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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.

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