The analysis of a batch electrochemical reactor with continuously recirculating electrolyte

Elecrrochimica Acta, 1973Vol. 18, pp. 835-837. PergamonPress.Printedin GreatBritain

THE ANALYSIS OF A BATCH ELECTROCHEMICAL REACTOR WITH CONTINUOUSLY RECIRCULATING ELECTROLYTE D.J.

RCKETT

Department of Chemical Engineering, The University of Manchester Institute of Science and

Technology, Manchester M60 lQD, England (Received 5 April 1973)

Abstract-An analysis has been made to describe the variation of reactant concentration with time in an electrochemical reactor through which a batch of electrolyte is continuously recirculated, the electrochemical reaction being mass transfer controlled. Application of the analysis has been made to a hypothetical copper electrowinning process employing a parallel plate electrochemical cell.

INTRODUCTION

C,

Recent studies[l, 21 have considered the use of electrochemical reactors for the treatment of dilute solutions of metal ions by continuously recirculating a batch of electrolyte through the reactor. It appears, however, that no theoretical predictions exist that describe the variation of reactant concentration with time in terms of such variables as flow rate, electrode area and cell and electrolyte volumes. Such an analysis has relevance in batch electrochemical processes in general where continuous circulation of electrolyte could increase limiting current densities and offer substantially higher average production rates. This note describes a preliminary analysis which could be tested in cells of various designs.

Cell R

CO _=

ANALYSIS

Consider the electrolytic system shown in Fig. 1. R denotes the net volume of the cell, A4 the volume of eiectrolyte outside the cell and Y the volumetric flow rate. It is evident that both CL the inlet cell concentration and CO the outlet cell concentration vary with electrolysis time, so that two equations are necessary to describe the concentration variation. Under limiting current conditions the concentration in the cell, C,, is given by vcI=

where k, electrode In the assumed

vco+-

RdC, dt

is the mass transfer area. electrolyte reservoir to take place

+kLAC’o,

Since C, and C1 are mathematical terms for the same property the variation of concentration C with time can be obtained by eliminating either C, or CO in (1) and (2). The resulting differential equation is

(1)

coefficient and A, the where mixing

Fig. 1. The electrolytic system.

can be

where To and 7M are the respective electrolyte residence times in the cell and reservoir. For conditions where TV = 0, M= 0 (no reservoir) (3) becomes -- R,dtC=kLAC

D.5.

836 The

boundary

conditions

for (3) are

C=C,att=O

(5)

PICKETT

It is interesting reduces to

A4dC -= dr

and from (4) and (5) =kLACO The solution of equation conditions is

to note that for R -+O (TV = 0), (3)

(6)

(3) with the above boundary

/cLA for y 9 1. Equation

--kLAC

(8) is identical

(8) to (4) with

M = R. In this case the celI is so small that it can be regarded as part of the reservoir which then becomes equivalent to a cell of large volume but with very small electrode area.

(7) Application to parallel plate cells for copper electrowinning

with

Consider the case of copper deposition in a parallel plate cell with turbulent flow where the mass transfer coefficient can be predicted by [3]. and

where d, is the cell equivalent diameter, p and p the density and viscosity of the electrolyte and D the reactant diffusivity. With a parallel plate cell the assumption of perfect mixing in the cell implied by (1) is not strictly valid.

where

Fig. 2. Predicted

variations

of concentration

with time.

The analysis of a batch electrochemical

reactor with continuously

The last term on the right hand side of (1) should contain the mean concentration. However, for a small reactant conversion per pass which would occur under most operational conditions, the mean concentration is approximately equal to the outlet concentration. The form of (9) implies that k, is proportional to V’.* and 0*j3 if the diffusivity is concentration dependent. If the latter is true then an exact solution of (3) will be extremely difficult. Accordingly, in the following examples D will be assumed constant. The following data for the parameters are used :

R = 0.1 m3, M = O-1 m3, A = 10 m2 p = lo3 kg/m’, p = 10e3 kg/m s, D = 3 x 1O-‘o mz/s Case 1 V = 0.0025 m 3/s

(Re = 9800)

Then +I = -0~0007135, e

Case 2 V= OW50 m”ls

(Re = 19600)

R

electrolyte

837

42 = 0.1007145, =0001428 ’

’

DISCUSSION The calculated concentration-time curves for the above cases are plotted in Fig. 2 as dimensionless concentration us time. It can be seen that for any given conversion less time is required with increasing circulation rate as is obvious, and this will be accompanied by greater power requirements for circulation and electrolysis. Practical limitations will occur when the reaction becomes charge transfer controlled which for copper deposition appears to be at a Reynolds number of about 20000[4]. Quantitative comparison with experiment& data is not at present possible but work is in progress to examine the implication of the analysis together with optimisation studies. REFERENCES

Then & = O-000410, & = 0*050410, k,A = 0@00819. R

recirculating

D. S. Flett, Gem. 2nd. 7, 300 (1971). A. T. Kuhn and B. Marquis, .T. appf. Electrochem. 2,

275 (1972). K. L. Ong, Ph.D. Thesis, University of Manchester (1972). B. R. Stanmore, M.Sc. Thesis, University of Manchester (1970).