, 97.04%, and 96.73%, and absolute relative deviation or ARD magnitudes of 13.22%, 11.73%, and 11.44%. The new proposed correlations can be simply implemented in numerical/analytical modeling and commercial software packages to obtain the non-equilibrium mass transfer coefficients of components in the gas phase. The sensitivity analysis also reveals that condensate shrinkage has a significant effect on the amount of mass transfer and vaporization. Methane shows a relatively higher potential to strip the liquid condensate in comparison with other gases in the experiments. Among the liquid hydrocarbons, pentane has a higher tendency to evaporate into the flowing gas phase, followed by hexane and heptane. It is also found that porous system cases with larger mean grain size offer more suitable conditions for enhancement of mass transfer. The findings of this study can help to better understand the mass transfer during gas injection in gas condensate reserves under transient condition.

Dual‐Permeability Model Improvements for Representation of Preferential Flow in Fractured Clays

AbstractDual‐permeability models assume that the complete porous media system can be represented by two different interacting subsystems: the matrix and the fracture pore domain. For some soils like fractured clays, the fracture domain may be empty, which makes its physical behavior differ significantly from capillary flow. Our main hypothesis is that this kind of preferential flow systems can be represented as a dual‐permeability porous media by adapting the 2‐D formulation and initial conditions of the fracture domain and the mass exchange function. The performance of the dual‐permeability finite element solution was evaluated by comparing it to its equivalent 2‐D explicit fracture single‐permeability finite element model. The results of the numerical experiments show that the 2‐D dual‐permeability concept allows to simulate preferential flow in soils with fractures. This was achieved by improving the parameterization of the Mualem‐van Genuchten soil water retention curve of the fractured domain and the hydraulic conductivity exchange function for the first‐order mass exchange term for fractured soils. The exchange term hydraulic conductivity evaluated at the minimum value of the pressure heads of the two domains considerably improved the results as compared to using the well‐established arithmetic average of the hydraulic conductivity values from both domains. These two improvements of the dual‐permeability model approach are especially useful in cases where preferential flow systems consist mostly of relatively large, noncapillary fractures and macropores.

Physico-chemical and dielectric parameters for the monitoring of carbon sequestration in basalt and silica media

Abstract Currently, there are concerns about the safety of carbon sequestration in the geological media. To assuage this concern, scientists and engineers have the tasks to demonstrate fool-proof and comprehensive techniques that can monitor the movement, or otherwise, concentration of the injected CO2 in the subsurface. In this work, well-defined laboratory experiments were used to demonstrate the key physico-chemical characteristics and dielectric parameters that are useful in monitoring carbon sequestration sites. The porous materials used were basalt and silica sand samples to demonstrate the possibility of CO2 injection into different media. To simulate the resident fluids, distilled and brine water samples were used in separate experimentations. Also, the pressures and temperatures were chosen to correspond to different geological depths which are relevant for CO2 injection. The pH, bulk electrical conductivity ( σ b ) and bulk dielectric permittivity ( e b ) of the system were measured for the two different media. On one hand, the decrease in pH was clearly observed in both the basalt and silica sand after the exposure to CO2. On the other hand, σ b and e b increased as CO2 was injected. Our results further revealed a higher ion mobilisation​ potential in basalt medium than that in silica sand. This results in lower pH and higher electrical conductivity in the basalt medium than the silica medium. Thus, a simultaneous measurement of pH, σ b and e b are proposed as a multiparameter approach to monitor CO2 leakage from the storage reservoir. As far as we are aware, this is the first work in the open literature that reports simultaneous dielectric and electrical behaviours of CO2 –water–porous media system for basalt porous medium in connection with carbon sequestration.

Magnetic resonance imaging of enhanced mobility of light non aqueous phase liquid (LNAPL) during drying of water wet porous media

Visualization of NAPLs in multiphase systems in porous media is important for determining contaminant transport in the environment. In this study, magnetic resonance imaging (MRI) was used to confirm the recent observations of mobilisation of a light non aqueous phase liquid (LNAPL) trapped in wet sand under natural drying conditions of the wet porous medium. Visualization of LNAPL (motor oil) and water mobility during the drying of wet glass beads (0.5 mm) in a cylindrical glass column (15 mm ID, 45 mm long) was obtained using spin echo-based NMR microimaging performed at 500 MHz, corresponding to a field of ca. 11.75 T. Sagittal and axial images of LNAPL and water in the porous medium were obtained at a spatial resolution of 59 μm/pixel at different time intervals. A rise of 15–20 mm was observed in the presence of evaporation of water as compared to a 2–3 mm rise in the absence of evaporation in a time span of about 1400 min. The spatio-temporal MRI scans of the water and LNAPL in the glass column reveals that LNAPL rise occurs when the water evaporation front reaches the LNAPL layer. This implied that the enhanced LNAPL rise was strongly linked to the process of water evaporation. A linear correlation of the MRI signal intensities of LNAPL and water with reference to different saturation levels of LNAPL and water in the porous media was obtained. This calibration information was used to quantify the saturation levels of the LNAPL and water during the drying process. These findings show the application of non-invasive techniques such as MRI in quantifying and understanding the mechanism of fate and transport of LNAPLs in porous media, towards effective environmental quality assessment.

Geoelectrical characterisation of CO2\u2013water systems in porous media: application to carbon sequestration

Carbon sequestration is a promising method for the reduction of carbon dioxide (CO2) emissions as it permits the storage of compressed CO2 in the subsurface. The carbon sequestration sites must be monitored to detect potential leaks; one possible method involves the monitoring of geoelectrical properties such as electrical conductivity (σb) and dielectric constant (εb). This investigation focuses on using a time domain reflectometry (TDR) sensor to determine the influence of different factors on the measurements of the electrical conductivity (σb) and dielectric constant (εb) of a porous rock reservoir in relation to the soil water saturation (Sw). The factors investigated were presence of surfactant, salt concentration, pH and rock type which are unique to a given storage site. A number of dynamic two-phase flow experiments were performed using gaseous CO2. It was found that salt concentration, rock type and presence of a surfactant had a notable effect on the σb–Sw and εb–Sw relationships. Higher salt concentrations were found to give higher values for σb and εb for given Sw values. Limestone was found to result in the highest values of both σb and εb for any given Sw, followed by silica and basalt samples. The presence of a surfactant resulted in higher values for σb at higher Sw values and lower values for σb at lower Sw values compared to the case when no surfactant was present. Surfactant presence also resulted in lower values for εb at given Sw values. Initial pH values (with silica sand) were found to have no significant effect on the σb–Sw and εb–Sw relationships. The measurements of σb and εb indicate that the use of TDR presents a viable monitoring option. Furthermore, statistical analysis using non-linear regression was carried out on the experimental results and the model shows a good reliability in the prediction of the monitoring process in geological carbon sequestration.

Experimental investigation on foam formation through deformable porous media

AbstractFoam formation in porous media is a topic of growing scientific and industrial interest due to its range of applications, from daily life consumer products to oil recovery. Despite the work done so far on foams flowing through complex structures, such as rigid porous media, this subject still needs to be fully elucidated. An additional complexity to the problem arises when the porous medium is deformable, a situation which has only been faced, to our knowledge, from a modelling point of view. In this work, the investigation of foam formation in deformable porous media is carried out by using commercial sponges as a deformable porous media system, with special emphasis on the effect of confinement on foam bubble size distribution. Foam is formed by wetting the sponge with an aqueous surfactant solution and then squeezing the sponge either between two glass cover slides or between a plastic net and a cover slide. Our experimental data reveal that the latter system allows the formation of drier foams (ie, with lower liquid fraction, fL < 0.3), more similar to the ones obtained in dish‐washing applications. Moreover, the effect of sponge type, in terms of material and microstructure, on final foam is presented. Our results are of potential interest for the optimization of foams in complex structures, such as in deformable porous media.

Impact of time-dependent wettability alteration on the dynamics of capillary pressure

Wettability is a pore-scale property that has an important impact on capillarity, residual trapping, and hysteresis in porous media systems. In many applications, the wettability of the rock surface is assumed to be constant in time and uniform in space. However, many fluids are capable of altering the wettability of rock surfaces permanently and dynamically in time. Experiments have shown wettability alteration (WA) can significantly decrease capillarity in CO2 storage applications. For these systems, the standard capillary-pressure model that assumes static wettability is insufficient to describe the physics. In this paper, we develop a new dynamic capillary-pressure model that takes into account changes in wettability at the pore-level by adding a dynamic term to the standard capillary pressure function. We assume a pore-scale WA mechanism that follows a sorption-based model that is dependent on exposure time to a WA agent. This model is coupled with a bundle-of-tubes (BoT) model to simulate time-dependent WA induced capillary pressure data. The resulting capillary pressure curves are then used to quantify the dynamic component of the capillary pressure function. This study shows the importance of time-dependent wettability for determining capillary pressure over timescales of months to years. The impact of wettability has implications for experimental methodology as well as macroscale simulation of wettability-altering fluids.

Unsuitability of the Beavers–Joseph interface condition for filtration problems

Coupled free-flow and porous-medium systems appear in a variety of industrial and environmental applications. Fluid flow in the free-flow domain is typically described by the (Navier–)Stokes equations while Darcy’s law is applied in the porous medium. The correct choice of coupling conditions on the fluid–porous interface is crucial for accurate numerical simulations of coupled problems. We found out that the Beavers–Joseph interface condition, which is widely used not only for fluid flow parallel to the porous layer but also for filtration problems, is unsuitable for arbitrary flow directions. To validate our statement, we provide several examples and compare numerical simulation results for the coupled Stokes–Darcy problems to the pore-scale resolved models. We show also that the Beavers–Joseph parameter cannot be fitted for arbitrary flow directions.

A multi-layer reduced model for flow in porous media with a fault and surrounding damage zones

In this work, we present a new conceptual model to describe fluid flow in a porous media system in presence of a large fault. Geological faults are often modeled simply as interfaces in the rock matrix, but they are complex structures where the high strain core is surrounded by the so called damage zones, characterized by the presence of smaller fractures which enhance the permeability of the medium. To obtain reliable simulation outcomes, the damage zone as well as the fault, have to be accurately described. The new model proposed in this work considers both these regions as lower dimensional and embedded in the rock matrix. The model is presented, analyzed, and tested in several configurations to prove its robustness and ability to capture many important features, such as high contrast and heterogeneity of permeability.

A mathematical model of the non-stationary filtration process for oil-supercritical CO2 system in a homogeneous porous medium under various modes of oil displacement

The phase diagram of the system “transformer oil-supercritical CO2” is built. The modes of miscible and microbubble displacement of oil are determined. Oil was displaced by carbon dioxide in a supercritical state on isotherms 313 and 333 K in the pressure range up to 12 MPa at the experimental bench created by the authors. New data have been obtained on the coefficient of oil displacement by supercritical CO2 from a model of a homogeneous oil reservoir in a miscible and micro-bubble mode of supercritical CO2 filtration. It was revealed that the miscible regime of oil displacement by supercritical CO2 has the greatest technological efficiency. For the region of a mixed filtration regime, a mathematical model was created and solved for the process of filtering the unsteady flow of “supercritical CO2-oil” in a homogeneous terrigenous porous medium in the pressure range up to 12 MPa, temperatures up to 333 K, the calculated curve agrees with the experimental data on the oil displacement coefficient. The convergence and stability of the difference scheme of the computational process is ensured. It was found that in the transition region of supercritical CO2 filtration on the boundary curve in the phase diagram and in the region of microbubble filtration of supercritical CO2, the process of oil displacement is more intense, which is associated with the appearance of a supercritical sublayer on the pore surface, which leads to slipping of the fluid inside the pore. For the transition-filtering region on the boundary curve in the phase diagram and in the region of the microbubble displacement of oil by supercritical carbon dioxide, a method for increasing technological efficiency is proposed based on the injection of supercritical CO2 and water rims to prevent the transition of microbubble carbon dioxide to the free phase.

Effect of Hydraulic Resistivity on a Weakly Nonlinear Thermal Flow in a Porous Layer

Heat and mass transfer through porous media has been a topic of research interest because of its importance in various applications. The flow system in porous media is modelled by a set of partial differential equations. The momentum equation which is derived from Darcy’s law contains a resistivity parameter. We investigate the effect of hydraulic resistivity on a weakly nonlinear thermal flow in a horizontal porous layer. The present study is a realistic study of nonlinear convection flow with variable resistivity whose rate of variation is arbitrary in general. This is a first step for considering more general problems in applications that involve variable resistivity that may include both variations in permeability and viscosity of the porous layer. Such problems are important for understanding properties of underground flow, migration of moisture in fibrous insulations, underground disposal of nuclear waste, welding process, petrochemical generation, drug delivery in vascular tumor, etc. Using weakly non-linear procedure, the linear and first-order systems are derived. The critical Rayleigh number and the critical wave number are obtained from the linear system using the normal mode approach for the two-dimensional case. The linear and first-order systems are solved numerically using the fourth-order Runge-Kutta and shooting methods. Numerical results for the temperature are presented in tabular and graphical forms for different resistivities. Through this study, it is observed that a stabilizing effect on the dependent variables occurs in the case of a positive vertical rate of change in resistivity, whereas a destabilizing effect is noticed in the case of a negative vertical rate of change in resistivity. The results obtained indicate that the convective flow due to the buoyancy force is more effective for weaker resistivity.

Dynamic and static gelation behavior of phenol formaldehyde resin gel system in ampoule bottles and porous media

The dynamic and static gelation process in porous media of the phenol formaldehyde resin gel was studied for successful application in conformance control and water shutoff. Shear rate was the most important factor affecting the dynamic gelation in porous media. Compare to static gelation in ampoule bottles and in porous media, the dynamic gelation time in porous media was extended by 2–6 times. The ability of migration and plugging after dynamic gelation was controlled by system concentration. The porous media permeability was the key factor for dynamic gelling time and strength. The quantitative relationship equation was established between dynamic gelling strength and permeability to choose the appropriate permeability for polymer gel treatment.

Asymptotic Stability of Solutions to the Porous Media System with Hysteresis

The long time behavior of solutions to the autonomous PDE system describing fluid diffusion in a viscoelastic porous medium with capillary hysteresis is studied with homogeneous Dirichlet conditions for the displacement of the solid and homogeneous Neumann boundary conditions for the capillary pressure. Although the set of possible equilibria is very large, a detailed investigation of the hysteresis memory dynamics shows that all global solution trajectories converge to an equilibrium in the state space of all admissible memory configurations as time tends to infinity.

Homogenization theory with multiscale perturbation analysis for supervised learning of complex adsorption-desorption process in porous-media systems

Engineered and natural adsorbers, which undergo both adsorption and desorption mechanisms during operations, are dominant treatment technologies to remove difficult contaminants from influent sources to safeguard supplies of potable water to local communities. The slow net adsorption, i.e. adsorption rate greater than desorption rate, of contaminants over long periods of operational time contributes to chemical clogging inside an operating adsorber which complexity continues to be difficult for engineers to quantify, particularly on the adsorption and desorption processes coexisting during their near-equilibrium concentration state which builds towards its exhaustion stage for maintenance purpose.In this study, we leverage on the homogenization theory with the multiscale perturbation analysis to develop an engineering model which encapsulates the complex adsorption-desorption mechanics in adsorbers. The desired model contributes towards the primary objective of having the required capabilities to perform predictive maintenance of adsorbers to garner operational benefits, especially for large-scale systems. The hybrid analytical approach systematically derives a unique homogenized representation which contains an unknown reaction rate parameter responsible for the adsorption-desorption processes taking place over a significantly long period of time leading to the adsorber’s exhaustion stage. Dimensional analysis is then carried out to express the reaction rate parameter as a function of the known physical parameters to predict the transient variations in an adsorber’s effluent concentration during its gradual build-up towards exhaustion.Measured data from both the literature and our own adsorber experimental runs are then acquired to train and validate the model’s predictive capability, via supervised learning methods, which yields an average error deviation of 10 % or less for the optimal training period determined. Finally, we demonstrate quantitatively how the model can be useful to engineers to estimate: (a) the timing for an operating adsorber to reach its exhaustion stage; and (b) the associated Damköhler number, adsorption and desorption coefficients and etc., responsible for the concerned adsorber’s effluent concentration profile for the varying types of contaminants removed.

Thermal and chemical enhanced recovery of heavy chlorinated organic compounds in saturated porous media: 1D cell drainage-imbibition experiments

Chemical and thermal enhanced recovery of pure heavy chlorinated organic compounds (DNAPL; dense non-aqueous phase liquids) was investigated by using lab-scale 1D cells. Temperature was increased to reduce DNAPL viscosity (and hence increase its mobility), while surfactant was added to decrease capillary forces involved in the entrapment of DNAPL in porous media. Laboratory scale experiments, based on mass balance and indirect monitoring methods (i.e., permittivity, electrical resistivity and optical density), were conducted to quantify the effects of these enhancements. Heating the DNAPL up to 50 °C decreased its viscosity by a factor of two. The addition of a surfactant; i.e., Sodium Dodecyl Benzene Sulfonate (SDBS), at its Critical Micelle Concentration (to prevent DNAPL solubilization), decreased interfacial tensions by a factor of 12. Drainage-imbibition experiments performed in 1D cells provided retention curves (capillary pressure as a function of water saturation) of a two-phase (DNAPL-water) system in experimental glass bead porous media. The observed reduction of residual saturation (Srn) obtained with SDBS was 28% for 0.5 mm-diameter glass beads (GB) and 46% for 0.1 mm GB. No significant decrease in Sm was observed with thermal enhancement. The van Genuchten – Mualem model was found to satisfactorily reproduce the measured retention curves. Indirect measurements of water saturations (Sw) showed that: i. measured permittivities were very close to values modeled with the Complex Refractive Index Model (CRIM); ii. Archie's Law was less successful in reproducing measured electrical resistivities; iii. optical densities provide accurate estimations of Sw. At field scale, the combined monitoring of electrical resistivity (which provides a global picture) and permittivity (which yields locally precise but spatially limited information) is expected to significantly improve the collection of information on residual saturations Srn.

Global higher integrability of weak solutions of porous medium systems

We establish higher integrability up to the boundary for the gradient of solutions to porous medium type systems, whose model case is given by \begin{document}$ \begin{equation*} \partial_t u-\Delta(|u|^{m-1}u) = \mathrm{div}\,F\,, \end{equation*} $\end{document} where $ m>1 $. More precisely, we prove that under suitable assumptions the spatial gradient $ D(|u|^{m-1}u) $ of any weak solution is integrable to a larger power than the natural power $ 2 $. Our analysis includes both the case of the lateral boundary and the initial boundary.