Chemical Papers 68 (3) 324–329 (2014) DOI: 10.2478/s11696-013-0456-z

ORIGINAL PAPER

Determination of limiting current density for different electrodialysis modules‡ Natália Káňavová*, Lubomír Machuča, David Tvrzník MemBrain s.r.o., Pod Vinicí 87, 471 27 Stráž pod Ralskem, Czech Republic Received 4 June 2013; Revised 28 June 2013; Accepted 28 June 2013

Limiting current density of ammonium nitrate solution in laboratory-, pilot-, and industrial-scale electrodialysis modules were determined to provide a method for the prediction of the limiting current density of ammonium nitrate solutions at any conditions. The current–voltage curve was measured in each case and the limiting current density was evaluated using the dependence of the derivative, dI/dU, on the electric current, I. The limiting current was determined as a current at which the derivative dI/dU equals zero. The developed method enables not only the prediction of the limiting current density but the limiting cut and limiting flux can be determined concurrently at any linear flow velocity of the diluate and inlet ammonium nitrate concentration. It could help to prevent working in the overlimiting region and to avoid undesirable decrease of current efficiency and pH changes. The limiting cut is the maximal cut that can be obtained at certain linear flow velocity and module geometry irrespective of the inlet ammonium nitrate concentration and it is very useful information when designing a new electrodialysis unit for specific application. c 2013 Institute of Chemistry, Slovak Academy of Sciences
Keywords: desalination, electrodialysis, ion exchange membrane, current–voltage curve, limiting current density

Introduction Electrodialysis is an electrochemical separation process using ion exchange membranes to separate ions from the solution. Driving force of this process is the electric potential difference. Well-known applications of electrodialysis are: production of potable water and desalination of sea and brackish water/NaCl production (Davis et al., 2001). It is often used for sweet and salty whey desalination (Šímová et al., 2009; Kinčl et al., 2012). Other applications of electrodialysis are: treatment of wastewater from power industry (Marek, 2012), deacidification of fruit juices (Vera et al., 2003), removal of potassium tartrate from wine (Gon¸calves et al., 2003), treatment of condensate from ammonium nitrate production (Machuča et al., 2012), etc. In a smaller scale, electrodialysis has been applied also in the separation of organic acids, e.g. oxalic acid

(Kaláb & Palatý, 2012) and formic acid from wastewaters (Jaime Ferrer et al., 2006). Basic principle of ion separation has been reviewed by Strathmann (1991). An electrodialysis (ED) module is composed of a membrane stack placed between two electrodes, which consists of alternating cation and anion exchange membranes separated with spacers. Ions are accumulated in concentrate cells and removed from diluate cells. The electrodialysis performance can be influenced by several factors; mainly by the number of cell pairs, length of the solution path in the stack, applied voltage, flow rate and concentration of the feed solution, temperature, etc. The quality of the feed solution is also important because hardness and organic pollution cause membrane scaling and fouling. The transport rate of ions depends on the value of electric current flowing between electrodes. It is thus desirable to work at high current density. In certain

*Corresponding author, e-mail: [email protected] ‡ Presented at the 40th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, Slovakia, 27–31 May 2013.

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Fig. 2. Dependence of electric resistance on the reciprocal electric current and determination of the limiting current.

Fig. 1. Typical current–voltage curve within the Ohmic region, limiting current region and water splitting region.

range of currents, the relationship between the applied voltage, U, and the electric current, I, is described by the Ohm’s law U = IR

(1)

where the electric resistance, R, is the sum of partial resistances in the stack including resistances of ion exchange membranes and diluate/concentrate cells. The transport rate of ions is limited by their transport rate through the membrane. At a certain current level, the transport rate through membrane becomes higher than the diffusion through the laminar boundary layer (diffusion layer) on the membrane surface. This value of electric current is called the limiting current. Reaching the limiting current, the concentration of cations on the cation exchange membrane surface or that of anions on the anion exchange membrane surface becomes zero. The electric resistance of diluate cells sharply increases as a result of ion depletion and the water splitting takes place on the membrane surface in order to generate ions. The Ohm’s law is no longer valid (Valerdi-Pérez & Ibᘠnez-Mengual, 2001; Krol et al., 1999). Typical current–voltage curve is shown in Fig. 1. In cells, pH changes occur and the current efficiency of electrodialysis decreases as a result of H+ and OH− transport. This is the reason of the need to know the value of the limiting current density, which is influenced by many parameters as membrane properties, type and concentration of the electrolyte or hydrodynamic properties (Lee et al., 2006). The limiting current density can be determined from the experimental current–voltage curve (Fig. 1). If the limiting current region is not well defined, the dependence of electric resistance on the reciprocal value of the current can be used. The limiting current is determined by the intersection of two extrapolated sloping lines (Fig. 2) and, after dividing it by the membrane effective area, the limiting current den-

sity is obtained (Mulder, 1996). Rapp and Pfromm (1998) modified this method when they used the 4th order polynomial regression of the R vs. I −1 curve and the limiting current was determined by its minimum. Barragán and Ruíz-Bauzá (1998) described another method of experimental current–voltage curves evaluation. They derived the equation which permits the adjustment of the experimental data and one of the adjustment parameters is the limiting current density, ilim ; this method is however only applicable when the measured current densities are below the limiting current density. Meng et al. (2005) used the dependence of the desalting efficiency on the electric current to determine the limiting current value in their work. Another method for the determination of the limiting current density is the evaluation of the derivative, dI/dU, plotted against the electric current, I. The limiting current can be found as the value of current at which dI/dU equals zero (corresponding to the plateau in the current–voltage curve in Fig. 1) (Ponce-de-León et al., 2007).

Theoretical The limiting current, Ilim , can be expressed as follows: cD |zC νC | F kAmem 
Ilim = l (2) S η tM C − tC where cD l is the mean logarithmic electrolyte concentration in diluate, zC the valence of cations, ν C the stoichiometric coefficient of cations, F the Faraday constant, k the mass transfer coefficient, Amem the effective membrane area, η the electric current effiS ciency, and tM C and tC the transport numbers of cations in the membrane and solution, respectively. Usually, the mass transfer coefficient is unknown but it can be calculated from the experimentally determined limiting current value using reordered Eq. (2). Assuming the mass transfer coefficient to be independent of the inlet electrolyte concentration (according to the results obtained by Nikonenko et al. (2008) this is reasonable in the used concentration range) the following

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equation can be written: k = aub

(3)

where u is the diluate linear flow velocity and a, b are empirical parameters. The limiting flux, Jlim , can be calculated by Eq. (4): ∆cV˙ D (4) Jlim = N wl where ∆c is the difference between the electrolyte inlet and outlet concentration in the diluate, V˙ D the diluate volumetric flow, N the number of cell pairs, w the effective width of the membrane, and l the effective length of the membrane. From the mass balance of diluate, Eq. (5) for the calculation of the outlet electrolyte concentration, cD,out , in the diluate can be derived: 

cD,out

kN wlη = cD,in exp −
 S V˙ D tM C − tC

Fig. 3. Scheme of the ED unit for the determination of the limiting current density with three circuits for diluate (dotted line), concentrate (dashed line), and electrode solution (full line).

 (5)

Then, the limiting cut, ϕ, can be calculated using Eq. (6):   cD,out ϕ = 1− 100 % (6) cD,in When a sufficient amount of experimental results is available, the mass transfer coefficient dependence on the linear flow velocity can be determined and parameters a, b in Eq. (3) can be estimated. Finally, Eqs. (2) and (4)–(6) enable to calculate the limiting current, limiting flux, and limiting cut at any inlet electrolyte concentration, diluate linear flow velocity, and module geometry (using the same type of spacer). Limiting flux is a useful parameter enabling a comparison of the maximal specific mass transfer rate at different conditions and for different ED modules. Limiting cut determines the maximal amount of electrolyte that can be removed from the solution in one passage through the ED stack at a given linear flow velocity and inlet salt concentration.

Experimental Ammonium nitrate p.a. NH4 NO3 (Lach-ner, Neratovice, Czech Republic) and RO water were used to prepare test solutions for the experiments. Cation and anion exchange membranes RALEX (Mega, Stráž pod Ralskem, Czech Republic) were used in the laboratory-, pilot-, and industrial-scale ED modules (Mega, Stráž pod Ralskem, Czech Republic) for the determination of limiting current densities. The scheme of the electrodialysis unit is presented in Fig. 3. The laboratory-scale module consisted of ten cell pairs with the effective membrane area of 0.064 m2 . The pilot-scale module consisted of 15 cell pairs with the effective membrane area of 0.6 m2 . The industrial-scale

module consisted of 600 cell pairs with the effective membrane area of 249.6 m2 . In each case, the spacer thickness was 0.8 mm. Feed solution from the tank with the temperature of 25 ◦C was passed through the ED module in three circuits: for diluate, concentrate, and electrode solution. The inlet ammonium nitrate concentration was changing in the range of 6.25–25 mmol L−1 and the linear flow velocity of the diluate in the range of 2.6– 15.1 cm s−1 . Samples for the measurement of conductivity, pH, and temperature were collected before and after the passage of the feed through the stack. The applied voltage was increasing in the range of 0.5–5 V per cell pair and the corresponding current values were recorded.

Results and discussion From the wide spectrum of methods for the evaluation of experimental current–voltage curves, two were chosen and used in this work. The first is the determination of the limiting current density from the plot of electric resistance, R, vs. the reciprocal current, I−1 . This method is widely used for this purpose but some authors consider it to be not sufficiently exact and underestimating the limiting current density values (Ponce-de-León & Field, 2000). For this reason, the second method was used and the limiting current density was also determined from the plot of the derivative dI/dU vs. the electric current, I. The limiting current was evaluated as an electric current at which dI/dU equals zero. The results obtained by both methods at different diluate linear flow velocities, u, and inlet ammonium nitrate concentrations, c, in the laboratory-scale ED module are presented in Table 1. It is clear that values obtained by the derivative method are from 10 % to 60 % higher than those obtained by the R vs. I−1 method, and the difference becomes more significant with the increasing

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Table 1. Results of the determination of the limiting current density at different diluate linear flow velocities and ammonium nitrate concentrations from experimental data obtained in the laboratory-scale ED module

u (cm

s−1 )

2.604 3.906 4.774 5.208 6.076 8.681

c (mmol

L−1 )

6.25 12.49 6.25 12.49 9.37 6.25 12.49 9.37 12.49

ilim · 103 (A cm−2 ) R vs. I−1

dI/dU vs. I

2.969 5.213 3.438 5.936 4.844 4.063 6.719 5.938 9.375

3.281 6.250 4.219 7.656 6.835 5.000 9.375 8.438 15.469

Table 2. Comparison of experimentally determined and predicted values of the limiting current density for the industrial-scale ED module u (cm s−1 )

6.51

ilim (A cm−2 )

c (mmol L−1 )

12.5 25 37.5

Fig. 4. Dependence of mass transfer coefficient on the linear flow velocity and comparison of experimental ( ) and fitted data (—).

linear flow velocity. This fact confirms the underestimation of the limiting current density by the R vs. I−1 method, therefore, the results obtained by the second method were used in further considerations. As the data obtained using the pilot-scale ED module represent a transition point between the laboratory and industrial sphere, they were used to evaluate the dependence of the mass transfer coefficient, k, on the diluate linear flow velocity, u, and to estimate parameters a, b in Eq. (3). In each case, the limiting current, Ilim , was determined and then the corresponding value of k was calculated according to the reordered Eq. (2). Estimated values of the parameters are: a = 0.001232 and b = 0.667. The agreement of experimen-

experimental

predicted

4.808.10−3 7.740.10−3 12.091.10−3

4.409.10−3 8.793.10−3 13.072.10−3

tal and fitted data is shown in Fig. 4. All input requirements for the limiting current density prediction method are presented as these parameters are known. Fig. 5 presents the agreement of experimentally determined and predicted values of the limiting current densities in the laboratory- and pilot-scale ED modules at various diluate linear flow velocities and ammonium nitrate inlet concentrations. The same comparison for industrial-scale ED module is shown in Table 2. In each case, the agreement of data is satisfactory. The submitted data confirm the suitability and correctness of the proposed method. It is able to reliably predict the limiting current density of ammonium nitrate solutions at any inlet concentration and diluate linear flow velocity either in laboratory-, pilot-, or industrial-scale ED module (when using a defined type of spacer). At the same time, the limiting cut and limiting flux can be calculated as it is depicted in Fig. 6, where predicted values of ilim , Jlim , and ϕlim in a broad range of inlet concentrations and diluate linear flow velocities in the pilot-scale ED module are shown. It is clear that the limiting cut is independent of the inlet ammonium nitrate concentration. The value of the limiting cut presents the maximal cut that can be obtained at a given ED module geometry and linear flow velocity. This means that the limiting cut cannot be exceeded even when using higher voltage; the increase of the voltage only results in the decrease of the current efficiency. The only way of increasing the limiting cut is to decrease the diluate linear flow velocity.

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Fig. 5. Comparison of experimentally determined (
) and predicted limiting current densities at various linear flow velocities and inlet ammonium nitrate concentrations of 6.25 mmol L−1 (full line), 12.5 mmol L−1 (dotted line), and 25 mmol L−1 (dashed line) in the laboratory-scale (a) and pilot-scale (b) modules.

Fig. 6. Predicted values of limiting current density (a), limiting cut (b), and limiting flux (c) in the considered range of ammonium nitrate inlet concentrations and diluate linear flow velocities.

Conclusions Limiting current densities were successfully determined in the range of ammonium nitrate inlet con-

centrations and diluate linear flow velocities in laboratory, pilot, and industrial electrodialysis modules. To evaluate the experimental data, the dI/dU vs. I plot was applied and the limiting current was set as

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the current at which derivative dI/dU = 0. The data obtained in the pilot-scale ED module were taken and the dependence of the mass transfer coefficient on the linear flow velocity was examined. Subsequently, parameters a, b from Eq. (3) were estimated as follows: a = 0.001232 and b = 0.667. In order to verify the reliability of the proposed method, predicted data and those obtained experimentally in the laboratory-, pilot- and industrial-scale ED module were compared and the agreement was recognized as satisfactory, which proved the method to be applicable for various types of ED modules. An important benefit of this method is the ability to calculate not only the limiting current density but also the limiting cut and limiting flux in a broad range of electrodialysis input parameters (only the type of the spacer must be the same). The limiting cut is a useful design parameter as it is actually the maximal cut that can be obtained with the defined ED module and linear flow velocity. Acknowledgements. The work was supported by the Ministry of Industry and Trade of the Czech Republic within the framework of the project ”Research, development and application of new generation electromembrane modules” program TIP No. FR-TI4/398, using the infrastructure of the Membrane Innovation Centre (No.CZ 1.05/2.1.00/03.0084).

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