- About this Journal ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Volume 2013 (2013), Article ID 865727, 12 pages
Electrodialysis of Phosphates in Industrial-Grade Phosphoric Acid
1Centro de Investigación y Desarrollo Tecnológico en Electroquímica S.C. Parque, Tecnológico Querétaro, 76703 Sanfandila Pedro Escobedo, QRO, Mexico
2Universidad Tecnológica de Querétaro, 76148 Querétaro, QRO, Mexico
3Universidad del Mar, Ciudad Universitaria, Puerto Ángel, 70902 Distrito de San Pedro Pochutla, OAX, Mexico
Received 27 August 2013; Accepted 31 October 2013
Academic Editors: M. Barragán and H. Zhao
Copyright © 2013 J. J. Machorro et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The objective of this research was to study the purification of industrial-grade phosphoric acid (P2O5) by conventional electrodialysis. The experiments were conducted using a three-compartment cell with anion and cation membranes, and industrial acid solution was introduced into the central compartment. The elemental analysis of the diluted solution indicated that the composition of magnesium, phosphates, and sodium was reduced in the central compartment. The ratios of the concentration of the ions and the phosphates were essentially unchanged by the process. Consequently, electrodialysis could not purify the acid in the central compartment, and the migration of phosphate ions to the anolyte produced a highly concentrated phosphoric acid solution containing sulfates and chlorides as impurities. However, the migration of the phosphate ions across the membrane consumed a large amount of energy. Detailed speciation diagrams were constructed in this study. These diagrams showed that metal-phosphate complexes were predominant in the industrial phosphoric acid solution. This result explains why the ratios of the concentrations of the ion metals and the phosphates did not change in the purification process. The energy consumed in the electrodialysis indicated that the metal-phosphate complexes were less mobile than the free-phosphate ions. The speciation diagrams explained the experimental results satisfactorily.
The annual global phosphorus consumption is approximately 20,764 million metric tons . Phosphoric acid and phosphate salts have several applications. For example, phosphoric acid fuel cells use liquid phosphoric acid as an electrolyte [2, 3]. Industrial-grade phosphoric acid is produced from phosphate rock and consequently has a high content of mineral impurities, which lower the acid quality for commercial use. This industrial-grade phosphoric acid (52–54% P2O5) is also named as merchant-grade acid. Phosphoric acid purification is a major challenge, and a variety of methods have been used to eliminate the impurities in the industrial-grade phosphoric acid [4–18]. These methods which are described in the literature are enumerated in Table 1. In addition, Table 2 shows electrodialysis process for concentrating industrial-grade phosphoric acid [19–27]. These studies in Table 2 provided more comprehensive and consistent information on the energy requirements for the process. Comparing these methods is very difficult for the following reasons: (a) there is a wide variation in the types of the impurities in industrial-grade acid because ores of similar grades can originate from different mines; (b) consequently, the studies investigated different metal impurities; (c) the studies were neither consisted nor complete in their description of the acid purity; and (d) the studies used dissimilar efficiency criteria. Therefore, the methods described in Table 1 cannot be ranked in terms of their relative efficacies. Nonetheless, the studies of electrodialysis show that concentrated phosphoric acid with a low concentration of metal impurities can be obtained by electrodialysis; see Table 2.
Table 1 serves to display the great importance of the acid purification. Although a variety of problem-solving techniques have been identified, there are a limited number of studies with acceptable results. The production of food-grade phosphoric acid is a difficult business.
A significant factor for elucidating the purification process is the speciation of the metals in the concentrated acids. However, the studies presented in Tables 1 and 2 do not address this issue. Therefore, in this study, speciation diagrams were constructed to more thoroughly analyze the purification process.
The goal of this work is to evaluate the viability of electrodialysis for the production of high-value chemicals from raw materials that are abundant in the central region of Mexico and therefore these would be feasible resources for mass production. Other studies are also being conducted in our laboratory on a different highly pure raw material. The current study will serve as an important benchmark for our future research.
2. Materials and Methods
2.1. Materials and Reagents
Two samples of industrial-grade phosphoric acid (also called wet-industrial phosphoric acid) were obtained from Fertinal S. A. (Mexico). These raw materials were produced by the acid digestion of phosphate rock. Pure phosphoric acid 86% was purchased from J. T. Baker (ACS Grade). All other reagents were of analytical grade and were obtained from commercial sources and used without further purification. The high ionic strength of industrial phosphoric acid can produce a layer of precipitates of metal-phosphates, metal-sulfates, and so forth, on the membrane surface. Thus, a dilution solution of industrial acid at 5% w/w was used to prevent membrane fouling.
A trace element mineral analysis was performed by inductively coupled plasma mass spectrometry (Perkin Elmer, USA, model Optima 3300 DV) and by flame atomic absorption spectrophotometry (Perkin Elmer, USA, model AAnalyst 200). The presence of sulfate, fluoride, and phosphate was identified by UV-Vis spectrometry. Samples taken from a phosphoric acid production site were analyzed by potentiometric titration with a NaOH solution.
The membranes were purchased from Ameridia (the US representative of Tokuyama Corporation, Japan). The main characteristic of these membranes is their excellent exchange capacity (mequiv g−1 of ion in the dry membrane form). An AMX-Neosepta anion exchange membrane was used with an exchange capacity of 1.25 mequiv g−1. A CMX-Neosepta cation exchange membrane was used with an exchange capacity 1.62 mequiv g−1. Neosepta-AMX contains quaternary ammonium groups as fixed charges, and Neosepta-CMX contains sulfonic acid groups as fixed charges . These membranes were equilibrated with 1 M KCl solution for 12 h before each experiment.
2.2. Speciation Calculations
The speciation diagrams predict the value of α, the fraction of ions that are free or associated, at a given pH value. The dissociation equilibrium for the phosphate-containing species in the diagrams is given by
The HA acids were HF, HCl, and H2SO4, and the respective anions were , , , and . The general dissociation acid reaction is given by
Note that the silicon concentration is related to the fluoride concentration. That is, during industrial phosphoric acid production, fluoride is produced in the form of fluorosilicic acid. However, this acid and the ion dissociate into Si(HO)4 and HF. The dissociation reactions are as follows:
Therefore, Si(HO)4 and were also included in the speciation diagrams. In addition, 18 metal-phosphate complexes or ion-pairs, that is, , , and so forth, were included with their respective simple cations, that is, , , and so forth. The general equation of the chemical equilibrium for the metal-phosphate complexes is where equals 1, 2, or 3, depending on the partial deprotonation of the phosphoric acid and can vary between 1 and 3. Values derived from the literature [29–31] were used for the equilibrium constants to . The quantity α is defined by the following equation: where  is the concentration of species and is the total concentration of all the species that contain . Material balances must be formulated to determine the fraction α. The total quantities of the metal impurities (), the acids (), and the phosphates () are fixed in a closed system; therefore, the following set of equations holds:
Equations (10), (11) or (12) can be combined with the equilibrium constants (1)–(5) and (8) and (9) to obtain a set of α-fractions as functions of [H+]. The α-fraction for the species is defined by the following equation: where [H+] denotes the proton concentration which was related to the pH and denotes the equilibrium constants to . The α-fractions of the metal-phosphate complexes were directly related to the α-fraction of species and their equilibrium constants; for example
The speciation diagrams were calculated for solutions at 25°C and zero ionic strength. The ionic strength varied during the experiments; however, the equilibrium constants have been reported to depend weakly on the ionic strength (0.40/value) . The temperature increased by 10°C during the experiments. However, only a small variation with temperature has been reported for the equilibrium constants for complex formation (0.045/deg) . Thus, the concentration fractions in diagrams were representative of the actual values.
2.3. Experimental Apparatus
The system consisted of an electrodialysis cell from Asahi Glass Co., DS-0 (Japan), three storage tanks, three hydraulic pumps and a DC power source. The electrodes (each with an effective area of 0.02 m2) were made of titanium coated with platinum and stainless steel. The solution flowed through a plastic schedule 40 polyvinyl chloride pipe. Hydraulic pumps, propelled the electrolyte solution from the storage tank to the electrodialysis cell, through the pipe and back to the storage tanks. A bypass was introduced to control the flow rate (at 5 L/min) at each inlet.
Figure 1 is a schematic of the experimental apparatus for phosphoric acid demineralization. The two membranes were separated by 1.5 mm, and the gap in the anolyte and the catholyte compartments was 2.25 mm.
Prior to each experiment, the three compartments were fed with a 0.01 M NaCl solution (for 30 min), which was replaced a posteriori with the respective solutions (for 30 min), and finally with fresh solutions for demineralization. The central compartment was filled with the solutions shown in Figure 1. Then, the central compartment contained a 0.1 M NaCl solution in 5% w/w analytical-grade phosphoric acid. Also, solutions of 5% w/w industrial-grade acid were introduced into the central compartment, and the behavior of the solutions was compared.
The current-voltage curves were obtained in a galvanodynamic mode, and the limiting current density was obtained from the electrical resistance (R) versus 1/electrical current (I) plots, as described by Sorensen . The temperature, the conductivity, the flow rate, the electrical voltage, and the electrical current were measured during the experiments. More details of the apparatus are provided in our previous work . The Toroidal Conductivity Sensor (Model 226, Rosemount Analytical, USA) was calibrated with KCl solutions. The experiments were performed in triplicate.
3.1. Speciation Diagrams
The industrial-grade phosphoric acid was chemically analyzed for eleven components (see Table 3). The concentration of the impurities was 71.33 g/L, which was representative of the raw material produced by Fertinal (Mexico). The pH of the industrial phosphoric acid was approximately 1; consequently, the speciation diagrams (Figure 2) were concentrated in the acidic region.
During the manufacture of industrial-grade phosphoric acid by treating the rock with acids, fluoride was volatilized and lost in the residues and approximately 3 g/L of fluoride remains in the phosphoric acid. Figure 2(a) shows that hydrogen fluoride (HF) and siliceous acid Si(OH)4 were the predominant species in the industrial acid. The speciation diagrams show that electrodialysis cannot be used to remove fluoride and silicon because the Coulombic attraction was lowered considerably. To be precise, electrodialysis only can remove ionic impurities from industrial acid by using an electric current to pull these ions across the membrane. For HF and Si(OH)4, there is no net driving Coulombic force to produce a migration; that is, nonionic compounds did not migrate when an electric field was imposed. Figure 2(b) shows eight negatively charged species; however, only two ions (sulfates and chlorides) have high concentrations. Therefore, elevated migration can only be expected for these ions. Figure 2(c) shows the seven positively charged species in the pH region that was studied. However, only a few ionic species (K+, Na+, and Mg2+) have high concentrations and consequently will migrate abundantly. Moreover, only about 40% of Ca2+ ions can migrate. Figures 2(d) and 2(e) predict that metal-phosphate complexes or ion-pairs, such as , can form for most metal impurities. Although included in the mathematical analysis, the amounts of the ion-pairs of sodium or potassium were always negligible in our solutions, for example, ; see Figure 2(f). Migneault and Forcé  and Pethybridge et al.  found lower ion-pair association constants of sodium or potassium.
These complexes or ion-pairs are essentially larger ions with lower effective electric charge density. The implication of this lower charge is an increase in the electrical resistance; to be precise, their positive charges allow the complexes to migrate near to the membrane, when electric field is applied across the cell. However, their large size prevents their passage abundantly through the membrane. Consequently, these charged molecules tend to accumulate on the dilute side of membrane and result in a buildup of membrane electrical resistance.
The industrial-grade phosphate had high concentration of phosphate and consequently the metal-phosphate complexes and ion-pairs were formed copiously. However, the studies presented in Table 1 did not address this issue because the speciation diagrams were not consulted. The implication of this is that studies cannot comprehensively analyze their purification process. On the other hand, the construction of the speciation diagrams implied very time-consuming calculations. However, there are software can easily constructed the diagrams. For example MEDUSA with its thermodynamic constants database HYDRA  is able to draw the diagrams. The database HYDRA is incomplete for the metal-phosphate complexes and ion-pairs constant, but it is possible added data. The diagrams constructed using the software MEDUSA and our diagrams were compared. The results are not shown for the sake of brevity. The computational software can be applied to create efficiently the speciation diagrams.
Azaroual et al.  recently show preliminary results for quantifying the undesirable mineral impurities from phosphate ores using a computation tool (SCALE2000 software). However, it is not possible yet to compare the estimated diagrams of aqueous speciation of phosphoric acid.
Figure 3 shows that the conductance of the industrial phosphoric acid was higher than that of the analytical-grade acid. The low conductivity of the pure acid was because the ion comprised only 6% of the phosphate concentration. However, the conductance of the industrial acid was related to the high ion concentration. The industrial phosphoric acid viscosity has also been reported to increase with the phosphoric acid concentration . Note that pure H3PO4 consists of tetragonal groups that are linked by hydrogen bonds . This structure results in a high viscosity fluid, especially at high phosphoric acid concentrations. The dimeric anion () has been found at high acid concentrations, but has not been observed in dilute solutions at room temperature [41, 42]. For solutions below 50% phosphoric acid, there are more bonds between the phosphate ions and water than between the phosphate ions themselves . These larger anions pass scarcely through the positively charged anion exchange membrane. Therefore, electrodialysis was conducted in dilute acid solutions to prevent the formation of phosphate dimeric anions.
3.2. Limiting Current Densities
The limiting current densities (Table 4) were obtained from the current-potential curves (Figure 4). These limiting currents were obtained directly from plots of the electrical resistance versus the reciprocal of the electrical current (which are not shown for brevity), using a method that has been described elsewhere [33, 34]. The inflexion point in the curve for the solution of NaCl in the analytical-grade acid was produced at steady state; that is, the numbers of ions entering the membrane equaled the number of ions entering the diffusion zone. The limiting currents of the industrial-grade phosphoric acid were difficult to obtain, whereas the limiting currents of the analytical-grade acid solutions were straightforward to determine. In addition, the limiting current was also selected to avoid damage to the membrane. Therefore, the limiting current values for the solutions of NaCl in analytical-grade phosphoric acid were selected for the electrodialysis of the industrial-grade phosphoric acid. These current-potential behaviors were affected by the electrical resistance of the electrodialysis cell, which was given by the sum of the solution and membrane resistances. In addition, the formation of the polarization layers adjacent to both sides of the membranes produced a great contribution to the electrical resistance of the cell.
The electrical resistances of the solution are discussed first. The solution of NaCl in the analytical-grade acid produced the highest electrical current. This behavior was observed because the sodium and chlorine ions were moving faster than the metal-phosphate complexes. More precisely, the motion of these ions was unimpeded by attachment to phosphates. Metals, such as aluminum, would have to drag their phosphate ligands along, resulting in a high electrical resistance for the complex. Similar results were obtained by Diallo et al. , who observed that the electrophoretic mobility of ions was proportional to the ion charge/size ratio. Diallo et al.  observed that ion mobility in an electric field range could be ranked in descending order as follows: . Therefore, the complexes decreased the electrostatic interactions resulting in a low electrical current (Figure 4). The phosphate-free ions (see Figures 2(b) and 2(c)) had more mobility than the acids (Figure 2(a)) and the metal-phosphate complexes (Figure 2(d)). The membranes electrical resistances are discussed next. Pismenskaya et al. [44, 45] reported a low electrical conductivity for an anionic-exchange membrane in contact with a phosphate solution. Koter and Kultys  observed a low efficiency for phosphoric acid removal by electrodialysis with anionic membranes. Koter and Kultys  theoretically calculated an association equilibrium constant between and the fixed charges of the anionic membrane. This association diminished the efficacy of the separation process because the neutralized the fixed charges in the anionic membrane. In a previous study, we observed a similar association between nitrate ions and the fixed charges in an anionic membrane using Raman spectroscopy and electrochemical impedance spectroscopy . The excessive potential drop across the cation exchange membrane was because only the protons and the phosphate-free cations were able to migrate effectively. The metal-phosphate complexes had large ionic radii and low charge densities, which decreased their electrostatic interactions and mobilities inside the membrane. This increase of the electrical resistance was explained in Section 3.1. The speciation diagrams clearly show that most positive ions migrated with a very low efficiency because of their reduced ionic charge. However, proton transfer across the membrane increased at the highest electrical currents, depleting the proton concentrations inside the membrane. Therefore, the internal membrane resistance increased.
3.3. Demineralization of Industrial- and Analytical-Grade Acids
The conductance of the acids decreased during the electrodialysis process, as shown in Figure 5. The pH decreased slightly during the demineralization, while the temperature increased by 10°C. These changes did not alter the chemical composition of the solutions and the transport of ions was negligibly affected by the small temperature change.
Hannachi et al.  observed that the highest cation removal occurred for the Mg2+ species; see Table 1. This result is supported by the speciation diagrams (Figure 2), which clearly show that the Mg2+ and phosphate can migrate independently of each other. It is known that Mg2+ and phosphate do not form a covalent complex; for example, Raman spectroscopy has been used to show that the intermolecular Mg–O–P bonding in phosphate salts is more ionic than for other metal–O–P bonds . These ions were selected as a representative species to determine the electrodialysis efficiency. The initial and final concentrations of these species are listed in Table 5. The Mg2+ concentration decreased by approximately 63% on average of its initial value, whereas approximately 70% of the phosphates migrated, which was more than expected. However, the ratio between the concentration of the Mg2+ ions and that of the phosphoric acid was the same before and after the demineralization process (see Figure 6). The same behavior was observed for the ratio between the concentration of the Na+ ions and that of the analytical-grade phosphoric acid. These results show that electrodialysis cannot be used to purify the acid in the central compartment. The migration of phosphates could produce a highly concentrated phosphoric acid solution in the anolyte; however, the sulfates and chlorides would also migrate. Consequently, electrodialysis would produce an anolyte solution containing anionic impurities. The low migration of free cations could be used to produce a catholyte containing cationic impurities.
The energy consumed in the migration of the Na+ and Cl− species was compared with the energy consumption for the electrodialysis of the industrial-grade acid (see Table 6). The energy consumption for the migration of the Na+ and Cl− ions was ten times more effective than the industrial-grade acid demineralization. That is, the energy consumed in Cl− migration (1.57 kWh/kg) was lower than the energy consumed in migration (7.8 kWh/kg). This result can be explained by the mass transfer limitations at low concentrations. The discussion on the electrical resistances of the solution and the membrane, which was previously presented in Section 3.2, can also explain this result.
There is insufficient energy consumption data to compare the studies in Table 1 with the present study. On the other hand, the data in Table 6 show that electrodialysis produced phosphoric acid concentrations that were similar to those reported by the studies in Table 2. Hanley et al.  reported lower energy consumption, and this author also reported a higher acid concentration than that was observed in the present study; but did not report the final concentration of impurities; see Table 2.
The energy consumption for the Na+ and Cl− migration showed that the membranes performed acceptably for electrodialysis; however, the energy consumption for the industrial-grade acid showed that phosphate ions could not migrate efficiently across the membranes.
Many methods have been evaluated in the literature for the purification and concentration of merchant-grade phosphoric acid (52% P2O5); see Table 1. However, these methods cannot be ranked in terms of efficacy because speciation diagrams have not been considered. The speciation diagrams in this study showed that the formation of metal-phosphate complexes decreased electrostatic interactions because of the lower mobility of the complexes. This observation was in fair agreement with the electrodialysis results. The speciation diagrams predicted that the low resistance of sodium and chloride ions relative to the other ions can facilitate phosphoric acid removal, which was verified by the observed energy consumption in the electrodialysis process. The results of the studies in Tables 1 and 2 must be reexamined in light of the speciation diagrams that were constructed in the present work. For example, Mg2+ purification was higher than that for the other metal impurities as speciation diagrams predicted.
A dilute industrial phosphoric acid solution was used to prevent membrane fouling. The three-compartment cell produced a highly concentrated phosphoric acid solution with ionic impurities in the anolyte. In the central compartment, the acid concentration decreased without purifying the acid. Previous electrodialysis studies [20, 21] have assumed that phosphate ions can efficiently migrate across membranes; however, our results show that such a migration process consumes a large amount of energy and would therefore be extremely costly. In addition, the voltages of the ED process were sufficient to damage the membrane. Our results show that electrodialysis is not commercially viable for purifying industrial-grade phosphoric acid. Nevertheless, in future research, our group will test another phosphate raw material, Na3PO4, by the electrodialysis technique, using this study as a benchmark.
The authors would like to acknowledge the financial support provided by Project from CONACYT (FOSIHGO 1999025008).
- G. Villalba, Y. Liu, H. Schroder, and R. U. Ayres, “Global phosphorus flows in the industrial economy from a production perspective,” Journal of Industrial Ecology, vol. 12, no. 4, pp. 557–569, 2008.
- M. Ghouse and H. Abaoud, “Materials used in the development of a 1 kW phospshoric acid fuel cell stack,” Journal of New Materials for Electrochemical Systems, vol. 2, no. 3, pp. 201–206, 1999.
- H.-Y. Kwak, H.-S. Lee, J.-Y. Jung, J.-S. Jeon, and D.-R. Park, “Exergetic and thermoeconomic analysis of a 200 kW phosphoric acid fuel cell plant,” Fuel, vol. 83, no. 14-15, pp. 2087–2094, 2004.
- R. J. Kepfer and W. R. Devor, “Phosphoric acid purification,” U.S. Patent 2,174,158, 1939.
- D. Goldstein, “Phosphoric acid purification,” U.S. Patent 3,819,810, 1974.
- D. H. Michalski and V. Srinivasan, “Process of removing cationic impurities from wet process phosphoric acid,” U.S. Patent 4,639,359, 1987.
- L. W. Bierman, M. L. Lopez, and J. E. Perkins, “Purification of phosphoric acid,” U.S. Patent: 4,877,594, 1989.
- A. I. Alonso, A. M. Urtiaga, S. Zamacona, A. Irabien, and I. Ortiz, “Kinetic modelling of cadmium removal from phosphoric acid by non-dispersive solvent extraction,” Journal of Membrane Science, vol. 130, no. 1-2, pp. 193–203, 1997.
- H. F. T. Haraldsen, “Method for removal of heavy metals from phosphoric acid containing solutions,” U.S. Patent 4,986,970, 1991.
- H. J. Skidmore and K. J. Hutter, “Methods of purifying phosphoric acid,” U.S. Patent 5,945,000, 1999.
- L. H. Reyes, I. S. Medina, R. N. Mendoza, J. R. Vázquez, M. A. Rodríguez, and E. Guibal, “Extraction of cadmium from phosphoric acid using resins impregnated with organophosphorus extractants,” Industrial and Engineering Chemistry Research, vol. 40, no. 5, pp. 1422–1433, 2001.
- M. P. González, R. Navarro, I. Saucedo, M. Avila, J. Revilla, and C. Bouchard, “Purification of phosphoric acid solutions by reverse osmosis and nanofiltration,” Desalination, vol. 147, no. 1–3, pp. 315–320, 2002.
- K. Hotta and F. Kubota, “Method for purification of phosphoric acid high purity polyphosphoric acid,” U.S. Patent: 6,861,039, 2005.
- M. P. González Muñoz, R. Navarro, I. Saucedo et al., “Hydrofluoric acid treatment for improved performance of a nanofiltration membrane,” Desalination, vol. 191, no. 1–3, pp. 273–278, 2006.
- A. Hannachi, D. Habaili, C. Chtara, and A. Ratel, “Purification of wet process phosphoric acid by solvent extraction with TBP and MIBK mixtures,” Separation and Purification Technology, vol. 55, no. 2, pp. 212–216, 2007.
- A. A. El-Asmy, H. M. Serag, M. A. Mahdy, and M. I. Amin, “Purification of phosphoric acid by minimizing iron, copper, cadmium and fluoride,” Separation and Purification Technology, vol. 61, no. 3, pp. 287–292, 2008.
- K. Ishikawa, K. Yokoi, K. Takeuchi, Y. Kurita, and H. Uchiyama, “High purity phosphoric acid and process of producing the same,” U.S. Patent: 7,470,414,B2, 2008.
- M. I. Amin, M. M. Ali, H. M. Kamal, A. M. Youssef, and M. A. Akl, “Recovery of high grade phosphoric acid from wet process acid by solvent extraction with aliphatic alcohols,” Hydrometallurgy, vol. 105, no. 1-2, pp. 115–119, 2010.
- K. W. Loest and J. T. Schaefer, “Production of monobasic potassium phosphate by electrodialysis,” US Patent: 4,033,842, 1977.
- T. R. Hanley, H.-K. Chiu, and R. J. Urban, “Phosphoric acid concentration by electrodialysis,” AIChE Symposium Series, vol. 82, pp. 121–132, 1986.
- D. Touaibia, H. Kerdjoudj, and A. T. Cherif, “Concentration and purification of wet industrial phosphoric acid by electro-electrodialysis,” Journal of Applied Electrochemistry, vol. 26, no. 10, pp. 1071–1073, 1996.
- S. A. Ueda, “Method for purifying phosphoric acid,” Japanese Patent Kokai No. Sho 48 -10312, 1973.
- M. B. C. Elleuch, M. B. Amor, and G. Pourcelly, “Phosphoric acid purification by a membrane process: electrodeionization on ion-exchange textiles,” Separation and Purification Technology, vol. 51, no. 3, pp. 285–290, 2006.
- Y. K. Litsis and B. A. Popov, “Method of extraction of phosphoric acid,” Russian Inventor's Certification No.443839, 1974.
- T. Yamabe, “Method for the manufacture of phosphoric acid,” Japanese Patent Kokai No. Sho 48 -106696, 1976.
- T. Yoshihara, “A method for refining phosphoric acid,” Japanese Patent Kokai No. Sho 53 -96994, 1978.
- K. Moeglich, “Electrochemical processes utilizing layered membrane electrochemical processes utilizing layered membrane,” U.S. Patent 4,326,935, 1982.
- P. Długołecki, K. Nymeijer, S. Metz, and M. Wessling, “Current status of ion exchange membranes for power generation from salinity gradients,” Journal of Membrane Science, vol. 319, no. 1-2, pp. 214–222, 2008.
- E. Högfeldt, Stability Constants of Metal-Ion Complexes. Part A: Inorganic Ligands, vol. 21 of IUPAC Chemical Data Series, Pergamon Press, 1982.
- D. D. Perrin, Dissociation Constants of Inorganic Acids and Bases in Aqueous Solution, IUPAC, Butterworths, London, UK, 1969.
- A. E. Martell and R. M. Smith, Critical Stability Constants, vol. 4 of Inorganic Complexes, Plenum Press, New York, NY, USA, 1976.
- J. N. Butler, Ionic Equilibrium: Solubility and PH Calculations, John Wiley & Sons, Toronto, Canada, 1998.
- T. S. Sorensen, Interfacial Electrodynamics of Membranes and Polymer Films, in Surface Chemistry and Electrochemistry of Membranes, CRC Press, New York, NY, USA, 1999.
- U. López-García, R. Antaño-López, G. Orozco, T. Chapman, and F. Castaneda, “Characterization of electrodialysis membranes by electrochemical impedance spectroscopy at low polarization and by Raman spectroscopy,” Separation and Purification Technology, vol. 68, no. 3, pp. 375–381, 2009.
- D. R. Migneault and R. K. Forcé, “Dissociation constants of phosphoric acid at 25°C and the ion pairing of sodium with orthophosphate ligands at 25°C,” Journal of Solution Chemistry, vol. 17, no. 10, pp. 987–997, 1988.
- A. D. Pethybridge, J. D. R. Talbot, and W. A. House, “Precise conductance measurements on dilute aqueous solutions of sodium and potassium hydrogenphosphate and dihydrogenphosphate,” Journal of Solution Chemistry, vol. 35, no. 3, pp. 381–393, 2006.
- I. Puigdomenech, Make Equilibrium Diagrams Using Sophisticated Algorithms (MEDUSA), Inorganic Chemistry, Royal Institute of Technology, Stockholm, Sweden, 2004.
- M. Azaroual, C. Kervevan, A. Lassin et al., “Thermo-kinetic and physico-chemical modeling of processes generating scaling problems in phosphoric acid and fertilizers production industries,” Procedia Engineering, vol. 46, pp. 68–675, 2012.
- V. M. M. Lobo, Handbook of Electrolyte Solutions, Part A. Physical, vol. 41 of Sciences Data, Elsevier Science, New York, NY, USA, 1989.
- F. A. Cotton and G. Wilkinson, Química Inorgánica Avanzada, Limusa, Cancun, Mexico, 1st edition, 1993.
- M. Cherif, A. Mgaidi, N. Ammar, G. Vallée, and W. Fürst, “A new investigation of aqueous orthophosphoric acid speciation using Raman spectroscopy,” Journal of Solution Chemistry, vol. 29, no. 3, pp. 255–269, 2000.
- W. W. Rudolph, “Raman-spectroscopic measurements of the first dissociation constant of aqueous phosphoric acid solution from 5 to 301°C,” Journal of Solution Chemistry, vol. 41, no. 4, pp. 630–645, 2012.
- H. Diallo, M. Rabiller-Baudry, K. Khaless, and B. Chaufer, “On the electrostatic interactions in the transfer mechanisms of iron during nanofiltration in high concentrated phosphoric acid,” Journal of Membrane Science, vol. 427, pp. 37–47, 2013.
- N. Pismenskaya, E. Laktionov, V. Nikonenko, A. El Attar, B. Auclair, and G. Pourcelly, “Dependence of composition of anion-exchange membranes and their electrical conductivity on concentration of sodium salts of carbonic and phosphoric acids,” Journal of Membrane Science, vol. 181, no. 2, pp. 185–197, 2001.
- N. Pismenskaya, V. Nikonenko, B. Auclair, and G. Pourcelly, “Transport of weak-electrolyte anions through anion exchange membranes: Current-voltage characteristics,” Journal of Membrane Science, vol. 189, no. 1, pp. 129–140, 2001.
- S. Koter and M. Kultys, “Modeling the electric transport of sulfuric and phosphoric acids through anion-exchange membranes,” Separation and Purification Technology, vol. 73, no. 2, pp. 219–229, 2010.
- V. Koleva and V. Stefov, “Phosphate ion vibrations in dihydrogen phosphate salts of the type M(H2PO4)2·2H2O (M = Mg, Mn, Co, Ni, Zn, Cd): Spectra-structure correlate,” Vibrational Spectroscopy, vol. 64, pp. 89–100, 2013.