- Email: [email protected]
Hydrodynamic behaviour of the FM01-LC reactor
Elecrrochimtco
Pergamon
Acra. Vol. 41. No. 4. pp. 493-502. 19% Copyright G 1995 El&&r Science Ltd. Britain. All nghts reserved 0013-4686/96Sl5.00+ 0.00
Printed in Great
HYDRODYNAMIC
BEHAVIOUR
OF THE FMOl-LC
REACTOR and F. C. WALSH?
P. TRINIDAD*
School of Chemistry, Physics and Radiography, Division of Chemistry, University of Portsmouth, St Michael’s Building, White Swan Road, Portsmouth PO1 2DT, England (Received 24 January 1995)
Abstract-Various working electrode configurations have been studied in order to characterise hydrodynamic behaviour in the FMOl-LC reactor. A simple experimental arrangement has been used to generate data from electrolytic conductivity measurements in a series of impulse-response experiments. First and second moments of the tracer curves were calculated and the degree of dispersion was established as a function of the moments of the curves. The dispersion coefficient was found to increase with flow velocity and to be higher in the presence of turbulence promoters and three-dimensional electrodes. The Peclet numbers indicate that as the bulk velocity of the marker material increased, the degree of dispersion rose by a similar degree. Key words: impulse-response
technique,
flow dispersion,
NOTATION C
Tracer
D E L
;t)e t u V
X
(potassium
chloride)
concentration
(mol dm-j) Dispersion coefficient (cm’ s - ‘) E curve (s- ‘) Effective length of the reactor (cm) Fluid velocity exponent defined in equation Peclet number (= VL/D) (Dimensionless) Time (s) Linear superficial fluid velocity (cm s- ‘) Linear interstitial fluid velocity (cm s- ‘) Axial position (cm)
(8)
Greek a
MI M,
u2 T 1
dispersion
coefficients,
filterpress
electrochemi-
_
cal reactor, three-dimendional porous-electrodes.
Reactor porosity ( = free volume/total volume) (Dimensionless) First moment (s) Second moment (s’) Variance of tracer curve (s2) Mean residence time of fluid in reactor ( = W) (s) Constant defined in equation (8)
1. INTRODUCTION In the case of flow characteristics within an electrochemical reactor, two types of limiting hydrodynamic behaviour may be considered within the
* On leave from The Chemical Engineering Department, University of Salamanca, Spain; present address: Chemical Process Group, EA Technology, Capenhurst, Cheshire CHl6ES. t Author to whom correspondence should be addressed.
reactor, namely, plug flow and perfect mixing. In practice, reactors always show deviation from these simple models, which can lead to errors in design when non-ideal flow is not considered. Fluid flow conditions are also important to other aspects of electrochemical engineering such as mass transport, current distribution, gas removal from the electrodes and selectivity in organic electrosynthesis[ 11. The (64cm’ projected electrode area) FMOl-LC cell has been developed (by ICI plc) as a scaleddown version of the FM21-SP (21 dm2) reactor. The FMOl-LC reactor may be modelled as a plug flow reactor but the fluid flow does not reach a fully developed state before leaving the cell due to inlet and outlet effects. Previous studies on this reactor have considered the space-averaged mass transport to 2-dimensional electrodes[2] and 3-dimensional electrodes[3], together with the distribution of mass transport over a flat plate electrode[4]. The comparison of space averaged mass transport to 2dimensional electrodes on scale up has also been discussed[S, 61 and the use of the reactor in electrosynthesis has been briefly outlined[6, 73. Despite the literature on mass transport and electrosynthesis in the FMOl-LC electrolyser, there have been no reported studies of fluid flow within the reactor. Several methods have been employed in order to characterise fluid flow and mass transport in electrochemical reactors. Global mass transport coefficients can be calculated from the steady state limiting current when the system is under mass transport control due to convective-diffusion of the reactant towards the electrode surface[l]. Fluid flow characteristics are usually studied from stimulus-response techniques where a solution with a marker is allowed to pass through the cell and the concentration of marker is monitored at the outlet as a function of
494
P.
TRINIDAD
and F. C.
time. A pulse of an electroactive species, such as Cu*+, can be used as a marker pulse input and the detection of the response can be monitored via a pair of electrodes held at a potential corresponding to the diffusion limiting current[& 93. However, several problems arise since the electrodes are sensitive to potential gradients as well as local changes in concentration. A much easier method involves the injection of a marker pulse of KC1 at the inlet accompanied by detection of the solution conductance at the outlet[lO]. Dispersion in the reactor will produce a roughly skew-Gaussian response from which dispersion data can be extracted following the assumption of a standard flow model. In this paper, a Levenspiel-type approach[ll-131 is used which adopts a moment analysis to provide a simple treatment of the data.
2. EXPERIMENTAL
DETAILS
The flow circuit, which is shown in Fig. 1, was operated at 295 + 1 K. All interconnecting tubing was made of silicone rubber having an internal diameter of approximately 7mm. The electrolyte (typically 0.0001 M KC1 in distilled water) was pumped (Totton EMP 40/4 magnetically coupled pump) from a glass reservoir of capacity 2 dm3, measured by a rotameter (KDG X14) and controlled by a valve. At the reactor inlet, 1 ml of an aqueous, saturated solution of KC1 was carefully and rapidly injected into a polypropylene “T” piece containing a neoprene septum cap. A conductivity cell consisting of platinised platinum foil electrodes and having an approximate cell constant of 1 cm-‘, was used. This was connected into a “T” piece at the reactor outlet and a chart-recorder registered the outlet conductivity (as an analogue of concentration) vs. time. The
WALSH
conductance of the initial electrolyte was monitored with time until a steady base line reading was achieved (typically 2min). The injection of KC1 at the inlet was then made. Studies were confined to conditions where the conductance of aqueous KC1 at the reactor outlet was directly proportional to its concentration. Each flow injection experiment was performed several times and the data are presented as mean values for 3 repeat trials; values deviating more than f 15% from the mean were discarded. The FMOl-LC laboratory reactor (Fig. 2a) was used in the undivided configuration (Fig. 2b). The reactor is fully described elsewhere[2-71 and permits the use of a combination of spacers and gaskets compressed (by a torque wrench to a value of 25Nm) between two end plates. Electrolyte was distributed in the reactor flow channel by internal manifolds incorporated within the cell spacers (Fig. 2~). Several working electrode configurations were used in this study (Table 1). In all cases, the electrolyte compartment in the reactor involved a projected electrode area of 4 x 16cm and the counter electrode was always a flat nickel plate. The first working electrode configuration used a flat plate electrode (Fig. 3c) plus an extruded plastic (polyolefin) mesh promoter (Fig. 3a) having an approximate nominal open area of 60% and an overall thickness of 4.5 mm with both a short and long diagonal of approximately 11 mm. The second configuration employed a flat nickel plate electrode plus a metal minimesh having a mesh size of 1 x 1 mm squares (Fig. 3b). The third configuration used a flat plate electrode (Fig. 3c) in an empty channel. The fourth configuration involved a slotted nickel plate electrode (Fig. 3d). The final configuration, which used a flat nickel plate electrode plus a nickel expanded mesh three-dimensional electrode (Fig. 3e), is fully described elsewhere, being referred to as “EXP !I” in Ref. [4]. The metal meshes
saturated KC1 injection
g FMOl-LC REACTOR
to waste
0 Fig. 1. Hydraulic flow circuit for tracer experiments. (a) Fluid reservoir; (b) Circulation pump; (c) Rotameter; (d) FMOl-LC electrochemical reactor; (e) Electrolytic conductance probe; (f) Digital/analogue conductivity meter; (g) Chart-recorder.
Hydrodynamic
behaviour
of the FMOl-LC
reactor
(a)
1%’
G
E
G
Electrode
(c) Fig. 2. The FMOl-LC reactor. (a) Exploded view, showing the electrodes sandwiched between the spacers (S) and gaskets (G). (b) Cross sectional view, showing the reactor configuration used to achieve a nominal reactor volume of 44.7cm3, using a single spacer; BP, insulated steel backplate; E, nickel electrode; G, polymer gaskets; S, insulating spacers (glass-tilled polymer. (c) A spacer frame, showing the position of the internal manifolds.
496
P. TRINIDADand F. C. WALSH Table 1. Characteristics of the nickel electrodes
Electrode type
Figure
Number used
Minimesh Flat plate Slotted plate? Expanded mesh*
3b 3c 3d 3e
4 1 1 2
CD /mm
LD /mm
Strand width /mm
Strand thickness /mm
Porosity
1.0 N/A N/A 3.5
1.0 N/A N/A 10.5
1.0 N/A N/A 1.33
1.25 N/A N/A 0.7
0.62 N/A N/A 0.70
N/A not applicable. CD internal short diagonal of mesh. LD internal long diagonal of mesh. * Made from expanded nickel mesh type 197V (Expanded Metal Company). t 2 mm rectangular fingers at 2 mm spacing with an electrode thickness of 2 mm. were spot-welded to the plate to ensure good electrical conductivity. Nominal reactor volumes of 44.7, 70.0, 95.3 and 120.0cm’ in the electrolyte compartment were achieved by using 1, 2, 3 or 4 spacers respectively (see Fig. 2a and 2b), corresponding to interelectrode gaps of 2.5 mm, 4.Omm, 5.5 mm and 7.0 mm after compression of the reactor assembly.
3. THEORY
M,=-
It is necessary to assume a flow model for the interpretation of the tracer curves. Two models may be considered in the absence of any (electro)chemical reaction. 3.1. Dispersion model (moment method) The dispersion model assumes that concentration fluctuations, when rapid and numerous may be considered to be random and this behaviour can be described by a diffusion-type equation similar to Fick’s law, where D (the dispersion coefficient) includes the random mixing of fluid and the molecular diffusion. The general dispersion model considers that the dispersion coefficient and the fluid velocity are both functions of the position. The dispersion coefficient, D is, therefore, non-isotropic[ 111 and may be represented by a second-order tensor. The mathematical model is greatly simplified if it is considered that the only observable dispersion takes place in the direction of fluid-flow. The formulation of this dispersion model leads to the equation. LX D azc ac -=--_at UL ax2 ax
(1)
This differential equation can be resolved by the use of Laplace transforms but Levenspiel and Smith have found a relationship between the first and second moment of the tracer curves and the Peclet number[12, 133. The relationship is a function of the degree of dispersion and the boundary conditions:
l; tE dt
M1= 1; M2=
and axial dispersion characteristics for beds of adsorbent particles by using the moment analysis[14]. The general case it is greatly simplified when adsorption and intra-particular diffusion are neglected[15] and a dispersion coefficient in the axial direction to flow may be calculated from the expression. 2LDu= u3
where a, the reactor porosity, is evaluated from the expression :
4. RESULTS
AND DISCUSSION
The first and second moments from the E curves obtained (section 3.1) were calculated using equations (2) and (3), the integrals being evaluated numerically. Firstly, the influence of reactor volume on dispersion was studied using the axial dispersion model. The first and second moment were calculated and the following equation was applied to calculate the dispersion coeflicient[ 161. -
D
VL
= 0.5 ;
(6)
where r is the mean residence time in the reactor and a2 is the variance. In all cases studied, the value of D/UL was greater than 0.025, indicating a large value of dispersion; hence equation (6) could not be successfully applied. When the dispersion value is high, the boundary conditions play an important role and must be taken into account. The experimental conditions agree with the “closed-open vessel” model[16], in which the relationship between the moments of the curves and the dispersion coefficient is[ll]: 2
E dt
j; t=E dt SomEdt -M:
3.2. Schneider-Smith model Schneider and Smith have developed a method for determining equilibrium constants, rate constants
Figure 4 compares an experimental curve with the theoretical curve assuming a low degree of dispersion and it is seen that the agreement between the experimental curve and the theoretical one is relatively poor. A comparison with the “closed-open vessel” model for the case of high dispersion is not
Hydrodynamic
behaviour
of the FMOl-LC
reactor
497
0a
0e
Fig. 3. Photographs of the plastic mesh turbulence promoter used in the FMOl-LC reactor. (a) Plastic mesh; (b) Nickel electrode; (d) Slotted plate nickel electrode; (e) Expanded
possible since an analytical expression for the curve is not available[13]. Figure 5 shows dispersion vs. flow rate curves for several reactor volumes. An increase in the degree of dispersion with flow rate is evident and larger dispersion values are found for
(a) and nickel electrode structures (b)-(e) minimesh electrode; (c) Flat plate nickel nickel mesh on a flat plate electrode.
small reactor volumes, due to the more important inlet and outlet effects in small reactors. The Schneider-Smith model was also applied to the case when the reactor contained turbulence promoters and three-dimensional electrodes. The first
P.
498
TRINIDADand
F. C.
WALSH
50
40
2 c
30
P ; a 3 Lrl 2o
0
E
6
4
2
8
10
12
14
GXJ) is Fig. 6. Plot for the calculation of reactor void fraction using equation (5). (+) Minimesh electrode (as in Fig. 3b); (0) Expanded mesh electrode (as in Fig. 3e); (m) Flat plate plus plastic net (as in Fig. 3a). Reactor volume 95.3 cm3.
5 10
non linear, expression[ 1,3, IS] : R
0 0
D=AV” I
0.5
(8)
,
1
1.5
2
2.5
3
3.5
Dimensionless Time
Fig. 4. Comparison between an experimental E curve (0) and the predicted behaviour for a low degree of dispersion Ly;ctIat plate electrode (Fg. 3c) in an empty channel. volume = 44.7cm . Linear fluid velocity = 9.95cm-1.
where V = u/a, the interstitial equations (8) and (4) gives:
which may be expanded : M2V
step was the evaluation of the reactor free volume (reactor porosity) using equation (5) (see Fig. 6 and Table 2). The second moment was plotted vs. l/U’ (equation (4)), allowing D to be calculated from the slopes of the line. Curves were obtained instead of straight lines (Fig. 7), due to a functional dependence of D on flow velocity, according to the following,
"0
5
10
15
velocity. Combining
log
-
2L
= log a + (n - 2) log v
(10)
The function log M2 V/2L was plotted vs. log V, allowing the 1 and n coefficients to be calculated (Fig. 8). Figures 9 and 10 shows dispersion vs. superficial velocity and it is seen that larger values of dispersion coefficient are experienced in the smaller volume reactors. In addition, the three-dimensional
20
25
30
35
40
Flow rate /cm&s’
Fig. 5. Dispersion coefficient vs. volumetric flow rate of electrolyte for a flat plate electrode in the absence of a turbulence promoter. Reactor volumes of: (m) 44.7cm”; (0) 70cm3; (0) 95.3cm3; (0) 120cm3.
Hydrodynamic behaviour of the FMOl-LC reactor
499
Table 2. Data from tracer experiments for various turbulence promoters, reactor volumes and electrode types according to correlations of the form D = AV”according to equation (8) Reactor volume /cm 3
Turbulence promoter tyve
Electrode type
44.1
Metal minimesh Plastic mesh Metal minimesh Plastic mesh None None
Flat plate Flat plate Flat plate Flat plate Expanded metal mesh Slotted plate
44.7 95.3 95.3 95.3 95.3
I
,900
Constant A 1.129 0.756 1.18 0.864 1.029 0.907
Fluid velocity exponent n
Reactor porosity *:
1.352 1.019 1.02 1.043 1.152
0.53 0.50 0.78 0.89 0.62
1
I
I
0.10
0.20
0.30
(l/U?
0.40
0 50
/s3cni3
Fig. 7. Second moment vs. l/U3 curves for various reactor configurations. (B) Flat plate (Fig. 3c) in an empty channel; (+) Flat plate plus plastic net (Fig. 3a); (0) Flat plate plus mmimesh electrode (Fig. 3b); (0) Flat plate plus slotted plate electrode (Fig. 3d). Volume of reactor = 95.3 cm3.
Fig. 8. Plot used for the calculation of 1 and n parameters according to equation (10). ( x ) Flat plate plus mesh electrode (volume of reactor = 44.7cm”; (W) Flat plate plus plastic net (volume of reactor = 44.7cma); (+) Flat plate plus mesh electrode (volume of reactor = 953cm’); (0) Flat plate plus plastic net (volume of reactor = 95.3 cm’).
500
P. TRINIDADand F. C. WALSH
0” 2
I
I
4
6 8 10 12 Linear velocity /cm s1 Fig. 9. Dispersion coetlkient vs. mean linear electrolyte velocity, showing the effect of turbulence promoters at a flat plate electrode. (m) Flat plate in empty channel; (0) Flat plate plus plastic net (Fig. 3a); (+) Flat plate plus minimesh electrode (Fig. 3b). Volume of reactor = 44.7cm3.
electrode and the metal minimesh turbulence promoter show higher values of dispersion coefficient, the plastic mesh promoter showing small values of dispersion. Table 2 shows 1 and n values calculated from a least squares fit, according to equation (8). Figure 11 shows a comparison between the axial dispersion model and the Schneider-Smith model, agreement being closer at low values of velocity. Finally, the Peclet number, defined as: pe
=$
(11)
was plotted against flow velocity (Fig. 12). The small slope of the lines for the turbulence promoters in this plot indicates that as the bulk velocity increases, the
degree of dispersion rises by approximately the same degree. As the Peclet number increases the hydrodynamic behaviour shows closer agreement with the plug flow model. For the case of the empty channel (in the presence of a flat plate or a slotted plate electrode) the relationship between the Peclet number and the mean linear flow velocity is simple; the Pe values decrease at higher velocity until a critical value of Pe is reached. At higher flow velocities, the electrolyte velocity is fast enough to carry the reactant with a lower degree of dispersion[21]. The plastic turbulence promoter gives rise to a more uniform current distribution as well as an enhanced rate of mass transport[17] and the present work shows that Peclet number for this configuration is sufficiently high to justify the choice of reactor model as a plug flow reactor with a degree of dispersion.
_I
4 3 5 6 Linear velocity /cm s.1 Fig. 10. Dispersion coetlicient vs. mean linear electrolyte velocity. (+) Flat plate in empty channel; ( x ) Flat plate plus plastic net (Fig. 3a); (0) Flat plate plus minimesh electrode (Fig. 3b); (0) Slotted plate electrode (Fig. 3d); (m) Flat plate plus expanded mesh electrode (Fig. 3e). Reactor volume = 95.3 cm3. 1
2
501
Hydrodynamic behaviour of the FMOi-LC reactcr
19 17 -
:I
1
1::
11 9 7 -
J
2
1.5
1
2.5
3
3.5
Linear velocity
4
4.5
5
5.5
/cm s-’
Fig. 11. Comparison between flow models via a plot of Peclet number against linear electrolyte flow velocity. Flat plate plus minimesh electrode (Fig. 3b). (0) Axial dispersion model considering high dispersion (“closed-open vessel”); (m) Shneider-Smith model. Reactor volume = 95.3 cm3.
Metal produced
minimesh a larger
and
expanded
mesh
5. CONCLUSIONS
electrodes
degree of dispersion than the plastic promoter (as evidenced by the smaller Peclet number for the former). The promoters result in a reduction of the Nernst diffusion layer thickness (6,) and an enhanced mass transport coefficient. However, dispersion produces a deviation from the plug flow model and a lower performance, since it is well known that, under mass transport control and, for constant inlet conditions, surface area and mass transport conditions, plug flow reactors achieve better results than the perfectly mixed reactor case[W201.
A simple and rapid marker-pulse method has been used to characterise hydrodynamic behaviour in an electrochemical, laboratory filterpress reactor using regression of the data in the time domain. The axial dispersion and Schneider-Smith models were considered to measure deviation from the ideal plug flow model. Many problems arise from the application of these models, particularly the appearance of tailing in the tracer curves leading to error. Nevertheless, qualitative conclusions can be drawn in order to provide a better understanding of the flow
20 ,
10
’ 1
I
I
2
I
I
3
4
5
6
Linear velocity /cm s-1 Fig. 12. Peclet number vs. mean electrolyte velocity for various reactor configurations. (+) Flat plate (Fig. 3c) in empty channel; (m) Flat plate plus minimesh electrode (Fig. 3b); ( x) plate plus plastic net (Fig. 3a); (0) Flat plate plus expanded mesh electrode (Fig. 3e); (0) Slotted plate electrode (Fig. 3d). Reactor volume = 95.3 cm3.
502
P. TRINIDADan d F. C. WALSH
modifications generated within several reactor configurations. It has been found that a higher value of the dispersion coefficient is experienced in lower volume reactors. In all cases, the degree of dispersion increased and flow velocity and in the presence of turbulence promoters. The plastic mesh promoters help to provide a higher mass transport and more uniform current distribution in the reactor, together with reduced entrance effects near the inlet manifoldC4, 171. The Peclet number showed little change with the electrolyte flow velocity or in the presence of turbulence promoters. This was attributable to an increase in the interstitial flow velocity that mitigates against the increase of dispersion, this effect being particularly marked in the case of the plastic mesh turbulence promoter. The applicability of several dispersion models for filterpress reactors is currently being examined, including more refined methods of data analysis such as an non-linear least squares fit and Laplace transformations[22], assuming the flow to consist of (a) the sum of two dispersive axial plug flows and (b) fast and stagnant phases[23]. Acknowledgements-These studies have been carried out via an ERASMUS scheme which facilitated a visit by P. T. to the University of Portsmouth from the University of Salamanca. The authors are grateful to Professors M. Galan (Salamanca) and T. A. Crabb (Portsmouth) for enabling this research. REFERENCES 1. F. Walsh, A First Course in Electrochemical Engineering, The Electrochemical Consuhancy, Romsey, (1993). 2. C. J. Brown, D. Pletcher, F. C. Walsh, J. K. Hammond and D. Robinson, J. appl. Electrochem. 23, 38 (1993). 3. C. J. Brown, D. Pletcher, F. C. Walsh, J. K. Hammond and D. Robinson, J. appl. Electrochem. 24,95 (1994). 4. C. J. Brown, D. Pletcher, F. C. Walsh, J. K. Hammond and D. Robinson, J. appl. Electrochem. 22, 613 (1992).
5. C. J. Brown, J. K. Hammond, D. Pletcher, D. Robinson and F. C. Walsh, Dechema Monograph, 123,299 (Edited by G. Kreysa), VCH, Weinheim, (1992). 6. J. K. Hammond, D. Robinson and F. C. Walsh, Dechema Monograph, 123, 279 (Edited by G. Kreysa), VCH, Weinheim, (1992). 7. D. Robinson, in Electrosynthesis --from Laboratory to Pilot to Production, (Edited by J. D. Genders and D. Pletcher) The Electrosynthesis Co, Buffalo, New York, (1990). 8. R. E. W. Jannson and R. J. Marshall, Electrochim. Acta 7, 823 (1982). 9. R. J. Marshall,
Ph.D Thesis, University of Southampton, (1982). 10. J. Harrel and J. Perona, Ind. Eng. Chem. Process Des. & Deo. 77,464 (1968).
11. K. Bischoff and 0. Levenspiel, Chem. Engl. Sci. 17, 245 (1962). 12. 0. Levenspiel and W. Smith, Chem. Eng. Sci. 6, 227
(1957). 13. 0. Levenspiel, The Chemical Reactor Omnibook, OSU, Corvallis, (1979). 14. P. Schneider and J. Smith, A. J. Ch. E. Journal 14, 762 (1968). 15. D. Cantero, R. Gil de Rebolefio and M. Gal&r, Anales de Quimica, 83,641 (1987).
16. 0. Levenspiel, “Chemical Reaction Engineering”, 2nd Ed, John Wiley, New York, (1972). 17. F. C. Walsh and G. W. Reade, The Analyst 119, 797 (1994). 18. F. C. Walsh, Electrochim. Acta 38, 465 (1993). 19. F. Coeuret, Introduccibn a la Ingenieria Electroquimica,
Ed Revert& Barcelona, (1992). 20. P. Trinidad and F. C. Walsh, paper submitted to Int. J. Engng. Ed. 21. P. Trinidad, Comportamiento Hidrodiruimico y Optimization de las Variables de Operation en Reactores Electroquimicos, Grado de Salamanca, University
of Salamanca, Spain, (1994). 22. M. Fleischmann and R. E. W. Jansson, Chem. Ing. Tech. 49, 283 (1977). 23. P. Trinidad, D. Gilroy and F. C. Walsh, paper presented at Electrochem 95, University of Wales, Bangor, lo-14 September, 1995; Trans. I. Chem. E., in preparation.
Pergamon
Acra. Vol. 41. No. 4. pp. 493-502. 19% Copyright G 1995 El&&r Science Ltd. Britain. All nghts reserved 0013-4686/96Sl5.00+ 0.00
Printed in Great
HYDRODYNAMIC
BEHAVIOUR
OF THE FMOl-LC
REACTOR and F. C. WALSH?
P. TRINIDAD*
School of Chemistry, Physics and Radiography, Division of Chemistry, University of Portsmouth, St Michael’s Building, White Swan Road, Portsmouth PO1 2DT, England (Received 24 January 1995)
Abstract-Various working electrode configurations have been studied in order to characterise hydrodynamic behaviour in the FMOl-LC reactor. A simple experimental arrangement has been used to generate data from electrolytic conductivity measurements in a series of impulse-response experiments. First and second moments of the tracer curves were calculated and the degree of dispersion was established as a function of the moments of the curves. The dispersion coefficient was found to increase with flow velocity and to be higher in the presence of turbulence promoters and three-dimensional electrodes. The Peclet numbers indicate that as the bulk velocity of the marker material increased, the degree of dispersion rose by a similar degree. Key words: impulse-response
technique,
flow dispersion,
NOTATION C
Tracer
D E L
;t)e t u V
X
(potassium
chloride)
concentration
(mol dm-j) Dispersion coefficient (cm’ s - ‘) E curve (s- ‘) Effective length of the reactor (cm) Fluid velocity exponent defined in equation Peclet number (= VL/D) (Dimensionless) Time (s) Linear superficial fluid velocity (cm s- ‘) Linear interstitial fluid velocity (cm s- ‘) Axial position (cm)
(8)
Greek a
MI M,
u2 T 1
dispersion
coefficients,
filterpress
electrochemi-
_
cal reactor, three-dimendional porous-electrodes.
Reactor porosity ( = free volume/total volume) (Dimensionless) First moment (s) Second moment (s’) Variance of tracer curve (s2) Mean residence time of fluid in reactor ( = W) (s) Constant defined in equation (8)
1. INTRODUCTION In the case of flow characteristics within an electrochemical reactor, two types of limiting hydrodynamic behaviour may be considered within the
* On leave from The Chemical Engineering Department, University of Salamanca, Spain; present address: Chemical Process Group, EA Technology, Capenhurst, Cheshire CHl6ES. t Author to whom correspondence should be addressed.
reactor, namely, plug flow and perfect mixing. In practice, reactors always show deviation from these simple models, which can lead to errors in design when non-ideal flow is not considered. Fluid flow conditions are also important to other aspects of electrochemical engineering such as mass transport, current distribution, gas removal from the electrodes and selectivity in organic electrosynthesis[ 11. The (64cm’ projected electrode area) FMOl-LC cell has been developed (by ICI plc) as a scaleddown version of the FM21-SP (21 dm2) reactor. The FMOl-LC reactor may be modelled as a plug flow reactor but the fluid flow does not reach a fully developed state before leaving the cell due to inlet and outlet effects. Previous studies on this reactor have considered the space-averaged mass transport to 2-dimensional electrodes[2] and 3-dimensional electrodes[3], together with the distribution of mass transport over a flat plate electrode[4]. The comparison of space averaged mass transport to 2dimensional electrodes on scale up has also been discussed[S, 61 and the use of the reactor in electrosynthesis has been briefly outlined[6, 73. Despite the literature on mass transport and electrosynthesis in the FMOl-LC electrolyser, there have been no reported studies of fluid flow within the reactor. Several methods have been employed in order to characterise fluid flow and mass transport in electrochemical reactors. Global mass transport coefficients can be calculated from the steady state limiting current when the system is under mass transport control due to convective-diffusion of the reactant towards the electrode surface[l]. Fluid flow characteristics are usually studied from stimulus-response techniques where a solution with a marker is allowed to pass through the cell and the concentration of marker is monitored at the outlet as a function of
494
P.
TRINIDAD
and F. C.
time. A pulse of an electroactive species, such as Cu*+, can be used as a marker pulse input and the detection of the response can be monitored via a pair of electrodes held at a potential corresponding to the diffusion limiting current[& 93. However, several problems arise since the electrodes are sensitive to potential gradients as well as local changes in concentration. A much easier method involves the injection of a marker pulse of KC1 at the inlet accompanied by detection of the solution conductance at the outlet[lO]. Dispersion in the reactor will produce a roughly skew-Gaussian response from which dispersion data can be extracted following the assumption of a standard flow model. In this paper, a Levenspiel-type approach[ll-131 is used which adopts a moment analysis to provide a simple treatment of the data.
2. EXPERIMENTAL
DETAILS
The flow circuit, which is shown in Fig. 1, was operated at 295 + 1 K. All interconnecting tubing was made of silicone rubber having an internal diameter of approximately 7mm. The electrolyte (typically 0.0001 M KC1 in distilled water) was pumped (Totton EMP 40/4 magnetically coupled pump) from a glass reservoir of capacity 2 dm3, measured by a rotameter (KDG X14) and controlled by a valve. At the reactor inlet, 1 ml of an aqueous, saturated solution of KC1 was carefully and rapidly injected into a polypropylene “T” piece containing a neoprene septum cap. A conductivity cell consisting of platinised platinum foil electrodes and having an approximate cell constant of 1 cm-‘, was used. This was connected into a “T” piece at the reactor outlet and a chart-recorder registered the outlet conductivity (as an analogue of concentration) vs. time. The
WALSH
conductance of the initial electrolyte was monitored with time until a steady base line reading was achieved (typically 2min). The injection of KC1 at the inlet was then made. Studies were confined to conditions where the conductance of aqueous KC1 at the reactor outlet was directly proportional to its concentration. Each flow injection experiment was performed several times and the data are presented as mean values for 3 repeat trials; values deviating more than f 15% from the mean were discarded. The FMOl-LC laboratory reactor (Fig. 2a) was used in the undivided configuration (Fig. 2b). The reactor is fully described elsewhere[2-71 and permits the use of a combination of spacers and gaskets compressed (by a torque wrench to a value of 25Nm) between two end plates. Electrolyte was distributed in the reactor flow channel by internal manifolds incorporated within the cell spacers (Fig. 2~). Several working electrode configurations were used in this study (Table 1). In all cases, the electrolyte compartment in the reactor involved a projected electrode area of 4 x 16cm and the counter electrode was always a flat nickel plate. The first working electrode configuration used a flat plate electrode (Fig. 3c) plus an extruded plastic (polyolefin) mesh promoter (Fig. 3a) having an approximate nominal open area of 60% and an overall thickness of 4.5 mm with both a short and long diagonal of approximately 11 mm. The second configuration employed a flat nickel plate electrode plus a metal minimesh having a mesh size of 1 x 1 mm squares (Fig. 3b). The third configuration used a flat plate electrode (Fig. 3c) in an empty channel. The fourth configuration involved a slotted nickel plate electrode (Fig. 3d). The final configuration, which used a flat nickel plate electrode plus a nickel expanded mesh three-dimensional electrode (Fig. 3e), is fully described elsewhere, being referred to as “EXP !I” in Ref. [4]. The metal meshes
saturated KC1 injection
g FMOl-LC REACTOR
to waste
0 Fig. 1. Hydraulic flow circuit for tracer experiments. (a) Fluid reservoir; (b) Circulation pump; (c) Rotameter; (d) FMOl-LC electrochemical reactor; (e) Electrolytic conductance probe; (f) Digital/analogue conductivity meter; (g) Chart-recorder.
Hydrodynamic
behaviour
of the FMOl-LC
reactor
(a)
1%’
G
E
G
Electrode
(c) Fig. 2. The FMOl-LC reactor. (a) Exploded view, showing the electrodes sandwiched between the spacers (S) and gaskets (G). (b) Cross sectional view, showing the reactor configuration used to achieve a nominal reactor volume of 44.7cm3, using a single spacer; BP, insulated steel backplate; E, nickel electrode; G, polymer gaskets; S, insulating spacers (glass-tilled polymer. (c) A spacer frame, showing the position of the internal manifolds.
496
P. TRINIDADand F. C. WALSH Table 1. Characteristics of the nickel electrodes
Electrode type
Figure
Number used
Minimesh Flat plate Slotted plate? Expanded mesh*
3b 3c 3d 3e
4 1 1 2
CD /mm
LD /mm
Strand width /mm
Strand thickness /mm
Porosity
1.0 N/A N/A 3.5
1.0 N/A N/A 10.5
1.0 N/A N/A 1.33
1.25 N/A N/A 0.7
0.62 N/A N/A 0.70
N/A not applicable. CD internal short diagonal of mesh. LD internal long diagonal of mesh. * Made from expanded nickel mesh type 197V (Expanded Metal Company). t 2 mm rectangular fingers at 2 mm spacing with an electrode thickness of 2 mm. were spot-welded to the plate to ensure good electrical conductivity. Nominal reactor volumes of 44.7, 70.0, 95.3 and 120.0cm’ in the electrolyte compartment were achieved by using 1, 2, 3 or 4 spacers respectively (see Fig. 2a and 2b), corresponding to interelectrode gaps of 2.5 mm, 4.Omm, 5.5 mm and 7.0 mm after compression of the reactor assembly.
3. THEORY
M,=-
It is necessary to assume a flow model for the interpretation of the tracer curves. Two models may be considered in the absence of any (electro)chemical reaction. 3.1. Dispersion model (moment method) The dispersion model assumes that concentration fluctuations, when rapid and numerous may be considered to be random and this behaviour can be described by a diffusion-type equation similar to Fick’s law, where D (the dispersion coefficient) includes the random mixing of fluid and the molecular diffusion. The general dispersion model considers that the dispersion coefficient and the fluid velocity are both functions of the position. The dispersion coefficient, D is, therefore, non-isotropic[ 111 and may be represented by a second-order tensor. The mathematical model is greatly simplified if it is considered that the only observable dispersion takes place in the direction of fluid-flow. The formulation of this dispersion model leads to the equation. LX D azc ac -=--_at UL ax2 ax
(1)
This differential equation can be resolved by the use of Laplace transforms but Levenspiel and Smith have found a relationship between the first and second moment of the tracer curves and the Peclet number[12, 133. The relationship is a function of the degree of dispersion and the boundary conditions:
l; tE dt
M1= 1; M2=
and axial dispersion characteristics for beds of adsorbent particles by using the moment analysis[14]. The general case it is greatly simplified when adsorption and intra-particular diffusion are neglected[15] and a dispersion coefficient in the axial direction to flow may be calculated from the expression. 2LDu= u3
where a, the reactor porosity, is evaluated from the expression :
4. RESULTS
AND DISCUSSION
The first and second moments from the E curves obtained (section 3.1) were calculated using equations (2) and (3), the integrals being evaluated numerically. Firstly, the influence of reactor volume on dispersion was studied using the axial dispersion model. The first and second moment were calculated and the following equation was applied to calculate the dispersion coeflicient[ 161. -
D
VL
= 0.5 ;
(6)
where r is the mean residence time in the reactor and a2 is the variance. In all cases studied, the value of D/UL was greater than 0.025, indicating a large value of dispersion; hence equation (6) could not be successfully applied. When the dispersion value is high, the boundary conditions play an important role and must be taken into account. The experimental conditions agree with the “closed-open vessel” model[16], in which the relationship between the moments of the curves and the dispersion coefficient is[ll]: 2
E dt
j; t=E dt SomEdt -M:
3.2. Schneider-Smith model Schneider and Smith have developed a method for determining equilibrium constants, rate constants
Figure 4 compares an experimental curve with the theoretical curve assuming a low degree of dispersion and it is seen that the agreement between the experimental curve and the theoretical one is relatively poor. A comparison with the “closed-open vessel” model for the case of high dispersion is not
Hydrodynamic
behaviour
of the FMOl-LC
reactor
497
0a
0e
Fig. 3. Photographs of the plastic mesh turbulence promoter used in the FMOl-LC reactor. (a) Plastic mesh; (b) Nickel electrode; (d) Slotted plate nickel electrode; (e) Expanded
possible since an analytical expression for the curve is not available[13]. Figure 5 shows dispersion vs. flow rate curves for several reactor volumes. An increase in the degree of dispersion with flow rate is evident and larger dispersion values are found for
(a) and nickel electrode structures (b)-(e) minimesh electrode; (c) Flat plate nickel nickel mesh on a flat plate electrode.
small reactor volumes, due to the more important inlet and outlet effects in small reactors. The Schneider-Smith model was also applied to the case when the reactor contained turbulence promoters and three-dimensional electrodes. The first
P.
498
TRINIDADand
F. C.
WALSH
50
40
2 c
30
P ; a 3 Lrl 2o
0
E
6
4
2
8
10
12
14
GXJ) is Fig. 6. Plot for the calculation of reactor void fraction using equation (5). (+) Minimesh electrode (as in Fig. 3b); (0) Expanded mesh electrode (as in Fig. 3e); (m) Flat plate plus plastic net (as in Fig. 3a). Reactor volume 95.3 cm3.
5 10
non linear, expression[ 1,3, IS] : R
0 0
D=AV” I
0.5
(8)
,
1
1.5
2
2.5
3
3.5
Dimensionless Time
Fig. 4. Comparison between an experimental E curve (0) and the predicted behaviour for a low degree of dispersion Ly;ctIat plate electrode (Fg. 3c) in an empty channel. volume = 44.7cm . Linear fluid velocity = 9.95cm-1.
where V = u/a, the interstitial equations (8) and (4) gives:
which may be expanded : M2V
step was the evaluation of the reactor free volume (reactor porosity) using equation (5) (see Fig. 6 and Table 2). The second moment was plotted vs. l/U’ (equation (4)), allowing D to be calculated from the slopes of the line. Curves were obtained instead of straight lines (Fig. 7), due to a functional dependence of D on flow velocity, according to the following,
"0
5
10
15
velocity. Combining
log
-
2L
= log a + (n - 2) log v
(10)
The function log M2 V/2L was plotted vs. log V, allowing the 1 and n coefficients to be calculated (Fig. 8). Figures 9 and 10 shows dispersion vs. superficial velocity and it is seen that larger values of dispersion coefficient are experienced in the smaller volume reactors. In addition, the three-dimensional
20
25
30
35
40
Flow rate /cm&s’
Fig. 5. Dispersion coefficient vs. volumetric flow rate of electrolyte for a flat plate electrode in the absence of a turbulence promoter. Reactor volumes of: (m) 44.7cm”; (0) 70cm3; (0) 95.3cm3; (0) 120cm3.
Hydrodynamic behaviour of the FMOl-LC reactor
499
Table 2. Data from tracer experiments for various turbulence promoters, reactor volumes and electrode types according to correlations of the form D = AV”according to equation (8) Reactor volume /cm 3
Turbulence promoter tyve
Electrode type
44.1
Metal minimesh Plastic mesh Metal minimesh Plastic mesh None None
Flat plate Flat plate Flat plate Flat plate Expanded metal mesh Slotted plate
44.7 95.3 95.3 95.3 95.3
I
,900
Constant A 1.129 0.756 1.18 0.864 1.029 0.907
Fluid velocity exponent n
Reactor porosity *:
1.352 1.019 1.02 1.043 1.152
0.53 0.50 0.78 0.89 0.62
1
I
I
0.10
0.20
0.30
(l/U?
0.40
0 50
/s3cni3
Fig. 7. Second moment vs. l/U3 curves for various reactor configurations. (B) Flat plate (Fig. 3c) in an empty channel; (+) Flat plate plus plastic net (Fig. 3a); (0) Flat plate plus mmimesh electrode (Fig. 3b); (0) Flat plate plus slotted plate electrode (Fig. 3d). Volume of reactor = 95.3 cm3.
Fig. 8. Plot used for the calculation of 1 and n parameters according to equation (10). ( x ) Flat plate plus mesh electrode (volume of reactor = 44.7cm”; (W) Flat plate plus plastic net (volume of reactor = 44.7cma); (+) Flat plate plus mesh electrode (volume of reactor = 953cm’); (0) Flat plate plus plastic net (volume of reactor = 95.3 cm’).
500
P. TRINIDADand F. C. WALSH
0” 2
I
I
4
6 8 10 12 Linear velocity /cm s1 Fig. 9. Dispersion coetlkient vs. mean linear electrolyte velocity, showing the effect of turbulence promoters at a flat plate electrode. (m) Flat plate in empty channel; (0) Flat plate plus plastic net (Fig. 3a); (+) Flat plate plus minimesh electrode (Fig. 3b). Volume of reactor = 44.7cm3.
electrode and the metal minimesh turbulence promoter show higher values of dispersion coefficient, the plastic mesh promoter showing small values of dispersion. Table 2 shows 1 and n values calculated from a least squares fit, according to equation (8). Figure 11 shows a comparison between the axial dispersion model and the Schneider-Smith model, agreement being closer at low values of velocity. Finally, the Peclet number, defined as: pe
=$
(11)
was plotted against flow velocity (Fig. 12). The small slope of the lines for the turbulence promoters in this plot indicates that as the bulk velocity increases, the
degree of dispersion rises by approximately the same degree. As the Peclet number increases the hydrodynamic behaviour shows closer agreement with the plug flow model. For the case of the empty channel (in the presence of a flat plate or a slotted plate electrode) the relationship between the Peclet number and the mean linear flow velocity is simple; the Pe values decrease at higher velocity until a critical value of Pe is reached. At higher flow velocities, the electrolyte velocity is fast enough to carry the reactant with a lower degree of dispersion[21]. The plastic turbulence promoter gives rise to a more uniform current distribution as well as an enhanced rate of mass transport[17] and the present work shows that Peclet number for this configuration is sufficiently high to justify the choice of reactor model as a plug flow reactor with a degree of dispersion.
_I
4 3 5 6 Linear velocity /cm s.1 Fig. 10. Dispersion coetlicient vs. mean linear electrolyte velocity. (+) Flat plate in empty channel; ( x ) Flat plate plus plastic net (Fig. 3a); (0) Flat plate plus minimesh electrode (Fig. 3b); (0) Slotted plate electrode (Fig. 3d); (m) Flat plate plus expanded mesh electrode (Fig. 3e). Reactor volume = 95.3 cm3. 1
2
501
Hydrodynamic behaviour of the FMOi-LC reactcr
19 17 -
:I
1
1::
11 9 7 -
J
2
1.5
1
2.5
3
3.5
Linear velocity
4
4.5
5
5.5
/cm s-’
Fig. 11. Comparison between flow models via a plot of Peclet number against linear electrolyte flow velocity. Flat plate plus minimesh electrode (Fig. 3b). (0) Axial dispersion model considering high dispersion (“closed-open vessel”); (m) Shneider-Smith model. Reactor volume = 95.3 cm3.
Metal produced
minimesh a larger
and
expanded
mesh
5. CONCLUSIONS
electrodes
degree of dispersion than the plastic promoter (as evidenced by the smaller Peclet number for the former). The promoters result in a reduction of the Nernst diffusion layer thickness (6,) and an enhanced mass transport coefficient. However, dispersion produces a deviation from the plug flow model and a lower performance, since it is well known that, under mass transport control and, for constant inlet conditions, surface area and mass transport conditions, plug flow reactors achieve better results than the perfectly mixed reactor case[W201.
A simple and rapid marker-pulse method has been used to characterise hydrodynamic behaviour in an electrochemical, laboratory filterpress reactor using regression of the data in the time domain. The axial dispersion and Schneider-Smith models were considered to measure deviation from the ideal plug flow model. Many problems arise from the application of these models, particularly the appearance of tailing in the tracer curves leading to error. Nevertheless, qualitative conclusions can be drawn in order to provide a better understanding of the flow
20 ,
10
’ 1
I
I
2
I
I
3
4
5
6
Linear velocity /cm s-1 Fig. 12. Peclet number vs. mean electrolyte velocity for various reactor configurations. (+) Flat plate (Fig. 3c) in empty channel; (m) Flat plate plus minimesh electrode (Fig. 3b); ( x) plate plus plastic net (Fig. 3a); (0) Flat plate plus expanded mesh electrode (Fig. 3e); (0) Slotted plate electrode (Fig. 3d). Reactor volume = 95.3 cm3.
502
P. TRINIDADan d F. C. WALSH
modifications generated within several reactor configurations. It has been found that a higher value of the dispersion coefficient is experienced in lower volume reactors. In all cases, the degree of dispersion increased and flow velocity and in the presence of turbulence promoters. The plastic mesh promoters help to provide a higher mass transport and more uniform current distribution in the reactor, together with reduced entrance effects near the inlet manifoldC4, 171. The Peclet number showed little change with the electrolyte flow velocity or in the presence of turbulence promoters. This was attributable to an increase in the interstitial flow velocity that mitigates against the increase of dispersion, this effect being particularly marked in the case of the plastic mesh turbulence promoter. The applicability of several dispersion models for filterpress reactors is currently being examined, including more refined methods of data analysis such as an non-linear least squares fit and Laplace transformations[22], assuming the flow to consist of (a) the sum of two dispersive axial plug flows and (b) fast and stagnant phases[23]. Acknowledgements-These studies have been carried out via an ERASMUS scheme which facilitated a visit by P. T. to the University of Portsmouth from the University of Salamanca. The authors are grateful to Professors M. Galan (Salamanca) and T. A. Crabb (Portsmouth) for enabling this research. REFERENCES 1. F. Walsh, A First Course in Electrochemical Engineering, The Electrochemical Consuhancy, Romsey, (1993). 2. C. J. Brown, D. Pletcher, F. C. Walsh, J. K. Hammond and D. Robinson, J. appl. Electrochem. 23, 38 (1993). 3. C. J. Brown, D. Pletcher, F. C. Walsh, J. K. Hammond and D. Robinson, J. appl. Electrochem. 24,95 (1994). 4. C. J. Brown, D. Pletcher, F. C. Walsh, J. K. Hammond and D. Robinson, J. appl. Electrochem. 22, 613 (1992).
5. C. J. Brown, J. K. Hammond, D. Pletcher, D. Robinson and F. C. Walsh, Dechema Monograph, 123,299 (Edited by G. Kreysa), VCH, Weinheim, (1992). 6. J. K. Hammond, D. Robinson and F. C. Walsh, Dechema Monograph, 123, 279 (Edited by G. Kreysa), VCH, Weinheim, (1992). 7. D. Robinson, in Electrosynthesis --from Laboratory to Pilot to Production, (Edited by J. D. Genders and D. Pletcher) The Electrosynthesis Co, Buffalo, New York, (1990). 8. R. E. W. Jannson and R. J. Marshall, Electrochim. Acta 7, 823 (1982). 9. R. J. Marshall,
Ph.D Thesis, University of Southampton, (1982). 10. J. Harrel and J. Perona, Ind. Eng. Chem. Process Des. & Deo. 77,464 (1968).
11. K. Bischoff and 0. Levenspiel, Chem. Engl. Sci. 17, 245 (1962). 12. 0. Levenspiel and W. Smith, Chem. Eng. Sci. 6, 227
(1957). 13. 0. Levenspiel, The Chemical Reactor Omnibook, OSU, Corvallis, (1979). 14. P. Schneider and J. Smith, A. J. Ch. E. Journal 14, 762 (1968). 15. D. Cantero, R. Gil de Rebolefio and M. Gal&r, Anales de Quimica, 83,641 (1987).
16. 0. Levenspiel, “Chemical Reaction Engineering”, 2nd Ed, John Wiley, New York, (1972). 17. F. C. Walsh and G. W. Reade, The Analyst 119, 797 (1994). 18. F. C. Walsh, Electrochim. Acta 38, 465 (1993). 19. F. Coeuret, Introduccibn a la Ingenieria Electroquimica,
Ed Revert& Barcelona, (1992). 20. P. Trinidad and F. C. Walsh, paper submitted to Int. J. Engng. Ed. 21. P. Trinidad, Comportamiento Hidrodiruimico y Optimization de las Variables de Operation en Reactores Electroquimicos, Grado de Salamanca, University
of Salamanca, Spain, (1994). 22. M. Fleischmann and R. E. W. Jansson, Chem. Ing. Tech. 49, 283 (1977). 23. P. Trinidad, D. Gilroy and F. C. Walsh, paper presented at Electrochem 95, University of Wales, Bangor, lo-14 September, 1995; Trans. I. Chem. E., in preparation.