3702
Ind. Eng. Chem. Res. 1996, 35, 3702-3706
Absorption of Sulfur Dioxide into Aqueous Solutions: Equilibrium MgO-SO2-H2O and Graphical Presentation of Mass Balances in an Equilibrium Diagram Martin Zidar, Janvit Golob,* and Marjan Veber Faculty of Chemistry and Chemical Technology, University of Ljubljana, 61001 Ljubljana, Slovenia
Described herein is a procedure for calculating the relevant concentrations of sulfur dioxide in a MgO-SO2-H2O system and the construction of an equilibrium diagram showing the relationships between total SO2, combined SO2, true free SO2, and pH. The procedure used the Rudzinski method for determining the pH of complex aqueous solutions and the modified DebyeHu¨ckel expression for calculating activity coefficients. The calculated concentrations matched closely those obtained from Hagefeldt’s diagram and measured concentrations from an actual industrial magnesium based pulping process. The equilibrium diagram was used for the graphical representation of the mass balances of the industrial absorption process. Introduction Considerable basic and applied research has been carried out on SO2 absorption into aqueous solutions, which is important in pulp production and environmental protection. One of the earliest contributions dealing with the equilibria in the MgO-SO2-H2O system at 298 K is the work published by Hagefeldt,1 where experimental data are presented in a diagram showing the concentrations of total SO2, combined SO2, true free SO2, and pH of the solution. As long as the sulfite process was limited to acid bisulfite pulping, these definitions were conventionally accepted and useful for reaction control.2 The diagram was designed for the quick determination of sulfite solutions in the sulfite process described in the literature.3,4 Apart from industrial process control applications, fundamental research on the equilibrium in electrolyte system has also been published.5,6 Pasiuk-Bronikowska and Rudzinski presented a method of modeling SO2 absorption into aqueous solutions containing sulfites, based on the film theory of gas absorption and the chemical-equilibrium treatment of chemical reactions. Rudzinski also proposed a method of calculating pH in complex aqueous solutions. This method can be applied both to systems where all the reactions are in equilibrium and for the kinetic modeling of complex chemical reactions in aqueous solutions involving instantaneous acid-base dissociations. For strong electrolyte solutions the influence of the electrostatic contributions to the activity coefficients of the ions was expressed by the modified Debye-Hu¨ckel equation.7 Among publications3,4,8 describing the industrial operation of equipment for the absorption of SO2 from dilute gas streams by various solutions used in Venturi scrubbers, a more recent study8 has contributed to the fundamental understanding of the pulp production and flue gas desulfurization. The results from these studies form the basis of our work which has the following aims: (1) to quantitatively represent the relationships between the concentrations of total SO2, of combined SO2, of true free SO2, and of the pH of the solution and to compare the computed values with experimental values1 and with the corresponding measurements from an actual industrial magnesium based pulping process; (2) to graphically represent in the equilibrium diagram the mass balances for S0888-5885(95)00623-3 CCC: $12.00
mixing of flows, for absorption of SO2, and for the reaction of SO2 with MgO occurring within the industrial SO2 absorption unit. Equilibrium Diagram Concentrations of ionic species Mg2+, H3O+, OH-, HSO3-, and SO32-, which are required for the calculation of ionic activities, were determined using experimental pH values, total SO2 (ctot.), combined SO2 (ccom), and true free SO2 (Y) concentrations.1 The calculation procedure contains the relevant equilibrium reactions with the thermodynamic equilibrium constants for the SO2-HSO3--SO32--H2O system, mass balance equations, a charge balance equation, and the modified Debye-Hu¨ckel equation. The quantities ctot., ccom, and Y are expressed in terms of the amount of total SO2, Mg2+, and the hydrogen ion concentration (1-3).2,6
ctot. ) cSO2 + cSO32- + cHSO3cH3O+ -
]/[
Kw,c cH3O+
[
ctot. ) 2cMg2+ +
K1,ccH3O+ + 2K1,cK2,c
cH3O+2 + K1,ccH3O+ + K1,cK2,c
]
(1a,b)
ccom ) cSO32- + 0.5cHSO3K1,cK2,c + 0.5K1,ccH3O+ ccom ) ctot. (2a,b) cH3O+2 + K1,ccH3O+ + K1,cK2,c Y ) ctot. - 2ccom
(3)
K1,c, K2,c, and Kw,c are the concentration equilibrium constants. The thermodynamic dissociation constant (K1 ) 0.014, K2 ) 7.1 × 10-8, Kw ) 1.0 × 10-14) data are taken from the literature and refer to a temperature of 298 K.9 The ionic strength µ of the industrial magnesium based pulping solutions varied from 0.5 to 2.0 mol/L.1,3,4 The best correlation between the experimental1 and calculated values is obtained when the activity coefficients are calculated using the modified Debye-Hu¨ckel © 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3703
to sum of the initial concentration of HSO3- and 2x moles of SO2 being absorbed. Industrial Application
Figure 1. Equilibrium diagram of MgO-SO2-H2O.
equation (4) with the parameters A ) 2.70, B ) 1.75, and C ) 0.109. The calculation procedure is given in the Appendix.
-log(γi) )
AZi2µ0.5 1 + BRiµ0.5
+ CZi2µ
(4)
In eq 4 µ is the ionic strength of the solution, Zi is the charge on species i, and Ri is the effective diameter of the hydrated ion i (RH3O+ ) 9.0 Å, ROH- ) 3.5 Å, RMg2+ ) 8.0 Å, RSO32- ) 4.5 Å, RHSO3- ) 4.5 Å).10 The results of a linear regression analysis comparing experimental and computed data show an acceptable agreement between the two sets of values: ccom,exp ) 0.997ccom,model + 0.0004 (Rval ) 0.9999); Yexp ) 1.015Ymodel - 0.0001 (Rval ) 0.996). The graphical representation of these calculations is shown in the equilibrium diagram (Figure 1). The lines in the equilibrium diagram for ctot., ccom can be explained in terms of basic chemical reactions. The magnesium hydroxide in the slurry reacts with the magnesium bisulfite acid forming magnesium sulfite according to the following reaction 5:11
Mg(HSO3)2 + Mg(OH)2 f 2MgSO3 + 2H2O (5) The resulting magnesium sulfite then reacts with the SO2 from the gas stream (6):11
MgSO3 + SO2 + H2O f 2Mg(HSO3)2
(6)
While reaction 5 takes place at constant concentrations of total SO2, reaction 6 occurs at constant combined SO2 concentrations (slanting and vertical lines in Figure 1). To explain why the concentration of combined SO2 remains constant from the beginning to the end of the absorption process, expressions 7 and 8 are introduced into a defining expression for ccom (2a).2
cSO32-,end ) cSO32-,start - x
(7)
cHSO3-,end ) cHSO3-,start + 2x
(8)
During the absorption process, the concentration of SO32- (7) is equal to the difference between the initial concentration of SO32- and x moles of SO2 being absorbed and the concentration of HSO3- (8) is equal
(a) Description of Industrial Plant. A schematic flow diagram of the commercial Venturi absorption system and of the fortification system of the magnesium pulping process is shown in Figure 2. The gas, containing up to 1.3 vol % SO2 flows through a series of four commercial Venturi absorbers. Additional sulfur dioxide enters the fourth commercial Venturi absorber as overgas from the fortifying tower. Each Venturi discharges into a collection tank for complete separation of acid from the gas stream. Acid is then recirculated from the collection tank and sprayed cocurrent into the gas stream above the Venturi throat. Magnesium hydroxide is added into the recirculation tube of each of the four Venturis. The acid then flows from one stage to the next by gravity through overflow pipes into the collection tanks. The acid produced in the absorption system contains total SO2 from 4.4 to 5.2 wt % as sulfur dioxide and is divided into two acid flows, one going to the cooking acid storage tank and the other to the fortification tower. The fortification tower is to provide the contact between acid and sulfur dioxide gas from the sulfur burner. The enriched acid from the fortification tower is then mixed with the acid in the cooking acid storage tank to produce the required concentration of acid for the pulping cycle. (b) Industrial Plant Data. The pH and the concentrations of total SO2 and of combined SO2 were determined in filtered samples obtained from the industrial plant’s Venturi absorption system and fortification system (Figure 2: 1M, 2M, 3M, 4M, 5M, 6M). The pHs of the sulfite cooking solutions were measured using a PHM AUTOCAL pH meter, and the standard method (Merkblatt I/6/70) was used for analyzing the amount of total and combined SO2 in the sulfite cooking solutions. Table 1 shows the experimental values and results of calculations using total and component mass balance equations. The experimental values are the average of eight measurements. The density of the solutions varied from 1000 to 1060 kg/m3. Thus, for unit conversions to weight percent, the density was assumed to be 1000 kg/m3 as long as it did not exceed an acceptable tolerance, which depends on the experimental error for the concentrations of species under consideration. The process flow data are taken from industrial instruments. Results and Discussion The equilibrium diagram and data from industrial operation were used for a comparison between the measured values and computed data and for representing the mass balances of the absorption process. The experimental values in Table 1 were measured during the industrial process at the sites shown in Figure 2 and compared with the computed values for the true free SO2 and combined SO2 in the equilibrium diagram (Figure 1). A linear regression analysis between experimental and computed values show a satisfactory agreement between the two sets of values: ccom,exp ) 1.030ccom,model - 0.031 (Rval ) 0.996); Yexp ) 1.024Ymodel - 0.021 (Rval ) 0.977). The commercial Venturi absorption system and fortification system (Figure 2) can be described quantitatively by using the equilibrium diagram (Figure 1), data
3704 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996
Figure 2. Flow diagram of a commercial Venturi absorption system and of the fortification system of the magnesia pulping process (a, commercial four-Venturi absorption system; b, fortification tower; c, cooking acid storage tank; 1-4, - first, second, third, fourth commercial Venturi; 1a-4a, - first, second, third, fourth spray; 1b-4b, first, second, third, fourth collection tanks; 1M-6M, measured sites for ctot., ccom, and pH). Table 1. Measured and Calculated Data from the Operation of the Commercial Venturi Absorption and Fortification System Shown in Figure 2 L0 (m3/h) L6 (m3/h) LR,1 (m3/h) LR,2 (m3/h) LR,3 (m3/h) LR,4 (m3/h) L1,MgO (m3/h) L2,MgO (m3/h) L3,MgO (m3/h) L4,MgO (m3/h) L5,MgO (m3/h) Lventuri (m3/h) Ginput,1 (Nm3/h) Goutput (Nm3/h) Ginput,2 (Nm3/h) Goutput,2 (Nm3/h) eg,input,2 (vol %) cg,output (vol %) cg,input,1 (vol %)
Measured Values 12.0 ( 0.1 ctot.,0 (wt %) 45.0 ( 1.4 ctot.,1 (wt %) 650 ( 20 ccom,1 (wt %) 650 ( 20 pH1 650 ( 20 ctot.,2 (wt %) 650 ( 20 ccom,2 (wt %) 4.7 ( 0.15 pH2 2.5 ( 0.1 ctot.,3 (wt %) 3.0 ( 0.1 ccom,3 (wt %) 0.0 pH3 0.0 ctot.,4 (wt %) 22.8 ( 0.7 ccom,4 (wt %) 50000 ( 1500 pH4 50000 ( 1500 ctot.,5 (wt %) 1000 ( 30 ccom,5 (wt %) 1000 ( 30 pH5 16 ( 1 ctot.,6 (wt %) 0.030 ( 0.001 ccom,6 (wt %) 1.30 ( 0.0 pH6
0.0 1.06 ( 0.1 1.06 ( 0.1 8.04 ( 0.2 2.30 ( 0.3 1.66 ( 0.3 5.89 ( 0.1 3.93 ( 0.2 2.24 ( 0.2 5.06 ( 0.1 4.86 ( 0.2 2.57 ( 0.1 4.57 ( 0.1 6.50 ( 0.3 3.11 ( 0.2 2.74 ( 0.1 5.69 ( 0.5 2.86 ( 0.2 3.68 ( 0.1
L1 (m3/h) L2 (m3/h) L3 (m3/h) L4 (m3/h)
Calculated Values 16.7 L4,a (m3/h) 19.2 L4,b (m3/h) 45.0 L5 (m3/h) 45.0 cg,output,2 (vol %)
22.5 22.5 22.5 3.1
from Table 1, and the gravity principle technique and by taking into account the reactions 5 and 6. The lines in Figure 3 show the absorption of SO2 and the flow from the previous stage, the flow of MgO suspension and the circulation flow in each stage, and mixing of the fortified solution with the solution from stage 4. Each stage from 1 to 4 is shown in the diagram and represents the operation of four commercial Venturis. The operation of the fortification tower and the acid cooking storage tank is shown as stage 5. The coordinates of points B′ of each stage from 1 to 4 and the coordinates of points A, B′, and B of stage 5 are measured values. The coordinates of points B were calculated using the gravity principle technique, and the coordinates of points C were obtained as intersections of lines, which represent reactions 5 and 6. The
Figure 3. Graphical representation of mass balances for mixing of flows, of absorption of SO2, and of the reaction of SO2 with MgO in the equilibrium diagram (1M-6M, measured values of ctot., ccom, and pH of each stage; 1-5, stages of four commercial Venturis and of the fortification tower with the acid cooking storage tank (Figure 2); DETAIL, represents the operation of each stage from 1 to 5).
coordinates of points A were obtained by using the fact the coordinates of point A from stage i (i is the integer value from 1 to 4) are equal to the coordinations of point B′ from the previous stage i - 1 (i is the integer value from 1 to 3). The coordinates of points A, B′, B, and C and the ratios of distances AB′ to B′B for each stage from 1 to 5 in Figure 3 are given in Table 2. Each straight distance represents AB′B mixing, B′C reaction 5, and CB reaction 6. Conclusion A quantitative method for the construction of an equilibrium diagram for a MgO-SO2-H2O system based on fundamental thermodynamic relationships is described. The calculated values of the model are found to be in good agreement with available experimental data when the activity of the ion species of the system were determined using a modified Debye-Hu¨ckel equation. The equilibrium diagram constructed from the calculated concentrations of the total SO2, of combined
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3705 Table 2. Values of Points A, B′, B, C and the Ratios AB′ to B′B for Each Stage Shown in Figure 3 stage 1 A B′ B C
stage 2
stage 3
stage 4
stage 5
ccom
Y+3
ccom
Y+3
ccom
Y+3
ccom
Y+3
ccom
Y+3
0.58 1.06 1.07 1.07
1.84 1.94 1.94 1.92
1.06 1.66 1.68 1.68
1.84 1.98 1.98 1.95
1.66 2.24 2.29 2.29
1.98 2.45 2.49 2.35
2.24 2.57 2.60 2.60
2.45 2.72 2.74 2.66
2.57 2.86 3.11 3.11
2.72 2.97 3.28 1.62
AB′:B′B
AB′:B′B
AB′:B′B
AB′:B′B
AB′:B′B
54:1
39:1
11:1
11:1
1:1
SO2, of true free SO2, and the pH is useful for a graphical representation of the mass balances in the absorption process.
4b ) acid from fourth commercial Venturi to fortification tower 5,MgO ) magnesium hydroxide slurry to the acid from fourth commerical Venturi
Nomenclature
Appendix
A, B, C ) parameters from the modified Debye-Hu¨ckel equation (dimensionless) c ) concentration (mol/L, wt %, or mol/m3) G ) flow of gas ((N m3)/h) K1, K2, Kw ) thermodynamic equilibrium constants (dimensionless) K1,c, K2,c, Kw,c ) concentration equilibrium constant (dimensionless) L ) flow (m3/h) pH ) negative log of activity of H3O+ ions in the solutions Rval ) correlation coefficient x ) number of moles absorbed into the solutions (mol) Y ) concentration of true free SO2 (wt %) Zi ) charge on the species H3O+, OH-, Mg2+, HSO3-, SO32(dimensionless)
Steps for calculating the amounts of species in solution and the variables ctot., ccom, Y, and pH and the parameters A ) 2.70, B ) 1.75, and C ) 0.109.
Greek Letters Ri ) effective diameter of the hydrated H3O+, OH-, Mg2+, HSO3-, or SO32- ion (Å) γi ) activity coefficient of H3O+, OH-, Mg2+, HSO3-, or SO32- (dimensionless) µ ) ionic strength of the solution (mol/L) Subscripts com ) combined SO2 end ) after absorption of SO2 H3O+, OH-, Mg2+, HSO3-, SO32- ) species in solutions input,1 ) sulfur dioxide from the recovery furnace input,2 ) sulfur dioxide from the sulfur burner g ) flue gas MgO ) feeding of magnesium hydroxide slurry to the recirculated acid output ) sulfur dioxide from the commercial Venturi absorption system output,2 ) sulfur dioxide from the fortification tower R ) recirculated acid start ) before absorption of SO2 tot. ) total SO2 venturi ) make up water flow 0 ) water 1, 2, 3, 4, 5, 6 ) acid from first, second, third, fourth commercial Venturi, from fortification tower, or from cooking acid storage tank 4a ) acid from fourth commercial Venturi to cooking acid storage tank
Literature Cited (1) Hagefeldt, K. Fast analysis of magnesium bisulphite. Sven. Papperstidn. 1970, 73 (13-14 (Jul 15)), 435-437. (2) Ingruber, V.; Kocurek, M. J.; Wong, A. In Pulp and Paper Manufacture, 3rd ed.; Ingruber, O. V., Ed.; Sulfite Science and Technology; 1985; Vol. 4, pp 1-19. (3) Kovasin, K.; Tuomi, A. Bleaching: The Options of Oxigen. Pulp Pap. Int. 1990, 32 (5 (May)) 108-109. (4) Clement, J. L. Magnesium Oxide Recovery System, Design and Performance. Tappi 1966, 49 (8 (Aug)), 127A-134A. (5) Pasiuk-Bronikowska, W.; Rudzinski, K. J. Absorption of SO2 into Aqueous Systems. Chem. Eng. Sci. 1991, 46 (9), 2281-2291.
3706 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 (6) Rudzinski, K. J. Calculation of the pH Value of a Mixture of Solutions-A Supplement. Chem. Eng. Sci. 1984, 39, (1), 196198. (7) Butler, J. N. Ionic Equilibrium; Addison-Wesley: Reading, MA, 1964. (8) Hills, J. H. Behavior of Venturi Scrubbers as Chemical Reactors. Ind. Eng. Chem. Process Des. Dev. 1995, 34, 4254-4259. (9) Goldberg, R. N.; Parker, V. B. Thermodynamics of Solutions of SO2,g in Water and of Aqueous Sulfur Dioxide Solutions. J. Res. Natl. Bur. Stand. 1985, 90 (5 (Sept-Oct)), 341-358. (10) Skoog, D. A.; West, D. M.; Holler, F. J. Fundamentals of Analytical Chemistry, 6th ed.; Saunders College: New York, 1992; pp 146-157.
(11) Markant, H. P., Mcllroy, R. A.; Matty, R. E. Absorption Studies MgO-SO2 Systems. Tappi 1962, 45 (11 (Nov)), 849-854.
Received for review October 12, 1995 Revised manuscript received June 3, 1996 Accepted June 10, 1996X IE950623Z
X Abstract published in Advance ACS Abstracts, August 15, 1996.
