Computationally efficient solution techniques for adsorption problems involving steep gradients in bidisperse particles

A piecewise uniform fitted mesh method turns out to be sufficient for the solution of a surprisingly wide variety of singularly perturbed problems involving steep gradients. The technique is applied to a model of adsorption in bidisperse solids for which two fitted mesh techniques, a fitted-mesh finite difference method (FMFDM) and fitted mesh collocation method (FMCM) are presented. A combination (FMCMD) of FMCM and the DASSL integration package is found to be most effective in solving the problems. Numerical solutions (FMFDM and FMCMD) were found to match the analytical solution when the adsorption isotherm is linear, even under conditions involving steep gradients for which global collocation fails. In particular, FMCMD is highly efficient for macropore diffusion control or micropore diffusion control. These techniques are simple and there is no limit on the range of the parameters. The techniques can be applied to a variety of adsorption and desorption problems in bidisperse solids with non-linear isotherm and for arbitrary particle geometry.

Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas-solid and fluid-solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection-diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection-diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov-Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor-corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus. (C) 2001 Elsevier Science Ltd. All rights reserved.

Process systems modelling and applications in granulation: A review

Granulation is one of the fundamental operations in particulate processing and has a very ancient history and widespread use. Much fundamental particle science has occurred in the last two decades to help understand the underlying phenomena. Yet, until recently the development of granulation systems was mostly based on popular practice. The use of process systems approaches to the integrated understanding of these operations is providing improved insight into the complex nature of the processes. Improved mathematical representations, new solution techniques and the application of the models to industrial processes are yielding better designs, improved optimisation and tighter control of these systems. The parallel development of advanced instrumentation and the use of inferential approaches provide real-time access to system parameters necessary for improvements in operation. The use of advanced models to help develop real-time plant diagnostic systems provides further evidence of the utility of process system approaches to granulation processes. This paper highlights some of those aspects of granulation. (c) 2005 Elsevier Ltd. All rights reserved.

Analytical solution to the zero-inertia problem for surge flow phenomena in nonprismatic channels

Surge flow phenomena. e.g.. as a consequence of a dam failure or a flash flood, represent free boundary problems. ne extending computational domain together with the discontinuities involved renders their numerical solution a cumbersome procedure. This contribution proposes an analytical solution to the problem, It is based on the slightly modified zero-inertia (ZI) differential equations for nonprismatic channels and uses exclusively physical parameters. Employing the concept of a momentum-representative cross section of the moving water body together with a specific relationship for describing the cross sectional geometry leads, after considerable mathematical calculus. to the analytical solution. The hydrodynamic analytical model is free of numerical troubles, easy to run, computationally efficient. and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model compares very favorably with a full hydrodynamic numerical model in respect to published results of surge flow simulations in different types of prismatic channels. In order to extend these considerations to natural rivers, the accuracy of the analytical model in describing an irregular cross section is investigated and tested successfully. A sensitivity and error analysis reveals the important impact of the hydraulic radius on the velocity of the surge, and this underlines the importance of an adequate description of the topography, The new approach is finally applied to simulate a surge propagating down the irregularly shaped Isar Valley in the Bavarian Alps after a hypothetical dam failure. The straightforward and fully stable computation of the flood hydrograph along the Isar Valley clearly reflects the impact of the strongly varying topographic characteristics on the How phenomenon. Apart from treating surge flow phenomena as a whole, the analytical solution also offers a rigorous alternative to both (a) the approximate Whitham solution, for generating initial values, and (b) the rough volume balance techniques used to model the wave tip in numerical surge flow computations.

A new wavelet-based method for the solution of the population balance equation

A new wavelet-based method for solving population balance equations with simultaneous nucleation, growth and agglomeration is proposed, which uses wavelets to express the functions. The technique is very general, powerful and overcomes the crucial problems of numerical diffusion and stability that often characterize previous techniques in this area. It is also applicable to an arbitrary grid to control resolution and computational efficiency. The proposed technique has been tested for pure agglomeration, simultaneous nucleation and growth, and simultaneous growth and agglomeration. In all cases, the predicted and analytical particle size distributions are in excellent agreement. The presence of moving sharp fronts can be addressed without the prior investigation of the characteristics of the processes. (C) 2001 Published by Elsevier Science Ltd.

Characterisation and environmental application of an Australian natural zeolite for basic dye removal from aqueous solution

An Australian natural zeolite was collected, characterised and employed for basic dye adsorption in aqueous solution. The natural zeolite is mainly composed of clinoptiloite, quartz and mordenite and has cation-exchange capacity of 120 meq/100 g. The natural zeolite presents higher adsorption capacity for methylene blue than rhodamine B with the maximal adsorption capacity of 2.8 x 10(-5) and 7.9 x 10(-5) Mot/g at 50 degrees C for rhodamine B and methylene blue, respectively. Kinetic studies indicated that the adsorption followed the pseudo second-order kinetics and could be described as two-stage diffusion process. The adsorption isotherm could be fitted by the Langmuir and Freundlich models. Thermodynamic calculations showed that the adsorption is endothermic process with Delta H degrees at 2.0 and 8.7 kJ/mol for rhodamine B and methylene blue. It has also found that the regenerated zeolites by high-temperature calcination and Fenton oxidation showed similar adsorption capacity but lower than the fresh sample. Only 60% capacity could be recovered by the two regeneration techniques. (c) 2006 Elsevier B.V. All rights reserved.

2D strain - a new approach to strain and strain rate: the solution to the angle-dependence of tissue Doppler?

Purpose: Tissue Doppler strain rate imaging (SRI) have been validated and applied in various clinical settings, but the clinical use of this modality is still limited due to time-consuming postprocessing, unfavorable signal to noise ratio and major angle dependency of image acquisition. 2D Strain (2DS) measures strain parameters through automated tissue tracking (Lagrangian strain) rather than tissue velocity regression. We sought to compare the accuracy of this technique with SRI and evaluate whether it overcomes the above limitations. Methods: We assessed 26 patients (13 female, age 60±5yrs) at low risk of CAD and with normal DSE at both baseline and peak stress. End systolic strain (ESS), peak systolic strain rate (SR), and timing parameters were measured by two independent observers using SRI and 2D Strain. Myocardial segments were excluded from the analyses if the insonation angle exceeded 30 degrees or if the segments were not visualized; 417 segments were evaluated. Results: Normal ranges for TVI and CEB approaches were comparable for SR (-0.99 ± 0.39 vs -0.88 ± 0.36, p=NS), ESS (-15.1 ± 6.5 vs -14.9 ± 6.3, p=NS), time to end of systole (174 ± 47 vs 174 ± 53, p=NS) and time to peak SR (TTP; 340 ± 34 vs 375 ± 57). The best correlations between the techniques were for time to end systole (rest r=0.6, p

On compliance of business processes with business contracts

This paper addresses the problem of ensuring compliance of business processes, implemented within and across organisational boundaries, with the constraints stated in related business contracts. In order to deal with the complexity of this problem we propose two solutions that allow for a systematic and increasingly automated support for addressing two specific compliance issues. One solution provides a set of guidelines for progressively transforming contract conditions into business processes that are consistent with contract conditions thus avoiding violation of the rules in contract. Another solution compares rules in business contracts and rules in business processes to check for possible inconsistencies. Both approaches rely on a computer interpretable representation of contract conditions that embodies contract semantics. This semantics is described in terms of a logic based formalism allowing for the description of obligations, prohibitions, permissions and violations conditions in contracts. This semantics was based on an analysis of typical building blocks of many commercial, financial and government contracts. The study proved that our contract formalism provides a good foundation for describing key types of conditions in contracts, and has also given several insights into valuable transformation techniques and formalisms needed to establish better alignment between these two, traditionally separate areas of research and endeavour. The study also revealed a number of new areas of research, some of which we intend to address in near future.

From Midden to Sieve: The Impact of Differential Recovery and Quantification Techniques on Interpretations of Shellfish Remains in Australian Coastal Archaeology

Experimental mechanical sieving methods are applied to samples of shellfish remains from three sites in southeast Queensland, Seven Mile Creek Mound, Sandstone Point and One-Tree, to test the efficacy of various recovery and quantification procedures commonly applied to shellfish assemblages in Australia. There has been considerable debate regarding the most appropriate sieve sizes and quantification methods that should be applied in the recovery of vertebrate faunal remains. Few studies, however, have addressed the impact of recovery and quantification methods on the interpretation of invertebrates, specifically shellfish remains. In this study, five shellfish taxa representing four bivalves (Anadara trapezia, Trichomya hirsutus, Saccostrea glomerata, Donax deltoides) and one gastropod (Pyrazus ebeninus) common in eastern Australian midden assemblages are sieved through 10mm, 6.3mm and 3.15mm mesh. Results are quantified using MNI, NISP and weight. Analyses indicate that different structural properties and pre- and postdepositional factors affect recovery rates. Fragile taxa (T. hirsutus) or those with foliated structure (S. glomerata) tend to be overrepresented by NISP measures in smaller sieve fractions, while more robust taxa (A. trapezia and P. ebeninus) tend to be overrepresented by weight measures. Results demonstrate that for all quantification methods tested a 3mm sieve should be used on all sites to allow for regional comparability and to effectively collect all available information about the shellfish remains.

Towards realistic simulations of lava dome growth using the level set method

The level set method has been implemented in a computational volcanology context. New techniques are presented to solve the advection equation and the reinitialisation equation. These techniques are based upon an algorithm developed in the finite difference context, but are modified to take advantage of the robustness of the finite element method. The resulting algorithm is tested on a well documented Rayleigh–Taylor instability benchmark [19], and on an axisymmetric problem where the analytical solution is known. Finally, the algorithm is applied to a basic study of lava dome growth.

Analytical solution of forced convection in a duct of rectangular cross-section saturated by a porous medium

A theoretical analysis is presented to investigate fully developed (both thermally and hydrodynamically) forced convection in a duct of rectangular cross-section filled with a hyper-porous medium. The Darcy-Brinkman model for flow through porous media was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [1], is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.

Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature

A numerical study is reported to investigate both the First and the Second Law of Thermodynamics for thermally developing forced convection in a circular tube filled by a saturated porous medium, with uniform wall temperature, and with the effects of viscous dissipation included. A theoretical analysis is also presented to study the problem for the asymptotic region applying the perturbation solution of the Brinkman momentum equation reported by Hooman and Kani [1]. Expressions are reported for the temperature profile, the Nusselt number, the Bejan number, and the dimensionless entropy generation rate in the asymptotic region. Numerical results are found to be in good agreement with theoretical counterparts.

Exact solution of the A(n-1)((1)) trigonometric vertex model with non-diagonal open boundaries

The A(n-1)((1)) trigonometric vertex model with generic non-diagonal boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.