Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls

Heat transfer and entropy generation analysis of the thermally developing forced convection in a porous-saturated duct of rectangular cross-section, with walls maintained at a constant and uniform heat flux, is investigated based on the Brinkman flow model. The classical Galerkin method is used to obtain the fully developed velocity distribution. To solve the thermal energy equation, with the effects of viscous dissipation being included, the Extended Weighted Residuals Method (EWRM) is applied. The local (three dimensional) temperature field is solved by utilizing the Green’s function solution based on the EWRM where symbolic algebra is being used for convenience in presentation. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate, the aspect ratio, the Darcy number, the viscosity ratio, and the Brinkman number. With the velocity and temperature field being determined, the Second Law (of Thermodynamics) aspect of the problem is also investigated. Approximate closed form solutions are also presented for two limiting cases of MDa values. It is observed that decreasing the aspect ratio and MDa values increases the entropy generation rate.

A mathematical model for estimating the extent of solute- and water-flux heterogeneity in multiple sample percolation experiments

Multiple sampling is widely used in vadose zone percolation experiments to investigate the extent in which soil structure heterogeneities influence the spatial and temporal distributions of water and solutes. In this note, a simple, robust, mathematical model, based on the beta-statistical distribution, is proposed as a method of quantifying the magnitude of heterogeneity in such experiments. The model relies on fitting two parameters, alpha and zeta to the cumulative elution curves generated in multiple-sample percolation experiments. The model does not require knowledge of the soil structure. A homogeneous or uniform distribution of a solute and/or soil-water is indicated by alpha = zeta = 1, Using these parameters, a heterogeneity index (HI) is defined as root 3 times the ratio of the standard deviation and mean. Uniform or homogeneous flow of water or solutes is indicated by HI = 1 and heterogeneity is indicated by HI > 1. A large value for this index may indicate preferential flow. The heterogeneity index relies only on knowledge of the elution curves generated from multiple sample percolation experiments and is, therefore, easily calculated. The index may also be used to describe and compare the differences in solute and soil-water percolation from different experiments. The use of this index is discussed for several different leaching experiments. (C) 1999 Elsevier Science B.V. All rights reserved.

Finite element analysis of heat transfer and mineralization in layered hydrothermal systems with upward throughflow

We use the finite element method to solve the coupled problem between convective pore-fluid flow, heat transfer and mineralization in layered hydrothermal systems with upward throughflow. In particular, we present the improved rock alteration index (IRAI) concept for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in the systems. To validate the numerical method used in the computation, analytical solutions to a benchmark problem have been derived. After the numerical method is validated, it is used to investigate the pattern of pore-fluid Aom, the distribution of temperature and the mineralization pattern of gold minerals in a layered hydrothermal system with upward throughflow. The related numerical results have demonstrated that the present concept of IRAI is useful and applicable for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in hydrothermal systems. (C) 2000 Elsevier Science S.A. All rights reserved.

Finite element modeling of fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins

In order to use the finite element method for solving fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins effectively and efficiently, we have presented, in this paper, the new concept and numerical algorithms to deal with the fundamental issues associated with the fluid-rock interaction problems. These fundamental issues are often overlooked by some purely numerical modelers. (1) Since the fluid-rock interaction problem involves heterogeneous chemical reactions between reactive aqueous chemical species in the pore-fluid and solid minerals in the rock masses, it is necessary to develop the new concept of the generalized concentration of a solid mineral, so that two types of reactive mass transport equations, namely, the conventional mass transport equation for the aqueous chemical species in the pore-fluid and the degenerated mass transport equation for the solid minerals in the rock mass, can be solved simultaneously in computation. (2) Since the reaction area between the pore-fluid and mineral surfaces is basically a function of the generalized concentration of the solid mineral, there is a definite need to appropriately consider the dependence of the dissolution rate of a dissolving mineral on its generalized concentration in the numerical analysis. (3) Considering the direct consequence of the porosity evolution with time in the transient analysis of fluid-rock interaction problems; we have proposed the term splitting algorithm and the concept of the equivalent source/sink terms in mass transport equations so that the problem of variable mesh Peclet number and Courant number has been successfully converted into the problem of constant mesh Peclet and Courant numbers. The numerical results from an application example have demonstrated the usefulness of the proposed concepts and the robustness of the proposed numerical algorithms in dealing with fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins. (C) 2001 Elsevier Science B.V. All rights reserved.

Finite element modelling of rock alteration and metamorphic process in hydrothermal systems

We use the finite element method to simulate the rock alteration and metamorphic process in hydrothermal systems. In particular, we consider the fluid-rock interaction problems in pore-fluid saturated porous rocks. Since the fluid rock interaction takes place at the contact interface between the pore-fluid and solid minerals, it is governed by the chemical reaction which usually takes place very slowly at this contact interface, from the geochemical point of view. Due to the relative slowness of the rate of the chemical reaction to the velocity of the pore-fluid flow in the hydrothermal system to be considered, there exists a retardation zone, in which the conventional static theory in geochemistry does not hold true. Since this issue is often overlooked by some purely numerical modellers, it is emphasized in this paper. The related results from a typical rock alteration and metamorphic problem in a hydrothermal system have shown not only the detailed rock alteration and metamorphic process, but also the size of the retardation zone in the hydrothermal system. Copyright (C) 2001 John Wiley & Sons, Ltd.

Finite element modelling of reactive fluids mixing and mineralization in pore-fluid saturated hydrothermal/sedimentary basins

We present the finite element simulations of reactive mineral carrying fluids mixing and mineralization in pore-fluid saturated hydrothermal/sedimentary basins. In particular we explore the mixing of reactive sulfide and sulfate fluids and the relevant patterns of mineralization for Load, zinc and iron minerals in the regime of temperature-gradient-driven convective flow. Since the mineralization and ore body formation may last quite a long period of time in a hydrothermal basin, it is commonly assumed that, in the geochemistry, the solutions of minerals are in an equilibrium state or near an equilibrium state. Therefore, the mineralization rate of a particular kind of mineral can be expressed as the product of the pore-fluid velocity and the equilibrium concentration of this particular kind of mineral Using the present mineralization rate of a mineral, the potential of the modern mineralization theory is illustrated by means of finite element studies related to reactive mineral-carrying fluids mixing problems in materially homogeneous and inhomogeneous porous rock basins.

Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined.

Hydraulic tracer studies in a pilot scale subsurface flow constructed wetland

Current design procedures for Subsurface Flow (SSF) Wetlands are based on the simplifying assumptions of plug flow and first order decay of pollutants. These design procedures do yield functional wetlands but result in over-design and inadequate descriptions of the pollutant removal mechanisms which occur within them. Even though these deficiencies are often noted, few authors have attempted to improve modelling of either flow or pollutant removal in such systems. Consequently the Oxley Creek Wetland, a pilot scale SSF wetland designed to enable rigorous monitoring, has recently been constructed in Brisbane, Australia. Tracer studies have been carried out in order to determine the hydraulics of this wetland prior to commissioning it with sealed sewage. The tracer studies will continue during the wetland's commissioning and operational phases. These studies will improve our understanding of the hydraulics of newly built SSF wetlands and the changes brought on by operational factors such as biological films and wetland plant root structures. Results to date indicate that the flow through the gravel beds is not uniform and cannot be adequately modelled by a single parameter, plug flow with dispersion, model. We have developed a multiparameter model, incorporating four plug flow reactors, which provides a better approximation of our experimental data. With further development this model will allow improvements to current SSF wetland design procedures and operational strategies, and will underpin investigations into the pollutant removal mechanisms at the Oxley Creek Wetland. (C) 1997 IAWQ. Published by Elsevier Science Ltd.

A generalised dynamic model for char particle gasification with structure evolution and peripheral fragmentation

A generalised model for the prediction of single char particle gasification dynamics, accounting for multi-component mass transfer with chemical reaction, heat transfer, as well as structure evolution and peripheral fragmentation is developed in this paper. Maxwell-Stefan analysis is uniquely applied to both micro and macropores within the framework of the dusty-gas model to account for the bidisperse nature of the char, which differs significantly from the conventional models that are based on a single pore type. The peripheral fragmentation and random-pore correlation incorporated into the model enable prediction of structure/reactivity relationships. The occurrence of chemical reaction within the boundary layer reported by Biggs and Agarwal (Chem. Eng. Sci. 52 (1997) 941) has been confirmed through an analysis of CO/CO2 product ratio obtained from model simulations. However, it is also quantitatively observed that the significance of boundary layer reaction reduces notably with the reduction of oxygen concentration in the flue gas, operational pressure and film thickness. Computations have also shown that in the presence of diffusional gradients peripheral fragmentation occurs in the early stages on the surface, after which conversion quickens significantly due to small particle size. Results of the early commencement of peripheral fragmentation at relatively low overall conversion obtained from a large number of simulations agree well with experimental observations reported by Feng and Bhatia (Energy & Fuels 14 (2000) 297). Comprehensive analysis of simulation results is carried out based on well accepted physical principles to rationalise model prediction. (C) 2001 Elsevier Science Ltd. AH rights reserved.

Surface diffusion and adsorption of hydrocarbons in activated carbon

Adsorption and diffusion in a porous media were studied theoretically and experimentally with a differential transient permeation method. The porous medium is allowed to equilibrate at some specified loading, and then the time trajectory of the permeation process is followed after a small difference between the pressures at the end faces of the porous medium is introduced at time t = 0 +. Such a trajectory us. time would contain adsorption and diffusion characteristics of the system. By studying this for various surface loadings, pore and surface diffusions can be fully characterized. Mathematical modeling of transient permeation is detailed for pure gases or vapors diffusion and adsorption in porous media. Effects of nonlinearity of adsorption isotherm, pressure, temperature and heat effects were considered in the model. Experimental data of diffusion and adsorption of propane, n-butane and n-hexane in activated carbon at different temperatures and loadings show the potential of this method as a useful tool to study adsorption kinetics in porous media. Validity of the model is best tested against the transient data where the kinetics curves exhibit sigmoidal shape, which is a result of the diffusion and adsorption rate during the initial stage of permeation.

Characterization of micro-mesoporous carbon media

A simple method to characterize the micro and mesoporous carbon media is discussed. In this method, the overall adsorption quantity is the sum of capacities of all pores (slit shape is assumed), in each of which the process of adsorption occurs in two sequential steps: the multi-layering followed by pore filling steps. The critical factor in these two steps is the enhancement of the pressure of occluded 'free' molecules in the pore as well as the enhancement of the adsorption layer thickness. Both of these enhancements are due to the overlapping of the potential fields contributed by the two opposite walls. The classical BET and modified Kelvin equations are assumed to be applicable for the two steps mentioned above, with the allowance for the enhanced pore pressure, the enhanced adsorption energy and the enhanced BET constant,all of which vary with pore width. The method is then applied to data of many carbon samples of different sources to derive their respective pore size distributions, which are compared with those obtained from DFT analysis. Similar pore size distributions (PSDs) are observed although our method gives sharper distribution. Furthermore, we use our theory to analyze adsorption data of nitrogen at 77 K and that of benzene at 303 K (ambient temperature). The PSDs derived from these two different probe molecules are similar, with some small differences that could be attributed to the molecular properties, such as the collision diameter. Permeation characteristics of sub-critical fluids are also discussed in this paper. (C) 2001 Elsevier Science B.V. All rights reserved.

On the surface diffusion of hydrocarbons in microporous activated carbon

This paper addresses the current status of the various diffusion theories for surface diffusion in the literature. The inadequacy of these models to explain the surface diffusion of many hydrocarbons in microporous activated carbon is shown in this paper. They all can explain the increase of the surface diffusivity (D-mu) with loading, but cannot explain the increase of the surface permeability (D(mu)partial derivativeC(mu)/partial derivativeP) with loading as observed in our data of diffusion of hydrocarbons in activated carbon, even when the surface heterogeneity is accounted for in those models. The explanation for their failure was presented, and we have put forward a theory to explain the increase of surface diffusion permeability with loading. This new theory assumes the variation of the activation energy for surface diffusion with surface loading, and it is validated with diffusion data of propane, n-butane, n-hexane, benzene and ethanol in activated carbon. (C) 2001 Elsevier Science Ltd. All rights reserved.

Experimental investigation of liquid flow shift due to gas cross flow in non-wetted packed beds

An experimental study has been carried out for the gas-liquid two-phase flow in a packed bed simulating conditions of the gas and liquid flows in the lower part of blast furnace. The localised liquid flow phenomenon in presence of gas cross flow, which usually occurs around the cohesive zone and raceway in blast furnace, was investigated in detail. Such liquid flow is characterised in terms of liquid shift distance or liquid shift angle that can effectively be measured by the experiments involved in the current study. It is found that liquid shift angle does not significantly increase or decrease with different packing depth. This finding supports the hypothesis of the force balance model where a vectorial relationship among acting forces, i.e. gas drag force, gravitational force and solid-liquid friction force, and liquid shift angle does exist. Liquid shift angle is inversely proportional to particle size and liquid density, and proportional to square of gas superficial velocity, but is almost independent on liquid flowrate and liquid viscosity. The gas-liquid drag coefficient, an important aspect for quantifying the interaction between gas and liquid flows, was conceptually modified based on the discrete feature of liquid flow through a packed bed and evaluated by the combined theoretical and experimental investigation. Experimental measurements suggest that the gas-liquid drag coefficient is approximately a constant (C-DG(')=5.4+/-1.0) and is independent on liquid properties, gas velocity and packing structure. The result shows a good agreement with previous experimental data and prediction of the existing liquid flow model.

Structural basis for control of secondary vessels in the long-finned eel, Anguilla reinhardtii

Histological sections of primary segmental arteries and associated interarterial anastomoses and secondary vessels from the long-finned eel Anguilla reinhardtii were examined by light and transmission electron microscopy. Interarterial anastomoses were found to originate from the primary vasculature as depressions through the tunica intima and media, from where they ran perpendicularly to the adventitial layer, before coiling extensively. From here the anastomoses travelled a relatively linear path in the outer margin of the adventitia to anastomose with a secondary vessel running in parallel with the primary counterpart. In contrast to findings from other species, secondary vessels had a structure quite similar to that of primary vessels; they were lined by endothelial cells on a continuous basement membrane, with a single layer of smooth muscle cells surrounding the vessel. Smooth muscle cells were also found in the vicinity of interarterial anastomoses in the adventitia, but these appeared more longitudinally orientated. The presence of smooth muscle cells on all aspects of the secondary circulation suggests that this vascular system is regulated in a similar manner as the primary vascular system. Because interarterial anastomoses are structurally integrated with the primary vessel from which they originate, it is anticipated that flow through secondary vessels to some extent is affected by the vascular tone of the primary vessel. Immunohistochemical studies showed that primary segmental arteries displayed moderate immunoreactivity to antibodies against 5-hydroxytryptamine and substance P, while interarterial anastomoses and secondary vessels showed dense immunoreactivity. No immunoreactivity was observed on primary or secondary arteries against neuropeptide Y or calcitonin gene-related peptide.

Characterizing the physical and chemical properties of a vermicompost filter bed

Vermicompost filtration is a new on-site waste treatment system. Consequently, little is known about the filter medium properties. The aim of this preliminary study was to quantify physical and compositional properties of vermicompost filter beds that had been used to treat domestic solid organic waste and wastewater. This paper presents the trials performed on pilot-scale reactors filled with vermicompost from a full-scale vermicompost filtration system. Household solid organic waste and raw wastewater at the rate of 130 L/m(2)/d was applied to the reactor bed surface over a four-month period. It was found that fresh casts laid on the bed surface had a BOD of 1290 mg/g VS while casts buried to a depth of 10 cm had a BOD of 605 mg/g VS. Below this depth there was little further biodegradation of earthworm casts despite cast ages of up to five years. Solid material in the reactor accounted for only 7-10% of the reactor volume. The total voidage comprised of large free-draining pores, which accounted for 15-20% of the reactor volume and 60-70% micropores, able to hold up water against gravity. It was shown that water could flow through the medium micropores and macropores following a wastewater application. The wastewater flow characteristics were modeled by a two-region model based on the Richards Equation, an equation used to describe porous spatially heterogeneous materials.