Drying Of Porous Media Research Articles

The problem of melting ice in a porous medium saturated with ice and gas

The problem of ice formation in a dry, cold, porous medium saturated with ice and gas (air) when pumping warm water is considered in a flat one-dimensional self-similar formulation. The task was considered in volume area. During the injection of warm water from the beginning deep into the reservoir, it spread in a volume region that will divide the reservoir into 3 zones. The first zone was filled with water, the second zone was filled with ice and water, and the third zone was filled with ice and gas. To describe the process of heat and mass transfer, the following hypotheses were used: the temperature of the saturated substance (water, ice or gas) is equal to the temperature of the porous medium; ice and skeleton still; water, ice and skeleton of the reservoir are incompressible; skeletal porosity is constant. On the basis of constructed self-similar solutions, a numerical analysis was performed illustrating the effect of the initial parameters of a dry porous medium saturated with ice and gas, as well as the temperature of the injected water on the temperature and pressure distribution in the porous medium. It has been established that an increase in the temperature of the injected water does not lead to a significant increase in the area of ice decomposition. It is also established that if the pressure of the injected water is increased, this will not lead to a large increase in the area of ice decomposition. However, based on the results obtained, it can be seen that the speed of movement of the melting boundary increases, in particular, as the pressure increases by <i>p<sub>e</sub></i>=0.05 MPa, the intermediate region increases by one and a half times. It was found that it is economically more profitable to pump water with a lower temperature, because water with a higher temperature slightly increases the freezing area of the porous soil.

Temperature gradient induced double stabilization of the evaporation front within a drying porous medium

Drying of porous media very often occurs in the presence of significant temperature gradients because heat fluxes are imposed in many situations in order to decrease the drying time or to facilitate the moisture removal at a higher humidity of the surrounding gas phase. Here we consider the situation where the temperature increases with depth. We show from experiments with a micromodel that the temperature gradient induces the stabilization of the evaporation front within the model porous medium according to two different mechanisms occurring consecutively. The first mechanism occurs in the liquid phase and is explained by the dependence of surface tension upon temperature. This results in the preferential invasion of the warmer zones. The second mechanism occurs gas-sided due to the dependence of saturation vapor pressure upon temperature. We show that the time scales of both mechanisms are different leading to the temporary formation of distinctive phase patterns from which different periods of drying can be discriminated.

Influence of non-adsorbing polymers on drying of fresh mortars

In this paper, we compare the drying of non-reactive materials (glass beads packing) with the one of fresh mortars. Through the sample drying process, the existing literature on the general underlying physical processes involved in drying of porous media allows for the identification of two distinct regimes. These regimes drive the drying kinetics. We then measure the drying kinetics of the same materials containing polymers, which do not absorb on the cement grains. Our results and analysis suggest that the increase in the viscosity of the interstitial water due to polymer addition is at the origin of a decrease in drying rate. As drying of fresh cementitious materials strongly impacts the final properties in configuration with large exposed surfaces, we suggest that such polymer addition could slow down the overall drying of cementitious materials and improve their service life properties.

Numerical simulation of salt transport and crystallization in drying Prague sandstone using an experimentally consistent multiphase model

Drying of porous media in the presence of salt is a very common phenomenon with many applications but it is not totally understood so far. Some experiments that recently appeared in the literature have shown that the kinetics of drying not only strongly depends upon the quantity of precipitated salt but also upon the form in which the salt precipitates. In this paper, a coupled multiphase model that is capable of describing the different drying kinetics taking into account the different efflorescence formations is presented. The model is then validated through two different experimental campaigns on drying in presence of NaCl solution.

Effect of wind turbulence on gas transport in porous media: experimental method and preliminary results

We demonstrate a novel experimental arrangement for measuring wind turbulence‐induced gas transport in dry porous media under controlled conditions. This equipment was applied to assess the effect of wind turbulence on gas transport (quantified as a dispersion coefficient) as a function of distance to the surface of the porous medium exposed to wind. Two different strategies for the measurement of wind‐induced gas transport were compared. Experiments were carried out with O2 and CO2 as tracer gases with average vertical wind speeds of 0.02–1.06 m s−1. Oxygen breakthrough curves as a function of distance to the wind‐exposed surface of the porous medium were analysed numerically with a finite‐difference‐based model to assess gas transport. We showed that wind turbulence‐induced gas transport is an important transport mechanism that can be 20–70 times larger than molecular diffusion‐induced transport. Wind conditions and properties of the porous medium had strong controlling effects on this relationship. Importantly, we show that even though wind‐induced gas transport is greatest near to the wind‐exposed surface, it can have marked effects on the variation in gas concentration at much greater depths.Highlights We explored the effect of atmospheric wind turbulence on gas transport in porous media. We measured the depth relation of wind‐induced dispersion in porous media for real wind conditions. Wind‐induced gas dispersion coefficients were 20–70 times larger than molecular diffusion. Wind turbulence can potentially have a considerable effect on gas transport in porous media.

Free and forced gas convection in highly permeable, dry porous media

The spatial and temporal distribution of gas species within the vadose zone is determined by biochemical sources and by transport mechanisms. Here, two mechanisms that can transfer gas at high rates across the earth-atmosphere interface are studied. The first is thermal convection venting (TCV), a free convection process that develops under conditions of sufficient temperature and density gradients. The second mechanism is wind-induced convection (WIC), an outcome of atmospheric surface winds that drive air movement within the porous media by a forced-convection process. Both of these advective mechanisms can dominate gas transport in high permeability porous media, and the objective of this study was to determine the permeability values that are relevant for these mechanisms to become significant for gas transport. Experiments were performed using large columns filled with four different single-sized spherical particles of 1 to 4cm in diameter. The experiments were conducted in a climate-controlled laboratory, where surface winds and temperature gradients were imposed and monitored. A tracer gas of CO2-enriched air was used to quantify the impact of TCV and WIC on gas exchange between the porous media and the atmosphere. A permeability range of 10−7 to 10−6m2 was found to be sufficient for the onset of TCV when imposed temperature gradients were similar to standard nighttime atmospheric conditions, leading to full or partial venting of the column. Surface wind with a velocity of 1.5ms−1 drove WIC to a depth of 0.3m in most experimental conditions. The impact of WIC on net gas transport was not observed at the bottom-most sensor (0.9m), except under conditions of very high permeability (2.4 10−6m2) and a large temperature difference (6.5°Cm−1), when both TCV and WIC worked simultaneously. Results confirm that TCV and WIC can significantly contribute to gas transport through porous media with sufficiently high permeability.

Using micro-ct to investigate nanofluid droplet sorption in dry powder beds

Liquid droplet sorption in dry porous media is an important process for a wide range of scientific and engineering applications. However, visualizing droplet sorption is difficult due to the opacity of the porous media used in most of the applications. In this study, micro-CT technology is used to characterize the sorption profiles of nanofluid droplets in PMMA powder beds. Scan results reveal that the region of the powder bed wetted by the nanofluid has substantially higher pixel index values than the dry powder, thus enabling visualization of the sorption profile. The wetted regions themselves consistently have semi-spheroid shapes with craters on the top surface. The craters may be induced by powder repacking rather than droplet inertia ejecting well-settled powder particles. The sorption of multiple droplets maintains the features of a single droplet granule but increases the lateral spreading more than the penetration in the vertical direction. The inhomogeneous distribution of the pixel index value suggests accumulation of the nanofluid near the wetting front due to inhomogeneous porosity in the wetted region of the powder bed. It is considered that droplet sorption and capillary force may cause the powder particles to repack to generate a low porosity in the center of the wetted region. Nanoparticle distribution in the powder bed after complete evaporation of the nanofluid was also visualized. In conclusion, nanoparticle-enhanced micro-CT imaging has demonstrated the feasibility to visualize three-dimensional sorption profiles of a fluid in dry porous powder beds and thus provided an efficient means to study the sorption process in an opaque porous medium. We also envision that micro-CT can be utilized to characterize nanoparticle distribution in porous media in applications where nanomaterials are introduced for additional functionality of the final products.

A DIFFUSIVITY MODEL FOR GAS DIFFUSION IN DRY POROUS MEDIA COMPOSED OF CONVERGING–DIVERGING CAPILLARIES

Gas diffusion in dry porous media has been a hot topic in several areas of technology for many years. In this paper, a diffusivity model for gas diffusion in dry porous media is developed based on fractal theory and Fick’s law, which incorporates the effects of converging–diverging pores and tortuous characteristics of capillaries as well as Knudsen diffusion. The effective gas diffusivity model is expressed as a function of the fluctuation amplitude of the capillary cross-section size variations, the porosity, the pore area fractal dimension and the tortuosity fractal dimension. The results show that the relative diffusivity decreases with the increase of the fluctuation amplitude and increases with the increase of pore area fractal dimension. To verify the validity of the present model, the relative diffusivity from the proposed fractal model is compared with the existing experimental data as well as two available models of Bruggeman and Shou. Our proposed diffusivity model with pore converging–diverging effect included is in good agreement with reported experimental data.

Modeling drying in thin porous media after coupling pore-level drying dynamics with external flow field

ABSTRACTThis article uses a novel, fully coupled method to solve the isothermal slow drying of porous media in laminar flow. The film effect is included and a novel logistic equation is used to relate the pore network variables with the external field variables. The model is used to simulate the drying of several thin porous media with different aspect ratios in a flow. One, two, or all sides of the pore network are opened to the flow. The studies show that the higher exposed area vs. total volume ratio leads to faster drying while the orientation of the porous media is immaterial.

Gravity-driven unsteady-state slug fall in capillaries – modeling and experimental verification

ABSTRACTInfiltration of liquid droplets into dry porous media often occurs in industrial and natural settings, which has been widely modeled as liquid slug flow in capillaries. This work focuses on gravity-driven slug motion in vertically oriented capillary tubes. To model the propagation and evolution of the slug, a mathematical model was set on the basis of Newton’s second law and the law of conservation of mass. The model includes terms like slug’s inertia, deposited film, dynamic contact angle, slug’s advancing and receding menisci hysteresis, and it particularly highlights the direct effect of the trailing film on the change of slug mass. In order to verify this model, experiments on water slug with different lengths of initial slugs were conducted in two Pyrex glass capillaries that are partially wettable. It was found that both the length and the velocity of the slug vary during the slug motion in every case. Then the experimental results were simulated with the established model by carefully presetting two fitting parameters, αa and αh, that are related to the dynamic contact angle at the advancing meniscus and the thickness of the trailing film, respectively. The good agreement between the experimental and theoretical results demonstrates that the present model is capable of describing the unsteady-state dynamics of slugs fall in porous media.

Drying of Porous Media

Drying of porous media is part of our daily experience, yet this common process is central to many environmental and engineering applications ranging from soil evaporation affecting hydrological water balance and climatic processes, to the drying of food and building materials, and driving plant life through transpiration. Drying rates from porous media may exhibit complex dynamics reflecting internal transport mechanisms and motion of phase change fronts that determine rates of drying and critically affect surface energy partitioning. These interactions and resulting drying dynamics present a challenge to the prediction of drying rates and interplay among mass and energy exchange even for fixed boundary conditions.

Drying of salt contaminated porous media: Effect of primary and secondary nucleation

The drying of porous media is of major importance for civil engineering, geophysics, petrophysics, and the conservation of stone artworks and buildings. More often than not, stones contain salts that can be mobilized by water (e.g., rain) and crystallize during drying. The drying speed is strongly influenced by the crystallization of the salts, but its dynamics remains incompletely understood. Here, we report that the mechanisms of salt precipitation, specifically the primary or secondary nucleation, and the crystal growth are the key factors that determine the drying behaviour of salt contaminated porous materials and the physical weathering generated by salt crystallization. When the same amount of water is used to dissolve the salt present in a stone, depending on whether this is done by a rapid saturation with liquid water or by a slow saturation using water vapor, different evaporation kinetics and salt weathering due to different crystallization pathways are observed.

Density‐Driven Migration of Heavy NAPL Vapor in the Unsaturated Zone

Contaminant vapor (gas) plumes emanating from liquid sources migrate easily in the unsaturated zone. Heavy vapors preferentially migrate downward due to their greater density and thus pose a potential threat to underlying aquifers. Large‐scale column experiments and numerical simulations were conducted to investigate the density‐driven migration of carbon disulfide (CS2) vapor. Carbon disulfide, among others used to manufacture viscous rayon, is an industrial, non‐polar solvent. It is highly volatile and characterized by a very high density (1.6) relative to air when in a gaseous state. The experiments were conducted in large, vertical columns (i.d. = 0.109 m) of 4‐m length packed with a dry porous medium. Different types of glass beads were used to investigate the sensitivity of migration to permeability. The porous medium was kept dry to avoid partitioning effects into pore water. Gas samples were taken along the column throughout the experiment to quantify time and space dependent vapor migration. The experiments characterized the migration behavior of a heavy CS2 vapor plume injected in the middle of the column. The vapor plume steadily migrated downward dependent on the total mass of injected CS2 and permeability. The setup of the experiment was reproduced in a 1‐D, two‐phase, two‐component, isothermal, numerical model. Simulation results were compared with data from the vapor migration experiments. The results of the numerical model satisfactorily reproduced the migration behavior observed in the experiments but suggested slightly higher velocities than those observed. Thus the research presented improves the understanding of density driven, advective migration of a heavy contaminant vapor in a dry porous medium at a large scale. It provides valuable experimental data not only for future research but particularly for the transfer to field situations.

CONSEQUENCE OF BACKWARD EULER AND CRANK-NICOLSOM TECHNIQUES IN THE FINITE ELEMENT MODEL FOR THE NUMERICAL SOLUTION OF VARIABLY SATURATED FLOW PROBLEMS

Modeling water flow in variably saturated, porous media is important in many branches of science and engineering. Highly nonlinear relationships between water content and hydraulic conductivity and soil-water pressure result in very steep wetting fronts causing numerical problems. These include poor efficiency when modeling water infiltration into very dry porous media, and numerical oscillation near a steep wetting front. A one-dimensional finite element formulation is developed for the numerical simulation of variably saturated flow systems. First order backward Euler implicit and second order Crank?Nicolson time discretization schemes are adopted as a solution strategy in this formulation based on Picard and Newton iterative techniques. Five examples are used to investigate the numerical performance of two approaches and the different factors are highlighted that can affect their convergence and efficiency. The first test case deals with sharp moisture front that infiltrates into the soil column. It shows the capability of providing a mass-conservative behavior. Saturated conditions are not developed in the second test case. Involving of dry initial condition and steep wetting front are the main numerical complexity of the third test example. Fourth test case is a rapid infiltration of water from the surface, followed by a period of redistribution of the water due to the dynamic boundary condition. The last one-dimensional test case involves flow into a layered soil with variable initial conditions. The numerical results indicate that the Crank?Nicolson scheme is inefficient compared to fully implicit backward Euler scheme for the layered soil problem but offers same accuracy for the other homogeneous soil cases.

Mathematical models for fluids with pressure-dependent viscosity flowing in porous media

In this paper we study three filtration problems through porous media, assuming that the viscosity of the fluid depends on pressure. After showing that in this case Darcy’s law is “formally” preserved (meaning that the formal relation remains unchanged except for viscosity that now depends on pressure), we focus on the following problems: Green–Ampt infiltration through a dry porous medium; the Dam problem; the Muskat problem. For each model (free boundary problems) we obtain explicit solutions that allow to quantify the detachment from the classical case, where with the word “classical” we mean that viscosity is taken constant.

Colloid mobilization and transport during capillary fringe fluctuations.

Capillary fringe fluctuations due to changing water tables lead to displacement of air-water interfaces in soils and sediments. These moving air-water interfaces can mobilize colloids. We visualized colloids interacting with moving air-water interfaces during capillary fringe fluctuations by confocal microscopy. We simulated capillary fringe fluctuations in a glass-bead-filled column. We studied four specific conditions: (1) colloids suspended in the aqueous phase, (2) colloids attached to the glass beads in an initially wet porous medium, (3) colloids attached to the glass beads in an initially dry porous medium, and (4) colloids suspended in the aqueous phase with the presence of a static air bubble. Confocal images confirmed that the capillary fringe fluctuations affect colloid transport behavior. Hydrophilic negatively charged colloids initially suspended in the aqueous phase were deposited at the solid-water interface after a drainage passage, but then were removed by subsequent capillary fringe fluctuations. The colloids that were initially attached to the wet or dry glass bead surface were detached by moving air-water interfaces in the capillary fringe. Hydrophilic negatively charged colloids did not attach to static air-bubbles, but hydrophobic negatively charged and hydrophilic positively charged colloids did. Our results demonstrate that capillary fringe fluctuations are an effective means for colloid mobilization.

Determination of Sorption Isotherm Based on the Measured Bottom Contaminant Flux

We determine the sorption isotherm in the infiltration model of contaminated water into porous media. We assume that the contaminated water infiltrates into the dry porous media, flow through the sample and flows out at the other side of the sample. We suppose that the contaminant dissolved in the water reversibly adsorbs into the porous media. We use the Richards equation with van Genuchten relation between effective saturation and pressure head. Further, we use Fick’s law to model the contaminant transport in the water and arbitrary adsorption isotherm to model the evolution of the adsorption. By running the direct problem simulation, we obtain the “measurements” of the expelled water mass and its concentration. Then we “forget” the adsorption isotherm function. We solve this inverse problem by evaluating the gradient of the distance function (between “measured” and computed bottom contaminant flux) in an iterative way. We construct the gradient (variation) of the distance function by solving the corresponding dual system of partial differential equations.

Material Behavior of Porous Media

The drying of porous media is studied in this paper by means of the continuous approach and the control volume method. Both transport phenomena inside the porous medium and overall drying kinetics are analyzed. The model utilized in this study requires a lot of physical properties. All of them have been established experimentally. The capillary pressure, which depends on the moisture content, is obtained by a mercury intrusion curve.

Effective strength of saturated double porous media with a Drucker–Prager solid phase

SUMMARYThis study aims at determining the macroscopic strength of porous materials having a Drucker–Prager solid phase at microscale and two populations of saturated pores with different pressures at both micro and meso scales. To this end, and taking account of the available results by Maghous et al. (2009), we first derive a closed‐form expression of approximate criterion for a dry porous medium whose matrix obeys to a general elliptic criterion. The methodology to formulate this criterion is based on limit analysis of a hollow sphere subjected to a uniform strain rate boundary conditions. The obtained results are then implemented in a two‐step homogenization procedure, which interestingly delivers analytical expression of the macroscopic criterion for dry double porous media whose solid phase at microscale obeys to a Drucker–Prager criterion. After a brief discussion of the results, we propose an extension to double porous saturated media, allowing therefore to quantify the simultaneous effects of the different pore pressures applied on each voids population. The results are discussed in terms of the existence or not of effective stresses. Finally, they are assessed by comparing them to recently available results. Copyright © 2013 John Wiley & Sons, Ltd.

Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium

Infiltration of water in dry porous media is subject to a powerful gravity-driven instability. Although the phenomenon of unstable infiltration is well known, its description using continuum mathematical models has posed a significant challenge for several decades. The classical model of water flow in the unsaturated flow, the Richards equation, is unable to reproduce the instability. Here, we present a computational study of a model of unsaturated flow in porous media that extends the Richards equation and is capable of predicting the instability and captures the key features of gravity fingering quantitatively. The extended model is based on a phase-field formulation and is fourth-order in space. The new model poses a set of challenges for numerical discretizations, such as resolution of evolving interfaces, stiffness in space and time, treatment of singularly perturbed equations, and discretization of higher-order spatial partial–differential operators. We develop a numerical algorithm based on Isogeometric Analysis, a generalization of the finite element method that permits the use of globally-smooth basis functions, leading to a simple and efficient discretization of higher-order spatial operators in variational form. We illustrate the accuracy, efficiency and robustness of our method with several examples in two and three dimensions in both homogeneous and strongly heterogeneous media. We simulate, for the first time, unstable gravity-driven infiltration in three dimensions, and confirm that the new theory reproduces the fundamental features of water infiltration into a porous medium. Our results are consistent with classical experimental observations that demonstrate a transition from stable to unstable fronts depending on the infiltration flux.