Equilibria in Limestone-Based FGD Process: Magnesium Addition

Ind. Eng. Chem. Res. 2006, 45, 1945-1954

1945

Equilibria in Limestone-Based FGD Process: Magnesium Addition Jacek A. Michalski* Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland

On the basis of chemical equilibria, the model of sulfur dioxide solubility in solutions applied in FGD (flue gas desulfurization) systems with magnesium salts addition is developed. The influence of magnesium chloride or magnesium sulfate on solution ability to absorb SO2, pH, ions concentration, and calcium salts solubility is presented. The mechanisms leading to a decrease of calcium carbonate solubility and/or to limestone particle blinding caused by magnesium salts addition are proposed. Introduction Limestones applied in a wet flue gas desulfurization (FGD) process are usually contaminated by magnesium species, mostly in the form of magnesium carbonate. Magnesium is introduced to the solution during sorbent particles dissolution. Because of a much better solubility of magnesium salts in comparison to salts formed by calcium, the accumulation of magnesium species dissolved in the solution can occur. In the 1970s, it was commonly expected that the addition of magnesium species (mostly in the form of MgSO4 or MgO) to the FGD solution improves sulfur dioxide absorption because of an increase of alkalinity of the solution.1,2 However, because of several problems met in the industrial scale of the FGD process based on limestone or lime sorbent, it is still used for the lowest possible content of magnesium species.3,4 Therefore, phenomena leading to the malfunctioning of an FGD installation operating with magnesium salts addition are worth exploring. In chemical engineering, it is commonly assumed that the driving force of the process is dependent on the difference of a locally estimated leading parameter and its value corresponding to thermodynamic equilibrium which can be reached by the system. Such a simple definition is valid for macroscopic flows, mass and heat transfers, chemical reactions, etc. Especially in the systems in which reversible (completely or partially only) processes are going, calculation of parameters describing equilibrium state is important for estimation of every acting driving force. Moreover, the calculation of equilibria can indicate regions of certain thermodynamic limitations of the process caused by new phase nucleation. It shows that the prediction of numerical values of parameters (mostly species concentrations) describing the equilibrium state is important in the case of FGD processes, because they are performed in multiphase and multicomponent system. First complex calculations concerning thermodynamic equilibrium have been performed assuming pure limestone application for the wet FGD technology.5 The dependencies of gaseous sulfur dioxide and sorbent particles solubilities in the liquid phase have been obtained in relation to the concentrations of calcium sulfite, gypsum, and dissolved carbon dioxide. In addition, the concentration of every ion (including pH) in the solution has been determined. The influence of calcium chloride presence on the theromodynamic equilibrium has been examined. It has been detected that, in some region dependent mostly on the amount of dissolved carbon dioxide and the CaCl2 * To whom correspondence should be addressed. Tel.: +48 22 3433380. Fax: +48 22 3433333. E-mail: [email protected].

concentration, limestone became insoluble in such a system.5 This result is able to explain technological problems observed in the large installations much better than the assumed kinetic effects described in the literature.6 Hypothetically, the rates of certain processes going in the solution are dependent on ion and/or ion pair concentrations. It is not a case of limestone dissolution only,7 but it concerns chemical reaction kinetics also.8 The best example is sulfiteto-sulfate oxidation, for which the rate depends on the concentrations of HSO3- and MeHSO3+ ions8 (Me ) bivalent metal). For this reason, ion concentrations should be calculated more precisely than is performed using simplified models for thermodynamic equilibria prediction.7 The aim of this paper is the analysis of the thermodynamic equilibria of the FGD system contaminated by magnesium salts. The method applied is based on simultaneous solution of equations defining dissociation constants of species introduced to the liquid phase and Henry’s law describing solubilities of gases in the solution. The Model Results presented in a previous paper5 concern the calculation of thermodynamic equilibria in a “pure” FGD system that consisted of an inert gas with the addition of gaseous carbon and sulfur dioxides (gas phase), a water solution of CO2, gypsum, calcium sulfite, calcium carbonate, or SO2 (liquid phase), and crystals of CaSO4‚H2O and CaCO3 particles (solid phase). The influence of the addition of gaseous hydrogen chloride to the system is discussed also. However, the analysis shows that, in the thermodynamic equilibrium state, this pollutant has to be completely absorbed and converted into dissolved calcium chloride in the environment under consideration. The influence of the addition of magnesium species on the thermodynamic equilibrium achieved by the FGD system is discussed in the current paper. The introduction of the second metal cation to the solution requires certain modifications of the assumptions made for the previous model formulation.5 Sulfur dioxide absorption and sulfite-to-sulfate oxidation induce certain reactions taking place in the FGD system. However, consideration of the equilibrium state requires an analysis of the system in which every reaction is completed and species concentrations are time-independent. Then, obtained results are representative for the thermodynamically stable

10.1021/ie050160p CCC: $33.50 © 2006 American Chemical Society Published on Web 02/08/2006

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Ind. Eng. Chem. Res., Vol. 45, No. 6, 2006

system. Such a condition demands the introduction of the following assumptions, similar to those formulated previously:5 1. Reactions of calcium and magnesium carbonates with absorbed sulfur dioxide are completed. 2. The enhancement of sulfur dioxide solubility in the solution of calcium and magnesium salts, in comparison to the waterSO2 system, is caused by the formation of MeHSO3+ ion pairs. 3. The appearance of MeHCO3+ ion pairs in the solution is responsible for the increase of carbon dioxide solubility in calcium and magnesium salts solution in comparison to that in pure water. 4. Large gypsum crystals content in the FGD slurry causes saturation of the solution by CaSO4. 5. Pyrosulfites formation is neglected because of a low content of absorbed sulfur dioxide and low sulfites concentration in the FGD solutions. The prediction of the driving force of limestone dissolution and its neutralization rate the demand calculation of thermodynamic equilibria in the vicinity of sorbent particles where carbonate concentrations can vary from zero (bulk of the solution) up to saturation (particle surface). Such a relation can be expected in the dynamic system because of opposite streams of carbonates and absorbed sulfur dioxide. Thus, according to assumption 1, the analysis of the system equilibrium versus carbonates concentration has to be performed. Points 2 and 3 allow one to assume that the amounts of dissolved SO2 or CO2 in the solution are sums of their content in pure water and the amount converted into MeHSO3+ or MeHCO3+ forms, respectively. Considering experimentally verified results of modeling of sulfur dioxide solubility in calcium sulfite water solutions and moderately concentrated solutions of magnesium sulfite,9 the influence of calcium and magnesium salts content on Henry’s constant can be neglected. A similar assumption can be introduced for Henry’s constant describing carbon dioxide solubility. Usually, slurry applied for sulfur dioxide absorption in the wet FGD technology contains large amount of fine gypsum crystals. This means that, in the calculation of thermodynamic equilibrium, complete saturation of the water solution by CaSO4 can be assumed.5 A low concentration of sulfur dioxide in the liquid phase can be achieved because of its low content in the burner gas. Additionally, CaHSO3+ ions formation and/or the neutralization of SO2 by sorbent result in a decrease of the concentration of HSO3- ions in the solution. In such a case, formation of pyrosulfite ions can be neglected.5,9 Considering salts and gases dissolved in the FGD solution, the equilibria of the following liquid-phase reactions have to be taken into account:

CaSO4 ) Ca2+ + SO42-

(1a)

HSO4- ) H+ + SO42-

(1b)

CaOH+ ) Ca2+ + OH -

(1c)

H2O ) H+ + OH -

(1d)

H2O + SO2 ) H+ + HSO3-

(1e)

HSO3- ) H+ + SO32-

(1f)

CaHSO3+ ) Ca2+ + HSO3-

(1g)

H2O + CO2 ) H+ + HCO3-

(1h)

HCO3- ) H+ + CO32-

(1i)

CaHCO3+ ) Ca2+ + HCO3-

(1j)

CaSO3 ) Ca2+ + SO32-

(1k)

CaCO3 ) Ca2+ + CO32-

(1l)

CaCl2 ) Ca2+ + 2Cl -

(1m)

MgCl2 ) Mg2+ + 2Cl-

(1n)

MgSO4 ) Mg2+ + SO42-

(1o)

MgOH+ ) Mg2+ + OH-

(1p)

MgHSO3+ ) Mg2+ + HSO3-

(1q)

MgHCO3+ ) Mg2+ + HCO3-

(1r)

MgCO3 ) Mg2+ + CO32-

(1s)

MgSO3 ) Mg2+ + SO32-

(1t)

However, because of the precipitation conditions, the following reactions have to be completed:

CaCl2 + MgSO4 fV CaSO4 + MgCl2

(2a)

CaCl2 + MgSO3 fV CaSO3 + MgCl2

(2b)

CaCl2 + MgCO3 fV CaCO3 + MgCl2

(2c)

CaSO4 + MgSO3 fV CaSO3 + MgSO4

(2d)

CaSO4 + MgCO3 fV CaCO3 + MgSO4

(2e)

It is very important that, according to calculations of thermodynamic potential (Gibbs free energy) performed for the most hydrated salts in FGD process temperature, reactions (2a-2e) have to be completed even if the concentrations are sufficiently low and they are not able to meet criteria of solubility products. It means that, in the presence of calcium chloride or gypsum, the appearing magnesium carbonate and/or sulfite is converted into calcium species. This confirms the conclusion previously presented1 that magnesium introduced into the system occurs in the liquid phase in sulfate or chloride form. Interestingly, according to equations (2a-2e), the mixture of two salts solution is converted into a solution in which the salt with the lowest solubility product is formed. Considering thermodynamic equilibria and the above reasoning, no magnesium sulfite and/ or carbonate can be expected in the FGD environment. Taking into account mass and charge balances, the concentration of ions appearing in the system are expressed as follows:

[Ca2+] ) yCaSO4 + yCaSO3 + yCaCO3 + yCaCl2 - XCa - WCa RCa (3a) [SO42-] ) yCaSO4 + yMgSO4 - Y

(3b)

Ind. Eng. Chem. Res., Vol. 45, No. 6, 2006 1947

[HSO4-] ) Y

(3c)

[CaOH+] ) XCa

(3d)

[CaHSO3+] ) WCa

(3e)

[SO32-] ) yCaSO3 + Z

(3f)

[HSO3-] ) V - WCa - WMg - Z

(3g)

[CaHCO3+] ) RCa

(3h)

[CO32-] ) yCaCO3 + U

(3i)

[HCO3-] ) S - U - RCa - RMg

(3j)

[OH-] ) yH2O - XCa - XMg

(3k)

[H+] ) yH2O + V + Z + S + U - Y

(3l)

[Cl-] ) 2(yCaCl2 + yMgCl2)

(3m)

(4)

carbon dioxides solubilies in the solution are caused by MeHSO3+ and MeHCO3+ ions formation (terms WCa and WMg, and RCa and RMg, respectively). As is described in the previous paper,5 the calculations are performed for three possible cases: (1) the solution with carbonates when their concentration varies from zero to saturation and the lack of “sulfurous” acid; (2) the solution without carbonates when absorbed sulfurous acid is consumed, resulting in sulfites-to-hydrogen sulfites conversion, and (3) the solution without carbonates when absorbed sulfur dioxide is in equilibrium with that in the gas. In the first case, ion concentrations are calculated as a solution of the set of equations defining the equilibrium constant of reactions 1a-1d and 1f-1r and the carbon dioxide solubility (eq 6b). In the second one, reactions 1a-1d, 1f-1k, and 1m-1r and SO2 and CO2 solubilities (eqs 6a and 6b) are taken into account. In the last case, the computation of ion concentrations is performed for reactions 1a-1k and 1m-1r and for equilibrium with components in the gaseous phase (eqs 6a and 6b). From a thermodynamic point of view, carbonates (calcium and pro forma magnesium) can be present in the solution only when there is no sulfur dioxide in the gaseous phase. Their concentration can be less than that corresponding to the saturation point only when there are no carbonates in the solid state. The analysis of the next two cases can be performed only when carbonates are present neither in liquid nor solid phases. During conversion of sulfites to hydrogen sulfite forms (second case), whole absorbed sulfurous acid is consumed for these reactions.5 When this conversion is completed, the amount of absorbed sulfur dioxide is equal to the sum of the amount absorbed in pure water and that appearing in the form of MeHSO3+ ion pairs (third case). The amount of sulfur dioxide necessary for the complete conversion of sulfites to hydrogen sulfites is denoted as V0 and calculated according to the previously discussed third case for PSO2 f 0 and yCaCO3 ) 0. Finally, similarly to the previously developed model,5 the amount of absorbed sulfur dioxide for the second and third cases is expressed by

(5)

yH O‚SO + WCa + WMg V g V0 and PSO2 g 0 ySO2 ) V 2 0 e2 V e V and P ) 0 0 SO2

[Mg2+] ) yMgSO4 + yMgCl2 - XMg - WMg - RMg (3n) [MgOH+] ) XMg

(3o)

[MgHSO3+] ) WMg

(3p)

[MgHCO3+] ) RMg

(3q)

Ion activities are calculated according to the relation formulated on the basis of the Debye-Hu¨ckel theory,10

γi ) 10[-(Rzi xI)/(1+βD0xI)] 2

for ionic strength computed from the following equation:

I ) 0.5

∑ zi2[i]

The relation βD0 ) 1 is fulfilled in the FGD system.4,5 The parameter R was tabularized and presented in the monograph by Newman.10 Gas-water equilibria described by Henry’s law for carbon and sulfur dioxides are applied in the following form:

yH2O‚SO2 ) HSO2PSO2

(6a)

yH2O‚CO2 ) HCO2PCO2

(6b)

It has to be stressed that the amounts of dissolved but not dissociated sulfur and carbon dioxides are described the same way as in the previous paper5 by the following relations:

[H2O + SO2] ) yH2O‚SO2 + WCa + WMg - V

(7a)

[H2O + CO2] ) yH2O‚CO2 + RCa + RMg - S

(7b)

Determination of these concentrations is necessary for calculation of dissociation constant of reactions (eqs 1e and 1h). It is noteworthy that, in both relations, assumptions 2 and 3 are taken into account, which means that improvement of sulfur and

{

(8)

The numerical values of dissociation constants and solubility products are given in Table 1. The Henry’s constants characterizing solubilities of sulfur and carbon dioxides in the liquid phase are presented in Table 2. Results and Discussion The previous discussion (eqs 2a-2e) of equilibria states shows that, in the FGD environment, magnesium species can appear in the solution in the form of chloride and/or sulfate. This means that, in the described system, the influence of these salts only on the FGD process behavior can be considered. Typically, the wet flue gas desulfurization process is performed in the temperature range of 313.15-333.15 K. Thus, presented calculations are carried out for the temperature of 323.15 K. MgCl2 Addition. Magnesium chloride can appear in the FGD process when sulfur dioxide and hydrogen chloride are simultaneously absorbed from the exhausted gas and the applied limestone is contaminated by the magnesium species. In such a case, calcium chloride can also be present in the solution.4 Since the influence of CaCl2 content on FGD solution charac-

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Table 1. Dissociation Constants and Solubility Products of Magnesium Species at Temperature 323.15 K

a

reaction no.

equilibrium constant

1a 1b 1c 1d 1e 1f 1g 1h 1i 1j 1k 1l 1m 1n 1o 1p 1q 1r 1s 1t

2.39 × 10-5 5.67 × 10-3 7.08 × 10-3 5.31 × 10-14 7.15 × 10-3 5.39 × 10-8 8.86 × 10-4 5.18 × 10-7 6.69 × 10-11 6.21 × 10-2 6.01 × 10-8 1.74 × 10-9 infinity infinity infinity 1.46 × 10-2 8 × 10-3 7.22 × 10-2 8.13 × 10-7 1.82 × 10-4

source 11 11 14 11 14 14 9 11 11 11 13 15

11 estimated, 9 11 12a 13a

Evaluated on the basis of salt solubility in water.

Table 2. Henry’s Constants at Temperature 323.15 K eq

Henry’s constant (mol/dm3/Pa)

source

6a 6b

5.54 × 10-6 1.92 × 10-7

14 11

teristics is shown in a previous paper,5 here its concentration is assumed as zero (yCaCl2 ) 0). This assumption allows one to discuss only the influence of the magnesium chloride presence, without effects caused by calcium chloride addition. Considering reactions 2a-2e, this means that every magnesium species on the limestone particle surface is completely washed out and only pure calcium carbonate is contacted with the solution. The equilibrium curves describing gaseous sulfur dioxide dissolution in a gypsum-saturated solution with the addition of magnesium chloride and calcium sulfite are presented in Figure 1. The obtained results show that the absorbed amount of SO2 in the solution rises with the growth of the partial pressure of sulfur dioxide in gas. The increase of calcium sulfite content causes an increase of the amount of SO2 necessary for the conversion of sulfite to hydrogen sulfite. Similarly to the procedure described earlier,5 this process is performed for PSO2 ) 0. The enlargement of magnesium chloride concentration induces a sulfur dioxide solubility rise. This effect is caused by the increase of ionic strength of the solution and the formation of MgHSO3+ ion pairs. However, in comparison to the solution with calcium chloride,5 this relation is weaker. From an FGD point of view, the most important factor is the ability for sulfur dioxide absorption in sprayed slurry. It is dependent on sorbent particles content and their dissolution rate, which in turn depends on the concentration of dissolved carbonates, which is additionally dependent on the neutralization rate. The driving forces of both dissolution and neutralization rates are dependent on carbonates concentration, which can be reached in the equilibrium state in a certain place of the system. In general, the amount of sulfur dioxide which can be absorbed in the solution depends on the concentration of dissolved carbonates, the concentration of sulfites which can be converted to bisulfites form, and the physical equilibrium of SO2 present in the gaseous and liquid phases.5 Because of thermodynamic restrictions, carbonates can be present in the solution only when there are no bisulfites and/or SO2 dissolved. Such region can be found in the vicinity of sorbent particles. It shows that, in this area, the solution ability for sulfur dioxide

Figure 1. Partial pressure of sulfur dioxide in gas versus concentration of dissolved SO2 for solution with addition of magnesium chloride and calcium sulfite.

absorption should be determined by the concentration of calcium carbonate when reactions 2c and 2e are taken into account. In the case of a lack of carbonates, i.e., the presence of bisulfites and/or SO2 dissolved, the ability of the solution for sulfur dioxide absorption should be described by eq 8. The relation of solution pH versus solution ability to absorb sulfur dioxide (calcium carbonate concentration and then dissolved sulfur dioxide content) is presented in Figure 2 parts a and b, respectively. Similar to the previously shown results,5 the pH decreases with the calcium carbonate concentration drop and with the increase of absorbed sulfur dioxide. The enlargement of dissolved carbon dioxide content, characterized by CO2 partial pressure in gas, causes a pH drop. However, this dependence is very weak for big concentrations of dissolved SO2. Calcium sulfite addition results in the pH rise in the whole range of variation of the calcium carbonate concentration and in the range of conversion of sulfite to hydrogen sulfite (ySO2 ) 0 up to line A in Figure 2b). This effect is most pronounced for low concentrations of dissolved carbon dioxide. The drop of pH is observed with the growth of magnesium chloride concentration. However, the influence of MgCl2 addition on the pH is slightly weaker than the one observed for the system with a calcium chloride presence.5 Variations of the concentration of hydrogen sulfite ion with CaCO3 content and the concentration of dissolved sulfur dioxide (Figure 3) are qualitatively similar to those observed in the system with calcium chloride addition.5 It has to be stressed that HSO3- concentration is much less influenced by MgCl2 presence than by that of CaCl2. This observation is significant because of a direct dependence of sulfites-to-sulfates oxidation rate on the concentration of these ions.8 Dependence of MeHSO3+ ion pairs concentrations on calcium carbonate content and the amount of dissolved sulfur dioxide is presented in Figure 4 parts a and b, respectively. The concentration of MeHSO3+ ion pairs is increasing with the decrease of calcium carbonate concentration and then with the increase of the amount of absorbed sulfur dioxide. The enlargement of the amount of dissolved carbon dioxide causes the MeHSO3+ ion pairs concentration rise for solutions with calcium sulfite addition. Solution without sulfite is very weakly influenced by CO2 content. It is noteworthy that the addition of magnesium chloride causes a decrease of CaHSO3+ ion pairs concentration. This


Figure 3. Hydrogen sulfite ion concentration versus system ability to absorb sulfur dioxide in the liquid phase.

Figure 2. Dependence of solution pH versus calcium carbonate concentration and dissolved sulfur dioxide concentration in the solution: (a) with lack of calcium sulfite and (b) with addition of CaSO3.

effect is opposite to that observed in the system involving calcium chloride.5 MgHSO3+ concentration increases with the increase of magnesium chloride content in the system. In general, concentration growth of these ion pairs leads to the improvement of sulfites species oxidation rate;8 however, the strict relation is still unknown. Similar to the previously obtained results,5 gypsum solubility increases with a decrease of concentration of dissolved calcium carbonate and then with an increase of the amount of absorbed sulfur dioxide (Figure 5). However, in the discussed case, gypsum solubility continuously grows with the magnesium chloride concentration rise. Such an effect is caused by the increase of the ionic strength of the solution. In the calcium chloride case,5 because of the common cation presence for low CaCl2 content, a minimum of gypsum solubility can be found. Considering the equilibrium state at the limestone particle surface, the saturation of the solution with calcium carbonate has to be assumed.5 However, the concentration of CaCO3 is dependent on the content of dissolved carbon dioxide.5 Sulfites content in FGD solution has to be maintained to prevent their precipitation on the surface of limestone particles. Then, the

Figure 4. MeHSO3+ ion pairs concentration as a function of calcium carbonate content and the amount of dissolved sulfur dioxide.

dependence of the concentration of the saturated solution of calcium carbonate and sulfite on the amount of dissolved carbon dioxide is presented in Figure 6. It shows that concentrations

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Figure 5. Gypsum solubility versus solution ability to absorb sulfur dioxide.

Figure 7. Gypsum solubility and solution pH versus content of dissolved carbon dioxide.

Figure 8. Partial pressure of sulfur dioxide in relation to the amount of absorbed SO2 for the system with magnesium sulfate addition. Figure 6. Calcium carbonate and sulfite solubilities in the vicinity of limestone particle versus dissolved carbon dioxide concentration characterized by CO2 partial pressure in gas.

of both salts are continuously increasing with the increased amount of dissolved CO2 (characterized by its partial pressure in gas) and with the increase of the amount of magnesium chloride introduced to the liquid phase. It is noteworthy that, for the system with calcium chloride,5 the relation of CaCO3 solubility versus CO2 content has a minimum and the CaCl2 concentration rise causes a calcium carbonate solubility drop. Figure 7 exhibits the dependences of gypsum solubility and solution pH on the dissolved carbon dioxide content in the limestone particle vicinity. It shows that gypsum solubility and pH of the solution are decreasing with the increase of the amount of soluted CO2. It should be stressed that the relation for CaSO4 solubility is opposite to that presented for the system with CaCl2.5 Such an effect can be responsible for gypsum precipitation at the surface of limestone particles in the system with magnesium chloride. In general, the enlargement of MgCl2 content results in a gypsum solubility rise. Magnesium chloride addition causes a decrease of the pH; however, the observed drop is weaker than that induced by the dissolved calcium chloride.5

MgSO4 Addition. Magnesium sulfate can appear in the system when the burner gas is free of hydrogen chloride or when this contaminant is absorbed in a prescrubber and then the partially cleaned gas is introduced to the scrubber. Such a technical solution is preferably applied by some FGD system producers (Marsulex Environmental Technology, Inc., formerly General Electric Environmental Services, Inc.). Magnesium species, mostly in the form of magnesium carbonate, are introduced to the system as limestone contaminants. Let us discuss a system consisting of the gaseous phase with sulfur and carbon dioxide mixed with inert gas, the liquid phase with dissolved SO2 and CO2, calcium sulfite and magnesium sulfate, saturated by gypsum, and the solid phase with gypsum crystals. Depending on the amount of introduced sulfur dioxide, calcium carbonate can be present in such a system in the liquid and solid phases. The dependence of the sulfur dioxide partial pressure in gas on the amount of dissolved SO2 is presented in Figure 8. Similar to the result shown in Figure 1, the equilibrium conditions (see assumption 1) can be fulfilled only in the case of the lack of soluted calcium carbonate. Contrary to the systems with calcium or magnesium chlorides, the addition of magnesium sulfate causes only a slight decrease of sulfur dioxide solubility in the


Figure 10. The dependence of hydrogen sulfite ions concentration on the content of CaCO3 or SO2 for the system with MgSO4 added.

Figure 9. Solution pH versus ability to absorb sulfur dioxide of the system with MgSO4 added.

discussed system independent of the sulfites presence. However, the influence of dissolved carbon dioxide remains negligibly small, and the character of changes caused by the calcium sulfite addition is similar to those in the systems with CaCl2 or MgCl2 because of a conversion of sulfite to the hydrogen sulfite form. It is noteworthy that, for a larger content of dissolved sulfur dioxide, the influence of MgSO4 addition becomes negligibly small. The dependence of pH on the solution ability to absorb sulfur dioxide (calcium carbonate concentration and then SO2 content) is presented in Figure 9 parts a and b. They show that the pH is decreasing with the decrease of CaCO3 concentration and then with the increase of sulfur dioxide content. Similar to the results obtained for systems with calcium chloride5 and with magnesium chloride (Figure 2 parts a and b), a rise of carbon dioxide concentration causes the drop of the solution pH. On the other hand, sulfites addition (Figure 9b) results in the increase of pH. However, this effect is significant only for a low content of CO2. The addition of magnesium sulfate causes a pH decrease in the regions where calcium carbonate is present or the conversion of sulfites to hydrogen sulfites form takes place (Figure 9b, between ySO2 ) 0 and line A). In a region with a relatively large

content of absorbed sulfur dioxide, the increase of pH with the rise of MgSO4 content is observed. The dependence of HSO3- ions concentration on dissolved calcium carbonate content and the amount of absorbed sulfur dioxide is shown in Figure 10. The concentration of these ions is increasing with the decrease of CaCO3 content and with an enlargement of the amount of the captured SO2. A CO2 content rise leads to an increase of HSO3- ions concentration. However, this effect is significant only in the case of the simultaneous presence of calcium sulfite and carbonate or during the conversion of sulfites to hydrogen sulfites. An addition of magnesium sulfate causes the increase of the concentration of hydrogen sulfite ions. It is noteworthy that this effect is opposite to those observed for the systems with CaCl2 5 or MgCl2 added (Figure 3). Dependencies of the MeHSO3+ ion pair concentration on the contents of CaCO3, CO2 and SO2, and CaSO3 are qualitatively the same in the systems with MgCl2 (Figure 4) and MgSO4 (Figure 11) added. However, the system is more sensitive to the content of magnesium sulfate than to that of magnesium chloride. In other words, the same change of MeHSO3+ concentration is caused by a lower change of the concentration of MgSO4 than that of MgCl2. Such an effect is caused by the presence of the common anion SO42- and due to its concentration influence (except ionic strength of solution only) on gypsum solubility in the system consisting of CaSO4 and MgSO4. The relation between gypsum solubility and the system ability to absorb sulfur dioxide is less influenced by the concentration of magnesium sulfate (Figure 12) than that of calcium chloride.5 For low concentrations of CaCl2 or MgSO4, the decrease of CaSO4 solubility with an increase of the additive content is detected. This effect contradicts the result obtained for the previously described system with MgCl2 addition, where the enlargement of magnesium chloride concentration improves gypsum solubility because of the rise of ionic strength of the solution (Figure 5). It is remarkable that, only in the system with magnesium sulfate addition, a significant decrease of gypsum solubility occurs close to the point of saturation of the solution by calcium carbonate, i.e., close to the surface of the sorbent particles. Considering equilibrium conditions, the solution at the surface of the limestone particles has to be saturated by calcium

1952


Figure 12. Gypsum solubility versus system ability to absorb sulfur dioxide (the case of MgSO4 addition).

Figure 11. MeHSO3+ ion concentrations versus the system ability to absorb sulfur dioxide when MgSO4 added.

carbonate. Additionally, calcium sulfite concentration should not exceed the saturation to prevent the sorbent particle blinding by the layer of CaSO3 crystals. The dependences of saturation concentrations of CaCO3 and CaSO3 on the amount of dissolved carbon dioxide, characterized by its partial pressure in gas, and on the magnesium sulfate content are presented in Figure 13. The character of the changes is similar to those observed for the system with magnesium chloride addition. However, the system with MgSO4 is more sensitive to its concentration than the system with MgCl2, i.e., the same change of the salts solubility is caused by a smaller change of magnesium sulfate concentration than that of magnesium chloride. The influence of magnesium sulfate concentration on the relation of solution pH and gypsum solubility versus the concentration of the dissolved carbon dioxide is presented in Figure 14. The results shown refer to the solution saturated by calcium carbonate and sulfite very close to the limestone particle surface. Contrary to the results presented previously for calcium5 and magnesium chlorides (Figure 7), the addition of magnesium sulfate causes a pH increase (Figure 14). Gypsum solubility decreases with the increase of dissolved carbon dioxide content, and this decrease is significantly stronger when the MgSO4 concentration rises for a larger amount of dissolved CO2. This

Figure 13. MgSO4 influence on the relation of CaCO3 and CaSO3 solubilities versus the amount of dissolved carbon dioxide at the limestone particle surface.

effect contradicts the gypsum solubility trends observed for the system with calcium chloride added.5 It is much more pronounced than both in the case of magnesium chloride introduction (Figure 7) or in the FGD system without chloride and magnesium species addition. In the case under consideration, the enlargement of the solubility of calcium carbonate and sulfite with the carbon dioxide content rise causes the increase of concentration of Ca2+ ions due to the dissociation of these salts. The growth of magnesium sulfate content and the subsequent rise of SO42- ions concentration results in the drop of the amount of dissolved gypsum necessary to fulfill CaSO4 solubility product. Notably, the described mechanism leads to the limestone particle blinding by the gypsum layer when the increase of limestone dissolution rate occurs and the amount of released CO2 increases because of limestone neutralization by a growing amount of sulfurous acid introduced to the FGD solution. A consequence of the discussed mechanizm is presented in Figure 15. It shows the dependence of magnesium sulfate concentration (in this case, gypsum is insoluble in the system) on dissolved CO2 content characterized by its partial pressure


Figure 14. Influence of MgSO4 addition on the gypsum solubility and solution pH in the vicinity of the limestone particle surface.

Figure 15. Relation of MgSO4 concentration (for which gypsum becomes insoluble in the solution) versus the content of dissolved carbon dioxide characterized by its partial pressure in gas.

in the gaseous phase. The calculations are performed for a solution saturated by calcium carbonate and the lack of calcium sulfite (continuous line) and a solution saturated by both calcium species (CaCO3 and CaSO3) (dashed line). In both cases, the concentration of MgSO4, impeding gypsum solubility, is decreasing with the increase of the content of dissolved carbon dioxide. In the bulk of the solution, gypsum solubility is much better (Figure 12) than it is close to sorbent particle surface for the same magnesium sulfate concentration. However, near a limestone particle, the introduction of a very little amount of CaSO4 to the solution corresponds to relative gypsum oversaturation equal to infinity (Figure 15). Considering that the gypsum precipitation occurs for this parameter slightly exceeding unity, the sorbent particles can be blinded by gypsum, incoming from the bulk of the solution, for a much lower magnesium sulfate concentration than those presented in Figure 15. Remarks on the MgCO3 and MgSO3 Conversion. Magnesium is introduced to the FGD system during dissolution of the limestone contaminated by magnesium carbonate. According

to eqs 2c or 2e, in the vicinity of the limestone particle surface, MgCO3 is converted into a form of CaCO3. In agreement with the CaCO3 solubility product, appearing calcium carbonate is decreasing the amount of calcium carbonate which can be directly dissolved from the limestone particle. This mechanism shows that the presence of MgCO3 in limestone limits the rate of calcium species introduction to the FGD solution. Additionally, the quality of the mixing of CaCO3 and MgCO3 inside the limestone particle plays a significant role in limestone dissolution, especially because of the accessibility of both components by the solution. In the case of a large content of sulfurous acid in the solution when its neutralization occurs almost at the limestone particle surface, the conversion of magnesium sulfite to calcium sulfite (reactions 2b or 2d) can lead to particle blinding by precipitating calcium sulfite due to its solubility product overdraw. Incoming sulfurous acid will dissolve the appearing layer. However, the limestone dissolution rate will be lower than that in the case of pure CaCO3 particles because of the effect of layer growing and diminishing. It should be stressed that the model described previously5 and here is the first one describing consistently the thermodynamical properties and limitations of the FGD process. Its predictions are in quantitative agreement with experimental findings observed for the binary systems for calcium and magnesium (CO2 gas-saturated solution of MeCO3, SO2 gassaturated solution MeSO3, etc.) and in qualitative agreement with the observations for the system consisting of water, CaSO4, and acid. Moreover, the obtained results are in qualitative agreement with the experiments performed for the FGD system operating with chloride and/or magnesium additions. It should be stressed that limited rates of ion formation, conversion, and diffusion can result in the appearance of the other phenomena, but still a proper description of these process driving forces will be dependent on the quality of chemical equilibria analysis. Currently available experimental data collected in FGD installations allows one only to formulate hypotheses concerning the thermodynamic or kinetic nature of observed effects. Conclusions Introduction of magnesium chloride to the solution containing a certain amount of dissolved calcium sulfite and saturated by gypsum improves sulfur dioxide absorption in the liquid phase. However, the addition of magnesium sulfate to such a solution causes a slight reduction of SO2 solubility. The solution pH decreases with an increase of MgCl2 content in the whole range of variation of the solution ability to absorb sulfur dioxide (calcium carbonate concentration and then content of dissolved sulfur dioxide). A similar trend is observed for the MgSO4 addition for the solution with calcium carbonate and in the region of conversion of sulfites into the hydrogen sulfites form. For a larger amount of dissolved SO2, the increase of solution pH with an increase of magnesium sulfate content is detected. The concentration of hydrogen sulfite and MeHSO3+ ions is almost constant when calcium carbonate is present in the solution. The increase of the concentration of dissolved sulfur dioxide results in an increase of the content of these ions. The rise of MgCl2 content in the solution leads to concentration growth of hydrogen sulfite ions, but the increase of the amount of MgSO4 results in a drop of the content of these ions. The reduction of CaHSO3+ ion pairs concentration and the increase

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of MgHSO3+ ion pairs concentration with the rise of the amount of dissolved magnesium chloride or magnesium sulfate is observed. Gypsum solubility increases with a decrease of the concentration of dissolved calcium carbonate and then with an increase of the content of sulfur dioxide present in the solution. The concentration of dissolved CaSO4 rises with the growth of magnesium chloride concentration. However, the increase of the magnesium sulfate content causes the reduction of CaSO4 solubility. In the limestone particle vicinity, the enlargement of magnesium chloride or magnesium sulfate concentration generates the rise of calcium carbonate and sulfite solubility. The same change of these salts solubilities is caused by a lower variation of MgSO4 content than that of MgCl2. Magnesium chloride addition causes a gypsum solubility rise, opposite to the effect of gypsum solubility drop generated by the growth of magnesium sulfate content. The pH of the solution decreases with the increase of MgCl2 concentration and grows with the rise of magnesium sulfate content. The addition of a certain amount of magnesium sulfate to the solution results in a drop of gypsum solubility to zero. The concentration of MgSO4 leading to such an effect decreases with the increase of the amount of dissolved carbon dioxide in the solution. It is remarkable that this phenomenon can result in the limestone particle blinding by the precipitating gypsum layer. Conversion of magnesium carbonate to calcium carbonate, appearing close to the surface of limestone particle, leads to a decrease of the introduction rate of calcium species into the FGD solution. This effect can be gained by MgSO3-to-CaSO3 conversion and calcium sulfite precipitation at the limestone particles surface, i.e., limestone particles blinding. Additionally, for the large limestone dissolution rates, an appearing thin gaseous (CO2) surrounding can separate the limestone particle from the solution. Symbols Used D0 ) average ion diameter (nm) Hi ) Henry’s constant for ith gas (SO2 or CO2) (mol/dm3/Pa) I ) ionic strength (mol/dm3) j ) subscript describing metal (calcium or magnesium) Pi ) partial pressure of ith gas (SO2 or CO2) in gaseous phase (Pa) Rj ) concentration of MeHCO3+ ions (mol/dm3) S ) amount of hydrogen ions produced in reaction 1h (mol/ dm3) Xj ) concentration of MeOH+ ions (mol/dm3) yCaCl2 ) amount of dissolved calcium chloride (mol/dm3) yCaCO3 ) amount of dissolved limestone (mol/dm3) yCaSO3 ) amount of dissolved calcium sulfite (mol/dm3) yCaSO4 ) amount of dissolved gypsum (mol/dm3) yH2O ) amount of dissociated water (mol/dm3) yH2O‚CO2 ) concentration of CO2 dissolved in pure water corresponding to PCO2 in gas (mol/dm3) yH2O‚SO2 ) concentration of SO2 dissolved in pure water corresponding to PSO2 in gas (mol/dm3) yMgCl2 ) amount of dissolved magnesium chloride (mol/dm3)

yMgSO4 ) amount of dissolved magnesium sulfate (mol/dm3) ySO2 ) amount of sulfur dioxide dissolved in the solution (mol/ dm3) Y ) concentration of HSO4- ions (mol/dm3) U ) amount of hydrogen ions produced (positive) or consumed (negative) in reaction 1i (mol/dm3) V ) amount of hydrogen ions produced in reaction 1e (mol/ dm3) V0 ) amount of dissolved SO2 necessary for complete conversion of calcium sulfite to calcium hydrogen sulfite in the solution (mol/dm3) Wj ) concentration of MeHSO3+ ions (mol/dm3) zi ) ith ion charge Z ) amount of hydrogen ions produced (positive) or consumed (negative) in reaction 1f (mol/dm3) R ) Debye-Hu¨ckel theory parameter ((dm3/mol)0.5) β ) Debye-Hu¨ckel theory parameter ((dm3/mol)0.5/nm) γi ) activity coefficient for ith ion [i] ) molar concentration of ith ions or ith species (mol/dm3) Literature Cited (1) Rochelle, G. T.; King, C. J. The effect of additives on mass transfer in CaCO3 or CaO slurry scrubbing of SO2 from waste gases. Ind. Eng. Chem. Fundam. 1977, 16 (1), 67. (2) Raymond, W. J.; Sliger, A. G. The Kellogg/Weir scrubbing system. Chem. Eng. Prog. 1978, 74 (2), 75. (3) Saleem, A. Design and operation of single train spray tower FGD system. Presented at The 1991 SO2 Control Symposium, Washington, DC, 1991. (4) Brogren, C.; Karlsson, H. T. Modeling the absorption of SO2 in a spray scrubber using the penetration theory. Chem. Eng. Sci. 1997, 52 (18), 3085. (5) Michalski, J. A. Equilibria in limestone based FGD processsA pure system and chlorides addition. Chem. Eng. Technol. 2001, 24 (10), 1059. (6) Chan, P. K.; Rochelle, G. T. Modeling of SO2 Removal by Slurry Scrubbing: Effects of Chlorides. Presented at EPA/EPRI Symposium on Flue Gas Desulfurization, New Orleans, LA, 1983. (7) Brogren, C.; Karlsson, H. T. A model for prediction of limestone dissolution in wet flue gas desulfurization applications. Ind. Eng. Chem. Res. 1997, 36 (9), 3889. (8) Pasiuk-Bronikowska, W.; Ziajka, J.; Bronikowski, T. Autoxidation of sulphur compounds: PWN-Polish Scientific Publishers-Ellis Horwood: Warszawa-New York-London-Toronto-Sydney-Tokyo-Singapore, 1992. (9) Michalski, J. A. Sulphur dioxide solubility in aqueous solutions of calcium or magnesium sulphites. Chem. Eng. Technol. 2000, 23 (6), 521. (10) Newman, J. S. Elektro-khimitsheskiye Sistemy; Mir: Moscow, 1977. (Translation of Newman, J. S. Electro-Chemical Systems; Prentice Hall Inc.: Engelwood Cliffs, NJ, 1973.) (11) Stumm, W.; Morgan, J. J. Aquatic chemistry; John Wiley & Sons: New York-Chichester-Brisbane-Toronto-Singapore, 1996. (12) Perry, H. Chemical engineers handbook; McGraw-Hill: New York, 1973. (13) Kertes, A. S.; Masson, M. R. Solubility Data Series, Vol. 26: Sulfites, Selenites and Tellurites; Pergamon Press: Oxford, U.K., 1986. (14) Pasiuk-Bronikowska, W.; Rudzinski, K. J. Absorption of SO2 into aqueous systems. Chem. Eng. Sci. 1991, 46 (9), 2281. (15) Butler, J. N. Carbon dioxide equilibria and their applications; Lewis: Chelsea, MI, 1991.

ReceiVed for reView February 9, 2005 ReVised manuscript receiVed October 7, 2005 Accepted January 9, 2006 IE050160P

Equilibria in Limestone-Based FGD Process: Magnesium Addition

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