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A simple model to predict the removal of oil suspensions from water using the electrocoagulation technique
Chemical Engineering Science 61 (2006) 1237 – 1246 www.elsevier.com/locate/ces
A simple model to predict the removal of oil suspensions from water using the electrocoagulation technique Manuel Carmonaa,∗ , Mohamed Khemisb , Jean-Pierre Leclercb , François Lapicqueb a Department of Chemical Engineering, University of Castilla—La Mancha, Avda. de Camilo José Cela s/n, 13004 Ciudad Real, Spain b Laboratoire des Sciences du Génie Chimique, CNRS-ENSIC, BP 451, F-54001 Nancy, France
Received 30 November 2004; received in revised form 26 July 2005; accepted 23 August 2005 Available online 30 September 2005
Abstract A simple model has been developed to predict the removal of hydrocarbon fractions from wastewater using sacrificial Al anodes. The model was successfully applied to the interpretation of experimental data obtained in a laboratory electrochemical cell operated in a batchwise manner. The adsorption equilibrium of organic matter on Al hydroxide was modelled using three equations, with the best results obtained using a Langmuir-type equation. The model was able to describe the effects of current density and pollutant concentration on the efficiency of wastewater treatment. Different values were obtained for the parameters depending on the nature of the hydrocarbon suspension. Aluminium hydroxide showed a far higher affinity for the oil/kerosene suspension but exhibited a higher capacity to remove heavy oil suspensions. The removal rates of pollutants were found to depend on the initial concentration and the current density. When the current density was sufficient to destabilise the emulsion, the zeta potential of the clear fraction measured at pH 7.0 became positive. This change was also characterised by a significant reduction in turbidity. Furthermore, the application of higher current densities did not allow further treatment of the water. However, the efficiency of emulsion destabilisation was found to depend on the concentration and current densities that were too low were ineffective. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Adsorption; Emulsion; Turbidity; Zeta potential
1. Introduction Oil/water (O/W) emulsions are widely used in metal industries, e.g., rolling mills, forges and metal workshops, because these emulsions exhibit properties that include lubrication, surface cooling, cleaning and corrosion prevention—all of which are required by metals under mechanical operations. The main problem encountered with O/W emulsions is the substantial degradation of some components with time at the working temperature, which usually ranges from 45 ◦ C to 90 ◦ C. These emulsions therefore need to be regularly replaced, often several times per year. The emulsions have high oil contents, in the range 1 × 10−1 –30 kg/m3 depending on the specific application, and metal contents and used oil suspensions are toxic and must be treated in such a way that water recycling is possible.
∗ Corresponding author. Tel.: +34 926 295437; fax: +34 926 295318.
E-mail address: [email protected] (M. Carmona). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.08.030
According to current environmental regulations, hydrocarbon concentrations in wastewater must be below 1 × 10−2 kg/m3 (Ríos et al., 1998). Several techniques have been applied to treat these types of waste. Lin and Lan (1998) used combined ultrafiltration and ion exchange, reaching removal yields up to 91%. Ríos et al. (1998) employed inorganic salts as coagulants and removed more than 90% of the initial oil content. Oil destabilisation was reported by these authors to be favoured at higher temperatures. Poolea and Cord-Ruwisch (2004) described the ability of the aerobic microbial cultures to destabilise the emulsion and found that removal yields could reach 97% after 7 days of treatment. Mostefa and Tir (2004) found that electrochemical methods in combination with a chemical process were suitable for the separation of oil from oily wastewater and achieved a separation yield of almost 99% in the treatment of a concentrated emulsion of 4 w/w%. Electrocoagulation has been used for the treatment of wastewater by various authors, and several differences were found in comparison to the chemical
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coagulation process (Kumar et al., 2004; Larue and Vorobiev, 2003; Holt et al., 2002). Electrocoagulation (EC) is an effective process for the destabilisation of finely dispersed particles by removing hydrocarbons, greases, suspended solids and even heavy metals from different types of waste water (Inan et al., 2004; Kumar et al., 2004; Chen et al., 2002; Sanchez-Calvo et al., 2003; Saur et al., 1996; Hosny, 1996). Aluminium or iron are usually used as electrodes and their cations are generated by dissolution of sacrificial anodes upon the application of a direct current. The metal ions generated are hydrolysed in the electrochemical cell to produce metal hydroxide ions and only neutral M(OH)3 has a very low solubility (Duan and Gregory, 2003), mainly at pH values in the range 6.0–7.0 (Pinotti and Zaritzky, 2001; Gregor et al., 1997). Metal species react with negatively charged particles in the water to form flocs (Chen et al., 2002; Saur et al., 1996). The in situ generation of coagulants means that electrocoagulation processes do not require the addition of any chemicals. The gases produced during the electrolysis of water and metal dissolution (Picard et al., 2000) allow the resulting flocs to flotate (Saur et al., 1996). Although the electrocoagulation technique has been available for more than a century, it now appears now to be one of the most effective approaches. The design of an industrial plant and an electrocoagulation cell is mainly based on empirical knowledge, with little consideration of the electrocoagulation mechanism (Sanchez-Calvo et al., 2003). Hosny (1996) used a pseudo-first order kinetic with respect to the oil concentration to predict its time variation at different current densities with good accuracy. Nevertheless, this model is not able to predict oil removal when the concentration tends to its asymptotic level at the end of the operation. In addition, this approach does not provide physical interpretation of the oil removal process from the liquid phase. The present paper involves the description of a simple model for the prediction of the elimination of suspended organic matter and this relies upon the adsorption properties exhibited by aluminium hydroxide complexes (Inan et al., 2004; Kumar et al., 2004; Bache and Papavasilopoulos, 2003). The main objectives of the present study, which was conducted with two different organic emulsions, are asfollows: (i) To develop a mathematical model that allows the prediction of the decrease in the amount of organic suspensions in the liquid phase with time, taking into account the physicochemical interactions between the organic matter and aluminium hydroxides at pH values > 6.5. Kobya et al. (2003) found that under these conditions the interactions can be considered as being due to physical adsorption of the organic matter on the coagulants. (ii) To evaluate the effects of the various physical parameters on the adsorption isotherm. (iii) To select the most suitable adsorption model for the reliable prediction of the course of electrocoagulation runs for the removal O/W emulsions from wastewater.
2. Mathematical model Model equations were derived on the basis of the following simplifying assumptions: (i) The amount of aluminium (Al3+ ) that is produced in the cell is times higher than the value predicted by Faraday’s law. Experiments carried out by Khemis et al. (2004) with Al electrodes showed that the quantity of Al species dissolved was higher than the value predicted by Faraday’s law at alkaline pH for current densities varying from 100 to 300 A/m2 , with little effect on the nature of the suspended matter. The value of was taken as 1.5 in the application of the model and this is in accordance with experimental data published previously. Indeed, oxidation of aluminium is produced in two ways: electrochemical oxidation at the anode and chemical attack on both electrode surfaces (Cañizares et al., 2005; Kobya et al., 2003; Picard et al., 2000; Chen et al., 2000). The electrochemical oxidation reaction at the anode is represented as Al0 ⇒ Al3+ + 3e− .
(1)
The presence of chloride ions catalyses the aluminium corrosion and this corrosion can produce more aluminium hydroxide flocs (Shen et al., 2003). The cathode may be chemically attacked by OH− at high pH values with a high rate of hydrogen formation (Bayramoglu et al., 2004). Thus, the following overall reactions Eqs. (2) and (3) can enhance the dissolution of aluminium on the surface of the two electrodes depending on the pH (Chen et al., 2000). 2Al0 + 6H+ ⇒ 2Al3+ + 3H2(g) ,
(2)
2Al0 + 6H2 O + 2OH− ⇒ 2Al(OH)− 4 + 3H2(g) .
(3)
In addition, the water reduction occurs on the cathode and leads to a great formation of OH− ions. These ions favor the aluminium dissolution as mentioned above. 2H2 O + 2e− ⇒ 2OH− + H2(g) .
(4)
(ii) The Al3+ species produced in the cell is entirely converted to aluminium hydroxide Al(OH)3 in the reactor under the physicochemical conditions of the process. This assumption is consistent with the electrocoagulation mechanism proposed by Saur et al. (1996) in which the reaction leading to Al complex formation is fast and leads to various forms of hydroxide. Al(OH)3 is the main species for pH values close to 7, according to the predominant zone diagram for aluminium hydroxide (Holt et al., 2002). (iii) The metal hydroxides form the nucleus of colloidal particles and adsorption takes place around the nucleus (Inan et al., 2004). (iv) Solute concentration gradients do not exist inside the solid particle: the concentration inside the particle is the external solid concentration or the equilibrium concentration. Growth of the solid particles around the hydroxide
M. Carmona et al. / Chemical Engineering Science 61 (2006) 1237 – 1246
nanoparticles is ensured by the adsorption of organic matter: initial solid particles are small in size and they grow by adsorption of organic species. The adsorption changes the properties of aluminium hydroxide and allows flotation. (v) The solid phase is always in equilibrium with the liquid phase. Freshly formed “sweep flocs” of amorphous Al(OH)3 have a large surface area and this allows a rapid external mass transfer rate: the overall process of adsorption and trapping of colloidal particles is therefore a fast process (Kobya et al., 2003). (vi) The oil does not undergo any chemical reaction within the reactor. Taking into account the assumptions outlined above, the model was developed as follows: The flux of Al3+ species produced in the cell is given by NAl3+ =
I , nI
(5)
where is the faradaic yield of Al dissolution, I is the current, n is the number of electrons involved in the anode oxidation, and I is the Faraday constant. Taking into account assumption (ii), Eq. (5) becomes m ˙ Al(OH)3 =
I PMAl(OH)3 , nI
(6)
where m ˙ Al(OH)3 is the weight flux of Al(OH)3 and PMAl(OH)3 is the molecular weight of the Al(OH)3 . The cell considered in the model was a parallel plate electrode reactor, as used in previous investigations (Khemis et al., 2004). The hydrodynamic behaviour of the electrochemical cell was assumed to be that of a plug flow reactor. Despite gas formation, the liquid flow rate in the cell was assumed to be unchanged. The mass balance for Al hydroxide in the cell can be written as c jCAl(III)
jt
= −u
c jCAl(III)
jx
i PMAl(OH)3 , + h nI
(7)
c where CAl(III) is the aluminium hydroxide concentration in the electrocoagulation cell at x, h is the electrode gap, CAl(III) is the aluminium hydroxide concentration in the reactor, i the current density and u is the superficial velocity. Initial and boundary conditions for the electrochemical cell are:
t = 0;
0 < x L;
t > 0;
x = 0;
c CAl(III) = 0,
c CAl(III) = CAl(III) ,
(8)
dCAl(III) V c = F (CAl(III) |x=L − CAl(III) ), dt
Eq. (11) is a Langmuir-type empirical equation (LTEE) derived from ion exchange and has been successfully applied in various investigations (Monteagudo et al., 2003; Bilba et al., 1999; De Lucas et al., 1998; Fernández et al., 1995; Costa et al., 1984). q∗ =
n∞ KC ∗ , C0 + (K − 1)C ∗
(11)
where n∞ is the aluminium hydroxide capacity, q ∗ and C ∗ are, respectively, the solid and liquid phase equilibrium concentrations, C0 is the initial organic concentration, and K is the separation factor. Eq. (12) is the Langmuir equation (LE) that has been used for various gas–solid and liquid–solid isotherms. This equation is applicable for monolayer models, assuming that all active sites of the solid have the same affinity for the solute under investigation (Chern and Chien, 2002; Langmuir, 1915). q∗ =
∗ n∞ I KI C , 1 + KI C ∗
(12)
where n∞ I is the total monolayer capacity of the Al hydroxide and KI is the conditional Langmuir equilibrium constant. Eq. (13) is the Freundlich isotherm (FE), which is a consecutive layer model with unlimited sorption sites (Chern and Chien, 2002; Freundlich and Heller, 1939). q ∗ = KII C ∗m ,
(13)
where KII is the conditional Freundlich stability constant and m is the mass action stoichiometric coefficient, which is equal to or lower than unity. Taking into account assumptions (iv) and (v), the mass balance between the liquid and the solid phase at the equilibrium condition can be expressed as follows: q∗ =
C0 − C ∗ . CAl(III)
(14)
The two-equation system was solved for each isotherm model considered and this yielded the following relations: For LTEE, the solution depends on the K value: If K = 1, −
C ∗2 +
C02 = 0, K −1
(9) If K = 1,
where L is the electrode length. The mass balance for the stirred-tank reactor is
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C∗ =
(C0 (2 − K) + n∞ KC Al(III) ) ∗ C K −1 (15)
C02 . C0 + n∞ CAl(III)
(16)
For the Langmuir isotherm, (10)
where V is the volume of the reactor and F is the liquid recirculation flow rate. Three different adsorption equilibrium isotherms were tested in order to model the experimental data.
C ∗2 +
C2 (1 + n∞ I KI CAl(III) − KI C0 ) ∗ C − 0 = 0. KI KI
(17)
For the Freundlich isotherm, KII CAl(III) C ∗m + C ∗ − C0 = 0.
(18)
M. Carmona et al. / Chemical Engineering Science 61 (2006) 1237 – 1246
The final model is formed by three equations, namely the partial differential equation (7), differential equation (10) and finally, one of Eqs. (15)–(18)—the choice of which depends on the isotherm used. Partial differential equation (7) is transformed into a system of l ordinary differential equations, with l being the number of nodes along the length of the cell. The l + 1 differential equations were integrated numerically by the fourth-order Runge–Kutta method (Press et al., 1992). In the case of the Freundlich isotherm, the Newton–Raphson method was used to find the positive root of Eq. (18) (Press et al., 1992). Two parameters are involved in the adsorption isotherm; Marquardt’s algorithm (Marquardt, 1963) was used to estimate these parameters from the experimental data obtained in the present work or reported previously (Khemis et al., 2004). A visual basic application was developed for the calculations.
1.0 Concentration of Al3+ [kg/m3]
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Model
0.8 0.6 0.4 0.2 0.0 0
500
1000
1500 Time [s]
2000
2500
3000
Fig. 1. Flow effect on the gradient of aluminium hydroxide concentration between the EC cell and the reactor.
3. Simulation results 1.0 100 A/m2 200 A/m2 300 A/m2
0.8
C/C0
0.6 0.4 0.2
0
1000
2000
3000 Time [s]
4000
5000
6000
Fig. 2. Effects of the current density on the adsorption curves, C/C0 vs. t (F = 6.2 × 10−6 m3 /s; K = 1.1; n∞ = 10 kg/kg; C0 = 50 kg/m3 ).
1.0 K=1 K=10 K=50
0.8 0.6 C/C0
Simulations were carried out to observe the effect of physical parameters on the treatment process. The electrochemical cell described in the experimental section was considered for the calculations. Initial tests showed the low impact of the number of nodes, i.e., the number of stirred vessels in the cascade simulating the plug flow. In fact, modelling the cell by a single stirred vessel led to Al hydroxide concentrations that were 3% lower in the tank reactor than the value obtained with a series of 100 small CSTRs with the same total volume. The effect of the flow rate through the cell on the average Al(III) concentration in the cell and in the reactor is shown in Fig. 1. Lower flow rates result in higher Al(III) concentrations in the cell and this is due to longer residence times. The concentration difference between the cell and the tank reactor is then increased. Conversely, smaller differences are obtained for high flow rates, but the gas generated at the electrodes can accumulate in the cell and increase the ohmic resistance and therefore the voltage required. As can be seen in Fig. 1, the model represents very well the experimental data for aluminium formation regardless of the current density used. However, flow rates that are too high may be detrimental to agglomerate formation during the emulsion destabilisation. For the experimental setup described below, a velocity in the order 6.2 × 10−2 m/s, corresponding to a flow rate of 6.2 × 10−6 m3 /s in the cell under investigation, was found to correspond to suitable operating conditions. The effect of current density on the abatement yield of the contaminant is represented in Fig. 2. The removal yield of waste is higher with high current densities. This is due to high formation rates of Al(OH)3 in the cell. However, for long operation times the liquid concentration reaches an asymptotic level and applying further increases in current to the cell has no effect. This behaviour indicates that an optimum electrical charge can be found and this corresponds to minimum energy consumption in the treatment. The effect of the separation factor on the response curves for a fixed set of parameters is shown in Fig. 3. As expected, the removal of pollutant from the wastewater decreases with lower K values. The lowest value of K used gives an equilibrium
0.4 0.2 0.0 0
300
600
900
1200
Time [s] Fig. 3. Effects of the separation factor on the adsorption curves, C/C0 vs. t (F = 6.2 × 10−6 m3 /s; i = 300 A/m2 ; n∞ = 10 kg/kg; C0 = 50 kg/m3 ).
isotherm with a linear shape, but when the K value increases the equilibrium becomes more favourable and the solid tends to reach immediately its maximum capacity and a sharp increase in the removal of pollutant from the liquid phase is observed.
M. Carmona et al. / Chemical Engineering Science 61 (2006) 1237 – 1246
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4. Experimental section Chemical. Aluminium alloy A-U4G (2017-Al) was used as the electrode material and had the following metal contents: Cu (4%), Fe (0.7%), Mg (0.7%), Mn (0.7%), Si (0.5%), Zn (0.25%) and Cr (0.1%). Sodium chloride of analytical grade was supplied by Prolabo, France. The soluble oil (Sol 1000TM , Molydal, France) consisted of mineral oils (70%), glycol ethers, amines and chlorinated alkanes. Kerosene (BP 175–325 ◦ C) was supplied by Sigma-Aldrich, France. Demineralized water was used with a conductivity value lower than 5 s/cm. Procedure. The experimental system is represented schematically in Fig. 4. The system consisted of an EC cell, a reactor, a peristaltic pump and a sampling valve. The EC cell contained two parallel plate aluminium electrodes, each with a dimension of 100 mm × 50 mm × 12 mm and an effective area of 5.0 × 10−3 m2 . The electrode gap was maintained constant at 20 mm. The reactor was a water-jacketed glass reservoir with a capacity of 1.5 × 10−3 m3 , hermetically sealed but provided with three holes—two for wastewater recirculation and the other for purging the gases. The tank was magnetically stirred at 140 rpm. The peristaltic pump (Masterflex L/S model 752445) was calibrated prior to carrying out the experiments. The sampling system consisted of a standard three-port valve. All experiments were carried out in a batchwise manner, with recirculation of the emulsion through the electrochemical cell. For reasons discussed above, the flow rate was fixed at 6.2 × 10−6 m3 /s, which corresponds to a liquid velocity in the cell of 6.2 × 10−2 m/s. Treatment of oil/water emulsions was carried out as described previously (Khemis et al., 2004). In addition, oil/kerosene emulsions in water were also investigated. For both emulsions the current density was varied from 100 to 300 A/m2 . In all experiments, sodium chloride was added at 1.5 kg/m3 to give sufficient conductivity in the medium to be treated, as suggested by Sánchez-Calvo et al. (2003). The electrical conductivity of the resulting emulsions was in the range 0.38–0.49 s/m at room temperature. Observation of the samples by microscopy showed that the characteristics of both types of emulsion were not affected by the addition of supporting electrolyte. The pH values of the media prepared were as close as possible to 9.0 for oil emulsions and 8.6 for oil/kerosene mixtures. In spite of the evolution of OH− at the cathode, the pH in the reactor increased by less than 0.5 during the run. This is due to the buffering character of Al(III) species, especially in this pH region (Kobya et al., 2003). All experiments were carried out at 25 ◦ C. The pH of liquid samples was adjusted to 7.0 (±0.2) by the addition of aliquots of concentrated hydrochloric acid for optimal precipitation of aluminium hydroxide (Bard et al., 1985). The samples were kept for 24 h prior to analysis of the clear fraction. After each experiment the electrochemical cell was cleaned with detergent and then rinsed thoroughly to avoid passivation of the electrode surface (Mollah et al., 2001). Chemical analysis. The amount of pollutants contained in the samples was followed by determination of chemical oxygen demand (COD), the total organic carbon (TOC), turbidity and zeta
Fig. 4. Schematic diagram of the experimental system.
potential. COD was determined using a standard calorimetric technique with an excess of Cr(VI)—sulfuric acid medium and measurement of the optical density of the recovered solution at 520 nm using a Hach DR/2500 spectrophotometer. The TOC levels were determined through combustion of the samples at 680 ◦ C using a non-dispersive IR source (Tekmar Dohrmann Apollo 9000). The accuracy of both determinations was estimated at 3%. Wastewater turbidity in Nephelometric Turbidity Units (NTU) was measured using a Hanna LP-2000 turbidimeter. Zeta potential was measured using a Malvern Zetasizer 3000HS. 5. Results and discussion COD and TOC levels have previously been shown to be directly proportional to the amount of organic compounds in the water. TOC was selected for analysis, since it appears to provide a closer representation of the organic matter content. The most suitable isotherm model was selected by carrying out a set of experiments in which the current density was varied and 50 kg/m3 oil/water emulsions were used. Reliable values for the model parameters were obtained by fitting the experimental data by non-linear regression to the mathematical models described above. The parameters found for the three isotherms studied are shown in Table 1. The model accuracy was evaluated by calculating the coefficient of determination using the following formula: nexp exp (C − C ∗ ) R 2 = 1 − ni=1 , exp exp − C exp ) i=1 (C
(19)
where C exp is the experimental concentration of hydrocarbons in the liquid phase, C exp the average experimental concentration and nexp is the number of experimental data considered. Best fitting was found using LTEE and Freundlich isotherms, as shown in Table 1. LTEE was finally selected for subsequent
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Table 1 Parameters of the different empirical equations used to reproduce the equilibrium between the two phases for the oil emulsion and the coefficient of determination, R 2 , for the EC process of oil emulsions at 298 K R2
Parameters
n∞ KC ∗
q ∗ = C +(K−1)C ∗ 0 q ∗ = KII C ∗m n∞ K C ∗
I I q ∗ = 1+K ∗ IC
n∞ 78.904
K 2.963
0.973
m 0.658
KII 7.229
0.972
n∞ I 40.624
KI 5.959
Freundlich equation Langmuir type equation Langmuir equation
80 q* [kg/kg]
Equation
100
60 40 20 0 0
0.841
10
20
30
40
50
C* [kg/m3] Fig. 6. Equilibrium isotherms.
50 Liquid phase concentration of oil [kg/m3]
100 A/m2 140 A/m2
40
170 A/m2 200 A/m2
30
260 A/m2 300 A/m2 Theoretical Model
20 10 0 0
1500
Solid phase concentration of oil [kg/kg]
(a)
3000 4500 Time [s]
6000
7500
80 100 A/m2 140 A/m2 170 A/m2
60
200 A/m2 260 A/m2 300 A/m2
40
20
0 0 (b)
1500
3000 4500 Time [s]
6000
7500
Fig. 5. Oil concentration in the two phases using the LTEE: (a) Experimental data and theoretical prediction at different current densities; and (b) evolution of the oil concentration on solid phase.
calculations because of its lower variation according to the coefficients of determination obtained. It can be seen from Fig. 5a that good agreement was found between experimental data and the predictions yielded by the LTEE model. At low times, the high removal yield increases regularly with current density. This effect is due to the higher formation rates of aluminium hydroxide, which in turn leads to higher adsorption rates of oil from the liquid phase. However, for longer times the effect of the current is less significant. The amount of oil adsorbed onto the solid at each time can be obtained by using the equilibrium relation Eq. (11); the
data are represented in Fig. 5b. As can be seen, the higher the current density the lower the amount of oil on the solid at any given time. Nevertheless, the total removal of oil from the liquid phase is greater in this situation. This phenomenon can be explained by considering Eq. (14), which indicates that the amount of Al(OH)3 is reciprocal to the amount of oil on the solid at equilibrium. Thus, the higher the rate of formation of aluminium hydroxide, the lower the time required for emulsion abatement. It can be seen from Fig. 5b that the initially formed particles are able to remove the maximum oil from the liquid phase. This observation can be explained in terms of the high organic concentration and minimum amount of solid that exist under these conditions. This behaviour would indicate that adsorption and desorption phenomena could take place simultaneously in the reactor: desorption of oil occurs from the old particles and adsorption onto new particles occurs toward the new instantaneous equilibrium. It can be concluded that high removal rates can be obtained using high current density with shorter operation times. This operational procedure also allows passivation of the cathode surface to be reduced (Mollah et al., 2001). The differences exhibited by the three adsorption models can be attributed to the form of the isotherms shown in Fig. 6, which gives the isotherm curves with parameter values reported in Table 1. LTEE and FE isotherms are very similar and the differences obtained in the elimination levels can be explained by the fact that the Freundlich equation predicts a higher solid capacity for initial liquid phase concentration and, therefore, a higher initial elimination rate. The poor fitting given by the Langmuir isotherm could be due to the sharp profile exhibited at low concentrations followed by a long plateau: for this reason the equilibrium constant may be significantly overestimated by this model. The amount of oil removed from the emulsion by electrocoagulation processes can be predicted with satisfactory accuracy using an adsorption model whatever the current density. Thus, the lower the current, the longer the time required to reach the asymptotic plateau. The predicted adsorption capacity deduced from the experimental data for oil removal is very high,
M. Carmona et al. / Chemical Engineering Science 61 (2006) 1237 – 1246
100 A/m2 300 A/m2 200 A/m2 100 A/m2 Theoretical Model
100
50
5x105 100 A/m2; C0=150 kg/m3 300 A/m2; C0=150 kg/m3 200 A/m2; C0=100 kg/m3 100 A/m2; C0=50 kg/m3
4x105 Turbidity [NTU]
Liquid phase concentration of Oil/Kerosene [kg/m3]
150
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3x105 2x105 1x105
0 0
1500
3000 4500 Time [s]
6000
7500
Fig. 7. Behaviour of the different emulsion oil/kerosene in water by electrocoagulation. (F = 6.2 × 10−6 m3 /s; T = 25 ◦ C).
indicating a high affinity of aluminium hydroxide for the oil. Finally, it can be concluded that this model is reliable in providing an insight into the behaviour of emulsions in electrocoagulation processes. Oil/kerosene in water emulsions were prepared with a kerosene/oil ratio of one. Experiments were carried out by varying the emulsion concentration and the current density. All the experimental data were fitted by non-linear regression to the mathematical model based on the LTEE isotherm. Values for the parameters K and n∞ were determined to be 31.226 and 60.258 kg/kg, respectively. Good agreement between experiment and theory was obtained for oil/kerosene in water emulsions, as shown in Fig. 7. The electrocoagulation process is able to remove large amounts of hydrocarbons from wastewater but the removal rate depends on the current density. When a minimum current density is applied to the highest concentration, the removal yield decreases linearly with time, but the use of a low current rate means that the liquid cannot be treated within the time period ascribed. However, for higher current densities, treatment of the waste is successfully achieved by the process regardless of the concentration. The course of hydrocarbon removal from the wastewaters is consistent with the variations of turbidity [Fig. (8)] and zeta potential [Fig. (9)] during the treatment process. Consideration of Fig. 8 suggests that the most concentrated emulsions cannot be destabilised by electrocoagulation with the lowest current density. In the other cases, however, turbidity can be reduced to a great extent. Changes in turbidity exhibited the same trends as in previous studies (Holt et al., 2002) and electrocoagulation follows a three-stage process: in the first stage, turbidity increases due to formation of aluminium hydroxide particles from the electrodes (Larue and Vorobiev, 2003); a “reactive” stage then occurs, with a sharp decrease in turbidity; the final stage is characterised by almost constant turbidity levels, which correspond to the final concentration of suspensions that cannot be removed by the electrochemical process. The time variations in the zeta potential are shown in Fig. 9 and suggest that the addition of Al3+ neutralizes the negative
0 0
1500
3000 4500 Time [s]
6000
7500
Fig. 8. Turbidity evolution with the time for different experiments studied.
Fig. 9. Zeta potential evolution with the time for different experiments studied, measured at pH 7.0.
charges on the particle surfaces for sufficient current density in relation to the suspension concentration. The zeta potential of the clear fraction from the samples measured at pH 7.0 becomes positive when the emulsion is demulsified: this situation is encountered under the same conditions as found for the turbidity and the TOC level, namely high current density and/or low to moderate concentrations. In addition, both turbidity and TOC still show appreciable decays when the zeta potential is zero. However, the time required for the maximum reduction in turbidity and TOC is somewhat longer than that corresponding to the change in the sign of the zeta potential of the sample. This indicates that even after the change in the sign of the zeta potential, adsorption of organic matter continues to some extent. Different parameter values were obtained depending on the type of emulsion studied. The separation factor (K) for the oil/kerosene emulsion was far higher than that for the oil/water emulsion. This indicates that aluminium hydroxide prefers the “lighter” phase of the oil/kerosene suspension over the “heavy” ones obtained with oil alone. Nevertheless, the capacity parameter (n∞ ) is higher for oil than for the oil/kerosene emulsion:
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Optimal Condition
80 60 40 20
Hydrocarbon Removal [%]
100
50
40 30 Time [s ·10 -2]
20 20
10
we
40 60
Po
70
r [W
atts ]
0 100 80 60
0
Fig. 10. Effect of the power and the treatment time on hydrocarbon removal for the oil/kerosene emulsion in water. (F =6.2×10−6 m3 /s; C0 =100 kg/m3 ; K = 31.226; n∞ = 60.258 kg/kg).
aluminium hydroxide appears to be capable of adsorbing larger amounts of oil than oil/kerosene from the wastewater. The effect of the power and treatment time on the hydrocarbon removal from the emulsion is shown in Fig. 10. The cell voltage measured during the experiments was expressed through an empirical function of current density and initial concentration: the law obtained was used to calculate the electrical power consumed. It can be observed that at lower times the slope of the iso-power lines moves from a minimum (lowest power) up to a maximum (highest power). Such behaviour was also observed in Fig. 7, where 150 kg/m3 emulsions were treated at various current densities. Thus, electrical power represents a similar operating parameter for wastewater treatment as current density. Moreover, it can be observed that the minimum power required to achieve a 78% abatement is about 10 W (equivalent to a current density of 137.4 A/m2 ) within the highest operation time. However, this operating condition is of limited practical use due to passivation of the electrode surfaces. On the other hand, it was observed that the time required to reach the same abatement decreases with increasing power consumed. Therefore, a minimum power of 35 W (equivalent to a current density of 294.2 A/m2 ) must be applied for a period of 4500 s period to achieve an abatement yield over 90% with an Al consumption of almost 2 kg/m3 required (Fig. 10). Higher energy consumption for a larger treatment period does not result in significant further abatement. For the present system, a treatment period of 4500 s was also found to be the optimum time (see Fig. 7) for all conditions, provided that the current density was sufficient for destabilisation of the emulsions. Finally, Chen et al. (2002) developed a simplified model for the estimation of the cell voltage and this involved the electrode
potential of the anode and cathode, the activation overpotential, concentration overpotential and ohmic potential drop. They estimated the unknown overpotential by applying the Tafel equation and Nernst equation. For non-passivated and passivated aluminium electrodes, they found that the electrolysis voltage can be expressed by U0 = S +
h K2 i m1 i + K1 ln i + , k km
(20)
where h is the electrode gap, k is the conductivity of the water and i is the current density—the constants S, K1 , K2 , m1 and m must be determined experimentally. K2 has a value of zero for non-passivated electrodes. The basic electrode connection used is in monopolar mode. In this way, the total required cell voltage (U) is equal to the cell voltage (U0 ). Thus, using the same water and current density allows the following equation to be drawn from the above equation for two different electrode gaps. E2 Ai 2 =1− (h1 − h2 ), E1 kE 1
(21)
where E is the electrical power and subscripts 1 and 2 indicate the conditions at the two different electrode gaps. From this point of view, this expression can be used for non-passivated and passivated electrodes. As can be seen, it is possible to minimize the energy consumption by reducing the electrode gaps of the electrochemical cell (h2 < h1 ) to a few millimetres. Studies concerning the influence of the electrode gap were carried out by Sanchez-Calvo et al. (2003) and Cames et al. (2001) for three different scales (laboratory, pilot plant and industrial). Minimum energy consumption was also found for lower electrode gaps and it was determined that lower values can be used for larger scales. 6. Conclusions A simple adsorption model to predict hydrocarbon removal from wastewater by electrocoagulation has been developed. Adsorption of organic matter on Al hydroxide particles was modelled using three different adsorption isotherms and the Langmuir-type equation led to the best results. The model was able to describe the effects of current density and pollutant concentration on the abatement of two different emulsions (oil/water and oil/kerosene/water) as a function of only two adsorption parameters. Different parameter values were obtained depending on the emulsion studied. Aluminium hydroxide has a marked preference for the “light” fractions consisting of oil/kerosene emulsions but its capacity to remove the heavier contaminant (a single oil emulsion) was slightly higher. The destabilisation of the oil/kerosene emulsion was shown to depend on the initial concentration and the current density. When the current density was sufficient to destabilise the emulsion, the zeta potential became positive and a maximum reduction in the turbidity was obtained. However, low current densities are of low efficiency when applied to concentrated emulsions within the considered time period. The use of the adsorption
M. Carmona et al. / Chemical Engineering Science 61 (2006) 1237 – 1246
model allows the minimum power required to achieve the maximum hydrocarbon removal to be obtained without additional experimental data. Taking into account the cell voltage, it was found that a decrease in electrode gap leads to lower energy consumption. Notation A C∗ C0 C exp c CAl(III)
CAl(III) E = UI F I h i I k K KI KII l L m ˙ Al(OH)3 m n n∞ n∞ I nexp NAl3+ PMAl(OH)3 q∗ T u U U0 V x
electrode area, m2 concentration of oil in the solution phase at equilibrium, kg/m3 initial concentration of oil in the solution phase, kg/m3 experimental concentration of oil in the solution phase, kg/m3 concentration of aluminium hydroxide in the cell, kg/m3 concentration of aluminium hydroxide in the reactor, kg/m3 energy consumption, W liquid flow rate, m3 /s Faraday constant electrode gap, m current density, A/m2 cell current, A conductivity of water, s/m separation factor, using LTEE model, Eq. (11) Langmuir equilibrium constant, m3 /kg Freundlich model parameter, m3m /kgm Number of nodes along the cell length electrode length, m mass flux of Al(OH)3 , kg/s exponent of the Freundlich equation the number of electrons produced by anode oxidation aluminium hydroxide capacity, Eq. (11), kg/kg monolayer capacity of aluminium hydroxide, Eq. (12), kg/kg total number of experimental data used in the non-linear regression process flux of Al3+ species formed by dissolution, mol/s molecular weight of the Al(OH)3 (kg/mol) solid-phase concentration of oil, kg/kg time, s superficial velocity, m/s total required cell voltage, V cell voltage between electrodes, V volume of reactor, m3 position along the cell length
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Bard, A.J., Parsons, R., Jordan, J., 1985. Standard Potentials in Aqueous Solutions. Marcel Dekker, New York. Bayramoglu, M., Kobya, M., Can, O.T., Sozbir, M., 2004. Operating cost analysis of electrocoagulation of textile dye wastewater. Separation and Purification Technology 37, 117–125. Bilba, D., Bilba, N., Albu, M., 1999. Kinetics of cadmium ion sorption on ion exchange and chelating resins. Solvent Extraction and Ion Exchange 17, 1557–1569. Cames, M.C., Tanguy, G., Leclerc, J.P., Sanchez-Calvo, L., Valentin, G., Rostan, A., Muller, P., Lapicque, F., 2001. Design rules of a pilot cell for treatment of concentrated liquid wastes by electrocoagulation–electroflotation. Proceedings of the 6th World Congress on Chemical Engineering, September 23–27, Melbourne, Paper 637. Cañizares, P., Carmona, M., Lobato, J., Martínez, F., Rodrigo, M.A., 2005. Electrodissolution of aluminum electrodes in electrocoagulation processes. Industrial and Engineering Chemistry Research 44, 4178–4185. Costa, E., De Lucas, A., González, M.E., 1984. Ion-exchange. Determination of interdiffusion coefficients. Industrial and Engineering Chemistry Fundamentals 23, 400–405. Chen, X., Chen, G., Yue, P.L., 2000. Separation of pollutants from restaurant wastewater by electrocoagulation. Separation and Purification Technology 19, 65–76. Chen, X., Chen, G., Yue, P.L., 2002. Investigation on the electrolysis voltage of electrocoagulation. Chemical Engineering Science 57, 2449–2455. Chern, J.M., Chien, Y.W., 2002. Adsorption of nitrophenol onto activated carbon: isotherms and breakthrough curves. Water Research 36, 247–255. De Lucas, A., Cañizares, P., García, M., Gómez, J., Rodríguez, J.F., 1998. Recovery of nicotine from aqueous extracts of tobacco wastes by an H+ -form strong acid-ion exchanger. Industrial and Engineering Chemistry Research 37, 4783–4791. Duan, J., Gregory, J., 2003. Coagulation by hydrolysing metal salts. Advances in Colloid and Interface Science 100–102, 475–502. Fernández, A., Díaz, M., Rodrígues, A., 1995. Kinetic mechanisms in ion exchange processes. The Chemical Engineering Journal 57, 17–25. Freundlich, H., Heller, W., 1939. On adsorption in solution. Journal of American Chemical Society 61, 2228. Gregor, J.E., Nokes, C.J., Fenton, E., 1997. Optimising natural organic matter removal from low turbidity water by controlled pH adjustment of aluminium coagulation. Water Research 31, 2949–2958. Holt, P.K., Barton, G.W., Wark, M., Mitchell, C.A., 2002. A quantitative comparison between chemical dosing and electrocoagulation. Colloids and Surfaces A: Physicochemical Engineering Aspects 211, 233–248. Hosny, A.H., 1996. Separation oil from oil–water emulsions by electroflotation technique. Separation Technology 6, 9–17. Inan, H., Domoglo, A., Simsek, H., Karpuzcu, M., 2004. Olive oil mill wastewater treatment by means of electrocoagulation. Separation and Purification Technology 36, 23–31. Khemis, M., Tanguy, G., Leclerc, J.P., Valentin, G., Lapicque, F., 2004. Electrocoagulation for the treatment of oil suspensions: relation between the rates of electrode reactions and the efficiency of waste removal. Process Safety and Environmental Protection 82 (A6), 1–8. Kobya, M., Can, O.T., Bayramoglu, M., 2003. Treatment of textile wastewaters by electrocoagulation using iron and aluminium electrodes. Journal of Hazardous Materials B 100, 163–178. Kumar, P.R., Chaudhar, S., Khilar, K., Mahajan, C., 2004. Removal of arsenic from water by electrocoagulation. Chemosphere 55, 1245–1252. Langmuir, 1915. Journal of American Chemical Society 37, 1139. Larue, O., Vorobiev, E., 2003. Floc size estimation in iron induced electrocoagulation and coagulation using sedimentation data. International Journal of Mineral Processing 71, 1–15. Lin, S.H., Lan, W.J., 1998. Treatment of waste oil/water emulsion by ultrafiltration and ion exchange. Water Research 32, 2680–2688. Marquardt, D.W., 1963. An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society of Industrial and Applied Mathematics 11, 431–441. Mollah, M.Y.A., Schennach, R., Parga, J.R., Cocke, D.L., 2001. Electrocoagulation (EC)—science and applications. Journal of Hazardous Materials B 84, 29–41.
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Monteagudo, J.M., Durán, A., Carmona, M., Schwab, R., Higueras, P., 2003. Elimination of inorganic mercury from waste waters using crandallitetype compounds. Journal of Chemical Technology and Biotechnology 78, 1–7. Mostefa, N.M., Tir, M., 2004. Coupling flocculation with electroflotation for waste oil/water emulsion treatment. Optimisation of the operating conditions. Desalination 161, 115–121. Picard, T., Cathalifaud-Feuillade, G., Mazet, M., Vandensteendam, C., 2000. Cathodic dissolution in the electrocoagulation process using aluminium electrodes. Journal of Environmental Monitoring 2, 77–80. Pinotti, A., Zaritzky, N., 2001. Effect of aluminium sulphate and cationic polyelectrolytes on the destabilization of emulsified waste. Waste Management 21, 535–542. Poolea, A.J., Cord-Ruwisch, R., 2004. Treatment of strongflow wool scouring effluent by biological emulsion destabilisation. Water Research 38, 1419–1426.
Press, W., Teukolsky, S., Vetterling, W., 1992. In: Flannery, B. (Ed.), Numerical Fortran Recipes in Fortran, 2nd ed. Cambridge University Press, USA. Ríos, S., Pazos, C., Coca, J., 1998. Destabilization of cutting oil emulsions using inorganic salts as coagulants. Colloidal and Surfaces, A: Physicochemical and Engineering Aspects 138, 383–389. Sanchez-Calvo, L., Leclerc, J.-P., Tanguy, G., Cames, M.C., Paternotte, G., Valentin, G., Rostan, A., Lapicque, F., 2003. An electrocoagulation unit for the purification of soluble oil wastes of high COD. Environmental Progress 22, 57–65. Saur, I.F., Rubach, S., Forde, J.S., Kjaerheim, G., Syversen, U., 1996. Electroflocculation: removal of oil, heavy metals and organic compounds from oil-in-water emulsions. Filtration & Separation 33, 295–303. Shen, F., Chen, X., Gao, P., Chen, G., 2003. Electrochemical removal of fluoride ions from industrial wastewater. Chemical Engineering Science 58, 987–993.
A simple model to predict the removal of oil suspensions from water using the electrocoagulation technique Manuel Carmonaa,∗ , Mohamed Khemisb , Jean-Pierre Leclercb , François Lapicqueb a Department of Chemical Engineering, University of Castilla—La Mancha, Avda. de Camilo José Cela s/n, 13004 Ciudad Real, Spain b Laboratoire des Sciences du Génie Chimique, CNRS-ENSIC, BP 451, F-54001 Nancy, France
Received 30 November 2004; received in revised form 26 July 2005; accepted 23 August 2005 Available online 30 September 2005
Abstract A simple model has been developed to predict the removal of hydrocarbon fractions from wastewater using sacrificial Al anodes. The model was successfully applied to the interpretation of experimental data obtained in a laboratory electrochemical cell operated in a batchwise manner. The adsorption equilibrium of organic matter on Al hydroxide was modelled using three equations, with the best results obtained using a Langmuir-type equation. The model was able to describe the effects of current density and pollutant concentration on the efficiency of wastewater treatment. Different values were obtained for the parameters depending on the nature of the hydrocarbon suspension. Aluminium hydroxide showed a far higher affinity for the oil/kerosene suspension but exhibited a higher capacity to remove heavy oil suspensions. The removal rates of pollutants were found to depend on the initial concentration and the current density. When the current density was sufficient to destabilise the emulsion, the zeta potential of the clear fraction measured at pH 7.0 became positive. This change was also characterised by a significant reduction in turbidity. Furthermore, the application of higher current densities did not allow further treatment of the water. However, the efficiency of emulsion destabilisation was found to depend on the concentration and current densities that were too low were ineffective. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Adsorption; Emulsion; Turbidity; Zeta potential
1. Introduction Oil/water (O/W) emulsions are widely used in metal industries, e.g., rolling mills, forges and metal workshops, because these emulsions exhibit properties that include lubrication, surface cooling, cleaning and corrosion prevention—all of which are required by metals under mechanical operations. The main problem encountered with O/W emulsions is the substantial degradation of some components with time at the working temperature, which usually ranges from 45 ◦ C to 90 ◦ C. These emulsions therefore need to be regularly replaced, often several times per year. The emulsions have high oil contents, in the range 1 × 10−1 –30 kg/m3 depending on the specific application, and metal contents and used oil suspensions are toxic and must be treated in such a way that water recycling is possible.
∗ Corresponding author. Tel.: +34 926 295437; fax: +34 926 295318.
E-mail address: [email protected] (M. Carmona). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.08.030
According to current environmental regulations, hydrocarbon concentrations in wastewater must be below 1 × 10−2 kg/m3 (Ríos et al., 1998). Several techniques have been applied to treat these types of waste. Lin and Lan (1998) used combined ultrafiltration and ion exchange, reaching removal yields up to 91%. Ríos et al. (1998) employed inorganic salts as coagulants and removed more than 90% of the initial oil content. Oil destabilisation was reported by these authors to be favoured at higher temperatures. Poolea and Cord-Ruwisch (2004) described the ability of the aerobic microbial cultures to destabilise the emulsion and found that removal yields could reach 97% after 7 days of treatment. Mostefa and Tir (2004) found that electrochemical methods in combination with a chemical process were suitable for the separation of oil from oily wastewater and achieved a separation yield of almost 99% in the treatment of a concentrated emulsion of 4 w/w%. Electrocoagulation has been used for the treatment of wastewater by various authors, and several differences were found in comparison to the chemical
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coagulation process (Kumar et al., 2004; Larue and Vorobiev, 2003; Holt et al., 2002). Electrocoagulation (EC) is an effective process for the destabilisation of finely dispersed particles by removing hydrocarbons, greases, suspended solids and even heavy metals from different types of waste water (Inan et al., 2004; Kumar et al., 2004; Chen et al., 2002; Sanchez-Calvo et al., 2003; Saur et al., 1996; Hosny, 1996). Aluminium or iron are usually used as electrodes and their cations are generated by dissolution of sacrificial anodes upon the application of a direct current. The metal ions generated are hydrolysed in the electrochemical cell to produce metal hydroxide ions and only neutral M(OH)3 has a very low solubility (Duan and Gregory, 2003), mainly at pH values in the range 6.0–7.0 (Pinotti and Zaritzky, 2001; Gregor et al., 1997). Metal species react with negatively charged particles in the water to form flocs (Chen et al., 2002; Saur et al., 1996). The in situ generation of coagulants means that electrocoagulation processes do not require the addition of any chemicals. The gases produced during the electrolysis of water and metal dissolution (Picard et al., 2000) allow the resulting flocs to flotate (Saur et al., 1996). Although the electrocoagulation technique has been available for more than a century, it now appears now to be one of the most effective approaches. The design of an industrial plant and an electrocoagulation cell is mainly based on empirical knowledge, with little consideration of the electrocoagulation mechanism (Sanchez-Calvo et al., 2003). Hosny (1996) used a pseudo-first order kinetic with respect to the oil concentration to predict its time variation at different current densities with good accuracy. Nevertheless, this model is not able to predict oil removal when the concentration tends to its asymptotic level at the end of the operation. In addition, this approach does not provide physical interpretation of the oil removal process from the liquid phase. The present paper involves the description of a simple model for the prediction of the elimination of suspended organic matter and this relies upon the adsorption properties exhibited by aluminium hydroxide complexes (Inan et al., 2004; Kumar et al., 2004; Bache and Papavasilopoulos, 2003). The main objectives of the present study, which was conducted with two different organic emulsions, are asfollows: (i) To develop a mathematical model that allows the prediction of the decrease in the amount of organic suspensions in the liquid phase with time, taking into account the physicochemical interactions between the organic matter and aluminium hydroxides at pH values > 6.5. Kobya et al. (2003) found that under these conditions the interactions can be considered as being due to physical adsorption of the organic matter on the coagulants. (ii) To evaluate the effects of the various physical parameters on the adsorption isotherm. (iii) To select the most suitable adsorption model for the reliable prediction of the course of electrocoagulation runs for the removal O/W emulsions from wastewater.
2. Mathematical model Model equations were derived on the basis of the following simplifying assumptions: (i) The amount of aluminium (Al3+ ) that is produced in the cell is times higher than the value predicted by Faraday’s law. Experiments carried out by Khemis et al. (2004) with Al electrodes showed that the quantity of Al species dissolved was higher than the value predicted by Faraday’s law at alkaline pH for current densities varying from 100 to 300 A/m2 , with little effect on the nature of the suspended matter. The value of was taken as 1.5 in the application of the model and this is in accordance with experimental data published previously. Indeed, oxidation of aluminium is produced in two ways: electrochemical oxidation at the anode and chemical attack on both electrode surfaces (Cañizares et al., 2005; Kobya et al., 2003; Picard et al., 2000; Chen et al., 2000). The electrochemical oxidation reaction at the anode is represented as Al0 ⇒ Al3+ + 3e− .
(1)
The presence of chloride ions catalyses the aluminium corrosion and this corrosion can produce more aluminium hydroxide flocs (Shen et al., 2003). The cathode may be chemically attacked by OH− at high pH values with a high rate of hydrogen formation (Bayramoglu et al., 2004). Thus, the following overall reactions Eqs. (2) and (3) can enhance the dissolution of aluminium on the surface of the two electrodes depending on the pH (Chen et al., 2000). 2Al0 + 6H+ ⇒ 2Al3+ + 3H2(g) ,
(2)
2Al0 + 6H2 O + 2OH− ⇒ 2Al(OH)− 4 + 3H2(g) .
(3)
In addition, the water reduction occurs on the cathode and leads to a great formation of OH− ions. These ions favor the aluminium dissolution as mentioned above. 2H2 O + 2e− ⇒ 2OH− + H2(g) .
(4)
(ii) The Al3+ species produced in the cell is entirely converted to aluminium hydroxide Al(OH)3 in the reactor under the physicochemical conditions of the process. This assumption is consistent with the electrocoagulation mechanism proposed by Saur et al. (1996) in which the reaction leading to Al complex formation is fast and leads to various forms of hydroxide. Al(OH)3 is the main species for pH values close to 7, according to the predominant zone diagram for aluminium hydroxide (Holt et al., 2002). (iii) The metal hydroxides form the nucleus of colloidal particles and adsorption takes place around the nucleus (Inan et al., 2004). (iv) Solute concentration gradients do not exist inside the solid particle: the concentration inside the particle is the external solid concentration or the equilibrium concentration. Growth of the solid particles around the hydroxide
M. Carmona et al. / Chemical Engineering Science 61 (2006) 1237 – 1246
nanoparticles is ensured by the adsorption of organic matter: initial solid particles are small in size and they grow by adsorption of organic species. The adsorption changes the properties of aluminium hydroxide and allows flotation. (v) The solid phase is always in equilibrium with the liquid phase. Freshly formed “sweep flocs” of amorphous Al(OH)3 have a large surface area and this allows a rapid external mass transfer rate: the overall process of adsorption and trapping of colloidal particles is therefore a fast process (Kobya et al., 2003). (vi) The oil does not undergo any chemical reaction within the reactor. Taking into account the assumptions outlined above, the model was developed as follows: The flux of Al3+ species produced in the cell is given by NAl3+ =
I , nI
(5)
where is the faradaic yield of Al dissolution, I is the current, n is the number of electrons involved in the anode oxidation, and I is the Faraday constant. Taking into account assumption (ii), Eq. (5) becomes m ˙ Al(OH)3 =
I PMAl(OH)3 , nI
(6)
where m ˙ Al(OH)3 is the weight flux of Al(OH)3 and PMAl(OH)3 is the molecular weight of the Al(OH)3 . The cell considered in the model was a parallel plate electrode reactor, as used in previous investigations (Khemis et al., 2004). The hydrodynamic behaviour of the electrochemical cell was assumed to be that of a plug flow reactor. Despite gas formation, the liquid flow rate in the cell was assumed to be unchanged. The mass balance for Al hydroxide in the cell can be written as c jCAl(III)
jt
= −u
c jCAl(III)
jx
i PMAl(OH)3 , + h nI
(7)
c where CAl(III) is the aluminium hydroxide concentration in the electrocoagulation cell at x, h is the electrode gap, CAl(III) is the aluminium hydroxide concentration in the reactor, i the current density and u is the superficial velocity. Initial and boundary conditions for the electrochemical cell are:
t = 0;
0 < x L;
t > 0;
x = 0;
c CAl(III) = 0,
c CAl(III) = CAl(III) ,
(8)
dCAl(III) V c = F (CAl(III) |x=L − CAl(III) ), dt
Eq. (11) is a Langmuir-type empirical equation (LTEE) derived from ion exchange and has been successfully applied in various investigations (Monteagudo et al., 2003; Bilba et al., 1999; De Lucas et al., 1998; Fernández et al., 1995; Costa et al., 1984). q∗ =
n∞ KC ∗ , C0 + (K − 1)C ∗
(11)
where n∞ is the aluminium hydroxide capacity, q ∗ and C ∗ are, respectively, the solid and liquid phase equilibrium concentrations, C0 is the initial organic concentration, and K is the separation factor. Eq. (12) is the Langmuir equation (LE) that has been used for various gas–solid and liquid–solid isotherms. This equation is applicable for monolayer models, assuming that all active sites of the solid have the same affinity for the solute under investigation (Chern and Chien, 2002; Langmuir, 1915). q∗ =
∗ n∞ I KI C , 1 + KI C ∗
(12)
where n∞ I is the total monolayer capacity of the Al hydroxide and KI is the conditional Langmuir equilibrium constant. Eq. (13) is the Freundlich isotherm (FE), which is a consecutive layer model with unlimited sorption sites (Chern and Chien, 2002; Freundlich and Heller, 1939). q ∗ = KII C ∗m ,
(13)
where KII is the conditional Freundlich stability constant and m is the mass action stoichiometric coefficient, which is equal to or lower than unity. Taking into account assumptions (iv) and (v), the mass balance between the liquid and the solid phase at the equilibrium condition can be expressed as follows: q∗ =
C0 − C ∗ . CAl(III)
(14)
The two-equation system was solved for each isotherm model considered and this yielded the following relations: For LTEE, the solution depends on the K value: If K = 1, −
C ∗2 +
C02 = 0, K −1
(9) If K = 1,
where L is the electrode length. The mass balance for the stirred-tank reactor is
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C∗ =
(C0 (2 − K) + n∞ KC Al(III) ) ∗ C K −1 (15)
C02 . C0 + n∞ CAl(III)
(16)
For the Langmuir isotherm, (10)
where V is the volume of the reactor and F is the liquid recirculation flow rate. Three different adsorption equilibrium isotherms were tested in order to model the experimental data.
C ∗2 +
C2 (1 + n∞ I KI CAl(III) − KI C0 ) ∗ C − 0 = 0. KI KI
(17)
For the Freundlich isotherm, KII CAl(III) C ∗m + C ∗ − C0 = 0.
(18)
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The final model is formed by three equations, namely the partial differential equation (7), differential equation (10) and finally, one of Eqs. (15)–(18)—the choice of which depends on the isotherm used. Partial differential equation (7) is transformed into a system of l ordinary differential equations, with l being the number of nodes along the length of the cell. The l + 1 differential equations were integrated numerically by the fourth-order Runge–Kutta method (Press et al., 1992). In the case of the Freundlich isotherm, the Newton–Raphson method was used to find the positive root of Eq. (18) (Press et al., 1992). Two parameters are involved in the adsorption isotherm; Marquardt’s algorithm (Marquardt, 1963) was used to estimate these parameters from the experimental data obtained in the present work or reported previously (Khemis et al., 2004). A visual basic application was developed for the calculations.
1.0 Concentration of Al3+ [kg/m3]
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Model
0.8 0.6 0.4 0.2 0.0 0
500
1000
1500 Time [s]
2000
2500
3000
Fig. 1. Flow effect on the gradient of aluminium hydroxide concentration between the EC cell and the reactor.
3. Simulation results 1.0 100 A/m2 200 A/m2 300 A/m2
0.8
C/C0
0.6 0.4 0.2
0
1000
2000
3000 Time [s]
4000
5000
6000
Fig. 2. Effects of the current density on the adsorption curves, C/C0 vs. t (F = 6.2 × 10−6 m3 /s; K = 1.1; n∞ = 10 kg/kg; C0 = 50 kg/m3 ).
1.0 K=1 K=10 K=50
0.8 0.6 C/C0
Simulations were carried out to observe the effect of physical parameters on the treatment process. The electrochemical cell described in the experimental section was considered for the calculations. Initial tests showed the low impact of the number of nodes, i.e., the number of stirred vessels in the cascade simulating the plug flow. In fact, modelling the cell by a single stirred vessel led to Al hydroxide concentrations that were 3% lower in the tank reactor than the value obtained with a series of 100 small CSTRs with the same total volume. The effect of the flow rate through the cell on the average Al(III) concentration in the cell and in the reactor is shown in Fig. 1. Lower flow rates result in higher Al(III) concentrations in the cell and this is due to longer residence times. The concentration difference between the cell and the tank reactor is then increased. Conversely, smaller differences are obtained for high flow rates, but the gas generated at the electrodes can accumulate in the cell and increase the ohmic resistance and therefore the voltage required. As can be seen in Fig. 1, the model represents very well the experimental data for aluminium formation regardless of the current density used. However, flow rates that are too high may be detrimental to agglomerate formation during the emulsion destabilisation. For the experimental setup described below, a velocity in the order 6.2 × 10−2 m/s, corresponding to a flow rate of 6.2 × 10−6 m3 /s in the cell under investigation, was found to correspond to suitable operating conditions. The effect of current density on the abatement yield of the contaminant is represented in Fig. 2. The removal yield of waste is higher with high current densities. This is due to high formation rates of Al(OH)3 in the cell. However, for long operation times the liquid concentration reaches an asymptotic level and applying further increases in current to the cell has no effect. This behaviour indicates that an optimum electrical charge can be found and this corresponds to minimum energy consumption in the treatment. The effect of the separation factor on the response curves for a fixed set of parameters is shown in Fig. 3. As expected, the removal of pollutant from the wastewater decreases with lower K values. The lowest value of K used gives an equilibrium
0.4 0.2 0.0 0
300
600
900
1200
Time [s] Fig. 3. Effects of the separation factor on the adsorption curves, C/C0 vs. t (F = 6.2 × 10−6 m3 /s; i = 300 A/m2 ; n∞ = 10 kg/kg; C0 = 50 kg/m3 ).
isotherm with a linear shape, but when the K value increases the equilibrium becomes more favourable and the solid tends to reach immediately its maximum capacity and a sharp increase in the removal of pollutant from the liquid phase is observed.
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4. Experimental section Chemical. Aluminium alloy A-U4G (2017-Al) was used as the electrode material and had the following metal contents: Cu (4%), Fe (0.7%), Mg (0.7%), Mn (0.7%), Si (0.5%), Zn (0.25%) and Cr (0.1%). Sodium chloride of analytical grade was supplied by Prolabo, France. The soluble oil (Sol 1000TM , Molydal, France) consisted of mineral oils (70%), glycol ethers, amines and chlorinated alkanes. Kerosene (BP 175–325 ◦ C) was supplied by Sigma-Aldrich, France. Demineralized water was used with a conductivity value lower than 5 s/cm. Procedure. The experimental system is represented schematically in Fig. 4. The system consisted of an EC cell, a reactor, a peristaltic pump and a sampling valve. The EC cell contained two parallel plate aluminium electrodes, each with a dimension of 100 mm × 50 mm × 12 mm and an effective area of 5.0 × 10−3 m2 . The electrode gap was maintained constant at 20 mm. The reactor was a water-jacketed glass reservoir with a capacity of 1.5 × 10−3 m3 , hermetically sealed but provided with three holes—two for wastewater recirculation and the other for purging the gases. The tank was magnetically stirred at 140 rpm. The peristaltic pump (Masterflex L/S model 752445) was calibrated prior to carrying out the experiments. The sampling system consisted of a standard three-port valve. All experiments were carried out in a batchwise manner, with recirculation of the emulsion through the electrochemical cell. For reasons discussed above, the flow rate was fixed at 6.2 × 10−6 m3 /s, which corresponds to a liquid velocity in the cell of 6.2 × 10−2 m/s. Treatment of oil/water emulsions was carried out as described previously (Khemis et al., 2004). In addition, oil/kerosene emulsions in water were also investigated. For both emulsions the current density was varied from 100 to 300 A/m2 . In all experiments, sodium chloride was added at 1.5 kg/m3 to give sufficient conductivity in the medium to be treated, as suggested by Sánchez-Calvo et al. (2003). The electrical conductivity of the resulting emulsions was in the range 0.38–0.49 s/m at room temperature. Observation of the samples by microscopy showed that the characteristics of both types of emulsion were not affected by the addition of supporting electrolyte. The pH values of the media prepared were as close as possible to 9.0 for oil emulsions and 8.6 for oil/kerosene mixtures. In spite of the evolution of OH− at the cathode, the pH in the reactor increased by less than 0.5 during the run. This is due to the buffering character of Al(III) species, especially in this pH region (Kobya et al., 2003). All experiments were carried out at 25 ◦ C. The pH of liquid samples was adjusted to 7.0 (±0.2) by the addition of aliquots of concentrated hydrochloric acid for optimal precipitation of aluminium hydroxide (Bard et al., 1985). The samples were kept for 24 h prior to analysis of the clear fraction. After each experiment the electrochemical cell was cleaned with detergent and then rinsed thoroughly to avoid passivation of the electrode surface (Mollah et al., 2001). Chemical analysis. The amount of pollutants contained in the samples was followed by determination of chemical oxygen demand (COD), the total organic carbon (TOC), turbidity and zeta
Fig. 4. Schematic diagram of the experimental system.
potential. COD was determined using a standard calorimetric technique with an excess of Cr(VI)—sulfuric acid medium and measurement of the optical density of the recovered solution at 520 nm using a Hach DR/2500 spectrophotometer. The TOC levels were determined through combustion of the samples at 680 ◦ C using a non-dispersive IR source (Tekmar Dohrmann Apollo 9000). The accuracy of both determinations was estimated at 3%. Wastewater turbidity in Nephelometric Turbidity Units (NTU) was measured using a Hanna LP-2000 turbidimeter. Zeta potential was measured using a Malvern Zetasizer 3000HS. 5. Results and discussion COD and TOC levels have previously been shown to be directly proportional to the amount of organic compounds in the water. TOC was selected for analysis, since it appears to provide a closer representation of the organic matter content. The most suitable isotherm model was selected by carrying out a set of experiments in which the current density was varied and 50 kg/m3 oil/water emulsions were used. Reliable values for the model parameters were obtained by fitting the experimental data by non-linear regression to the mathematical models described above. The parameters found for the three isotherms studied are shown in Table 1. The model accuracy was evaluated by calculating the coefficient of determination using the following formula: nexp exp (C − C ∗ ) R 2 = 1 − ni=1 , exp exp − C exp ) i=1 (C
(19)
where C exp is the experimental concentration of hydrocarbons in the liquid phase, C exp the average experimental concentration and nexp is the number of experimental data considered. Best fitting was found using LTEE and Freundlich isotherms, as shown in Table 1. LTEE was finally selected for subsequent
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Table 1 Parameters of the different empirical equations used to reproduce the equilibrium between the two phases for the oil emulsion and the coefficient of determination, R 2 , for the EC process of oil emulsions at 298 K R2
Parameters
n∞ KC ∗
q ∗ = C +(K−1)C ∗ 0 q ∗ = KII C ∗m n∞ K C ∗
I I q ∗ = 1+K ∗ IC
n∞ 78.904
K 2.963
0.973
m 0.658
KII 7.229
0.972
n∞ I 40.624
KI 5.959
Freundlich equation Langmuir type equation Langmuir equation
80 q* [kg/kg]
Equation
100
60 40 20 0 0
0.841
10
20
30
40
50
C* [kg/m3] Fig. 6. Equilibrium isotherms.
50 Liquid phase concentration of oil [kg/m3]
100 A/m2 140 A/m2
40
170 A/m2 200 A/m2
30
260 A/m2 300 A/m2 Theoretical Model
20 10 0 0
1500
Solid phase concentration of oil [kg/kg]
(a)
3000 4500 Time [s]
6000
7500
80 100 A/m2 140 A/m2 170 A/m2
60
200 A/m2 260 A/m2 300 A/m2
40
20
0 0 (b)
1500
3000 4500 Time [s]
6000
7500
Fig. 5. Oil concentration in the two phases using the LTEE: (a) Experimental data and theoretical prediction at different current densities; and (b) evolution of the oil concentration on solid phase.
calculations because of its lower variation according to the coefficients of determination obtained. It can be seen from Fig. 5a that good agreement was found between experimental data and the predictions yielded by the LTEE model. At low times, the high removal yield increases regularly with current density. This effect is due to the higher formation rates of aluminium hydroxide, which in turn leads to higher adsorption rates of oil from the liquid phase. However, for longer times the effect of the current is less significant. The amount of oil adsorbed onto the solid at each time can be obtained by using the equilibrium relation Eq. (11); the
data are represented in Fig. 5b. As can be seen, the higher the current density the lower the amount of oil on the solid at any given time. Nevertheless, the total removal of oil from the liquid phase is greater in this situation. This phenomenon can be explained by considering Eq. (14), which indicates that the amount of Al(OH)3 is reciprocal to the amount of oil on the solid at equilibrium. Thus, the higher the rate of formation of aluminium hydroxide, the lower the time required for emulsion abatement. It can be seen from Fig. 5b that the initially formed particles are able to remove the maximum oil from the liquid phase. This observation can be explained in terms of the high organic concentration and minimum amount of solid that exist under these conditions. This behaviour would indicate that adsorption and desorption phenomena could take place simultaneously in the reactor: desorption of oil occurs from the old particles and adsorption onto new particles occurs toward the new instantaneous equilibrium. It can be concluded that high removal rates can be obtained using high current density with shorter operation times. This operational procedure also allows passivation of the cathode surface to be reduced (Mollah et al., 2001). The differences exhibited by the three adsorption models can be attributed to the form of the isotherms shown in Fig. 6, which gives the isotherm curves with parameter values reported in Table 1. LTEE and FE isotherms are very similar and the differences obtained in the elimination levels can be explained by the fact that the Freundlich equation predicts a higher solid capacity for initial liquid phase concentration and, therefore, a higher initial elimination rate. The poor fitting given by the Langmuir isotherm could be due to the sharp profile exhibited at low concentrations followed by a long plateau: for this reason the equilibrium constant may be significantly overestimated by this model. The amount of oil removed from the emulsion by electrocoagulation processes can be predicted with satisfactory accuracy using an adsorption model whatever the current density. Thus, the lower the current, the longer the time required to reach the asymptotic plateau. The predicted adsorption capacity deduced from the experimental data for oil removal is very high,
M. Carmona et al. / Chemical Engineering Science 61 (2006) 1237 – 1246
100 A/m2 300 A/m2 200 A/m2 100 A/m2 Theoretical Model
100
50
5x105 100 A/m2; C0=150 kg/m3 300 A/m2; C0=150 kg/m3 200 A/m2; C0=100 kg/m3 100 A/m2; C0=50 kg/m3
4x105 Turbidity [NTU]
Liquid phase concentration of Oil/Kerosene [kg/m3]
150
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3x105 2x105 1x105
0 0
1500
3000 4500 Time [s]
6000
7500
Fig. 7. Behaviour of the different emulsion oil/kerosene in water by electrocoagulation. (F = 6.2 × 10−6 m3 /s; T = 25 ◦ C).
indicating a high affinity of aluminium hydroxide for the oil. Finally, it can be concluded that this model is reliable in providing an insight into the behaviour of emulsions in electrocoagulation processes. Oil/kerosene in water emulsions were prepared with a kerosene/oil ratio of one. Experiments were carried out by varying the emulsion concentration and the current density. All the experimental data were fitted by non-linear regression to the mathematical model based on the LTEE isotherm. Values for the parameters K and n∞ were determined to be 31.226 and 60.258 kg/kg, respectively. Good agreement between experiment and theory was obtained for oil/kerosene in water emulsions, as shown in Fig. 7. The electrocoagulation process is able to remove large amounts of hydrocarbons from wastewater but the removal rate depends on the current density. When a minimum current density is applied to the highest concentration, the removal yield decreases linearly with time, but the use of a low current rate means that the liquid cannot be treated within the time period ascribed. However, for higher current densities, treatment of the waste is successfully achieved by the process regardless of the concentration. The course of hydrocarbon removal from the wastewaters is consistent with the variations of turbidity [Fig. (8)] and zeta potential [Fig. (9)] during the treatment process. Consideration of Fig. 8 suggests that the most concentrated emulsions cannot be destabilised by electrocoagulation with the lowest current density. In the other cases, however, turbidity can be reduced to a great extent. Changes in turbidity exhibited the same trends as in previous studies (Holt et al., 2002) and electrocoagulation follows a three-stage process: in the first stage, turbidity increases due to formation of aluminium hydroxide particles from the electrodes (Larue and Vorobiev, 2003); a “reactive” stage then occurs, with a sharp decrease in turbidity; the final stage is characterised by almost constant turbidity levels, which correspond to the final concentration of suspensions that cannot be removed by the electrochemical process. The time variations in the zeta potential are shown in Fig. 9 and suggest that the addition of Al3+ neutralizes the negative
0 0
1500
3000 4500 Time [s]
6000
7500
Fig. 8. Turbidity evolution with the time for different experiments studied.
Fig. 9. Zeta potential evolution with the time for different experiments studied, measured at pH 7.0.
charges on the particle surfaces for sufficient current density in relation to the suspension concentration. The zeta potential of the clear fraction from the samples measured at pH 7.0 becomes positive when the emulsion is demulsified: this situation is encountered under the same conditions as found for the turbidity and the TOC level, namely high current density and/or low to moderate concentrations. In addition, both turbidity and TOC still show appreciable decays when the zeta potential is zero. However, the time required for the maximum reduction in turbidity and TOC is somewhat longer than that corresponding to the change in the sign of the zeta potential of the sample. This indicates that even after the change in the sign of the zeta potential, adsorption of organic matter continues to some extent. Different parameter values were obtained depending on the type of emulsion studied. The separation factor (K) for the oil/kerosene emulsion was far higher than that for the oil/water emulsion. This indicates that aluminium hydroxide prefers the “lighter” phase of the oil/kerosene suspension over the “heavy” ones obtained with oil alone. Nevertheless, the capacity parameter (n∞ ) is higher for oil than for the oil/kerosene emulsion:
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Optimal Condition
80 60 40 20
Hydrocarbon Removal [%]
100
50
40 30 Time [s ·10 -2]
20 20
10
we
40 60
Po
70
r [W
atts ]
0 100 80 60
0
Fig. 10. Effect of the power and the treatment time on hydrocarbon removal for the oil/kerosene emulsion in water. (F =6.2×10−6 m3 /s; C0 =100 kg/m3 ; K = 31.226; n∞ = 60.258 kg/kg).
aluminium hydroxide appears to be capable of adsorbing larger amounts of oil than oil/kerosene from the wastewater. The effect of the power and treatment time on the hydrocarbon removal from the emulsion is shown in Fig. 10. The cell voltage measured during the experiments was expressed through an empirical function of current density and initial concentration: the law obtained was used to calculate the electrical power consumed. It can be observed that at lower times the slope of the iso-power lines moves from a minimum (lowest power) up to a maximum (highest power). Such behaviour was also observed in Fig. 7, where 150 kg/m3 emulsions were treated at various current densities. Thus, electrical power represents a similar operating parameter for wastewater treatment as current density. Moreover, it can be observed that the minimum power required to achieve a 78% abatement is about 10 W (equivalent to a current density of 137.4 A/m2 ) within the highest operation time. However, this operating condition is of limited practical use due to passivation of the electrode surfaces. On the other hand, it was observed that the time required to reach the same abatement decreases with increasing power consumed. Therefore, a minimum power of 35 W (equivalent to a current density of 294.2 A/m2 ) must be applied for a period of 4500 s period to achieve an abatement yield over 90% with an Al consumption of almost 2 kg/m3 required (Fig. 10). Higher energy consumption for a larger treatment period does not result in significant further abatement. For the present system, a treatment period of 4500 s was also found to be the optimum time (see Fig. 7) for all conditions, provided that the current density was sufficient for destabilisation of the emulsions. Finally, Chen et al. (2002) developed a simplified model for the estimation of the cell voltage and this involved the electrode
potential of the anode and cathode, the activation overpotential, concentration overpotential and ohmic potential drop. They estimated the unknown overpotential by applying the Tafel equation and Nernst equation. For non-passivated and passivated aluminium electrodes, they found that the electrolysis voltage can be expressed by U0 = S +
h K2 i m1 i + K1 ln i + , k km
(20)
where h is the electrode gap, k is the conductivity of the water and i is the current density—the constants S, K1 , K2 , m1 and m must be determined experimentally. K2 has a value of zero for non-passivated electrodes. The basic electrode connection used is in monopolar mode. In this way, the total required cell voltage (U) is equal to the cell voltage (U0 ). Thus, using the same water and current density allows the following equation to be drawn from the above equation for two different electrode gaps. E2 Ai 2 =1− (h1 − h2 ), E1 kE 1
(21)
where E is the electrical power and subscripts 1 and 2 indicate the conditions at the two different electrode gaps. From this point of view, this expression can be used for non-passivated and passivated electrodes. As can be seen, it is possible to minimize the energy consumption by reducing the electrode gaps of the electrochemical cell (h2 < h1 ) to a few millimetres. Studies concerning the influence of the electrode gap were carried out by Sanchez-Calvo et al. (2003) and Cames et al. (2001) for three different scales (laboratory, pilot plant and industrial). Minimum energy consumption was also found for lower electrode gaps and it was determined that lower values can be used for larger scales. 6. Conclusions A simple adsorption model to predict hydrocarbon removal from wastewater by electrocoagulation has been developed. Adsorption of organic matter on Al hydroxide particles was modelled using three different adsorption isotherms and the Langmuir-type equation led to the best results. The model was able to describe the effects of current density and pollutant concentration on the abatement of two different emulsions (oil/water and oil/kerosene/water) as a function of only two adsorption parameters. Different parameter values were obtained depending on the emulsion studied. Aluminium hydroxide has a marked preference for the “light” fractions consisting of oil/kerosene emulsions but its capacity to remove the heavier contaminant (a single oil emulsion) was slightly higher. The destabilisation of the oil/kerosene emulsion was shown to depend on the initial concentration and the current density. When the current density was sufficient to destabilise the emulsion, the zeta potential became positive and a maximum reduction in the turbidity was obtained. However, low current densities are of low efficiency when applied to concentrated emulsions within the considered time period. The use of the adsorption
M. Carmona et al. / Chemical Engineering Science 61 (2006) 1237 – 1246
model allows the minimum power required to achieve the maximum hydrocarbon removal to be obtained without additional experimental data. Taking into account the cell voltage, it was found that a decrease in electrode gap leads to lower energy consumption. Notation A C∗ C0 C exp c CAl(III)
CAl(III) E = UI F I h i I k K KI KII l L m ˙ Al(OH)3 m n n∞ n∞ I nexp NAl3+ PMAl(OH)3 q∗ T u U U0 V x
electrode area, m2 concentration of oil in the solution phase at equilibrium, kg/m3 initial concentration of oil in the solution phase, kg/m3 experimental concentration of oil in the solution phase, kg/m3 concentration of aluminium hydroxide in the cell, kg/m3 concentration of aluminium hydroxide in the reactor, kg/m3 energy consumption, W liquid flow rate, m3 /s Faraday constant electrode gap, m current density, A/m2 cell current, A conductivity of water, s/m separation factor, using LTEE model, Eq. (11) Langmuir equilibrium constant, m3 /kg Freundlich model parameter, m3m /kgm Number of nodes along the cell length electrode length, m mass flux of Al(OH)3 , kg/s exponent of the Freundlich equation the number of electrons produced by anode oxidation aluminium hydroxide capacity, Eq. (11), kg/kg monolayer capacity of aluminium hydroxide, Eq. (12), kg/kg total number of experimental data used in the non-linear regression process flux of Al3+ species formed by dissolution, mol/s molecular weight of the Al(OH)3 (kg/mol) solid-phase concentration of oil, kg/kg time, s superficial velocity, m/s total required cell voltage, V cell voltage between electrodes, V volume of reactor, m3 position along the cell length
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