Characterisation of porous solids using integrated nitrogen sorption and mercury porosimetry

The two different techniques of nitrogen sorption and mercury porosimetry, which are generally utilised completely separately, have been integrated into the same experiment to improve upon the information obtained from both methods. Nitrogen sorption isotherms have been run both before and after a mercury porosimetry experiment on the same sample. This experiment has revealed that for a particular type of sol-gel silica catalyst support the entrapped mercury is confined to only the very largest pores in the material. Light micrograph studies have shown that the spatial distribution of entrapped mercury is highly heterogeneous. These results suggest that mercury entrapment within the material is caused by a mechanism involving macroscopic () heterogeneities in the pore structure. These findings conflict with the usual assumptions generally made in simulations of porosimetry based on random pore bond network models. The new work has shown that, in conjunction with computer simulations involving the correct mercury retraction mechanism, mercury porosimetry and nitrogen sorption can be used to study the spatial distribution of all pore sizes within a mesoporous material. A percolation analysis of the nitrogen sorption data, obtained both before and after mercury entrapment, allowed broad features of the spatial disposition of variously sized pores to be determined. The results reported here also support the use of new, semi-empirical alternatives to the Washburn Equation to analyse raw mercury porosimetry data, rather than the traditional approach.     

Mercury intrusion porosimetry in pulp and paper technology

Mercury intrusion is frequently used for the characterization of porous materials, giving access to parameters such as porosity and pore size distribution as well as density (skeletal and bulk).The present work aims at studying the suitability of the mercury intrusion technique to evaluate the pore structure and related information of different kinds of woods used for pulp production, pulp handsheets and commercial paper sheets. Differences in wood structure, pulp composition and paper composition and structure could be easily detected by changes in the measured parameters, thus enabling a better understanding and/or prediction of the behaviour of these materials.     

A new approach for the characterization of the pore structure of dual porosity rocks

For the realistic representation of the pore space of dual porosity rocks, a new method of pore structure characterization is developed by combining experimental Hg intrusion/retraction curves with back-scattered scanning electron microscope (BSEM) images and inverse modeling algorithms. The pore space autocorrelation function measured by processing the digitized BSEM images is combined with the surface fractal dimension estimated from the high pressure Hg intrusion (MIP) data to derive a synthetic small-angle neutron scattering (SANS) intensity function, the inversion of which provides a volume-based pore body radius distribution (PBRD). The volume-based PBRD is fitted with a multimodal number-based PBRD consisting of two component distributions: one representing the macroporosity and another one representing the microporosity. Based on arguments of percolation theory, analytical mathematical models are developed to describe the Hg intrusion in and retraction from dual pore networks in terms of the complete PBRD, pore throat radius distribution (PTRD) of macroporosity, drainage accessibility functions (DAFs) of both porosities, and imbibition accessibility functions (IAFs) of both porosities. Inverse modeling of the Hg intrusion data set enables us to estimate the PTRD and DAFs. Inverse modeling of the Hg retraction datasets enables us to estimate a set of primary and secondary IAFs. The method is demonstrated by the pore structure characterization of four outcrop samples of carbonate and sandstone rocks. Analytic approximate equations developed from the critical path analysis (CPA) of percolation theory enable us to calculate explicitly the absolute permeability and the formation factor of the porous rocks using the estimated parameters (PBRD, PTRD, DAF) of the macroporosity. The measured permeability of cores is predicted satisfactorily and observed discrepancies may be attributed to large length-scale macro-heterogeneities which are not evident in BSEM images and Hg porosimetry data.     

Explicit numerical simulation of suspension flow with deposition in porous media: influence of local flow field variation on deposition processes predicted by trajectory methods

A new explicit numerical simulation (ENS) method based on lattice-gas automata (LGA) is introduced here for the flow of solid/fluid suspensions with deposition in porous media. The ENS method explicitly resolves the dynamics of the individual solid particles and the suspending fluid in the domain defined by the pore walls and solid particle surfaces. After describing the new method, it is applied to the study of solid/fluid suspension flow with deposition in a constriction and in a model random porous solid. This study clearly demonstrates that the deposits strongly influence the local flow fields, which in turn affect the deposition process indicating that this interplay should be modelled if accurate results are desired from trajectory methods.     

Modelling the flow of power-law fluids through anisotropic porous media at low-pore Reynolds number

The flow of power-law fluids through fibrous media at low-pore Reynolds number is investigated using the homogenization method for periodic structures with multiple scale expansions. This upscaling process shows that the macroscopic pressure gradient is also a power-law of the volume averaged velocity field. To determine the complete structure of the macroscopic flow law, numerical simulations have to be performed on representative elementary volume of porous media. In this paper, this has been achieved on 2D periodic arrays of parallel fibers with elliptical cross section of different aspect ratios. It is found that macroscopic flow models already proposed in the literature fail in reproducing numerical data within the whole volume fractions of fibers and aspect ratios ranges. Consequently, a novel methodology is proposed to establish the macroscopic tensorial seepage law within the framework of the theory of anisotropic tensor functions and using mechanical iso-dissipation curves. This methodology is illustrated through our numerical results.     

Transport analysis and model for the performance of an ultrasonically enhanced filtration process

This paper presents an analysis of a filtration technique that uses ultrasound to aid the collection of small particles (tens of microns in diameter) from suspension. In this method, particles are retained within a porous mesh that is subjected to a resonant ultrasonic field, even though the pore size of the mesh is two orders of magnitude greater than the particle diameter. The role of acoustic forces in driving the retention phenomena has previously been studied on a micro-scale, which included modeling and experimental verification of particle motion and trapping near a single element of the mesh. Here, we build on this work to develop an overall transport model to predict macroscopic performance criteria such as breakthrough times and the dynamics of the filtration performance. Results from this model compare favorably to experimental studies of the filtration phenomena; simulation results scale appropriately with experimental results in which inlet feed concentration and flow rate are varied.     

Finite-element modelling of combined free/porous flow regimes: simulation of flow through pleated cartridge filters

Mathematical modelling of creeping incompressible Stokes flow and low-permeability Darcy flow are well established and a number of reliable schemes for the simulation of these regimes are available in the literature. However, modelling of combined Stokes/Darcy regimes, such as those encountered in many types of industrial filters, still presents mathematical and practical challenges. In this paper, we present a finite-element model for the prediction and quantitative analyses of the hydrodynamic behaviour of deadend pleated cartridge filters. Elemental discretisation in this scheme is based on the use of unequal order approximation functions for velocity and pressure fields. We show that this discretisation generates unified stabilisation for both Stokes and Darcy equations and prevents ‘numerical locking’ whilst preserving the geometrical flexibility of the computational grid. Conducting a number of numerical tests, it is shown that the developed model is capable of yielding theoretically expected and accurate simulations for realistic industrially relevant problems. The model is tested for shear thickening non-Newtonian fluids, which represent fluids used in aeronautical applications and in some process industries. This study is part of a multi-disciplinary project undertaken by various investigators for the design and development of high-performance deadend pleated cartridge filters for aeronautical applications. It has been demonstrated that the developed model presents a cost effective, robust and reliable design tool to enable engineers to appraise the operation of such filters.     

Mathematical modelling of temperature induced moisture migration in bulk powders

This paper reviews the importance of temperature gradient induced moisture diffusion in powder beds. Redistribution of moisture by this mechanism is important for a wide variety of products, especially those which are crystalline in nature. Moisture transfer in these products can result in very high local water activity and lead to microbial spoilage and caking problems. A conceptual model was developed for heat and moisture transfer due to the application of thermal gradients across a one-dimensional powder bed. The validity of the key assumptions in the model formulation were demonstrated and a mathematical model was derived and solved numerically. The model was validated against experimental data collected using crystalline lactose powders as a working example.     

The traps in characterisation of PAN and carbon fibers by the mercury porosimetry method

The mechanical properties of a fiber relate to an average pore size or the pore size distribution in the fiber. In this study, the effects of testing sample preparation, crystallization rate, humidity, sizing agent, composition and processing conditions on the pore size distribution measurements were analyzed and discussed.     

Application of power addition as modelling technique for flow processes: Two case studies

In many of the continuum processes typically found in chemical engineering, the functional dependency of the dependent variable is only known for large and small values of the independent variable. Exact solutions in the transitional regime are often obscure for various reasons (e.g. narrow band within which the transition from one regime to the other occurs, inadequate knowledge of the physics in this area, etc.). An established method for the matching of limiting solutions is reviewed and subsequently applied. The method regards the known solutions as asymptotes and proposes addition to a power of such asymptotes. It yields a single, adjustable correlating equation that is applicable over the entire domain. This procedure circumvents the introduction of ad hoc curve fitting measures for the different regions and subsequent, unwanted discontinuities in piece-wise fitted correlative equations for the dependent variables. Experimental data of two diverse processes, namely flow in a straight-through diaphragm valve and the fluidisation of a packed bed, are analysed as case studies. Empirical results are investigated for possible asymptotic bounds whereafter power addition is applied to the functional dependencies. The outcome is compared to those of the empirical models and the results discussed. The procedure is revealed to be highly useful in the summarising and interpretation of experimental data in an elegant and simplistic manner. It may also, in general, aid the setup of experimental apparatus for investigation of continuum processes.     

Numerical modelling of fixed-cavity plate-and-frame filtration: Formulation, validation and optimisation

A model of fixed-cavity plate-and-frame filter presses is developed based on the theoretical framework developed by Buscall and White (1987. The consolidation of concentrated suspensions. Part 1. The theory of sedimentation. Journal of the Chemical Society. Faraday Transactions. I, Physical Chemistry in Condensed Phases 83, 873-891) and the piston-driven filtration model of Landman et al. (1991. Dewatering of flocculated suspensions by pressure filtration. Physics of Fluids. A, Fluid Dynamics 3(6), 1495-1509). The model properly accounts for compression of the suspension network structure within a filter cake in one dimension over a fixed cavity and allows for the effect of membrane resistance and ramping pressures. The model is validated by comparing on-site measurements of actual process performance at two water treatment plants with model predictions based on fundamental material properties of the feed slurries, the operating conditions and the press dimensions. The material properties are measured using laboratory based filtration tests. The model is then used to investigate the optimisation of press throughput and cake solids for a ferric water treatment slurry.     

Zeta-potential and local filtration properties: Constitutive relationships for TiO2 from experimental filtration measurements

The use of filtration to separate solid from liquids is a commonly-used unit operation employed in a range of different applications. The development of accurate models is therefore important in facilitating e.g. design, scale-up and troubleshooting. Accurate constitutive relationships between local filtration properties need to be formulated in order to form precise models of the filtration process. One important parameter that is seldom considered explicitly in filtration models is the inter particle forces, e.g. electrostatic forces. The aim of this study is to investigate local filtration properties, under controlled conditions, for the model material TiO₂ where the ζ-potential, and thereby one important parameter affecting the inter-particle interactions, is altered. In this study the local solidosity is measured during filtration by γ-attenuation, the local pressure is measured using capillary tubes. These data are used to calculate the local specific filtration resistance. The compressibility of the filtration cake was changed substantially by altering the ζ-potential. Several published constitutive relationships between local data and specific filtration resistance were applied; they yielded very similar parameters that were in good accordance with the characterization of the material.     

Modelling of catalyst particle skin effects using a 3-D pore network model and quantitive microscopy

The pore structure of fragments of steam reforming catalyst ring-shaped pellets was characterised so as to simulate a larger particle using larger pore networks comprising millions of pore segments. The pore size distribution generated for a 3-D stochastic network was deduced from the experimental mercury penetration curve. The penetration processes which take place within the pore network at different pressures can be visualised by randomly slicing irregular 3-D pore networks to create 2-D “Virtual reality slice” images. The experimental visualisation technique of low-melting alloy impregnation was applied to the larger ring catalyst fragments at several pressure levels in order to investigate the effect of size, the fragment geometry, and a suspected skin effect on the mercury penetration curve for these particles. The experimental scanning electron microscopy images, obtained from polished sections of a large 5-mm ring fragment, can be compared directly with the 2-D virtual slice images from randomised 3-D pore networks for direct quantification of the pore structure using image analysis techniques.     

Relation of Structure,Properties and Performance of Fibrous Media for Gas Filtration

The relation between the structure, permeability and filtration performance of needled nonwoven filter media is reported. Surface treated and untreated fabrics were studied, including microporous coated, laminated e‐PTFE, heated calendered and surface singed materials. Surface treatments appear to impart higher packing densities, but mean pore size is governed by the type of treatment with microporous and PTFE having the smaller values. Filtration performance was determined from graphs of pressure drop with filtration duration, differences in filtration efficiencies and the dust concentrations in gas emissions. Except for the singed materials, the treated fabrics depicted surface filtration and the untreated depth filtration. The trend for singed fabrics showed initial depth followed by surface filtration. Markedly higher filtration efficiencies were obtained with surface filtration, which corresponded with higher rates of pressure drop. Surface treatments, giving smaller mean pore sizes, resulted in higher filter cake resistance owing to low particle penetration through the base fabric.     

A network theory for the structured modelling of chemical processes

A structuring methodology for dynamic models of chemical engineering processes is presented. The main ideas of the methodology were outlined in a previous publication for the class of well-mixed systems. In this contribution, the methodology is extended to spatially distributed systems and to particulate processes. Furthermore, the structuring principle is used to make a conceptual link between the macroscopic world of process simulation and the microscopic world of molecular simulation. It is shown that a uniform structuring principle can be applied to the modularisation of most classes of chemical engineering models. The structuring principle can be used as a theoretical framework for the implementation of modular families of chemical engineering models in modern computer aided modelling tools.     

Studies of the entrapment of non-wetting fluid within nanoporous media using a synergistic combination of MRI and micro-computed X-ray tomography

Three-dimensional magnetic resonance imaging (MRI) and micro-computed X-ray tomography (micro-CXT) have been combined to study the entrapment of mercury within nanoporous silica materials following porosimetry. MR images have been used to construct structural models of particular porous media within which several simulations of mercury intrusion and retraction have been performed with variations in the mechanism for the ‘snap-off’ of the mercury menisci. The simulations gave rise to different predictions for the pattern of the macroscopic spatial distribution of entrapped mercury, depending on ‘snap-off’ mechanism, which were then compared with corresponding experimental data obtained from micro-CXT images of real pellets containing entrapped mercury. The information obtained from the micro-CXT images, and also from the porosimetry curves themselves, was then used to constrain a model for the microscopic mercury retraction mechanism. Additional predictions of the retraction model were then subsequently confirmed using scanning loop experiments. The simulations showed that the overall level of entrapment of mercury was determined by the close interaction between the pellet macroscopic structure (particularly pore size spatial correlation), and the microscopic mercury retraction mechanism. Hence, it was subsequently possible to explain fully why high mercury entrapment occurred within one particular type of sol-gel silica material, while only low entrapment occurred in another batch of superficially similar material.     

Effect of B4C,TiB2 and ZrSiO4 ceramic particles on mechanical properties of aluminium matrix composites: Experimental investigation and predictive modelling

This paper focuses on the influence of processing temperature and inclusion of micron-sized B₄C, TiB₂ and ZrSiO₄ on the mechanical performance of aluminium matrix composites fabricated through stir casting. The ceramic/aluminium composite could withstand greater external loads, due to interfacial ceramic/aluminium bonding effect on the movement of grain and twin boundaries. Based on experimental results, the tensile strength and hardness of ceramic reinforced composite are significantly increased. The maximum improvement is achieved through adding ZrSiO₄ and TiB₂, which has led to 52% and 125% increase in tensile strength and hardness, respectively. To predict the effect of incorporating ceramic reinforcements on the mechanical properties of composites, experimental data of mechanical tests are used to create 3 models named Levenberg–Marquardt Algorithm (LMA) neural networks. The results show that the LMA- neural networks models have a high level of accuracy in the prediction of mechanical properties for ceramic reinforced-aluminium matrix composites.     

Modelling and simulation of the nonlinear behaviour of paper: A cellular materials approach

Paper is a stochastic network of fibres, water and additives, and in that sense it may be envisaged as a composite material. Since fibres are much longer than the thickness of the paper sheet, the network is planar and almost two-dimensional. The two-dimensional structure governs many paper properties but the three-dimensional porous structure is also important. Insight into the structural changes that take place when paper is compressed in the paper machine may be gained by modelling and simulation of its viscoelastoplastic behaviour. The present work describes a mathematical model based on the cellular solids theory, characterising the nonlinear rheologic behaviour of the material. This approach results in an unsteady state problem and the resulting set of ODEs is solved by means of the DLSODES subroutine, which uses an integrator based in the Gear method. Experiments were conducted on a laboratory-scale dynamic press in order to validate the mechanical model.