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The performance of a 500 amp rotating cylinder electrode reactor. Part 3: Methods for the determination of mass transport data and the choice of reactor model
Hydrometallurgy, 33 ( 1 9 9 3 ) 3 6 7 - 3 8 5
367
Elsevier Science Publishers B.V., A m s t e r d a m
The performance of a 500 amp rotating cylinder electrode reactor. Part 3: Methods for the determination of mass transport data and the choice of reactor model F.C. Walsh Applied Electrochemistry Group, Chemistry Department, Universityof Portsmouth, White Swan Road, Portsmouth PO1 2DT, UK ( Received November 15, 1991; revised version accepted October 10, 1992 )
ABSTRACT Walsh, F.C., 1993. The performance of a 500 amp rotating cylinder electrode reactor. Part 3: Methods for the determination of mass transport data and the choice of reactor model. Hydrometallurgy, 33: 367-385. Methods for determining KLA (the product of mass transport coefficient and active cathode area ) are critically discussed for the case of a pilot-scale rotating cylinder electrode reactor. The reactor operation involved cupric ion removal from a 0.5 M H2SO4 solution at 35 °C via deposition of copper powder onto a cathode of diameter 0.25 m and length 0.254 m, having a projected area of 0.200 m 2, which was rotated at 750 rev. min-~. Limiting current, mass transport correlation and conversion data are considered; it is shown that conversion data provided the most satisfactory route towards KLA determinations. Five design equations are considered. The cell is treated as a plug flow reactor ( P F R ) or a continuous stirred tank reactor (CSTR) in the single pass mode. In the batch recycle mode of operation, PFR, CSTR and simple batch models are considered. It is seen that the reactor is best described by a CSTR model, which leads to reasonable agreement between averaged KLA values calculated from single pass and batch recycle data.
1. I N T R O D U C T I O N
Electrochemical reactors based upon rotating cylinder cathodes have been used to remove metal ions from a wide range o f dilute industrial process liquors [ 1 ]. Such rotating cylinder electrode (RCE) reactors (Fig. 1 ) are usually designed as modular devices which operate on a small scale. Typically, the cell current (I) lies within the range 10-5000 A, whilst the projected cathode area (A = 7rd l) has values o f 0.01-1 m 2 [ 2 ]. Examples of commercially Correspondence to. F.C. Walsh, Applied Electrochemistry Group, Chemistry D e p a r t m e n t , University o f P o r t s m o u t h , W h i t e Swan Road, P o r t s m o u t h PO1 2DT, UK.
0 3 0 4 - 3 8 6 X / 9 3 / $ 0 6 . 0 0 © 1993 Elsevier Science Publishers B.V. All rights reserved.
368
F.C.WALSH
t VT Cin,O --.~Cin,f
TANK
t
Couf,t g
IL
:/,
4
A RCE KL Vcelt REACTOR
f
~in,f Q
Fig. 1. Sketch of a rotating cylinder electrode reactor used in metal ion removal via cathodic deposition. The batch recycle mode is shown.
available RCE reactors include the MVH cell [3 ] (which has been developed from the Eco-Cell [ 4 - 6 ] ) , the Turbo-Cell [7,8] and devices marketed by Heraeus Elektrochemie G m b H [ 9 ]. A wide range of reactor designs is possible [ 1,10,11 ], depending upon the process requirements and the scale of operation. Rotation of the cylindrical cathode, which normally involves a peripheral velocity (U) in the range 2-12 m s-~, produces severely turbulent flow in the catholyte. This has several consequences: ( 1 ) The high rate of convective-diffusion of metal ions towards the cathode leads to a high rate of mass transfer. (2) The performance of the reactor, as indexed by the rate of metal extraction under given process conditions, may be controlled by the choice of an appropriate cathode size and rotation speed. ( 3 ) For a given size of RCE operating under fixed process conditions, the performance depends only on the rotation speed and is largely independent of the catholyte flow rate. (4) Metal often deposits in a roughened or powdery form, which gives rise to a high performance, due to enhancements in the active cathode area and the mass transport coefficient, which are, in turn, due to the induction of microturbulence near the RCE surface. (5) Cathode rotation provides a facility for the continuous removal of metal from the RCE via the use of scraping devices. (6) Metal powder may be fluidised within the catholyte chamber then entrained in the outlet flow, which provides a method for continuous product removal via conventional solid/liquid separation techniques such as gravity settlement, filtration or the use of a hydrocyclone. (7) The fluid around the RCE is very well mixed. This results in a uniform
THE PERFORMANCE OF A 500 AMP RCER PART 3
369
TABLEI
Characteristics of the RCE reactor and operating conditions in the present study Parameter
Value
Cathode Material Diameter, d Length, l Projected area*, A ( = n d l ) Rotation speed, o9 Peripheral velocity*, U C o m p a r t m e n t volume, Vcel,
Cu-plated stainless steel d r u m 0.251 m 0.254 m 0.200 m 2 750 m i n 986 0.0187 m 3
Catholyte Composition Temperature Total volume, Vx Volumetric flow rate, Q Single pass studies Batch recycle studies Kinematic viscosity, u Diffusion coefficient of cupric ions, D
0.5 M H 2 S O 4 + 4 8 0 g m -3 CuSO4 35+1°C 0.436
m 3
( 0 . 7 2 - 4 . 1 7 ) × 10 -4 m 3 S - I 4 . 1 7 × 1 0 - 4 m 3 s -1 8 . 5 2 × 10-7 m2 s -1 8 . 0 5 × 10 -1° m 2 s -~
*These values allow for a deposit build-up of 3 m m on the nominal RCE diameter of 0.248 m.
spatial concentration of metal ions within the reactor and the device approximates well to a continuous stirred tank reactor (CSTR) model. Recent publications [ 12,13 ] have described the operation of an industrial, pilot-scale RCE reactor having a nominal current rating of 0.5 kA. Both single pass [ 12 ] and batch recirculation [ 13 ] data were used to obtain mass transport data. In this way, the reactor performance could be characterised using a model system, namely deposition of copper from 0.5 M H2SO4 solutions at low levels of dissolved copper ( < 500 g m - 3 ) . The present paper considers theoretical expressions which describe the performance of such an RCE, followed by a critical consideration of two factors: ( 1 ) the method used to determine mass transport data; (2) the choice of reactor model employed. The reactor and process conditions used in the present work, which are summarised in Table 1, represent a subset of those described previously [ 12 ]. 2. M A S S T R A N S P O R T
EXPRESSIONS
2.1 General considerations Under complete mass transport controlled conditions, the rate of metal ion removal is restricted by the maximum partial current for metal deposition,
370
F.C.WALSH
which is known as the limiting current, IL [ 14,15 ]. The situation may be characterised by definition of the averaged mass transfer coefficient, KL: IL I~2 - z FA Ccell
(1)
where Cc~H= the metal ion concentration within the reactor; and A = the cathode area. For copper deposition from acid sulphate liquors, it may be assumed that z = 2 according to the reaction: C u 2+ + 2 e - - - . C u
(2)
and F = t h e Faraday constant (96485 A s mol-1 ). The cathode area is often difficult to determine accurately. For convenience, the parameter A in eq. ( 1 ) may be taken as the projected, geometrical area (A = n d l). This approach was adopted in previous studies [12,13], for simplicity, and KL values were calculated on this basis. In practice, appreciable roughening of the RCE surface occurs due to the deposition of metal flake or powder. This results in an effective cathode area which is much greater than the projected one. The high performance of RCE reactors is attributable to high values of both the mass transport coefficient, KL, and the effective cathode area, A. In practice, it is unnecessary to separate these effects. As noted elsewhere [ 14-16 ], expressions which describe mass transport, including design equations for RCE reactors, may be written in terms of the product KLA and this approach is adopted here. The increase in the active area may be considered to arise from the development of a pseudo 3-dimensional surface and it is interesting to note that similar problems of separating KL and A values occur when using porous 3-dimensional electrodes [ 17-19 ]. A knowledge of the factor KLA is essential when designing reactors, rationalising their performance and performing scale-up exercises. KLA may be directly related to the geometry of the RCE, its rotational speed and the process electrolyte conditions, including composition and temperature [ 1,2 ]. Several routes to the determination Of KLA will now be considered, starting with those which consider mass transport data. 2. 2 Determination o f KcA from limiting current measurements A simple rearrangement ofeq. ( 1 ) provides a direct expression for KLA:
K1.A
= Z/Cce.
(3 )
which, in principle, allows the elegant determination of KLA from limiting current observations at a known concentration of metal ions in the reactor [ 14 ]. In practice, however, this method is limited to model electrolyte systems, which give rise to well-defined limiting current plateau. Additionally, it
THE PERFORMANCE OF A 500 AMP RCER PART 3
371
must be realised that such measurements are usually made over a short experimental time scale and may not reflect the time development of surface roughness due to metal deposition [ 1,20-22 ]. In the case of reactors having a high fractional conversion per pass, an additional problem is caused by changes in the cell concentration due to variations in current during measurements, as shown in [ 12 ]. It is also very difficult to sustain steady state conditions in pilot-scale reactors. The above considerations limit the usefulness of the direct limiting current technique outside of the well-controlled laboratory operation of small-scale devices. It was noted previously [ 12 ] that direct IL measurements at 60 °C resulted in an overestimation of mass transport. According to eq. (3), the limiting current should be proportional to the reactor concentration if the mass transport coefficient is constant. Figure 2 shows such a plot at 35 °C; two data sets are shown, corresponding to the use of control potentials of - 0 . 5 0 0 V and - 0 . 4 5 0 V vs SCE. Both sets of data shows reasonable linearity, with a higher slope being observed in the case of IL/A 4O0
i
i
i j
l/
[
-0.500 V/,,'-OJ+50 V vs SEE
300
200
100
I
I
I
I
50
100
150
200
I
250 300 Cce[[ / g m-3
Fig. 2. Limiting current for copper deposition as a function o f the copper c o n c e n t r a t i o n in the reactor. Two sets o f data are shown which have been d e t e r m i n e d via estimation of the limiting current from polarisation curves at potentials of - 0 . 4 5 0 V a n d - 0 . 5 0 0 V versus SCE (saturated calomel electrode). T h e lines represent linear least-squares fits to each data set a n d correspond to KLA values o f 6.2 × 10 -4 m 3 s -1. The limits o f reproducibility are shown for three separate d e t e r m i n a t i o n s at each concentration. T = 35 ° C; co = 750 m i n - t.
3"72
F.C.WALSH
the more negative potential. The choice of potential is a compromise; it must be sufficiently negative that full mass transport control is involved, whilst excessive negative values may incur some contribution from hydrogen evolution. In the present case, both sets of results have been corrected by subtracting the background current. The results allow averaged KLA values to be calculated as 6.86X l0 -4 m 3 s-~ and 6.21 × 10 -4 m 3 S - 1 at --0.500 V and - 0 . 4 5 0 V vs SCE.
2 3 Determination OfKLAfrom dimensionless group mass transport correlations It is useful to estimate KLA from mass transport correlations, which are normally written in dimensionless group format: Sh = a RebScc
(4)
where Sh, Re and Sc represent the mass transport, fluid flow and transport properties of the electrolyte. The empirically determined constants a, b and c depend upon the surface state of the RCE and, to some extent, on the reactor geometry [ 1,2,10,22 ]. In the case of metal powder deposition, work by Holland [4-6] has suggested an empirical correlation, largely based upon copper deposition from acid sulphate solutions, which may be approximated to: Sh = 0.079 Re°925c 0"33
(5)
A previous paper [13 ] considered correlations of this type in terms of a Stanton number, St = KL/U. This dimensionless group is related to the Sherwood number by the expression: St = Sh/ReSc. Expansion of the dimensionless groups yields the following expression: (-~)
~---0 . 0 7 9 ( ~ ) ° 9 2 (D)°33
(6)
which may be rearranged as: KLA=0.079n d 0"92 ]~p-0.59 00.67 U0.92
(7)
Equation (7) shows that KLA depends upon the size of the RCE (hence its diameter and length), its rotational speed and diameter (hence its peripheral velocity) and the transport properties of the electrolyte; that is, kinematic viscosity and the diffusion coefficient of metal ions (which, in turn, depend upon composition and temperature). In practice, dimensionless group correlations provide a convenient engineering method for the correlation of a wide range of experimental parameters. They must be used with caution, however, as they represent approximate, averaged expressions. Changes in the RCE surface state, due to alterations in the metal, the electrolyte or the
THE PERFORMANCE OF A 500 AMP RCER PART 3
373
process conditions (such as temperature, or cathode potential) will result in a modified correlation [ 1 ]. A striking example is the difference between the predicted values of mass transport for surfaces involving metal powder deposition and those which are hydrodynamically smooth. For a smooth RCE, the analogous expression to equation ( 5 ) is [ 1, 23 ]: Sh = 0.079 Re °'7° Sc 0"33
(8)
or;
KLA=O.O79n d °v° ~p-0.37 D0.67 UO.7O
(9)
Division of eq. (7) by eq. (9) provides an indication of the relative performance, 7: y = d °-22 v -°-22 U °-2° (10) Enhancement of the performance is seen to be dependent upon the size (hence diameter) of the RCE, its peripheral velocity and the kinematic viscosity of the electrolyte. For example, it has been shown [ 13 ] that the performance of a given RCE may be improved by increasing the temperature (which lowers v), or by the use of a faster rotation rate (which elevates U). 3. C O N V E R S I O N
EXPRESSIONS
Whilst many options exist, common modes of operation include those of single pass, batch recycle and simple batch, as shown in Fig. 3. Design equations may be written for each of these cases, allowing the factor KLA to be extracted [ 14,15,24]. In the case of continuous flow reactors (Fig. 3a and b) it is necessary to adopt a reactor model, the most obvious choices being a plug flow reactor (PFR), in which no mixing occurs in the direction of electrolyte flow, and the continuous stirred tank reactor (CSTR), which assumes perfect mixing within the cell. The PFR therefore involves a concentration gradient within the reactor, while, in the CSTR, the inlet concentration steps down to the reactor concentration at inlet manifold. This reactor concentration is maintained as fluid leaves the reactor. The RCE reactor, with its turbulent hydrodynamics, usually approximates to CSTR behaviour [ 1,2 ]. 3.1 The single pass mode
A mass balance over an ideal PFR in the steady state leads to the expression: Cout = f i n exp(--KLA/Q)
(11)
The fractional conversion per pass through the reactor is defined by: x P sP FR
~ 1 --
(Cout/Cin)
(12)
374
F.C. WALSH
",iout,~ Q
f-oui" cg [STR [celt
PFR
(o)
{b)
tin ~ Q
Cin~xQ [out,f Q
t
Vcett PFR or" [STR
TANK
[in,t (c)
r-~,t (1
[in,O --'~[in,t (d] Fig. 3. Modes of operation for a rotating cylinder electrode reactor. (a) Single pass plug flow reactor. (b) Single pass, continuous stirred tank reactor. (c) Batch recycle via a holding tank. (d) The system as a whole approximates to simple batch behaviour. which allows eq. ( 11 ) to be written as:
xPFR 1-exp(-KLA/Q) SP
(13)
F o r an ideal C S T R , the analogous eqs. to ( 11 ) and ( 13 ) are: 1
C°u' = C i " [1 +
(I~A/Q)]
and:
[
~sPVPFR= 1 -- 1 +
' (K~A/Q)
(14)
]
( 15 )
The difference b e t w e e n the fractional conversions p r e d i c t e d by eqs. ( 13 ) a n d ( 15 ) m a y be illustrated b y considering typical data f r o m [ 12 ]. In the case o f an R C E o f d i a m e t e r 0.25 m and a p r o j e c t e d area o f 0.200 m 2, rotating at 750 rev. r a i n - ~, the average KLA value was 5.68 × 10 .4 m 3 s - ~ at a temper-
375
THE PERFORMANCE OF A 500 AMP RCER PART 3
ature of 3 5 ° C. Substituting these values into eqs. ( 13 ) and ( 15 ) produces the curves shown in Fig. 4, which describe the fractional conversion per pass as a function of volumetric flow rate. The PFR case clearly gives a superior fractional conversion to the CSTR under the experimental conditions; the data closely conform to the CSTR predictions. It is interesting to examine the case of larger volumetric flow rates. As the throughput increases (i.e., as the fractional conversion per pass decreases), the PFR and CSTR predictions converge, as shown in Fig. 5. The suitability of a CSTR model is also confirmed in Fig. 6, showing the conversion factor [(Cin/Cout)-l] v e r s u s the reciprocal flow rate, 1/Q. Equation ( 14 ) may be rearranged as: '
Co.t/
=Q (KLA)
(16)
and a plot of the left hand side versus 1/Q should be a straight line of slope = KLA. In Fig. 6, an averaged KLA value of 5.68 X 10 -4 m 3 s-t has been used to predict the idealised behaviour according to eq. ( 16 ). The experimenXSp 1.0
I
I
I
\
0.8
0.6
0.4 normot operoting range
(STR
0~2
0
0
'
20
40
60
80
Q / dm3 min-I
Fig. 4. Predicted fractional conversion of cupric ions per pass as a function of volumetric flow rate of electrolyte. The theoretical data are derived from assumption of PFR behaviour, according to eq. ( 13 ), or C S T R behaviour, according to eq. ( 15 ). In both cases, KLA = 5.68 X 10 - 4 m 3 s-~; T = 3 5 ° C ; o 9 = 7 5 0 min - l .
F.C. WALSH
376
XSp 1.0~
\
0.8
r
i
'
'
'
' ' " 1
i i
.i r r
\ PFR [STR '
0~6
design point O..Z, l
normo[ operQting ronge '<---
0.2 -
0
1
0101 •
0
3 0 /dm 3 min-1
Fig. 5. Predicted fractional conversion per pass as a function of volumetric flow rate. Semilogarithmic plot showing convergence of conversion values at high flow rates. The data are pred i c t e d by the PFR model, according to eq. ( 1 3 ) , or the C S T R one, according to eq. ( 1 5 ) . KLA= 5.68 × 10 - 4 m 3 s-1; T = 35 ° C; 09--750 m i n - 1 . The design basis for the reactor is shown as Xsp = 0.52 at Q = 25 dm 3 m i n - i.
tal data are well described by this theoretical line at high flow rates, but the data lie below the theoretical line at low flow rates and hence at high values of fractional conversion per pass. As noted in [ 12 ], this may be due to a degree of redissolution of the metal via corrosion. However this problem is slight at the operating temperature used in these experiments (35 °C), in contrast to the higher temperature (60 ° C) reported previously [ 12 ]. In practice, the fractional conversion per pass is often relatively small and difficult to measure accurately via the usual analytical techniques such as atomic absorption spectrophotometry. This factor limits the usefulness of the technique. Indeed, the data reported here and in previous studies [ 12,13 ] describe unusually high fractional conversions per pass (typically 0.5-0.9 ). It has been more usual to experience values in the range 0.02-0.3 for laboratory and pilot-scale RCE reactors [ 1,2,4 ]. The most versatile and most generally suitable technique for KLA determination in the present system is the use of batch recirculation, which will now be described.
THE PERFORMANCE OF A 500 AMP RCER PART 3
377
Cin -1 Couf 16 IIPFR
I
,,_
12
I
normczI operQfing r~nge
0
I
L~
I
8
> l
12 16 1 103Q/cm3s-I
Fig. 6. Conversion factor versus reciprocal volumetric flow rate in the single pass mode. The solid lines represent idealised behaviour according to P F R (eq. (13) ) or CSTR (eq. ( 15 ) ) models with KLA= 5.68 × 10 -4 m 3 s-1. The range of actual values is shown as a range for six experiments at each flow rate. Note the increasing divergence of the experimental data from the predicted CSTR line at high values of 1/Q; that is, at low flow rates. T = 35 °C; to= 750 m i n - ~.
3.2 The batch recirculation mode .3.2. I General The recycling o f electrolyte around a loop consisting of the reactor and a well-mixed tank provides a convenient process strategy in which the volume o f process liquor m a y be readily adjusted. The tank also provides a facility for sampling, monitoring temperature control, feedstock preparation and, in some cases, product extraction [ 15 ]. Depending upon the residence time of fluid in the reactor versus that in the tank and the fractional conversion per pass, there are 3 possible models: ( 1 ) a CSTR in batch recycle; (2) a P F R in batch recycle; (3) the system as a whole approximates to a batch reactor. The applicability o f each o f these cases may be examined for a typical data set which was reported, in part, in [ 13 ]. Once again, the reactor involved has a diameter o f 0.25 m and a projected area of 0.200 m 2, the rotation speed
378
F.C. WALSH
being 750 m i n - l in a 0.5 M I"I2804 solution at 35°C. The initial cupric ion level is 480 g m -3.
3.2.2 The CSTR in batch recycle An approximate [24,25] but practical [15,22] conversion expression for this system is: (7'in,t = Cin,o exp
X CSTR
( 17 )
where tT is the mean residence time of electrolyte in the tank: (18)
~T = V T / Q
and the fractional conversion per pass is given by eq. ( 15 ). Equation (16) is valid for the case of a very low ratio of rR to Vx, that is, for rR >> rT which is fulfilled for the present system where Vce,>> VT (0.0187 m 3 >> 0.436 m 3).
3.2. 3 The PFR in batch recycle The analogous expression to equation ( 17 ) is: (ln,t = Cin,o exp
X~'evR
(19)
where X~'ffR is given by eqs. ( 12 ) and ( 13 ).
3.2.4 A simple batch behaviour If the fractional conversion per pass through the reactor is sufficiently low, both eqs. (17) and (19) may be reduced to:
{ KLA\ Cin,t=Cin.oexp~--wt )
(20)
which is an expression for a simple batch process [ 15,24 ] and which does not involve the volumetric throughput.
3.2.5 A comparison of batch models The selection of a particular model depends upon its practical suitability (in terms of the known fluid flow) and its ability to predict KLA to a sufficient degree of accuracy. All three design equations for a batch system (eqs. ( 17 ), (19) and (20)) predict a first-order decay of metal ion concentration from its initial value. However, the apparent first order rate constant, k, defined by: G°,t = Ci,,o e x p ( - k t ) is different in each case:
(21 )
T H E P E R F O R M A N C E O F A 500 A M P R C E R P A R T 3
379
( 1 ) CSTR in batch recycle: k_
VCSTR/..
-- ASp
yCSTR /
/ 'T = ASp
~,Q~ V T )
(22)
(2) PFR in batch recycle: PFR k=Xsp /rT=x~FR(Q/VT)
(23)
( 3 ) simple batch behaviour: (24)
k= KLA
VT A comparison between predictions of the models, for the present data, is shown in Fig. 7 as a plot ofnormalised concentration versus time. The following points are noteworthy: ( 1 ) The three models each predict a linear decay on the semilogarithmic concentration time coordinates. ( 1 ) The rate of decay lies in the order: CSTR in batch recycle > PFR in batch recycle > simple batch, as given by eqs. (22-24). (3) The corresponding values of the apparent rate constants are 5.52 X 10 - - 4 S-l, 7.11X10-4s - l and 1 . 3 0 × 1 0 - 3 s -1. (4) The experimental data lie close to the predicted line for the CSTR in batch recycle model at shorter times (0 min < t< 80 min). At longer times, the metal ion concentration is higher than the predicted values and the rate of decay decreases with time. In other words, the KLA value over early parts of the batch electrolysis ( = 5.68 X 10 - 4 m 3 S-1 ) cannot be maintained at low metal ion concentrations. This behaviour has been observed previously [ 13 ] and may be attributed to a combination of a change in the nature of the rate control (from mass transfer to chemical steps), together with significant redissolution of metal. Under the chosen experimental conditions, therefore, the system is best modelled according to the 'CSTR in batch recycle' design equation. In addition to poor mathematical fits of the data to other models, it should be noted that the PFR model is unsuitable, due to the stirred tank hydrodynamics, resulting in a good CSTR approximation, which has been confirmed by spatial analysis of the catholyte (Table 2 ). The simple batch model is attractive in its simplicity but must be rejected in the present case as the fractional conversion per pass through the reactor is appreciable, as noted previously. The determination of KLA from a normalised metal on concentration versus time data set, via the 'CSTR in batch' model, involves the expression of the apparent first-order rate constant in terms of KLA. Inserting ASpV'CSTRfrom eq. ( 1 5 ) i n t o eq. (22)gives: KLA =
1- ( k V T / Q ) - 1
(25)
F.C. WALSH
380
[-in,t / Lin,O I00~ ,
I
i
I
]
I
I
10-1 X
X X
X X X X R
1 0-2
SBR
X BR -_
"~BR\
\10
-31 0
i
20
40
60
80
I
I
I
I00
120
140
160
18C
t/rain Fig. 7. Normalised inlet concentration of copper as a function of time in the batch recycle mode. The solid lines represent the predicted behaviour according to P F R batch recycle (eq. (19) ), CSTR batch recycle (eq. ( 1 7 ) ) or overall simple batch reactor (eq. ( 2 0 ) ) models, with KtA= 5.68× 10 -4 m 3 s - l . T = 35°C; 09=750 m i n - L
TABLE 2 Chemical analysis from various sampling points in the catholyte compartment of the RCE reactor Sample point
Copper concentration / g m -3
Inlet manifold Bottom of reactor, inlet side Top of reactor, inlet side Bottom of reactor, outlet side Top of reactor, outlet side Outlet manifold
480 _+ 12 267 + 7 262 + 7 259 _+6 250 _+6 255 _+6
Method: volumetric dilution followed by air/acetylene atomic absorption spectroscopy as described in [131.
THE PERFORMANCE OF A 500 AMP RCER PART 3
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The observed k value for 0 min < t < 80 min is 5.52 × 10-4 S - - 1 which leads to a KLA determination of 5.68 × 10-4 m 3 s-1 from equation (25 ). Similarly, for the P F R in batch recycle, the coupling ofeqs. (13) and (23), followed by rearrangement, yields:
KLA=- Q I n ( 1 - k ~ Z )
(26)
Equation ( 26 ) allows a KLA value of 3.59 × 10- 4 m 3 s- 1 to be determined from the experimental data shown in Fig. 7. If the system as a whole approximates to a batch reactor, then eqs. (20) and (24) apply. The latter equation may be rearranged to give:
KLA=kVT
(27)
Equation (27) results in a KLA value of 2.41 X 10 - 4 m 3 s- ~from the experimental data set in Fig. 7. 4. OVERALL COMPARISON OF TECHNIQUES FOR THE DETERMINATION OF KtA
Table 3 provides a summary of KLA values which have been calculated using the techniques considered in this paper under the stated experimental conditions. The choice of technique will depend upon convenience as well as the need for sufficient accuracy. At the design stage a specification for the reactor involved use of a mass transport correlation which had been derived from other RCE reactors [ 1,4,22]. Thus eq. (7) predicted a KLA value of 4.62X 1 0 - a m 3 s -1. It was considered prudent, however, to make a conservative estimate which was approximately 10% lower than this value in order to avoid any scale-up problems. Mass transport correlations provide a useful guide to behaviour over a wide range of experimental parameters but cannot be expected to provide an accurate prediction Of KLA under specific process conditions. In principle, direct, limiting current determinations provide an elegant route to KLA but, as discussed in section 2.2, there are experimental difficulties associated with changes in the reactor concentration and surface state of the RCE. These problems are more significant in the case of a high fractional conversion per pass, as in the present case. The choice of cathode potential for IL estimation is also problematic; the potential must correspond to a plateau current caused by full mass transport control (i.e., it must be sufficiently negative), whilst avoiding contributions from hydrogen evolution (at too negative a potential). A suitable compromise is a potential of - 0 . 4 5 0 V vs SCE, where an averaged value of 6.2 X 10 - 4 m 3 S-1 is achieved over a range of reactor concentrations. This value is only slightly higher (11%) than the ones achieved in regular process trials ( 5.7 + 0.4 ) X 10- 4 m 3 s- 1. The use of a
F.C. WALSH
382 TABLE 3
,Comparison of typical KLA values obtained from various techniques Technique
KLA /10 4 m 3 s - I
Limiting current determination as a :function of concentration at - 0 . 5 0 0 V vs SCE at - 0 . 4 5 0 V vs SCE ]Prediction from a mass transport correlation via eq. ( 7 ) Single pass conversion data CSTR via eq. (14) P F R via eq. ( 11 ) Batch recycle conversion data CSTR via eq. (16) P F R via eq. ( 18 ) Simple batch via eq. (19) Design specification Process experience
6.9+0.3 6.2 4.62
5.75 3.58 5.68 3.59 2.41 4.2 5.7 _+0.4
All values refer to copper deposition from an electrolyte containing 0.5 M H2SO 4 at 35 °C. The inlet or initial copper concentration is 480 g m - 3 . The volumetric flow rate is 0.417 m 3 s - l through an RCE reactor of diameter 0.25 m, and the projected area 0.200 m 2 rotating at 750 m i n - L
higher cathode potential ( - 0 . 5 0 0 V vs SCE) results in an overestimation of
KLA. It is much more satisfactory to measure KLA via conversion techniques. In the present case, the very turbulent flow conditions inside the RCE reactor naturally lead to the adoption of a CSTR reactor model. Reasonable agreement between KLA values was achieved in the single pass and batch recycle cases using a CSTR model. Moreover, these values of 5.75 and 5.68× 1 0 - 4 m 3 s - 1 agree well with those experienced during later process trials. The use of single pass conversion data is only possible, however, if there is an accurately measurable difference in metal ion concentration at the inlet and outlet of the reactor; that is, if the fractional conversion per pass is high. Under these conditions, there is a marked difference in the behaviour of the PFR and CSTR models. While PFR behaviour theoretically leads to higher conversions, the axial concentration gradient along the reactor would lead to a variation in the rate of deposition due to the non-uniform current distribution. Indeed, the present reactor incorporated manifolds which were designed to encourage good axial mixing according to the CSTR approximation. Chemical analysis (Table 2 ) has confirmed effective mixing. The (incorrect) adoption of a PFR model to the single pass and batch recycle concentration
THE PERFORMANCEOF A 500 AMP RCERPART 3
383
versus time data leads to a marked underestimation Of KLA, by factors of 38% and 37%, respectively. In the batch recirculation mode of operation, it is clearly important to use the CSTR in batch recycle model to describe the experimental conditions. The application of a simple batch model results in an underestimation Of KLA by 58%. Finally, it should be stressed that the suitability of a reactor model critically depends not only on a knowledge of the flow conditions within the reactor but also upon reactor performance (i.e., the size OfKLA ) and the volumetric flow rate. Hence, at very high values Of KLA/Q, the fractional conversion per pass is very small and the PFR and CSTR models converge [ 19 ]. In the batch recycle case under these conditions, the system as a whole approximates well to :simple batch behaviour [ 14,19,24,25 ]. However, such conditions are not appropriate to the present case where a high value of KLA/Q (,~ 1.36 ) provides a significant fractional conversion per pass (Xsp~ 0.58 ). It is also important to note that discrepancies in the overall fractional conversion between batch recycle models will increase with processing time. The time evolution of errors in determining KLA in such systems will be discussed elsewhere [26 ]. NOMENCLATURE
a, b, c constants in eq. (4) cathode area, m 2 A cupric ion concentration in the cell (reactor), mol m-3 Ccell concentration at reactor inlet, mol m-3 G. concentration at reactor outlet, mol m - 3 Gout inlet concentration at time t, mol m - 3 Cin,t inlet concentration at time zero, mol m-3 Cin,o d rotating cylinder diameter, m D diffusion coefficient of cupric ions, m 2 sF Faraday Constant, (96485 A s mol-~ ) limiting current due to convective diffusion, A IL k apparent rate constant, sKL mass transfer coefficient, m s- 1 active length of rotating cylinder cathode, m Q volumetric flow rate m 3 st batch time, s U peripheral velocity of cathode, m 3 s- l overall space occupied by reactor Vcell effective electrolyte volume within the reactor m 3 VR effective electrolyte volume in the holding tank m 3 VT fractional conversion of reactant in a single pass through the reactor Xsp
384 Z
F.C. WALSH
number o f electrons per copper atom deposited
Dimensionless Groups Re
Sc Sh St
Reynolds N u m b e r ( = Ud/v) Schmidt N u m b e r ( = v/D) Sherwood N u m b e r ( = kLd/D) Stanton N u m b e r ( = kL/U)
Greek //
"rR "rv (/2
relative (mass transport) performance factor defined by eq. ( 1 0 ) kinematic viscosity o f electrolyte, m 2 s - 1 nominal residence time in reactor ( = VR/Q), s nominal residence time in tank ( = VT/Q), s rotation speed o f cathode, rev s -
Abbreviations CSTR continuous stirred tank reactor plug flow reactor PFR
REFERENCES 1 Walsh, F.C., The role of the rotating cylinder electrode reactor in metal ion removal. In: G.D. Genders and N.L. Weinberg (Editors), Electrochemical Technology for a Cleaner Environment. Electrosynthesis, Layton, USA ( 1992 ), pp. 101-159. 2 Walsh, F.C. and Gabe, D.R., Trans. Inst. Chem. Eng., 68B ( 1990): 107-114. 3 MVH b.v., The MVH Cell. MVH b.v., Uden, The Netherlands. 4 Holland, F.S., Chem. Ind., July (1978): 453-458. 5 Holland, F.S., British Pat. 1444367 (1978). 6 Holland, F.S., British Pat. 1505736 (1978). 7 Anon, Turbocel. Sessler Galvanotechnik GmbH, Keltern, Germany, and Werner Fluhman AG, Dubendorf, Switzerland, 8 Puippe, J.C., Turbocell--a metals recycling device. Meet. Surface Technology in the Europe of the 90's. Europ. Acad. Surface Technol., Schwabisch Gmund (1990). 9 Mayr, M., Blatt, W., Busse, B. and Heinke, H., 4th Int. Forum on Electrolysis in the Chemical Industry (Fort Lauderdale, Fla., Nov. 11-15) (1990). 10 Gabe, D.R. and Walsh, F.C., J. Appl. Electrochem., 13 (1983): 3-22. 11 Gardner, N.A. and Walsh, F.C., Design and applications of rotating cylinder electrode technology to continuous production of metal. In: R.E. White (Editor), Electrochemical Cell Design. Plenum, New York (1984), pp. 225-258. 12 Robinson, D. and Walsh, F.C., The performance of a 500 Amp rotating cylinder electrode reactor. Part 1: Current potential data and single pass studies. Hydrometallurgy, 26 ( 1991 ): 93-114. 13 Robinson D. and Walsh F.C., The performance of a 500 Amp rotating cylinder electrode reactor. Part 2: Batch recirculation studies and overall mass transport. Hydrometallurgy, 26 (1991): 115-133.
THE PERFORMANCE OF A 500 AMP RCER PART 3
385
14 Walsh, F.C., A First Course in Electrochemical Engineering. The Electrochemical Consultancy, Romsey (1993) (in press). 15 Pletcher, D. and Walsh, F.C., Industrial Electrochemistry. Chapman and Hall, London, 2nd ed. (1990). 16 Walsh, F.C., Bull. Electrochem., 6 ( 1990): 283-293. 17 Scannell, R.A. and Walsh, F.C., Inst. Chem. Eng. Symp. Ser., 112 ( 1989): 59-69. 18 Langlois, S. and Coeuret, F., J. Appl. Electrochem., 20 ( 1990): 749-755. 19 Ford, W.P.J., Walsh, F.C. and Whyte, I., Inst. Chem. Eng. Symp. Ser., 127 ( 1992): 111126. 20 Gabe, D.R. and Walsh, F.C., J. Appl. Electrochem., 14 (1984): 555-564. 21 Gabe, D.R. and Walsh, F.C., J. Appl. Electrochem., 14 ( 1984): 565-572. 22 Gabe, D.R. and Walsh, F.C., J. Appl. Electrochem., 15 ( 1985): 807-824. 23 Eisenberg, M, Tobias, C.W. and Wilke, C.R., J. Electrochem. Soc., 101 ( 1954): 306-319. 24 Pickett, D.J., Electrochemical Reactor Design. Elsevier, Amsterdam, 2nd Ed. (1979). 25 Walker, A.T.S. and Wragg, A.A., Electrochim. Acta, 22 ( 1977): 1129-1134. 26 Walsh, F.C. and Reade, G.W., Trans. Inst. Chem. Eng. (in prep.).
367
Elsevier Science Publishers B.V., A m s t e r d a m
The performance of a 500 amp rotating cylinder electrode reactor. Part 3: Methods for the determination of mass transport data and the choice of reactor model F.C. Walsh Applied Electrochemistry Group, Chemistry Department, Universityof Portsmouth, White Swan Road, Portsmouth PO1 2DT, UK ( Received November 15, 1991; revised version accepted October 10, 1992 )
ABSTRACT Walsh, F.C., 1993. The performance of a 500 amp rotating cylinder electrode reactor. Part 3: Methods for the determination of mass transport data and the choice of reactor model. Hydrometallurgy, 33: 367-385. Methods for determining KLA (the product of mass transport coefficient and active cathode area ) are critically discussed for the case of a pilot-scale rotating cylinder electrode reactor. The reactor operation involved cupric ion removal from a 0.5 M H2SO4 solution at 35 °C via deposition of copper powder onto a cathode of diameter 0.25 m and length 0.254 m, having a projected area of 0.200 m 2, which was rotated at 750 rev. min-~. Limiting current, mass transport correlation and conversion data are considered; it is shown that conversion data provided the most satisfactory route towards KLA determinations. Five design equations are considered. The cell is treated as a plug flow reactor ( P F R ) or a continuous stirred tank reactor (CSTR) in the single pass mode. In the batch recycle mode of operation, PFR, CSTR and simple batch models are considered. It is seen that the reactor is best described by a CSTR model, which leads to reasonable agreement between averaged KLA values calculated from single pass and batch recycle data.
1. I N T R O D U C T I O N
Electrochemical reactors based upon rotating cylinder cathodes have been used to remove metal ions from a wide range o f dilute industrial process liquors [ 1 ]. Such rotating cylinder electrode (RCE) reactors (Fig. 1 ) are usually designed as modular devices which operate on a small scale. Typically, the cell current (I) lies within the range 10-5000 A, whilst the projected cathode area (A = 7rd l) has values o f 0.01-1 m 2 [ 2 ]. Examples of commercially Correspondence to. F.C. Walsh, Applied Electrochemistry Group, Chemistry D e p a r t m e n t , University o f P o r t s m o u t h , W h i t e Swan Road, P o r t s m o u t h PO1 2DT, UK.
0 3 0 4 - 3 8 6 X / 9 3 / $ 0 6 . 0 0 © 1993 Elsevier Science Publishers B.V. All rights reserved.
368
F.C.WALSH
t VT Cin,O --.~Cin,f
TANK
t
Couf,t g
IL
:/,
4
A RCE KL Vcelt REACTOR
f
~in,f Q
Fig. 1. Sketch of a rotating cylinder electrode reactor used in metal ion removal via cathodic deposition. The batch recycle mode is shown.
available RCE reactors include the MVH cell [3 ] (which has been developed from the Eco-Cell [ 4 - 6 ] ) , the Turbo-Cell [7,8] and devices marketed by Heraeus Elektrochemie G m b H [ 9 ]. A wide range of reactor designs is possible [ 1,10,11 ], depending upon the process requirements and the scale of operation. Rotation of the cylindrical cathode, which normally involves a peripheral velocity (U) in the range 2-12 m s-~, produces severely turbulent flow in the catholyte. This has several consequences: ( 1 ) The high rate of convective-diffusion of metal ions towards the cathode leads to a high rate of mass transfer. (2) The performance of the reactor, as indexed by the rate of metal extraction under given process conditions, may be controlled by the choice of an appropriate cathode size and rotation speed. ( 3 ) For a given size of RCE operating under fixed process conditions, the performance depends only on the rotation speed and is largely independent of the catholyte flow rate. (4) Metal often deposits in a roughened or powdery form, which gives rise to a high performance, due to enhancements in the active cathode area and the mass transport coefficient, which are, in turn, due to the induction of microturbulence near the RCE surface. (5) Cathode rotation provides a facility for the continuous removal of metal from the RCE via the use of scraping devices. (6) Metal powder may be fluidised within the catholyte chamber then entrained in the outlet flow, which provides a method for continuous product removal via conventional solid/liquid separation techniques such as gravity settlement, filtration or the use of a hydrocyclone. (7) The fluid around the RCE is very well mixed. This results in a uniform
THE PERFORMANCE OF A 500 AMP RCER PART 3
369
TABLEI
Characteristics of the RCE reactor and operating conditions in the present study Parameter
Value
Cathode Material Diameter, d Length, l Projected area*, A ( = n d l ) Rotation speed, o9 Peripheral velocity*, U C o m p a r t m e n t volume, Vcel,
Cu-plated stainless steel d r u m 0.251 m 0.254 m 0.200 m 2 750 m i n 986 0.0187 m 3
Catholyte Composition Temperature Total volume, Vx Volumetric flow rate, Q Single pass studies Batch recycle studies Kinematic viscosity, u Diffusion coefficient of cupric ions, D
0.5 M H 2 S O 4 + 4 8 0 g m -3 CuSO4 35+1°C 0.436
m 3
( 0 . 7 2 - 4 . 1 7 ) × 10 -4 m 3 S - I 4 . 1 7 × 1 0 - 4 m 3 s -1 8 . 5 2 × 10-7 m2 s -1 8 . 0 5 × 10 -1° m 2 s -~
*These values allow for a deposit build-up of 3 m m on the nominal RCE diameter of 0.248 m.
spatial concentration of metal ions within the reactor and the device approximates well to a continuous stirred tank reactor (CSTR) model. Recent publications [ 12,13 ] have described the operation of an industrial, pilot-scale RCE reactor having a nominal current rating of 0.5 kA. Both single pass [ 12 ] and batch recirculation [ 13 ] data were used to obtain mass transport data. In this way, the reactor performance could be characterised using a model system, namely deposition of copper from 0.5 M H2SO4 solutions at low levels of dissolved copper ( < 500 g m - 3 ) . The present paper considers theoretical expressions which describe the performance of such an RCE, followed by a critical consideration of two factors: ( 1 ) the method used to determine mass transport data; (2) the choice of reactor model employed. The reactor and process conditions used in the present work, which are summarised in Table 1, represent a subset of those described previously [ 12 ]. 2. M A S S T R A N S P O R T
EXPRESSIONS
2.1 General considerations Under complete mass transport controlled conditions, the rate of metal ion removal is restricted by the maximum partial current for metal deposition,
370
F.C.WALSH
which is known as the limiting current, IL [ 14,15 ]. The situation may be characterised by definition of the averaged mass transfer coefficient, KL: IL I~2 - z FA Ccell
(1)
where Cc~H= the metal ion concentration within the reactor; and A = the cathode area. For copper deposition from acid sulphate liquors, it may be assumed that z = 2 according to the reaction: C u 2+ + 2 e - - - . C u
(2)
and F = t h e Faraday constant (96485 A s mol-1 ). The cathode area is often difficult to determine accurately. For convenience, the parameter A in eq. ( 1 ) may be taken as the projected, geometrical area (A = n d l). This approach was adopted in previous studies [12,13], for simplicity, and KL values were calculated on this basis. In practice, appreciable roughening of the RCE surface occurs due to the deposition of metal flake or powder. This results in an effective cathode area which is much greater than the projected one. The high performance of RCE reactors is attributable to high values of both the mass transport coefficient, KL, and the effective cathode area, A. In practice, it is unnecessary to separate these effects. As noted elsewhere [ 14-16 ], expressions which describe mass transport, including design equations for RCE reactors, may be written in terms of the product KLA and this approach is adopted here. The increase in the active area may be considered to arise from the development of a pseudo 3-dimensional surface and it is interesting to note that similar problems of separating KL and A values occur when using porous 3-dimensional electrodes [ 17-19 ]. A knowledge of the factor KLA is essential when designing reactors, rationalising their performance and performing scale-up exercises. KLA may be directly related to the geometry of the RCE, its rotational speed and the process electrolyte conditions, including composition and temperature [ 1,2 ]. Several routes to the determination Of KLA will now be considered, starting with those which consider mass transport data. 2. 2 Determination o f KcA from limiting current measurements A simple rearrangement ofeq. ( 1 ) provides a direct expression for KLA:
K1.A
= Z/Cce.
(3 )
which, in principle, allows the elegant determination of KLA from limiting current observations at a known concentration of metal ions in the reactor [ 14 ]. In practice, however, this method is limited to model electrolyte systems, which give rise to well-defined limiting current plateau. Additionally, it
THE PERFORMANCE OF A 500 AMP RCER PART 3
371
must be realised that such measurements are usually made over a short experimental time scale and may not reflect the time development of surface roughness due to metal deposition [ 1,20-22 ]. In the case of reactors having a high fractional conversion per pass, an additional problem is caused by changes in the cell concentration due to variations in current during measurements, as shown in [ 12 ]. It is also very difficult to sustain steady state conditions in pilot-scale reactors. The above considerations limit the usefulness of the direct limiting current technique outside of the well-controlled laboratory operation of small-scale devices. It was noted previously [ 12 ] that direct IL measurements at 60 °C resulted in an overestimation of mass transport. According to eq. (3), the limiting current should be proportional to the reactor concentration if the mass transport coefficient is constant. Figure 2 shows such a plot at 35 °C; two data sets are shown, corresponding to the use of control potentials of - 0 . 5 0 0 V and - 0 . 4 5 0 V vs SCE. Both sets of data shows reasonable linearity, with a higher slope being observed in the case of IL/A 4O0
i
i
i j
l/
[
-0.500 V/,,'-OJ+50 V vs SEE
300
200
100
I
I
I
I
50
100
150
200
I
250 300 Cce[[ / g m-3
Fig. 2. Limiting current for copper deposition as a function o f the copper c o n c e n t r a t i o n in the reactor. Two sets o f data are shown which have been d e t e r m i n e d via estimation of the limiting current from polarisation curves at potentials of - 0 . 4 5 0 V a n d - 0 . 5 0 0 V versus SCE (saturated calomel electrode). T h e lines represent linear least-squares fits to each data set a n d correspond to KLA values o f 6.2 × 10 -4 m 3 s -1. The limits o f reproducibility are shown for three separate d e t e r m i n a t i o n s at each concentration. T = 35 ° C; co = 750 m i n - t.
3"72
F.C.WALSH
the more negative potential. The choice of potential is a compromise; it must be sufficiently negative that full mass transport control is involved, whilst excessive negative values may incur some contribution from hydrogen evolution. In the present case, both sets of results have been corrected by subtracting the background current. The results allow averaged KLA values to be calculated as 6.86X l0 -4 m 3 s-~ and 6.21 × 10 -4 m 3 S - 1 at --0.500 V and - 0 . 4 5 0 V vs SCE.
2 3 Determination OfKLAfrom dimensionless group mass transport correlations It is useful to estimate KLA from mass transport correlations, which are normally written in dimensionless group format: Sh = a RebScc
(4)
where Sh, Re and Sc represent the mass transport, fluid flow and transport properties of the electrolyte. The empirically determined constants a, b and c depend upon the surface state of the RCE and, to some extent, on the reactor geometry [ 1,2,10,22 ]. In the case of metal powder deposition, work by Holland [4-6] has suggested an empirical correlation, largely based upon copper deposition from acid sulphate solutions, which may be approximated to: Sh = 0.079 Re°925c 0"33
(5)
A previous paper [13 ] considered correlations of this type in terms of a Stanton number, St = KL/U. This dimensionless group is related to the Sherwood number by the expression: St = Sh/ReSc. Expansion of the dimensionless groups yields the following expression: (-~)
~---0 . 0 7 9 ( ~ ) ° 9 2 (D)°33
(6)
which may be rearranged as: KLA=0.079n d 0"92 ]~p-0.59 00.67 U0.92
(7)
Equation (7) shows that KLA depends upon the size of the RCE (hence its diameter and length), its rotational speed and diameter (hence its peripheral velocity) and the transport properties of the electrolyte; that is, kinematic viscosity and the diffusion coefficient of metal ions (which, in turn, depend upon composition and temperature). In practice, dimensionless group correlations provide a convenient engineering method for the correlation of a wide range of experimental parameters. They must be used with caution, however, as they represent approximate, averaged expressions. Changes in the RCE surface state, due to alterations in the metal, the electrolyte or the
THE PERFORMANCE OF A 500 AMP RCER PART 3
373
process conditions (such as temperature, or cathode potential) will result in a modified correlation [ 1 ]. A striking example is the difference between the predicted values of mass transport for surfaces involving metal powder deposition and those which are hydrodynamically smooth. For a smooth RCE, the analogous expression to equation ( 5 ) is [ 1, 23 ]: Sh = 0.079 Re °'7° Sc 0"33
(8)
or;
KLA=O.O79n d °v° ~p-0.37 D0.67 UO.7O
(9)
Division of eq. (7) by eq. (9) provides an indication of the relative performance, 7: y = d °-22 v -°-22 U °-2° (10) Enhancement of the performance is seen to be dependent upon the size (hence diameter) of the RCE, its peripheral velocity and the kinematic viscosity of the electrolyte. For example, it has been shown [ 13 ] that the performance of a given RCE may be improved by increasing the temperature (which lowers v), or by the use of a faster rotation rate (which elevates U). 3. C O N V E R S I O N
EXPRESSIONS
Whilst many options exist, common modes of operation include those of single pass, batch recycle and simple batch, as shown in Fig. 3. Design equations may be written for each of these cases, allowing the factor KLA to be extracted [ 14,15,24]. In the case of continuous flow reactors (Fig. 3a and b) it is necessary to adopt a reactor model, the most obvious choices being a plug flow reactor (PFR), in which no mixing occurs in the direction of electrolyte flow, and the continuous stirred tank reactor (CSTR), which assumes perfect mixing within the cell. The PFR therefore involves a concentration gradient within the reactor, while, in the CSTR, the inlet concentration steps down to the reactor concentration at inlet manifold. This reactor concentration is maintained as fluid leaves the reactor. The RCE reactor, with its turbulent hydrodynamics, usually approximates to CSTR behaviour [ 1,2 ]. 3.1 The single pass mode
A mass balance over an ideal PFR in the steady state leads to the expression: Cout = f i n exp(--KLA/Q)
(11)
The fractional conversion per pass through the reactor is defined by: x P sP FR
~ 1 --
(Cout/Cin)
(12)
374
F.C. WALSH
",iout,~ Q
f-oui" cg [STR [celt
PFR
(o)
{b)
tin ~ Q
Cin~xQ [out,f Q
t
Vcett PFR or" [STR
TANK
[in,t (c)
r-~,t (1
[in,O --'~[in,t (d] Fig. 3. Modes of operation for a rotating cylinder electrode reactor. (a) Single pass plug flow reactor. (b) Single pass, continuous stirred tank reactor. (c) Batch recycle via a holding tank. (d) The system as a whole approximates to simple batch behaviour. which allows eq. ( 11 ) to be written as:
xPFR 1-exp(-KLA/Q) SP
(13)
F o r an ideal C S T R , the analogous eqs. to ( 11 ) and ( 13 ) are: 1
C°u' = C i " [1 +
(I~A/Q)]
and:
[
~sPVPFR= 1 -- 1 +
' (K~A/Q)
(14)
]
( 15 )
The difference b e t w e e n the fractional conversions p r e d i c t e d by eqs. ( 13 ) a n d ( 15 ) m a y be illustrated b y considering typical data f r o m [ 12 ]. In the case o f an R C E o f d i a m e t e r 0.25 m and a p r o j e c t e d area o f 0.200 m 2, rotating at 750 rev. r a i n - ~, the average KLA value was 5.68 × 10 .4 m 3 s - ~ at a temper-
375
THE PERFORMANCE OF A 500 AMP RCER PART 3
ature of 3 5 ° C. Substituting these values into eqs. ( 13 ) and ( 15 ) produces the curves shown in Fig. 4, which describe the fractional conversion per pass as a function of volumetric flow rate. The PFR case clearly gives a superior fractional conversion to the CSTR under the experimental conditions; the data closely conform to the CSTR predictions. It is interesting to examine the case of larger volumetric flow rates. As the throughput increases (i.e., as the fractional conversion per pass decreases), the PFR and CSTR predictions converge, as shown in Fig. 5. The suitability of a CSTR model is also confirmed in Fig. 6, showing the conversion factor [(Cin/Cout)-l] v e r s u s the reciprocal flow rate, 1/Q. Equation ( 14 ) may be rearranged as: '
Co.t/
=Q (KLA)
(16)
and a plot of the left hand side versus 1/Q should be a straight line of slope = KLA. In Fig. 6, an averaged KLA value of 5.68 X 10 -4 m 3 s-t has been used to predict the idealised behaviour according to eq. ( 16 ). The experimenXSp 1.0
I
I
I
\
0.8
0.6
0.4 normot operoting range
(STR
0~2
0
0
'
20
40
60
80
Q / dm3 min-I
Fig. 4. Predicted fractional conversion of cupric ions per pass as a function of volumetric flow rate of electrolyte. The theoretical data are derived from assumption of PFR behaviour, according to eq. ( 13 ), or C S T R behaviour, according to eq. ( 15 ). In both cases, KLA = 5.68 X 10 - 4 m 3 s-~; T = 3 5 ° C ; o 9 = 7 5 0 min - l .
F.C. WALSH
376
XSp 1.0~
\
0.8
r
i
'
'
'
' ' " 1
i i
.i r r
\ PFR [STR '
0~6
design point O..Z, l
normo[ operQting ronge '<---
0.2 -
0
1
0101 •
0
3 0 /dm 3 min-1
Fig. 5. Predicted fractional conversion per pass as a function of volumetric flow rate. Semilogarithmic plot showing convergence of conversion values at high flow rates. The data are pred i c t e d by the PFR model, according to eq. ( 1 3 ) , or the C S T R one, according to eq. ( 1 5 ) . KLA= 5.68 × 10 - 4 m 3 s-1; T = 35 ° C; 09--750 m i n - 1 . The design basis for the reactor is shown as Xsp = 0.52 at Q = 25 dm 3 m i n - i.
tal data are well described by this theoretical line at high flow rates, but the data lie below the theoretical line at low flow rates and hence at high values of fractional conversion per pass. As noted in [ 12 ], this may be due to a degree of redissolution of the metal via corrosion. However this problem is slight at the operating temperature used in these experiments (35 °C), in contrast to the higher temperature (60 ° C) reported previously [ 12 ]. In practice, the fractional conversion per pass is often relatively small and difficult to measure accurately via the usual analytical techniques such as atomic absorption spectrophotometry. This factor limits the usefulness of the technique. Indeed, the data reported here and in previous studies [ 12,13 ] describe unusually high fractional conversions per pass (typically 0.5-0.9 ). It has been more usual to experience values in the range 0.02-0.3 for laboratory and pilot-scale RCE reactors [ 1,2,4 ]. The most versatile and most generally suitable technique for KLA determination in the present system is the use of batch recirculation, which will now be described.
THE PERFORMANCE OF A 500 AMP RCER PART 3
377
Cin -1 Couf 16 IIPFR
I
,,_
12
I
normczI operQfing r~nge
0
I
L~
I
8
> l
12 16 1 103Q/cm3s-I
Fig. 6. Conversion factor versus reciprocal volumetric flow rate in the single pass mode. The solid lines represent idealised behaviour according to P F R (eq. (13) ) or CSTR (eq. ( 15 ) ) models with KLA= 5.68 × 10 -4 m 3 s-1. The range of actual values is shown as a range for six experiments at each flow rate. Note the increasing divergence of the experimental data from the predicted CSTR line at high values of 1/Q; that is, at low flow rates. T = 35 °C; to= 750 m i n - ~.
3.2 The batch recirculation mode .3.2. I General The recycling o f electrolyte around a loop consisting of the reactor and a well-mixed tank provides a convenient process strategy in which the volume o f process liquor m a y be readily adjusted. The tank also provides a facility for sampling, monitoring temperature control, feedstock preparation and, in some cases, product extraction [ 15 ]. Depending upon the residence time of fluid in the reactor versus that in the tank and the fractional conversion per pass, there are 3 possible models: ( 1 ) a CSTR in batch recycle; (2) a P F R in batch recycle; (3) the system as a whole approximates to a batch reactor. The applicability o f each o f these cases may be examined for a typical data set which was reported, in part, in [ 13 ]. Once again, the reactor involved has a diameter o f 0.25 m and a projected area of 0.200 m 2, the rotation speed
378
F.C. WALSH
being 750 m i n - l in a 0.5 M I"I2804 solution at 35°C. The initial cupric ion level is 480 g m -3.
3.2.2 The CSTR in batch recycle An approximate [24,25] but practical [15,22] conversion expression for this system is: (7'in,t = Cin,o exp
X CSTR
( 17 )
where tT is the mean residence time of electrolyte in the tank: (18)
~T = V T / Q
and the fractional conversion per pass is given by eq. ( 15 ). Equation (16) is valid for the case of a very low ratio of rR to Vx, that is, for rR >> rT which is fulfilled for the present system where Vce,>> VT (0.0187 m 3 >> 0.436 m 3).
3.2. 3 The PFR in batch recycle The analogous expression to equation ( 17 ) is: (ln,t = Cin,o exp
X~'evR
(19)
where X~'ffR is given by eqs. ( 12 ) and ( 13 ).
3.2.4 A simple batch behaviour If the fractional conversion per pass through the reactor is sufficiently low, both eqs. (17) and (19) may be reduced to:
{ KLA\ Cin,t=Cin.oexp~--wt )
(20)
which is an expression for a simple batch process [ 15,24 ] and which does not involve the volumetric throughput.
3.2.5 A comparison of batch models The selection of a particular model depends upon its practical suitability (in terms of the known fluid flow) and its ability to predict KLA to a sufficient degree of accuracy. All three design equations for a batch system (eqs. ( 17 ), (19) and (20)) predict a first-order decay of metal ion concentration from its initial value. However, the apparent first order rate constant, k, defined by: G°,t = Ci,,o e x p ( - k t ) is different in each case:
(21 )
T H E P E R F O R M A N C E O F A 500 A M P R C E R P A R T 3
379
( 1 ) CSTR in batch recycle: k_
VCSTR/..
-- ASp
yCSTR /
/ 'T = ASp
~,Q~ V T )
(22)
(2) PFR in batch recycle: PFR k=Xsp /rT=x~FR(Q/VT)
(23)
( 3 ) simple batch behaviour: (24)
k= KLA
VT A comparison between predictions of the models, for the present data, is shown in Fig. 7 as a plot ofnormalised concentration versus time. The following points are noteworthy: ( 1 ) The three models each predict a linear decay on the semilogarithmic concentration time coordinates. ( 1 ) The rate of decay lies in the order: CSTR in batch recycle > PFR in batch recycle > simple batch, as given by eqs. (22-24). (3) The corresponding values of the apparent rate constants are 5.52 X 10 - - 4 S-l, 7.11X10-4s - l and 1 . 3 0 × 1 0 - 3 s -1. (4) The experimental data lie close to the predicted line for the CSTR in batch recycle model at shorter times (0 min < t< 80 min). At longer times, the metal ion concentration is higher than the predicted values and the rate of decay decreases with time. In other words, the KLA value over early parts of the batch electrolysis ( = 5.68 X 10 - 4 m 3 S-1 ) cannot be maintained at low metal ion concentrations. This behaviour has been observed previously [ 13 ] and may be attributed to a combination of a change in the nature of the rate control (from mass transfer to chemical steps), together with significant redissolution of metal. Under the chosen experimental conditions, therefore, the system is best modelled according to the 'CSTR in batch recycle' design equation. In addition to poor mathematical fits of the data to other models, it should be noted that the PFR model is unsuitable, due to the stirred tank hydrodynamics, resulting in a good CSTR approximation, which has been confirmed by spatial analysis of the catholyte (Table 2 ). The simple batch model is attractive in its simplicity but must be rejected in the present case as the fractional conversion per pass through the reactor is appreciable, as noted previously. The determination of KLA from a normalised metal on concentration versus time data set, via the 'CSTR in batch' model, involves the expression of the apparent first-order rate constant in terms of KLA. Inserting ASpV'CSTRfrom eq. ( 1 5 ) i n t o eq. (22)gives: KLA =
1- ( k V T / Q ) - 1
(25)
F.C. WALSH
380
[-in,t / Lin,O I00~ ,
I
i
I
]
I
I
10-1 X
X X
X X X X R
1 0-2
SBR
X BR -_
"~BR\
\10
-31 0
i
20
40
60
80
I
I
I
I00
120
140
160
18C
t/rain Fig. 7. Normalised inlet concentration of copper as a function of time in the batch recycle mode. The solid lines represent the predicted behaviour according to P F R batch recycle (eq. (19) ), CSTR batch recycle (eq. ( 1 7 ) ) or overall simple batch reactor (eq. ( 2 0 ) ) models, with KtA= 5.68× 10 -4 m 3 s - l . T = 35°C; 09=750 m i n - L
TABLE 2 Chemical analysis from various sampling points in the catholyte compartment of the RCE reactor Sample point
Copper concentration / g m -3
Inlet manifold Bottom of reactor, inlet side Top of reactor, inlet side Bottom of reactor, outlet side Top of reactor, outlet side Outlet manifold
480 _+ 12 267 + 7 262 + 7 259 _+6 250 _+6 255 _+6
Method: volumetric dilution followed by air/acetylene atomic absorption spectroscopy as described in [131.
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381
The observed k value for 0 min < t < 80 min is 5.52 × 10-4 S - - 1 which leads to a KLA determination of 5.68 × 10-4 m 3 s-1 from equation (25 ). Similarly, for the P F R in batch recycle, the coupling ofeqs. (13) and (23), followed by rearrangement, yields:
KLA=- Q I n ( 1 - k ~ Z )
(26)
Equation ( 26 ) allows a KLA value of 3.59 × 10- 4 m 3 s- 1 to be determined from the experimental data shown in Fig. 7. If the system as a whole approximates to a batch reactor, then eqs. (20) and (24) apply. The latter equation may be rearranged to give:
KLA=kVT
(27)
Equation (27) results in a KLA value of 2.41 X 10 - 4 m 3 s- ~from the experimental data set in Fig. 7. 4. OVERALL COMPARISON OF TECHNIQUES FOR THE DETERMINATION OF KtA
Table 3 provides a summary of KLA values which have been calculated using the techniques considered in this paper under the stated experimental conditions. The choice of technique will depend upon convenience as well as the need for sufficient accuracy. At the design stage a specification for the reactor involved use of a mass transport correlation which had been derived from other RCE reactors [ 1,4,22]. Thus eq. (7) predicted a KLA value of 4.62X 1 0 - a m 3 s -1. It was considered prudent, however, to make a conservative estimate which was approximately 10% lower than this value in order to avoid any scale-up problems. Mass transport correlations provide a useful guide to behaviour over a wide range of experimental parameters but cannot be expected to provide an accurate prediction Of KLA under specific process conditions. In principle, direct, limiting current determinations provide an elegant route to KLA but, as discussed in section 2.2, there are experimental difficulties associated with changes in the reactor concentration and surface state of the RCE. These problems are more significant in the case of a high fractional conversion per pass, as in the present case. The choice of cathode potential for IL estimation is also problematic; the potential must correspond to a plateau current caused by full mass transport control (i.e., it must be sufficiently negative), whilst avoiding contributions from hydrogen evolution (at too negative a potential). A suitable compromise is a potential of - 0 . 4 5 0 V vs SCE, where an averaged value of 6.2 X 10 - 4 m 3 S-1 is achieved over a range of reactor concentrations. This value is only slightly higher (11%) than the ones achieved in regular process trials ( 5.7 + 0.4 ) X 10- 4 m 3 s- 1. The use of a
F.C. WALSH
382 TABLE 3
,Comparison of typical KLA values obtained from various techniques Technique
KLA /10 4 m 3 s - I
Limiting current determination as a :function of concentration at - 0 . 5 0 0 V vs SCE at - 0 . 4 5 0 V vs SCE ]Prediction from a mass transport correlation via eq. ( 7 ) Single pass conversion data CSTR via eq. (14) P F R via eq. ( 11 ) Batch recycle conversion data CSTR via eq. (16) P F R via eq. ( 18 ) Simple batch via eq. (19) Design specification Process experience
6.9+0.3 6.2 4.62
5.75 3.58 5.68 3.59 2.41 4.2 5.7 _+0.4
All values refer to copper deposition from an electrolyte containing 0.5 M H2SO 4 at 35 °C. The inlet or initial copper concentration is 480 g m - 3 . The volumetric flow rate is 0.417 m 3 s - l through an RCE reactor of diameter 0.25 m, and the projected area 0.200 m 2 rotating at 750 m i n - L
higher cathode potential ( - 0 . 5 0 0 V vs SCE) results in an overestimation of
KLA. It is much more satisfactory to measure KLA via conversion techniques. In the present case, the very turbulent flow conditions inside the RCE reactor naturally lead to the adoption of a CSTR reactor model. Reasonable agreement between KLA values was achieved in the single pass and batch recycle cases using a CSTR model. Moreover, these values of 5.75 and 5.68× 1 0 - 4 m 3 s - 1 agree well with those experienced during later process trials. The use of single pass conversion data is only possible, however, if there is an accurately measurable difference in metal ion concentration at the inlet and outlet of the reactor; that is, if the fractional conversion per pass is high. Under these conditions, there is a marked difference in the behaviour of the PFR and CSTR models. While PFR behaviour theoretically leads to higher conversions, the axial concentration gradient along the reactor would lead to a variation in the rate of deposition due to the non-uniform current distribution. Indeed, the present reactor incorporated manifolds which were designed to encourage good axial mixing according to the CSTR approximation. Chemical analysis (Table 2 ) has confirmed effective mixing. The (incorrect) adoption of a PFR model to the single pass and batch recycle concentration
THE PERFORMANCEOF A 500 AMP RCERPART 3
383
versus time data leads to a marked underestimation Of KLA, by factors of 38% and 37%, respectively. In the batch recirculation mode of operation, it is clearly important to use the CSTR in batch recycle model to describe the experimental conditions. The application of a simple batch model results in an underestimation Of KLA by 58%. Finally, it should be stressed that the suitability of a reactor model critically depends not only on a knowledge of the flow conditions within the reactor but also upon reactor performance (i.e., the size OfKLA ) and the volumetric flow rate. Hence, at very high values Of KLA/Q, the fractional conversion per pass is very small and the PFR and CSTR models converge [ 19 ]. In the batch recycle case under these conditions, the system as a whole approximates well to :simple batch behaviour [ 14,19,24,25 ]. However, such conditions are not appropriate to the present case where a high value of KLA/Q (,~ 1.36 ) provides a significant fractional conversion per pass (Xsp~ 0.58 ). It is also important to note that discrepancies in the overall fractional conversion between batch recycle models will increase with processing time. The time evolution of errors in determining KLA in such systems will be discussed elsewhere [26 ]. NOMENCLATURE
a, b, c constants in eq. (4) cathode area, m 2 A cupric ion concentration in the cell (reactor), mol m-3 Ccell concentration at reactor inlet, mol m-3 G. concentration at reactor outlet, mol m - 3 Gout inlet concentration at time t, mol m - 3 Cin,t inlet concentration at time zero, mol m-3 Cin,o d rotating cylinder diameter, m D diffusion coefficient of cupric ions, m 2 sF Faraday Constant, (96485 A s mol-~ ) limiting current due to convective diffusion, A IL k apparent rate constant, sKL mass transfer coefficient, m s- 1 active length of rotating cylinder cathode, m Q volumetric flow rate m 3 st batch time, s U peripheral velocity of cathode, m 3 s- l overall space occupied by reactor Vcell effective electrolyte volume within the reactor m 3 VR effective electrolyte volume in the holding tank m 3 VT fractional conversion of reactant in a single pass through the reactor Xsp
384 Z
F.C. WALSH
number o f electrons per copper atom deposited
Dimensionless Groups Re
Sc Sh St
Reynolds N u m b e r ( = Ud/v) Schmidt N u m b e r ( = v/D) Sherwood N u m b e r ( = kLd/D) Stanton N u m b e r ( = kL/U)
Greek //
"rR "rv (/2
relative (mass transport) performance factor defined by eq. ( 1 0 ) kinematic viscosity o f electrolyte, m 2 s - 1 nominal residence time in reactor ( = VR/Q), s nominal residence time in tank ( = VT/Q), s rotation speed o f cathode, rev s -
Abbreviations CSTR continuous stirred tank reactor plug flow reactor PFR
REFERENCES 1 Walsh, F.C., The role of the rotating cylinder electrode reactor in metal ion removal. In: G.D. Genders and N.L. Weinberg (Editors), Electrochemical Technology for a Cleaner Environment. Electrosynthesis, Layton, USA ( 1992 ), pp. 101-159. 2 Walsh, F.C. and Gabe, D.R., Trans. Inst. Chem. Eng., 68B ( 1990): 107-114. 3 MVH b.v., The MVH Cell. MVH b.v., Uden, The Netherlands. 4 Holland, F.S., Chem. Ind., July (1978): 453-458. 5 Holland, F.S., British Pat. 1444367 (1978). 6 Holland, F.S., British Pat. 1505736 (1978). 7 Anon, Turbocel. Sessler Galvanotechnik GmbH, Keltern, Germany, and Werner Fluhman AG, Dubendorf, Switzerland, 8 Puippe, J.C., Turbocell--a metals recycling device. Meet. Surface Technology in the Europe of the 90's. Europ. Acad. Surface Technol., Schwabisch Gmund (1990). 9 Mayr, M., Blatt, W., Busse, B. and Heinke, H., 4th Int. Forum on Electrolysis in the Chemical Industry (Fort Lauderdale, Fla., Nov. 11-15) (1990). 10 Gabe, D.R. and Walsh, F.C., J. Appl. Electrochem., 13 (1983): 3-22. 11 Gardner, N.A. and Walsh, F.C., Design and applications of rotating cylinder electrode technology to continuous production of metal. In: R.E. White (Editor), Electrochemical Cell Design. Plenum, New York (1984), pp. 225-258. 12 Robinson, D. and Walsh, F.C., The performance of a 500 Amp rotating cylinder electrode reactor. Part 1: Current potential data and single pass studies. Hydrometallurgy, 26 ( 1991 ): 93-114. 13 Robinson D. and Walsh F.C., The performance of a 500 Amp rotating cylinder electrode reactor. Part 2: Batch recirculation studies and overall mass transport. Hydrometallurgy, 26 (1991): 115-133.
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14 Walsh, F.C., A First Course in Electrochemical Engineering. The Electrochemical Consultancy, Romsey (1993) (in press). 15 Pletcher, D. and Walsh, F.C., Industrial Electrochemistry. Chapman and Hall, London, 2nd ed. (1990). 16 Walsh, F.C., Bull. Electrochem., 6 ( 1990): 283-293. 17 Scannell, R.A. and Walsh, F.C., Inst. Chem. Eng. Symp. Ser., 112 ( 1989): 59-69. 18 Langlois, S. and Coeuret, F., J. Appl. Electrochem., 20 ( 1990): 749-755. 19 Ford, W.P.J., Walsh, F.C. and Whyte, I., Inst. Chem. Eng. Symp. Ser., 127 ( 1992): 111126. 20 Gabe, D.R. and Walsh, F.C., J. Appl. Electrochem., 14 (1984): 555-564. 21 Gabe, D.R. and Walsh, F.C., J. Appl. Electrochem., 14 ( 1984): 565-572. 22 Gabe, D.R. and Walsh, F.C., J. Appl. Electrochem., 15 ( 1985): 807-824. 23 Eisenberg, M, Tobias, C.W. and Wilke, C.R., J. Electrochem. Soc., 101 ( 1954): 306-319. 24 Pickett, D.J., Electrochemical Reactor Design. Elsevier, Amsterdam, 2nd Ed. (1979). 25 Walker, A.T.S. and Wragg, A.A., Electrochim. Acta, 22 ( 1977): 1129-1134. 26 Walsh, F.C. and Reade, G.W., Trans. Inst. Chem. Eng. (in prep.).