-implementation of a solubility based on the Pitzer ... report 90.pdf · -implementation of a...

Modelling the scaling of burkeite

-implementation of a solubility based on the Pitzer-formalism into WinGEMS

Rickard Wadsborn

2005

According to Innventia Confidentiality Policy this report is public since 2011-02-04

a report from STFI-Packforsk

Modelling the scaling of burkeite

-implementation of a solubility model based on the Pitzer-formalism into WinGEMS

Rickard Wadsborn

STFI-Packforsk Report no.: 90 | December 2005

Cluster:Chemical Pulp Restricted distribution to: AGA, AssiDomän Cartonboard, Billerud, Borregaard, Eka

Chemicals, Holmen Paper, Kemira, Korsnäs, M-real, Mondi Packaging, Peterson & Son, Stora Enso, Södra Cell, Voith

According to STFI-Packforsk's Confidentiality Policy this report is assigned category 2

Modelling the scaling of burkeite STFI-Packforsk report no. 90

Acknowledgements The author is indebted to Marta Bialik, Peter Sedin and Hans Theliander at the division of Forest of Products and Chemical Engineering, Chalmers University of Technology, Gothenburg, for essential support during this work.

Per Ulmgren, STFI-Packforsk AB, is acknowledged for valuable discussions.



Modelling the scaling of burkeiteSTFI-Packforsk report no. 90

Table of contents Page

1 Summary .................................................................................................... 1

2 Introduction................................................................................................ 3

2.1 Objective ........................................................................................... 4

3 Theory......................................................................................................... 5

3.1 Pitzer-formalism ................................................................................ 5

3.2 Solubility model ................................................................................. 6

3.3 Implementation of the solubility model into WinGEMS...................... 7

4 Results and discussion............................................................................. 9

4.1 Validation .......................................................................................... 9 4.1.1 Single electrolyte solutions ...........................................................................9 4.1.2 Multicomponent solutions ...........................................................................10 4.2 Black liquors.................................................................................... 12 4.2.1 General trends in the results from the model .............................................12 4.2.2 Effect of temperature ..................................................................................13 4.2.3 Extension of the model with temperature dependence ..............................14 4.2.4 Effect of hydroxide ions ..............................................................................17 4.2.5 Comparison to other simulation methods ...................................................19

5 Limitations in the current model and future work................................. 21

6 Conclusions ............................................................................................. 22

7 References ............................................................................................... 23

Appendix 1- Pitzer interaction theory for electrolyte solutions at high ionic strength ........................................................................................... 27

Appendix 2- Pitzer parameters .................................................................. 30





1

1 Summary An interface designed to estimate the risk of precipitation of sodium salts in the black liquor evaporation has been developed for the process simulation program WinGEMS. The interface uses a solubility model for the sodium salts which is based on the Pitzer-formalism for the description of the activity of the ions in solution at high ionic strength.

The implementation of the Pitzer-formalism into the process simulation tool has been validated against literature data for single and multiple electrolyte solutions.

The temperature dependence of the solubility model has been extended by the use of literature data of solubility of the pure salts sodium carbonate and sodium sulphate.

Comparison of the solubility model against another method used to estimate the risk of precipitation of sodium salts demonstrates that the current model overestimates the activities of the inorganic ions in solution. A reason for this might be that the interaction between inorganic and organic phase is not included in the present model.

The formulation and implementation of the chemical solubility models for sodium salts provides an accessible method to estimate the risk for precipitation of troublesome scales in the black liquor evaporation.



Modelling the scaling of burkeite STFI-Packforsk report no. 90 2

Sammanfattning Ett användargränssnitt för att uppskatta risken för utfällningar av natriumsalter i svartlutsindustningen har utvecklats för processimuleringsprogrammet WinGEMS. Gränssnittet använder sig av en löslighetsmodell för natriumsalterna som är baserad på Pitzer formalismen för att beskriva aktiviteten på de lösta jonerna vid höga jonstyrkor.

Implementeringen av Pitzer formalismen har validerats mot litteraturdata på lösningar av en och flera olika elektrolyter.

Temperaturberoendet i löslighetsmodellen har utökats genom att data för rena lösningar av natrium karbonat eller natrium sulfat har använts.

Jämförelser av resultat från användningen av löslighetsmodellen mot en annan metod att uppskatta lösligheten för natriumsalter i indunstningen visar att den nuvarande modellen överskattar aktiviteten på de lösta organiska jonerna. En anledning är att interaktionen mellan organisk och oorganisk fas ännu inte är inkluderad i modellen.

Formuleringen och implementeringen av den kemiska löslighetsmodellen för natriumsalterna visar att detta är en framkomlig metod för att uppskatta risken för utfällningar av salter i svartlutsindustningen.




3

2 Introduction Burkeite is a mineral with the chemical composition Na2CO3·2Na2SO4. This compound precipitates during black liquor evaporation at dry solids around and above 50% and form scales on the heat transfer surfaces in black liquor evaporation units. These scales must be removed by washing or by boiling out with low dry solids black liquor, causing a decrease in the availability of the process equipment.

The field of burkeite research has been very active during the last decade. Recent research has showed that the composition of the “burkeite” salts formed during black liquor evaporation changes with varying composition of the liquid phase (Frederick et al. 2004; Shi et al. 2003b; Shi and Rousseau 2001; Shi and Rousseau 2003). A high ratio of [CO3]/([CO3] +[SO4]) in the black liquor results in a precipitate with high content of carbonate. When the carbonate fraction gets high enough (above 0.8), another mineral, dicarbonate (2 Na2CO3•Na2SO4), is proposed to form. The negative effect of the fouling of dicarbonate has been proposed to be more pronounced than the fouling of burkeite due to the higher affinity of dicarbonate for heat exchanger surfaces etc (Shi et al. 2003b; Verrill and Giehl 2004).

Another factor affecting the precipitation of sodium salts is the calcium ion content. Added calcium ions have been showed to hinder the primary nucleation of sodium salts, resulting in an increase in size of the crystals in the solid phase. It has been found that added calcium ions affected the degree of supersaturation needed for the sodium salt to precipitated: a higher temperature was needed to precipitate the sodium salt when calcium was present (Shi et al. 2003a).

Another important salt forming insoluble scales in the black liquor evaporation is calcium carbonate. These scales are very difficult to remove, as the solubility of the salt is rather low in water and alkaline solutions at temperatures above 100ºC. Recent research have shown that the scaling of calcium carbonate and burkeite interacts in kraft pulp mills (Sirén 2003). A simultaneous precipitation of both burkeite and calcium carbonate was advantageous for the studied mills, compared to when calcium carbonate precipitated before the sodium salt.

Due to the negative effects, fouling of sodium and calcium salts in black liquor evaporators must be minimized or at least controlled. It is therefore interesting to describe the precipitation of the fouling scales through computer modelling or simulations. This have also been the objective of previous studies: Adams proposes s simple equation for calculation of the critical dry content of the liquor based on the inorganic content of the liquor (Adams 2001). Another approach is the so-called NAELS-model (non-ideal aqueous electrolyte simulator) (Golike et al. 1998).

Literature data has been used to formulate a solubility model of the solid phase at a given chemical composition of the inorganic phase (Bialik et al. 2005) by using the so-called Pitzer formalism (Pitzer 1991). The implementation of this solubility model into a process simulation tool such as WinGEMS would facilitate the use of the chemical model, which in turn would facilitate the study of effects of different process conditions on the risk of




scaling of both calcium carbonate and burkeite in the evaporation train. This approach would contribute to the addressing of methods to avoid scaling of both sodium and calcium salts.

2.1 Objective The objective of the present study was to implement the previously developed solubility models of sodium salts (burkeite) using the Pitzer-formalism into the process simulation tool WinGEMS.




5

3 Theory

3.1 Pitzer-formalism Consider the chemical reaction

)(sSaltAnionCation Ac →+νν (i)

The activity of solid substances is defined to unity, which means that the solubility product of the precipitating salt may be expressed as

( ) ( ) ACACAACCACsp mmaaK νννν γγ=⋅= (ii)

where a is activity of the ions, ν is the stoichiometric constants for the anions and cations (subscript A and C, respectively), m is the molality and γ is the activity coefficient for each ion.

Normally, i.e. in less diluted solutions at low ionic strengths, the activity coefficient may be modelled as a function of ionic strength using the Debye-Hückel model. The validity of the model is however limited to low ionic strengths. Another approach is the constant media approach, were the ionic strength varies only in a small interval, and the variation in activity coefficient may by modelled either with Debye-Hückel equation, Davies equation, or a similar equation (Stumm and Morgan 1996). In the simplest cases the activity constants may be set to unity. However, the variation in ionic strength is large during black liquor evaporation and other models have to be considered in order to model the activity coefficient of the electrolytes over the entire range of ion strength.

One of these models is the Pitzer-formalism (Pitzer 1973; Pitzer 1975; Pitzer and Kim 1974; Pitzer and Mayorga 1973; Pitzer and Mayorga 1974), which has been proven to be a versatile model for describing the activity coefficients of single and multicomponent electrolyte solutions (Park and Englezos 1998; Park and Englezos 1999). The formalism is derived from the excess free energy which is related to change in osmotic pressure and potential energy between ions in solution. The interested reader is referred to the book of Pitzer for the complete derivation of equations (Pitzer 1991). For a more detailed revision of appropriate equations used in the present work, please see appendix 1. See appendix 2 for a compilation of the Pitzer-parameters.

Although the equations in appendix 1 look rather tedious, they do permit a straightforward approach to the simulation of the activity of ions at high ionic strength. The same approach was also used by Bialik (Bialik et al. 2005), and that is the approach that has been implemented into WinGEMS via a interface designed and built at STFI-Packforsk during the present study.




3.2 Solubility model The solubility model applied in this study is based on findings within the FRAM-program (Bialik et al. 2005). In that work an extended literature survey was performed, under the objective to construct a simulation model for the precipitation of burkeite. The literature data found was used to construct a solubility model for the system Na-CO3-SO4-OH. One of the results of this study is the relation of the solubility product of burkeite to the composition of the solid phase formed. The solubility product of the solid phase was calculated using the Pitzer-formalism together with Pitzer parameters from the literature. The effect of temperature correction was only considered in the osmotic coefficient of water, where the coefficient was modelled according to expression of Chen (Chen et al. 1982).

Figure 1 shows some of the data used by Bialik (Bialik et al. 2005) to estimate the apparent solubility product of the solid phase formed. The figure shows that the composition of the solid phase is a function of the composition of the liquid phase. Between carbonate mol-fractions 0.2 and 0.79 (defined as [CO3]/([CO3]+[SO4]) is burkeite formed (Shi and Rousseau 2003) according to the following equation

)79.02.0( 0824.07882.01785.1949.0 23 ≤≤++−= XXXXy (iii)

where X and y are weight fractions of sodium carbonate in the liquid and solid, respectively, on a solvent-free basis (Shi et al. 2003b). A sudden rise in the carbonate fraction of the solid phase is observed at high carbonate fractions in the liquid phase. This

0

0.2

0.4

0.6

0.8

1

0.0 0.2 0.4 0.6 0.8 1.0

Mole fraction CO3 solution

Mol

e fr

actio

n C

O3

solid

pha

se

Shi

Green & Frattali

Figure 1. Composition of burkeite crystals formed. In -data used for model construction (Bialik et al. 2005). Experimental data published by (Shi and Rousseau 2003) and (Green and Frattali 1946).




7

has been explained by the formation of the compound dicarbonate ( 2 Na2CO3·Na2SO4), at carbonate mole fractions in the liquid phase between 0.8 and 0.9 (Shi and Rousseau 2003).

The work of Bialik resulted in an expression for the apparent solubility product of the solid phase formed that relates the composition of the solid phase to the apparent solubility product of the solid salts with a quadratic function, figure 2.

In figure 2 the variable x is defined as the deviation from the ideal composition of pure burkeite (in which CO3:SO4=1:2) of the solid phase formed. An x-value above 0 corresponds to carbonate excess in the solid phase, and below 0 to a sulphate excess, all compared to ideal composition of pure burkeite.

The data in figure 2 shows that the magnitude of the apparent solubility product, as calculated by the implementation of the Pitzer-formalism, is lowest for the compound with the ideal composition of burkeite (x=0). The solubility increases with both carbonate and sulphate excess.

3.3 Implementation of the solubility model into WinGEMS Previously, an extension tool (called MeteQ) for WinGEMS, used to predict the distribution of metals and the risk of scaling of partly soluble salts in the bleach plant, have been developed and validated by STFI-Packforsk (Berggren et al. 2003). The MeteQ-block is designed to minimise the Gibbs free energy of a system at equilibrium governed by a chemical equilibrium model for the actual system. Normally, the stoichiometry is fixed in a chemical model, and that is the case for the model of the bleach plant (Ulmgren 2003).

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

-0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

x, deviation from ideal burkeite

Ksp

, sol

id p

hase

Ksp=f(x)

Figure 2. Apparent solubility product (Ksp) of the solid phase formed at 100-115ºC (Bialik et al. 2005). The variable x is defined as the deviation from ideal composition of burkeite.




However, the composition and thus the formation constants vary in the chemical model developed for sodium salts (Bialik et al. 2005). This fact initiated the design of a less complicated interface than the MeteQ-block that handles only the necessary parameters for estimating the risk of precipitation of sodium salts. This also simplifies the debugging of the interface as well as the extension of the chemical model.

The findings within the project made by using the chemical model in combination with the simplified interface for sodium salt precipitation may be implemented into the MeteQ-block in the future for a more rigorous treatment of the composition of the process streams at equilibrium.




9

4 Results and discussion

4.1 Validation One of the most important issues when performing such implementation as in this study is the validation of the simulation program. Without a proper validation, it is impossible to know whether the results from the simulations are correct or not. In the current case the equations used were rather complicated and the ability to draw conclusions while just looking at them was low. This made validation particularly important. Thus, validation was performed on two levels: single electrolyte solution and multiple electrolyte solutions which included the work of Bialik (Bialik et al. 2005).

4.1.1 Single electrolyte solutions A comparison of the mean activity coefficient for both sodium chloride and sodium sulphate is shown in figure 3. Literature data was taken from Zeimatis (Zeimatis et al. 1986) which publishes activity coefficient data for several single and multicomponent electrolyte solutions calculated according to several different methods. WinGEMS data were calculated using the sub-routine developed within this project.

During the calculations of the mean activity coefficient, a routine developed for a multicomponent solution was used. A possible third component in the solution was plainly omitted. As observed in figure 3, the subroutine did give similar results as previously published calculations, which was expected. This confirms the validity of the designed interface.




0

0.25

0.5

0.75

1

0 1 2 3 4

molality

Mea

n ac

tivity

coe

ffici

ent,

NaC

l

WinGEMSLiterature

0

0.25

0.5

0.75

1

0 1 2 3 4 5

molality

Mea

n ac

tivity

cof

ficie

nt, N

a2SO

4 WinGEMSLiterature

Figure 3. Mean activity coefficient of NaCl and Na2SO4 calculated by the Pitzer-formalism. Upper part: NaCl, lower part Na2SO4. Data from WinGEMS subroutine compared to literature values (Zeimatis et al. 1986).

4.1.2 Multicomponent solutions In order to validate the model, data used in and resulting from the work of Bialik was used as reference (Bialik et al. 2005). One reason to use these sets of data is that this is the system for which the sub-routine was designed. Another reason was that calculated activity coefficients for multicomponent solutions are rarely published in the literature, in contrast to the methods used for their estimation.

Composition of the liquid phase of the Na-CO3-SO4-system published by Green and Frattali (Green and Frattali 1946) and Shi (Shi and Rousseau 2003) was used as input for simulations of the activity coefficients. Then the similar approach as performed by Bialik was performed:




11

1. Composition of the liquid phase at saturation was known.

2. As 1. was given, so was the composition of the resulting solid phase by data in figure 1.

3. Knowing the stoichiometric composition of the solid provided a possibility to calculate the correct apparent solubility product of the solid phase, using the Pitzer-formalism and the known concentrations of dissolved ions.

4. Comparison of calculated apparent solubility products from WinGEMS with data from Bialik would agree if the sub-routine has worked properly.

The apparent solubility product as calculated by WinGEMS using the developed interface at different composition of the solid phase is plotted in figure 4.

0.0E+00

2.0E-04

4.0E-04

6.0E-04

8.0E-04

1.0E-03

1.2E-03

1.4E-03

-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

x, deviation from ideal burkeite

Ksp

, bur

keit

Shi, 115C

G&F, 100C

Bialik expression

Figure 4. Apparent solubility products of solid phases as calculated by WinGEMS as a function of the composition of the solid phase. The x-values are defined as the deviation from the ideal composition of burkeite. Ksp-values calculated by WinGEMS-interface according to equations 2, 8 and 9 in appendix 1. Solid line is the expression for apparent solubility product previously presented (Bialik et al. 2005).

In addition, the expression for the apparent solubility product given by Bialik is plotted. The figure shows that exactly the same values of the apparent solubility product as presented by Bialik are returned from the WinGEMS using the developed interface. This means that the activity coefficients are calculated accurately compared to procedures developed by Pitzer (Pitzer 1991). (Of course, this is true only if the work of Bialik was correctly performed. However, the risk of having two completely different researchers ending up with similar erroneous conclusions is however negligible.)




4.2 Black liquors This section shows results from simulations using fictitious composition of black liquors as input. The composition of the black liquors used in the simulations was chosen to represent mean values of Scandinavian black liquors. Data describing the original black liquors used while simulating evaporation is showed in table 1.

Table 1. Composition of black liquors used during the simulations. Total dry solids (%) 15.8-17.5

Na+ mmol/kg TS 9800-10700

OH- mmol/kg TS 135-150

CO32- mmol/kg TS 35-960

SO42- mmol/kg TS 135-150

Dissolved wood solids (% of total dry solids) 56-63

4.2.1 General trends in the results from the model The subroutine developed in this subproject was used to calculate the activity coefficients of the dissolved ions according to the Pitzer-model. The output of the subroutine is that the composition of the outgoing stream is calculated according to the solubility model, along with activity coefficients of the ions Na+, OH-, CO3

2- and SO42-.

The simulations were performed as follows: black liquor with the dry content of around 15% was used as input. The components in the ingoing black liquor were all considered as dissolved, and the respective amount of each component corresponded to a standardised industrial black liquor. Then water was withdrawn from the sample to the final dry content, specified by the user. Then the solubility product was calculated and dissolved concentrations of sodium, carbonate and sulphate corrected in order to satisfy the solution criteria given in figure 4.

The results from the model may be illustrated in several forms, and in this report the method shown in figure 5 has been chosen. On the y-axis is the fraction of the total available sodium (both in solid and in liquid phase) that is found in the solid phase as a precipitated salt plotted, and on the x-axis the final dry content of the black liquor plotted. A y-value of zero means that the no solid sodium salt has formed and all the ions are dissolved. According to figure 5, the sodium salt first to precipitate is found in the black liquor with the carbonate fraction of 0.5. The precipitation occurs at the dry content of 50%. For black liquors with both high and lower carbonate fractions was the solubility higher, as the precipitate started to form at higher dry contents. This is in accordance with the solubility model (Bialik et al. 2005).

Several other methods of illustration also exist: solid content in the particular process stream, amount of formed burkeite per metric ton pulp etc.




13

0

0.005

0.01

0.015

0.02

0.025

0.03

0.45 0.47 0.49 0.51 0.53 0.55 0.57

Dry content (frac)

Frac

tion

of N

a in

sol

id p

hase

0.250.500.73

Carbonate fraction in liquid phase

Figure 5. General trend from the simulation of evaporation black liquors to a dry solids content given by the x-axis. Y-axis corresponds to fraction of total sodium in black liquor found in solid phase. Carbonate fraction defined as the molar ratio of [CO3]/([CO3]+[SO4]) in the initial liquid phase. Activities of ions in liquid phase calculated by the Pitzer-model using the developed WinGEMS-interface.

4.2.2 Effect of temperature The temperature varies considerably along the evaporation train, which means that implementation of the temperature dependence of both solubility and activity coefficients would be advantageous. For burkeite, the solubility has been reported to decrease with increasing temperature (Hedrick and Kent 1992; Shi and Rousseau 2001).

The temperature effect observed in initial simulations is shown in figure 6.




0

0.01

0.02

0.03

0.04

0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54

Dry content (frac)

Frac

tion

of N

a in

sol

id p

hase

100 C Uncorrected120 C Uncorrected

Figure 6. Fraction of total sodium present in solid phase as a function of increasing dry content at different temperatures and without temperature correction. Initial composition of black liquors same at both temperatures.

At dry solids below 46.5% was no solid phase presented according to the figure 6, all inorganic ions are dissolved at both 100 and 120 ºC. At 100ºC the solubility limits was exceeded and burkeite started to form at the dry solids content 47%, although in relative small amounts. However, at 120 ºC and dry content of 47%, at which the solubility should be lower compared to 100ºC (Hedrick and Kent 1992; Shi and Rousseau 2001), no solid phase was formed. At 120ºC the dry content had to be increased to over 50% before burkeite started to precipitate. Thus, the results were quite opposite to what was known from the literature. The reason to this deviation between literature and model data may be found in how the solubility is modelled. The only temperature dependent factor in the original model was the osmotic coefficient of water, AΦ. This coefficient was modelled according to a formula given by Chen (Chen et al. 1982) and the value of the coefficient increases with temperature. Consequently this lowers the activity of the ions according to equation 10 in appendix 1. With a lower activity coefficient at higher temperatures, the apparent solubility will increase, as indicated by the data in figure 6. This implies the results from the model in terms of temperature dependence so far to be unreasonable compared to literature data.

4.2.3 Extension of the model with temperature dependence The need for extending the current model with temperature dependent data was obvious from the results in figure 6. In order to include the temperature dependence of the apparent solubility product of burkeite, data from saturated systems containing only Na2CO3 or Na2SO4 was considered.

Solubility data from literature was used as input (Linke 1965), and the mean activity coefficients and solubility products were calculated using the Pitzer-formalism using the developed sub-routine . The apparent solubility product of the precipitating salts was




15

normalised to represent a salt containing six sodium atoms, as burkeite holds six sodium atoms, i.e., the mean activity coefficient of Na2CO3 was calculated as Na6(CO3)3.This approach takes the effect of the activity of sodium into account in the same manner as the solubility product for burkeite.

R2 = 0.994

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 20 40 60 80 100 120 140 160

T (C)

Ksp

Figure 7. Apparent solubility product of Na2SO4 at different temperatures. Activities calculated with Pitzer-formalism, product normalized to six Na-atoms (Na6(SO4)3). Data was calculated using literature values (Linke 1965).

R2 = 0.973

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

0 20 40 60 80 100 120 140 160 180

T (C)

Ksp

Figure 8. Apparent solubility product of Na2CO3 at different temperatures. Activities calculated with Pitzer-formalism, product normalized to six Na-atoms (Na6(CO3)3). Data was calculated using literature values (Linke 1965).

The resulting apparent solubility products for Na6(CO3)3 and Na6(SO4)3 are shown in figure 7 and 8 respectively. For these two substances, the apparent solubility product




decreased with an increasing temperature, which also was indicated by the solubility data (Linke 1965).

The apparent solubility product of the two salts were normalised to unity at 115 ºC, which was the temperature used in previous studies (Shi and Rousseau 2001). This enabled the estimation of the relative change in apparent solubility product of the salts at any given temperature compared to 115º C

0

0.5

1

1.5

2

2.5

3

3.5

80 90 100 110 120 130 140 150

T (C)

Rel

ativ

e ch

ange

in K

sp

Na2CO3

Na2SO4

Figure 9. Relative values of apparent solubility products of solid phase at different temperatures using the Pitzer-formalism compared to the value at 115ºC.

As can be seen in figure 9, was the relative change in apparent solubility product similar for both the sodium carbonate and the sodium sulphate. Thus, it was assumed that the relative change in apparent solubility product for the formed solid phase of the double salt at any given temperature in the evaporation train may be related to the solubility at 115 ºC using the relation showed in figure 9.

This procedure is an approximation and may introduce an error compared to the measurements performed on the actual solid phase that precipitates in mixtures of Na2CO3 and Na2SO4. A correction factor for the solubility of burkeite has been published previously (Hedrick and Kent 1992). The correction factor in that work is slightly smaller compared to the factor estimated in the current work.

The results from the application of the relation in figure 9 onto black liquors are shown in figure 10. Here, the same calculations as in figure 6 is shown, but with a temperature dependence of apparent solubility product added.




17

0

0.01

0.02

0.03

0.04

0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54

Dry content (frac)

Frac

tion

of N

a in

sol

id p

hase

100 C Uncorrected100 C Corrected120 C Uncorrected120 C Corrected

Figure 10. Fraction of total sodium present in solid phase as a function of increasing dry solids content at different temperatures and with temperature correction. Initial composition of black liquors same in both cases.

Now, using the relation in figure 9, the precipitation according to the simulations occurred in the expected order. Removing water (evaporation) from the same black liquor at different temperatures resulted in an increased amount of formed solid sodium salt at 120 ºC compared to 100 ºC at a given dry content between 49% and, at least, 53%. The dry content at which the precipitation started was also simulated to occur in the same order as expected.

4.2.4 Effect of hydroxide ions The concentration of hydroxide ions will affect the precipitation point of burkeite, even if the ion itself is not present in the solid phase. The activity of both the sodium ions and the constituting anions will be affected by the hydroxide ion, and the magnitude is given implicitly by the Pitzer-parameters (see appendix 2).

An example of the effect of hydroxide ions upon the precipitation point, expressed as dry content of the black liquor at the onset of crystallization, is shown in figure 11. Here, the initial concentration of hydroxide ions was 2.6, 5.1 and 7.6 g/l. The sodium ion concentration was varied along with the hydroxide ion, with the hydroxide ion concentration of 5.1 g/l as reference point. The precipitation point decreased with increasing residual alkali in the black liquor.




0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54

Dry content (frac)

Frac

tion

of N

a in

osl

id p

hase

2.6 Na corr5.17.7 Na corr

Figure 11. Fraction of total sodium present in solid phase as a function of increasing dry content at different concentrations of hydroxide ions. Figures in legend define concentrations of hydroxide ions at the initial dry content. Sodium ion content corrected for increasing hydroxide ions concentration.

The effect shown in figure 11 is attributed to the effect of increasing both sodium and hydroxide ion content in the liquor. This effect was also expected as sodium is included in the expression of the apparent solubility product where it is raised to the power of six. Increasing the sodium concentration would therefore strongly affect the precipitation point.

The effect of increasing only the hydroxide ion concentration and not the sodium ion concentration is exemplified in figure 12. The similar conclusion may be drawn as from figure 11: a higher residual alkali concentration in the black liquor lead to a lower precipitation point of the sodium salt. Comparing the data sets with and without sodium adjustment shows that the sodium has a clear effect on the apparent solubility product as adjusting the sodium levels lead to a wider range of precipitation points in the simulated cases.

A notable difference between results from using corrected and uncorrected sodium levels is the deviation from the condition of electronegativity. In reality this means that the nature of the organic phase has been adjusted between the two data sets as the inorganic part of the liquor remains the same, except for the sodium content. The modelling of the interaction between the organic and inorganic is not included in the current version of the model.




19

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54

Dry content (frac)

Frac

tion

of N

a in

sol

id p

hase

2.6 Na corr5.17.7 Na corr2.67.7

Figure 12. Fraction of total sodium present in solid phase as a function of increasing dry content at different concentrations of hydroxide ions. Figures in legend define concentration of hydroxide ions at the initial dry content. Sodium ion content both corrected and not corrected for varied hydroxide ion concentration.

4.2.5 Comparison to other simulation methods One convenient way to estimate the critical dry solids at which the precipitation of sodium salts occurs is to use the so called Adams critical solids formula (Adams 2001). This formula expresses the dry content as function of inorganic content of the black liquor as

where ACS is the critical dry solids and all the other variables are weight fractions of black liquor dry solids of each compound.

Comparing the output from the simulations of the current work with data using the formula for Adam’s critical dry solids, figure 13, constantly gives an underestimation of the critical dry from the WinGEMS simulations. Additionally, high carbonate/sulphate fractions, at which the solubility of the formed salt is higher, leads to a smaller difference between the two models compared to low carbonate fractions. The information provided by using the Pitzer-formalism was more detailed, which was expected.

( )131.032

323.042

365.018.611

CONaSONaNaACS

total⋅⋅⋅+

= (iv)




45

50

55

60

65

70

75

0 1 2 3 4 5 6

Na2SO4, Weight fraction of DS (%)

Crit

ical

dry

sol

ids

(%)

ACS, 0.79ACS, 0.5Pitzer, 0.79Pitzer 0.5

Figure 13.Critical dry solids content of black liquors with different sulphate and carbonate content estimated either by using Adam’s formula (Adams 2001), or by using the solubility model based on the Pitzer formalism. Figures in legend correspond to the molar ratio [CO3]/([CO3]+[SO4]) in the black liquor. Total sodium content 20 w-% of dry solids, temperature 115ºC.

One reason for this deviation may be that the activity of the ions is overrated by the Pitzer-routine, as the only interactions considered are the interactions between inorganic ions in the solution. The formula for critical dry solids was developed using data from Grace (Grace 1976), who studied the solubility of sodium carbonate and sodium sulphate in black liquors. Grace proposed that the only effect from the organic content of the black liquor is the common-ion effect, i.e. the additional sodium content of the solution due to the neutralization of anionic groups in the dissolved wood solids. The conclusion was drawn by Grace after comparison of own laboratory data with literature data originating from solutions with no organic phase present (Green and Frattali 1946), at 45% dry content. At this relatively low dry solids content does data by Grace compare well with data from Green and Frattali, but at higher dry solids content is a difference between the two data observed. This suggests that parameters describing the interaction between dissolved wood solids and cations would be useful, despite the note about the common ion effect in the work of Grace.

A similar phenomena has also been observed previously (Golike et al. 1998) when interpreting the data of Grace. Here, the addition of an interaction parameter between the organic content of the black liquor and sodium increased the accuracy of the description of the solubility of burkeite using data from Gace (Grace 1976). Unfortunately, the details about the simulation model given by Golike et al. is rather limited, and does not reveal which approach that was used to implement the interaction parameter between sodium and the organic phase, and to what magnitude that approach was implemented.




21

5 Limitations in the current model and future work The current study is an interesting start in the field of steady-state modelling of the solubility of salts in black liquor evaporation units. Many interesting topics remains however to be studied in the laboratory and implemented into the solubility model and the interface between the solubility model and the process simulator. Examples of such topics are:

• The temperature dependence of the solubility of sodium scales has to be verified by laboratory experiments. The temperature dependence in the current version of the interface is only a relation to literature values describing the temperature dependence of the solubility of the pure salts Na2CO3 and Na2SO4.

• The solubility of dicarbonate has to be described by the methodology used in this study. The chemical model of Bialik (Bialik et al. 2005) has only been proved valid in the burkeite-range.

• Pitzer-parameters for the interesting metal ions and anions in the dicarbonate region have to be measured experimentally in order to describe the solubility of the salts in the dicarbonate region.

• The use of Pitzer-parameters for the estimation of the effect of the dissolved wood components upon the activity of inorganic ions has to be evaluated by laboratory experiments.

• Effects of calcium ions and other impurities (Shi et al. 2003a) upon the activity and precipitation of sodium scales has to be modelled and implemented properly.




6 Conclusions Implementation of a previously developed solubility model for the double salt burkeite has been successfully implemented into a commercial process simulation program. The solubility model calculates the apparent solubility product for burkeite with a varying chemical composition. The activities of the dissolved ions are calculated according to the Pitzer-formalism in the system Na-OH-CO3-SO4. The implementation of the solubility model provides a useful tool that may be used in order to describe the process chemistry of the sodium and calcium salts forming troublesome scales in the evaporation train of kraft pulp mills.

The solubility model has been extended with a temperature effect which has been derived from solubility data of the pure salts Na2CO3 and Na2SO4.

Comparison with another method used to estimate the precipitation point of the double salt shows that the Pitzer-formalism as used in this work gave a lower solubility of the double salt. This implies that the interaction between the inorganic and the organic phase in the black liquor needs to be included into the detailed solubility model.




23

7 References Adams T N Sodium salt scaling in black liquor evaporators and concentrators Tappi J. 84(2001):6, 1-18 Berggren R, Lindgren K, Sarman S, Samuelsson Å Apparent solubility of sparingly soluble salts in the fiber line- validation of equilibrium calculations in WinGEMS STFI Report CHEM 106 (2003) Bialik M, Sedin P, Theliander H Model for solubilities of Na2CO3 and Na2SO4 in high temperature solutions-FRAM report no 49 Chalmers institute of technology (2005) Chen C-C, Britt H-I, Boston J F, Evans L B Local composition model for ecxess Gibbs energy of electrolyte systems, Part 1: Single solvent, single completely dissociated electrolyte systems AIChE J. 28(1982), 588 Frederick W J, Shi B, Euhus D D, Rousseau R W Crystallization an control of sodium salt scales in black liquor concentrators Tappi J 3(2004):6, 7-13 Golike G P, Pu Q, Holman K L, Carlson K R, Wollwage P C, Folster H G NAELS: a new method for calculating equilibrium solubility of burkeite and sodium carbonate in black liquor International chemical recovery conference: Tamp, Florida, 1998, 1, 403-418 Grace T M Solubility limits in black liquors AIChe Symp. Ser. 72(1976):157, 73-82 Green S J, Frattali F J The system sodium carbonate-sodium sulphate-sodium hydroxide-water at 100C J.Amer.Chem.Soc. 68(1946), 1789-1794 Hedrick R H, Kent J S Crystallizing sodium salts from black liquor Tappi J 75(1992):12, 107-111 Linke W F Solubilities, inorganic and metal-organic compounds, K-Z ACS, Washington, 2 (1965) Park H, Englezos P Osmotic coefficent data for Na2SiO3 and Na2SiO3-NaOH by an isopiestic method and modeling using Pitzer's model Fluid Phase Equil. 153(1998), 87-104




Park H, Englezos P Osmotic coefficient data for NaOH-NaCl-NaAl(OH)4-H2O system measured by an isopiestic method and modeled using Ptzer's model at 298.15 K Fluid Phase Equil. 155(1999), 251-259 Pitzer K S Thermodynamics of electrolytes. I. Theoretical basis and general equations J. Phys. Chem. 77(1973):2, 268-277 Pitzer K S Thermodynamics of electrolytes. V. Effects of higher-order electrostatic terms J. Solution. Chem. 249(1975):4, 1975 Pitzer K S Activity coefficients in electrolyte solution CRC Press, Boca Raton, (1991) Pitzer K S, Kim J J Thermodynamics of electrolytes. IV: Activity and osmotic coefficients for mixed electrolytes J.Amer.Chem.Soc. 96(1974):18, 5701-5707 Pitzer K S, Mayorga G Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent J. Phys. Chem. 77(1973):19, 2300-2308 Pitzer K S, Mayorga G Thermodynamics of electrolytes. III. Activity and osmotic coefficients for 2-2 electrolytes J. Solution. Chem. 3(1974):7, 539-546 Shi B, Frederick W J, Rousseau R W Effects of calcium and other impurities on the primary nucleation of burkeite Ind. Eng. Chem. Res. 42(2003a):12, 2861-2869 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. 42(2003b):25, 6343-6347 Shi B, Rousseau R W Crystal properties and nucleation kinetics from aqueous solutions of Na2CO3 and Na2SO4 Ind. Eng. Chem. Res. 40(2001):6, 1541-1547 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. 107(2003):29, 6932-6937 Sirén K STATUS REPORT for project: Behaviour of NPEs under technical conditions-subproject CaCO3-scaling (2003) Stumm W, Morgan J Aquatic chemistry John Wiley & Sons, New York, (1996)




25

Ulmgren P Solubility of slightly soluble compounds in bleach plant filtrates - a summary. STFI Report CHEM 88 (2003) Verrill C L, Giehl F T Manipulation of crystallization to resolve severe concentrator scaling 2004 International Chemical Recovery Conference: Charleston, SC, USA, 2004, 1, 441-453 Zeimatis J F, Clark D M, Rafal M, Scrivner N C Handbook of aqueous electrolyte thermodynamics AIChe, New York, (1986)







27

Appendix 1- Pitzer interaction theory for electrolyte solutions at high ionic strength The literature within this field contains several printing errors, and it is sometimes troublesome to find correct versions of the equations. It may thus be useful to provide a detailed compilation of some of the equations that have been used throughout this work, and the equations are given below.

Consider the chemical reaction

)(sSaltAnionCation Ac →+νν (1)

The activity of solid substances is defined to unity, which means that the solubility product of the precipitating salt may be expressed as

( ) ( ) ACACAACCACsp mmaaK νννν γγ=⋅= (2)

where a is activity of the ions, ν is the stochimetric constants for the anions and cations (subscript A and C, respectively), m is the molality and γ is the activity coefficient for each ion.

The mean activity coefficient for a single salt may according to Pitzer be expressed as:

where

The osmotic coefficient of water is defined as

Additional parameters are defined as

where m is molality, z is the charge of the anion and cation, ν is the stochiometric number of the electrolyte , b is a constant. The Pitzer-parameters α, β and C±

φ may be found for

( ) 2.1,1ln21

=⎟⎟⎠

⎞⎜⎜⎝

⎛++

+−= Φ bIb

bIbIAf γ (4)

10002

31 0

3ANd

DkTeA π

⎟⎠⎞

⎜⎝⎛=Φ (5)

( ) ( )[ ]

( ) ( )[ ]IIII

IIII

B

22222

2

2

12112

1

10

exp5.0112...

...exp5.01122

ααααβ

ααααβ

βγ

−−+−+

+−−+−+=±(6)

φγ±± = CC

23 (7)

( ) γγγ

ννν

νννγ ±

−+±

+−+± ⎥

⎦

⎤⎢⎣

⎡+⎥⎦

⎤⎢⎣⎡ −+= CmBmfzz

5.12 22ln (3)




different electrolytes in the literature: α1 is 2 for all but 2:2 electrolytes where the value is set to 12. Parameters α2 and β2 are equal to zero for all but 2-2 electrolytes.

The equations given above are valid for single electrolyte solutions. For multicomponent electrolytes the activity for each individual cation (M or c) and anion (X or a) is calculated separately according to the following equations:

The Debye-Hückel term is included in the term F according to

Furthermore,

[ ]

∑∑∑∑

∑ ∑∑+Ψ+

+⎥⎦

⎤⎢⎣

⎡Ψ+Φ+++=

c acaacM

a aMaaaa

c aMcaaMcc

aMaMaaMM

Cmmzmm

mmZCBmFz

'''

2

...

...22ln γ (8)

[ ]

∑∑∑∑

∑ ∑∑+Ψ+

+⎥⎦

⎤⎢⎣

⎡Ψ+Φ+++=

c acaacX

c cXcccc

a ccXacXaa

ccXcXcXX

Cmmzmm

mmZCBmFz

'''

2

...

...22ln γ(9)

∑∑∑∑∑∑<<

Φ+Φ++=a a

aaaacccc c

cc a

caac mmmmBmmfF'

'''

'''

'

'γ (10)

(11) ∑=i

ii zmZ

( ) ( )[ ] ( ) ( )[ ]III

III

BMX 2222

2112

1

10 exp112exp112 αα

αβαα

αββ −+−+−+−+= (12)

xMMX

zzCC

2

φ±= (14)

( ) ( )[ ]

( ) ( )[ ]IIII

IIII

BMX

222222

2

2

12

11221

1'

exp5.0112...

..exp5.0112

ααααβ

ααααβ

−+++−+

+−+++−=

(13)




29

The term θij is a tabulated parameter for each par of ions and account for interaction between ions with charge of the same sign. The terms Eθij and Eθij

’ (I) accounts for interaction of ions with same sign but different charges. The values are functions of ionic strength, and may normally be neglected for 2-1 electrolytes. The term ψijk is tabulated mixing parameters specific to anion-anion-cations or cation-cation-anion ion triplets.

For any given pair of ions forming a solid phase, the mean activity coefficient is related to the single ion activity coefficients according to

where ν=νM+ νX. (18)

Please see appendix 2 for the Pitzer-parameters used throughout this work.

)('' IijE

ij

ijE

ijij

θ

θθ

=Φ

+=Φ (15) (16)

νγνγνγ XxMM lnlnln +

=±

(17)




Appendix 2- Pitzer parameters A number of different Pitzer-parameters have been published for the current system. In order to apply previous results (Bialik et al. 2005), the same Pitzer parameters (Pitzer 1991) was used in the current study.

Primary interaction parameters:

Secondary interaction parameters:

Tertiary interaction parameters

00175875.022

2

300938.0

22

113.1484.175.0019575.0261.075.0

:

0018375.022

2

30098.0

22

50975.1013.275.0036225.00483.075.0

:

0022.02

0044.012

253.00864.0:

25

1

0

42

25

1

0

32

1

0

42

42

32

32

=⋅

==

=⋅==⋅=

=⋅

==

=⋅==⋅=

===

==

φ

φ

φ

ββ

ββ

ββ

SONaSONa

CONaCONa

NaOHNaOH

CC

SONa

CC

CONa

CC

NaOH

02.0

013.0

1632.0

24

23

24

23

=

−=

−=

−−

−−

−−

−

−

−

SOCO

SOOH

COOH

θ

θ

θ

005.0

009.0

0172.0

24

23

24

23

−=Ψ

−=Ψ

=Ψ

+−−

+−−

+−−

−−

−−

−−

NaSOCO

NaSOOH

NaCOOH


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