Variance Of Residence Time Distribution Research Articles

Computational fluid dynamics study on first reaction chamber of internal circulation anaerobic reactor

This study aims to investigate the characteristics of gas–liquid-solid three-phase flow in an Internal Circulation (IC) anaerobic reactor during the treatment of wastewater. Through computational fluid dynamics (CFD) simulations of the gas–liquid-solid three-phase in the first reaction chamber and based on the anaerobic granule swarms drag coefficient model, the study investigates the effects of superficial liquid velocity and superficial gas velocity on granules distribution, uniformity index, gas holdup, flow velocities of each phase, and the dimensionless variance of residence time distribution. In addition, the relationship between the fully mixed superficial velocities of gas and liquid in the first reaction chamber is also determined.

Characteristics of residence time distribution in a continuous high shear mixer granulation using scraper rotation

Characteristics of residence time distribution (RTD) in a continuous high shear mixer granulation were investigated to promote the development of a continuous manufacturing process in the pharmaceutical industry. A continuous granulator with an impeller and a scraper was utilized. The tracer behavior in the continuous wet granulation was verified in impulse-response experiments with acetaminophen. The RTD of acetaminophen changed depending on the scraper speed (15–50 rpm), and the mean residence time could be adjusted by the scraper speed in the wet granulation. The impact of changes in the liquid-to-solid ratio (0.10–0.20) and the addition of binder were also examined, and the variance of RTD was influenced by both. The degree of axial mixing was quantitatively evaluated with a dimensionless index, the Peclet number (Pe). Higher scraper speed was found to suppress fluctuations of the axial mixing that occurred with changes in the liquid feed. Moreover, the transition of granule size distribution with the change in liquid feed reached a steady state more quickly under the higher scraper speed. These results show that scraper rotation can help to adjust the RTD and the axial mixing, leading to a more robust continuous granulation.

Age distribution and the degree of mixing in continuous flow stirred tank reactors

New development of mean age theory is discussed for quantitative analysis of mixing and age distribution in steady continuous flow stirred tank reactors. A new relationship between the moments of age and the moments of residence time are derived. With this new relationship the variance of residence time distribution can be computed much more efficiently and accurately. The relationships of three existing variances of age are described and a new set of variances and the degree of mixing are defined. The theory is used to characterize mixing performance in a CFSTR with different layouts of an inlet and an outlet. Mean age and higher moments of age in the reactors are obtained from CFD solutions of their steady transport equations. The spatial distribution of mean age reveals details of the spatial non-uniformity in mixing. Variances of age and the degree of mixing discussed by Danckwerts and Zwietering are computed for the first time in the literature for non-ideal stirred tank reactors. It is found that although these measures are useful, certain key features in non-uniform mixing are not reflected accurately. Results show that the new set of variances and the degree of mixing more accurately characterize the non-uniform mixing in the reactors.

Computational simulation of fluid dynamics in a tubular stirred reactor

The flow and concentration fields in a new style tubular stirred reactor were simulated by simulating the fluids dynamics(CFD), in which FLUENT software was used and the standard k—ɛ model and multiple reference frame(MRF) were adopted. The various values of initial rotating speed and inlet flow rate were adopted. Simulations were validated with experimental residence time distribution(RTD) determination. It is shown that the fluid flow is very turbulent and the flow pattern approaches to the plug flow. The velocity increases from shaft to the end of impeller, and the gradient is enlarged by increasing the rotating speed. Comparison between RTD curves shows that agitation can improve the performance of reactor. As the flow rate increases, the mean residence time decreases proportionally, and the variance of RTD lessens as well. When rotating speed increases to a certain value, the variance of RTD is enlarged by increasing rotating speed, but the mean residence time has no obvious change.

Simulation of groundwater age distributions

The objective of our work is to examine how to simulate the age of groundwater in such a way that it can be compared to actual measurements. We start by showing that computation of kinematic age, the one obtained by tracking water along streamlines, is ill posed in heterogeneous aquifers. This, together with its inability to account for mixing processes, makes it inadequate for comparison with age measurements, which are the result of some averaging of the age distribution in the water sample (the type of averaging depends on the measurement procedure). Therefore we go on to write the equations for the cumulative distribution function of residence time under transient flow conditions. This allows us to derive transient equations for the mean age, as well as for the higher‐order moments of its distribution, which generalize previous results by others. These moments can be used for approximating age measurements, which need not be equal to the mean age of the water sample. Using both a synthetic and a real example, we show that mean age is an acceptable estimate of radiometric age measurements in many cases. Including a second‐order correction (variance of residence time distribution) always improves results. On the other hand, higher‐order approximations converge slowly for old (compared to half‐life) waters, to the point that third‐order approximations often worsen the results.

Hemodynamic influences upon the variance of disposition residence time distribution of drugs

A recirculation model of drug disposition is used to interpret the physiological meaning of the variance of residence time distribution (VDRT). The pharmacokinetic parameter VDRT is determined by the means and variances of the transfer times across the organs, as well as by the respective blood flow and extraction ratios. The model is illustrated for a specified distribution of organ transit times assuming flow limited mass transport. Based on data from the literature, the influence of changes in cardiac output and its regional distribution on the variance of recirculation and residence times, respectively, is predicted for lidocaine. Thereby the study is focused on the effect of certain cardiovascular states (shock, hypoxia, exercise, sympathomimetic drugs). Unlike pharmacokinetic parameters derived from the zeroth and first curve moments, the relative residence time dispersion is found to be affected by a redistribution of the blood flow among the noneliminating organs. The equations presented allow a simple and rapid calculation of clinically relevant pharmacokinetic parameters from physiological and physicochemical data.