Mass Transfer In Porous Media Research Articles

Integration of vorticity–velocity formulation in a lattice Boltzmann method for porous media

A lattice Boltzmann method (LBM) is proposed to address the two-dimensional macroscopic equations of velocity–vorticity for porous media in incompressible flows. The macroscopic equations of two-dimensional porous media using the representative element volume scale approach, employing various models, are shown. The momentum equations are transformed and presented in the velocity and vorticity format. Additionally, the energy and concentration equations are thoroughly examined. Subsequently, the LBM is presented to restore the dimensional macroscopic equations of the velocity–vorticity format for various porous models, accounting for external forces. The paper provides proof and derivations of the equations for the LBM, which are then demonstrated and discussed. The suggested approach is evaluated across a variety of well-established benchmark examples within the realm of fluid flow, heat, and mass transfer in porous media. Importantly, the LBM approach significantly reduces computational time compared to previous methods in the field by eliminating pressure in the momentum equation, thereby reducing the number of unknown variables and transforming the equation into a convection–diffusion form. This modification leads to a linear equilibrium distribution function and a noteworthy decrease in computational costs.

Model Validation and Sensitivity Analysis of Coupled Non‐Equilibrium Heat and Mass Transfer in Porous Media With Application to Evaporation From Bare Soils

AbstractMathematical models in engineering play an important role in understanding and predicting the behavior of a system. A mechanistic coupled liquid water, water vapor and heat transfer model incorporating kinetic phase change accounting for real‐time interfacial area between water and gas phases was developed to predict coupled subsurface processes and evaporation (drying) rates from bare soils. To enhance the model capability to predict evaporation rates, the air resistance associated with the viscous sublayer was implemented in energy and mass exchange across the soil‐air interface (the land‐atmosphere boundary condition [BC]). The atmospheric stability condition was also considered in the calculation of sensible heat and vapor fluxes at the ground surface. This comprehensive model was validated against measured field data from bare soil test plots from a green roof study, during temperate summer conditions in Canada, demonstrating that the model captured the main coupled processes in the subsurface of bare soil during drying periods. A sensitivity analysis was performed to determine the importance of various components of the comprehensive model. Removal of viscous sublayer resistance in the vapor transfer BC resulted in poorer predictions of evaporation (drying) rates. Incorporating the atmospheric stability function accounting for real‐time atmospheric conditions did not improve the predictive capability for the simulated drying events compared to the case when only a neutral atmospheric condition was implemented. Neglecting heat transfer associated with hydrodynamic dispersion of water vapor in the subsurface had limited impact on subsurface temperature predictions.

Evaluation of Dual Domain Mass Transfer in Porous Media at the Pore Scale.

Dual-porosity models are often used to describe solute transport in heterogeneous media, but the parameters within these models (e.g., immobile porosity and mobile/immobile exchange rate coefficients) are difficult to identify experimentally or relate to measurable quantities. Here, we performed synthetic, pore-scale millifluidics simulations that coupled fluid flow, solute transport, and electrical resistivity (ER). A conductive-tracer test and the associated geoelectrical signatures were simulated for four flow rates in two distinct pore-scale model scenarios: one with intergranular porosity, and a second with an intragranular porosity also defined. With these models, we explore how the effective characteristic-length scale estimated from a best-fit dual-domain mass transfer (DDMT) model compares to geometric aspects of the flow field. In both model scenarios we find that: (1) mobile domains and immobile domains develop even in a system that is explicitly defined with one domain; (2) the ratio of immobile to mobile porosity is larger at faster flow rates as is the mass-transfer rate; and (3) a comparison of length scales associated with the mass-transfer rate (Lα ) and those associated with calculation of the Peclet number (LPe ) show LPe is commonly larger than Lα . These results suggest that estimated immobile porosities from a DDMT model are not only a function of physically mobile or immobile pore space, but also are a function of the average linear pore-water velocity and physical obstructions to flow, which can drive the development of immobile porosity even in single-porosity domains.

State-of-the-art in the mechanistic modeling of the drying of solids: A review of 40 years of progress and perspectives

This review paper was written on the occasion of the 40th anniversary of the Drying Technology Journal. Interestingly, most of the progress made in the domain of drying modeling and simulation has occurred over the last 40 years. Indeed, 40 years ago, the comprehensive formulation of coupled heat and mass transfer in porous media was available; however, its potential use for computational simulation was only in its nascent stage. This is therefore an ideal time span in which to take a full historical context, to present the state-of-the-art and to give insights into its future trajectory. All aspects are deliberately presented in a pedagogical manner with many illustrations to make the text accessible to young scientists. However, for the benefit of experts, detailed formulations are provided in the annexes. The main points addressed in this work include: The description of the comprehensive macroscopic formulation, An historical perspective of the progress made in computational simulation, The contribution of modeling in parameter characterization, The mechanical aspects of drying: strain and stress induced by drying, including the case of large deformations, The impact of non-local equilibrium, The promising domain of the digital twin in parameter tuning and control/command.

Numerical pore-scale simulation of propane injection for heavy oil displacement processes

Solvent injection processes offer a promising alternative to steam-based techniques for heavy oil recovery. Multiple mass transfer mechanisms, including interphase mass transfer, diffusion, and convection, would affect the process efficiency and recovery performance. Understanding the mass transfer processes in solvent-based heavy oil recovery processes is fundamental to accurately model the solvent/heavy oil interfacial dynamics and design efficient solvent recovery methods.A robust simulation framework based on the level-set method is proposed in this study to simulate the injection of a vaporized solvent (i.e., propane) into a bitumen-oil system. A pore-scale two-phase multi-component flow simulation is constructed. The solution of the Navier-Stokes equation is coupled with the level-set formulation to track the fluid/fluid interface; a concentration jump is applied to simulate the mass transfer across the gas-liquid interface. The model is validated against several bulk fluid systems where analytical solutions can be derived. Next, the model is tested using a more complex pore-scale system; a macro-scale mass transfer coefficient is estimated based on the linear mass transfer model. The values are compared to those described in the literature.The level-set simulation framework is useful for simulating multiphase multi-component interphase mass transfer in porous media. It serves as a tool to examine these different mechanisms' interactions and relative importance under various conditions. The proposed simulation framework can be readily applied to studying other subsurface processes, including carbon dioxide storage and groundwater flow.

Effect of Pore Space Stagnant Zones on Interphase Mass Transfer in Porous Media, for Two-Phase Flow Conditions

Interphase mass transfer is an important solute transport process in two-phase flow in porous media. During two-phase flow, hydrodynamically stagnant and flowing zones are formed, with the stagnant ones being adjacent to the interfaces through which the interphase mass transfer happens. Due to the existence of these stagnant zones in the vicinity of the interface, the mass transfer coefficient decreases to a certain extent. There seems to be a phenomenological correlation between the mass transfer coefficient and the extent of the stagnant zone which, however, is not yet fully understood. In this study, the phase-field method-based continuous species transfer model is applied to simulate the interphase mass transfer of a dissolved species from the immobile, residual, non-aqueous phase liquid (NAPL) to the flowing aqueous phase. Both scenarios, this of a simple cavity and this of a porous medium, are investigated. The effects of flow rates on the mass transfer coefficient are significantly reduced when the stagnant zone and the diffusion length are larger. It is found that the stagnant zone saturation can be a proxy of the overall diffusion length of the terminal menisci in the porous medium system. The early-stage mass transfer coefficient continuously decreases due to the depletion of the solute in the small NAPL clusters that are in direct contact with the flowing water. The long-term mass transfer mainly happens on the interfaces associated with large NAPL clusters with larger diffusion lengths, and the mass transfer coefficient is mainly determined by the stagnant zone saturation.

Discrete Heaped Model of Tobacco Strips Drying and Characteristics Analysis of Heat and Mass Transfer

To accurately study the drying characteristics of tobacco strips in the process of redrying, a discrete heaped physical model of tobacco strips is built. Based on this model, a convective drying multiphase porous media model of the heaped tobacco strips is established, which considers the binary diffusion and transport of vapor inside and outside the tobacco leaf. The model is solved using COMSOL Multiphysics, and the accuracy of the model is verified by experiments. The changes in hot air velocity, vapor and moisture content, and evaporation rate in heaped tobacco strips with different thicknesses are analyzed. The results show that: it is feasible to study the drying characteristics of tobacco strips in redrying using a discrete heaped model; there were significant differences in water content, evaporation rate, and temperature in different regions of heaped tobacco strips; the increase in heaping thickness will significantly reduce the uniformity of heat and mass transfer of tobacco strips in the process of convection drying. This model can provide a reference for the study of heat and mass transfer in porous media, such as tobacco strips in the heaping state.

Investigation of supercritical CO2 mass transfer in porous media using X-ray micro-computed tomography

Understanding the mass transfer of CO2 into formation brine both qualitatively and quantitatively is important for improving the security of geologic carbon sequestration. In this study, quasi-dynamic X-ray micro-computed tomographic (MCT) imaging was used to track the time-evolution of supercritical CO2 (scCO2) clusters in a sandstone throughout brine injection. A cluster-matching workflow enabled the identification of depletion, merging, and snap-off of the scCO2 clusters, and subsequently the mass transfer coefficient of individual scCO2 clusters was found to range between 3.0×10−5 and 3.5×10−4 mm/s. The macroscopic average mass transfer coefficient was estimated as 1.4×10−4 mm/s. For application to geologic carbon sequestration, these values give an indication of the range of mass transfer coefficients that may be expected for similar state and flow conditions. With the macroscopic average mass transfer coefficient evaluated, we back-calculated the in-situ CO2 concentration field for brine, which provides quantitative insight of the distribution of dissolved CO2 in the sample. Despite slow injection rate (Ca = 10−7), mobilization of small scCO2 clusters was also observed, and was attributed to the combined effect of incomplete dissolution of snapped-off clusters and the reduction in the fluid–fluid interfacial tension (IFT) due to the high local CO2 concentration in brine accompanying scCO2 dissolution. This highlights the coupling of dissolution and mobilization processes and demonstrates the need to understand these interlinked dynamics to improve CO2 storage in geological formations.

An upwind generalized finite difference method (GFDM) for meshless analysis of heat and mass transfer in porous media

In this paper, an upwind GFDM is developed for coupled heat and mass transfer problems in porous media. GFDM is a meshless method that can obtain the difference schemes of spatial derivatives by using Taylor expansion in local node influence domains and the weighted least squares method. The first-order single-point upstream scheme in the FDM/FVM-based reservoir simulator is introduced to GFDM to form the upwind GFDM, based on which a sequential coupled discrete scheme of the pressure diffusion equation and the heat convection-conduction equation is solved to obtain pressure and temperature profiles. This paper demonstrates that this method can be used to obtain the meshless solution of the convection–diffusion equation with a stable upwind effect. For porous flow problems, the upwind GFDM is more practical and stable than the method of manually adjusting the influence domain based on the prior information of the flow field to achieve the upwind effect. Two types of calculation errors are analyzed, and three numerical examples are implemented to illustrate the good calculation accuracy and convergence of the upwind GFDM for heat and mass transfer problems in porous media and indicate the increase in the radius of the node influence domain will increase the calculation error of temperature profiles. Overall, the upwind GFDM discretizes the computational domain using only a point cloud that is generated with much less topological constraints than the generated mesh, but achieves good computational performance as the mesh-based approaches, and therefore has great potential to be developed as a general-purpose numerical simulator for various porous flow problems in domains with complex geometry.

Thermal desorption characteristics of the adsorbate in activated carbon based on a two-dimensional heat and mass transfer model

• A multiphase model of heat and mass transfer in porous media is established. • The multiphase model is validated to simulate the thermal desorption behavior of activated carbon adsorption. • A simplified evaporation rate formula is proposed, and the agreement between the model and the experimental results are verified. • The effect of high thermal conductivity activated carbon on thermal regeneration time is analyzed. • The effects of polar and non-polar adsorbates on model accuracy are analyzed. Thermal desorption of adsorbate in activated carbon is the main part in the thermal regeneration process of spent activated carbon, and previous studies have carried out a series of numerical simulations on it. However, since activated carbon is a porous medium, the heat and mass transfer in activated carbon is different from that in solid. In this paper, a multiphase model of heat and mass transfer in porous media was constructed to study the thermal desorption characteristics of adsorbate in spent activated carbon. In addition, a simplified evaporation rate formula is proposed in this paper, and the agreement between the simulation and the experimental results is verified. When the surroundingtemperature is less than 673.15 K, increasing the surrounding temperature has a significant effect on reducing the thermal desorption time of the adsorbate. Using activated carbon with a thermal conductivity of 5 W / m ∙ K can save about 40% of energy consumption. The model established in this paper can accurately simulate the thermal desorption of adsorbate in activated carbon, which is helpful to deeply understand the mechanism of activated carbon thermal regeneration. In engineering practice, the model can provide technical support for optimizing the thermal regeneration process of spent activated carbon and reducing energy consumption in a targeted manner.

Experimental assessment of the similarity law for a heat conduction problem

Similarities are mathematical laws, which are based on the dimensionless formulation of the governing equation of a physical phenomenon. Consequently, a set of characteristic dimensionless numbers is obtained. Similarities aim, via these numbers, to find equivalences between particular configurations. This approach is widely adopted, especially in fluid and aerodynamic problems. In the building context, the phenomena of heat and mass transfer in porous media occur with slow kinetics. Thus, similarities can be employed to reduce the duration of experimental campaigns to characterize material properties. These laws were investigated here in the case of a heat transfer problem through an experimental campaign. Two equivalent configurations were submitted to a heat stress. Temperatures inside materials were measured and compared to assess the validity of thermal similarity. A complete evaluation of uncertainty propagation was then carried out. Uncertainties related to the sensor position, its response time, the omission of mass transfer, the sensor systematic accuracy, the random measurement aspect, the one-dimensional transfer hypothesis and the boundary condition modeling were evaluated. The comparison of both configurations was carried out based on the confidence interval of both measurements. The results showed a good agreement between the reference and reduced experiment. On the basis of these findings, similarities were experimentally verified within a margin of discrepancy that was justified. Thus, they can be adopted in heat transfer experiments in order to identify equivalent configurations that are easier to conduct.

Influence of distribution characteristics of residual DNAPL on mass transfer in porous media under ethanol co-solvent flushing

The remediation of residual dense non-aqueous phase liquid (DNAPL) enhanced by co-solvents or surfactants has been investigated in many studies. Nevertheless, the influences of the residual DNAPL distribution characteristics in a porous medium, and the concentrations of the co-solvents or surfactants on the mass transfer rate of DNAPL remain relatively unexplored. For this reason, existing empirical models neglect the effects of the heterogeneity in the distribution of residual DNAPL, and the compositions of flushing floods on the DNAPL mass transfer rate. In this work, a two-dimensional micro-model is used to quantify the lumped mass transfer rate coefficients of PCE. Results show that increasing the injection rate and the ethanol concentration of flushing floods improves the mass transfer rate of PCE. Moreover, this micro-model allows for accurate quantification of variations in morphological characteristics of PCE blobs. The relative standard deviation σ of residual PCE saturation, as an indicator of morphological characteristics of PCE blobs, varies with decreasing saturation. Standard saturation S0 is used to represent the heterogeneity of residual PCE distribution. The more heterogeneous the PCE distribution, the larger the S0, and the slower the mass transfer rate. According to the variation of relative standard deviation σ with saturation, the PCE dissolution process can be divided into three stages, where the strong convection, weak convection, and diffusion within a limited distance are the primary controlling mechanisms for PCE mass transfer, respectively. Based on our study, a new empirical model, considering the distribution characteristics of residual PCE and the ethanol concentrations, is proposed to predict the PCE mass transfer process dominated by different mass transfer mechanisms in different dissolution stages.

Experimental verification of permeability and inertial resistance coefficient model in the goaf

ABSTRACT Numerical simulation is an important method of studying the flow, temperature, and concentration fields in the goaf. In a simulation, the permeability and inertial resistance coefficient are the key factors. For the verification of goaf permeability model, scholars usually use field data for verification. However, the site conditions of coal mine are complex, and the gas emission and air leakage in the goaf are difficult to control, which will lead to inaccurate verification of permeability model. Therefore, this paper verifies the goaf permeability model under experimental conditions, which can ensure that the experimental conditions are consistent with the numerical simulation conditions and realize the accurate verification of the model. An experimental scenario of a thermodynamic disasters in the goaf can be built, based on gas flow, and heat and mass transfer in porous media. The permeability and inertial resistance coefficient models can then be experimentally verified. Experimental results show that methane concentration increases with increased distance from the working face, hence the methane concentration in the return roadway side is higher than that in the intake roadway side. As distance from the coal seam floor increases, the methane concentration shows a downward trend. After releasing methane from the floor for 120 min, the concentration field inside the goaf stabilizes; therefore, coal spontaneous combustion experiments are started after a 120 minute lapse time period. In a numerical simulation, the goaf is the porous media seepage model, and the boundary conditions of the numerical model are set according to experimental conditions. The numerical simulation results concurred well with the experimental results; verifying the suitability of the authors’ proposed goaf permeability and inertial resistance coefficient model.

A Fractal Model for Thermal Dispersion Coefficients of Porous Media

The thermal dispersion coefficient is an important parameter to characterize heat and mass transfer in porous media, which is related to the physical properties of fluid and the structure of porous media. The pore-throat structure model for fractal porous media was established, and the local head loss and the velocity dispersion effect were studied for the fluid changing from the turbulent state to the laminar state around the pore-throat structure. The thermal dispersion coefficient formula was derived under the influences of the micropore-throat structure and the velocity dispersion effect. The results show that, the thermal dispersion coefficient is directly proportional to the pore-throat ratio, the number of pore-throat structures and the tortuous fractal dimension, and is inversely proportional to the porosity and the area fractal dimension. Furthermore, in the range of 1~150, the pore-throat ratio has a significant influence on the velocity dispersion effect, and the fluid has a local head loss around the pore-throat structure, which leads to an enhancement of the velocity dispersion effect and an increase of the thermal dispersion coefficient.

Effects of Dissolution Fingering on Mass Transfer Rate in Three‐Dimensional Porous Media

AbstractDissolution mass transfer from the trapped phase to the flowing phase in porous media occurs in various hydrogeology processes. One of the important phenomena is dissolution fingering and its effect on dissolution mass transfer. In this work, dissolution mass transfer in porous media with various particle sizes and distribution was investigated in pore scale and meso‐scale by using X‐ray microcomputed tomography. The specific interfacial area and mass transfer coefficient were measured by following the representative elementary volume concept, and the effect of dissolution fingering was evaluated. Linear instability theory was used for the prediction of dissolution finger width () at the onset of dissolution fingering. Although dissolution fingering tends to develop when the porous media container diameter () is smaller than half of , its effect on mass transfer coefficient starts to occur when is larger than the whole . Starting this point, dissolution fingering decreases the mass transfer coefficient by three times. For validation, an additional experiment with a larger porous media container size was performed, and three dissolution fingers were successfully observed. Their size was found to be comparable with the theoretical prediction based on linear instability theory.

Study on the mass and heat transfer of gas-liquid two-phase flow in the porous media based on the 3D reconstruction model

In the study, carbon fiber as porous medium, polycarbosilane-xylene solution and air as fluid, the heat and mass transfer in porous media was investigated. CT images of micro pores were obtained by applying Micro-CT technology. Based on the reconstruction model, 3D structure reconstruction was carried out. The surface tension model and contact angle model were introduced to establish the CFD model for simulation, which was verified by experiments. The effects of feed pressure P and liquid viscosity μ on the mass and heat transfer were systematically studied. It was found that under different P, the liquid holdup α, average temperature T and heat Q absorbed by liquid phase increase with time until stable. The larger the P, the smaller the stable values of T and Q. When μ was larger, the breakthrough time was longer, and the time for T and Q to reach stable values was longer.

Comparison of Suction/Injection Effect on Flow, Heat and Mass Transfer in Porous Media Using a Combined Similarity-Numerical Solution

This investigation deals with a comparison of suction/injection effect on flow, heat and mass transfer in porous media using a combined similarity-numerical solution. With this method of transformation, the governing transport PDEs are transformed into ODE and then solved numerically. The study reveals that suction/injection effect is more pronounce on the velocity distribution of a creeping flow (Darcy flow). The Darcy-Forchheimer flow has the steepest velocity curves due to non-linearity and has higher skin friction, heat and mass transfer rate when compared to the other porous media investigated.

Numerical modeling on hydrate formation and evaluating the influencing factors of its heterogeneity in core-scale sandy sediment

Natural gas hydrate (NGH) has been regarded as a fossil fuel reserve for the future on account of its tremendous potential. The numerical modeling on NGH formation/dissociation mechanism contributes to better understanding its accumulation and distribution feature, and optimizing the development program. This paper aims to develop a new simulator for the NGH formation in the core-scale sandy sediments based on the computational fluids dynamic (CFD) methods. The mathematical model is established based on the kinetic reaction model of hydrate formation, the permeability reduction model by the NGH, model of heat and mass transfer in porous media. The hydrate formation model is programmed by C language, and used as a subroutine for Fluent software which is adopted to solve the governing equations of the multiphase flow. The simulator scheme is verified by comparison with the experiment and numerical simulation in literature. What's more, this study reproduces the same fluctuant tendency of temperature as the experiment during the 1.0 h–2.0 h for the first time. Different reaction surface models of NGH formation/dissociation are evaluated by the developed codes. The effects of the reaction surface of hydrate (RSH) model and the initial fluids distribution on the hydrate formation process are simulated and analyzed. The variation of the RSH in NGH formation/dissociation should be taken into consideration when modeling the hydrate re-formation in the exploitation of NGH. The initial distribution of water and gas has a great impact on the hydrate formation in the sealed reactor. The hydrate distribution is ununiform, even when assuming the water and methane are mixed uniformly in a homogeneous porous media. This study provides new insight for the parametric estimation of the RSH model in the hydrate formation and dissociation modeling.

Effects of thermal environment on dehydroxylation of porous silica preform in two‐step CVD synthesis

AbstractTwo‐step chemical vapor deposition (CVD) method is a promising technique for industrial fabrication of low‐hydroxyl silica glass ingot, in which a porous silica preform is first synthesized by flame hydrolysis deposition, which is subsequently sintered and vitrified to form silica glass. During sintering hydroxyls can be easily removed through the small pores in porous silica preform, which is called dehydroxylation. A deep understanding of the heat and mass transport characteristics involved in the dehydroxylation process is prerequisite to its controlling. In our previous work, a numerical model was developed to simulate the sintering and dehydroxylation of porous silica preform considering heat and mass transfer in porous media at high temperatures, chemical reaction of dehydroxylation, and volume shrinkage of preform. The results revealed that the dehydroxylation effect largely depends on the temperature fields in the furnace. In present work, the influences of thermal environments, including heating curve, heater position, and crucible structure on the dehydroxylation process of porous silica preform are systematically studied by numerical methods. Based on the results, increasing temperature at either stage is helpful for hydroxyl removal as well as increasing the hydroxyl distribution uniformity. However, long‐time exposure to 1500°C will instead worsen the dehydroxylation effect. Compared to top or bottom heating, side heating is more beneficial to hydroxyl removal. To improve the dehydroxylation condition at the bottom of porous silica preform, a novel crucible structure is designed which shows better performance than the ordinary crucible. At last, an optimized heating scheme is proposed in this study, which obtains much better dehydroxylation effect than other cases.

Pore-scale investigation on nonaqueous phase liquid dissolution and mass transfer in 2D and 3D porous media

Fluid–fluid interphase mass transfer in porous media plays an important role in the remediation of soil and groundwater contaminated by nonaqueous phase liquid (NAPL). In this study, we experimentally elucidated the pore-scale dissolution process and the macroscopic interphase mass transfer coefficient inside the porous media. Further, the local characteristics of the residual phase, including saturation and interfacial area, were determined during the dissolution process using nondestructive visualization technologies. The dynamic dissolution process indicated that not all blobs are equally exposed to flowing water and the dead-end pores considerably decreased the dissolution rate. According to the linear driving force model, the NAPL concentration in mobile water was predicted from the residual saturation. Further, the local and overall mass transfer coefficients corrected with concentration and interfacial area were estimated. The results showed that the NAPL concentration in mobile water increased along the water injection direction because of the NAPL dissolved in water. The local mass transfer coefficient exhibited a uniform distribution along the sample, indicating that the mass transfer coefficient is independent of the concentration difference. The effect of pore structure on the dissolution process of entrapped NAPL was studied by comparing a two-dimensional (2D) micromodel and a three-dimensional (3D) packed bed. The overall mass transfer coefficient was higher in the 3D packed bed under Darcy flow conditions. The major differences between the 3D packed bed and 2D micromodel can be attributed to the heterogeneity of pore geometry and the differences in pore connectivity.