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Brazilian Journal of Chemical Engineering

Print version ISSN 0104-6632On-line version ISSN 1678-4383

Braz. J. Chem. Eng. vol.19 no.1 São Paulo Jan./Mar. 2002 




L.A.M.Ruotolo1 and J.C.Gubulin2
Federal University of São Carlos, Department of Chemical Engineering,
P.O.Box 676, 13565-905 São Carlos – SP, Brazil


(Received: December 6, 2001; Accepted: January 16, 200 )



Abstract - The kinetic and hydrodynamic behaviour of a fixed-bed electrochemical reactor was studied in terms of current efficiency (CE) and energy efficiency (EE). In the kinetic experiments the effects of fixed bed thickness (L), current density (i) and initial concentration of copper (C0) were studied. In the hydrodynamic experiments the permeability (k) of the electrode and the coefficient for inertial forces (c) were also studied as functions of the applied current density. At low current densities and bed thicknesses greater than 1.0 cm, negative CE and EE were observed as a consequence of the dissolution of the porous matrix. At high current densities low CE and EE were observed and a powdery deposit was formed on the surface of the particles. From the results of the kinetic study bed thickness and the range of current densities employed in the hydrodynamic experiments were chosen. In these experiments the electrodeposition process continued until the whole electrode had been clogged and no more electrolyte could pass through it. The relationship between pressure drop and flow rate was well described by the Forchheimer equation. It was observed that the reduction in porosity due to copper electrodeposition causes the flow rate to decrease because of the decrease in electrode permeability, but it had no influence on current efficiency.
Keywords: fixed-bed, electrochemical reactor, hidrodynamic.




Due to the ecological and economic problems they cause, recovery of heavy metals (Cu, Pb, Zn, Ni and Cr) from dilute aqueous solutions is necessary. These metals are produced as industrial wastes by electroplating industries and by metal extraction.

From an ecological standpoint, effluents with even low concentrations of heavy metal ions are extremely toxic and can cause several types of pollution, such as mud formation, exterminate aquatic life and create hazards to human health.

The methods normally used for metal ion recovery are precipitation as hydroxides, sulphides and oxalates; ion exchange by chemical or electrochemical means; reverse osmosis; chemical or physical adsorption; chemical reduction and biochemical remediation (Rajeshwar and Ibañez, 1997). As an alternative to conventional methods, an electrochemical process was developed. This process can be described as a clean technology, as permanent residues are absent. From an economic point of view, the electrochemical method may offer some advantages, such as labour reduction, partial or total elimination of stock areas and reintegration of metals into the main process (due to the high degree of purity of the metal obtained).

However, for metal electrodeposition from dilute solutions, the plain electrode was inadequate because of poor mass transfer rates. Therefore, the electrolytic removal and recovery of metal ions from dilute solutions requires the use of electrodes with large surface areas, like the three-dimensional particulate electrode.

Although the fixed bed reactor has been reported to be the most efficient for metal electrodeposition (Chu et al., 1974; Sioda and Piotrowska, 1980), it has the disadvantage that its porous matrix becomes clogged with metallic deposit, which renders continuous operation of the process impossible. However, with dilute solutions the operational time becomes so long that use of the porous matrix as a refill may be justified.

The electrodeposition process has frequently been evaluated by using two parameters to achieve an overall understanding of the three-dimensional electrodes: current efficiencies and energy efficiency. Current efficiency (CE) is the ratio of the mass of metal deposited at a given time to the mass that would be deposited if all of electric current were used in the electrolytic process (Equation 1). Energy efficiency (EE) is the ratio of the mass of metal deposited to the electric energy applied to the system during the same time span (Equation 2).

where zi is the number of electrons involved in the electrochemical reaction (for copper, z = 2), F is the Faraday constant (96487 Coulomb/mol), Mi is atomic weight (63,546 g.mol-1 for the copper ), m is the mass electroprocessed during the time interval dt (g), I is the electric current (A) and V is the voltage drop throughout the bed (volts);

In this work the effect of pore clogging on the hydrodynamics of the system was evaluated based on parameter permeability (k) and factor c (the coefficient for the inertial forces), using the quadratic Forchheimer equation, which can be applied to high rates of flow through a porous medium (Scheidegger, 1974):

where DP is the pressure drop (, L is bed thickness (m), m is electrolyte viscosity (kg.m-1.s-1), r is electrolyte density (kg.m-3), e is electrode porosity (non-dimensional), k(e) is permeability at given e (m2), c(e) is Forchheimer's factor c at given e (non-dimensional) and q is the superficial velocity of the electrolyte (m.s-1).

Permeability and factor c are porosity-dependent parameters that may be established first, as shown in Equations 4 and 5.

Taking into account different particle shapes, it is then possible to obtain constants k0 and c0 as functions of the initial particle characteristics:

where dp is the equivalent diameter of the particle (m) and f is particle sphericity (non-dimensional).

For measurement of fixed bed porosity we have been unable to develop an efficient method to obtain experimental readings at points throughout the bed thickness. We decided to use a medium porosity, calculated from the mass balance of copper in the system. The system was operated as a closed circuit with finite quantities of solution and copper particles. The following equation, deduced from the global mass balance in the system, was used to calculate medium e:

where e0 is the initial porosity of the fixed bed (non-dimensional), is the initial mass of copper in the electrolyte (kg), rm is the density of the porous matrix (kg.m-3), VL is the total fixed bed volume (m3), CCu is the copper concentration in the electrolyte measured at a given time ( and C0 is its value at time zero (

From the curve for pressure drop in the bed versus flow rate, it was thus possible to determine the hydrodynamic parameters, using Equation 3, as a function of instantaneous fixed bed porosity, determined from Equation 8. Functions fk(e) and fc(e), as well as constants k0 and c0 from Equations 4 and 5 were determined for the particles used in these experiments.

The purposes of this work were: 1) to study the influence of the parameters concentration of copper, current density and fixed bed thickness on CE and EE and 2) to study the hydrodynamic behaviour of the pore clogging of the packed bed electrode in the electrodeposition process.



Kinetic Experiments

The experimental unit and a detailed view of the electrochemical reactor used for the kinetic experiments are schematically shown in Figure 1.



The electrolyte was prepared using copper sulphate and sulphuric acid (0.5 M). A flow-by electrode configuration with downward electrolyte flow was adopted. The porous cathode consisted of 1.0 mm equilateral cylindrical copper particles. The inner diameter of the reactor was 4.0 cm and all pieces were made of acrylic.

The procedure consisted of these stages: with the particles up to a selected thickness and the electric current selected the electrolyte was flowed through the reactor and after a minute, the supply of electric current and the time measurement started simultaneously. At regular intervals the voltage drop was measured and electrolyte samples were taken for subsequent measurement of concentration, employing a SpectrAA Varian atomic absorption spectrometer. At the end of the process the flow and the electric supply were interrupted and the reactor was prepared for another run by adjusting the parameters. All experiments were carried out at constant flow rates and controlled temperatures (25-27° C). This procedure was repeated for nine current densities and four bed thicknesses. A galvanostatic source of current was employed, and the values of current densities were calculated using the cross-sectional area of the current feeder.

Hydrodynamic Experiments

A schematic sketch of the system and a detailed view of the electrochemical reactor are shown in Figure 2. The reactor has a cylindrical body consisting of moveable parts, which can be joined together to give a desired bed thickness. The inner diameter available for the stream of electrolyte is 7.0 cm. A liquid distributor, followed by a perforated lead plate that was the counter electrode, was inserted into the electrolyte entrance region. This reactor had two orifices of 1.0 mm, used to measure the pressure drop across the bed.



The first step was to determine the initial values of k and c. For that purpose, the centrifugal pump was turned on and the main valve was completely opened, allowing the electrolyte to flow through the electrode. Then the pressure drop was measured for three or four different flow rates, obtained by closing the main valve. After that the main valve was again completely opened and the electrodeposition process started supplying a constant current density. At several times during the process, an aliquot of electrolyte was taken to analyse the concentration (using a Varian SPECAA100 atomic absorption spectrophotometer) and the voltage drop was measured. To determine the values of k and c at these times the same procedure as that used for their initial determination was followed, and at the end of each measurement the main valve was once completely opened to observe the decrease in flow rate as a function of electrode clogging. The by-pass valve remained completely closed during all these experiments. The electrodeposition process continued until the electrode had been completely clogged. This procedure was repeated for two different current densities.

The current densities and the bed thickness used for the hydrodynamic experiments were chosen on the basis of the results of the kinetic experiments.

Using Equation 6 and the measured concentrations at a given time, the average values of bed porosity at that time were obtained. The particles used were 1.0 mm-equilateral copper cylinders that had an initial porosity of 33%. The initial electrolyte composition was 0.5 M of sulphuric acid and about 5000 of copper ions, which was enough to clog the electrode completely.



Kinetic Study

a) Effect of Concentration.

Figure 3 shows the kinetics of the decrease in copper concentration in the electrolyte. Figure 4 shows mass deposition versus time, calculated by mass balance. It can be noted that the curves are linear up to the moment when they become exponential in time. Using the gradient of the curves shown in Figure 4, we obtain the deposition rate (dm/dt), and using Equation 1, we obtain the curves shown in Figure 5, which clearly indicate the effect of concentration on the current efficiency of the process. Current efficiency remains at a constant value (corresponding to the linear portion of the curve in Figure 4) when electrolyte concentration is greater than approximately 100 At concentrations lower than this value, CE decreases quickly.







Given the above results, it was decided that concentrations higher than 100 mg dm-3 would be used throughout processing time in subsequent experiments. With this procedure, CE and EE remained practically constant and the process was easily evaluated in terms of the parameters studied.

b) Effects of Current Density and Fixed Bed Thickness.

In three-dimensional electrodes, such as packed, fluidized, circulating and spouted beds, the electric field will not be uniform. This non-uniformity results in an overpotential profile (Olive and Lacoste, 1980) and a current density profile (Doherty et al., 1996). The intensity of the electric field is high near the counter electrode, where high potentials and high electric currents are found, and as a consequence the reaction rates are high, as experimentally observed by Lanza and Bertazolli (2000).

Also, flow rate has an influence on the overpotential and current density profiles because it is directly related to mass transfer rates.

In this work all the experiments were carried out under constant flow rates, but the profiles for overpotential and current densities were certainly affected by concentration depletion, constant current densities and bed thickness. The process was evaluated in terms of overall CE and EE that embody all the effects of the overpotential and current density profiles and the effect of the decrease in porosity, which are difficult to measure.

The effectiveness of three-dimensional electrodes like the packed bed must be evaluated not only by kinetics, but also by CE and EE, which are decisive in establishing operational conditions with lower costs. In theory, an increase in bed thickness would increase the active area of the reaction, and high electric currents could be applied in order to decrease the operational time. But due to the non-uniformity of the electrical field, this does not happen.

In Figures 7 and 8 it is possible to observe the different behaviors of the curve for a bed thickness of 1.0 cm and of the other curves.







For a bed thickness greater than 1.0 cm we can see that at low current densities there are negative values for CE and EE. This happens because of the increase in dissolution of the copper particles that compose the porous matrix, which results in an increase in the electrolyte concentration of copper ions. This dissolution occurs because of the depth of penetration of the electric field (Hadzismajlovic et al., 1996). The greater the bed thickness, the lower the depth of cathodic current penetration and the lower the values of CE and EE (see Figure 6).

When increasing the current density at a given bed thickness, the zone of anodic dissolution decreases and consequently CE and EE increase. During the same time that dissolution was taking place, an intense electrodeposition of copper occurred near the counter electrode. Therefore, CE and EE were a consequence of the balance between the mass of electrodeposited copper and the mass of dissolved copper. Even when CE and EE were negative, it was possible to observe that the electrodeposition process took place, but the dissolution reaction was greater than the electrodeposition, so the concentration of copper in the electrolyte increased.

Although CE and EE increase when the current density increases, there is a maximum limit, after which they start to fall again. However, these maximum limits for CE and EE were lower than the values observed for a bed thickness of 1.0 cm. The values of CE and EE can be best observed in the table shown in the appendix.

Because the current profile resulted from the non-uniformity of the electric field, in the electrodes with 2.0, 3.0 and 4.0 cm thickness there are zones of positive overpotential that cause the anodic reaction of copper oxidation. At a given current density, the thicker the electrode, the larger the zones of dissolution, so that the rate of oxidation becomes higher than that of reduction. Thus, the two reactions occur at the same time, as could be visually confirmed during the experiment (Hadzismajlovic et al., 1996; Lanza and Bertazolli, 2000). It was also observed that a thin layer of the porous matrix near the counter electrode was sintered in all experiments, while most of the electrode porosity remained unchanged. When the current density increased, probably the positive overpotential zones decreased, resulting in a strengthening of the cathodic reaction relative to the anodic. This suggests that at a thickness of 1.0 cm or less, there are no more anodic zones within the range of current densities tested because of the high current efficiencies shown. However, for the 1.0 cm bed, when increasing the current density, CE and EE values start to fall (Figures 7 and 8). As we were working in a galvanostatic mode, when the current density was greater than the limit current, a parallel reaction, which used part of the supplied current, occurred and consequently decreased CE and EE. This could also explain why the maximum values for CE and EE for bed thicknesses of 2.0, 3.0 and 4.0 cm are lower than those for the bed thickness of 1.0 cm and why CE and EE start to decrease after reaching their maximum values.

At current densities greater than 796 A.m-2, a powdery deposit was observed on the electrode and the rate of its production increased as current density increased. Through an X-ray analysis of this powder we verified that it was composed of metallic copper and cuprite.

As it is interesting to operate the process at high values of CE and EE, it is suggested that a thin electrode be used. To reduce the processing time it is helpful to use small particle diameters because this will allow the use of high electric currents while maintaining the same current density.

Hydrodynamic Study

On the basis of the kinetic study the bed thickness chosen for the hydrodynamic study was 0.5 cm because this thickness provided most of the reaction activity (Lanza and Bertazzoli, 2000). The current densities chosen were 318 and 477 A.m-2 because with these values the best current efficiencies were achieved without formation of a powdery deposit.

Figure 9 shows how the pressure drop in the electrode falls as a function of superficial flow velocity. The values for velocity (q) were taken with the main valve completely open so the decrease in superficial velocity was a consequence of the decrease in electrode porosity that increased the resistance to electrolyte passage (because of its clogging). It is interesting to note that the current density had little influence on the increase in pressure drop and in the decrease in flow rate.



Figure 10 shows the experimental results of the pressure drop as a function of the superficial velocity of the electrolyte obtained for each time or electrode porosity. The first point on the right of each curve in Figure 10 corresponds to the points shown in Figure 9. The other points in Figure 10 were obtained by closing the main valve and measuring the pressure drop and the flow rate, and then these results were used to calculate the values of permeability (k) and factor c at a determined time, i.e., at a determined porosity. The curves in Figure 10 indicate that it was adequate to use the quadratic Forchheimer equation to represent the system.



Figure 11 shows the kinetics of electrodeposition as the mass deposited over time. It is interesting to observe in these curves that the electrodeposition rate was practically constant, implying that the process was not influenced by the decrease in flow rate over the time. Hence current efficiencies at the two current densities studied were constant, the values being 94.0% and 98.2% for current densities of 318 and 477 A.m-2, respectively. Some authors have studied the effect of flow rate on the efficiency of porous electrodes (Ateya et al., 1977; Mustoe and Wragg, 1983; El-Shakre et al., 1994), and it is known that current efficiency decreases when flow rate decreases at a constant current density. This happens because of the decrease in mass transfer rate. However, these works don't consider the decrease in porosity over the time that permits the interstitial electrolyte velocity to increase (also increasing the local mass transfer rate), which could explain the constant high values obtained for current efficiency throughout the process, even with the decreasing flow rate.



Because of the high values obtained for current efficiency, the contribution of hydrogen reaction to the total pressure drop in the packed bed is not believed to be very important (Stankovic et al., 1995).

It can be observed that the curves for energy efficiency versus time in Figure 12 fall slowly during the process up to a certain point, where an abrupt fall takes place. In both cases, this point corresponds to approximately 75% of the total time used for the electrode to clog.



Once the variation in pressure drop with velocity flow (Figure 10) is known, it is possible to use Equation 3 to calculate the values of k and c plotted in Figure 13 and 14. The values for porosity were calculated using Equation 8 and the values for experimentally measured copper concentration.





The equations fitted to the experimental points are the following:

It was found that k and c were practically independent of current density and that Equations 9 and 10 could be used for the range of current densities studied.

It was once again observed that electrode clogging occurred on the upper surface of the particles next to the counter electrode, while in the lower region, which is in contact with the current feeder, the particles were sintered, even though porosity was barely altered. Therefore, it was supposed that the rapid fall in electrode permeability at the initial moments of the process (see Figure 13) was due to the initial electrodeposition on the electrode surface, which caused an abrupt alteration in the local surface porosity and hence in the flow of electrolyte. After these initial moments, the electrodeposit grew in a direction perpendicular to the counter electrode, resulting in less intense clogging and a less abrupt fall in permeability. In spite of this porosity profile, the use of medium porosity calculated by Equation 8 was an easy way to quantify the electrode clogging and then evaluate its effects on hydrodynamics.

The fast rise in factor c during the final moments of the process (Figure 14) is due to the increase in inertial forces that takes place as the area available for the flow of electrolyte through the electrode is reduced because of decreasing porosity (Figure 15).



Once the kinetic and hydrodynamic behaviours of the fixed bed were known, empirical relations were sought that could be used to design packed-bed electrochemical reactors within the range of current densities studied.

From Figure 15, which shows the decrease in porosity as a function of time, it is clear that the decrease is linear, i.e.,

where f(i) is the slope of the straight line formed and a function of the current density (i). In this experiment two current densities were used and the results could be fitted to a straight line.

Substituting Equation 12 into Equation 10 results in

To establish the optimal operating time for the system, it is necessary to determine some appropriate criteria. During operation the system has constant current efficiency and flow rate. Consequently, these parameters cannot be used as criteria. In addition the system could be at near- zero flow rates and still have high values of CE and EE.

However, analysing energy efficiency, it can be observed that at a given flow rate there is a point when an abrupt fall occurs, resulting in a sharp rise in energy consumption that implies the economic unfeasibility of the run (see Figure 12). This suggests an optimal operational time for the electrode of 75% of the time necessary for total electrode clogging, i.e.,

Substituting Equation 14 into Equation 13 with the final porosity equal to zero (the electrode is totally clogged), we obtain Equation 15, which represents the time during the reactor must be operated as a function of current density, in agreement with the criteria previously established.

Compared with the experimental results, the maximum deviation for operational time, calculated using Equation 15, was 8.7% for i = 318 A.m-2 and the minimum deviation was 1.9% for i = 477 A.m-2.



The following main conclusions can be drawn from this work:

1) It was confirmed that the fixed bed could yield high CE and EE (near 100%) when operated under the conditions of low bed thickness (lower than 1.0 cm) and low current densities (lower than or equal to 477 A.m-2);
2) The fixed bed operates at constant current efficiency up to concentrations of approximately 100;
3) It was found that the reaction is not distributed uniformly throughout the electrode, but rather occurs intensely on the particle surfaces near the counter electrode, while most of the electrodes are practically unused in the electrodeposition process;
4) At high bed thicknesses, zones of distinct electrochemical activities can appear. For a given current density, the thicker the electrode, the larger the zones of anodic reaction. However, an increase in current density will cause these zones of anodic reaction to decrease.
5) The fall in porosity and flow rates has no effects on current efficiency during the process. Energy efficiency behaved differently, remaining on a constant plateau for 75% of the total time necessary for electrode clogging and then falling abruptly due to the increased voltage drop across the bed;
6) The rapid fall in electrode permeability at the beginning of the process was explained by an initial metal electrodeposition that occurred preferentially on the surface of particles near the counter electrode. As the process continued this electrodeposit was extended in a vertical direction and the permeability decreased more slowly. The rapid increase in factor c at the end of the experiments was explained by an increase in the inertial forces caused by a decrease in the area available to the flow of electrolyte;
7) Using 75% of the total time as a criterion to establish the optimal operational time for electrode clogging, Equation 9 was obtained. It could be used to establish the best operational conditions for a fixed-bed electrochemical reactor operating with copper ion electrodeposition at a range of current densities between 318 and 477, which is the range within which current efficiency is approximately 100% and the consumption of energy is minimised.



This work was supported by FAPESP (São Paulo State Research Aid Foundation, Brazil) under project number 96/6699-9.



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