Numerical estimation of effective diffusion coefficients for charged porous materials based on micro-scale analyses

In order to describe diffusive transport of solutes through a porous material, estimation of effective diffusion coefficients is required. It has been shown theoretically that in the case of uncharged porous materials the effective diffusion coefficient of solutes is a function of the pore morphology of the material and can be described by the tortuosity (tensor) (Bear, 1988 [1]). Given detailed information of the pore geometry at the micro-scale the tortuosity of different materials can be accurately estimated using homogenization procedures. However, many engineering materials (e.g., clays and shales) are characterized by electrical surface charges on particles of the porous material which strongly affect the (diffusive) transport properties of ions. For these type of materials, estimation of effective diffusion coefficients have been mostly based on phenomenological equations with no link to underlying micro-scale properties of these charged materials although a few recent studies have used alternative methods to obtain the diffusion parameters (Jougnot et al., 2009; Pivonka et al., 2009; Revil and Linde, 2006 2, 3 and 4). In this paper we employ a recently proposed up-scaled Poisson–Nernst–Planck type of equation (PNP) and its micro-scale counterpart to estimate effective ion diffusion coefficients in thin charged membranes. We investigate a variety of different pore geometries together with different surface charges on particles. Here, we show that independent of the charges on particles, a (generalized) tortuosity factor can be identified as function of the pore morphology only using the new PNP model. On the other hand, all electro-static interactions of ions and charges on particles can consistently be captured by the ratio of average concentration to effective intrinsic concentration in the macroscopic PNP equations. Using this formulation allows to consistently take into account electrochemical interactions of ions and charges on particles and so excludes any ambiguity generally encountered in phenomenological equations.     

Characterisation of conduction phenomena in soils at the particle-scale: Finite element analyses in conjunction with synthetic 3D imaging

This paper describes an innovative method to characterise conduction parameters in geomaterials at the particle-scale. The technique is exemplified using 3D synthetic grain packing generated with discrete element approaches. This creates a geo-mechanically viable user-defined 3D granular image through which the particle skeleton and the corresponding pore network are constructed. Images are then imported into the finite element analyses to solve the governing equations of hydraulic and thermal conduction. Navier–Stokes equation is uniquely upscaled to Darcy’s law to assess hydraulic conductivity in soils, while a similar approach implements the Fourier equation to evaluate thermal conduction through grain chains and pore network. High performance computing is used to meet demanding numerical calculations of 3D meshed geometries. Packing density (i.e., porosity) and inter-particle contact areas are explored as variables to highlight the effects of pore volume and inter-particle contact condition in hydraulic and thermal conduction. This emerging technique allows not only characterising the macro-scale behaviour of conduction phenomena in soils but also quantifying and visualising the preferential and local conduction behaviour at the particle-scale. Laboratory measurements of hydraulic and thermal conductivities support numerically obtained results and validate the viability of the new methods used herein. This study introduces an alternative way to determine physical parameters of soils using emerging technology of rigorous numerical simulations in conjunction with 3D images, and to enable fundamental observation of particle-scale mechanisms of macro-scale manifestation.     

Experimental investigation of dry density effects on dielectric properties of soil–water mixtures with different specific surface areas

The dielectric constant of soil is used to estimate its water content in a range of applications. Unlike the widely known effect of water content on the soil dielectric constant (consistent direct proportionality), only a limited number of studies have reported the effects of soil dry density, however, with equivocal results. This paper, therefore, investigates the effects of dry density or degree of compaction on the dielectric constant of five different soil types. The results of the experimental work for the soils ranging from sand to Bentonite clay with distinct specific surface areas were evaluated based on the use of two simple mixture models (De Loor and Birchak). The effects of dry density on the soil dielectric constant were found to be soil type dependent. This is demonstrated by the experimental data and further proven by the modified De Loor model. The behavior is shown to be defined by the changes in the free water, bound water, and solid particle volume fractions, ultimately controlled by the soil specific surface area. The dielectric constant changes from being directly proportional to dry density to inversely proportional at a threshold specific surface area of between 122 and 147 m²/g. Supported by the experimental observations, parametric analysis has revealed that the range for the dielectric constant of bound water was found to be 9–37, while the geometrical parameter α in the Birchak model was found to be 0.4–0.8.

     

Upscaling of Navier–Stokes equations in porous media: Theoretical, numerical and experimental approach

The accurate estimation of hydraulic conductivity is important for many geotechnical engineering applications, as the presence of fluids affects all aspects of soil behaviour, including its strength. Darcy’s law is the key experimental (or phenomenological) equation employed to model ground water flow. Yet, this phenomenological equation can be linked to a more fundamental microscale model of flow through the pore spaces of the porous material. This paper provides an experimental verification of the relationships between Darcy’s law (macroscale) and the Navier–Stokes equations (microscale) for actual complex pore geometries of a granular material. The pore geometries are experimentally obtained through state-of-the-art X-ray computer assisted micro-tomography. From the numerical modelling of the microscale flow based on actual pore geometries, it is possible to quantify and visualize the development of pore-scale fluid preferential flow-paths through the porous material, and to assess the importance of pore connectivity in soil transport properties.     

Physical characterization of core samples recovered from Gulf of Mexico

Seventy whole rounds from conventional cores obtained during drilling to 300 mbsf at Atwater Valley and Keathley Canyon in the Gulf of Mexico in April and May 2005 were tested to determine geophysical and geomechanical parameters (liquid and plastic limit, porosity, specific surface, pH, sediment electrical conductivity, P- and S-wave velocities and undrained shear strength). Available data from a pressure core are included as well. Results show that the sediments are high specific surface plastic clays, and exhibit pronounced time-dependent stiffness recovery. Strains during coring disturb specimens, yet, the water content retains the effective stress history and permits gaining stiffness and strength information from conventional cores. Remolding is exacerbated when gas expands upon decompression; the limited pressure core data available show the advantages of preserving the pore fluid pressure during core recovery and testing. Valuable parameters for sediment characterization and engineering analysis are extracted from the data using pre-existing soil models.     

Evaluating the effective thermal conductivity of geothermal pavements constructed using demolition wastes by DEM and 3D printing techniques

Acta Geotechnica - This paper studies the effect of various parameters on the effective thermal conductivity (λeff) of the geothermal pavement system when constructed using construction and...