Drying Of Porous Media Research Articles

Computational Cosserat periporomechanics for strain localization and cracking in deformable porous media

Strain localization and cracking in porous media are significant issues in engineering and science. Periporomechanics is a strong nonlocal framework for modeling the mechanics and physics of porous media with evolving discontinuities. In periporomechanics, the horizon that usually lacks a physical meaning serves as a nonlocal parameter. In this article, as a new contribution, we formulate a Cosserat periporomechanics paradigm incorporating a micro-structure related length scale for modeling shear banding and cracking in dry porous media. In this new Cosserat-periporomechanics framework, each material point is endowed with both translational and rotational degrees of freedom following the Cosserat continuum theory. We formulate a stabilized Cosserat constitutive correspondence principle through which classical micro-polar constitutive models for porous media can be used in Cosserat periporomechanics. We have numerically implemented the Cosserat periporomechanics paradigm through an explicit Lagrangian meshfree algorithm. We first present numerical examples to validate the implemented computational Cosserat periporomechanics paradigm for modeling shear bands and cracks. We then present numerical examples to demonstrate the efficacy and robustness of the Cosserat periporomechanics for modeling the shear banding bifurcation and crack branching in dry porous media.

Fluid injection‐induced cavity expansion in dry porous medium

AbstractFluid injection‐induced deformation around a cylindrical cavity is of particular interest in the area of subsurface energy extraction. In this study, a model is proposed to analyze the time‐dependent expansion of a cavity caused by fluid injection in an elastoplastic dry porous medium. This problem is characterized by the existence of two moving boundaries, a permeation front and an elastoplastic interface, which leads to distinct time‐dependent zones governed by different sets of equations. The interplay between these two boundaries leads to three phases of solution. The a priori unknown partitioning of the injection rate into the rate of change of cavity volume and infiltration in the porous medium necessitates the introduction of a time‐dependent permeation coefficient as one of the primary variables. The method of solution takes advantage of the quasi‐static and quasi‐stationary nature of the problem, which makes it possible to treat time as a parameter rather than a variable. It follows that the problem can be solved in two steps. In a first step, closed‐form expressions for the pore pressure, displacement, and stress fields in each zone are derived, with parameters in these expressions depending explicitly on four time‐dependent variables, namely the positions of the two interfaces, the cavity radius, and the permeation coefficient. In a second step, the rate equations governing the evolution of these variables during different phases are derived and solved numerically. The paper concludes with a parametric analysis of the influence of the stiffness and strength of the material on the solution.

Irregular and stepwise behaviour of hydraulic fracturing: insights from linear cohesive crack modelling with maximum stress criterion

There is growing evidence that fracture advancement in saturated and dry porous media may be smooth or stepwise. In the stepwise behaviour, there are also pressure oscillations in saturated porous materials, as predicted by Biot’s theory. The type of behavior depends on the specifications of the problem and material properties. Not all the adopted numerical models are capable of capturing stepwise behaviour. While non-local fracturing models are perfectly adapted to capture the stepwise behaviour, it is shown that cohesive models are also capable to model such a behaviour. In fact, it is necessary to satisfy a consistency condition for the numerical solution; in other words, the fracture advancement/time-stepping algorithm must not impose a constraint on the tip advancement speed. This is peculiar to cohesive models because there the unit of fracture advancement is specified beforehand, while in other models, such as peridynamics, it is an outcome of the analysis. In inhomogeneous media, it can be expected to capture irregular results from hydraulic fracturing (HF); however, homogeneous media can also show such behaviour as presented herein. In this study, the eXtended Finite Element Method (XFEM) is used in conjunction with a cohesive crack model to investigate the stepwise or irregular behaviour of HF in homogeneous saturated porous media both under quasistatic and dynamic conditions. The results clearly show that the extent of irregularity depends directly on the intensity of dynamic effects in the problem. Moreover, fracture forerunning is one of the reasons of the stepwise fracture growth in the solutions. Although the results are obtained by XFEM, the conclusions are not restricted to this particular numerical method, and the findings can provide useful insights into the necessary aspects of the numerical algorithms for dynamic HF modelling.

Semi-continuum modeling of unsaturated porous media flow to explain Bauters' paradox

Abstract. In the gravity-driven free infiltration of a wetting liquid into a homogeneous unsaturated porous medium, the flow pattern is known to depend significantly on the initial saturation. Point source infiltration of a liquid into an initially dry porous medium produces a single finger with an oversaturated tip and an undersaturated tail. In an initially wet medium, a diffusion-like plume is produced with a monotonic saturation profile. We present a semi-continuum model, based on a proper scaling of the retention curve, which is discrete in space and continuous in time. We show that the semi-continuum model is able to describe this transition and to capture the experimentally observed dependence of the saturation overshoot and the finger velocity on the initial saturation.

Percolating and nonpercolating liquid phase continuum model of drying in capillary porous media with application to solute transport in the very low Péclet number limit

Drying in porous media is characterized by the fragmentation of the liquid phase in many evolving clusters. Here, a drying model is presented considering explicitly the fragmentation process within the framework of the continuum approach to porous media. The model is extended so as to predict the evolution of a solute in the fragmented liquid phase during drying.

Euler characteristic during drying of porous media

This study aims to elucidate the dynamics of fluid topology during drainage and evaporation of wetting and non-wetting fluids via evaluation of their Euler characteristic (EC) and Betti numbers from designed experiments. The results showed that the EC of the non-wetting fluid remained constant at a high wetting fluid saturation and then decreased nonlinearly. However, the EC of the wetting fluid exhibited more complex trends. In the 2-D micromodel, the number of loops decreased monotonously, reached zero, and remained constant for lower saturations, while the number of distinct components fluctuated because of the appearance and disappearance of disconnected clusters. In the 2-D model, the number of distinct components played a significant role; in the 3-D X-ray CT experiment, the number of loops of pendular rings dominated the EC. The findings suggest that the trends observed in the 2-D micromodel may not apply under 3-D conditions.

A personal perspective on prediction of saline water evaporation from porous media

Using the great opportunity for contributing a paper to the Special Issue of Drying Technology on the occasion of 30 years of pore-network modeling of drying, we discuss some of the open questions regarding description of saline water evaporation from porous media, which is a topic relevant to a number of environmental and engineering processes and applications, including but not limited to soil salinization, preservation of building materials, and CO2 sequestration. This note is not meant to be an in-depth review article, but more to serve as a summary of open challenges regarding prediction of saline water evaporation from porous media, based on the authors’ recent experimental and computational results and analysis. We focus on the formation of crystalized porous salt layers during drying of porous media and their consequences on the evaporative water losses. Suggestions are made on the future perspective and research directions to predict saline water evaporation from porous media.

Particle Deposition in Drying Porous Media

The drying of porous media is a ubiquitous phenomenon in soils and building materials. The fluid often contains suspended particles. Particle deposition may modify significantly the final material, as it could be pollutants or clogging the pores, decreasing the porosity, such as in salt, in which particles and drying kinetics are coupled. Here, we used SEM and X-ray microtomography to investigate the dried porous media initially saturated by nanoparticle suspensions. As the suspensions were dried, nanoparticles formed a solid deposit, which added to the initial solid matrix and decreased the porosity. We demonstrate that since the drying occurred through the top surface, the deposit is not uniform as a function of depth. Indeed, the particles were advected by the liquid flow toward the evaporative surface; the deposit was significant over a depth that depended on the initial volume fraction, but the pore size was affected over a very narrow length. These findings were interpreted in the frame of a physical model. This study may help to design better porous media and take into account particle influence in drying processes.

Lattice Boltzmann Modeling of Drying of Porous Media Considering Contact Angle Hysteresis

Drying of porous media is governed by a combination of evaporation and movement of the liquid phase within the porous structure. Contact angle hysteresis induced by surface roughness is shown to influence multi-phase flows, such as contact line motion of droplet, phase distribution during drainage and coffee ring formed after droplet drying in constant contact radius mode. However, the influence of contact angle hysteresis on liquid drying in porous media is still an unanswered question. Lattice Boltzmann model (LBM) is an advanced numerical approach increasingly used to study phase change problems including drying. In this paper, based on a geometric formulation scheme to prescribe contact angle, we implement a contact angle hysteresis model within the framework of a two-phase pseudopotential LBM. The capability and accuracy of prescribing and automatically measuring contact angles over a large range are tested and validated by simulating droplets sitting on flat and curved surfaces. Afterward, the proposed contact angle hysteresis model is validated by modeling droplet drying on flat and curved surfaces. Then, drying of two connected capillary tubes is studied, considering the influence of different contact angle hysteresis ranges on drying dynamics. Finally, the model is applied to study drying of a dual-porosity porous medium, where phase distribution and drying rate are compared with and without contact angle hysteresis. The proposed model is shown to be capable of dealing with different contact angle hysteresis ranges accurately and of capturing the physical mechanisms during drying in different porous media including flat and curved geometries.

NUMERICAL STUDY OF ISOTHERMAL DRYING IN POROUS MEDIA

NUMERICAL STUDY OF ISOTHERMAL DRYING IN POROUS MEDIA

Simulation of Preferential Flow in Snow With a 2‐D Non‐Equilibrium Richards Model and Evaluation Against Laboratory Data

AbstractRecent studies of water flow through dry porous media have shown progress in simulating preferential flow propagation. However, current methods applied to snowpacks have neglected the dynamic nature of the capillary pressure, such as conditions for capillary pressure overshoot, resulting in a rather limited representation of the water flow patterns through snowpacks observed in laboratory and field experiments. Indeed, previous snowmelt models using a water entry pressure to simulate preferential flow paths do not work for natural snowpack conditions where snow densities are less than 380 kg m−3. Because preferential flow in snowpacks greatly alters the flow velocity and the timing of delivery of meltwater to the base of a snowpack early in the melt season, a better understanding of this process would aid hydrological predictions. This study presents a 2‐D water flow through snow model that solves the non‐equilibrium Richards equation. This model, coupled with random perturbations of snow properties, can represent realistic preferential flow patterns. Using 1‐D laboratory data, two model parameters were linked to snow properties and model boundary conditions. Parameterizations of these model parameters were evaluated against 2‐D snowpack observations from a laboratory experiment, and the resulting model sensitivity to varying inputs and boundary conditions was calculated. The model advances both the physical understanding of and ability to simulate water flow through snowpacks and can be used in the future to parameterize 1‐D snowmelt models to incorporate flow variations due to preferential flow path formation.

Water level and mobilisation of colloids in porous media

Unforeseen clogging and low well productivity during exploitation of oil and gas reservoirs result from a mobilisation of densely deposited particles. The proposed model predicts the mobilisation in unsaturated porous media based on the changes in water level, and hydrophilicity and size of mobilisable particles. Domains of particle attachment, sliding, rolling, and lifting were found from a phase diagram based on a mechanical equilibrium. The degree of mobilisation was correlated with experimental data through a maximum retention function. The validity of the proposed model was confirmed by a close match of theoretical predictions with results of 46 laboratory tests on particle detachment.Our analysis shows that it is practically impossible to remove 2 μm charged colloids from a dry porous media. Nearly desalinated water with ionic strength of 0.001 M or less are needed to mobilise particles in saturated media at typical groundwater conditions. A gradual increase in water level is key for mobilisation in unsaturated media. The proposed model can be used to forecast a potential well clogging.

Drying of porous media by concurrent drainage and evaporation: A pore network modeling study

Drainage and evaporation can occur simultaneously during the drying of porous media, but the interactions between these processes and their effects on drying are rarely studied. In this work, we develop a pore network model that considers drainage, evaporation, and rarefied multi-component gas transport in porous media with nanoscale pores. Using this model, we investigate the drying of a liquid solvent-saturated porous medium enabled by the flow of purge gas through it. Simulations show that drying progresses in three stages, and the solvent removal by drainage effects (evaporation effects) becomes weaker (stronger) as drying progresses through these stages. Interestingly, drainage can contribute considerably to solvent removal even after evaporation effects become very strong, especially when the applied pressure difference across the porous medium is low. We show that these phenomena are the results of the coupling between the drainage and evaporation effects and this coupling depends on the operating conditions and the stage of drying.

Lattice Boltzmann simulations for micro-macro interactions during isothermal drying of bundle of capillaries

The fundamental understanding of the multiphase phenomena involved in drying of porous media is still a challenging task. Pore network models (PNMs) reveal the micro–macro interactions. However, PNMs have shortfalls in using true geometry, and in revealing capillary instabilities and film-effects. In this work, Shan Chen representation of Lattice Boltzmann Method (LBM) is applied to elucidate such complicated multiphase phenomena, i.e. micro-scale-dynamics evolution during drying. In a bundle of capillaries, liquid transport is explained with two pressure gradients. First, the pressure gradient between capillaries leading to capillary pumping, second, the pressure gradient within each capillary along the liquid–gas interface resulting in formation of hydraulic films. Transformation of hydraulic films to adsorbed films is revealed in irregular pore structures. Péclet number is employed to elucidate the effect of boundary layer thickness and temperature on drying kinetics. Characteristics of drying are re-established using the LBM for pore structures with bimodal size distribution.

Mechanistic understanding of microwave-vacuum drying of non-deformable porous media

This work proposed a mathematical model for describing the drying of porous media submitted to microwave heating under vacuum. The model was based on a multiphase flow inside the porous media in which a non-equilibrium formulation described moisture phase change. The numerical solution used the finite element method, and the experimental drying of ceramic samples made of sintered glass microspheres validated the simulated drying kinetics. After heating (1st phase), it was observed two drying rate periods where the water left the medium mainly as a liquid in the 2nd phase, and vapor in the 3rd phase. Overall, about 79% of water was removed in the liquid phase, innovatively demonstrating the drainage as the primary mode of transport in microwave vacuum drying of a saturated porous medium. The proposed model evaluated the energy dissipation and the average moisture content, describing the resulting relatively high-pressure gradients. The sensitivity analysis indicated the evaporation rate constant as a key-parameter in microwave-vacuum drying, once it impacts on local pressure increase into the medium that is the driving force for drainage and major factor on drying kinetics. The approach using Lambert’s Law was able to describe the drying kinetics while saving time in simulating this complex system.

A Numerical Implementation of the Soret Effect in Drying Processes

Drying of porous media is strictly governed by heat and mass transfer. However, contrary to the definition that drying is simultaneous transport mechanisms of heat and mass, most past and current models either account for temperature or concentration gradient effects on drying. Even though the complexity of computations of these processes varies with area of application, in most cases, the Dufour and Soret effects are neglected. This leads to deviations and uncertainties on the assumptions and interpretations of these and other relevant effects on drying. This paper covers the theoretical methods to derive the coupled transfer effects. In addition, this work proposes and formulates relevant heat and mass transfer equations, as well as the governing equations for drying processes with Dufour and Soret effects. The application of a numerical approach to solve the equations allows for studying of the influence of these effects on the design and operation of dryers. It is shown that the Soret effect can be highly relevant on drying operations with dynamic heating operation. While for drying processes where the steady state drying process predominates, the effect is deemed negligible.

Numerical Study of Heat and Mass Transfer during the Evaporative Drying of Porous Media

The paper deals with numerical study of drying process of porous media of sand during the evaporation of a liquid saturated porous layer within parallel vertical channel. The liquid and air streams are modeled as two coupled laminar boundary layers incorporating non-Darcian models of the inertia and boundary effects. The governing equations and the associated boundary conditions are discretized by means of the finite volume method implemented on a staggered mesh and the velocity-pressure coupling is processed by the SIMPLER algorithm. The influences of the inlet mass flow of the drying gas, porous layer thickness and the porosity on the drying process are analyzed. Results show that the drying rate of the porous media is improved by the reduction of the porosity and porous layer thickness a large drying rate is obtained with high inlet mass flow and high inlet gas temperature.

Numerical Investigation of Multiphase Transport Model for Hot-Air Drying of Food

Kurutma gıda ürününden sıvı miktarının buharlaştırılarak mikrobiyal bozulmayı önlemek için yaygın şekilde kullanılır. Enerji tüketimini azaltmak ve gıda kalitesini artırmak için kurutma sürecinin modellenmesi çok önemlidir. Literatürde kurutma karakteristiklerinin araştırılmasında farklı yaklaşımlar kullanılmıştır. Bu yaklaşımlar arasında gözenekli ortam yaklaşımı karmaşık bir mekanizmaya sahiptir. Gözenekli ortamda kurutma modelinde gazlar (su buharı ve hava) için moleküler difüzyon, sıvı (su) için difüzyon ve konveksiyon mekanizmaları kullanılmaktadır. Bu çalışmada öncelikle gözenekli malzemenin kurutulması üzerinde büzülme etkisi araştırıldı. Kurutma probleminde hava ve gıda ürünü için lineer olmayan kısmi diferansiyel denklemleri zamana bağlı olarak çözüldü. Kurutma işlemindeki büzülme etkisi ALE (Arbitrary Lagrangian Eulerian) metodu kullanılarak araştırıldı.

Luikov’s Analytical Solution with Complex Eigenvalues in Intensive Drying

Luikov’s equations of heat and mass transfer with pressure gradient have significant applications especially in the case of intensive drying in porous media. The established analytical solution of Luikov’s equations including pressure gradient effect in a complete form is presented in this work. The existence of complex roots in the analytical solution describing intensive drying with pressure gradient was overlooked in literature. A Matlab function capable of searching and sorting out the complex eigenvalues is also showcased. Three test cases are analyzed and compared with numerical solutions: one theoretical case to emphasize the importance of complex roots in analytical solution while two cases of drying process in ceramic and barley kernel to ensure practical applicability. Excellent matching between analytical and numerical results is noticed when complex eigenvalues are included.

Pore Network Simulation of Gas-Liquid Distribution in Porous Transport Layers

Pore network models are powerful tools to simulate invasion and transport processes in porous media. They are widely applied in the field of geology and the drying of porous media, and have recently also received attention in fuel cell applications. Here we want to describe and discuss how pore network models can be used as a prescriptive tool for future water electrolysis technologies. In detail, we suggest in a first approach a pore network model of drainage for the prediction of the oxygen and water invasion process inside the anodic porous transport layer at high current densities. We neglect wetting liquid films and show that, in this situation, numerous isolated liquid clusters develop when oxygen invades the pore network. In the simulation with narrow pore size distribution, the volumetric ratio of the liquid transporting clusters connected between the catalyst layer and the water supply channel is only around 3% of the total liquid volume contained inside the pore network at the moment when the water supply route through the pore network is interrupted; whereas around 40% of the volume is occupied by the continuous gas phase. The majority of liquid clusters are disconnected from the water supply routes through the pore network if liquid films along the walls of the porous transport layer are disregarded. Moreover, these clusters hinder the countercurrent oxygen transport. A higher ratio of liquid transporting clusters was obtained for greater pore size distribution. Based on the results of pore network drainage simulations, we sketch a new route for the extraction of transport parameters from Monte Carlo simulations, incorporating pore scale flow computations and Darcy flow.