Mathematical Modeling of Wet Magnesia Flue Gas Desulphurization Process

Abstract

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]: SO₂dSiffOu₂sionthroughthegasfilmDiffusion(1)SO₂g⟶SO₂aq.Dissolution(2)Haq.+H₂O⟶H₂SO₃Dissociation(3)₂HSSOO₃₃₋⟶H⁺+HSO₃₋Dissociation(4)MgOs+H₂⟶H⁺+SO₃₂₋Dissociation(5)MgOH₂O⟶MgOH₂aq.Dissolution(6)DspSieffOcui₂esisoninaoqlfi.qdu⟶iisdsofilMvlmegd²⁺ch+em2OicHal⁻DDiisffsoulsuiotinon((78))SO₂+2OH⁻⟶SO₃₂₋+H₂OReaction(9)HSO+₃₋SO₃₂₋+H₂O⟶2HSO₃₋Reaction(10)+OH⁻⟶SO₃₂₋+H₂OReaction.(11)SO₂SO₂HSO₃₋OH⁻SO₂HSO₃₋OH⁻SO₂SO₃₂₋SO₂/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, SO₃⁻² 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 SO₃⁻² 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].

(a)

(b)

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: 𝐷_𝐴⋅𝑑²𝑑𝑧²𝐶_𝐴−𝐾^𝑠⋅1+2⋅𝐶_𝐴⋅𝐷_𝐴/𝐶^𝐵𝑠⋅𝐷_𝐵⋅𝐴^𝑝⋅𝐶_𝐵𝑠2=0,(12), 𝐷_𝐸𝑑²𝑑𝑧²𝐶_𝐸−𝐾_𝑠⋅1+𝐶^𝐹⋅𝐷_𝐹𝐶_𝐵𝑠⋅𝐷_𝐵⋅𝐴^𝑝𝐷⋅𝐶_𝐵𝑆=0,_𝐹⋅𝑑²𝑑𝑧²𝐶_𝐹−𝐾_𝑠⋅1+𝐶^𝐹⋅𝐷_𝐹𝐶_𝐵𝑠⋅𝐷_𝐵⋅𝐴^𝑝⋅𝐶_𝐵𝑠=0.(14), 𝐷_𝐵⋅𝑑²𝑑𝑧²𝐶_𝐵𝐷+𝐾_𝑠⋅𝐴_𝑃⋅𝐶_𝐵𝑠−𝐶_𝐵=0,(15)_𝐸⋅𝑑²𝑑𝑧²𝐶_𝐸=0.(16), and at𝑧=0,𝐶_𝐴=𝐶_𝐴𝑖𝑑𝑑𝑧𝐶^𝐹at𝑧=𝑧₁=0,−𝐷,_𝐹𝐶_𝐴=𝐶_𝐸=0,𝐶_𝐹=𝐶_𝐹∗,⋅𝑑𝑑𝑧𝐶^𝐹=𝐷_𝐸⋅𝑑𝑑𝑧𝐶^𝐸−𝐷_𝐹⋅𝑑𝑑𝑧𝐶^{𝐹∣1−𝑧=𝑧}+𝐷_𝐹⋅𝑑𝑑𝑧𝐶^𝐹∣_𝑧=𝑧1+=2⋅𝐷_𝐸⋅𝑑𝑑_𝑧𝐶_𝐸∣_𝑧=𝑧1+at𝑧=𝐷𝑧_2𝐵,𝐶_𝐵=𝐶_𝐹=0,𝐶_𝐸=𝐶_𝐸∗,⋅𝑑𝑑𝑧𝐶^𝐵=−𝐷_𝐹⋅𝑑𝑑𝑧𝐶^𝐹=𝐷_𝐸⋅𝑑𝑑𝑧𝐶^𝐸∣_{𝑧=𝑧2−}−𝐷_𝐸⋅𝑑𝑑𝑧𝐶^𝐸∣_𝑧=𝑧2+at𝑧=𝑧_𝐿,𝐶_𝐵=𝐶_𝐵𝑠,𝐶_𝐸=𝐶_𝐸0=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 𝐶_𝐸∗ within the liquid film. The subscripts 𝐶_𝐹∗ in the equations, respectively, indicate the chemical species 𝐸, 𝑧₂, 𝐹 and 𝑧₁.

Liquid film—Region I: it holds that 𝑑²𝑑𝑥²𝑌_𝐴−𝑁⋅𝑌_𝐴=𝑁2⋅𝑟_𝐴⋅𝑞_𝐴𝑑,(18)₂𝑑𝑥²𝑌_𝐹−𝑁⋅𝑌_𝐹=𝑁𝑟_𝐹,(19)𝑑²𝑑𝑥²𝑌_𝐸−𝑁⋅𝑟^𝐹𝑟_𝐸⋅𝑌_𝐸=−𝑁𝑟_𝐸𝑑,(20)₂𝑑𝑥²𝑌_𝐹−𝑁⋅𝑌_𝐹=𝑁𝑟_𝐹,(21)Liquid film—Region II: it holds that 𝑑²𝑑𝑥²𝑌_𝐵𝑑−𝑁⋅𝑌_𝐵=−𝑁,₂𝑑𝑥²𝑌_𝐸=0(22)Liquid film—Region III: it holds that

𝑥=0;𝑌_𝐴=1,𝑑𝑌^𝐹𝑥=𝑥₁𝑑𝑥=0,−𝑟_𝐴;𝑌_𝐴=𝑌_𝐸=0,𝑌_𝐹=𝑌_𝐹∗,⋅𝑞_𝐴⋅𝑑𝑑𝑥𝑌^𝐴=𝑟_𝐸⋅𝑑𝑑𝑥𝑌^𝐸−𝑟_𝐹,⋅𝑑𝑑𝑥𝑌^𝐹∣_{𝑋=𝑋1−}+𝑟^𝐹⋅𝑑𝑑𝑥𝑌^𝐹∣_𝑋=𝑋1+=2⋅𝑟_𝐸⋅𝑑𝑑𝑥𝑌^𝐸∣_𝑋=𝑋1+𝑥=𝑥₂,;𝑑𝑌_𝐵=𝑌_𝐹=0,𝑌_𝐸=𝑌_𝐸∗,𝑑𝑥𝑌^𝐵=−𝑟_𝐹⋅𝑑𝑑𝑥𝑌^𝐹=𝑟_𝐸⋅𝑑𝑑𝑥𝑌^𝐸∣_{𝑋=𝑋2−}−𝑟^𝐸⋅𝑑𝑑𝑥𝑌^𝐸∣_𝑋=𝑋2+𝑥=1;𝑌_𝐵,=1,𝑌_𝐸=0.(23) The boundary conditions imposed are as follows: 𝑑²𝑑𝑥²𝑌_𝐴=𝑁2⋅𝑟_𝐴⋅𝑞_𝐴𝑑,(24)₂𝑑𝑥²𝑌_𝐹=𝑁𝑟_𝐹.(25) Here, 𝑑²𝑑𝑥²𝑌_𝐸=𝑁𝑟_𝐸𝑑,(26)₂𝑑𝑥²𝑌_𝐹=𝑁𝑟_𝐹,(27) and 𝐸=𝑁⋅𝑥¹4⋅𝑟_𝐴⋅𝑞_𝐴+1𝑥₁.(28) represent the concentrations of 𝐸₀ at Mg(OH)₂ and 𝐸₀=1+12⋅𝑟_𝐴⋅𝑞_𝐴.(29) at 𝑥₁, respectively.

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

Region I: 𝑥₂𝑥2²−𝑥4¹⋅𝑁𝑟^𝐴𝑞_𝐴𝑥₁+1−𝑥²1−𝑥₁⋅√𝑁tanh√𝑁⋅1−𝑥₂+𝑁⋅𝑥²−𝑥₁32=0,2⋅𝑥¹−𝑥₂⋅𝑁+2𝑥²−𝑥₁−11−𝑥₂⋅𝑟^𝐴⋅𝑞_𝐴𝑥₁−𝑥²2−𝑥4¹⋅𝑁=0.(30)Region II: 𝑟_𝐴𝑞_𝐴

Region III: 𝑁 subject to 𝑟_𝐴 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: 𝑞_𝐴𝑁Region II: (𝐸/𝐸₀)𝑞_𝐴

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

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

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 𝐶_𝐴𝑖, 𝑁, and 𝑞_𝐴. The values of SO₂, Mg(OH)₂, and 𝑞_𝐴 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 𝑞_𝐴 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 𝑟_𝐴. It indicates that when 𝑞_𝐴 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.

(a)

(b)

(c)

Figure 2 

Enhancement factors as a function of 𝑁 for the 𝑁–SO2 slurry system. Enhancement factors as a function of Mg(OH)2 for the 𝑁–SO2 slurry system. Enhancement factors as a function of Mg(OH)2 for the 𝑁–SO2 slurry system.

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

(a)

(b)

(c)

Figure 3 

Enhancement factors as a function of SO2 for the 𝐸/𝐸0–𝑟𝐴 slurry system. Enhancement factors as a function of 𝑟𝐴 for the SO2–Mg(OH)2 slurry system. Enhancement factors as a function of SO2 for the Mg(OH)2–Mg(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 𝐴_𝑝 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 6⋅𝑤/𝜌⋅𝑑_𝑝 decreases as 𝐶 increases.

Figure 4 

Enhancement factor as a function of 𝐷 for 𝑑𝑝–𝐸 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 𝑘𝑠–𝑁 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 𝑘_𝑠⋅𝐴_𝑝⋅(𝑍_𝐿)²/𝐷_𝐵. slurry with the help of two reaction planes.

Numerical solutions for the absorption of 𝑞_𝐴 in aqueous slurries of 𝐶_𝐴𝑖/𝐶_𝐵𝑠 are presented in Figures 2–5. The dissolution of fine solid 𝑟₁ particles has significant effect on enhancement factor which contributes to the absorption rate of (𝐷_𝐼/𝐷_𝐵)(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/𝑍_𝐿 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∶
𝐴∶:	SO2
𝐵∶:	OH−
𝐸∶:	Dimensionless distance from gas-liquid interface = SO32−
𝐹∶:	HSO3−
𝐼∶:	𝑆∶
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

CO2	Analysis of variance

Subscripts

Ca(OH)2	Mg(OH)2
SO2	SO2
SO2	Mg(OH)2
SO2	NO2
Ca(OH)2	At the gas-liquid interface
Mg(OH)2	At the surface of solid particle
	In the bulk of the liquid

Acknowledgment

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