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Dispersion in three dimensional electrodes Gao, Lixin
Abstract
Dispersion of mass is a measure of the deviation of transportation of fluid in a reactor from ideal reactor behavior (perfect mixing or plug flow) caused by the combined effects of diffusion, convection and migration. Axial dispersion is always undesirable because it reduces the driving force of the reaction and therefore causes a lower level of conversion. On the other hand, transverse dispersion is often a desirable feature since good transverse mixing will reduce the transverse concentration and temperature gradients and hence improve the selectivity of a thermochemical reactor. Transverse dispersion of mass is of more importance in a three-dimensional flow-by electrochemical reactor than that in a thermochemical reactor because the potential drop is in the transverse direction and the reaction rate and selectivity are determined by the potential as well as concentration and temperature distributions. The transverse dispersion of mass is expected to have a more profound effect on the performance of a 3D electrochemical reactor due to the strong interaction among the concentration, temperature and potential distributions in the transverse direction. In the present work, the axial and transverse dispersion of mass were studied with a twodimensional dispersion model in two types of rectangular packed bed: i) randomly packed glass beads with the average bead diameter of 2 mm and a macroscopic bed porosity of 0.41; ii) a representation of a 3D flow-by electrode - consisting of a bed of carbon felt with the carbon fibre diameter of 20 μm and a macroscopic bed porosity of 0.95. A tracer stimulation-response system was set up and axial and transverse dispersion of 0.7M CuSO₄ in a flow of 12 wt % Na₂S0₄ were measured in a 32cm long by 5cm wide by 2.6cm thick rectangular tested bed filled with glass beads and with carbon felt, for Reynolds number ranging respectively from 1.8 to 7.2, and from 0.008 to 0.032. Axial and transverse dispersion coefficients D[sub a] and D[sub t] were found by parameter estimation based on a pulse tracer experiment. D[sub a] and D[sub t] were selected such that they gave the least sum of squares of the differences between the measured and calculated tracer concentrations. The latter were calculated by employing a computer program written in FemLab and MatLab to solve the two-dimensional time-dependent partial differential material balance equation governing the tracer concentration distribution within the tested bed, assuming that the transverse and lateral dispersion coefficients were of the same magnitude and the tracer concentration gradients were equal in the two directions, except near the walls of the bed. Traditionally, a two step experimental technique has been employed to find axial and transverse dispersion coefficients in packed beds: the axial dispersion coefficient D[sub a] is first estimated from a pulse tracer experiment with the assumption that there is no concentration gradient in the transverse direction; then the transverse dispersion coefficient D[sub t] is calculated from a step tracer measurement with the previously calculated D[sub a]. Two improvements were achieved in the present work by finding axial and transverse dispersion coefficients simultaneously from one single set of pulse tracer experiment. First, the potential of the systematic error introduced by assuming no transverse concentration gradient for calculating D[sub a] was eliminated. Second, the accuracy of the parameter estimation of D[sub a] and D[sub t] was improved by the greater number of tracer sampling points obtained from a pulse tracer experiment technique than have been obtained from step tracer measurements. Simultaneously estimated axial and transverse dispersion coefficients and other parameters are summarized in Table 1, along with a comparison to literature values [3, 9]. Axial dispersion parameters were also estimated from the variances of two tracer concentration curves measured at two points, which were at the same horizontal but different vertical positions within the tested bed, assuming that the lateral and transverse dispersion effects were negligible. The results are summarized in Table 2. It seems that the axial dispersion coefficient was slightly overestimated when the effects of transverse and lateral dispersion were neglected. The axial and transverse dispersion coefficients were not affected by repacking of the beds and the axial dispersion coefficient was uniform throughout the entire bed. The axial dispersion parameters for glass beads bed agree with the literature values. The transverse Peclet number of the glass beads bed was only one-fourth that of the literature values and this may be caused by the different reactor configuration (rectangular) of the bed tested in the present work compared with that of the previous investigations (cylindrical). No comparison data were found in the literature for dispersion parameters in a packed bed with similar characteristics to carbon felt in terms of bed porosity and bed material dimension.
Item Metadata
Title |
Dispersion in three dimensional electrodes
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2001
|
Description |
Dispersion of mass is a measure of the deviation of transportation of fluid in a reactor
from ideal reactor behavior (perfect mixing or plug flow) caused by the combined effects of
diffusion, convection and migration.
Axial dispersion is always undesirable because it reduces the driving force of the reaction
and therefore causes a lower level of conversion. On the other hand, transverse dispersion is
often a desirable feature since good transverse mixing will reduce the transverse concentration
and temperature gradients and hence improve the selectivity of a thermochemical reactor.
Transverse dispersion of mass is of more importance in a three-dimensional flow-by
electrochemical reactor than that in a thermochemical reactor because the potential drop is in the
transverse direction and the reaction rate and selectivity are determined by the potential as well as
concentration and temperature distributions. The transverse dispersion of mass is expected to
have a more profound effect on the performance of a 3D electrochemical reactor due to the
strong interaction among the concentration, temperature and potential distributions in the
transverse direction.
In the present work, the axial and transverse dispersion of mass were studied with a twodimensional
dispersion model in two types of rectangular packed bed: i) randomly packed glass
beads with the average bead diameter of 2 mm and a macroscopic bed porosity of 0.41; ii) a
representation of a 3D flow-by electrode - consisting of a bed of carbon felt with the carbon fibre
diameter of 20 μm and a macroscopic bed porosity of 0.95.
A tracer stimulation-response system was set up and axial and transverse dispersion of
0.7M CuSO₄ in a flow of 12 wt % Na₂S0₄ were measured in a 32cm long by 5cm wide by 2.6cm
thick rectangular tested bed filled with glass beads and with carbon felt, for Reynolds number
ranging respectively from 1.8 to 7.2, and from 0.008 to 0.032.
Axial and transverse dispersion coefficients D[sub a] and D[sub t] were found by parameter estimation
based on a pulse tracer experiment. D[sub a] and D[sub t] were selected such that they gave the least sum of
squares of the differences between the measured and calculated tracer concentrations. The latter
were calculated by employing a computer program written in FemLab and MatLab to solve the
two-dimensional time-dependent partial differential material balance equation governing the tracer
concentration distribution within the tested bed, assuming that the transverse and lateral
dispersion coefficients were of the same magnitude and the tracer concentration gradients were
equal in the two directions, except near the walls of the bed.
Traditionally, a two step experimental technique has been employed to find axial and
transverse dispersion coefficients in packed beds: the axial dispersion coefficient D[sub a] is first
estimated from a pulse tracer experiment with the assumption that there is no concentration
gradient in the transverse direction; then the transverse dispersion coefficient D[sub t] is calculated from
a step tracer measurement with the previously calculated D[sub a].
Two improvements were achieved in the present work by finding axial and transverse
dispersion coefficients simultaneously from one single set of pulse tracer experiment. First, the
potential of the systematic error introduced by assuming no transverse concentration gradient for
calculating D[sub a] was eliminated. Second, the accuracy of the parameter estimation of D[sub a] and D[sub t]
was improved by the greater number of tracer sampling points obtained from a pulse tracer
experiment technique than have been obtained from step tracer measurements.
Simultaneously estimated axial and transverse dispersion coefficients and other parameters
are summarized in Table 1, along with a comparison to literature values [3, 9].
Axial dispersion parameters were also estimated from the variances of two tracer
concentration curves measured at two points, which were at the same horizontal but different
vertical positions within the tested bed, assuming that the lateral and transverse dispersion effects
were negligible. The results are summarized in Table 2.
It seems that the axial dispersion coefficient was slightly overestimated when the effects of
transverse and lateral dispersion were neglected.
The axial and transverse dispersion coefficients were not affected by repacking of the beds
and the axial dispersion coefficient was uniform throughout the entire bed.
The axial dispersion parameters for glass beads bed agree with the literature values. The
transverse Peclet number of the glass beads bed was only one-fourth that of the literature values
and this may be caused by the different reactor configuration (rectangular) of the bed tested in the
present work compared with that of the previous investigations (cylindrical).
No comparison data were found in the literature for dispersion parameters in a packed bed
with similar characteristics to carbon felt in terms of bed porosity and bed material dimension.
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Extent |
5232603 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-07-27
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0058816
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2001-05
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.