Scale-up of rotating cylinder electrode electrochemical reactor for Cu(II) recovery: Experimental and simulation study in turbulence regimen

Electrochimica Acta 77 (2012) 262–271

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Scale-up of rotating cylinder electrode electrochemical reactor for Cu(II) recovery: Experimental and simulation study in turbulence regimen Francisco J. Almazán-Ruiz a , Francisco V. Caballero a , Martín R. Cruz-Díaz a,∗ , Eligio P. Rivero b , Ignacio González c a División de Química y Bioquímica, Tecnológico de Estudios Superiores de Ecatepec, Av. Tecnológico S/N, Esq. Av. Hank González, Valle de Anáhuac, C.P. 55120 Ecatepec, Edo de México, Mexico b Facultad de Estudios Superiores Cuautitlán, Departamento de Ingeniería y Tecnología, Universidad Nacional Autónoma de México, Av. 1o de Mayo Col. Sta. María las Torres, C.P. 54740 Cuautitlán Izcalli, Edo de México, Mexico c Departamento de Química, Universidad Autónoma Metropolitana, San Rafael Atlixco 186, C.P. 09340 México, D.F., Mexico

a r t i c l e

i n f o

Article history: Received 25 May 2012 Accepted 2 June 2012 Available online 9 June 2012 This paper is dedicated in memoriam to Prof. Dr. José González, Universidad de Alicante, Spain. Keywords: Rotating cylinder electrode (RCE) Electrochemical reactor scale-up Electroplating industry Cu(II) recovery Hydrodynamics and mass transport in turbulence regimen Computational simulation with Comsol Multiphysics 3.5a

a b s t r a c t This paper describes a methodology for scaling-up a RCE bench scale reactor (0.350 L) to pilot scale reactor (RCE-PP, 10 L) by means of geometric correlations, dimensionless numbers, and computational simulation (Comsol Multiphysics 3.5a) in 2D for hydrodynamics and mass transport in turbulence regimen. The methodology proposed is validated by experimental data of Cu(II) recovery from a solution mimicking an effluent of electroplating industry (0.019 M CuSO4 and 1 M H2 SO4 ). The experimental conditions of Taylor number (5.22 × 105 to 7.84 × 105 ) and limiting current (51.56–74.67 mA cm−2 ) used in the present work ensure a turbulent flow regime and electrochemical reaction controlled by mass transport, respectively. Under these experimental conditions, the hydrodynamic behavior was described using the Reynolds-averaged Navier–Stokes equations and the –ε turbulence model as well as the wall functions based on the universal distribution of velocities for the near-wall region. The diffusion-convection equation was solved using the Kays–Crawford model for turbulent Schmidt number (ScT ) and mass transfer wall functions of Launder–Spalding type. The simulation results of the RCE bench scale in 2D, using the fitting parameter A reported by Rivero et al. [1], predict the experimental data (error <8%) of copper concentration decay in the RCE-PP up to 80% of galvanostatic copper recovery. © 2012 Elsevier Ltd. All rights reserved.

1. Introduction The removal of heavy metals present in the rinsing water (RW) from technologies based on chemical precipitation, ionic exchange resins, evaporation-osmosis, electroosmosis, and electrofloculation process has been widely used for the treatment of these RW. The management of solid wastes generated by any of these technologies, or the high-cost operation of some of them have pushed to search for other technological alternatives. Electrochemical metal recovery has recently attracted attention, because the metal is recovered in its most valuable form, that is, a zero-oxidation state, without requiring addition of chemicals, and thereby not generating by-products which would later require treatment or confinement [1–6]. Moreover, electro-recovered metals, and waters treated using these electrochemical methods, can

∗ Corresponding author. Tel.: +52 55 50002324; fax: +52 55 50002304. E-mail addresses: [email protected], [email protected] (M.R. Cruz-Díaz). 0013-4686/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.electacta.2012.06.003

be reused in the same process, which is further cost-effective and diminish water consumption and environmental impact. Recently the rotating cylinder electrode (RCE) electrochemical reactor has become a good alternative due to the high rate of mass transfer and uniform distribution of current and potential. One of the main correlations on mass transfer in the RCE was reported in 1954 [7]. Low et al. [8] published a review of RCE application for metal recovery. Nowadays this device has been used to recover silver [9], cadmium [3,10], tin [2,4], nickel [11] copper [1,6,12], and also in removing toxic metals, such as arsenic [13,14]. Another interesting issue that has been studied in bench scale RCE reactors in recent decades is the improvement of mass transport enhanced factor through: (1) roughening cathode surface [15]; (2) using a wiper blade [16]; (3) simultaneous generation of gas with the main reaction on the cathode surface [17]; (4) reticulated vitreous carbon or expanded metal, as rotating cylinder electrode, to increase the active area [18]; and (5) rotating cylinder electrodes with turbulence promoter layers [19]. However, the amount of RW generated by typical electroplating process is very large (V > 3000 L day−1 ); as a consequence it is

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necessary to scale-up the RCE to pilot plant (RCE-PP) and its subsequent industrial development. On the other hand, in metal recovery the RCE electrochemical reactor typically operates under turbulence regimen and limited current conditions [20,21]. Therefore, it is indispensable to know the mass transfer coefficient (Km ) as a key factor for scale-up. Usually, the parameter Km is determined by experiments at different hydrodynamic conditions, the following is a typical dimensionless correlation [12]. Sh = 0.014Re0.91 Sc 0.356

(1)

Gabe and Walsh [15,22,23] obtained dimensionless mass transport correlations and mass transport enhanced factors in ECO-CELL reactor pilot plant. The Km data reported for pilot plant reactor were different from those obtained on bench cells. Later, Robinson and Walsh [24,25] evaluated the performance of a 500A industrial scale RCE reactor for copper removal, too. The results of mass transport characterization, obtained by means of electrolysis test system, were compared with dimensionless correlation obtained by Holland in hydrodynamically smooth RCE bench cell [26]. The mass transport coefficients obtained in industrial RCE reactor were different from those predicted by Holland correlation [26]. These results confirm that, despite the dimensionless number correlation is a common strategy for evaluating mass transfer coefficient, there are many limitations when pilot and industrial RCE reactors are evaluated. In order to avoid these limitations, works in the literature recommend extensive experimental trials on a new pilot scale reactor, with the objective of characterizing the reactor performance as a function of Km . An alternative to diminishing the number of experiments and limitations mentioned before, is to perform simulations by computational fluid dynamic (CFD), and later, validate against experimental work. CFD will thus become increasingly common for the analysis of electrochemical reactors design. Mandin et al. [27] have considered the modeling of the natural/forced convection regime around a rotating cylinder electrode cell using a computational flow dynamics approach. Low et al. [20] studied the primary, secondary and tertiary current distributions in a rotating cylinder Hull (RCH) cell using standard finite element software (FEMLABTM ); the simulations have been carried out under conditions of forced convection. Real-Ramirez et al. [28] reported the hydrodynamic characterization of an electrochemical cell with rotating disc electrode (RDE) through a three-dimensional biphasic model (Fluent). As was mentioned before, important progresses are made in fluid hydrodynamics, mass transport, as well as in current and potential distribution in turbulence flows, but significant work is necessary for electrochemical reactor design at pilot and industrial scale. It may be difficult due to larger Schmidt numbers that are important in electrochemical reactors, which could imply that mass transfer calculations require much finer computational grids in the solid–liquid interfacial zone than hydrodynamic simulations [29]. Nevertheless, commercial CFD solvers will often be adopted. For example, Rivero et al. [1] studied the hydrodynamics and mass transport in turbulence regimen in a RCE-LC (bench scale reactor), by simulating the electrolysis process of Cu(II) employing finite element method in Comsol Multiphysics 3.5a. In this work, the “wall functions” were implemented to describe the velocity and concentration profiles through the three zones of boundary layer, and the use of this methodology led to a considerable decrease in the number of nodes generated in the computational cell. This work presents a methodology for scaling-up RCE bench scale to pilot scale (RCE-PP), employing geometric correlations, dimensionless numbers, and computational simulation in 2D for hydrodynamics and mass transport in turbulence regimen (based on methodology proposed by Rivero et al. [1]). The methodology used herein is validated with Cu(II) recovery experimental data present in a solution mimicking effluent from the electroplating

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industry (0.019 M CuSO4 in 1 M H2 SO4 ) under mass transport control. Electrolysis at different operating conditions in a RCE bench scale of 0.350 L and RCE pilot scale (RCE-PP) of 10 L were carried out. 2. Process description of RCE-PP The RCE scale up strategy is developed considering the previous data obtained in a RCE-LC (bench scale) [1,6,12]. The RCE fabricated for the laboratory studies, consisted of a 500 cm3 glass reactor with a temperature bath. A 316-type stainless steel cylinder with a 3.8 cm diameter and a length of 11 cm was used as a cathode. Six RuO2 /TiO2 dimensional stable anodes (DSA), 13 cm long, 2 cm wide and 0.3 cm thick, which were attached to the reactor wall and connected to each other, were used as anodes. The experimental study on macro-electrolysis of Cu(II) recovery was performed in a pilot plant RCE reactor (RCE-PP) of 10 L capacity, built using the methodology proposed here (Fig. 1). The RCE-PP is equipped with: (a) rotating cylinder of S316 stainless steel as cathode with a 12 cm diameter and 21.12 cm effective height, (b) six plates of DSA (dimensional stable anodes) made of RuO2 /TiO2 , whose width and thickness were 4 cm and 0.3 cm, respectively; anode plates were connected to power supply by means of screws. The cathode was rotated with a (c) variable revolution engine controller (Yaskawa J1000TM ). The sulfate saturated electrode, SSE (Hg/HgSO4 /K2 SO4(sat) ) was used as reference electrode. The model solution mimicking a rinsing electroplating solution was prepared with analytical grade reactants and deionized water MilliQTM. The Cu(II) concentration was 18.8 mM in 1 M H2 SO4 . The macro-electrolysis was carried out under galvanostatic control: 48.71, 56.08 and 70.54 mA cm−2 . These values were evaluated from the correlation JL = (zi FDC/d)0.014Re0.91 Sc 0.356 reported by Rivera et al. [6,12] (see Section 3.5), using three rotating velocities (600, 700 and 900 rpm). The power supply used was DynaPowerTM connected to midi LOGGER GL200ATM interface, whereas the data acquisition was carried out by means of GL200-800-APS Ver 1.01. The Cu(II) concentration depletion in the liquid bulk as a function of time was followed by atomic absorption spectrophotometer (VarianTM Model 220 FS). 3. Scale-up method for a RCE bench scale electrochemical reactor The strategy used to scale-up RCE-LC to RCE-PP consisted of four issues that were considered the “dominant criteria” in RCE reactor: (a) the new geometric dimensions of RCE-PP; (b) the similitude of hydrodynamic study with computational fluid dynamics (Comsol Multiphysics 3.5a) and dimensionless numbers, i.e. Reynolds and Taylor numbers; (c) the similitude of mass transport study with computational fluid dynamics, and (d) validation of scale-up methodology with experimental data. 3.1. Geometric dimensions of the pilot scale reactor The geometric dimensions of RCE-PP were determined on the basis of RCE-LC geometric dimensions employed in the previous works [1,6]; the dominant similarities were obtained using dimensionless geometric correlations that involved the new volume operation, as well as length and area characteristics of the electrodes (Eqs. (2)–(5)). VR = L(r22 − r12 )

(2)

r2 − r1 = 1.33 r1

(3)

Lef 2r1

= 1.76

Aef = 2r1 Lef

(4) (5)

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Fig. 1. Rotating cylinder electrode electrochemical reactor pilot plant (RCE-PP). (a) Schema of RCE-PP, (b) schema of RCE-PP top view and (c) RCE-PP photography.

where VR is the reactor volume, r1 is the internal radius or cathode radius (cm), r2 is the external radius or reactor shell (cm), Lef and Aef are the effective longitude and area of the electrodes (cm). The RCE-PP reactor volume was fixed at 10 L; the other variables are unknown and they are found by solving equation set (2)–(5). In the present work the counter-electrode thicknesses were not taken into account in order to save costs in the construction of the new RCE-PP. Therefore, the thicknesses of counter-electrodes were similar to those used in RCE-LC.

density, y+ the dimensionless distance to the wall (=y( w /)1/2 /), y the distance to the wall and  the von Karman constant. A schema of the RCE reactor is shown in the Fig. 2, where is represented the geometry of the 2D simulation domain and the regions near to walls of RCE and counter-electrode. To establish the hydrodynamic similitude between the RCELC and RCE-PP, the dimensionless velocity profile calculated in this study and the corresponding Taylor numbers are compared as a function of radius ratio ((r − r1 )/(r2 − r1 )) in both scales.

3.2. Hydrodynamic similitude 3.3. Mass transport similitude The hydrodynamic study under turbulent flow on the liquid bulk within RCE reactor was approximated using the Reynoldsaveraged Navier–Stokes (RANS) equation (Eq. (6)), where the so-called Reynolds stresses are expressed in terms of turbulent viscosity (T ) and the gradient of mean velocity. The turbulent viscosity is specified by Eq. (7) according to the standard k–ε turbulence model. (u · ∇ )u = −∇ P + ∇ · ( + T )(∇ u + ∇ uT ) + F T = C

k ε

Once the hydrodynamics in the RCE has been established, its effect on the mass transport rate has to be determined in order to evaluate the similitude between both scales of RCE and finally

(6) (7)

In these equations, u is the average of velocity vector, P is the average pressure,  is the viscosity, T is the turbulent viscosity, F is any external force,  is the density, C is a turbulence model constant, k is the turbulent kinetic energy and ε is the turbulent energy dissipation rate. Principles and development of RANS equations as well as the k and ε transport equations are given elsewhere [30]. The model is applicable under turbulent and isotropic flow conditions, for that reason the near-wall region is inaccessible for the model due to the decrease in velocity when approaching a solid surface. One way of solving this problem is by using wall functions [30–32], which circumvents the need to solve the transport equations in this region. The wall function based on the universal velocity distribution, given by Eq. (8), is used instead of no-slip boundary condition at the wall for solving Eq. (6). u+ = 5.5 +

1 ln y+ 

(8)

where u+ is a dimensionless velocity (=(u − uw )/( w /)1/2 ), u the velocity, uw the velocity of the wall,  w the wall shear stress,  the

Fig. 2. Schema of the RCE reactor showing the geometry of the 2D simulation domain and the conditions near the RCE and counter-electrode walls. For the sake of clarity only one of the six counter electrodes is depicted.

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the comparison against experimental data. Therefore, the study of the mass transport of Cu(II) from the bulk to the RCE electrode surface was carried out using the approach reported previously [1], as follows. In electrochemical system with no chemical reaction in the bulk solution and under turbulent flow, the material balance of charged species i is given by Eq. (9), where the concentration and velocity fluctuation terms have been grouped into the so-called turbulent diffusion term (·Di,T Ci ) of a Reynolds-averaged mass transport equation, analogous to RANS equation. ∂Ci = −u · ∇ Ci + zi F ∇ · (umi Ci ∇ ˚) + ∇ · (Di + Di,T )∇ Ci ∂t

(9)

where Ci is the average concentration of electroactive species i, t is the temporal variable, zi is the charge number of the ion, F is the Faraday constant, umi is the ionic mobility, ˚ is the electric potential, Di is the diffusion coefficient and Di,T is the turbulent diffusion coefficient. The first term in the right-hand side of Eq. (9) represents the ion transport by convection due to the motion of the fluid with the average velocity u. The second term corresponds to migration of charged species i due to the electric field. The last term describes the movement of specie i by molecular and turbulent diffusion. Eq. (9) must be solved simultaneously with charge balance and electroneutrality equation in order to determine the potential. The problem is simplified, assuming that electroactive species are present in small amounts and a supporting electrolyte is added to electrolytic solution diminishing the effect of electric field. Then, the migration term of Eq. (9) can be neglected and the following equation is obtained. ∂Ci = −u · ∇ Ci + ∇ · (Di + Di,T )∇ Ci ∂t

(10)

Eddy diffusivity or turbulent diffusivity can be evaluated considering analogy between transport phenomena. If eddy diffusivities of heat and mass are assumed to be equivalent to each other (˛T = Di,T ), the respective dimensionless turbulent numbers, PrT and ScT , are equal and Kays–Crawford model [34] can be used in terms of ScT according to Eq. (11).



1 + 2ScT ∞

ScT =





1 − exp



0.3



ScT ∞

T T − 0.3 Di Di

−1

−Di 0.3T





(11)

ScT ∞

where ScT∞ = 0.85. In the model here proposed, Eqs. (10) and (11) might be applied only to the bulk fluid region. In the region close to the wall, a dimensionless concentration distribution C+ can be considered. The following distribution was adapted to the mass transport, where Eq. (12) corresponds to the laminar sublayer and Eq. (13) to the turbulent layer. C + = Sc y+ C + = ScT where

C+

1 

ln y+ + 5.5 + Pc



(12)

layer and can be calculated with the following empirical equation that has provided good results in mass transfer simulation [1,33]. Pc = A

 3/4 Sc ScT

 −1

(15)

where A is a constant whose value (A = 9.24) has been determined from experimental data of heat transfer on smooth pipes. In the case of copper recovery in a RCE-LC the value of A has been determined (A = 2.9) [1]. This value of the constant A takes into account the enhanced mass transport as compared to smooth pipes caused by the dendritic metal deposit. The boundary conditions used for solving Eq. (10) are: (i) wall functions (Eq. (13)) on the surface of the RCE and (ii) impermeable boundary in all other walls (n·(−Di Ci + uCi ) = 0), where n is the vector normal to the surface of the RCE (see Fig. 2). 3.4. Computational strategy for process simulation Transport equations were solved numerically by finite elements using commercial software (Comsol Multiphysics 3.5a). Due to higher computer resources demanded by turbulent flow simulations as the reactor size increases, the transport phenomena of process simulation of Cu(II) recovery were carried out in 2D instead of a 3D simulation domain, since the movement of the fluid is mainly in the azimuthal direction with no important dependence of velocity profile on axial direction (z) [1]. The hydrodynamic model was solved in steady state and the results obtained were stored through the option available in the program, in order to be used in the mass transfer model. Afterwards, the transient diffusion-convection equation (Eq. (10)) along with Kays Crawford model (Eq. (11)) and mass transport wall functions given by Eqs. (13)–(15), were solved using the results of the hydrodynamic calculation: (i) the time-averaged velocity to evaluate the convection term in Eq. (10), (ii) the turbulent viscosity to obtain the turbulent diffusivity through Eq. (11), and (iii) the eddy kinetic energy required in Eq. (14) for evaluating Ji,w from the wall function. Upon verifying numerical solutions reached at different values of y+ and mesh size, the y+ value and mesh size were fixed for solving the hydrodynamics. The time dependent mass transport problem was solved using the same y+ value and mesh size and a time step of 1 s. The following properties were used in the simulation:  = 0.001 kg m−1 s−1 ,  = 1059 kg m−3 and Di = 7.2 × 10−10 m2 s−1 [1]. 3.5. Validation of scale-up methodology 3.5.1. Limit current density for RCE-PP To validate the scale-up it is necessary to keep constant the Taylor number in both scales. The Taylor number was obtained by means of Eq. (16) Ta = Re1/2

(13)

 r−r  1 r2 − r1

(16)

where the Re number is defined by (Eq. (17))

is defined as: Re =

1/4

C+ =

265

(Ci,w − Ci )C k1/2 Ji,w

(14)

Ci,w is the fluid concentration on the solid surface, Ci is the concentration at a distance y+ from the wall and Ji,w is the diffusion flux in the near-wall region. The term Pc takes into account the change of mass transfer resistance from the viscous sublayer to the turbulent

ud 

(17)

where u is the angular velocity of the rotating electrode, cylinder diameter d = 2r1 ,  and  are the density and viscosity of the liquid phase, respectively. The next step was to determine limit current density applied to RCE-PP in order to carry out macro-electrolysis for mass transport similitude validation. The limit current density

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Table 1 Characteristic dimensions used in RCE bench scale and RCE-PP. Dimension characteristics

RCE bench scale

RCE-PP

Internal diameter (2r1 )/cm External diameter (2r2 )/cm Effective high (Lef )/cm Effective area (Aef ) Anode thickness/cm

3.8 8.8 6.7 80 0.3

12 28 21.12 796.2 Hypothetic/actual 3.3/0.3 1.33 1.76

[(r2 − r1 )/r1 ] Lef /2r1

1.33 1.76

was calculated using the following correlation reported in [12] for a RCE bench scale reactor. JL =

zi FDi C 0.014Re0.91 Sc 0.356 d

(18)

Eq. (18) is useful because it incorporates geometry, hydrodynamics, and mass transport coefficients in an implicit way, as well as the electrochemical reaction parameters, where, JL is the limit current density (A cm−2 ), z is the electron number transfer in the electrochemical reaction, F is the Faraday constant (95485 C mol−1 ), Di is the diffusion coefficient of the electroactive species, C0 is the initial concentration of the electroactive species (mol cm−3 ), d is the diameter of the rotating electrode (cm); Re is the Reynolds number (Eq. (17)) and Sc is the Schmidt number (/D). The constant values a = 0.014, b = 0.91, and c = 0.356 are associated with shape and cell dimensions, hydrodynamic and mass transport regimens, respectively. 4. Results and discussion 4.1. Characteristic dimensions of both RCEs The characteristic dimensions found for RCE-PP through equation set (2)–(5) are shown in Table 1, together with the geometric similitude in both scales. These similarities were the interelectrode gap ((r2 − r1 )/r1 ) and length–diameter cathode ratio (L/2r1 ) keeping the same values with a different magnitude of characteristic dimensions used in RCE bench scale and RCE-PP.

Fig. 3. Simulation of the velocity field in the RCE with 6 counter electrodes at Taylor number of 7.84 × 105 . (a) RCE bench scale and (b) RCE-PP with hypothetical thicknesses of the counter-electrode (3.3 cm).

4.2. Velocity profile similitude Fig. 3 shows the velocity field obtained in the simulation at two different scale reactors and the same Taylor number (Ta = 7.84 × 105 ); Fig. 3a corresponds to the RCE bench scale reactor (ω = 91 rpm) and Fig. 3b to RCE-PP with a hypothetical counter-electrode thicknesses (3.3 cm) scaled-up proportionally with respect to RCE bench scale dimensions (ω = 900 rpm). The behavior of dimensionless velocity profile in both scales is very similar; high velocity regions close to the rotating cylinder and stagnant zones near the wall of the reactor vessel are clearly distinguished. It is important to consider that RANS equations were solved from a distance ı of all walls (Fig. 2) so that the velocity field within this small film is not shown in Fig. 3. Fig. 4 shows the dimensionless velocity field simulation results of the RCE-PP with actual counter-electrode thickness (0.3 cm). As can be seen, the behavior of dimensionless velocity profile is different with respect to velocity profile obtained in both RCE bench scale and RCE-PP with a hypothetical counter-electrode thicknesses (Fig. 3). This demonstrates that despite both RCE reactors operate under the same Re and Ta number, the velocity field exhibits non identical behavior. On the other hand, the contour lines included in Fig. 4 show a deformation of the concentric circles pattern caused by the presence of the six plate counter electrode. In the bench scale reactor the velocity field contour lines show the formation

Fig. 4. Simulation of the velocity profile in the RCE-PP with actual counter electrodes (0.3 cm) at Taylor number of 7.84 × 105 .

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counter-electrode. In the first case, the velocity decreases continuously along the r direction and in the second, a plateau between 0.3 and 0.85 of the dimensionless radius is formed. The profiles of the Ta number of the RCE-PP with hypothetical counter-electrode thicknesses follow the same trend of the profiles of the RCE bench scale (overlapped). On the other hand, the profiles of the Ta number of the RCE-PP with actual counter-electrode closely follow the profiles of the bench scale unit with a minor difference, despite the lack of scale-up proportionality with regard to counter-electrode thickness. Although the proportionality of the counter-electrode thickness was not preserved during scale-up procedure, the present methodology considered that preserving the electro-active area in both scales was more important; such hypothesis is confirmed in the next section.

4.3. Mass transport field similitude

Fig. 5. Taylor number as a function of dimensionless radial position in the RCE bench scale and RCE-PP with hypothetical counter-electrode thicknesses (solid line), RCEPP with actual counter-electrode (dashed line); (a) in front of the reactor vessel wall (between two plates) and (b) in front of the counter electrode.

of a nearly regular hexagon, while in the pilot plant reactor the contour lines exhibit more complex pattern. A greater spacing between cathode and counter electrode and small arc length of the 10 L RCE-PP reactor give rise to the formation of a local maximum in front of each counter electrode. This is because the thickness of the counter-electrode was not scaled-up proportionally with respect to RCE bench scale dimensions. When the thickness proportional to RCE bench scale dimensions is taken into account, as was presented in Fig. 3, the flow patterns are similar in both RCE reactors. In order to show more clearly how similar are the hydrodynamic behaviors in both scales, Fig. 5 shows the values of Ta number as a function of the dimensionless radial position in the inter-electrode gap using the following expression (Eq. (16)). Ta = Re1/2

 r−r  1 r2 − r1

where “r” represents the radial position in the inter-electrode gap. Fig. 5a shows the Ta as a function of dimensionless radial position in front of the counter electrode; meanwhile Fig. 5b shows the Ta in front of the reactor vessel wall (between two plates). The solid line represents the Ta behavior of RCE bench scale and RCE-PP with hypothetical counter-electrode thicknesses (overlapped), and the dashed line represents the Ta behavior of RCE-PP with actual

Fig. 6 shows the simulation results of the hydrodynamic effect on the dimensionless concentration field in the RCE bench scale (Fig. 6a), RCE-PP with hypothetical counter-electrode thickness (Fig. 6b), and RCE-PP with actual counter-electrode (Fig. 6c) at Ta = 7.84 × 105 , C0 = 18.8 mM, and t = 1800 s. In all cases, contour lines near to RCE zone are concentric (Fig. 6) following the same hydrodynamic pattern as showed in Fig. 3a, b and 4. In Fig. 6(a) and (b), the dimensionless concentration field are practically similar, however, the dimensionless concentration field in Fig. 6(c) shows minor deviations with respect to RCE bench scale. The main differences are observed near the counter-electrode; in this region, the counter line for RCE bench scale forms a hexagon, while in RCE-PP with a hypothetical counter-electrode thicknesses it presents a minor deformation (practically a concentric circle), which is due to minor counter-electrode thicknesses. On the other hand, near the RCE zone, the counter lines are the same in both cases. In order to show the similarity of mass transport behavior in both reactors, Fig. 7 exhibits the experimental evolution of dimensionless concentration as a function of electrolysis time compared with simulation result at different Ta numbers ((a) Ta = 5.22 × 105 , (b) Ta = 6.09 × 105 , (c) Ta = 7.84 × 105 ). Full symbols and empty symbols correspond to experimental data of copper concentration obtained from galvanostatic electrolysis in RCE bench scale and RCE-PP with actual counter-electrode, respectively. The solid lines represent the simulation results of the RCE bench scale and RCE-PP with hypothetic counter-electrode thicknesses (overlapped lines); dotted lines show the simulation results of the RCE-PP with actual counter-electrode. All simulations were carried out using the same value of the A constant (A = 2.9) reported previously [1]. This value takes into account the increased surface roughness of the electrode, caused by deposition of copper, compared with the value reported (A = 9.24) for heat transport in smooth pipes [1]. The simulation results agree very well with experimental data in both reactors until a dimensionless concentration of C/C0 = 0.4, after which the simulated concentrations are greater than the experimental ones. The faster experimental copper depletion rate is expected considering that, under galvanostatic control, the current applied becomes greater than the limiting current of copper reduction as the electroactive species concentration decreases. The excess of current is used by secondary side reactions, such as the reduction of protons; gas bubbles produced a complete change in hydrodynamics and mass transport, aspects not included in the model. The empirical constant A = 2.9, used previously to fit experimental data of mass transfer in copper recovery in a RCE bench scale [1], in the present study shows to be able to predict the copper

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Fig. 7. Experimental evolution of the dimensionless concentration as a function of electrolysis time ((a) Ta = 5.22 × 105 , (b) Ta = 6.09 × 105 , (c) Ta = 7.84 × 105 ). Symbols represent the experimental data. 䊉 RCE bench scale;  RCE-PP. The lines represent the simulation results. – RCE bench scale and RCE-PP with hypothetical counterelectrode thickness (0.3 cm) (overlapped),·· · · RCE-PP with actual counter-electrode thickness (3.3 cm).

Fig. 6. Simulation of the dimensionless concentration in the RCE reactors with 6 counter electrodes at Ta = 7.84 × 105 . (a) RCE bench scale, (b) RCE-PP with hypothetical counter-electrode thicknesses (3.3 cm), and (c) RCE-PP with actual counter-electrode (0.3 cm).

concentration decay in a larger reactor (32 times the volume and 10 times the cathode area). These results mean that upon varying the reactor size and using three different rotation velocities, the changes in hydrodynamics are taken into account correctly and mass transfer resistance is modified in accordance with the model proposed. In this model, the mechanism of Cu(II) transport towards RCE takes place in different regions. In the bulk region for y+ greater than 22, the transfer takes place principally by turbulent diffusion; and in the near-wall region, turbulent contribution slowly decreases as the distance to

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269

Fig. 8. Experimental mass transfer coefficients (Km ) and those determined by simulation as a function of Taylor number. Experimental data: 䊉 RCE bench scale and  RCE-PP. Simulation results: – RCE bench scale;.–. RCE-PP with actual counterelectrode thickness.

the electrode diminishes until the transfer takes place by molecular diffusion in the viscous sublayer. The magnitude of turbulent diffusivity and thicknesses of different layers, which determine mass transfer rate, depend on the hydrodynamics prevailing in each region. Thus, the constant A operates as a fitting parameter to amplify or diminish the local mass transfer flux for each hydrodynamic condition; for this reason, in the absence of additional phenomena, such as hydrogen gas evolution from the cathode, for example, one single value of A can be sufficient to represent the decay of concentration at different hydrodynamic conditions at the rotating cylinder. Finally, to observe the similarities in the mass transport from the experimental and simulated data to different Taylor numbers, the mass transport coefficient (Km ) was calculated using Eq. (19) and considering that the deposition of copper follows a first-order kinetics. ∂Ci,av ∂t

=

Km ARCE Ci,av VR

(19)

where Ci,av is the average concentration of the electroactive species in the reactor at a determined time, Km the overall mass transfer coefficient, ARCE the surface area of the electrode and VR the reactor volume. In Fig. 8 the symbols represent the experimental mass transfer coefficients ( RCE bench scale and 䊉 RCE-PP), and the lines represent those determined by simulation: (– RCE bench scale;.–. RCE-PP). The mass transport coefficient in copper recovery follows the same trends with a deviation of 0.34% for RCE bench scale and RCE-PP (Fig. 8) confirming the similarity in mass transport. The concordance between experimental mass transfer coefficient and those obtained with simulation in both reactor scales (RCE bench scale and RCE-PP) at three hydrodynamic conditions (Taylor numbers) show that the model takes into proper account the effect of the hydrodynamics in the mass transport.



t

I(t)d(t)

(21)

0

Fig. 9 shows the current efficiency as a function of electrolysis time at different Taylor numbers, 5.22 × 105 , 6.09 × 105 , and 7.84 × 105 . These curves were obtained by the following Eq. (20). zFCVr Qt

where C = (C0 − Ct ) is the concentration difference (mol cm−3 ) and Qt is the total charge in the electrolysis defined as: Qt =

4.4. Current efficiency

ϕ=

Fig. 9. Variation of the current efficiency in the pilot scale reactor with electrolysis time at different Taylor numbers (a) Ta = 5.22 × 105 , (b) Ta = 6.09 × 105 , (c) Ta = 7.84 × 105 .

(20)

The current efficiency diminishes as electrolysis times increases (Fig. 9a–c), this behavior is typical for electrolysis performed in a galvanostatic mode, since the current applied becomes greater than the limiting current of copper reduction as the electroactive species concentration decreases. The excess of current is used by secondary side reactions, such as the reduction of protons; gas

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bubbles produced a complete change in hydrodynamics and mass transport. On the other hand, the electrolysis time where the current efficiency is near 100% raises as Taylor increases.

5. Conclusions A strategy was developed to scale-up a RCE reactor used for copper recovery from rinse water of electroplating industry. Three issues were taken into account in the strategy: (1) the geometric similitude between the laboratory unit and the pilot scale of the RCE reactor where relevant geometrical ratios (interelectrode gap/RCE diameter and RCE length/RCE radius) were kept; (2) the hydrodynamic similitude evaluated through CFD simulation where the velocity profile in the RCE-PP reactor was identical to that in the bench scale RCE reactor (although minor differences in the flow pattern were revealed by velocity contour lines); and (3) the mass transport similitude shown in the CFD simulation where the copper concentration decay curves exhibited the same behavior in both scales of the RCE reactor. The simulations were performed with a widely used fluid flow model (RANS equations, k–ε turbulence model and proper wall functions) and a mass transport model consisting of the averaged convection-diffusion equation, the Kays–Crawford equation in terms of the turbulent Schmidt number and the Launder–Spalding wall functions adapted to mass transport, using the same value of a fitting parameter (A = 2.9) of the mass transport wall function reported previously for the bench scale RCE reactor. The simulation results showed the ability of the model to predict successfully the experimental copper decay in the pre-pilot scale RCE reactor (error < 8%) until 80% of copper recovery. A unique value of parameter A for simulating both scales is a worthy fact, since this opens the possibility to apply the proposed methodology for scaling-up the RCE reactor to a pilot or fully industrial size. In addition, the 2D simulation analysis (instead of 3D simulation), used in this work, saves time and computational resources allowing the efficient scale-up and optimization study of the reactor. On the other hand, the electrolytic removal of Cu(II) using the RCE pre-pilot scale generated the desired copper powders at high angular velocities and high mass transfer rates, with current density (JL ) between 48 and 70 mA cm−2 . Results presented in this study show the pre-pilot-scale RCE to produce similar yields in comparison with laboratory scale reactors reported in the literature. Therefore, the scaling-up of RCE reactors on the basis of the three similarities described in the methodology lead to a reactor design that fulfills the desired operational characteristics.

Acknowledgements Francisco J. Almazán-Ruiz acknowledges the financial support provided by ICyT-DF, México through agreement: ICyTDF/013/2009.

Appendix A. Nomenclature Description

Symbol

Dimensionless numbers Taylor number Reynolds number Schmidt number = /(Di ) Sherwood number Turbulent Schmidt number = T /(Di,T )

Ta Re Sc Sh ScT

Description

Symbol

Units

Internal diameter or diameter of the RCE External diameter Radial coordinate Effective high Effective area Energy consumption Initial concentration of the electroactive species Dimensionless concentration = 1/4 (Ci,w − Ci )C k1/2 /Ji,w Mass transfer flux at the wall Concentration of electroactive species Average concentration of electroactive species Concentration of electroactive species at the wall Constant of the –ε turbulence model Reactor volume Mass transfer coefficient Limit current density Charge number of the ion Ionic mobility Diffusion coefficient Turbulent diffusion coefficient Constant of the Kays–Crawford model Factor of integration of resistances in near-wall layers Empirical constant of equation for Pc Faraday constant Tangential velocity of the cylinder Dimensionless velocity = u/( w /)1/2 Cartesian coordinates Dimensionless distance to the wall = y( w /)1/2 / Vector normal to the wall Velocity vector External force in Navier–Stokes equation Time Pressure Greek letters Turbulent thermal diffusivity Turbulent energy dissipation rate Electric potential Density Viscosity Current efficient Turbulent viscosity Turbulent kinetic energy von Karman constant Angular velocity Wall shear stress Shear stress Thickness of the boundary layer near the wall

2r1 ,d 2r2 r Lef Aef Econ Ci,0 C+

m m m m m2 KW h m−3 mol cm3 –

Ji,w Ci /Cu2+ t Ci,av Ci,w C VR Km JL zi umi Di Di,T ScT∞ Pc

mol cm−2 s−1 mol cm3 mol cm3 mol cm3 – m3 m s−1 mA cm−2 – – m2 s−1 m2 s−1 – –

A F u u+ x, y, z y+

– C mol−1 m s−1 – – –

n u F t P

– – – s Pa

˛T ε ˚   T k  ω w  ı

– – V kg m−3 kg m−1 s−1 – kg m−1 s−1 m2 s−2 m2 s−3 rad s−1 – – –

References [1] E.P. Rivero, P. Granados, F.F. Rivera, M. Cruz, I. Gonzalez, Mass transfer modeling and simulation at a rotating cylinder electrode (RCE) reactor under turbulent flow for copper recovery, Chemical Engineering Science 65 (2010) 3042. [2] J.C. Bazan, J.M. Bisang, Electrochemical removal of tin from dilute aqueous sulfate solutions using a rotating cylinder electrode of expanded metal, Journal of Applied Electrochemistry 34 (2004) 501. [3] J.M. Grau, J.M. Bisang, Removal of cadmium and production of cadmium powder using a continuous undivided electrochemical reactor with a rotating cylinder electrode, Journal of Chemical Technology and Biotechnology 77 (2002) 465. [4] J.M. Grau, J.M. Bisang, Electrochemical removal of tin from dilute aqueous sulfate solutions using a rotating cylinder electrode of expanded metal, Journal of Applied Electrochemistry 37 (2004) 501. [5] M. Hunsom, K. Pruksathorn, S. Damronglerd, H. Vergnes, P. Duverneuil, Electrochemical treatment of heavy metals (Cu2+ , Cr6+ , Ni2+ ) from industrial effluent and modeling of copper reduction, Water Research 39 (2005) 610. [6] F.F. Rivera, I. González, J.L. Nava, Copper removal from an effluent generated by a plastics chromium-plating industry using a rotating cylinder electrode (RCE) reactor, Environmental Technology 29 (2008) 817. [7] M. Eisenberg, C.W. Tobias, C.R. Wilke, Mass transfer at rotating cylinders, Chemical Engineering Progress Symposium Series 51 (1955) 1. [8] J. Low, C. Ponce de Leon, F.C. Walsh, The rotating cylinder electrode (RCE) and its application to the electrodeposition of metals, Australian Journal of Chemistry 58 (2005) 246. [9] G. Kreysa, Elektrochemie mit dreidimensionalen elektrode (Electrochemistry with three-dimensional electrodes), Chemie Ingenieur Technik 55 (1983) 23.

F.J. Almazán-Ruiz et al. / Electrochimica Acta 77 (2012) 262–271 [10] J.M. Grau, J.M. Bisang, Removal of cadmium from dilute aqueous solutions with a rotating cylinder electrode of expanded metal, Journal of Chemical Technology and Biotechnology 78 (2003) 1032. [11] L. Koene, L.J.J. Janssen, Removal of nickel from industrial process liquids, Electrochimica Acta 47 (2001) 695. [12] F.F. Rivera, J.L. Nava, Mass transport studies at rotating cylinder electrode (RCE): influence of using plates and concentric cylinder as counter electrodes, Electrochimica Acta 52 (2007) 5868. ˜ P.E. Jensen, L.M. Ottosen, Electrochemical [13] C. Gutiérrez, H.K. Hansen, P. Nunez, peroxidation as a tool to remove arsenic and copper from smelter wastewater, Journal of Applied Electrochemistry 40 (2010) 1031. [14] J.M. Bisang, F. Bogado, M.O. Rivera, O.L. Dorbessan, Electrochemical removal of arsenic from technical grade phosphoric acid, Journal of Applied Electrochemistry 34 (2004) 375. [15] D.R. Gabe, F.C. Walsh, Enhanced mass transfer at the rotating cylinder electrode: characterization of a smooth cylinder and roughness development in solutions of constant concentration, Journal of Applied Electrochemistry 14 (1984) 555. [16] P.R. Nadebaum, T.Z. Fahidy, The rate of mass transfer at a rotating cylindrical electrode with wiper blades, Canadian Journal of Chemical Engineering 53 (1975) 259. [17] A. Radwan, A. El-Kyar, H.A. Farag, G.H. Sedahmed, The role of mass transfer in the electrolytic reduction of hexavalent chromium at gas evolving rotating cylinders, Journal of Applied Electrochemistry 22 (1992) 1161. [18] A.H. Nahlé, G.W. Reade, F.C. Walsh, Mass transport to reticulated vitreous carbon rotating cylinder electrodes, Journal of Applied Electrochemistry 25 (1955) 450. [19] J.M. Grau, J.M. Bisang, Mass transfer at rotating cylinder electrodes of expanded metal, Journal of Applied Electrochemistry 35 (2005) 285. [20] C.T.J. Low, E.P.L. Roberts, F.C. Walsh, Numerical simulation of the current, potential and concentration distributions along the cathode of a rotating cylinder Hull cell, Electrochimica Acta 52 (2007) 3831. [21] G. Prentice, Electrochemical Engineering Principles, Prentice Hall, NJ, 1991. [22] D.R. Gabe, F.C. Walsh, Enhanced mass transfer at the rotating cylinder electrode. II. Development of roughness for solutions of decreasing concentration, Journal of Applied Electrochemistry 14 (1984) 565.

271

[23] D.R. Gabe, F.C. Walsh, Enhanced mass transfer at the rotating cylinder electrode: III. Pilot and production plant experience, Journal of Applied Electrochemistry 15 (1985) 807. [24] D. Robinson, F.C. Walsh, The performance of a 500 Amp rotating cylinder electrode reactor. Part 1: Current–potential data and single pass studies, Hydrometallurgy 26 (1991) 93. [25] D. Robinson, F.C. Walsh, The performance of a 500 Amp rotating cylinder electrode reactor. Part 2: Batch recirculation studies and overall mass transport, Hydrometallurgy 26 (1991) 115. [26] F.S. Holland. Improvements in or relating to the electrolytic production of metals, British Patent Number 1 505 736, (1978). [27] Ph. Mandin, C. Fabian, D. Lincot, Importance of the density gradient effects in modelling electro deposition process at a rotating cylinder electrode, Electrochimica Acta 51 (2006) 4067. [28] C.A. Real-Ramirez, R. Miranda-Tello, L.F. Hoyos-Reyes, J.I. Gonzalez-Trejo, Hydrodynamic characterization of an electrochemical cell with rotating disc electrode: a three-dimensional biphasic model, International Journal of Chemical Reactor Engineering 8 (2010) 1 (Article A95). [29] J. Deliang Yang, V. Modi, A.C. West, Analysis of Mass Transfer and Fluid Flow for Electrochemical Process. Modern Aspects of Electrochemistry, Academic/Plenum Publishers, New York, 1999. [30] P.S. Bernard, J.M. Wallace, Turbulent Flow: Analysis, Measurement, and Prediction, John Wiley & Sons, NJ, 2002. [31] L. Eς a, M. Hoekstra, Near-wall profiles of mean flow and turbulence quantities predicted by eddy-viscosity turbulence models, International Journal for Numerical Methods in Fluids 63 (2010) 953. [32] D. Lacasse, E. Turgeon, D. Pelletier, On the judicious use of the k–ε model, wall functions and adaptivity, International Journal of Thermal Sciences 43 (2004) 925. [33] F.J. Trujillo, T. Safinski, A.A. Adesina, Solid–liquid mass transfer analysis in a multi-phase tank reactor containing submerged coated inclined-plates: a computational fluid dynamics approach, Chemical Engineering Science 42 (2009) 1143. [34] B. Weigand, J.R. Ferguson, M.E. Crawford, An extended Kays and Crawford turbulent Prandtl number model, International Journal of Heat and Mass Transfer 40 (1997) 4191.