On the effect of tracer density on axial dispersion in a batch oscillatory baffled column

In this paper, we report our modelling evaluation on the effect of tracer density on axial dispersion in a batch oscillatory baffled column (OBC). Tracer solution of potassium nitrite, its specific density ranged from 1.0 to 1.5, was used in the study, and was injected to the vertical column from either the top or bottom. Local concentration profiles are measured using conductivity probes at two locations along the height of the column. Using the experimental measured concentration profiles together with both 'Tank-in-Series' and 'Plug Flow with Axial Dispersion' models, axial dispersion coefficients were determined and used to describe the effect of specific tracer density on mixing in the OBC. The results showed that the axial dispersion coefficients evaluated by the two models are very similar in both magnitudes and trends, and the range of variations in such coefficients is generally larger for the bottom injection than for the top one. Empirical correlations linking the mechanical energy for mixing, the specific density of tracer and axial dispersion coefficient were established. Using these correlations, we identified the enhancements of up to 269% on axial dispersion for various specific tracer densities. (C) 2002 Elsevier Science B.V. All rights reserved.

Flow and axial dispersion simulation for traveling axisymmetric Taylor vortices

Numerical experiments using a finite difference method were carried out to determine the motion of axisymmetric Taylor vortices for narrow-gap Taylor vortex flow. When a pressure gradient is imposed on the flow the vortices are observed to move with an axial speed of 1.16 +/- 0.005 times the mean axial flow velocity. The method of Brenner was used to calculate the long-time axial spread of material in the flow. For flows where there is no pressure gradient, the axial dispersion scales with the square root of the molecular diffusion, in agreement with the results of Rosen-bluth et al. for high Peclet number dispersion in spatially periodic flows with a roll structure. When a pressure gradient is imposed the dispersion increases by an amount approximately equal to 6.5 x 10(-4) (W) over bar(2)d(2)/D-m, where (W) over bar is the average axial velocity in the annulus, analogous to Taylor dispersion for laminar flow in an empty tube.

Residence time distributions of gas flowing through rotating drum bioreactors

Residence time distribution studies of gas through a rotating drum bioreactor for solid-state fermentation were performed using carbon monoxide as a tracer gas. The exit concentration as a function of time differed considerably from profiles expected for plug flow, plug flow with axial dispersion, and continuous stirred tank reactor (CSTR) models. The data were then fitted by least-squares analysis to mathematical models describing a central plug flow region surrounded by either one dead region (a three-parameter model) or two dead regions (a five-parameter model). Model parameters were the dispersion coefficient in the central plug flow region, the volumes of the dead regions, and the exchange rates between the different regions. The superficial velocity of the gas through the reactor has a large effect on parameter values. Increased superficial velocity tends to decrease dead region volumes, interregion transfer rates, and axial dispersion. The significant deviation from CSTR, plug flow, and plug flow with axial dispersion of the residence time distribution of gas within small-scale reactors can lead to underestimation of the calculation of mass and heat transfer coefficients and hence has implications for reactor design and scaleup. (C) 2001 John Wiley & Sons, Inc.

Modeling of hepatic elimination and organ distribution kinetics with the extended convection-dispersion model

The conventional convection-dispersion (also called axial dispersion) model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. An extended form of the convection-dispersion model has been developed to adequately describe the outflow concentration-time profiles for vascular markers at both short and long times after bolus injections into perfused livers. The model, based on flux concentration and a convolution of catheters and large vessels, assumes that solute elimination in hepatocytes follows either fast distribution into or radial diffusion in hepatocytes. The model includes a secondary vascular compartment, postulated to be interconnecting sinusoids. Analysis of the mean hepatic transit time (MTT) and normalized variance (CV2) of solutes with extraction showed that the discrepancy between the predictions of MTT and CV2 for the extended and conventional models are essentially identical irrespective of the magnitude of rate constants representing permeability, volume, and clearance parameters, providing that there is significant hepatic extraction. In conclusion, the application of a newly developed extended convection-dispersion model has shown that the unweighted conventional convection-dispersion model can be used to describe the disposition of extracted solutes and, in particular, to estimate hepatic availability and clearance in booth experimental and clinical situations.

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.

On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed

The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicit a priori assumption of the model is that the transit time density of intravascular indicators is approximated by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vascular indicators. A sum of two inverse Gaussian functions is proposed as ail alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models. (C) 1997 Society for Mathematical Biology.

Commentary: Using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyanaa in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application. (C) 2000 Wiley-Liss Inc. and the American Pharmaceutical Association J Pharm Sci 89:1579-1586, 2000.

Cognitive deficits associated with cancer: A model of subjective and objective outcomes

Cancer and its treatment can affect many different aspects of quality of life. As a construct measured subjectively, quality of life shows an inconsistent relationship with objective outcome measures. That is, sometimes subjective and objective outcomes correspond with each other and sometimes they show little or no relationship. In this article, we propose a model for the relationship between subjective and objective outcomes using the example of cognitive function in people with cancer. The model and the research findings on which it is based help demonstrate that, in some circumstances, subjective measures of cognitive function correlate more strongly with psychosocial variables such as appraisal, coping, and emotions than with objective cognitive function. The model may provide a useful framework for research and clinical practice in quality of life for people with cancer.

Three-dimensional model for multi-component reactive transport with variable density groundwater flow

PHWAT is a new model that couples a geochemical reaction model (PHREEQC-2) with a density-dependent groundwater flow and solute transport model (SEAWAT) using the split-operator approach. PHWAT was developed to simulate multi-component reactive transport in variable density groundwater flow. Fluid density in PHWAT depends not on only the concentration of a single species as in SEAWAT, but also the concentrations of other dissolved chemicals that can be subject to reactive processes. Simulation results of PHWAT and PHREEQC-2 were compared in their predictions of effluent concentration from a column experiment. Both models produced identical results, showing that PHWAT has correctly coupled the sub-packages. PHWAT was then applied to the simulation of a tank experiment in which seawater intrusion was accompanied by cation exchange. The density dependence of the intrusion and the snow-plough effect in the breakthrough curves were reflected in the model simulations, which were in good agreement with the measured breakthrough data. Comparison simulations that, in turn, excluded density effects and reactions allowed us to quantify the marked effect of ignoring these processes. Next, we explored numerical issues involved in the practical application of PHWAT using the example of a dense plume flowing into a tank containing fresh water. It was shown that PHWAT could model physically unstable flow and that numerical instabilities were suppressed. Physical instability developed in the model in accordance with the increase of the modified Rayleigh number for density-dependent flow, in agreement with previous research. (c) 2004 Elsevier Ltd. All rights reserved.

A compartmental model of hepatic disposition kinetics: 1. Model development and application to linear kinetics

The conventional convection-dispersion model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. The extension of this model to include nonlinear kinetics and zonal heterogeneity of the liver is not straightforward and requires numerical solution of partial differential equation, which is not available in standard nonlinear regression analysis software. In this paper, we describe an alternative compartmental model representation of hepatic disposition (including elimination). The model allows the use of standard software for data analysis and accurately describes the outflow concentration-time profile for a vascular marker after bolus injection into the liver. In an evaluation of a number of different compartmental models, the most accurate model required eight vascular compartments, two of them with back mixing. In addition, the model includes two adjacent secondary vascular compartments to describe the tail section of the concentration-time profile for a reference marker. The model has the added flexibility of being easy to modify to model various enzyme distributions and nonlinear elimination. Model predictions of F, MTT, CV2, and concentration-time profile as well as parameter estimates for experimental data of an eliminated solute (palmitate) are comparable to those for the extended convection-dispersion model.

Axial mixing in rotating drums using magnetic resonance imaging using bran as a model for solid state fermentations

Magnetic resonance imaging (MRI) is an easily automated, reliable technique to investigate axial mixing within rotating drums. Moist bran can be clearly differentiated from dry bran using MRI allowing a non-segregating tracer for axial mixing. For a 20-cm diameter drum, the axial dispersion coefficient in the particle bed was 0.51 cm s(-2). Axial dispersion is scale-dependent.

Operation of polymer electrolyte membrane fuel cells with dry feeds: Design and operating strategies

The operation of polymer electrolyte membrane fuel cells (PEMFCs) with dry feeds has been examined with different fuel cell flow channel designs as functions of pressure, temperature and flow rate. Auto-humidified (or self-humidifying) PEMFC operation is improved at higher pressures and low gas velocities where axial dispersion enhances back-mixing of the product water with the dry feed. We demonstrate auto-humidified operation of the channel-less, self-draining fuel cell, based on a stirred tank reactor; data is presented showing auto-humidified operation from 25 to 115 degrees C at 1 and 3 atm. Design and operating requirements are derived for the auto-humidified operation of the channel-less, self-draining fuel cell. The auto-humidified self-draining fuel cell outperforms a fully humidified serpentine flow channel fuel cell at high current densities. The new design offers substantial benefits for simplicity of operation and control including: the ability to self-drain reducing flooding, the ability to uniformly disperse water removing current gradients and the ability to operate on dry feeds eliminating the need for humidifiers. Additionally, the design lends itself well to a modular design concept. (c) 2005 Elsevier B.V. All rights reserved.

Fixed bed reactors with catalyst poisoning - first order kinetics.

The long performance of an isothermal fixed bed reactor undergoing catalyst poisoning is theoretically analyzed using the dispersion model. First order reaction with dth order deactivation is assumed and the model equations are solved by matched asymptotic expansions for large Peclet number. Simple closed-form solutions, uniformly valid in time, are obtained.