Ind. Eng. Chem. Res. 2008, 47, 3233-3238
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Solubility and Solid-Phase Composition in Na2CO3-Na2SO4 Solutions at Boiling Temperature: A Modeling Approach Marta A. Bialik,* Hans Theliander, and Peter Sedin Forest Products and Chemical Engineering, Chalmers UniVersity of Technology, Gothenburg, Sweden
Christopher L. Verrill International Paper, Energy & Chemical RecoVery Solutions, LoVeland, Ohio
Nikolai DeMartini Institute of Paper Science and Technology at Georgia Institute of Technology, Atlanta, Georgia
Scaling caused by Na2CO3-Na2SO4 double salts constitutes a severe problem in black liquor evaporators. The ability to predict the solubility and solid-phase composition of these species would be conclusive in minimizing the adverse effects of scaling. Experimental solubility data for (sodium sulfate) dicarbonate, a carbonate-rich double salt identified in Na2CO3-Na2SO4 precipitates, were generated and used for fitting an empirical solubility model. A thermodynamically based approach for predicting the solubility and solidphase composition, previously used for burkeite precipitates, was applied to solid solutions of dicarbonate. Introduction The undesired formation of a solid encrustation layer on the heat exchange surface, commonly known as scaling, is a wellrecognized problem in various industries. Among the most common components of scale in black liquor evaporators are Na2CO3-Na2SO4 double salts; detailed properties of Na2CO3Na2SO4-type scales in black liquor have been discussed elsewhere.1,2 The most important aspects of sodium carbonate and sodium sulfate precipitates are reversed-temperature solubility behavior, causing a tendency to precipitate on the hot heat transfer surfaces and the formation of double-salt precipitates over a fairly wide range of mother liquor concentration. Two distinctive double salts have been identified in Na2CO3-Na2SO4 precipitates from high-temperature solutions: burkeite, 2Na2SO4‚Na2CO3, and sodium sulfate dicarbonate (also referred to as dicarbonate), Na2SO4‚2Na2CO3. The dicarbonate phase has been shown to have a higher tendency to foul heat transfer surfaces in black liquor evaporators than burkeite,3 although the fundamental reason for this difference is not well understood. The relationship between the composition of the mother liquor and the equilibrium solid phase in the Na2CO3-Na2SO4 system is shown in Figure 1. The burkeite double salt has been studied by several researchers.1-5 Among these were Golike et al.,9 who modeled the system by utilizing the principle of free energy minimization and introducing a hypothetical “organic” compound; however, no modeling parameters for the hypothetical compound were given. Recently, Bialik et al.1 proposed a model for calculating solubility and solid-phase composition in high-temperature Na2CO3-Na2SO4 systems precipitating as solid solutions of burkeite and Na2CO3. In contrast, sodium sulfate dicarbonate studies are rare, although the possible existence of a new, carbonate-rich double salt forming scales in black liquor evaporators was reported quite early. In 1970, Helvenston et al.10 described a new double salt with the formula (Na2SO4)4(Na2CO3)9 and presented a preliminary standard for its X-ray diffraction pattern. * To whom any correspondence should be addressed. Fax: +4631-772-2995. E-mail:
[email protected].
Figure 1. Solid composition regimes as a function of solution composition in the sulfate (S), burkeite (B), dicarbonate (D), and sodium carbonate (C) precipitation regions. Data from [, at 100 °C from Green and Frattali;4 ], at 100-110 °C from Novak;5 b, at 102-105 °C from Makarov and Krasnikov;6 O, at 115 °C from Shi;2 2, at 150 °C from Schroeder et al.;7 4, at 150 °C from Itkina and Kokhova.8
Unfortunately, the form of this publication (a patent) meant that it went virtually unnoticed. In the doctoral thesis of Novak5 a new, carbonate-rich double salt was also identified; its characteristic X-ray diffraction (XRD) patterns differed significantly from those known for burkeite solid solutions. The new double salt was reported as having a potential composition of Na2CO3‚Na2SO4, 2Na2CO3‚Na2SO4, or 3Na2CO3‚Na2SO4.5 However, in a widely cited article by Novak11 following his thesis work,5 he withdrew this statement and ascribed the unexpected XRD pattern to a burkeite solid solution. A breakthrough in dicarbonate studies can be credited to Shi and co-workers,2,12,13 who, after obtaining sufficiently large samples of dicarbonate salt from solubility experiments in salt solutions and black liquor, defined its composition and discussed its crystalline structure.2,12 The existence of dicarbonate as an independent salt has also been questioned due to its apparent instability in
10.1021/ie071436r CCC: $40.75 © 2008 American Chemical Society Published on Web 04/03/2008
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common storage conditions. Indeed, when exposed to air moisture, dicarbonate decomposes to burkeite and thermonatrite, Na2CO3‚H2O (further exposure to ambient air CO2 produces trona, Na2CO3‚NaHCO3‚H2O). Bayuadri et al.14,15 recently proved nevertheless that no decomposition of dicarbonate species takes place when stored in dry conditions or in equilibrium with its mother liquor. Researchers agree nowadays that sodium sulfate dicarbonate precipitates from the solutions with Na2CO3/(Na2CO3 + Na2SO4) mole proportion of approximately 0.8-0.9. The corresponding crystalline phase can form solid solutions with a Na2CO3 mole fraction of approximately 0.55-0.85, although both solution and crystal composition regimes corresponding to dicarbonate precipitates may vary slightly with temperature. Due to a limited amount of equilibrium solubility data and technical difficulties with obtaining large, pure dicarbonate crystals, no thorough studies of physicochemical or crystallographic properties of this salt have been performed so far. This work is thus devoted to summarizing solubility data and establishing a solubility constant for sodium sulfate dicarbonate based on equilibrium solubility data in boiling solutions. A comparison between the equilibrium and nucleation solubility data is also made. Experimental Procedures The experiments were conducted following the basic technique described by Shi and Rousseau.12 An unsaturated solution of sodium sulfate and sodium carbonate with the desired proportions of the respective salts was prepared by dissolving the ACS-grade reagents in deionized water under continuous stirring and subsequent heating to approximately 45 °C, where a relatively high solubility limit is expected. Disodium EDTA was added in the amount of approximately 1 g/kg solution in order to avoid the nucleation-inhibiting effect of the calcium ions that are present as a contaminant in Na2CO3 reactant.13 A weighed amount of solution was transferred into a 3-L stainless steel batch crystallizer, sealed, and brought to the desired temperature under continuous stirring. Once the desired temperature level was reached, continuous evaporation was conducted at a rate of 3-5 g/min and the amount of evaporated water was weighed. A sample of crystals and corresponding mother liquor was removed from the reactor through a preheated and pressurized (to avoid liquid flashing) filter chamber equipped with a 0.2 µm inline filter, and quantitatively diluted. In some of the experiments, the liquid and crystal samples were harvested immediately after the nucleation event which was observed by means of particle count readings from a focused beam reflectance measurement (FBRM) device. During the socalled “crystal aging experiments”, however, the evaporated solution was sealed and left for approximately 24 h equilibration (following multiple sampling from the same run, 22 h was determined as being a sufficient equilibration time). After separating the liquid sample from the crystals, the entire filtering assembly was connected to a washing unit. The crystals were washed with a sequence of solvents including 100-150 mL of preheated ethylene glycol-water solution (in 1:1 volumetric proportions), 100-150 mL of ethylene glycol, and two 75 mL portions of ethanol, being air-dried in between. Crystals were then dried in the oven at 150 °C, sieved, and stored in an evacuated desiccator. Such a procedure allowed the complete removal of residual mother liquor and solvents while preventing possible hydration and subsequent decomposition of the resulting crystals.15 Chemical analysis of the liquid samples was conducted in several steps. After analyzing the total solid content, the CO32-
ion concentration was determined by coulometry, while the Na+ and total sulfur contents (the latter assumed as coming exclusively from SO42- ions) were analyzed by inductively coupled plasma (ICP) atomic emission spectrometry. Since the ICP technique for SO42- content was found to be somewhat unreliable, the sulfate ion concentration was often calculated from the carbonate, sodium, and total solid contents, resulting in the accuracy interval of approximately (3%. After identification of the solid phase, the chemical analysis of the dissolved crystal samples was conducted in the same way as for the liquid samples. Results Solid-Phase Identification. A standard X-ray powder diffraction measurement was applied in order to determine the crystalline phase and confirm that the experiment indeed resulted in dicarbonate formation. Since no official standard for a powder diffraction pattern of sodium sulfate dicarbonate was available, an internal standard developed by the Institute of Paper Science and Technology at Georgia Tech was used. This standard was developed based on the work of Shi et al.2,12 and matched the earlier findings of Novak5 and Helvenston et al.10 as well as the results of the subsequent work of Bayuadri et al.14,15 and Verrill et al.;16 the latter included an example of an XRD diagram obtained during this work. A detailed discussion regarding the changes in the powder diffraction pattern due to a possible solid solution formation can be found elsewhere.12 Experimental Data. Figure 2 presents the solubility of dicarbonate, expressed as w/w % of total dissolved solids, as a function of solid-phase composition. The data points corresponding to the dicarbonate precipitation ranges from Shi2 and Schroeder et al.7 have also been plotted for comparison. The solubility data of Green and Frattali4 at 100 °C have also been included, although experimental work from Georgia Tech suggests that dicarbonate is not formed below approximately 110 °C.16 Figure 2 shows a significant difference in total solubility between the experiments involving an equilibration period and the experiments where crystals were harvested immediately after the nucleation, which include the data points of Shi.2 The equilibrium data from the experiments at 115 and 125 °C form a distinctive group within which the total solid content values are comparable; a similar trend can be observed among the nucleation data from 115 and 125 °C. When comparing these two distinctive groups, the width of the metastable zone for both temperature regions, 115 and 125 °C, can be preliminarily estimated as roughly 1-2% in terms of mass fraction of total dissolved solids. Although the earlier results2 may suggest a noticeable difference in the total solubility between the dicarbonate and burkeite precipitation regions, there seems to be no consistent solubility-solid composition trend within the dicarbonate precipitation range itself; see Figure 2. It was, however, impossible to make the detailed solubility comparison between these two double salts because no sufficiently comparable data sets at the two precipitation regions were available. The mass fraction of total dissolved solids was plotted versus the experiment temperature in order to examine the relationship between the total solubility and the temperature more thoroughly. The results can be seen in Figure 3. The total solubility within the dicarbonate precipitation region exhibits a clear decrease with increasing temperature, which is the expected behavior for the Na2SO4-Na2CO3 system. Figure 3 also shows a clear difference in total solubility between the nucleation and
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Figure 2. Total solubility of dicarbonate solid solutions versus solid-phase composition. Data from 2, Green and Frattali, 100 °C;4 [, Shi, 115 °C;2 +, Schroeder et al., 150 °C.7 This work: O, nucleation, 115 °C; b, equilibrium, 115 °C; 0, nucleation, 125 °C; 9, equilibrium, 125 °C.
Figure 3. Total solubility of dicarbonate solid solutions versus temperature. Data from 2, Green and Frattali;4 [, Shi;2 9, Schroeder et al.7 This work: O, nucleation experiments; b, equilibrium experiments. Dashed and solid lines represent the model fitting to the nucleation and equilibrium solubility data, respectively.
equilibrium experiments; here, the width of the metastable zone can be expressed as roughly 30 °C in terms of supersaturation temperature. A multiple linear regression using a least-squares technique was applied to the solubility results shown in Figure 3. After assuming that the width of the metastable zone within the temperature region analyzed was constant, two parallel lines were fitted simultaneously to the two sets of data corresponding to the nucleation and the equilibrium solubility values. Three of the data points, corresponding to 28.18% solid content at 125 °C, 32.48% at 145 °C, and 30.84% at 115 °C, were rejected because they were found to deviate substantially from the general trend. The linear correlation equations describing the total solid content S, (w/w %) as a function of temperature T (°C) for the data in Figure 3 have the following form:
S(nucleation) ) (-5.76 × 10-2)T + 39.6
(1)
S(equilibrium) ) (-5.76 × 10-2)T + 37.8
(2)
with the 95% confidence interval for the slope coefficient equal to (-5.76 ( 1.97) × 10-2 (°C)-1. The size of the metastable zone in terms of the total solid content can thus be expressed as a difference between the intercepts of the two lines and, in
terms of supersaturation temperature, as a ratio between the intercepts difference and the slope. The two values are 1.75% and 30.4 °C, respectively, or 5.7% relative supersaturation at the midpoint of the temperature range shown in Figure 3. The possible relationship between the experiment temperature and the composition of the resulting solid and liquid phases was also investigated. It can be seen from the results shown in Figure 4 that there is no explicit evidence that the experiment temperature influences the precipitation regime and the crystal composition over the liquid-phase composition range studied in these experiments. The results at 115 and 125 °C may suggest a smaller difference between the salt proportions in solid and liquid phases in the case of nucleation experiments, but it is impossible to draw a definite conclusion. Obtaining more experimental data is thus recommended in order to establish the exact boundaries of the precipitation regimes at different temperatures. Modeling of the Solubility Constant. The same technique as described by Bialik et al.1 for burkeite-type precipitates was used for the calculation of the apparent solubility constant for dicarbonate solid solutions over different temperature regions. First, the activity coefficients for all ions present in the mother liquor were calculated using the Pitzer method,17 with temper-
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Figure 4. Salt proportions in solid and liquid phases versus temperature. Data from + and !, Green and Frattali;4 0 and 9, Shi;2 O and b, Schroeder et al.7 This work: ] and [, nucleation; 4 and 2, equilibrium. Empty symbols refer to salt proportions in liquid phase, and filled symbols to those in solid phase.
Figure 5. Apparent solubility constant of dicarbonate as a function of solid-phase composition. Data from 4, Green and Frattali, 100 °C;4 2, Shi, 115 °C.2 This work: /, nucleation at 110 °C; 0, nucleation at 115 °C; 9, equilibrium at 115 °C; ], nucleation at 125 °C; [, equilibrium at 125 °C; O, nucleation at 135 °C; b, equilibrium at 145 °C.
ature-independent interaction coefficients from Pitzer.17 Then, the apparent solubility constant was calculated based on the general equation
Ksp )
acν ∏ aaν ) ∏(γcmc)ν ∏ (γama)ν ∏ c a c a c
a
c
a
(3)
where a is the activity, m is the molality, and γ is the activity coefficient of an ion in the saturated solution; the lower indices “c” and “a” represent a cation and an anion, respectively, while ν is the stoichiometric coefficient. The stoichiometric coefficients for each data point were calculated individually based on the solid-phase composition, according to the procedure reported earlier.1 The coefficient for sodium was assumed to equal 6, while those for the carbonate and sulfate ions varied, reflecting the proportions of respective ions in the solid phase and adding up to 3, as in the dicarbonate salt. Figure 5 presents the apparent solubility constant plotted versus the mole fraction of sodium carbonate in the solid. The decrease of the apparent solubility constant with increasing temperature, seen in Figure 5, can be ascribed to both reversed solubility-temperature behavior of dicarbonate and a significant decrease in ionic activity coefficient with increasing solution temperature.
Figure 5 may suggest a slight increase in the apparent solubility constant with increasing Na2CO3 content but, due to the limited number of data points in any given data set or at any given temperature, and the experimental uncertainty, no definite conclusions can be drawn. As seen in the previous figures, the values obtained from the nucleation experiments are significantly higher than the true solubility values measured after the equilibration of the saturated solution; the “nucleation” Ksp values are of the same order of magnitude as the “equilibrium” values for 10 °C-higher temperature. As far as the true equilibrium experiments are concerned, the apparent solubility constant values are very similar within the subsequent temperature regions. It was thus possible to calculate an average Ksp value for three different temperatures:
Ksp,av(115 °C) ) 1.052 × 10-3
(4)
Ksp,av(125 °C) ) 5.094 × 10-4
(5)
Ksp,av(145 °C) ) 5.500 × 10-5
(6)
The logarithms of apparent solubility constant values obtained from the equilibrium experiments were plotted versus the
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Figure 6. Logarithm of the apparent solubility constant of dicarbonate as a function of reciprocal temperature. Data from b, Green and Frattali;4 2, Schroeder et al.;7 [, this work (only the equilibrium data).
reciprocal temperature in absolute scale, 1/T; for comparison, the results of Green and Frattali4 and Schroeder et al.7 were also included in the diagram. As can be seen in Figure 6, the points can be approximated by a straight line, which is a good indicator of thermodynamic consistency of the model. The only substantial deviation can be observed for the data point of Schroeder et al.7 A possible explanation for this deviation may include a crystalline phase other than dicarbonate (the solid phase obtained by Schroeder et al. was actually identified as burkeite solid solution7) or an unidentified high-temperature effect. Based on the results of this analysis, two different methods for evaluating the probability of a precipitate occurring from a Na2SO4-Na2CO3 solution in the dicarbonate precipitation regime (with Na2CO3/(Na2CO3 + Na2SO4) mole ratio in liquid equal to 0.8-0.9, see Figure 1) can be proposed. The first, relatively simple, method is to compare the total solid content of the solution to the temperature-solubility equations suggested earlier. A second method includes an estimation of the activity coefficients for all ionic species in the solution and a subsequent calculation of the solubility product. The solubility product obtained can, in turn, be compared to the dicarbonate solubility constant for the appropriate temperature level obtained from interpolating the Ksp-temperature trend. Conclusions The total solubility and solid-phase composition of sodium sulfate dicarbonate type precipitates from Na2CO3-Na2SO4 solutions were analyzed. A noticeable difference in the total solubility value has been found between the results of the solubility measurements at the nucleation point and after the equilibration, which suggests the existence of a significant metastable zone. The total solubility has been found to be strongly dependent on temperature, and this dependence can be approximated by a linear equation fitted to the data. No definite relationship between the temperature of the solution and the composition of the precipitating crystals has been found, although the fact that it may exist cannot be excluded. The apparent solubility constant for dicarbonate was calculated according to the method described by Bialik et al.1 and plotted versus the solid-phase composition. In contrast to the case of burkeite, no consistent trend was found. The average value of the apparent solubility constant for the dicarbonate precipitate region was calculated for 115, 125, and 145 °C.
Establishing the experimental solubility limits and the apparent solubility constant for dicarbonate can hopefully lead to better understanding of the behavior of the system and, consequently, to the ability of predicting the conditions under which dicarbonate can form in industrial systems. Acknowledgment The authors are very grateful to S. J. Lien from The Institute of Paper Science and Technology at Georgia University of Technology for his contribution to the experimental work and data analysis. The work was supported by the State of Georgia Traditional Industries Program, the member companies of the Institute of Paper Science and Technology, the Swedish Energy Agency (STEM), and Metso Power AB. Nomenclature a ) ionic or water activity, mol/kg solvent Ksp ) solubility constant Ksp,av ) solubility constant, average value for a temperature level m ) salt molality, mol/kg solvent S ) solubility expressed as total solid content, wt % T ) solution temperature Greek Symbols ν ) stoichiometric coefficient of an ion in the precipitate γ ) ionic activity coefficient Subscripts a ) anion c ) cation Literature Cited (1) Bialik, M.; Theliander, H.; Sedin, P.; Frederick, W. J., Jr. Model for Solubility and Solid-Phase Composition in High-Temperature Na2CO3Na2SO4 Solutions, J. Pulp Pap. Sci. 2007, 3 (33), 150. (2) Shi, B. Crystallization of Solutes that Lead to Scale Formation in Black Liquor Evaporation. Ph.D. Thesis, Georgia Institute of Technology, 2002. (3) Frederick, W. J., Jr.; Shi, B.; Euhus, D. D.; Rousseau, R. W. Crystallization and Control of Sodium Salt Scales in Black Liquor Concentrators. Tappi J. 2004, 3 (6), 7. (4) Green, S. J.; Frattali, F. J. The System Sodium Carbonate-Sodium Sulfate-Sodium Hydroxide-Water at 100°. J. Am. Chem. Soc. 1946, 86, 1789.
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(5) Novak, L. Sodium Salt Scaling in Connection with Evaporation of Black Liquors and Pure Model Solutions. Ph.D. Thesis, Chalmers University of Technology, 1979. (6) Makarov, S. Z.; Krasnikov, S. N. The three-component equilibrium conditions at the boiling point in the four-component system Na2SO4-Na2CO3-NaCl-H2O. IzV. Sekt. Fiz. -Khim. Anal., Akad. Nauk SSSR 1956, 27, 367. (7) Schroeder, W. C.; Berk, A. A.; Gabriel, A. Solubility Equilibria of Sodium Sulfate at Temperatures from 150-350°. II. Effect of Sodium Hydroxide and Sodium Carbonate. J. Am. Chem. Soc. 1936, 58, 843. (8) Itkina, L. S.; Kokhova, V. F. The Solubility and Composition of Solid Phases in the System Na2SO4-Na2CO3-NaOH-H2O between 25 and 150°. Zh. Neorg. Khim. 1960, 5, 1290. (9) Golike, G. P.; Pu, Q.; Holman, K. L.; Carlson, K. R.; Wollwage, P. C.; Folster, H. G.; Rankin, S. NAELS: A New Method for Calculating Equilibrium Solubility of Burkeite and Sodium Carbonate in Black Liquor. Presented at the TAPPI International Chemical Recovery Conference, Tampa, FL, June 1-4, 1998. (10) Helvenston, E. P.; Stewart, D. A. Double salt having the formula (Na2SO4)4(Na2CO3)9. U.S. Patent 3,493,326, 1970. (11) Novak, L. Sodium salt scaling in connection with evaporation of black liquors and pure model solutions. SVen. Papperstidn. 1979, 8, 240.
(12) Shi, B.; Rousseau, R. W. Structure of Burkeite and a New Crystalline Species Obtained from Solutions of Sodium Carbonate and Sodium Sulfate. J. Phys. Chem. B 2003, 107 (29), 6932. (13) Shi, B.; Frederick, W. J., Jr.; Rousseau, R. W. Effects of Calcium and Other Ionic Impurities on the Primary Nucleation of Burkeite. Ind. Eng. Chem. Res. 2003, 42 (12), 2861. (14) Bayuadri, C. Stability of Sodium Sulfate Dicarbonate (∼2Na2CO3‚Na2SO4) Crystals. M.Sc. Thesis, Georgia Institute of Technology, 2006. (15) Bayuadri, C.; Verrill, C. L.; Rousseau, R. W. Stability of sodium sulfate dicarbonate (∼2Na2CO3‚Na2SO4) crystals obtained from evaporation of aqueous solutions of Na2CO3 and Na2SO4. Ind. Eng. Chem. Res. 2006, 45 (21), 7144. (16) Verrill, C. L.; Rousseau, R. W.; Wilkinson, A. W. Crystallization from Aqueous Solutions of Na2CO3 and Na2SO4 as Related to Heat Exchanger Fouling. Presented at the AIChE Annual Meeting, Cincinnati, OH, Oct 31-Nov 4, 2005. (17) Pitzer, K. S. Thermodynamics; McGraw-Hill Series in Advanced Chemistry; McGraw-Hill: New York, 1995.
ReceiVed for reView October 23, 2007 ReVised manuscript receiVed January 17, 2008 Accepted January 24, 2008 IE071436R
