Ind. Eng. Chem. Res. 2010, 49, 2401–2409
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Crystallization in a Pilot Evaporator: Aqueous Solutions of Na2CO3 and Na2SO4 Mathias Gourdon* and Lennart Vamling Energy and EnVironment, Chalmers UniVersity of Technology, Gothenburg, Sweden
Ulf Andersson and Lars Olausson Metso Power AB, Gothenburg, Sweden
Sodium carbonate and sodium sulfate cause problems by forming scales in black liquor evaporators, reducing heat transfer and cleaning intervals. An experimental investigation of the crystallization behavior during evaporation of different aqueous solutions of sodium carbonate and sodium sulfate has been carried out. The analysis is based on changes in heat transfer coefficients and crystal masses. The results from this work show large variation in the distribution of the crystal mass, depending on the composition of the solution. Solutions with the crystalline form of either dicarbonate or sodium carbonate exhibit high propensity to form scales on the heat transfer surface. Solutions with the crystalline form of burkeite, however, do not show the same attraction to the heat transfer surface; they are more likely to crystallize in the circulating solution. Thus, the heat transfer is not as affected as for dicarbonate or sodium carbonate. Introduction To avoid precipitation of soluble scales on the heat transfer surfaces in black liquor evaporators, knowledge of the crystallization behavior of black liquor is essential. In a survey of North American pulp mills performed by Schmidl and Frederick1 35% of the investigated mills were reported to have problems with soluble Na2CO3-Na2SO4 scales. The ratio between the two salts is an important parameter that affects the crystallization of these salts. The solvent-free mole fraction can be expressed as: x)
[Na2CO3] [Na2CO3] + [Na2SO4]
(1)
Depending on the mole fraction in the solution, different crystals will form. Shi and Rousseau2 reported four different crystal species that will form for different mole fractions. In the region x < 0.2 sodium sulfate will form, for 0.2 < x < 0.833 burkeite will form, for 0.833 < x < 0.9 sodium sulfate dicarbonate will form (further on referred to as dicarbonate), and for x > 0.9 sodium carbonate or thermonatrite will form. Burkeite, having a nominal formula of 2Na2SO4 · Na2CO3, may form crystals with various composition, depending on the mother solution’s composition. Burkeite crystals with compositions approximately between 0.22 < x < 0.5 have been reported.3 As for burkeite, dicarbonate also forms crystals diverging from the nominal composition of 2Na2CO3 · Na2SO4. Shi et al.3 reported crystals with compositions ranging between approximately 0.63 < x < 0.7. One important aspect of the crystallization is that both double salts have reverse solubility with temperature, causing a propensity to precipitate on the hot heat transfer surface. Euhus et al.4 investigated how the temperature difference, Reynolds number, and carbonate-to-sulfate ratio affected the fouling in a semibatch falling film evaporator. They found that a low temperature difference and low Reynolds number favored heat transfer fouling per unit of concentration increase. Contradicting the later results of Frederick et al.,5 they found a * To whom correspondence should be addressed. Tel.: +46 31 772 3017. E-mail:
[email protected].
solution in the dicarbonate region (x ) 0.87) to have lower fouling rates than a solution in the burkeite region (x ) 0.5). In the present work the crystallization behavior of different Na2CO3-Na2SO4 aqueous solutions was examined. The experiments focused on high carbonate-to-sulfate ratios, since these are the most frequent conditions used in industry. Compositions on both sides of the boundary between the burkeite and dicarbonate region were investigated and, as an extreme, pure sodium carbonate was also studied. The purpose was to see how the crystallization behavior changed with different composition and whether some conditions were favorable to avoid scaling on the heat transfer surface. A total of four different compositions were examined. The experimental part of this work was performed in a pilot evaporator. A method of operation that allowed the study of the crystallization behavior quantitatively was chosen. With this method, the crystallization is investigated by analyzing different crystal masses, in bulk and on surfaces. At all times during the evaporation, the crystal mass in the circulating solution and on surfaces is calculated. The crystals on surfaces can be located either as scales on the heat transfer surface or as crystals located on other types of surfaces. In the experiments, heat transfer coefficients are measured. From the results of these measurements, the relation between the two types of crystal masses on surfaces can be estimated. Experimental Equipment and Procedure A schematic of the experimental setup is seen in Figure 1. The main part of the research evaporator is a vertical tube, 60 mm in diameter and 4.5 m long, with the falling film on the outside. The evaporator is heated with steam, condensing on the inside of the tube. The most important outputs are temperatures, heat transfer coefficients (local and average), circulation mass flow rate, density, viscosity, particle counts, and mass of produced vapor condensate. The temperatures are measured using both thermocouples (type K) and PT-100 elements. The local heat transfer coefficients are calculated from local temperature measurements in the evaporator tube. The average solution and steam temperatures together with the mass flow rate of steam condensate are used to calculate the average heat
10.1021/ie901390c 2010 American Chemical Society Published on Web 02/08/2010
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flow rate was also kept constant at 0.700 m3/h. This means that, depending on the density, the mass flow rate, Γ, was between 1.15 and 1.42 kg/(m s). As the temperature was kept constant, the pressure was decreased because of the increased boiling point elevation with increasing concentration. The concentration was increased to and well above the solubility limit before the experiments were terminated. The operating procedure is designed to be able to identify different crystal masses in the evaporator. A detailed presentation of the calculation procedure can be found in Gourdon et al.7 Only the main concepts will be outlined here. The evaporator system is divided in three subsystems: the liquid part of the solution, the crystals in the solution, and crystals on surfaces (not accompanying the solution), see Figure 2. In the evaluation procedure, mass fractions are frequently used. The salt mass fraction (i.e., the fraction of sodium carbonate and sodium sulfate) is defined as:
Figure 1. Flow sheet of the research evaporator.
transfer coefficient. The particle counts are measured using a Lasentec FBRM D600L. The Lasentec FBRM uses a rotating laser to detect particles by backscattered light. It detects chord lengths rather than particle sizes, and the output from the equipments is a chord length distribution. The density and mass flow rate is measured with an Endress Hauser PROline promass 80 H Coriolis Mass Flow. The accuracy of the equipment according to the manufacturer for the density measurement is (0.002 kg/L and the repeatability is (0.0005 kg/L. The accuracy has been verified by density measurements of water at different temperatures. The viscosity is measured with a Marimex, Viscoscope - Sensor VA-300 L having a stated accuracy (1.0% of value. The mass of produced vapor condensate is weighted using a Mettler-Toledo scale with a stated accuracy of (1 g. Details of the research falling film evaporator and operating procedure are given in Gourdon et al.6,7 For this work a refractometer has been installed that measures the index of refraction of the circulating solution. The refractive index is known to change with both composition and temperature and can be used to determine concentration of solubles in the solution.8 The instrument is a K-Patent PR-23-SD with a wavelength of 589 nm that measures the refractive index between 1.32 and 1.52. Experimental Procedure and Theory of Operation. The evaporator experiments were performed in semibatch mode. Table 1 provides the composition of the solutions in the different experiments. For all compositions, two experiments with different saturated steam temperatures were performed. The solution temperature was always constant at 120 °C. Changing the temperature difference between the steam and the circulating solution will change the evaporation rate. The duration of the experiments varied between 2 and 6 h, mostly depending on the temperature difference. In the experiments, the solution was first heated to the operating temperature. When the operating temperature was reached, a continuous removal of vapor condensate from the evaporator was initiated, increasing the concentration. During the experiments the temperatures of both the saturated steam and the solution were then kept constant. The saturated steam temperature (or pressure) is regulated with an automated control valve on the inlet to the evaporator, and the solution temperature (or pressure) is regulated with an automated control valve on the vapor outlet to the condensor. The volumetric circulation
Xi )
msi msi + mwi
(2)
where i can be c, l, or s or combinations thereof according to Figure 2. By careful measurements of the amount of water in the system at all times, by weighing the vapor condensate, the water mass, mwl , is known. The salt mass (sodium carbonate and sodium sulfate) added to the system, msc+l+s, is carefully weighed before the start. The system’s total salt fraction can be expressed as: Xc+l+s(t) )
s mc+l+s s mc+l+s + mwl (t)
(3)
If the solubility, X*, l of the solution is known and the system is assumed to be at equilibrium, the total crystal mass (on surfaces and in the solution) can be calculated as: s (t) mc+s
)
s mc+l+s
mwl (t)X*l 1 - X*l
(4)
The fact that the total crystal mass is calculated from the solubility means that it will actually have a positive value from the moment when the solubility limit is passed. However, since the model assumes that the system is at equilibrium and no crystals exist until the metastable limit is passed, the value of the total crystal content has been set to zero before the metastable limit. The actual mass fraction in the circulating solution,Xc+l, which above the solubility limit is a liquid-solid mixture, is obtained from the density measurement. An ideal mixture between a solution at the solubility limit (X*,ν l *) l and pure crystals is assumed. In addition to the mass balance (MB) and salt balance (SB), a volume balance (VB) can thus be set up: MB: mc+l ) m*l + mc
(5)
SB: mc+lXc+l ) m*X l * l + mc · Xc
(6)
VB: mc+lνc+l ) m*ν l * l + mcνc
(7)
By combining eqs 5-7, the liquid-solid mixture mass fraction is obtained from the liquor specific volume as follows: Xc+l ) X*l +
(
)
Xc - X*l (νc+l - ν*) l νc - ν*l
(8)
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a
Table 1. Experimental Conditions
experiment number
Na2CO3/Na2SO4 Na2CO3/(Na2CO3 + Na2SO4) ∆T initial To,wall
g/g mol/mol °C °C
1
2
3
4
5
6
7
8
∞ 1 6 121.7
∞ 1 10 122.9
5 0.867 10 122.9
5 0.867 6 121.7
2.5 0.765 10 122.9
2.5 0.765 6 121.7
1.87 0.705 10 122.9
1.87 0.705 6 121.7
a
The presented sodium carbonate-sodium sulfate mass and mole ratios are for the initial solutions. ∆T is the temperature difference between the heating steam and the solution. Initial To,wall is the temperature of the tube-wall material closest to the solution in the beginning of the experiments (To,wall varies with the heat flux).
masses can be calculated by dividing the crystal masses with the total mass of the system: total: cfc+s(t) ) Figure 2. The evaporator subsystems and combinations of these.
on surfaces: cfs(t) )
where Xc is equal to 1 kg/kg and νc+l is the measured specific volume of circulating mixture. For the experiments with solely sodium carbonate, the specific volume of crystalline sodium carbonate was used (νc ) 0.395 dm3/kg), and for the mixture experiments, the specific volume of burkeite was used (νc ) 0.389 dm3/kg).9 From the mass fraction in the circulating solution, the total amount of salt in the circulating solution (i.e., subsystem c + l) can be calculated as:
s mc+l (t) ) mwl (t)
Xc+l(t) 1 - Xc+l(t)
(10)
Finally, the circulating crystal mass can be calculated as the difference of the total crystal mass and the mass on surfaces: s msc(t) ) mc+s (t) - mss(t)
(11)
During the release of the initial supersaturation, the circulating crystal mass is assumed to have an equilibration time of a few minutes, and thus during this period it is not fulfilling the crystal mass balance in eq 11. The crystal mass on surfaces can be divided in two categories, either crystals on the heat transfer surface or crystals on other surrounding surfaces. From the measurement of heat transfer coefficients (calculation procedure described elsewhere7) it is possible to see qualitatively whether scales are formed on the heat transfer surface. Thus, by examining the change in heat transfer, the location of the surface crystal mass can be estimated. To get an indication of how high the concentration of crystals is, the crystal fractions (in kg/kg) corresponding to the crystal
s mc+l+s + mwl (t)
mss(t) s mc+l+s + mwl (t)
msc(t) s mc+l+s + mwl (t)
(12)
(13)
(14)
The refractive index can also be used to measure concentration in a crystallizing solution. For the system NaSO4-CO3-H2O, unfortunately no literature data were found. A correlation for the refractive index at 120 °C was developed based on the experimental data below the solubility limit, according to the following general form:
(9)
With a known amount of circulating salt, the amount of crystals on surfaces can be expressed as the difference between the total amount of weighed salts and the circulating salt mass: s s mss(t) ) mc+l+s - mc+l (t)
in solution: cfc(t) )
s mc+s (t)
2CO3 2SO4 RI ) a1Xwl + a2XNa + a3XNa l l
(15)
where Xl is the mass fraction in the liquid solution. Using a least-squares regression, the parameters a1, a2, and a3 were determined to be 1.3144, 1.514, and 1.453, respectively, giving an R2 value of 0.9964. For a wavelength of 589 nm, saturated water at 120 °C is reported to have a refractive index of 1.3131.10 By assuming that the presence of crystals is not affecting the refractive index, this correlation can be used to measure the concentration of dissolved salts also above the solubility limit. Results Solubility Limits and Crystal Composition. An important parameter of the method to determine the different crystal masses is the solubility limit. Bialik et al.11 modeled the solubility limit of the system Na-SO4-CO3-H2O based on the available data from several studies. For the temperature range from 100 to 115 °C, three different studies were used, Shi,12 Green and Frattali,13 and Makarov and Krasnikov.14 For high carbonate-to-sulfate ratios, the data mainly consist of the data from Shi. For these data, Shi used an evaporative technique and actually did not measure the solubility limits; rather it was the metastable limits that were reported. On the basis of the technique developed by Shi, the solubility of high carbonateto-sulfate ratios has also been investigated by DeMartini and Verrill.15 The reference data are used for comparison with the experimentally obtained data in this study. In the experiments in this study, metastable limits and apparent solubility limits at 120 °C were measured. With the experimental procedure used, the concentration at the time of the first nucleation can be calculated, giving the metastable limit. The solubility is measured by filtering a part of the circulating
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Table 2. Supersaturation at the Metastable Limit (M.L.) Na2CO3/(Na2CO3 + Na2SO4) ∆T supersaturation @ M.L.
mol/mol °C %
1 6 6.2
1 10 6.3
mixture in the evaporator, without providing time for equilibration. The liquors were filtered through a tempered 0.5 µm filter and allowed to cool. The samples were analyzed and the composition at the time of the sampling, i.e. the solubility, was determined. The chemical analyses were performed at More ¨ rnsko¨ldsvik, Sweden, and consists of measureResearch in O ments of the concentrations of sodium, carbonate, and sulfate using standard methods SCAN-N 37:98, SCAN-N 32:98, and ISO 10304-1. From these results the supersaturation can be calculated according to: S)
Xl - X*l X*l
(16)
where Xl is the mass fraction of dissolved solids in the liquid phase and X*l is the mass fraction of dissolved solids in the liquid phase at the solubility limit. The obtained supersaturations at the metastable limits are presented in Table 2. The result of a high supersaturation at the metastable limit is that, upon nucleation, a larger crystal mass will form than that for a lower metastable limit. A rapid formation of a large crystal mass has the potential to generate severe heat transfer fouling. The results presented in Table 2 do not show any relationship between the obtained supersaturation and the temperature difference, i.e., the rate of evaporation. The measured solubility limits and metastable limits are presented in Figure 3 together with the data from Shi3,12 at 115 °C and from DeMartini and Verrill15 at 120 °C. Calcium is known to inhibit the nucleation of burkeite and dicarbonate, thereby increasing the metastable limit. In determining the metastable limits, Shi added EDTA to investigate the inherent nucleation of burkeite and dicarbonate. EDTA is known to be able to sequester calcium ions. Both the metastable limits with and without EDTA are presented in Figure 3. In this study EDTA was not added to the solutions. The measured metastable limits are comparable and share similar trends to the metastable
Figure 3. Solubility limits and metastable limits as a function of liquid composition for the system Na-SO4-CO3-H2O. Data from this work at 120 °C. Reference data obtained from Shi3,12 at 115 °C, both with and without EDTA (added to sequester calcium) and DeMartini and Verrill15 at 120 °C. The black line represents the correlated solubility, according to eq 17.
0.867 10 14.3
0.867 6 14.3
0.765 10 19.0
0.765 6 17.1
0.705 10 19.3
0.705 6 19.7
limits of Shi without EDTA. The solubility data also share similar trends, though the measured data are substantially more carbonate-rich. The data point from DeMartini and Verrill has a similar carbonate fraction, and the solubility shows a good match to the measured solubilities in this study. From the solubility data of the mixture solutions, a linear correlation for the solubility was made with the following expression: S ) 249.75x + 91.727 for 0.78 < x < 0.9 and T ) 120 °C (17) where S is the solubility in g/kg total and x is the mole fraction Na2CO3/(Na2CO3+Na2SO4). The maximum deviation between the correlation and the experimental data is 2.1 g/kg. The composition of the filtered crystals was also analyzed. The crystals were dissolved in water, and the composition of sodium, carbonate, and sulfate was determined in a similar way as for the solutions. In Figure 4 the relationship between the composition in the liquid and solid phase is shown. For comparison, the data of Green and Frattali13 and Shi3 have also been included. As the reference data imply, the carbonate and sulfate mixtures are seen to crystallize in both the burkeite and dicarbonate regions. For the experiments with an initial mole fraction Na2CO3/ (Na2CO3+Na2SO4) equal to 0.765, a second nucleation point was also observed, demonstrated in Figure 5 for experiment no. 5. In the figure, discontinuance in the refractive index measurement is seen at around 110 min. This is an indication of a second nucleation point with an altered crystal composition which can also be seen on the chord counts. With an altered crystal composition the development of the composition in the liquid phase will also change, and this is discussed further in the next section. The crystal compositions at the second nucleation points were also estimated. In these cases it was not possible to examine the composition of filtered crystals, as they
Figure 4. Solid composition regimes as a function of liquid composition for aqueous solutions adapted from Shi et al.3 The four regions listed are the sulfate (S), burkeite (B), dicarbonate (D), and carbonate (C). Data at 120 °C, first nucleation point through filtration and second nucleation point from the refractive index. Reference data obtained from Green and Frattali13 at 100 °C, Shi et al.3 at 115 °C.
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Figure 5. Chord counts between 1 and 500 µm and the refractive index versus time for experiment no. 5 where ∆T ) 10 °C and the initial x ) 0.765 mol/mol. The straight line around 90 min indicates the first nucleation point, and the dashed line around 110 min indicates the second nucleation point.
Figure 6. Mole fraction in the liquid phase, x, density and the system’s total salt fraction, Xc+l+s, versus time for experiment no. 4 where ∆T ) 6 °C and the initial x ) 0.867 mol/mol. The straight vertical line, around 210 min, indicates where the solubility limit is passed and the dotted vertical line, around 250 min, indicates where the metastable limit is passed.
are a mixture of both the previous crystals and of the new crystalline form. Instead an analysis based on the refractive index and the development of the experiment was used to estimate these. The salt mass balance will provide the crystal composition based on the liquid phase composition being specified. The refractive index can be modeled from the composition of the liquid phase. By minimizing the difference between the modeled and measured refractive indexes, the liquid phase composition is determined and thus also the crystal composition. These estimated secondary nucleation points are also presented in Figure 4. Evaporative Crystallization of Na2CO3-Na2SO4 Aqueous Solutions. Figure 6 exemplifies how the measured density and calculated total salt fraction, Xc+l+s, change in the course of an experiment. The stated accuracy of the density meter is (0.002 kg/L, and the salt fractions, determined from sample analysis and mass balances, are believed to have an accuracy of (1%. Time zero is defined as the time where the vapor removal is initiated. In this and in several following figures, the solubility limit is indicated with a straight vertical line, and the metastable limit with a dotted vertical line. Passing the metastable limit, the density drops rapidly because of the formation of crystals. This behavior is observed in all experiments. The molar ratio x in the liquid phase, calculated from the mass balances and the
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Figure 7. Average heat transfer coefficients and chord counts for three different size ranges versus time for experiment no. 4 where ∆T ) 6 °C and the initial x ) 0.867 mol/mol. The straight vertical line, around 210 min, indicates where the solubility limit is passed, and the dotted vertical line, around 250 min, indicates where the metastable limit is passed.
crystal composition, is also plotted. In all cases, except for pure sodium carbonate, this ratio will change during the course of the experiments, as the composition of the crystals formed will differ from the composition in the liquid phase. As the molar ratio x in the liquid phase changes during an experiment, so will the solubility according to Figure 3. The increased density after the first release of supersaturation is partly an effect of increased solubility, but mainly it is caused by the increasing amount of crystal mass in the solution. Figure 7 shows the outside (liquor side) heat transfer coefficient for the same experiment. The heat transfer coefficient has been adjusted for the change of physical properties with the concentration according to Gourdon et al.7 Seen in the heat transfer coefficient, there is a slight decrease from the start, i.e., already with low concentrations. This is not seen for all experiments, and there are no indications from visual observations that this would be caused by fouling. The physical properties adjustment used might not be fully adequate to describe the change in the fluid during this period, thereby giving it this appearance. In the evaporator, local heat transfer coefficients on the heat transfer surface are also measured. In a few of the experiments, a small area around one of these local points on the evaporator tube has been washed clean. The washing was done in the later part of the experiments (after the metastable limit), and the outcome is a heat transfer measurement for a clean surface. From these results the physical properties adjustment can be tested. For the conditions and time periods of the washings, the physical properties adjustment was in most cases found appropriate with deviations within (5%. In the experiment presented in Figure 7 the deviation was however more than 25%, thus confirming that the physical properties adjustment was not fully adequate. The sudden decrease of the heat transfer around 250 min is caused by fouling on the heat transfer surface following the release of supersaturation at the metastable limit. The decreased heat transfer between 265 and 285 min is the result of fouling due to the continuous crystallization occurring in the solution already containing crystals. Together with the heat transfer coefficient, the chord counts in the circulating liquor for three different size ranges are also presented. All sizes are seen to have increasing counts in connection with where the metastable limit is passed.
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Figure 8. Total, surface, and circulating crystal fractions together with the solubility versus time for experiment no. 4 where ∆T ) 6 °C and the initial x ) 0.867 mol/mol. The dotted part of the circulating crystal fraction is the assumed path before equilibrium is reached. The dashed vertical line indicates where the metastable limit is passed.
In the operation of the experiments, one of the purposes was to examine the different crystal masses in the evaporator. A typical result of the analysis of different crystal masses is shown in Figure 8 where the total crystal fraction, cfc+s, the circulating crystal fraction, cfc, and the surface crystal fraction, cfs, all in g/kg, are presented. In Figure 8 the solubility of the solution, according to eq 17, is also presented. The solubility, influencing both the total and circulating crystal masses, is modeled based on the composition presented in Figure 6. From Figure 8 one can see that the crystallization clearly exhibits two phases, one phase during the initial release of supersaturation and one phase during the time period afterward, with the continuous crystallization process. The first phase is fast because of high supersaturation, being the driving force for crystallization. To reach equilibrium, this will result in the formation of a large crystal mass. In the second phase the crystallization rate is slower and is controlled by the evaporation rate. The distribution between bulk and surface crystal masses is a key factor when looking at evaporator scaling. The two phases of the crystallization process do not necessarily have the same distributions; some conditions might favor crystallization and/or particulate accumulation on the surface in the first phase whereas accumulation in the bulk is favored in the second phase, or vice versa. As previously stated, the surface crystal mass does not specifically show how much fouling there is on the heat transfer surface. The surface crystal mass is the sum of the crystal masses on the heat transfer surface and on other surfaces. Crystals could, for example, adhere to surfaces where the flow velocities are low, or they can settle on horizontal surfaces. Both of these mechanisms were confirmed visually in the evaporator. On the picture taken in the evaporator seen in Figure 9, crystals deposited on the heat transfer tube as well as on the funnel around it are seen. A suitable way to evaluate fouling on the heat transfer area is to look at the resistance to heat transfer.16 The fouling resistance can be calculated with the following relationship: R)
1 1 hO(t) hO(t ) 0)
(18)
As the behavior will be different in the nucleation phase and continuous crystallization phase, these are investigated separately. The nucleation phase is denoted phase N and the continuous crystallization phase is denoted phase CC. The rates
Figure 9. Photograph from inside the evaporator during operation from experiment no. 5 where ∆T ) 10 °C and the initial x ) 0.765 mol/mol. The tube in the middle of the picture is the heat transfer area. The flow of the boiling salt solution is seen as bubbly and white and is covering the evaporator tube. Crystal formations are seen both on the evaporator tube and on the surroundings, i.e., on the funnel below and the supporting bars on the side.
Figure 10. Fouling resistance growth with respect to the system’s total salt fraction increase. Data for different initial solution compositions and temperature differences. Growth rates during nucleation phase (N) and continuous crystallization phase (CC).
at which the fouling resistances increase with the total salt fraction, Xc+l+s, for both phases are shown in Figure 10. As seen in the figure, the fouling growth is considerably higher for solutions crystallizing in the dicarbonate and sodium carbonate region compared to the burkeite region. During phase N, the fouling rate for dicarbonate, being highest, is approximately five times higher than the fouling rates of the solutions in the burkeite region. Looking at the effect of temperature difference, all solution compositions have higher fouling rates with the high temperature difference. The fouling rate during phase CC is the highest for the sodium carbonate solutions followed by dicarbonate solutions. Again solutions in the burkeite region show low fouling rates, only about onefourth of the rate of the sodium carbonates. The rate at which the surface crystal fraction, cfs, increases with the total salt fraction, Xc+l+s, during both phases N and CC is presented in Figure 11. A high surface crystal fraction growth means that the crystal mass on surfaces will be high and, consequently, the mass in the circulating solution will be low. Conversely, for a constant total crystal growth, if the surface crystal fraction is low, the circulating crystal fraction will be high and a large crystal mass will be formed in the solution. This second scenario is desired as surface fouling is avoided and also because the higher crystal mass in the solution may aid further formation and growth of crystals in the solution.
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Figure 11. Surface crystal fraction growth with respect to the system’s total salt fraction increase. Data for different initial solution compositions and temperature differences. Growth rates during nucleation phase (N) and continuous crystallization phase (CC).
During phase N, the surface fraction growth is highest for the solutions in the dicarbonate region. The sodium carbonate actually presents the lowest rates here. One should, however, remember that the surface crystal mass consists of crystals both on the heat transfer surface and on other surfaces. The surface crystal mass also represents the sum of surface crystallization and particulate accumulation. Examining the effect of the temperature difference, it is not always the high difference that has the highest crystallization rate with respect to the total salt fraction increase. One explanation for this is that sedimentation clearly contributes to surface crystal mass. As sedimentation could be considered a time-dependent process, the contribution of sedimentation to the surface fraction growth rate per unit of concentration increase will be higher for the low temperature differences. The sedimentation is a unique feature of this research evaporator, as it has large surfaces besides the heat transfer surface. This is not the case for commercial black liquor evaporators. In phase CC, the solutions in the sodium carbonate region exhibit high surface growth rates. The solutions in both the burkeite and dicarbonate regions only have low surface growth rates during the continuous crystallization process. In Figure 12 the rate at which the circulating crystal fraction, cfc, increases with the total salt fraction, Xc+l+s, during phases N and CC is presented. For phase N, the circulating crystal rate is decreasing with increasing carbonate content. The release of the initial supersaturation implies that a crystal mass needs to be created either on the surfaces or in the circulating solution. This result is thereby consistent with the results of the heat transfer measurements in Figure 10. High fouling resistance growth equals high surface growth rate and low circulating growth rate. The fact that the sodium carbonate solutions show both low growth rates on surfaces and in the circulating solution is because of the comparatively low supersaturation; see Table 2. From the distribution between the surface and the circulating solution, however, the dicarbonate and carbonate have the highest surface share during phase N. During phase CC, the solutions in both the burkeite and dicarbonate region only have a low surface growth rate and the crystallization is almost solely occurring in the circulating solution, seen in Figure 12. The experiment with pure sodium carbonate and ∆T ) 10 °C has a
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Figure 12. Circulating crystal fraction growth with respect to the system’s total salt fraction increase. Data for different initial solution compositions and temperature differences. Growth rates during nucleation phase (N) and continuous crystallization phase (CC).
negative circulating crystal growth rate, meaning that the circulating crystal mass, built up during the nucleation phase, is actually decreasing. Discussion Method of Analysis. An important part of the analysis in this work consists of measuring the amount of crystals in the circulating solution. With the method of operation used in this study the circulating crystal mass is calculated. One fundamental assumption is that the solution is considered to be in equilibrium. In reality there is nevertheless an equilibration time. Passing the metastable limit, the circulating crystal mass is assumed to deviate from the equilibrium for a few minutes as the supersaturation is high. After that, the equilibrium is believed to be attained. From the refractive index measurements, the time needed to release the initial supersaturation can be estimated and seems to be between 4 and 6 min. There is, however, also a circulation time in the equipment that is almost 3 min. Consequently, the actual equilibration time must be short, less than 3 min, and thus the assumption appears valid. The chord length distribution measurement, exemplified in Figure 7, could also be used as a measure of the circulating crystal mass. The difficulty of this measurement is to translate the chord length distribution into a crystal mass. By assuming spherical particles, a cubical weighting could be assumed appropriate, but this tends to overrate the particles on the upper margin of the distribution. Comparing these cubical weightings as well as the mean particle size for the different experiments in this study, no general trend is seen for the different solution compositions. Because of the uncertainties associated with this method, the calculation of the circulating crystal mass from the density and the mass balances is considered to be more reliable, and thus the analysis is concentrated on that method. Effect of Temperature Driving Force. One important parameter that was to be considered in this work was the consequence of the temperature difference between the heating steam and the circulating solution. A change in temperature difference will mainly affect two things: the wall temperature and the evaporation rate. In crystallization, the evaporation rate is known to affect the metastable limit. The temperature of the
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heat transfer surface could affect the crystallization. Because of the reversed solubility with temperature, a higher surface temperature will favor crystallization on the surface. Examining phase N, it is clear that a low temperature difference generates the lowest fouling growth rate. This is not a result of increased supersaturation at the metastable limit, with higher evaporation rate. As was seen in Table 2, no coupling was observed between the driving temperature difference and the supersaturation at the metastable limit. During phase CC, the opposite relationship with temperature difference is observed. Here, for the semibatch operation of the evaporator, actually a high temperature difference gives a lower fouling resistance growth rate with respect to the concentration increase. This was also the case for Euhus et al.4 who found that a low temperature difference favored heat transfer fouling per unit of concentration increase for a procedure similar to the one in phase CC. Assuming that there is a limitation in the available crystallization area on the heat transfer surface, then one reason could be that for a small temperature difference, the evaporation rate is low and the surface can take care of most of the crystallization work, whereas for a high temperature difference the distribution will be shifted and more of the crystals are forced to be formed in the circulating solution. Comparing the Nucleation and Continuous Crystallization Phases. When considering the growth rates of phases N and CC, it is obvious that phase N is much faster. The surface crystal growth rate is substantially higher during phase N, as well as the fouling growth rate. When examining the distribution between surface crystal growth and the circulating crystal growth between the two phases, the surface growth is larger during phase N for the solutions in the double salt regions but not for the pure sodium carbonate. For the double salts, this means that not only is the crystallization faster, but the attraction toward the surface is also higher, in phase N. These mechanisms combined will seriously affect the heat transfer upon passing the metastable limit. Effect of Solution Composition. All three investigated crystal compositions, burkeite, dicarbonate, and sodium carbonate, have shown to scale the heat transfer surface. The results show that the solutions crystallizing in the dicarbonate and sodium carbonate regions have significantly higher fouling growth rates compared to solutions in the burkeite region. This is true for both phases N and CC. Comparing the dicarbonate to the sodium carbonate solution, the dicarbonate solution exhibits higher fouling rates when passing the metastable limit. The considerably lower supersaturation at the metastable limit of the sodium carbonate solutions is decreasing the crystal mass needing to be released and could therefore be an explanation for the lower fouling rate. During phase CC, the sodium carbonate has the highest fouling rates and the dicarbonate solutions crystallize at a slightly lower rate. For sodium carbonate, the crystallization is highly concentrated to the surfaces, as was seen in Figure 12. The crystal mass in the circulating solution actually was seen to decrease in one experiment. Euhus et al.4 found a solution crystallizing in the dicarbonate region to have lower fouling rates than a solution crystallizing in the burkeite region. Shi,12 however, made evaporation experiments that indicated that dicarbonate could have a scaling tendency higher than that of burkeite. Frederick et al.5 also reported that the nucleation of dicarbonate from black liquor caused rapid fouling of the heat transfer surface which was not the case for nucleation of burkeite. In this study, comparing the two sodium double salts, burkeite has a much lower tendency to cause fouling. The reason why dicarbonate has a higher affinity to crystallize on the heat transfer surface is not known. The surface crystal fraction growth
is not much lower for burkeite. This means that the solutions in the burkeite region actually do precipitate on surfaces. The crystals are simply not as likely to crystallize and/or to remain on the heat transfer surface. This is also confirmed visually; the surface crystal mass for the dicarbonate solutions is concentrated on the heat transfer surface whereas the crystals formed with burkeite solutions are distributed between both the heat transfer surface and the surrounding surfaces. One hypothesis could be that the reversed solubility with temperature is stronger for dicarbonate than for burkeite. The temperature dependence of the solubilities found in literature, however, implies that this is not likely to be the cause. For dicarbonate, the solubility’s temperature dependence, (dS/ dT)dicarbonate, is equal to 0.576 g/kg/°C,,17 and for burkeite, the solubility’s temperature dependence, (dS/dT)burkeite, is equal to 0.77 g/kg/°C.18 The higher temperature dependence of burkeite would suggest that it would have the highest attraction to crystallize on the heat transfer surface. The absence of a relationship between the fouling rates and the temperature difference between the heating steam and the circulating solution, as discussed above, also supports the view that it is not the difference in reversed solubility that is causing the dissimilar fouling behaviors. Another hypothesis is that the supersaturation and the fouling rate could in some way be related and that the higher fouling rates of dicarbonate are connected with higher supersaturation at the metastable limit.19 The experimental data did not, however, support this hypothesis. Comparing the supersaturation at the metastable limit and the fouling growth rates during the nucleation phase, the sodium carbonate solution is seen to have the lowest supersaturation but only the second highest fouling rate. The highest fouling rate is observed for the solution crystallizing in the dicarbonate region, and this solution has the second lowest supersaturation. The solutions in the burkeite region have the highest supersaturation and the lowest fouling growth rates. Thus, no general relationship is seen between the supersaturation and the fouling rate. Bayuadri et al.20 showed that the dicarbonate crystals are spherical agglomerates of short rod-line structures, while burkeite forms plate-like crystal systems.9 One plausible hypothesis could be that the dicarbonate agglomerates, due to their morphology, are more likely to form or accumulate on the heat transfer surface. Second Nucleation Point. Another parameter that was analyzed in this study was the effect of passing a second nucleation point. The two experiments with an initial mole fraction Na2CO3/ (Na2CO3+Na2SO4) equal to 0.765 had a first nucleation in the burkeite region but also passed a second nucleation point at a mole fraction of about 0.9. This second nucleation point was consequently observed in the boundary between the dicarbonate and sodium carbonate regions and not before. The crystal compositions, seen in Figure 4, also suggest that these crystals are close to the invariant point where the solution composition and crystal composition are alike. For these experiments (with the initial x equal to 0.765), the result of the second nucleation is incorporated in the examination of phase CC. The fouling resistance growth is slightly higher than the less carbonate-rich solution (x ) 0.7) but is considerably lower than the dicarbonate solutions (x ) 0.9). No significant changes are seen in the analysis of crystal masses either. When examining the heat transfer coefficient in detail during the time period close to the second nucleation in these experiments, no change of the coefficient’s gradient is seen. This means that, even though a new crystalline species is formed and a new metastable limit is passed, the heat transfer (or surface crystal fraction growth) is more or less unaffected. Shi3 also conducted an evaporation experiment producing nucleation of both burkeite
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and dicarbonate. The experiments produced a thin layer of scales which consisted of both burkeite and dicarbonate. No quantitative measure of the distribution of the two species was, however, given.
s ) salt (sodium carbonate and sodium sulfate) w ) water * ) saturation
Conclusions
Literature Cited
On the basis of measurements of heat transfer coefficients and crystal masses during semibatch evaporation, the crystallization behavior of aqueous Na2CO3-Na2SO4 solutions was analyzed. Two distinct phases of the evaporative crystallization, denoted nucleation (N) and continuous crystallization (CC), were observed. The key findings of this work are as follows: • Phase N is a very fast process, occurring when the metastable limit is exceeded, and can result in very high fouling rates. In phase CC the fouling rates are lower and the crystallization rate is determined by the rate of evaporation. • The fouling behavior is strongly influenced by the solution compositions. Solutions crystallizing in the dicarbonate and sodium carbonate regions were seen to cause serious fouling on the heat transfer surface in both crystallization phases compared to solutions crystallizing burkeite. A difference in the reversed solubility with temperature is not considered to be the main cause of the difference in attraction to the heat transfer surface and neither is the supersaturation at the metastable limit. • During phase N, when passing the metastable limit, the temperature difference should be kept low to reduce crystallization on the heat transfer surface. A high temperature difference will promote crystallization on the surface. During phase CC, it is favorable to have a higher evaporation rate (high temperature difference) to suppress the fouling growth rate per unit of concentration increase.
(1) Schmidl, W.; Frederick, W. J. Current trends in evaporator fouling. 1998 International Chemical Recovery Conference; Tappi Press: Atlanta, GA, 1998; p 367. (2) 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. (3) Shi, B.; Frederick, W. J.; Rousseau, R. W. Nucleation, growth, and composition of crystals obtained from solutions of Na2CO3 and Na2SO4. Ind. Eng. Chem. Res. 2003, 42 (25), 6343. (4) Euhus, D. D.; Rousseau, R. W.; Frederick, W. J.; Lien, S. J. Sodium salt fouling in falling-film evaporators: a pilot study. 2001 International Chemical Recovery Conference; PAPTAC, Montreal, 2001, p 183. (5) 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. (6) Gourdon, M.; Stro¨mblad, D.; Vamling, L.; Olausson, L. Scale formation and growth when evaporating black liquor with high carbonate to sulphate ratio. Nord. Pulp Pap. Res. J. 2008, 23 (2), 231. (7) Gourdon, M.; Olausson, L.; Vamling, L. Evaporation of Na2CO3Na2SO4 solutions: A method to evaluate the distribution between bulk and surface crystallization. Tappi J., submitted. (8) Takubo, H. Refractive index as a measure for saturation and supersaturation in crystal growth of water-soluble substances. J. Cryst. Growth 1990, 104 (2), 239. (9) Giuseppetti, G.; Mazzi, F.; Tadini, C. The Crystal Structure of Synthetic Burkeite: Na2SO4(CO3)t(SO4)1-t. Neues Jahrb. Mineral. 1988, 5, 203. (10) IAPWS. The International Association for the Properties of Water and Steam. Release on the Refractive Index of Ordinary Water Substance as a Function of Wavelength, Temperature and Pressure, 1997. (11) 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, 33 (3), 150. (12) Shi, B. Crystallization of Solutes that lead to Scale Formation in Black Liquor Evaporation. Ph.D. Thesis, Georgia Institute of Technology, 2002. (13) Green, S.; Frattali, F. The system Sodium Carbonate-Sodium Sulfate-Sodium Hydroxide-Water at 100 °C. J. Am. Chem. Soc. 1946, 68, 1789. (14) Makarov, S.; Krasnikov, S. N. The three-component equilibrium conditions at the boiling point in the four-component system Na2SO4Na2CO3-NaCl-H2O. IzV. Sekt. Fiz. -Khim. Anal. Akad. Nauk SSSR 1956, 27, 367. (15) DeMartini, N.; Verrill, C. L. Minimizing soluble scales in black liquor evaporators: Application of metastable and solubility limit data for the Na-CO3-SO4 system. 2007 International Chemical Recovery Conference; Tappi Press: Atlanta, GA, 2007; p 479. (16) Gourdon, M.; Vamling, L.; Olausson, L. Fouling layer growth in black liquor falling film evaporation., 2007 International Chemical Recovery Conference; Tappi Press: Atlanta, GA, 2007; p 473. (17) Bialik, M. A.; Theliander, H.; Sedin, P.; Verrill, C. L.; DeMartini, N. Solubility and Solid-Phase Composition in Na2CO3-Na2SO4 Solutions at Boiling Temperature: A Modeling Approach. Ind. Eng. Chem. Res. 2008, 47 (9), 3233. (18) Shi, B.; Rousseau, R. W. Crystal properties and nucleation kinetics from aqueous solutions of Na2CO3 and Na2SO4. Ind. Eng. Chem. Res. 2001, 40 (6), 1541. (19) Verrill, C. L.; Frederick, W. J., Jr. Evaporator fouling 101 - Sodium salt crystallization and soluble-scale fouling., 2005 TAPPI Engineering, Pulping, Environmental Conference; Tappi Press: Atlanta, GA, 2006. (20) 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.
Acknowledgment The authors are grateful to the Swedish Energy Agency and Metso Power AB for financially supporting this project. We kindly thank Bengt Erichsen (at the Division for Heat and Power Technology, Chalmers University of Technology) for his valuable contribution to this work. Appendix Nomenclature cf ) crystal fraction, kg/kg ho ) outside heat transfer coefficient, W/m2K m ) mass, kg R ) fouling resistance, m2K/W RI ) refractive index S ) supersaturation t ) time, min x ) mole fraction Na2CO3/(Na2CO3 + Na2SO4), mol/mol X ) mass fraction, kg/kg Γ ) circulating mass flow rate per unit width, kg/ms ∆T ) temperature difference between steam and solution, K ν ) specific volume, kg/dm3 Subscripts c ) crystals in solution l ) liquid solution s ) crystals on surfaces Superscripts Na2CO3 ) sodium carbonate Na2SO4 ) sodium sulfate
ReceiVed for reView September 4, 2009 ReVised manuscript receiVed November 24, 2009 Accepted January 27, 2010 IE901390C
