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Modelling and Simulation in Engineering
Volume 2008 (2008), Article ID 871479, 6 pages
Research Article

Mathematical Modeling of Wet Magnesia Flue Gas Desulphurization Process

Department of Chemical Engineering and Technology, Institute of Technology, Banaras Hindu University, Varanasi 221005, Uttar Pradesh, India

Received 3 November 2007; Accepted 28 January 2008

Academic Editor: F. Gao

Copyright © 2008 M. K. Mondal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Desulphurization of flue gases from various chemical industries in a techno-econo-enviro manner is a demanding technology. The concentrations of sulphur dioxide in and around these plants overshoot the danger point. In recent years, the process analysis of chemical absorption in a slurry has become important in rational design and development of wet scrubbing processes for the removal of SO2 from flue gases. The elementary steps encountered in wet scrubbing by slurries are diffusion and reaction of gaseous species and solid dissolution in liquid film. In the present work, the process of the absorption of sulphur dioxide into wet magnesia slurry was theoretically analyzed according to the two-reaction plane model incorporating the solid dissolution promoted by the reactions with absorbed sulphur dioxide in the liquid film. A model based on Fick's second law has been developed to calculate enhancement factor for absorption of Sulphur dioxide into Mg(OH)2 slurry. The concentration of accumulated species in the bulk of the liquid phase (sulphite ions for this case) which substantially control the absorption rates was included in the model for the prediction of theoretical enhancement factor. The values of theoretical enhancement factors obtained from model were compared with experimental enhancement factors available in literature. The model values of enhancement factors agreed well with the values of experimental enhancement factor available in literature.

1. Introduction

It has long been known that besides being a hazard to human health, emission of sulphur dioxide contributes to the acidification of soil and waterways. Sulphur dioxide has also been reported to support the reactions which create ozone depletion in the stratosphere. Many countries have therefore adapted strict regulations regarding SO2 emissions from coal and oil fired boilers which are one of the primary sources of SO2 emissions. Many different methods are available in the market for reducing the emissions of SO2 from coal and oil fired boilers [1]. The dominating flue gas desulphurization (FGD) technology is based on wet scrubbing specially slurry scrubbing [2].

Slurry reactions have a widespread application in chemical and biochemical industries [3]. The gas absorption with chemical reaction in a slurry containing fine particles has become important in the development of processes for the removal of acidic pollutants. At present, most wet scrubbing processes for the removal of SO2 are by lime and limestone slurry. The major disadvantage of lime/limestone slurry processes is the problem of disposal of calcium sulphate sludge. Wet magnesia FGD system can eliminate scrubber sludge disposal problem and also provide saleable byproduct. In India, most of the sulphur is imported, and hence this process will be very useful to meet the sulphur need in the country.

Several models available for absorption of SO2 are based on lime/limestone slurry [4, 5]. Some models are also available in literature regarding the absorption of SO2 in sea water [6, 7]. A little work has been done on the modeling of wet magnesia FGD slurry. This paper focuses the model for wet magnesia FGD slurry process in terms of the two- reaction-plane model incorporating the solid dissolution promoted by the reactions with SO2 in the liquid film. The objective of this work has been to develop a model of the absorption of SO2 into wet magnesia slurry using an unsteady state mass transfer theory (i.e., Fick’s second law) and to use the model to quantify the enhancement of the absorption rate of SO2 into a slurry containing small reactive Mg(OH)2 particles.

2. Model Description

2.1. Model of Absorption through Reaction Planes

Regarding the SO2 absorption mechanism into wet magnesia slurry, the following processes can be considered [8]: SO2diusionthroughthegaslmDiusion(1)SO2gSO2aq.Dissolution(2)SO2aq.+H2OH2SO3HDissociation(3)2SO3H++HSO3Dissociation(4)HSO3H++SO32sDissociation(5)MgO+H2OMgOH2aq.Dissolution(6)MgOH2aq.Mg2++2OHDissolution(7)DiusionofdissolvedchemicalDiusionspeciesinliquidlm(8)SO2+2OHSO32+H2OReaction(9)SO2+SO32+H2O2HSO3Reaction(10)HSO3+OHSO32+H2OReaction.(11)SO2SO2HSO3OHSO2HSO3OHSO2SO32SO2/Mg(OH)2 Initially, SO2 gas diffuses from bulk of the gas phase to the gas-liquid film, dissolves into the bulk liquid and dissociates. Simultaneously, solid MgO also dissolves and dissociates. After that, the sulphite and hydroxyl ions react with each other in the liquid film according to (9)–(11). The principal chemical species of the reaction are subjected to acid dissociation; it is necessary to consider the pH of the absorbent liquid, which largely influences the degree of dissociation.

2.2. Basic Equations

In the process of OH absorption in magnesia slurry with no suspended particles, SO32 cannot coexist with HSO3, so that reaction (9) never takes place directly. The above condition shows that reactions (10) and (11) take place at two different located planes in the two-reaction-plane model. However, in the slurry process, to be considered here, both dissolve Mg(OH)2 and the 𝐴,𝐵,𝐸,𝐹, to be produced by reaction (10), can react with SO2 which is fed by the dissolution of the solid particles in the liquid film. So in this case, dissolved OH can be consumed by reactions (9) and (10) simultaneously. The concentration of SO32 in the bulk liquid increases as the absorption proceeds. For a saturated solution of magnesia, a plausible sketch of the concentration profile is given in Figure 1(a). When the particles are suspended in the liquid film, the concentration profiles shift as shown in Figure 1(b) [9].

Figure 1: Concentration profile for HSO3 slurry: (a) no suspended solids, (b) in the presence of suspended solids.

The model considers the presence of 4 basic species: 𝐷𝐴𝑑2𝑑𝑧2𝐶𝐴𝐾𝑠𝐶1+2𝐴𝐷𝐴/𝐶𝐵𝑠𝐷𝐵𝐴𝑝𝐶𝐵𝑠2=0,(12), 𝐷𝐸𝑑2𝑑𝑧2𝐶𝐸𝐾𝑠𝐶1+𝐹𝐷𝐹𝐶𝐵𝑠𝐷𝐵𝐴𝑝𝐶𝐵𝑆𝐷=0,𝐹𝑑2𝑑𝑧2𝐶𝐹𝐾𝑠𝐶1+𝐹𝐷𝐹𝐶𝐵𝑠𝐷𝐵𝐴𝑝𝐶𝐵𝑠=0.(14), 𝐷𝐵𝑑2𝑑𝑧2𝐶𝐵+𝐾𝑠𝐴𝑃𝐶𝐵𝑠𝐶𝐵𝐷=0,(15)𝐸𝑑2𝑑𝑧2𝐶𝐸=0.(16), and at𝑧=0,𝐶𝐴=𝐶𝐴𝑖𝑑𝐶𝑑𝑧𝐹=0,at𝑧=𝑧1,𝐶𝐴=𝐶𝐸=0,𝐶𝐹=𝐶𝐹,𝐷𝐹𝑑𝐶𝑑𝑧𝐹=𝐷𝐸𝑑𝐶𝑑𝑧𝐸𝐷𝐹𝑑𝐶𝑑𝑧𝐹1𝑧=𝑧+𝐷𝐹𝑑𝐶𝑑𝑧𝐹𝑧=𝑧1+=2𝐷𝐸𝑑𝑑𝑧𝐶𝐸𝑧=𝑧1+at𝑧=𝑧2,𝐶𝐵=𝐶𝐹=0,𝐶𝐸=𝐶𝐸,𝐷𝐵𝑑𝐶𝑑𝑧𝐵=𝐷𝐹𝑑𝐶𝑑𝑧𝐹=𝐷𝐸𝑑𝐶𝑑𝑧𝐸𝑧=𝑧2𝐷𝐸𝑑𝐶𝑑𝑧𝐸𝑧=𝑧2+at𝑧=𝑧𝐿,𝐶𝐵=𝐶𝐵𝑠,𝐶𝐸=𝐶𝐸0=0.(17). The basic equations were derived to form the mass balance of perspective chemical species as shown below. The first terms of (12)–(15) deal with the diffusion of the species according to Fick’s second law, while the second term shows the consumption due to their reaction with 𝐶𝐸 within the liquid film. The subscripts 𝐶𝐹 in the equations, respectively, indicate the chemical species 𝐸, 𝑧2, 𝐹 and 𝑧1.

Liquid film—Region I: it holds that 𝑑2𝑑𝑥2𝑌𝐴𝑁𝑌𝐴=𝑁2𝑟𝐴𝑞𝐴𝑑,(18)2𝑑𝑥2𝑌𝐹𝑁𝑌𝐹=𝑁𝑟𝐹,(19)𝑑2𝑑𝑥2𝑌𝐸𝑁𝑟𝐹𝑟𝐸𝑌𝐸=𝑁𝑟𝐸𝑑,(20)2𝑑𝑥2𝑌𝐹𝑁𝑌𝐹=𝑁𝑟𝐹,(21)Liquid film—Region II: it holds that 𝑑2𝑑𝑥2𝑌𝐵𝑁𝑌𝐵𝑑=𝑁,2𝑑𝑥2𝑌𝐸=0(22)Liquid film—Region III: it holds that

𝑥=0;𝑌𝐴=1,𝑑𝑌𝐹𝑑𝑥=0,𝑥=𝑥1;𝑌𝐴=𝑌𝐸=0,𝑌𝐹=𝑌𝐹,𝑟𝐴𝑞𝐴𝑑𝑌𝑑𝑥𝐴=𝑟𝐸𝑑𝑌𝑑𝑥𝐸,𝑟𝐹𝑑𝑌𝑑𝑥𝐹𝑋=𝑋1+𝑟𝐹𝑑𝑌𝑑𝑥𝐹𝑋=𝑋1+=2𝑟𝐸𝑑𝑌𝑑𝑥𝐸𝑋=𝑋1+,𝑥=𝑥2;𝑌𝐵=𝑌𝐹=0,𝑌𝐸=𝑌𝐸,𝑑𝑌𝑑𝑥𝐵=𝑟𝐹𝑑𝑌𝑑𝑥𝐹=𝑟𝐸𝑑𝑌𝑑𝑥𝐸𝑋=𝑋2𝑟𝐸𝑑𝑌𝑑𝑥𝐸𝑋=𝑋2+,𝑥=1;𝑌𝐵=1,𝑌𝐸=0.(23) The boundary conditions imposed are as follows: 𝑑2𝑑𝑥2𝑌𝐴=𝑁2𝑟𝐴𝑞𝐴𝑑,(24)2𝑑𝑥2𝑌𝐹=𝑁𝑟𝐹.(25) Here, 𝑑2𝑑𝑥2𝑌𝐸=𝑁𝑟𝐸𝑑,(26)2𝑑𝑥2𝑌𝐹=𝑁𝑟𝐹,(27) and 𝐸=𝑁𝑥14𝑟𝐴𝑞𝐴+1𝑥1.(28) represent the concentrations of 𝐸0 at Mg(OH)2 and 𝐸01=1+2𝑟𝐴𝑞𝐴.(29) at 𝑥1, respectively.

The mass balance equations in the dimensionless form reduce to the following.

Region I: 𝑥2𝑥22𝑥14𝑟𝑁𝐴𝑞𝐴𝑥1+1𝑥21𝑥1𝑁tanh𝑁1𝑥2+𝑥𝑁2𝑥123=0,2𝑥1𝑥2𝑁+2𝑥2𝑥111𝑥2𝑟𝐴𝑞𝐴𝑥1𝑥22𝑥14𝑁=0.(30)Region II: 𝑟𝐴𝑞𝐴

Region III: 𝑁 subject to 𝑟𝐴 When the concentration of gaseous species is extremely low and the enhancement factor for the solid dissolution can be regarded as unity, (18)–(21) are simplified as follows:

Region I: 𝑞𝐴𝑁Region II: (𝐸/𝐸0)𝑞𝐴

Equations (24)–(27), (22) give the enhancement factor as 𝐸/𝐸0𝑁 represents the enhancement factor for a clear solution saturated with 𝑟𝐴 and is defined by

SO2 The dimensionless positions of two reaction planes, 𝐸/𝐸0 and 𝑞𝐴, can be determined by the following equations [10]: 𝑞𝐴

3. Result and Discussion

3.1. Model Parameter Estimation

In order to have the numerical results of the above model regarding enhancement factor, it is necessary to know the values of the dimensionless parameters 𝐶𝐴𝑖, 𝑁, and 𝑞𝐴. The values of SO2, Mg(OH)2, and 𝑞𝐴 have been considered as same as the experimental data by various workers available in the literature. To show the contribution of the presence of the solids to the absorption rate, the ratio of enhancement factor into the slurry to that into saturated solution SO2 is plotted against Mg(OH)2 in Figures 2(a)2(c). The ratio 𝑞𝐴 represents the degree of enhancement owing to the presence of solid particles in the slurry. The parameter regarding the solid dissolution, SO2, is fixed (1.0–5.5), and the parameter Mg(OH)2 regarding the ratio of diffusivity of (𝑁) to that of liquid is also fixed (0.5–1.5). From the figures, it is observed that (𝐸/𝐸0) initially decreases with the increase in 𝑁, and then it is almost independent of 𝑟𝐴. It indicates that when 𝑞𝐴 is kept constant, the enhancement in gas absorption rate due to the presence of the suspended reactant particles is almost independent of the gas-phase concentration. The influences in gas-phase concentration and 𝐸/𝐸0 improve the absorption characteristics.

Figure 2: Enhancement factors as a function of 𝑁 for the 𝑁SO2 slurry system. Enhancement factors as a function of Mg(OH)2 for the 𝑁SO2 slurry system. Enhancement factors as a function of Mg(OH)2 for the 𝑁SO2 slurry system.

To show the effect of solid dissolution Mg(OH)2 on absorption rate, the ratio of enhancement factor 𝑟𝐴 is plotted against 𝐸/𝐸0 (see Figures 3(a)3(c)) for constant value of 𝑟𝐴. It is seen from the figures that the difference of the enhancement factors is very small with the variation of 𝑞𝐴 from 4 to 10, and 𝑁 is almost independent on SO2.

Figure 3: Enhancement factors as a function of SO2 for the 𝐸/𝐸0𝑟𝐴 slurry system. Enhancement factors as a function of 𝑟𝐴 for the SO2Mg(OH)2 slurry system. Enhancement factors as a function of SO2 for the Mg(OH)2Mg(OH)2 slurry system.

For the contribution of SO2 on absorption rate, a plot is drawn between Mg(OH)2 versus Mg(OH)2 by considering both SO2 and SO2 to be the same as shown in Figure 4. In this case, the diffusivity of SO32 in the slurry was assumed to be the same as that of the pure water, and the concentration of 𝐴𝑝 at the gas-liquid interface was assumed to be equal to the solubility of the hydroxide in the water. Under these circumstances, Figure 4 shows that 6𝑤/𝜌𝑑𝑝 decreases as 𝐶 increases.

Figure 4: Enhancement factor as a function of 𝐷 for 𝑑𝑝𝐸 slurry system.
3.2. Model Verification

Figure 5 shows the comparison between the experimental values available in literature [3, 11] and the values (obtained from model) of enhancement factor owing to the presence of solid particles for magnesium hydroxide in the slurry. It is evident that the experimental values available in literature and the model values are in good agreement.

Figure 5: Comparison between experimental values available in literature and model values of the enhancement factor for the 𝑘𝑠𝑁 slurry system.

4. Conclusion

In spite of noticeable progress in conventional flue gas desulphurization (FGD) process development, claims for more efficient, more economic, and nonpollutant technological innovations become more and more important. The new technology essentially is the wet magnesia FGD process which is technically and economically competitive with once-through FGD process. In this article, a model based on Fick’s Second law has been developed for dynamic absorption rate of sulphur dioxide into 𝑘𝑠𝐴𝑝(𝑍𝐿)2/𝐷𝐵. slurry with the help of two reaction planes.

Numerical solutions for the absorption of 𝑞𝐴 in aqueous slurries of 𝐶𝐴𝑖/𝐶𝐵𝑠 are presented in Figures 25. The dissolution of fine solid 𝑟1 particles has significant effect on enhancement factor which contributes to the absorption rate of (𝐷𝐼/𝐷𝐵)(𝐼=𝐴,𝐵,𝐸and𝐹) from bulk of the gas phase to the liquid. It is efficient to understand that the reaction of 𝑥 with accumulated species 𝑍/𝑍𝐿 promotes the absorption rate. The theoretical enhancement factors obtained from present model were compared well with experimental data available in literature. The model presented can be applied to any highly complicated reactive absorption processes. It should be stressed that analytical approximations are often oversimplified and cannot be expected to predict the absorption rates for a wide range of conditions.

List of Symbols
𝑥1:Surface area of solid particles = 𝑍1/𝑍𝐿 m2/m3 dispersion
𝑥2:Concentration in liquid phase (kmol/m3)
𝑍2/𝑍𝐿:Diffusivity in liquid phase, m2/s
𝑌:Average diameter of the solid particles, m
𝑧1,𝑧1:Enhancement factor
𝑧2,𝑧2:Mass transfer coefficient for solid dissolution, m/s
𝑧𝐿:Solid dissolution parameter = 𝜌
𝐸:Dimensionless distance from gas-liquid interface = SO32
0:Concentration in the liquid phase relative to that at the gas-liquid interface or at the solid surface
SO2:Position of one reaction plane as shown in Figure 1(m)
SO2:Position of another reaction plane as shown in Figure 1, m
NaHCO3/Na2CO3:Thickness of the liquid film (gas absorption), m

Greek Symbols
CO2Analysis of variance

Ca(OH)2At the gas-liquid interface
Mg(OH)2At the surface of solid particle
In the bulk of the liquid


M. K. Mondal gratefully acknowledges Banaras Hindu University for necessary support.


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