A Mathematical Model for a Parallel Plate Electrochemical Reactor, CSTR, and Associated Recirculation System

A model is presented for the reduction of hexavalent chromium in a parallel-plate electrochemical reactor via a homogenous reaction between Cr(VI) and Fe(II) generated at the iron anode. The effects of the space velocity of the feed solution, the concentration of supporting electrolyte, the distance between the electrodes, and the cell potential on conversion of Cr(VI) to Cr(III), are discussed. This study indicates that for reduction of Cr(VI) using Fe(II), the space velocity must be maintained below 0.02normals−1 or the system becomes limited by the rate of reduction of Cr(VI) by Fe(II). Increasing the current density by increasing the cell potential, increasing the amount of supporting electrolyte, and decreasing the distance between the electrodes increases single pass conversion of Cr(VI) to Cr(III); however, increasing the current density also increases the specific energy required by the system.

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“…15 Applying the one-step approximation 12 for the concentration gradient in the axial convection term yields…”

Section: Modelmentioning

confidence: 99%

Simulation of Reduction of Cr(VI) by Fe(II) Produced Electrochemically in a Parallel-Plate Electrochemical Reactor

Rayman

White

2009

J. Electrochem. Soc.

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“…Equations (18) to (22) relating the current densities and the concentrations of the different species in the reactor are obtained by eliminating surface concentrations between the two sets of Equations (8) to (12) and (13) to (17):…”

Section: Mathematical Developmentmentioning

confidence: 99%

“…Similar studies have been performed for electrolyses with potentiostatic control, to predict variations in space and time [11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

A model for the electrochemical reduction of 2-ethylpicolinate under galvanostatic control

2006

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A model is presented for the variation in reactant concentrations during the electrochemical reduction of 2-ethylpicolinate on a lead cathod in sulphuric acid solutions under galvanostatic conditions. The electrolyses were performed in a laboratory filter-press reactor. Successive or parallel electrochemical reactions coupled with chemical reactions are taken into account, according to a reaction scheme in agreement with the experimental results. Analytical expressions are used to describe the progress of the various reactions, taking into account both chemical and electrochemical kinetics and transfer properties. All reactions are assumed to be first or pseudo-first order. The variations in charge-transfer rate constants are considered as functions of reactant conversion. The effects of acidity, current efficiency, initial concentration of 2-ethylpicolinate and temperature are presented. The model aims at estimating the yield of electrolysis products under the experimental conditions necessary for obtaining 2-hydroxymethylpyridine in optimum quantities.Symbols C X concentration of species X in the cathodic compartment (mol m )3 ) C 0 X initial concentration of species X in the cathodic compartment (mol m )3 ) C XS concentration of species X at the surface of electrode (mol m )3 ) c width of cathodic compartment (direction perpendicular to flow) (31Â 10 )3 m)electrode potential/ECS (V), at I=0 for the electrochemical reaction i F=96487Faraday's constant (C mol )1 ) h thickness of the cathodic compartment (direction perpendicular to flow) (3Â 10 )3 m) [H 2 SO 4 ] sulphuric acid concentration (mol dm )3 in the formulas) I electrolysis current (A) j electrolysis current density (A m )2 ) j i current density of the electrochemical reaction i (A m )2 ) k dX mass-transfer coefficient of species X (m s )1 ) k fi charge-transfer constant for the electrochemical reaction i (m s )1 ) k fi0 charge transfer constant without overvoltage for the electrochemical reaction i (m s )1 ) k i rate constant for the chemical reaction i k¢ i apparent rate constant for the chemical reaction i M X molar mass of species X (g mol )1 ) n number of electrons exchanged p parameter for the expression of R f Q charge at time t per mol of reactant (F mol )1 ) Q V flow rate (12.8Â 10 )6 m 3 s )1 ) r i rate of the chemical reaction i R=8.314 ideal gas constant (J K )1 mol )1 ) XmReynolds number R f faradaic yield R X chemical yield in species X s slope

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“…Additionally, the ability to handle gas or liquid products, design simplicity, and capital and operation costs will eventually determine the system reliability and scalability. Earlier works by Parrish and Newman analyzed the current distribution in a channel flow cell, , and multiple reactions and boundary layer effects were later introduced to include product selectivity and yield in the analyses. , White et al used two-dimensional models to study the effects of separator, migration, and multiple reactions. , Using a linear approximation of the axial convective term, Mader modified the governing equation on convection and diffusion to reduce the model to one dimension. , Later works by Caban and Lee applied a one-dimensional (1D) approximation to the thin boundary layer in the electrowinning of Cu and in Zn/Br 2 systems. Recent work of Braff et al compared a two-dimensional model to a 1D approximation of a parallel-plate reactor in a hydrogen bromine flow battery and confirmed the accuracy of using the 1D approximation for modeling steady-state polarization.…”

Section: Introductionmentioning

confidence: 99%

Flue Gas CO₂ Capture via Electrochemically Mediated Amine Regeneration: Desorption Unit Design and Analysis

Wang

Hatton

2020

Ind. Eng. Chem. Res.

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We analyzed the performance of an electrochemical desorption unit to be implemented in an electrochemically mediated amine regeneration (EMAR) process, which separates CO2 and regenerates the amine upon modulation of a targeted species that complexes with the amine molecules. Using a simplified one-dimensional boundary layer model, we combined the kinetic expressions of the faradaic reactions with mass transfer effects to analyze the polarization behavior of the flow cell. Mass transfer limitations become dominant at high current densities, leading to increases in energy consumption. An understanding of scaling laws with key parameters, such as the Sherwood number, is required to achieve high power operation with minimal mass transfer losses. Because the EMAR chemistry is sensitive to temperature, heat distribution in the unit is also examined. Our results indicate that the desorption performance increases with addition of a high-temperature heat source. Additionally, incorporation of membrane crossover suggests energy losses because of diffusion and migration of active species. These findings inform on scaling laws for at-scale desorber design and provide a model for scaling up the EMAR system for larger scale operations.

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A Mathematical Model for a Parallel Plate Electrochemical Reactor, CSTR, and Associated Recirculation System

Cited by 20 publications

References 5 publications

Simulation of Reduction of Cr(VI) by Fe(II) Produced Electrochemically in a Parallel-Plate Electrochemical Reactor

Simulation of Reduction of Cr(VI) by Fe(II) Produced Electrochemically in a Parallel-Plate Electrochemical Reactor

A model for the electrochemical reduction of 2-ethylpicolinate under galvanostatic control

Flue Gas CO₂ Capture via Electrochemically Mediated Amine Regeneration: Desorption Unit Design and Analysis

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A Mathematical Model for a Parallel Plate Electrochemical Reactor, CSTR, and Associated Recirculation System

Cited by 20 publications

References 5 publications

Simulation of Reduction of Cr(VI) by Fe(II) Produced Electrochemically in a Parallel-Plate Electrochemical Reactor

Simulation of Reduction of Cr(VI) by Fe(II) Produced Electrochemically in a Parallel-Plate Electrochemical Reactor

A model for the electrochemical reduction of 2-ethylpicolinate under galvanostatic control

Flue Gas CO2 Capture via Electrochemically Mediated Amine Regeneration: Desorption Unit Design and Analysis

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Flue Gas CO₂ Capture via Electrochemically Mediated Amine Regeneration: Desorption Unit Design and Analysis