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Modeling the electrocoagulation process for the treatment of contaminated water
Accepted Manuscript Modeling the electrocoagulation process for the treatment of contaminated water Nuno S. Graça, Ana M. Ribeiro, Alírio E. Rodrigues PII: DOI: Reference:
S0009-2509(19)30030-2 https://doi.org/10.1016/j.ces.2018.12.038 CES 14688
To appear in:
Chemical Engineering Science
Received Date: Revised Date: Accepted Date:
2 August 2018 12 December 2018 21 December 2018
Please cite this article as: N.S. Graça, A.M. Ribeiro, A.E. Rodrigues, Modeling the electrocoagulation process for the treatment of contaminated water, Chemical Engineering Science (2019), doi: https://doi.org/10.1016/j.ces. 2018.12.038
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Modeling the electrocoagulation process for the treatment of contaminated water. Nuno S. Graça, Ana M. Ribeiro, Alírio E. Rodrigues
Laboratory of Separation and Reaction Engineering - Laboratory of Catalysis and Materials (LSRELCM), Department of Chemical Engineering, University of Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal.
Abstract
The
study
of
the
electro-dissolution
of
aluminum
electrodes
during
the
electrocoagulation process is important for understanding the mechanisms involved in the process. This study involved the experimental determination of both total and dissolved aluminum concentrations during the electrocoagulation processes operation. The total aluminum concentration was fitted with the Faraday’s equation and was obtained 1.6 of current efficiency, indicating a super-faradaic behavior of the electrochemical process at the given operating conditions. Additionally, a mathematical model was developed considering the electrochemical dissolution of the Al anode, water electrolysis, hydrolysis of dissolved Al and water dissociation reaction involved in the electrocoagulation process. The simulated results showed a good prediction of the evolution of both concentration of dissolved aluminum and pH during the electrocoagulation process operation. The model was also employed to simulate the removal of arsenic from water by electrocoagulation showing a good prediction of the experimental results at the operating conditions considered.
1. Introduction
The electrocoagulation (EC) process is a low cost and environmentally friendly technology for the treatment of water containing different kinds of contaminants such as heavy metals [1], organic compounds [2], oil [3] and suspended solids [4]. Moreover, due to its minimum requirement of chemicals, reduced risk of secondary pollution and low sludge production [5], it has been seen as an alternative to conventional chemical coagulation processes [6, 7]. Therefore, more research effort should be made in the next years to better understand the process and make the EC process competitive as a reference technology for water treatment. During the EC process, coagulant species are produced in-situ by the electrodissolution of the sacrificial anode. Aluminum and iron electrodes are typically used resulting in electro-generated ions of Al3+ or Fe2+; these ions undergo further hydrolysis reactions producing monomeric and polymeric species that will finally be transformed into solid flocs [8, 9]. These flocs have the potential for adsorption or entrapment of pollutants [10]. Therefore, the metal ionic species distribution is a determining factor of the EC performance [11]. Moreover, after the flocculation, the pollutants can be removed by sedimentation, filtration or flotation. The bubbles formed due to both oxygen and hydrogen evolution in the electrodes helps to increase the efficiency of the removal by flotation [12]. To better understand the phenomena involved in the EC process, an effort on the development of mathematical models that describe the physical system should be made. However, due to the complexity of the process the development of mathematical models able to describe all the mechanisms involved is hard to achieve. Therefore, the use of lumped-parameter models, where the process variables are independent of the position, depending only on the time could be an alternative. Matteson et al. [13] developed a mathematical model for the removal of suspended particles by EC using iron electrodes. This model considers both the electrophoretic concentration of particles near the anode, and their subsequent coagulation. Khemis et al. [14] proposed a mathematical model for
the prediction of liquid waste abatement in terms of COD (chemical oxygen demand) by complexation of suspended matter using aluminum electrodes. In this model is assumed that the limiting step in the EC is the complexation reaction between the coagulants species and the pollutants. It is also considered pseudo-equilibrium constants for the reaction between the coagulants and the pollutants. Lacasa et al. [15] proposed a mathematical model for the electrocoagulation of wastewaters with aluminum and iron electrodes. Similarly, to the Khemis et al. approach, this model considers that the interactions between the pollutants and coagulant species are very fast and therefore they can by represented by means of pseudo-equilibrium equations. These models can be used to simulate the EC process for the treatment of several water pollutants systems; however, a mathematical model that satisfactorily describes every process involved in this type of treatment is still long way off [16]. The following work proposes a mathematical model for the EC process able to predict both dissolved aluminum concentration and pH. The experimental determination of total and dissolved aluminum concentration during the EC operation was useful for the development and validation of the mathematical model. The mathematical model was also used to simulate the removal of arsenic from water by electrocoagulation at three different arsenic initial concentrations.
2. Experimental
2.1 Experimental apparatus
The electrocoagulation experiments were carried out using an acrylic tank, 0.18 x 0.18 x 0.18 m. Aluminum electrodes, 15 x 10 x 0.2 cm, with a total effective area of 0.0152 m2 were used. A magnetic stirrer at 200 rpm was used to maintain a homogeneous solution in the reactor. The conductivity and pH were measured using a multi-parameter meter (VWR MU 6100 L). Each experiment was performed using 3 L of deionized water and the conductivity was adjusted by adding some drops of a saturated sodium chloride solution (0.35 mg L-1). The electrodes were fixed on the top of the tank with a gap of 0.008 m between them and partially dipped on the solution (4 cm), the anode and cathode were connected to a DC power supply (Velleman LABPS3020) operating under galvanostatic conditions. Before each experiment, the electrodes were polished with
sandpaper and dipped in a 0.1 N NaOH solution for 5 min and then cleaned with deionized water.
2.2 Analytical methods
The
concentrations
of
Aluminum
and
Arsenic
were
determined
using
a
spectrophotometer (Merck Millipore Spectroquant Prove 300) and the respective analysis kit (Merck Millipore aluminum test 114825 and arsenic test 101747). To determine the total aluminum concentration, samples of 10 mL were collected and immediately analyzed. For the determination of the dissolved aluminum concentration, samples of 10 mL were collected and filtered before the analysis.
3. Mathematical model formulation
The model proposed in this work considers that electrochemical dissolution of aluminum, water electrolysis, hydrolysis dissolved Al and water dissociation reaction are involved in the electrocoagulation process [17]. Due to the complex nature of the mechanisms involved, the following general simplifications and assumptions should be made: 1) the parameters of the model do not depend on the position inside the reactor, therefore, mass transport phenomena are not considered; 2) the shrinkage of the anode due to its dissolution is neglected, since the dissolved mass is very small compared with the electrode mass; 3) the process is considered isothermal; 4) The effect of the presence of the Na+ and Cl- ions is not accounted in the model. When the electrical current is established an electrochemical process involving the aluminum dissolution and oxygen evolution on the anode (Eq. (1) and (2)) and the hydrogen evolution on the cathode (Eq. (3)) is initiated. (1)
(2)
(3)
The rate of aluminum dissolution on the anode can be determined based on the Faraday’s law (Eq.(4)). (4)
where
is the applied current intensity (A),
(
,
is the valence number of the metal
is Faraday’s constant (94,485 C∙mol-1), V is solution volume (m3) and
is
the current efficiency. The dissolved aluminum resulting from the electrochemical process can undergo different hydrolysis reactions producing several aluminum hydroxide monomeric species such as such as
, ,
, ,
and and
; and polymeric species [18]. However, to simplify
the model only the monomeric species will be considered. The formation of precipitates during the EC process can be attributed mainly to the formation of
[19, 20].
The equilibrium composition of the different aluminum hydroxide species can be determined from purely thermodynamic data [21, 22]: (5)
(6)
were
are the thermodynamic equilibrium constants. Figure 1 shows the solubility diagram resulting from the thermodynamic data
(Table 1) and Eq. (5) and (6).
Fig. 1 Aluminum solubility equilibrium diagram.
The hydrolysis reactions considered in the model are:
Reaction 1
(7) Reaction 2
(8) Reaction 3
(9) Reaction 4 (10)
Water dissociation reaction
(11)
The corresponding reaction rates are given by:
(12)
(13)
(14)
(15)
(16)
From the mass balance to the species we obtain:
,
,
,
,
and
(17)
(18)
(19)
(20)
(21)
(22)
From the application of the electro-neutrality criteria Eq. (23).
(23)
We get the evolution of
:
(24)
The model proposed here considers that after the saturation concentration value is achieved, the kinetic of formation of solid particles in the solution is directly proportional to the difference between the concentration of dissolved aluminum and the saturation concentration of dissolved aluminum is given by:
. Therefore, before saturation the concentration
(25) and after saturation,
(26) where the saturation concentration is obtained from Eq. (5) and (6) and is given by:
(27)
The system of differential equations (Eqs. (16)-(26)) was solved numerically using the commercial software gPROMS (general PROcess Modeling System, version 4.2.0). The initial concentration of species was considered zero except for for which the initial concentration is given by the initial pH.
Table 1 Thermodynamic equilibrium data and kinetic constants for the hydrolysis reactions.
[23]
[21]
1
4.2×104 s-1
9.6×10-6
2
4.2×104 s-1
5.3×10-5
3
5.6×104 s-1
2.0×10-6 2.7×10-9
4 w s
1.52×10-6 mol L-1 s-1
1.0×10-14 4.6×10-33
and
4. Results and discussion
4.1. Total Aluminum concentration
The total concentration of aluminum was determined experimentally during the EC operation for three different current intensities (40 mA, 100 mA and 190 mA). The results obtained are presented in Figure 2, showing that the total concentration of aluminum increases with the current intensity and during the time, which is in accordance with the Faraday’s law. From the fitting of the current efficiency parameter from Eq. (4) to the experimental data, a value of 1.6 was obtained which indicates a super-faradaic behavior of the electrochemical process. Previous published works attribute the super-faradaic production of aluminum to the corrosion of the cathode as consequence of the formation of alkaline pH on its surface due to the formation of associated with the hydrogen evolution (Eq. (3)) [24]. Also, the addiction of salts such as sodium chloride often used in the EC process to increase the conductivity can lead to the increase of the dissolution of the electrode to values above the one predicted by the Faraday’s equation [25]. It was shown that concentrations of sodium chloride above 8.8 g/m3 can result in up to 70% of extra aluminum dissolution [25]. A theoretical study by Guseva et al. [26] showed that from the dissolution of aluminum in a sodium chloride solution results in the formation of several species such as Al(OH) 2+, Al(OH)2+, Al(OH)3, Al(OH)4-,Al2(OH)24+, Al3(OH)45+, Al13O4(OH)247+, AlCl2+, Al(OH)Cl+, and Al(OH)2Cl. In the experimental results obtained it can be also noticed that for the higher currents and higher operation times the concentration obtained is slightly lower than the theoretical value. This decrease on the aluminum dissolution efficiency can be attributed to the competition between the water oxidation and aluminum dissolution (Eqs. (1) and (2)) that increases especially for high current values [24].
Fig. 2 Total concentration of aluminum during the time for different applied current intensities.
4.2. Dissolved Aluminum concentration
The dissolved aluminum concentration was determined experimentally during the EC operation for three different current intensities (40 mA, 100 mA and 190 mA). Each experiment was performed applying electrical current during the first 30 minutes of operation and after that the current was turned off, the electrodes were removed from the reactor and the experiment proceed for 1 hour more. The results obtained are presented in Figures 3, 4 and 5. From the analysis of the results obtained for the lowest current (Figure 3) it can be noticed that the dissolved aluminum concentration is almost the same as the total aluminum concentration for the first 30 minutes of operation. This indicates that the rate of formation of solid particles is lower than the aluminum dissolution rate. However, a different result was obtained for the two higher current intensities where the dissolved concentration begins to diverge from the total concentration between 10 and 15 minutes for the current intensity of 100 mA (Figure 4) and between 5 and 10 minutes for the current intensity of 190 mA (Figure 5). These results suggest that the rate of formation of solid particles is higher than the aluminum production rate and the rate of solid particles formation seams to increase for higher current intensities.
In all the experiments the dissolved aluminum concentration decreases after the removal of the electrodes, this is caused by the continuation of the formation solid particles.
Fig. 3 Total and dissolved aluminum concentration during the EC operation for an electrical current of 40 mA.
Fig. 4 Total and dissolved aluminum concentration during the EC operation for an electrical current of 100 mA.
Fig. 5 Total and dissolved aluminum concentration during the EC operation for an electrical current of 190 mA.
4.3. Model results
The simulation of the EC operation for the operating conditions described in the section 4.2 was performed by solving the mathematical model (Eqs. (17)-(26)). Rate and equilibrium constants obtained from the literature (Table 1) were used, except for which its value was chosen to provide the best fit in all the cases considered in the present work (
). Figure 6 presents the comparison between
experimental and simulated results obtained by adjusting the
parameter. The results
show that to fit the simulated values to the first 30 minutes operation; the model prediction fails for the next 1-hour of the experiment for the two higher currents where the rate of the particles formation seems to be lower than the one predicted by the model.
Fig. 6 Comparison of the experimental dissolved aluminum concentration with the values predicted with the 1-parameter model for different current intensities.
An alternative could be the use of two different parameters depending on the electrical current is on (
or off (
. The results obtained by adjusting the two parameters
are presented in Figure 7, and the adjusted values shown in Table 2. The results show that the coagulation rate constant increases with the current intensity for the first 30 minutes of operation. On the other side, the values for the next 1 hour of the experiment don't differ significantly. These results suggest that the mechanism of particle formation is directly affected by the presence of electrical current.
Fig. 7 Comparison of the experimental dissolved aluminum concentration with the values predicted with the 2-parameter model for different current intensities.
Table 2 Model parameters for the different current intensities.
1 parameter
2 parameters
I(mA) 40
1.1×10-4
1.1×10-4
100
8.0×10-4
8.0×10-4
190
1.0×10-3
1.0×10-3
1.0×10-4
The pH variation was determined experimentally during the EC operation for the experiments performed at three different current intensities (40 mA, 100 mA and 190 mA) as described in section 4.2. The experimental results obtained (Figures 8, 9 and 10) show that the pH increases for the three cases when the electrical current is applied (first 30 minutes). This increase of pH can be attributed to the production of hydroxide ions on the cathode (Eq. (3)). These hydroxide ions are not neutralized since the main reaction on the anode is the aluminum dissolution (Eq. (1)) and not the production of oxygen by the water electrolysis (Eq. (2)). For the second part of the experiment (no current), the pH decreases slowly until the end of the operation. This reduction in the pH can be attributed to the consumption of hydroxide ions in the formation of precipitates. The comparison between the experimental and simulated results (Figures 8,9 and 10) shows that the model reasonably predicts the trend of pH variation for the three currents considered.
Fig. 8 pH variation during the EC operation for an electrical current of 40 mA.
Fig. 9 pH variation during the EC operation for an electrical current of 100 mA.
Fig. 10 pH variation during the EC operation for an electrical current of 190 mA
5. Modeling the arsenic removal by Electrocoagulation
The mathematical modeling strategy employed in the present work is similar to the one used by Carmona et al. (2006) [27] which considers that concentration of the pollutant in the particle is always in equilibrium with liquid phase concentration. Therefore, the mass balance between solid and liquid phase concentrations in equilibrium can be expressed by: (28)
where
is the initial concentration of the pollutant,
and
pollutant concentrations in solid and liquid phase, respectively, and
are the equilibrium represents the
concentration of solid aluminum hydroxide particles. In the model proposed by Carmona et al. (2006) [27] was considered that the all the aluminum generated by the anode dissolution is converted in solid Al(OH)3 and its concentration is given by:
(29)
where
is the applied current intensity (A),
(
,
is the valence number of the metal
is Faraday’s constant (94,485 C∙mol-1), V is solution volume (m3) and
the current efficiency,
is
is the molecular mass of Al(OH)3 and t is the time
(min). However, the results obtained in the present work (see section 4.2) showed that the assumption made in Eq. 29 is not true when high current intensities were used (Figure 4 and 5). Therefore, in the model prosed the solid concentration is given by:
(30) where
is the total concentration of aluminum generated by the anode dissolution
and can be determined by a Faraday’s type equation (Eq. 4). The dissolved aluminum concentration,
, is determined by solving the Eqs. (17)-(26).
A Langmuir-type empirical equation was used to describe the adsorption equilibrium:
(31)
where Q is the solid capacity and K is the separation factor. By combining Eq. 28 and 31 results:
(32)
(33)
This model was used to simulate the removal of arsenic from water by electrocoagulation. Experimental arsenic removal experiments were performed in the set-up described in section 2.1 for three different arsenic initial concentrations (2, 3 and 4 mg/l of As) using a current intensity of 190 mA. The mathematical model was fit to the experimental data by adjusting the parameters of Eq. 31 (Q=7 mgAs.mgAl-1 and K=1.1). A comparison between the experimental and simulated arsenic removal results is presented in Figure 11.
Fig. 11 Experimental and simulated results for the removal of arsenic from water by EC for an electrical current of 190 mA.
The results shown that despite some difference at the 20-minute operation time, the proposed model reasonably describes the electrocoagulation operation for the three concentrations considered. The deviations between the model and experimental results can be attributed to the use of a relatively simple mechanism to describe the arsenic adsorption. The use of a more complex mechanism which considers the different arsenic species formed depending on the solution pH and oxidation potential, may provide a better model prediction. However, the use of such mechanism requires a more detailed study of the arsenic speciation and adsorption behavior during the electrocoagulation process.
6. Conclusions
The study of the electro-dissolution of the aluminum electrodes was performed experimentally in a batch EC reactor. Both total and dissolved aluminum concentrations were determined during the EC operation. The total aluminum concentration was fitted with the Faraday’s equation and a current efficiency values of 1.6 was obtained, indicating a super-faradaic behavior of the electrochemical process. The determination of the dissolved aluminum was performed for the cases when the electrical current is on and off. The results obtained indicated that different coagulation mechanism should be present in each case. A mathematical model was developed. The simulated results showed that the model reasonably predicts the evolution of both concentration of dissolved aluminum and pH. Additionally, the mathematical model developed is able to reasonably predict the EC operation performance for the removal of arsenic from water. Moreover, the presented model intends to be a base for the development of more complex models that may be required to predict the performance of the EC reactor to treat a specific effluent.
7. Acknowledgement
This work was financially supported by: Project POCI-01-0145-FEDER-006984 – Associate Laboratory LSRE-LCM funded by FEDER through COMPETE2020 Programa Operacional Competiti idade e nternacionali a o ( funds through FC
- Funda o para a Ci ncia e a
C ) – and by national
ecnologia
ro ect
4 funded by FC - Funda o para a Ci ncia e a ecnologia.
nn-
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Highlights
Molding the electro-dissolution of the Al anode during EC operation; Predicting both dissolved Al concentration and pH evolution during EC operation; Simulating the EC operation for arsenic removal from water.
S0009-2509(19)30030-2 https://doi.org/10.1016/j.ces.2018.12.038 CES 14688
To appear in:
Chemical Engineering Science
Received Date: Revised Date: Accepted Date:
2 August 2018 12 December 2018 21 December 2018
Please cite this article as: N.S. Graça, A.M. Ribeiro, A.E. Rodrigues, Modeling the electrocoagulation process for the treatment of contaminated water, Chemical Engineering Science (2019), doi: https://doi.org/10.1016/j.ces. 2018.12.038
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Modeling the electrocoagulation process for the treatment of contaminated water. Nuno S. Graça, Ana M. Ribeiro, Alírio E. Rodrigues
Laboratory of Separation and Reaction Engineering - Laboratory of Catalysis and Materials (LSRELCM), Department of Chemical Engineering, University of Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal.
Abstract
The
study
of
the
electro-dissolution
of
aluminum
electrodes
during
the
electrocoagulation process is important for understanding the mechanisms involved in the process. This study involved the experimental determination of both total and dissolved aluminum concentrations during the electrocoagulation processes operation. The total aluminum concentration was fitted with the Faraday’s equation and was obtained 1.6 of current efficiency, indicating a super-faradaic behavior of the electrochemical process at the given operating conditions. Additionally, a mathematical model was developed considering the electrochemical dissolution of the Al anode, water electrolysis, hydrolysis of dissolved Al and water dissociation reaction involved in the electrocoagulation process. The simulated results showed a good prediction of the evolution of both concentration of dissolved aluminum and pH during the electrocoagulation process operation. The model was also employed to simulate the removal of arsenic from water by electrocoagulation showing a good prediction of the experimental results at the operating conditions considered.
1. Introduction
The electrocoagulation (EC) process is a low cost and environmentally friendly technology for the treatment of water containing different kinds of contaminants such as heavy metals [1], organic compounds [2], oil [3] and suspended solids [4]. Moreover, due to its minimum requirement of chemicals, reduced risk of secondary pollution and low sludge production [5], it has been seen as an alternative to conventional chemical coagulation processes [6, 7]. Therefore, more research effort should be made in the next years to better understand the process and make the EC process competitive as a reference technology for water treatment. During the EC process, coagulant species are produced in-situ by the electrodissolution of the sacrificial anode. Aluminum and iron electrodes are typically used resulting in electro-generated ions of Al3+ or Fe2+; these ions undergo further hydrolysis reactions producing monomeric and polymeric species that will finally be transformed into solid flocs [8, 9]. These flocs have the potential for adsorption or entrapment of pollutants [10]. Therefore, the metal ionic species distribution is a determining factor of the EC performance [11]. Moreover, after the flocculation, the pollutants can be removed by sedimentation, filtration or flotation. The bubbles formed due to both oxygen and hydrogen evolution in the electrodes helps to increase the efficiency of the removal by flotation [12]. To better understand the phenomena involved in the EC process, an effort on the development of mathematical models that describe the physical system should be made. However, due to the complexity of the process the development of mathematical models able to describe all the mechanisms involved is hard to achieve. Therefore, the use of lumped-parameter models, where the process variables are independent of the position, depending only on the time could be an alternative. Matteson et al. [13] developed a mathematical model for the removal of suspended particles by EC using iron electrodes. This model considers both the electrophoretic concentration of particles near the anode, and their subsequent coagulation. Khemis et al. [14] proposed a mathematical model for
the prediction of liquid waste abatement in terms of COD (chemical oxygen demand) by complexation of suspended matter using aluminum electrodes. In this model is assumed that the limiting step in the EC is the complexation reaction between the coagulants species and the pollutants. It is also considered pseudo-equilibrium constants for the reaction between the coagulants and the pollutants. Lacasa et al. [15] proposed a mathematical model for the electrocoagulation of wastewaters with aluminum and iron electrodes. Similarly, to the Khemis et al. approach, this model considers that the interactions between the pollutants and coagulant species are very fast and therefore they can by represented by means of pseudo-equilibrium equations. These models can be used to simulate the EC process for the treatment of several water pollutants systems; however, a mathematical model that satisfactorily describes every process involved in this type of treatment is still long way off [16]. The following work proposes a mathematical model for the EC process able to predict both dissolved aluminum concentration and pH. The experimental determination of total and dissolved aluminum concentration during the EC operation was useful for the development and validation of the mathematical model. The mathematical model was also used to simulate the removal of arsenic from water by electrocoagulation at three different arsenic initial concentrations.
2. Experimental
2.1 Experimental apparatus
The electrocoagulation experiments were carried out using an acrylic tank, 0.18 x 0.18 x 0.18 m. Aluminum electrodes, 15 x 10 x 0.2 cm, with a total effective area of 0.0152 m2 were used. A magnetic stirrer at 200 rpm was used to maintain a homogeneous solution in the reactor. The conductivity and pH were measured using a multi-parameter meter (VWR MU 6100 L). Each experiment was performed using 3 L of deionized water and the conductivity was adjusted by adding some drops of a saturated sodium chloride solution (0.35 mg L-1). The electrodes were fixed on the top of the tank with a gap of 0.008 m between them and partially dipped on the solution (4 cm), the anode and cathode were connected to a DC power supply (Velleman LABPS3020) operating under galvanostatic conditions. Before each experiment, the electrodes were polished with
sandpaper and dipped in a 0.1 N NaOH solution for 5 min and then cleaned with deionized water.
2.2 Analytical methods
The
concentrations
of
Aluminum
and
Arsenic
were
determined
using
a
spectrophotometer (Merck Millipore Spectroquant Prove 300) and the respective analysis kit (Merck Millipore aluminum test 114825 and arsenic test 101747). To determine the total aluminum concentration, samples of 10 mL were collected and immediately analyzed. For the determination of the dissolved aluminum concentration, samples of 10 mL were collected and filtered before the analysis.
3. Mathematical model formulation
The model proposed in this work considers that electrochemical dissolution of aluminum, water electrolysis, hydrolysis dissolved Al and water dissociation reaction are involved in the electrocoagulation process [17]. Due to the complex nature of the mechanisms involved, the following general simplifications and assumptions should be made: 1) the parameters of the model do not depend on the position inside the reactor, therefore, mass transport phenomena are not considered; 2) the shrinkage of the anode due to its dissolution is neglected, since the dissolved mass is very small compared with the electrode mass; 3) the process is considered isothermal; 4) The effect of the presence of the Na+ and Cl- ions is not accounted in the model. When the electrical current is established an electrochemical process involving the aluminum dissolution and oxygen evolution on the anode (Eq. (1) and (2)) and the hydrogen evolution on the cathode (Eq. (3)) is initiated. (1)
(2)
(3)
The rate of aluminum dissolution on the anode can be determined based on the Faraday’s law (Eq.(4)). (4)
where
is the applied current intensity (A),
(
,
is the valence number of the metal
is Faraday’s constant (94,485 C∙mol-1), V is solution volume (m3) and
is
the current efficiency. The dissolved aluminum resulting from the electrochemical process can undergo different hydrolysis reactions producing several aluminum hydroxide monomeric species such as such as
, ,
, ,
and and
; and polymeric species [18]. However, to simplify
the model only the monomeric species will be considered. The formation of precipitates during the EC process can be attributed mainly to the formation of
[19, 20].
The equilibrium composition of the different aluminum hydroxide species can be determined from purely thermodynamic data [21, 22]: (5)
(6)
were
are the thermodynamic equilibrium constants. Figure 1 shows the solubility diagram resulting from the thermodynamic data
(Table 1) and Eq. (5) and (6).
Fig. 1 Aluminum solubility equilibrium diagram.
The hydrolysis reactions considered in the model are:
Reaction 1
(7) Reaction 2
(8) Reaction 3
(9) Reaction 4 (10)
Water dissociation reaction
(11)
The corresponding reaction rates are given by:
(12)
(13)
(14)
(15)
(16)
From the mass balance to the species we obtain:
,
,
,
,
and
(17)
(18)
(19)
(20)
(21)
(22)
From the application of the electro-neutrality criteria Eq. (23).
(23)
We get the evolution of
:
(24)
The model proposed here considers that after the saturation concentration value is achieved, the kinetic of formation of solid particles in the solution is directly proportional to the difference between the concentration of dissolved aluminum and the saturation concentration of dissolved aluminum is given by:
. Therefore, before saturation the concentration
(25) and after saturation,
(26) where the saturation concentration is obtained from Eq. (5) and (6) and is given by:
(27)
The system of differential equations (Eqs. (16)-(26)) was solved numerically using the commercial software gPROMS (general PROcess Modeling System, version 4.2.0). The initial concentration of species was considered zero except for for which the initial concentration is given by the initial pH.
Table 1 Thermodynamic equilibrium data and kinetic constants for the hydrolysis reactions.
[23]
[21]
1
4.2×104 s-1
9.6×10-6
2
4.2×104 s-1
5.3×10-5
3
5.6×104 s-1
2.0×10-6 2.7×10-9
4 w s
1.52×10-6 mol L-1 s-1
1.0×10-14 4.6×10-33
and
4. Results and discussion
4.1. Total Aluminum concentration
The total concentration of aluminum was determined experimentally during the EC operation for three different current intensities (40 mA, 100 mA and 190 mA). The results obtained are presented in Figure 2, showing that the total concentration of aluminum increases with the current intensity and during the time, which is in accordance with the Faraday’s law. From the fitting of the current efficiency parameter from Eq. (4) to the experimental data, a value of 1.6 was obtained which indicates a super-faradaic behavior of the electrochemical process. Previous published works attribute the super-faradaic production of aluminum to the corrosion of the cathode as consequence of the formation of alkaline pH on its surface due to the formation of associated with the hydrogen evolution (Eq. (3)) [24]. Also, the addiction of salts such as sodium chloride often used in the EC process to increase the conductivity can lead to the increase of the dissolution of the electrode to values above the one predicted by the Faraday’s equation [25]. It was shown that concentrations of sodium chloride above 8.8 g/m3 can result in up to 70% of extra aluminum dissolution [25]. A theoretical study by Guseva et al. [26] showed that from the dissolution of aluminum in a sodium chloride solution results in the formation of several species such as Al(OH) 2+, Al(OH)2+, Al(OH)3, Al(OH)4-,Al2(OH)24+, Al3(OH)45+, Al13O4(OH)247+, AlCl2+, Al(OH)Cl+, and Al(OH)2Cl. In the experimental results obtained it can be also noticed that for the higher currents and higher operation times the concentration obtained is slightly lower than the theoretical value. This decrease on the aluminum dissolution efficiency can be attributed to the competition between the water oxidation and aluminum dissolution (Eqs. (1) and (2)) that increases especially for high current values [24].
Fig. 2 Total concentration of aluminum during the time for different applied current intensities.
4.2. Dissolved Aluminum concentration
The dissolved aluminum concentration was determined experimentally during the EC operation for three different current intensities (40 mA, 100 mA and 190 mA). Each experiment was performed applying electrical current during the first 30 minutes of operation and after that the current was turned off, the electrodes were removed from the reactor and the experiment proceed for 1 hour more. The results obtained are presented in Figures 3, 4 and 5. From the analysis of the results obtained for the lowest current (Figure 3) it can be noticed that the dissolved aluminum concentration is almost the same as the total aluminum concentration for the first 30 minutes of operation. This indicates that the rate of formation of solid particles is lower than the aluminum dissolution rate. However, a different result was obtained for the two higher current intensities where the dissolved concentration begins to diverge from the total concentration between 10 and 15 minutes for the current intensity of 100 mA (Figure 4) and between 5 and 10 minutes for the current intensity of 190 mA (Figure 5). These results suggest that the rate of formation of solid particles is higher than the aluminum production rate and the rate of solid particles formation seams to increase for higher current intensities.
In all the experiments the dissolved aluminum concentration decreases after the removal of the electrodes, this is caused by the continuation of the formation solid particles.
Fig. 3 Total and dissolved aluminum concentration during the EC operation for an electrical current of 40 mA.
Fig. 4 Total and dissolved aluminum concentration during the EC operation for an electrical current of 100 mA.
Fig. 5 Total and dissolved aluminum concentration during the EC operation for an electrical current of 190 mA.
4.3. Model results
The simulation of the EC operation for the operating conditions described in the section 4.2 was performed by solving the mathematical model (Eqs. (17)-(26)). Rate and equilibrium constants obtained from the literature (Table 1) were used, except for which its value was chosen to provide the best fit in all the cases considered in the present work (
). Figure 6 presents the comparison between
experimental and simulated results obtained by adjusting the
parameter. The results
show that to fit the simulated values to the first 30 minutes operation; the model prediction fails for the next 1-hour of the experiment for the two higher currents where the rate of the particles formation seems to be lower than the one predicted by the model.
Fig. 6 Comparison of the experimental dissolved aluminum concentration with the values predicted with the 1-parameter model for different current intensities.
An alternative could be the use of two different parameters depending on the electrical current is on (
or off (
. The results obtained by adjusting the two parameters
are presented in Figure 7, and the adjusted values shown in Table 2. The results show that the coagulation rate constant increases with the current intensity for the first 30 minutes of operation. On the other side, the values for the next 1 hour of the experiment don't differ significantly. These results suggest that the mechanism of particle formation is directly affected by the presence of electrical current.
Fig. 7 Comparison of the experimental dissolved aluminum concentration with the values predicted with the 2-parameter model for different current intensities.
Table 2 Model parameters for the different current intensities.
1 parameter
2 parameters
I(mA) 40
1.1×10-4
1.1×10-4
100
8.0×10-4
8.0×10-4
190
1.0×10-3
1.0×10-3
1.0×10-4
The pH variation was determined experimentally during the EC operation for the experiments performed at three different current intensities (40 mA, 100 mA and 190 mA) as described in section 4.2. The experimental results obtained (Figures 8, 9 and 10) show that the pH increases for the three cases when the electrical current is applied (first 30 minutes). This increase of pH can be attributed to the production of hydroxide ions on the cathode (Eq. (3)). These hydroxide ions are not neutralized since the main reaction on the anode is the aluminum dissolution (Eq. (1)) and not the production of oxygen by the water electrolysis (Eq. (2)). For the second part of the experiment (no current), the pH decreases slowly until the end of the operation. This reduction in the pH can be attributed to the consumption of hydroxide ions in the formation of precipitates. The comparison between the experimental and simulated results (Figures 8,9 and 10) shows that the model reasonably predicts the trend of pH variation for the three currents considered.
Fig. 8 pH variation during the EC operation for an electrical current of 40 mA.
Fig. 9 pH variation during the EC operation for an electrical current of 100 mA.
Fig. 10 pH variation during the EC operation for an electrical current of 190 mA
5. Modeling the arsenic removal by Electrocoagulation
The mathematical modeling strategy employed in the present work is similar to the one used by Carmona et al. (2006) [27] which considers that concentration of the pollutant in the particle is always in equilibrium with liquid phase concentration. Therefore, the mass balance between solid and liquid phase concentrations in equilibrium can be expressed by: (28)
where
is the initial concentration of the pollutant,
and
pollutant concentrations in solid and liquid phase, respectively, and
are the equilibrium represents the
concentration of solid aluminum hydroxide particles. In the model proposed by Carmona et al. (2006) [27] was considered that the all the aluminum generated by the anode dissolution is converted in solid Al(OH)3 and its concentration is given by:
(29)
where
is the applied current intensity (A),
(
,
is the valence number of the metal
is Faraday’s constant (94,485 C∙mol-1), V is solution volume (m3) and
the current efficiency,
is
is the molecular mass of Al(OH)3 and t is the time
(min). However, the results obtained in the present work (see section 4.2) showed that the assumption made in Eq. 29 is not true when high current intensities were used (Figure 4 and 5). Therefore, in the model prosed the solid concentration is given by:
(30) where
is the total concentration of aluminum generated by the anode dissolution
and can be determined by a Faraday’s type equation (Eq. 4). The dissolved aluminum concentration,
, is determined by solving the Eqs. (17)-(26).
A Langmuir-type empirical equation was used to describe the adsorption equilibrium:
(31)
where Q is the solid capacity and K is the separation factor. By combining Eq. 28 and 31 results:
(32)
(33)
This model was used to simulate the removal of arsenic from water by electrocoagulation. Experimental arsenic removal experiments were performed in the set-up described in section 2.1 for three different arsenic initial concentrations (2, 3 and 4 mg/l of As) using a current intensity of 190 mA. The mathematical model was fit to the experimental data by adjusting the parameters of Eq. 31 (Q=7 mgAs.mgAl-1 and K=1.1). A comparison between the experimental and simulated arsenic removal results is presented in Figure 11.
Fig. 11 Experimental and simulated results for the removal of arsenic from water by EC for an electrical current of 190 mA.
The results shown that despite some difference at the 20-minute operation time, the proposed model reasonably describes the electrocoagulation operation for the three concentrations considered. The deviations between the model and experimental results can be attributed to the use of a relatively simple mechanism to describe the arsenic adsorption. The use of a more complex mechanism which considers the different arsenic species formed depending on the solution pH and oxidation potential, may provide a better model prediction. However, the use of such mechanism requires a more detailed study of the arsenic speciation and adsorption behavior during the electrocoagulation process.
6. Conclusions
The study of the electro-dissolution of the aluminum electrodes was performed experimentally in a batch EC reactor. Both total and dissolved aluminum concentrations were determined during the EC operation. The total aluminum concentration was fitted with the Faraday’s equation and a current efficiency values of 1.6 was obtained, indicating a super-faradaic behavior of the electrochemical process. The determination of the dissolved aluminum was performed for the cases when the electrical current is on and off. The results obtained indicated that different coagulation mechanism should be present in each case. A mathematical model was developed. The simulated results showed that the model reasonably predicts the evolution of both concentration of dissolved aluminum and pH. Additionally, the mathematical model developed is able to reasonably predict the EC operation performance for the removal of arsenic from water. Moreover, the presented model intends to be a base for the development of more complex models that may be required to predict the performance of the EC reactor to treat a specific effluent.
7. Acknowledgement
This work was financially supported by: Project POCI-01-0145-FEDER-006984 – Associate Laboratory LSRE-LCM funded by FEDER through COMPETE2020 Programa Operacional Competiti idade e nternacionali a o ( funds through FC
- Funda o para a Ci ncia e a
C ) – and by national
ecnologia
ro ect
4 funded by FC - Funda o para a Ci ncia e a ecnologia.
nn-
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Highlights
Molding the electro-dissolution of the Al anode during EC operation; Predicting both dissolved Al concentration and pH evolution during EC operation; Simulating the EC operation for arsenic removal from water.