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Nomenclature
C (t) E (t) Q v m ts
V r V d V a V p V s V c 2
K U p a c
1.
outlet tracer concentration (mol/L) residence time distribution function (s−1 ) liquid volumetric flow rate (mL/s) volumetric electrode mass (g) mean residence time (s) theoretical time (s) reactor volume (mL) reactor dead volume (mL) reactor active volume (mL) plug flow reactor volume (mL) continuous stirred tank reactor volume (mL) solution container volume (mL) variance of dispersion first order kinetic constant (min−1 ) fluid velocity (m/s) plug flow reactor residence time (s) continuous stirred tank reactor residence time (s) solution container residence time (s)
Introduction
Uncountable tonnes of precious or toxic metals are discarded each yearin the form of industrial wastewater, usually directly into natural environment. The recovery of metals (Fe, Cu, Al, Ni, Cd, Cr. . .) in diluted solution is an everyday problem associated with ecological and economic aspects. Electrochemical cleaningtechnology offers an efficientway to reduce pollution through the removal of transitions and heavy metal by redox reactions, without the disadvantages of conventional treatments. The inherentadvantage of this technology is its environmental compatibility due to the fact that the main reagent, the electron, is a “clean reagent”. Among the electrochemical processes, cementation is largely used in many industries to remove metal ionsfrom dilute solutions for either liquid purification or metal recovery (Olive and Lacoste, 1979). The kinetics of cementation reaction has been studied by a number of researchers in various electrochemical reactors with different kinds of electrodes such as rotating disc (Donmez et al., 1999), rotating cylinder (EL-Batouti, 2005), powder (Berkani et al., 1990), fixed and fluidized beds (Gros et al., 2005), volumetric electrode (Djoudi, 2007). The hydrodynamic behavior of electrolyte in volumetric electrode reactors is not well documented despite its importance for understanding and eventually optimizing the process. Hydrodynamics within real reactors never fully follow an ideal flow pattern and deviations appear due to fluid channeling and recycling, or stagnant regions in the vessel. These deviations lead to efficiency losses at pilot plant scale or at fully industrial scale. Therefore it is important to take into account thenon ideal flow pattern insidethe reactorsto determine the real reactor behavior (Levenspiel, 1999). One of the most usual methods to characterize the flow characteristics within a system consists in the measurement of residence time distribution (RTD). The residence time distribution (RTD) is a chemical engineering concept introduced by Dankwerts in 1953. It has been described in a multitude of scientific papers and applied for various industrial processes.
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The developmentof computerfluid dynamicsallowed improving the comprehension and optimization of such method. However, this approach remains difficult in case of complex reactors and electrodes. Therefore the extension of RTD concept is an alternative way to obtain information about hydrodynamics and help thusto improvethe process behavior knowledge (Leclerc et al., 2000). Literature reports a number of works using RTD method to determine the performance of various types of reactorsinvolving volumetric electrodes as turbulence enhancers (Andrade Lima et al., 2005; Tembhurkar and Mhaisalkar, 2006; XiaoChang et al., 2009; Yuan et al., 2004; Saravanathamizhan et al., 2008; Furman et al., 2005). This paper is a continuation of our previous works (Djoudi, 2007; Djoudi et al., 2007) to study the kinetics and to optimize the yield of copper cementation process in a laboratory-scale tubular reactor containing a new type of volumetric electrode used as turbulence promoter. In the current study, for reactor design and scale-up purposes, the residence time distribution (RTD) analysis is used as a tool to study the performances of thereactor andevaluate the flow behavior in the objective to develop a model. RTD data are measured by the “stimulus–response” technique using KCl solution as a tracer and interpreted with a suitable mathematical model owing to an industrial software package “DTS.PRO 4.2”.
2.
Materials and methods
RTD experiments were carried out using the apparatus schematically shown in Fig. 1. The laboratory-scale tubular reactor is made of 440 mm length glass tube of 50mm diameter and total volume of 863.5mL. It inlet zone is packed with glass spheres of 10mm diameter in order to distribute the fluid uniformly and to support the volumetric electrode. The volumetric electrode made of iron as grill in zigzag form is located in the reactor at different masses (0g, 10g and 20g). It is similar to that usedin our previous works devoted to study kinetics and process modeling for copper cementation (Djoudi, 2007; Djoudi et al., 2007). Its geometrical characteristics are shown in Fig. 2.
Fig. 1 – Schematic representation of the experimental device: (1) electrochemical reactor; (2) centrifugal pump; (3) glass container; (4) valve; (5) fow-meter; (6) bypass; (7) tracer injection zone; (8) conductivity electrode; (9) conductivity meter; (10) tracer evacuation container.
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Fig. 2 – Volumetric electrode characteristics.
The procedures adopted for the stimulus–response experiments are as follows. First, the reactor was continuously fed with distilled water at 25 ◦ C by a centrifugal pump at different flow rates (1L/min, 2L/min, 3L/min and 5 L/min). When the steady-state regime is established, 5 mL of KCl solution used as tracer are manually injected at thereactor inlet by a syringe as -Dirac pulse. At the reactor outlet, a conductivity electrode is located within the pipe to measure the conductivity with a Conductivity Meter (Ec 214 HANNA instruments) after suitable calibration with 0.01 N KCl solution. Conductivity measurements were performed with KCl solution of 3 mol/L and the data were collected each 3 s.
3.
Results and discussions
3.1.
Results
Fig. 3 – Effect of the flow rate on the residence time distribution at different mass of volumetric electrode.
The characteristic parameters of flowdynamics in the reactor can be extracted through modeling the experimental RTD curves investigated at different operating conditions. These parameters are defined in Table 1 and theirvalues are provided in Table 2. 3.2.
The principle of tracer experiments consists of a common impulse method: injection of a tracer at the inlet of a system and recording RTD distribution function E (t) at the outlet. For the exploitation of experimental RTDs, literature (Andrade Lima et al., 2005; Tembhurkar and Mhaisalkar, 2006; XiaoChang et al., 2009; Yuan et al., 2004; Saravanathamizhan et al., 2008) lists various methods: - Analysis in terms of statistical moments that yields at least theoretically to some global parameters as mean residence time (MRT) and dispersivity; - Adjustment of a model for flow parameters. The tracer conductance–time curve is called concentration (C) curves in RTD analysis and allowed to derive the age distribution frequency E (t) of the fluid elements leaving thereactor, which describes in a quantitative manner how long a fraction of fluid spent in the reactor, from: E( t) =
CC((tt)) dt ∞
Discussions
Fig. 3 shows the influence of tracer flow rate on RTD in the absence or the presence of volumetric electrode in the reactor used as turbulence promoter. In all cases, we note that, at low flow rates (1L/min and 2L/min), the RTD curves has a long tail and the residence time of tracer is comparatively large according to the results summarized in Table 1. At high liquid flow rates (3L/min and 5 L/min), the RTD curves becomes much narrow with a shorter tail. Similar results are obtained in literature (Yuan et al., 2004). The presence of tail in RTD curves under some conditions indicates the presence of stagnantzones or deadvolumein the reactor, which decreases with increasing of volumetric electrode mass (Table 2). For example, at a low flow rate (1L/min), the dead volume fraction (V d /V r = (1 − (tS / ) )) is equal to 34.27% Table 1 – Definition of different parameters ( Levenspiel, 1999; Villermaux, 1993).
Variable (1)
0
The tracer response curves ( E (t) curves) are plotted at different flow rates and at different masses of the volumetric electrode as shown in Fig. 3.
Mean residence time ( ts ) Theoretical time ( ) Dead volume (V d ) Active volume (V a ) Variance of dispersion ( 2 )
Definition ∞
( ) 1 V = V V ( ) tS
t·E t
=
0 V r = Q v
V d
=
r−
a
2
−
∞
=
0
tS
·
dt
·
V r
d
t − tS
2
·
E(t) · dt
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Table 2 – Experimental parameters calculated at different operating conditions (the reactor volume V r = 863.5 mL). Q v (L/min)
Q v (mL/s)
ts (s)
(s)
V d (mL)
V a (mL)
V d /V r (%)
m = 0 g
1 2 3 5
16.67 33.33 50.00 83.33
34.06 13.8 8.99 6.16
51.83 25.91 17.27 10.36
295.98 403.59 414 350.067
567.52 459.91 449.5 513.43
34.27 46.73 47.94 40.54
m =10g
1 2 3 5
16.67 33.33 50.00 83.33
39.1 17.71 13.16 9.65
51.83 25.91 17.27 10.36
212.08 273.28 205.5 59.18
651.42 590.22 658 804.32
24.56 31.64 23.79 6.85
m =20g
1 2 3 5
16.67 33.33 50.00 83.33
48.09 21.35 13.61 10.98
51.83 25.91 17.27 10.36
62.31 151.97 183 –
801.19 711.53 680.5 –
7.21 17.59 21.19 –
in the absence of volumetric electrode and decreases whenthe electrode mass m increases: 24.56% for m =10g and 7.21% for m = 20g. The same result is obtained at other flow rate values (2L/min, 3 L/min and 5 L/min). We can deduce that increasing the volumetric electrode mass contributes to reduce the dead volume fraction in the reactor and thus improve the cementation reaction. The presence of dead volume is confirmed by the values of the estimated mean residence time (ts ) that are smaller than the theoretical time in all cases except at high electrode mass( m = 20g) and at high flow rate (5L/min) where ts = . This implies that dead volumes areabsentand theliquid flow in the packed reactor tends to plug flow under these last conditions. Similar conclusions have also drawn by many authors using other types of volumetric electrodes (Xiao-Chang et al., 2009; Yuan et al., 2004; Saravanathamizhan et al., 2008; Furman et al., 2005). Theflowrateof5L/minoffers,inallcasesunderstudy,good working conditions because the corresponding RTD curves (Fig. 3) do not present any tailing and the dead volumes are minimal (Table 2) and even absent at highvolumetric electrode mass (m =20g). 3.3.
Mathematical model
More parameters of the flow dynamics can be extracted through modeling the experimental RTD curve, two classes of models are widely utilized: models with lumped parameters (compartment models-perfect mixing, plug flow, etc.) and dispersion model. In our case, the software used for flow
process modeling is the “DTS PRO 4.2” package. A software package has been developed to simulate the response to an input of any complex network of elementary reactors properly interconnected. Eight different elementary reactors of the software package may be chosen that are based on the perfect mixer and dispersion models. The parameters can be optimized by comparing the experimental data to the model response (Leclerc et al., 2000; Furman et al., 2005; Gros, 2005). Among the various flow models offered by the software, the arrangement of one plug flow reactor and three stirredtanks reactors in series appeared to be the most suitable to describe the hydrodynamics of the reactor under study. The same results were obtained from hydrodynamic studies in fixed and fluidized beds reactor for flow process modeling using “DTS PRO 4.2” package (Gros, 2005). Fig. 4 shows the comparison of simulated RTD curves with experimental data, of exit age distribution function E (t), at different operating conditions. It can be observed from these figures that the model predictions are in good agreement with the experimental results. The results of comparison between simulated and experimental data of mean residence time and variance are summarized in Table 3. From Table 3, it can be seen in general that, as the inlet flow rate increases, the mean residence time and the variance of RTD decrease proportionally. This result can be explained according to literature (Xiao-Chang et al., 2009) by the fact that the liquid flow in the reactor packed with volumetric electrode tends to plug flow with increasing of flow rate.
Table 3 – Comparison between numerical and experimental data of the mean residence time and variance.
Flow rate
m (g)
Q v (L/min)
Variance 2
Mean residence time ts (s) Simulated
Experimental
Simulated
Experimental
1 1 1
0 10 20
34.32 39.59 48.56
34.064 39.1 48.09
155.92 506.58 253.61
198.68 993 265.85
2 2 2
0 10 20
13.73 17.21 21.09
13.8 17.7 21.35
43.83 46.58 109.02
56.6 54.8 116.25
3 3 3
0 10 20
8.67 12.64 12.18
8.99 13.16 13.61
18.64 25.54 23.38
25 17.93 31.75
5 5 5
0 10 20
6.07 9.07 10.89
6.16 9.65 10.98
9.61 28.13 12.02
31.85 33.86 25.45
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Fig. 4 – Comparison of RTD curves by simulation with experimental data.
plug flow reactor, the three continuous stirred tank reactors and to the solution container respectively (Eqs. (2)–(6)). At least, the experimental observations of copper concentration kinetics are compared with theoretically calculated values of the model. The mass balance of the plug flow reactor is:
4. Model validation in copper cementation process The model developed by “DTS PRO 4.2” package of the electrochemical tubular reactor studied shown in Fig. 5 is applied in the case of cementation reaction. This step involves the application of the mass balance equation for the first order cementation reaction at unsteady state at the output of the
dC1 (x, t) dt
+
U
dC1 ( x, t) dx
= −K ·
C1 ( x, t)
Tubular reactor C1(x,t) V p, τ p
C2(t)
C3(t)
vs
vs
vs
C4(t)
Qv, C(t) vc Copper solution container
Fig. 5 – Schematic representation of the modeled reactor for copper cementation process.
(2)
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Fig. 6 – Comparison of model simulations with experimental observations of exit copper concentration.
The mass balance of the first continuous stirred tank reactor is:
a
dC2 ( t) dt
+
(1 + K · a ) · C2 (t) = C1 (x, t)
(3)
The mass balance of the second continuous stirred tank reactor is:
a
dC3 (t) dt
+
(1 + K · a ) · C3 (t) = C2 (t)
(4)
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Table 4 – The first order kinetic constant values from the copper cementation reaction ( Djoudi, 2007). Q v (L/min)
K (min−1 )
m =10g
1 2 3 5
0.011 0.0151 0.0162 0.0203
m =20g
1 2 3 5
0.0225 0.0291 0.0449 0.0586
Themass balance of thethird continuous stirred tank reactor is: a
dC4 ( t) dt
+
(1 + K · a ) · C4 (t) = C3 (t)
dC(t) dt
(t) = C4 (t)
(6)
+C
where: C1 (x, t), C2 (t), C3 (t), C4 (t) and C (t) are the concentration of copper at the exit of each reactor; K is the first order kinetic constant; U is the fluid velocity; p is the plug flow reactor residence time ( p = V p /Q v ); a is the continuous stirred tank reactor residence time ( a = V s /Q v ); c is the solution container residence time ( c = V c /Q v ); V p , V s are the plug flow and continuous stirred tank reactor volumes, respectively; V c is the solution container volume (V c =5L). Analytical solutions of Eqs. (2)–(6) f o r the exit copper concentration for each reactor are given as follow (Stanley and Walas, 1991): x C1 (x, t) = C0 · exp −K U
C2 (t) C1 (t)
=
C3 (t) C2 (t)
=
C4 (t) C3 ( t)
=
1 1 + K · a
1
1 + K · a 1 1 + K · a
=
C0 · exp(−K · t)
1 − exp [−(1 + K a )] ·
t a
C(t) = C4 ( t) + (C0 − C4 (t)) · exp
t −
c
(8)
a
1 − exp [−(1 + K a )]
(7)
t
t 1 − exp [−(1 + K a )] a
Conclusions
To complete our previous works about copper removal by cementation process, in a laboratory-scale tubular reactor containing a new type of volumetric electrode (grill in zigzag) used as a turbulence promoter; it was interesting to characterize the hydrodynamics behavior of the electrolyte in our reactor for further development and process optimization. This objective was reached by using a pulse tracer technique that is allowing simple on-line measurements of the flow parameters and the diagnosis of stagnant volume and by-pass zones. Some experimental parameters were determined at various operating conditions such as mean residence time (MRT), dead volume fraction and dispersivity. The analysis of residence time distribution curves provided the following relevant results:
(5)
If we consider the copper solution container as a continuous stirred tank reactor; it mass balance is as follows: c
5.
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(9)
(10)
(11)
The rate constant K was calculated from the experimental observations of copper cementation reaction kinetics at different operating conditions (the results of kinetics are not reported in this present study). These values (Table 4) were used in Eqs. (7)–(11) f or theoretical predictions. The comparison of the experimental observations with the model predictions are shown in Fig. 6. From Fig. 6, it can be observed that the concentration evolutions of copper concentration in the reactor studied are satisfactory matching with the theoretical concentration evolution given by the model.
- At low flow rates, the RTD curves present long tails and the mean residence time (MRT) are smaller than the theoretical time thus indicating the presence of dead volumes that are reduced with the increasing of the volumetric electrode mass. - The flow profile approaches to plug flow when the reactor works at high flow rate (5L/min) and at high electrode mass (20 g), these parameter values representing the optimal conditions of operating parameters. - From the variety of flow models offered by the software used, the arrangement of one plug flow reactor and three stirred tank reactors in series appeared to be the most suitable to describe the hydrodynamics of the reactor under study. - Themodel developed cansuccessfullyrepresent thegeneral behavior of the fluid inside the reactor in the case of copper cementation reaction at different operating conditions.
References Andrade Lima, L.R.P., Hodouin, D., 2005. Residence time distribution of an industrial mechanically agitated cyanidation tank. Miner. Eng. 18, 613–621. Berkani, A., Ozil, P., Delachaume, J.C., Caire, J.P., 1990. Cémentation électrochimique en réacteur agité: Etude du couple Cu2+ /Zn en milieu sulfate. Récents progrès en génie des procédés. Edition Lavoisier 5, 16, Grenoble, France, 223. Djoudi, W., 2007. Modélisation et optimisation du procédé de cémentation du cuivre dans un réacteur tubulaire à électrode volumique. Thèse de magister, université de Béjaia. Djoudi, W., Aissani-Benissad, F., Bourouina-Bacha, S., 2007. Optimization of copper cementation process by iron using central composite design experiments. Chem. Eng. J. 133, 1–6. Donmez, B., Servim, F., Sarac¸, H., 1999. A kinetic study of the cementation of copper from sulphate solution onto a rotating aluminium disc. Hydrometallurgy 53, 145–154. EL-Batouti, M., 2005. Removal of copper metal by cementation using a rotating iron cylinder. J. Colloid Interface Sci. 283, 123–129. Furman, L., Leclerc, J.-P., Stegowski, Z., 2005. Tracer investigation of a packed column under variable flow. Chem. Eng. Sci. 60, 3043–3048. Gros, F., 2005. Récupération intensifiée du cuivre en solution: cémentation électrochimique sur lits fixe et fluidisé, mono ou bicomposant, sous champs électromagnétique. Thèse de doctorat, Institut polytechnique de Grenoble. Gros, F., Baup, S., Aurousseau, M., 2005. Récupération intensifiée de métaux en solution: cémentation en lit fixe ou fluidisé sous
chemical engineering researchand design 9 0 ( 2 0 1 2 )
champ électromagnétique. Récents Progrès en Génie des Procédés, Numéro 92. Edition SFGP, Paris, France, pp. 1–8. Leclerc, J.-P., Claudel, S., Lintz, H-G., Potier, O., Antoine, B., 2000. Theoretical interpretation of residence time distribution measurements in industrial processes. Oil Gas Sci. Technol. 55, 159–169. Levenspiel, O., 1999. Chemical Reaction Engineering, third edition. John Wiley & sons, New York. Olive, H., Lacoste, G., 1979. Application of volumetric electrodes to the recuperation of metals in industrial effluents. Mass transfer in fixed beds of spherical conductive particles. Electrochim. Acta 24, 1109–1114. Saravanathamizhan, R., Paranthaman, R., Balasubramanian, N., Ahmed Basha, C., 2008. Residence time distribution in continuous stirred tank electrochemical reactor. Chem. Eng. J. 142, 209–216.
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Stanley, Walas, M., 1991. Modeling with Differential Equation in Chemical Engineering. Butterworth-Heinemann. Tembhurkar, A.R., Mhaisalkar, V.A., 2006. Study of hydrodynamic behavior of a laboratory scale up flow anaerobic fixed film fixed bed reactor. J. Environ. Sci. Eng. 48, 75–80. Villermaux, J., 1993. Génie de la réaction chimique: Conception et fonctionnement des réacteurs. Edition Tec & Doc-Lavoisier. Xiao-Chang, C., Ting-An, Z., Qiu-Yue, Z., 2009. Computational simulation of fluid dynamics in a tubular stirred reactor. Trans. Nonferrous Met. Soc. China 19, 489–495. Yuan, Y., Han, M., Wang, D., Jin, Y., 2004. Liquid phase residence time distribution for two-phase countercurrent flow in a packed column with a novel internal. Chem. Eng. Process. 43, 1469–1474.
