progress report on axial dispersion

8/3/2019 Progress Report on Axial Dispersion

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Studies in Hydrodynamics Aspect of Pulse Sieve Plate

Extraction Column

Progress report submitted in partial fulfilment of the requirements for theaward of the degree of

Masters of Chemical Engineering

By

Inderdip P Shere

Department Of Chemical Engineering

Institute Of Chemical Technology

University Of Mumbai

Dec 2011

VKR


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Studies in Hydrodynamics Aspect of Pulse Sieve Plate Extraction Column 2011

Institute of Chemical Technology, Mumbai. Page 1

INDEX

Serial

number

Contents Page

number

1 Introduction 2

2 Parameters affecting axial dispersion coefficient 4

3 Correlations 4

3.1 Power law on each parameters 4

3.2 Dimensionless parameters 7

4 Models 7

4.1 Axial dispersion model 7

4.2 Tank in series model 8

5 Conclusions 9

6 Further plans 9

7 References 10


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1. IntroductionScope on present project work

Taking into consideration the previous work on axial dispersion coefficient in

pulsed sieve plate column, it is observed that the single phase dispersion

coefficient values could be used to provide an accurate reference point for the

more difficult and complex two phase flow. With the new scale up there is further

need to study hydrodynamic of new column. It is also necessary to develop

correlation to estimate axial dispersion coefficient with operating and geometric

parameters, with suitable accuracy. Therefore, this project is divided into two

parts as a first step it is to study the single phase dispersion coefficient in pulsedsieve plate column and to get the fundamental mechanisms and the

hydrodynamics of local flow structures. Latter analysis of detail aspects of

various phenomena and develop a suitable correlation. The correlation could also

validate using computer simulation and experimental readings. Since the axial

dispersion coefficient in pulsed sieve plate column with simulation is not carried

out on a large size column diameter, it will be noteworthy to comprehend the

complex nature of local flow patterns in such kind of contactors. Keeping in view

of these points, the objectives of the present work could be summarized as;

i. Study of hydrodynamics and behavior of operating parameters on axialdispersion coefficient.

ii. Developing a correlation with respect to operating parameters and detailsaspect of the column such as drop dimensions, plate geometry, physo-

chemical properties, et cetera.

iii. Validating the correlation with suitable models and predicting for inter-convertible relationships.

iv. Combination of correlations for different column dimensions todevelopment most fundamental correlation


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Experiment setup

Experimental setup is as shown in figure 6

Figure 1: Experimental setup of Pulse sieve plate extraction column.


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2. Parameters affecting axial dispersion coefficient2.1 Effect of operating and geometric parameter

Table 1: Effect of operating and geometric parameters on axial dispersion coefficient

Parameters Effect on axial dispersion

Pulse velocity Direct

Continuous phase velocity Linear

Dispersed phase velocity Unclear

Pore diameter Inversely

Plate spacing Direct

Fractional free area Direct

3. Correlations3.1Use of Power law on each parameters

With using direct contribution of operation and geometric parameters the

following equation was developed.

.. Equation 1

A total of 129 data points were taken from previous studies preformed by

N. S. Kolhe. It gives the fair idea how each parameter affects the axial

dispersion coefficient. Regression analysis was performed on all the

parameters. Following is generalized method to carry out such analysis.

i. Data points are collected against all the parameters which are to bestudied.

ii. Model is selected which is to be tested, as power law represented inequation 1

iii. Logarithm to the base 10 is used to linearize the equation 1.


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iv. Based on least square method in regression following set ofequations is to be solved using matrix system.

[

| ]

[

]

[

]

..Equation 2

v. Using matrix calculation linear system of equations is solved.vi. With the correlation predicted value of y or axial dispersion

coefficient is calculated.

vii. Regression coefficient, r is calculated using following equations

..Equation 3

Where,

.Equation 4

Where,

..Equation 5

..Equation 6

viii. Standard deviation, Sy could also be found out as,

..Equation 7


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Results of power law are tabulated in table 2,

Table 2: Results of power law

Coefficient Values

a0 73.29933

a1 0.7625

a2 0.6216

a3 0.0193

a4 0.2287

a5 -0.2627

a6 1.2903

Following conclusions were drawn

a. Since regression coefficient, r is 0.594 which is much far less than 1,implies that Power law fits poorly for the system.

b. a3, which is coefficient for dispersed phase velocity is 0.0193 suggestthat Vd have least contribution on axial dispersion coefficient.

c. A6, which is coefficient for fraction free area is 1.2903 suggest that have maximum contribution on axial dispersion coefficient.

Following steps were taken,

a. Data points which have value of axial dispersion coefficient 60 cm 2/sechave been eliminate, since their errors were significantly higher that

rests of the data sets. Thus fetching regression coefficient, r value of

0.672. This is still less for accurate fit.

b. For regression, parameter Vd is removed to check the dependency ofdispersion coefficient. But it gave reduced value of regression

coefficient of 0.631


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3.2Use of dimension less parametersNon dimension less parameters are useful when there are large number of

parameters to be analyzed. In our system we have six operating and

geometric parameters, further we have not studied different physic-

chemical properties. So such approach is indeed a valuable step. To make

non dimension less numbers available parameters are arranged in such a

fashion that operating parameters stays at the numerator and geometric

parameters at the denominator so as to see immediate effect of parameters,

based on the significant effect of each parameters on axial dispersion.

Following dimensionless entities were formed

( ) ( ) () Other dimensionless entities for physical parameters

( ) ( ) ( )With the above stated matrix method we could further check the power law.

Following conclusion could be drawn,

a. The coefficient, a0 is dimension less.b. The regression coefficient, r is 0.92 which is fairly agreeable.c. In physical parameters of non dimensionless groups effect of dispersed

and continuous phase velocity on axial dispersion is directly seen, since

we have not studied other physical systems.

4. Models4.1.Axial dispersion model

Axial dispersion model is one of most widely used model for pulse

sieve extraction column. Above mentioned methods of correlation also

falls under the preview of axial dispersion model.

Axial dispersion is based on following equation

..Equation 8


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This model could be used for C-curve as well as F-curve. For C- curve,

generally relation between 2 and (E/uL) is used. For F-curve we

differentiate to get C-curve. Following equation is to be solved to get the

value of dispersion coefficient, E

( ) ( )..Equation 9

4.2.Tank in series model (Fogler H. S., 2004)

Tank in series is another one parameter model similar model to consider

axial dispersion. It calculates axial dispersion under the preview of similartanks in series. It requires set of following equations to be solved,

..Equation 10

..Equation 11

..Equation 12

..Equation 13

The number of tanks in series could also be converted to axial dispersion

coefficient using Peclet-Bodenstein number, Bo. It is related as,

..Equation 14

..Equation 15

It has an advantage of non dimensional variable, number of tanks in series,

to analyze axial dispersion. And it could be easily converted.


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5 Conclusions

Various correlations were used to find out direct relation of axial dispersioncoefficient with operating and geometry parameters. Significant accuracy

could be achieved in non dimensional analysis. Work has been undertaken

with consideration of dispersion model moreover other models also have

potential benefits.

There is non fundamental correlation develop for the different type ofcolumn geometry. Most of the correlation deals with the specific system

and dimension of column. Precise correlation of axial dispersion with

column is missing.

Various dimensionless entities have been developed and have significantimportance in generating correlations.

Some of the data sets points are to be curtain for proper fit of correlations.

6 Further plans on project

Considering the demand of project following action plan could be followed,

a. Piping fitting on 12 diameter column which is already set up.b. Obtain C curve on 12 diameter column for all the parameters. c. Calculate axial dispersion coefficient and number of tanks in series using

respective models.

d. Fit the data set to the most accurate correlation and find out level ofconfidence.

e. Develop a fundamental model using non dimensional entities.f. Validate the correlation by predicting and confirming the parameter.


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References

Fogler H. S., 2004. Elements of chemical reaction engineering, third ed., Prentice hall of

India private limited, New Delhi.

progress report on axial dispersion

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