Mass Transport In Porous Media Research Articles

Modelling of Mass Transport in Porous Materials: Analytical Solutions and Analysis

The pioneering works in the area of mass transport in porous media go back to the end of last century. The partial differential equations governing the mass and heat transfer can be solved using numerical techniques, and in this paper we solve them analytically under different boundary conditions including time-periodic boundary conditions. The nature of these solutions is discussed. Analytic solutions provide valuable physical insight and are usually easier to compute. In addition, these solutions may help to experimentally determine the parameters in a setting where both the mass and temperature gradients are present, without resorting to a simplified set of equations that govern heat and mass transfer separately.

Simulation of Subsea Gas Hydrate Exploitation

The recovery of methane from gas hydrate layers that have been detected in several subsea sediments and permafrost regions around the world is a promising perspective to overcome future shortages in natural gas supply. Being aware that conventional natural gas resources are limited, research is going on to develop required and sustainable technologies for the production of natural gas from such new sources since the early 1990s.In recent years, intensive research has focused on the capture and storage of CO2 from combustion processes to reduce climate impact. While different man-made or natural reservoirs like deep aquifers, exhausted oil and gas deposits or other geological formations are considered to store gaseous or liquid CO2, the storage of CO2 as hydrate in former methane hydrate deposits is another promising alternative. Due to beneficial stability conditions, methane recovery may be well combined with CO2 storage in the form of hydrates. Regarding technological implementation many problems have to be overcome.Within the scope of the German research project »SUGAR« different technological approaches for the optimized exploitation of gas hydrate deposits are evaluated and compared by means of dynamic system simulations and analysis. Detailed mathematical models for the most relevant chemical and physical processes are developed. The basic mechanisms of gas hydrate formation/ dissociation and heat and mass transport in porous media are considered and implemented into simulation programs.Simulations based on geological field data have been carried out. The effects occurring during gas production and CO2 storage within a hydrate deposit are identified and described for various scenarios. The behavior of relevant process parameters such as pressure, temperature and phase saturations is discussed for different strategies.Simulation results for different scenarios, e. g. simple depressurization and CO2 injection, reveal that both the production of natural gas and the CO2 storage are possible with acceptable rates. In case of simultaneous CO2 injection an increased production rate can be expected. The results strongly depend on deposit conditions, especially multiphase flow rates are dominated by permeability terms – in other words the reservoir permeability controls production and injection rates. Furthermore, the heat transport within heterogeneous layered deposits leads to enhanced hydrate decomposition and thus higher production rates.

Laplace-Transform Based Inversion Method for Fractional Dispersion

Partial differential equations with memory are challenging models for mass transport in porous media where fluid and tracer may be stored by the solid matrix, and then released. Moreover, integral transforms (generalizing time moments) of solutions to such models are linked to the corresponding transport parameters. Inverting that link provides a method to determine model parameters on the basis of solutions. It is checked using numerically generated profiles before passing to experimental data.

An experimental investigation of reaction zone controls on fluid flow and mass transport

This study examines homogeneous and heterogeneous mass transport in porous media featuring a solid-phase reaction zone that evolves and influences mass transport. It uses both flow-tank experiments and 2D reactive transport modeling to elucidate plume and reaction-zone behavior in situations with inherent complexity due to flow and transport and geochemical variability. The system is created by pumping a dilute Fe(ClO4)3 solution through a medium of glass beads and crushed calcite. As pH increases through the dissolution of calcite, amorphous ferric oxyhydroxide precipitates. The distribution of Fe, dissolved carbonate species, and pH are strongly coupled to the reaction zone because of the dissolution of CaCO3 and the precipitation of Fe(OH)3. Plugging influences the transport of dissolved constituents because it promotes fingering, hydraulic fracturing and flow bypassing. With the homogeneous systems, differences in the fingering produced by changing CaCO3 contents produced a heterogeneous distribution of Fe(OH)3(s) and dissolved Fe. As a result, a reaction zone with a complex shape developed due to the heterogeneity in hydraulic conductivity and CaCO3 content.

Humidity buffering using stabilised rammed earth materials

The humidity buffering potential of stabilised rammed earth materials is investigated based on the moisture buffer value concept. The moisture buffer value is (a) measured experimentally, (b) calculated from an analytical solution of the mass transfer and (c) simulated using a numerical solution of the combined heat and mass transfer. The numerical solution to the equations is described, as well as the modelling tool termed ‘CHAMP’ (coupled heat and mass transport in porous media). The results show that stabilised rammed earth can be a ‘good’ moisture buffering material under the Nordtest classification scheme. They also show that the moisture buffer value of stabilised rammed earth materials could be optimised or maximised by controlling the grading and mineralogy of the sub-soil and the manufacturing techniques. Sensitivity analysis of the moisture buffer value to the moisture transfer resistance at the surface is explored through numerical simulation and the need to control the experimental measurement carefully is explored.

Simulation of the relationship between porosity and tortuosity in porous media with cubic particles

Tortuosity is an important parameter used in areas such as vascular medicine, neurobiology, and the field of soil permeability and diffusion to express the mass transport in porous media. It is a function of the porosity and the shape and distribution of particles. In this paper, the tortuosity of cubic particles is calculated. With the assumption that the porous medium is homogeneous, the problem is converted to the micro-level over a unit cell, and geometry models of flow paths are proposed. In three-dimensional (3D) cells, the flow paths are too complicated to define. Hence, the 3D models are converted to two-dimensional (2D) models to simplify the calculation process. It is noticed that the path in the 2D model is shorter than that in the 3D model. As a result, triangular particles and the interaction are also taken into consideration to account for the longer distance respectively. We have proposed quadrate particle and interaction (QI) and quadrate and triangular particle (QT) models with cubic particles. Both models have shown good agreement with the experimental data. It is also found that they can predict the toruosities of some kinds of porous media, like freshwater sediment and Negev chalk.

Mass transport in porous media from first principles: An experimental and theoretical study

Abstract In the present work, the mass transport of helium through zeolite is experimentally determined by measuring the flow of helium through a zeolite membrane. By using a mathematical model, the mass transport through defects was accounted for to arrive at mass transport through zeolite pores. For the first time, we could thereby experimentally show that the mass transport of helium in zeolite pores is strongly controlled by the amount and location of hydrocarbons in the zeolite pores and varies several orders of magnitude. The mass transport of helium in ZSM-5 zeolite pores is first reduced gradually more than one order of magnitude when the loading of n-hexane is increased from 0 to 47% of saturation. As the loading of n-hexane is further increased to 54% of saturation, the mass transport of helium in the zeolite pores is further reduced abruptly by more than two orders of magnitude. This gradual decrease followed by an abrupt decrease of mass transport is caused by adsorption of n-hexane in the zeolite pores. In a similar yet different fashion, the mass transport of helium in the zeolite pores is reduced abruptly by almost two orders of magnitude when the loading of benzene is increased from 0 to 19% of saturation due to adsorption of benzene in the pore intersections. Effective medium approximation percolation models with parameters estimated using density functional theory employing the local density approximation, i.e. models with no adjustable parameters and the most sophisticated theory yet applied to this system, can adequately describe the experimental observations.

A modified dusty gas model in the form of a Fick's model for the prediction of multicomponent mass transport in a solid oxide fuel cell anode

The dusty gas model (DGM) is accurate but difficult to use for describing multicomponent mass transport in porous media. Based on a reasonable approximation that is exact for binary mixtures, the DGM is reformulated in the form of a Fick's model with explicit analytical expressions for the flux of each species. The validity of the new formulation, the DGMFM, is tested using a numerical model of a solid oxide fuel cell (SOFC) anode with realistic microstructure data and partially reformed methane fuel. Methane steam reforming and the water gas-shift reaction in the anode are included in the model. The accuracy of the DGMFM is checked by systematically varying the factors that may affect the mass transport in the porous anode, such as the pore radius, porosity, tortuosity factor, anode thickness, temperature, current density and fuel composition. The comprehensive study shows conclusively that the DGMFM is highly accurate in reproducing the DGM results for all practical SOFC operations.

Influence of growth modulation on the effective permeability of the vertebral end plate. A porcine experimental scoliosis model

Background Abnormal mechanical loading occurs in scoliosis as compared to normal spines. Intervertebral disc degeneration has been correlated with alteration of bone density in adjacent vertebral bodies. How vertebral end plate remodels in scoliosis and the consequences on disc homeostasis are not well understood. Permeability is a relevant physical measure to quantify mass transport in porous media. We hypothesized that effective permeability of the vertebral end plate was modified by growth modulation in a scoliosis animal model. Methods Flexible asymmetric posterior instrumentation was undertaken on six healthy four-week-old pigs. Two sets of left pedicle screws were inserted and connected with a stainless steel cable. After two months, the apical intervertebral unit and three units located cranially and caudally, were harvested. One central and two lateral specimens were investigated using a previously validated method for measuring permeability. Findings A three-dimensional deformity was obtained in all six animals with an average of 42° right thoracic curve, 44° lordosis and 21° rotation. Permeability was significantly greater in the center of the end plates than in the periphery and it was decreased by − 45% towards the apex of the deformity. Fluid flow direction did not play a significant role. No significant difference was found between the convex side and the concave side. Interpretation The end plate is a crucial zone for diffusive and convective transport and we showed in a scoliosis animal model that a growth modulation may decrease its effective permeability. The proposed methodology and associated results could help to understand degenerative changes in human spine.

A Holistic Approach with Special Reference to Heat Transfer in Multi-Component Porous Media Systems

Problems involving multiphase flow, heat transfer and multi-component mass transport in porous media arise in a number of scientific engineering disciplines. Important technological applications include thermally enhanced oil recovery, subsurface contamination and remediation, capillary assisted thermal technologies, drying process, thermal insulation materials, multiphase trickle bed reactors, nuclear reactor safety analysis, high level radioactive waste repositories and geothermal energy exploitation. In this paper we demonstrate multiphase flows in porous media are driven by gravitational, capillary and viscous forces. But gravity causes phase migration in the direction of the gravitational field. Microscopic modelling efforts were made to accurately incorporate microscopic interfacial phenomena. Multi-scale modelling approaches were attempted in order to transmit information over various lengths scales, ranging from micro-scale, meso-scale, macro-scale and finally to the field scale.

HYTEC results of the MoMas reactive transport benchmark

A specific benchmark has been developed by the French research group MoMas in order to improve numerical solution methods applied by reactive transport models, i.e., codes that couple hydrodynamic flow and mass transport in porous media with geochemical reactions. The HYTEC model has been applied to this benchmark exercise, and this paper summarizes some of the principal results. HYTEC is a general-purpose code, applied by industrials and research groups to a wide variety of domains, including soil pollution, nuclear waste storage, cement degradation, water purification systems, storage of CO2, and valorization of stabilized wastes. The code has been applied to the benchmark test-cases without any specific modification. Apart from the benchmark imposed output, additional information is provided to highlight the behavior of HYTEC specifically and the simulation results in particular.

Heat Transport Modeling in an Aquifer Downgradient a Municipal Solid Waste Landfill in Italy

Heat generation inside municipal solid waste (MSW) landfills is due to aerobic and anaerobic exothermic reactions occurring inside the waste. The result of heat generation and transport inside sanitary landfill leads to a temperature field that varies from mesophylic range (optimum at 30-40 °C) to thermophylic range (optimum at 50-60 °C). Due to high temperatures at the bottom of the landfill, liner systems can be severely damaged. The increment in convective and conductive heat transport could lead to an increase of the temperature in the surrounding geological layers and in the underlying aquifer. Hydrodynamic thermodispersion and convection are the most important mechanisms of heat transport in saturated porous medium with a moving fluid such as aquifer systems. The aim of the study is to model and investigate the origin of a thermal anomaly in the aquifer underneath a municipal landfill in the North of Italy. In order to model the system a detailed experimental analysis was conducted inside the landfill, measuring the temperature of the biogas and leachate, and in the aquifer system measuring the temperature in monitoring wells and conducting a constant rate pumping test. Heat transport model has been exploited using the analogy between heat and mass transport in porous media. The model showed that the thermal anomaly is due to convective and conductive heat transport from the landfill to the aquifer.

Comment on ‘Analytical solution for solute transport resulting from instantaneous injection in streams with transient storage’ by F. De Smedt, W. Brevis, and P. Debels, 2005 [Journal of Hydrology 315, 25–39

0 d e thank J. Huang, M.N. Goltz, a ur attention the analytical sol mobile zone models, which h olute transport in groundwate W nd P.V. Roberts to bring to o ution of so-called mobile– im ave been used to simulate s r, and are mathematically identical to transient storage models. In particular, we agree with the comment that the analytical solution of Goltz and Roberts (1984) is shown to be equivalent to the solution derived in De Smedt et al. (2005). We did not include in our literature review publications of other disciplines that deal with mathematically similar equations, because this field is very wide as it not only covers the so-called mobile–immobile zone transport models in groundwater, but also mass transport in porous media with non-equilibrium sorption, and similar processes in petroleum engineering, chromatography, etc. However, as far as we know the analytical solution presented by us in De Smedt et al. (2005) is unique and has never been presented

Mass Transport Modelling in Porous Media Using Delay Differential Equations

In this work the application of delay differential equations to the modelling of mass transport in porous media, where the convective transport of mass, is presented and discussed. The differences and advantages when compared with the Dispersion Model are highlighted. Using simplified models of the local structure of a porous media, in particular a network model made up by combining two different types of network elements, channels and chambers, the mass transport under transient conditions is described and related to the local geometrical characteristics. The delay differential equations system that describe the flow, arise from the combination of the mass balance equations for both the network elements, and after taking into account their flow characteristics. The solution is obtained using a time marching method, and the results show that the model is capable of describing the qualitative behaviour observed experimentally, allowing the analysis of the influence of the local geometrical and flow field characteristics on the mass transport.

Efficient algorithm for modeling transport in porous media with mass exchange between mobile fluid and reactive stationary media

We compare two approaches to numerically solve the mathematical model of reactive mass transport in porous media with exchange between the mobile fluid and the stationary medium. The first approach, named the “monolithic algorithm,” is the approach in which a standard finite-difference discretization of the governing transport equations yields a single system of equations to be solved at each time step. The second approach, named the “system-splitting algorithm,” is here applied for the first time to the problem of transport with mass exchange. The system-splitting algorithm (SSA) solves two separate systems of equations at each time step: one for transport in the mobile fluid, and one for uptake and reaction in the stationary medium. The two systems are coupled by a boundary condition at the mobile– immobile interface, and are solved iteratively. Because the SSA involves the solution of two smaller systems compared to that of the monolithic algorithm, the computation time may be greatly reduced if the iterative method converges rapidly. Thus, the main objective of this paper is to determine the conditions under which the SSA is superior to the monolithic algorithm (MA) in terms of computation time. We found that the SSA is superior under all the conditions that we tested, typically requiring only 0.3–50% of the computation time required by the MA. The two methods are indistinguishable in terms of accuracy. Further advantages to the SSA are that it employs a modular code that can easily be modified to accommodate different mathematical representations of the physical phenomena (e.g., different models for reaction kinetics within the stationary medium), and that each module of the code can employ a different numerical algorithm to optimize the solution.

Reply to comment: “Analytical solution for solute transport resulting from instantaneous injection in streams with transient storage” by F. De Smedt, W. Brevis, and P. Debels, 2005. Journal of Hydrology 315, 25–39

0 d e thank J. Huang, M.N. Goltz, a ur attention the analytical sol mobile zone models, which h olute transport in groundwate W nd P.V. Roberts to bring to o ution of so-called mobile– im ave been used to simulate s r, and are mathematically identical to transient storage models. In particular, we agree with the comment that the analytical solution of Goltz and Roberts (1984) is shown to be equivalent to the solution derived in De Smedt et al. (2005). We did not include in our literature review publications of other disciplines that deal with mathematically similar equations, because this field is very wide as it not only covers the so-called mobile–immobile zone transport models in groundwater, but also mass transport in porous media with non-equilibrium sorption, and similar processes in petroleum engineering, chromatography, etc. However, as far as we know the analytical solution presented by us in De Smedt et al. (2005) is unique and has never been presented

Nonlinear, multicomponent, mass transport in porous media

In this paper we consider multicomponent mass transport in porous media for non-dilute solutions. This process is described by coupled, nonlinear transport equations that must be spatially smoothed in order to be useful. This spatial smoothing, or upscaling, is achieved by the method of volume averaging for the case of negligible adsorption, desorption, and heterogeneous reaction. For pure diffusion, the results demonstrate that a single tortuosity tensor applies to the transport of all species. When convective transport is important, the process becomes much more complex and it is difficult to generalize about the behavior of the various dispersion tensors.

Gas Transport in Porous Electrodes of Solid Oxide Fuel Cells

Concentration polarization is a key SOFC performance parameter. It is caused by the limitation of transport of fuel or oxidant from the gas feeding channels through the electrodes to the reaction sites along the electrode/electrolyte interface. This paper presents the numerical simulations of gas transport in the porous electrodes of solid oxide fuel cells with an interdigitated flow channel design. By creating a convective component of mass transport in the porous electrodes, the interdigitated flow channel design could enhance the mass transport. The mass transport simulation was conducted using the FEMLAB software. Two porous media mass transport models, i.e. Fick's Model and the Dusty Gas Model (DGM) were used in the simulation. The simple but less accurate Fick's model is validated against the Dusty Gas Model results. It is found that for a combined diffusive and convective flow in the SOFC porous electrodes, when the fuel concentration is low and the pore size is small, the Dusty Gas Model should be used.

A new coupling algorithm for density‐driven flow in porous media

We consider the numerical solution of coupled fluid flow and heat or mass transport in porous media. The aim of this work is to provide some new mathematical development and algorithm to reduce the CPU costs of the solution of these strongly non‐linear coupled equations widely used in geosciences and environmental sciences, without lost of accuracy. Usually, the flow equation is solved first. We show that, by solving the transport equation first, the CPU time can be significantly reduced. This new algorithm is not dependent on the numerical scheme and is quite easy to implement in a numerical code. The accuracy of this new way of coupling flow and transport equations is evaluated with 2D and 3D numerical tests.

Finite element approximation of mass transfer in a porous medium with non equilibrium phase change

A finite element approximations with an implicit Euler scheme is analyzed. This involves numerical integration of a semi-linear parabolic-differential inclusion arising in a model of reactive mass transport in porous media with a dissolution/precipitation process. The model is composed of parabolic equations and variational inequalities. Equations are coupled by non-linear terms. We prove the existence of solutions for the approximated problem and the convergence of the scheme towards the solution of the continuous Problem