Modelling of Flow of a Liquid in Apparatus with Mobile Packing: Dispersion Model

1993 ◽  
Vol 58 (9) ◽  
pp. 2047-2058
Author(s):  
Zdeněk Palatý
Keyword(s):  
Differential Equation ◽  
Numerical Integration ◽  
Residence Time ◽  
Mean Residence Time ◽  
Peclet Number ◽  
Dispersion Model ◽  
Tracer Concentration ◽  
Optimization Of Parameters ◽  
Determination Of Parameters

The paper deals with determination of parameters of a dispersion model used for describing the flow of liquid on a plate with mobile packing in the region of gas velocities up to 1.5 m s-1. The parameters of the model - the diffusion Peclet number and mean residence time of liquid - were determined from the nonideal input impulse of tracer concentration and its response by the method of numerical integration of differential equation with subsequent optimization of parameters. The results of measurements are presented graphically and in the form of criterion equations.

Mass Transfer in Liquid in Apparatus with Mobile Packing. Application of Model of Cascade of Ideal Mixers

1994 ◽  
Vol 59 (2) ◽  
pp. 336-344
Author(s):  
Zdeněk Palatý
Keyword(s):  
Mass Transfer ◽  
Residence Time ◽  
Mean Residence Time ◽  
Liquid Velocity ◽  
Dispersion Model ◽  
Velocity Range ◽  
Bed Height ◽  
The Mean ◽  
Determination Of Parameters

The paper deals with the determination of parameters of a cascade of ideal mixers (i.e. their number and mean residence time of liquid in each member) in modelling the liquid flow on a plate with mobile packing. The number of cascade members has been found practically independent of the gas and liquid velocities and the static bed heights in the gas velocity range from 1.0 to 3.5 m s-1, liquid velocity range from 5.36 . 10-3 to 12.5 . 10-3 m s-1, and the range of static bed height from 21 . 10-3 to 47 . 10-3 m. The mean residence time is increased with increasing static bed height and is decreased with increasing velocities of both gas and liquid. The calculated parameters of the model of flow of liquid and the experimental data on desorption of CO2 from water by a stream of air have been used to calculate the values of mass transfer coefficient in liquid which have been compared with those obtained from the dispersion model. The both approaches have been found to give practically identical results.

Precipitation and filtration of zinc, magnesium, copper and aluminium hydroxides

1982 ◽  
Vol 47 (12) ◽  
pp. 3362-3370
Author(s):  
Otakar Söhnel ◽  
Eva Matějčková
Keyword(s):  
Residence Time ◽  
Mean Residence Time ◽  
Filtration Resistance ◽  
Filtration Pressure ◽  
Bed Porosity ◽  
The Mean ◽  
Filtration Properties

Filtration properties of batchwise precipitated suspensions of Zn(OH)2, Mg(OH)2 and Cu(OH)2 and continuously precipitated Al(OH)3 were studied. For batchwise precipitated suspensions was verified the theoretically predicted dependence of specific filtration resistance on initial supersaturation and for the continuously precipitated Al(OH)3 the relation between the specific filtration resistance and the mean residence time of suspension in the reactor. Dependences were also recorded between the bed porosity and concentration of precipitated solutions, specific filtration resistance and used filtration pressure and the effect of aging of the batchwise precipitated suspension of Mg(OH)2on its filtration properties. The used CST method for determination of filtration characteristics of Zn(OH)2 suspension was also studied.

RTD Measurement, Modeling, and Analysis of Liquid Phase of Three-Tube Industrial Pulp Digester

2019 ◽  
Vol 17 (4) ◽  
Author(s):  
Meenakshi Sheoran ◽  
Avinash Chandra ◽  
Sanjeev Ahuja ◽  
Haripada Bhunia ◽  
Harish J. Pant
Keyword(s):  
Liquid Phase ◽  
Flow Regime ◽  
Residence Time ◽  
Dispersion Model ◽  
Flow Behavior ◽  
Plug Flow ◽  
Hydrodynamic Performance ◽  
Concentration Data ◽  
Tracer Concentration ◽  
Dispersion Number

Abstract Residence-time distribution (RTD) experiments were performed to analyze an industrial scale three-tube series continuous pulping digester’s hydrodynamic performance. An impulse of radiotracer 82Br (γ energy source) was introduced at the inlet of the first tube. The radiotracer concentration in the liquid phase was traced at the outlet of each tube. The input behavior of the radiotracer converted to a non-ideal pulse tracer input for the second and third tubes of the digester. Numerical convolution is adopted to deal with the non-ideal pulse input of the radiotracer. A modeling procedure for determining the RTD from the outlet tracer concentration data is proposed. A plug flow component followed by axial dispersion model is considered, and is adjusted after its convolution with the inlet tracer concentration data to obtain the RTD of the individual tubes. The obtained RTD data are analyzed to explain the flow behavior, degree of dispersion, and flow abnormalities existing in the digester. The mean residence-time (MRT), and dispersion number are estimated for the model components for the three tubes. The vessel dispersion number is found to decrease from tube 1 to tube 3. Overall, the conversion of the highly dispersed flow regime into the plug-flow regime is observed in the whole digester.

scholarly journals Evaluation method of single blow experiment for the determination of heat transfer coefficient and dispersive Peclet number

2015 ◽  
Vol 36 (4) ◽  
pp. 3-24 ◽  
Author(s):  
Wilfried Roetzel ◽  
Chakkrit Na Ranong
Keyword(s):  
Heat Exchangers ◽  
Peclet Number ◽  
Numerical Evaluation ◽  
Evaluation Method ◽  
Dispersion Model ◽  
Tracer Experiment ◽  
Effective Number ◽  
Péclet Number ◽  
Modified Method

Abstract An evaluation method is developed for single blow experiments with liquids on heat exchangers. The method is based on the unity Mach number dispersion model. The evaluation of one experiment yields merely one equation for the two unknowns, the number of transfer units and the dispersive Peclet number. Calculations on an example confirm that one single blow test alone cannot provide reliable values of the unknowns. A second test with a liquid of differing heat capacity is required, or a tracer experiment for the measurement of the Peclet number. A modified method is developed for gases. One experiment yields the effective number of transfer units and approximate values of the two unknowns. The numerical evaluation of calculated experiments demonstrates the applicability of the evaluation methods.

Long-term Temporal Variation of Mean Residence Time in Spring and Groundwater After Thinning at a Forested Headwater Catchment

2020 ◽  
Author(s):  
Isabela Silveira Baptista ◽  
Maki Tsujimura ◽  
Yuichi Onda
Keyword(s):  
Temporal Variation ◽  
Residence Time ◽  
Mean Residence Time ◽  
Flow Model ◽  
Dispersion Model ◽  
Spring Water ◽  
Groundwater Storage ◽  
Flow Process ◽  
Piston Flow ◽  
The Mean

<p>Treatments on plantation forests, such as thinning, have a significant effect on the quality and quantity of water resources in the watersheds in Japan. However, few studies have performed intensive observations regarding the effects of thinning on the groundwater flow process with combined use of tracers, specially over a long period of time.</p><p>In this study, stable isotope analysis and hydrological observations were applied to investigate the temporal variation of spring water and groundwater mean residence time in a small watershed at Mount Karasawa, Tochigi Prefecture, Japan. We have monitored the research area since 2010, with periodical sampling once a month for 9 years, with a lack of data in some years after the thinning.  We analyzed the date for three different time periods, those are: Before Thinning, from July 2010 to September 2011, Soon After Thinning, from November 2011 to October 2013 and Long After Thinning, from September 2017 to August 2019.</p><p>The mean residence time of spring water and groundwater were evaluated by using the stable isotopes of hydrogen and oxygen as tracers, then estimating their d-excess variations using two Lumped-Parameter Models, Exponential-Piston Flow Model and Dispersion Model. The SF<sub>6</sub> concentrations were used as an Apparent Age analysis for determination of the model’s parameters. Both models show a tendency of the mean residence time getting older Soon After Thinning and then getting younger again Long After Thinning.</p><p>According to a selection of the best model for this area, the Exponential-Piston Flow Model shows that the spring water mean residence time was 25 months Before Thinning, 30 months Soon After Thinning and 26 months Long After Thinning; the groundwater at 15m deep mean residence time was 39 months Before Thinning, 46 months Soon After Thinning and 38 months Long After Thinning and the groundwater at 30m deep mean residence time was 38 months Before Thinning, 47 months Soon After Thinning and 45 months Long After Thinning. These results suggest that Soon After Thinning there is a reduction of forest interception and tree evapotranspiration, leading to an increase in infiltration and groundwater storage. Then, Long After Thinning, the forest interception and tree evapotranspiration rise back again with the recovery of the understory vegetation, which leads to a decrease in infiltration and groundwater storage.</p>

scholarly journals Physiologically Based Structure of Mean Residence Time

2012 ◽  
Vol 2012 ◽  
pp. 1-4
Author(s):  
Mária Ďurišová
Keyword(s):  
Pharmacokinetic Parameter ◽  
Residence Time ◽  
Dynamic Systems ◽  
Mean Residence Time ◽  
Structural Identification ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Physiologically Based

A mean residence time (MRT) is an important pharmacokinetic parameter. To the author's knowledge, however, a physiologically based structure of MRT (thereafter MRT structure) has not been published so far. Primarily this is because MRT structures cannot be identified by traditional pharmacokinetic methods used for the determination of MRT. Therefore, tools from the theory of linear dynamic systems were used for the structural identification of MRT in this study. The MRT structure identified is physiologically meaningful. Accordingly, it seems that the MRT structure identified may contribute to already established knowledge about MRT.

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