SO2âMg(OH) - American Chemical Society

1904

Ind. Eng. Chem. Res. 2007, 46, 1904-1913

Gas Absorption in Slurries of Fine Particles: SO2-Mg(OH)2-MgSO3 System Sajan Kakaraniya, Chandrakala Kari, Ravish Verma, and Anurag Mehra* Department of Chemical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai-400076, India

The problem of gas absorption with reaction, in a slurry containing fine particles, is important in the development of processes for the removal of acidic pollutants such as sulfur dioxide. Typically, lime and lime stone slurries can be used for removal of sulfur dioxide. However, magnesium hydroxide slurries may yield a higher scrubbing capacity as a result of the more soluble reaction product, magnesium sulfite, compared to the corresponding calcium salt. In this study, absorption experiments were carried out in a stirred cell and the resulting data is analyzed using the model proposed by Mehra [Chem. Eng. Sci. 1996, 51, 461-477]. The proposed theory incorporates the process of particle dissolution and the consequent change in particle size near the gas-liquid interface, using Higbie’s model of mass transfer with chemical reaction. A population balance approach is used to track the particle size distribution. Introduction Sulfur dioxide is one of the main pollutants from coal and fuel oil combustion in power plants. Absorption of acidic pollutants into reactive slurries containing fine sparingly soluble particles of reactant species has become important in the development of processes for removal of gases. The solid particles provide a continuous supply of this reactant to the aqueous phase wherein they react with the dissolved gaseous solute. Alkaline slurries of both calcium and magnesium hydroxide can be used for absorbing sulfur dioxide present in flue gas. However, magnesium hydroxide gives a higher scrubbing capacity because of the more soluble reaction product magnesium sulfite, relative to the corresponding calcium salt. An important aspect, relating to the rate behavior of these slurry absorbers, is the way in which the size of the suspended particles in the slurry affect the specific rate of absorption. Coarse particles can affect the absorption rate only through the bulk liquid-phase concentrations of the reacting species, but fine particles interact directly with the reactants near the gas-liquid interface thereby modifying the diffusional gradients of the reactive species and increasing the specific absorption rate. Consider the schematic drawing of a typical surface (penetration) element, a mosaic of which make up the gas-liquid interface, as shown in Figure 1. The diffusing solute gas, A, reacts with the dissolved species, B, supplied by the dissolving fine particles. Since B can also diffuse, a sufficiently fast reaction can cause substantial diffusional gradients of this species to be established. The establishment of significant depletion of B, with respect to its solubility, within the penetration element is a necessary condition for any dissolution of particles to occur in this near-interface zone, because the driving force for such dissolution is provided by the difference between the solubility of particle material in the liquid and the local concentration of B at any location in the element. Literature Review Studies in this field were reported initially by Ramachandran and Sharma,2 who presented an analysis using the film theory * To whom correspondence should be addressed. Tel.: 91-2227567750. Fax: 91-22-25721210. E-mail: [email protected].

Figure 1. Schematic representation of mass transfer with instantaneous reaction near the gas-liquid interface (penetration element) in a slurry of fine particles.

of mass transfer. The following simple reaction scheme was used to model the dissolution/reaction steps.

Ag f Aaq Bs f Baq Aaq + Baq f Products When the reactant particle size is large and there are no particles in the liquid film, near the gas-liquid interface, particle dissolution and reaction are in series. For fine particles, defined as those where the size is smaller than the film thickness, the solid dissolution and the reaction become parallel. Qualitatively, the absorption of gas increases due to a high concentration of the dissolved solid (B). As a result, the reaction plane (where the concentrations of A and B are zero) shifts toward the gas-liquid interface. For very fine solid particles, the dissolution becomes very rapid and the reaction plane almost touches the interface, i.e., λ f 0. Uchida et al.3 suggested that particle dissolution itself may be enhanced by reaction. Sada et al.4 extended the models of Ramachandran and Sharma2 and Uchida et al.; 3 the former study had assumed an average driving force for solid dissolution [(Bs - Bi)/2] for fast reactions, and Sada et al.4 improved the model by use of quasi-linearization.

10.1021/ie061461h CCC: $37.00 © 2007 American Chemical Society Published on Web 03/07/2007

Ind. Eng. Chem. Res., Vol. 46, No. 7, 2007 1905

Sada and co-workers have subsequently reported a large number of studies. These include experimental investigations, mostly on absorption of sulfur dioxide into slurries of fine magnesium hydroxide4-6 and theoretical extensions for the cases when the bulk aqueous phase is not saturated with the dissolved solid (finite slurries5) as well as when the reaction between the dissolved gas and solid is fast and not instantaneous (numerical solutions7). Uchida et al.3 classified the various mechanisms encountered in the three-phase gas absorption system and developed the mathematical model for each case based on the film concept. Uchida et al.8 reported some experimental data on the absorption of lean sulfur dioxide into fine limestone slurries. Sada et al.6 pointed out that the reaction of sulfur dioxide in aqueous slurries of alkaline-earth metal hydroxide or limestone must be regarded as being consecutive and parallel, resulting in two reaction planes being formed in the liquid film. They proposed a two-reaction plane model for two systems: (i) a SO2-CaCO3 slurry system and (ii) a SO2-Mg(OH)2 slurry system. For the SO2-CaCO3 slurry system, they proposed that at one reaction plane SO2 reacts as

SO2 + SO32- + H2O f 2HSO3- K = 107 SO2 + HCO3- f HSO3- + CO2 K = 104 and at the other reaction plane

CO32- + HSO3- f SO32- + HCO3- K = 103 Similarly, for the SO2-Mg(OH)2 slurry system they proposed the following reaction scheme

SO2 + SO32- + H2O f 2HSO3HSO3- + OH- f SO32- + H2O at the two reaction planes, respectively. Theoretical enhancement factors were compared with the experimental data on absorption, obtained using a stirred absorber with a plane gas-liquid interface at 25 °C. The calculated value exceeded the experimental results by a significant margin. They stated that as the SO2 partial pressure decreases, the reaction plane moves closer to the interface and so it is not appropriate to consider that particles are present in the region between the first reaction plane (primary) and gas-liquid interface, as the distance from the interface to the reaction plane is of the same order as the average particle size. Because existing models did not take this into account, the theoretical values of the enhancement factor considerably exceeded the experimental values at low concentrations of SO2. A penetration theory analog of Ramachandran and Sharma2 was proposed by Uchida et al.9 where they showed that, for equal diffusivity of reactants, an analytical solution could be found for the problem of a moving reaction front in the presence of fine, sparingly soluble, solid reactant particles, using the notion of negative concentrations. The predictions of rate values from this model have been demonstrated to be within a few percent of the film model computations. Yagi and Hikita10 criticized the work of Sada and co-workers as well as Uchida and co-workers. Their study provides a different view for dealing with gas absorption with instantaneous reaction; instead of using a mass transfer coefficient for solid dissolution, they used the diffusion coefficient of the gaseous solute, in two dimensions, and stated that this diffusion rate

depends upon the interparticle distance and hence on the size and concentration of the particles. However, the enhancement factor for the case of instantaneous reaction was found to be infinite. So, the authors suggested that their results are only qualitative, as they did not assume shrinkage of particles. The authors provided an expression for the upper bound value of the enhancement in the specific rate, by assuming that all the particles are present in “completely dissolved form” so that the extra reactant contained in the solid phase can be treated as being immediately available to the liquid phase. Mehra1 theoretically examined the process of particle dissolution near the gas-liquid interface for the first time and showed that changing particle size (including complete disappearance) on account of dissolution can drastically affect the specific rate of gas absorption, since the assumption of a fixed particle size implies an infinite source for solid reactant material. He also examined the nature of the bulk particle size distribution arising out of the change in particle size near the gas-liquid interface and its effect on the specific rate as well as solid conversion trajectories with batch time for a typical batch slurry contactor. The model essentially uses transient population balances over the particle size distribution, incorporated within the framework of Higbie’s penetration theory for mass transfer. The model was used to demonstrate that the width of the initial particle size distribution, which prevails within a penetration element upon its arrival at the gas-liquid interface, has considerable influence on the absorption rate because of the relatively faster disappearance of the smaller particles. Mehra,1 however, proposed this model for the simple, one-reaction scheme. Recently, Dagaonkar et al.11-13 pointed out that the earlier studies were carried out at very low values of liquid side mass transfer coefficient as compared to the realistic scenario of industrial reactors; however, they did not consider the change in particle size in their model. Scala and D’Ascenzo14 discussed the case of gas absorption followed by an instantaneous irreversible chemical reaction into a rigid droplet containing sparingly soluble, fine reactant particles, assuming slow reactant particle dissolution which implies that particle shrinkage is negligible. Conditions are also given for the applicability of the model. More recently, Scala15 developed a model for an infinitely deep quiescent liquid and for an agitated liquid using the film theory when the reactant particle dissolution in the liquid film next to the gas-liquid interface is non-negligible, but particle shrinkage is still neglected. The gas-liquid interface is taken to be planar, and the concentrations of diffusing species are assumed uniform over any plane parallel to the interface. Also, Ghiaasiaan and coworkers16,17 have examined the mechanism of gas absorption in a slurry droplet containing fine, reactive particles and its implications for a spray scrubber. In this study, experimental data is generated and the theoretical particle size distribution of the dissolving reactant particles is compared with the experimental size distributions. The theory proposed here incorporates the two-plane mechanism outlined earlier and population balances to track the particle sizes. This study also attempts to assess the approach of Mehra1 by direct experimental validation, unlike the indirect validation demonstrated earlier.18 Experimental Experiments were carried at different Mg(OH)2 holdups and mass transfer coefficients (stirring speeds) at room temperature (25 °C) and pressure. Particle size distribution data for the

1906

Ind. Eng. Chem. Res., Vol. 46, No. 7, 2007

Figure 2. Experimental setup for studying the dissolution of Mg(OH)2 particles. Table 1. Description of the Experimental Setup for Studying the Dissolution of Mg(OH)2 Particles stirred cell (reactor)

stirrer

motor

material-Borax glass internal diameter-90 mm depth-160 mm capacity-1 × 10-3 m3 material-glass type-flat blade turbine impeller-two shaft diameter-8 mm blades-40 mm blade height-18 mm diameter-55 mm type-GM 108 single-phase 1.2 A, 178 W 220/230 V, continuous duty

dissolving Mg(OH)2 particles was generated, and the procedure is described below. Experiments were carried out with magnesium hydroxide of 95% purity and sulfur dioxide of 99.9% purity. A glass stirred cell of 100 mm internal diameter and 1 × 10-3 m3 capacity was used. The reactor was equipped with a stirrer containing two turbine type impellers of 55 mm diameter, with four flat blades each. A mercury seal was used to prevent any gas leakage. A balloon containing sulfur dioxide at atmospheric pressure was connected to the stirred cell. Sampling ports, covered with a rubber septum, 20 mm from the reactor bottom, were employed, and the samples were collected with the help of a syringe. Figure 2 shows the typical experimental setup and the specifications are listed in Table 1. Magnesium hydroxide powder was added in excess to double distilled water and stirred for about 20 min to saturate the water with magnesium hydroxide. The slurry was then vacuum

filtered, first with Whatman filter paper and then with cellulose nitrate Sartorius filter paper, of 0.2 mm pore size, to get particlefree, saturated magnesium hydroxide solution. Magnesium hydroxide slurry with the desired solid holdup was prepared by adding a calculated amount of solid magnesium hydroxide powder to the saturated solution. The stirred cell was charged with the reactant slurry and sealed with silicone vacuum grease to avoid any leakage of sulfur dioxide gas. Purging with sulfur dioxide gas was done for about 15-20 s to displace the air present the reactor. The sulfur dioxide balloon was connected to the reactor, and the stirrers were started; the speed of the stirrer was kept low enough to maintain a flat gas-liquid interface. The reaction was carried out until low values of gas absorption rates were observed. Samples of 2 × 10-6 m3 (2 cm3) of reactant slurry were collected at different batch times through the septum and were photographed under optical microscope and analyzed with Image Pro-Plus Software. The software works on the principle of the difference in the optical properties of a continuous phase and the particles. The samples were also simultaneously analyzed with a Galai computerized inspection system for number concentration (total number of particles per unit volume of the slurry) data. The Galai CIS-1 uses a unique time-size mapping called the time-of-transition theory to measure the particle size directly. The results obtained from the Galai CIS-1 were combined with Image Pro-Plus to obtain number density plots at different batch times. For determination of mass transfer coefficients, experiments were carried out by the absorption pure sulfur dioxide gas in double distilled water. The bulk balance for SO2 gives

dCbA aGL / ) kL (C - CbA) dt VL A

Ind. Eng. Chem. Res., Vol. 46, No. 7, 2007 1907 Table 2. Liquid Side Mass Transfer Coefficient, kL, Values at Different Stirring Speeds for the Stirred Cell Setup

-

stirring speed (rpm)

volume of liquid, VL (cm3)

gas-liquid interfacial area per unit volume of slurry, aGL (m2/m3)

kL × 105 (m/s)

100 125 150

350 350 350

20 20 20

4.45 6.22 7.65

with the initial conditions

t ) 0,

CbA

)0

(

[

CbA ) C/A 1 - exp -kL

(

RA ) kLC/A exp -kL

aGL t VL

)]

where ksl is the solid-liquid mass transfer coefficient and is further expanded to ksl ) (DAShR)/R. Therefore, the total volumetric rate at which D is transferred to the liquid phase from all the particles is given by

DB

aGL t VL

)

A plot of ln(RA) vs t is a straight line with slope -kL(aGL/VL) and Y-intercept ln(kLC/A). The values of kL so obtained for different stirring speeds are tabulated in Table 2.

∂2CB ∂x

HSO3- (C) + OH- (D) f SO32- (B) + H2O [k3] Similar to the balances proposed by Mehra,1 the species balance for the diffusing, dissolving gaseous solute, SO2 (A), in the surface element can be written as

G(R, x, t) )

(4)

∂CA + k2CACB + k1CACD ∂t OH-

∂CB + k2CACB - k1CACD - k3CCCD ∂t

)

∂2CC 2

∂x

)

∂CC - 2k2CACB + k3CCCD ∂t

(5)

(6)

Mw s dR ) -ksl (C - CD) (R > 0) ) dt Fp D DAShR Mw s (C - CD) (7) R Fp D

(8)

The right-hand side of this equation is set to zero since there are no birth and death (death, i.e., exit of the particle from this range occurs only at the boundary, R ) 0) events within the particle size range 0-Rmax. The initial and boundary conditions (ICs and BCs, respectively) on the primary set of equations are given by ICs (t ) 0, all x)

(1)

(D), yields

2

DD

kslR2η(R, x, t) dR

∂η(R, x, t) ∂η(R, x, t)G(R, x, t) + ) 0 (R > 0) ∂t ∂R

SO2 (A) + SO32- (B) + H2O f 2HSO3- (C) [k2]

A balance for the liquid-phase reactant,

max

The population balance over the reactant particles is given by

SO2 (A) + 2OH- (D) f SO32- (B) + H2O [k1]

∂x

∫0R

Equation 3, after the left-hand side has been differentiated, gives the negative growth rate for a particle, and the resulting equation after rearranging becomes

The kinetic scheme for the SO2-Mg(OH)2-MgSO3 system is as follows:

)

2

DC

Theory

2

(3)

The material balances for the intermediate species, HSO3- (C) and SO32- (B), are

Combining this equation with the definition of average absorption rate, RA

∂2CA

)

RDd ) 4π(CsD - CD)

Integrating the above equation yields

DA

(

d Fp 4 3 πR ) ksl 4πR2(CsD - CD) dt Mw 3

CA ) CbA

(9)

CB ) CbB

(10)

CC ) CbC

(11)

CD ) CbD ) CsD

(12)

η(R, x, t) ) ηb(R)

(13)

x ) 0, CA ) C/A

(14)

∂CB )0 ∂x

(15)

∂CC )0 ∂x

(16)

∂ CD

∂CD + 2k1CACD + k3CCCD ) ∂t ∂x2

-4πksl(CsD - CD)

∫0R

R2η(R, x, t) dR

max

(2)

where η(R, x, t) dR is the number concentration (number per unit volume of the liquid phase) of solid reactant particles of size between R and R + dR, located at a distance x from the gas-liquid interface within a surface penetration element, at time t. The first and second terms in the above equations are the conventional diffusion and accumulation terms, respectively, while the third term in both the equations represents a secondorder, liquid-phase reaction. The last term in the above equation accounts for the amount of D that comes into the liquid phase by dissolution of the particles and may be derived as follows. The rate at which a single particle of size R supplies D to the liquid phase is given by

BCs (t > 0)

1908


∂CD )0 ∂x

(17)

x f ∞, CA ) CbA

(18)

CB )

(19)

CC ) CbC

(20)

CD ) CbD ) CsD

(21)

R ) Rmax, η(R, x, t) ) 0

(22)

A solution of the above equations along with the relevant conditions provides the required information. From Higbie’s penetration theory, the average rate of gas absorption is given by

∫

tc i R dt 0 A

a

∫0∞(CC(x, tc) - CbC)dx VGLL t1c + 2k2CbACbD - k3CbCCbD

(30)

CbB

1 RA ) tc

∂CbC ) ∂θ ∂CbD ) ∂θ

a

∫0∞(CD(x, tc) - CbD)dx VGLL t1c - 2k1CbACbD k3CbCCbD + 4πksl(CsD - CbD)

( )

x)0

(23)

(24)

and tc ) (4DA)/(πkL2) The other variables of interest are number concentration

∫0

η(R, x, t) dR

(25)

max

Rmean(x, t) )

Rη(R, x, t) dR N(x, t)

∫0R

(26)

R3η(R, x, t) dR

max

(27)

which, for low values of l, may also be taken to be the local, fractional volumetric holdup of the solid reactant. The variables, for a single penetration element, have to be related with their bulk counterparts, for a given reactor. For the case of a batch reactor, where the liquid is held in batch mode under a constant, unvarying gaseous environment, the material balances are described below. The net transfer of material from the interfacial region into the bulk liquid is embodied in terms containing the integrals across x, in the equations below.

∂CbA ) ∂θ

a

∫0∞(CA(x, tc) - CbA) dx VGLL t1c - k2CbACbB - k1CbACbD

(28)

∂CbB ) ∂θ

(33)

θ ) 0, CbC ) Cb,in C )0

(34)

s θ ) 0, CbD ) Cb,in D ) CD

(35)

a

a

∫0∞(CB(x, tc) - CbB)dx VGLL t1c - k2CbACbB + k1CbACbD + k3CbCCbD (29)

(36)

where the second term on the left-hand side is on account of the particle dissolution in the bulk phase. Because the bulk liquid has been taken to be saturated with D, the bulk (negative) growth rate, Gb(R, θ), is given by

Gb(R, x, t) ) 4π 3

θ ) 0, CbB ) Cb,in B )0

∫0∞[ηb(R, x, tc) - ηb(R, θ)]dx VGLL t1c

volumetric ratio of solid to liquid (holdup)

l(x, t) )

(32)

∂ b ∂ b η (R, θ) + [η (R, θ)Gb(R, θ)] ) ∂θ ∂R

average particle size

∫0R

θ ) 0, CbA ) Cb,in A )0

The population balances for the dissolving solids in the bulk liquid phase of the batch reactor are given by

Rmax

N(x, t) )

R2η(R, x, t) dR (31)

max

The first term on the right-hand side of the above equations represents the net rate of exchange of a species due to the convective motion of the penetration elements between the gasliquid interface and the bulk phase, over a time period tc, as the entire interface is renewed once over this time. The other terms on the right side denote the consumption or production of the species due to reaction. The initial conditions for the above balances are

where, the instantaneous specific rate of absorption is

∂CA RiA ) -DA ∂x

∫0R

Mw s dR ) -ksl (C - CbD) (R > 0) ) dθ Fp D DAShR Mw s (C - CbD) (37) R Fp D

becomes zero for CbD ) CsD, and hence, this term in eq 36 may be dropped. We thus have a situation of exclusive particle dissolution near the gas-liquid interface and none in the bulk. This is consistent with the case of fast reaction (no bulk reaction) and fine particles, which keep the bulk saturated. The initial condition on this bulk population balance is

θ ) 0, ηb(R, θ) ) ηb,in(R)

(38)

where ηb,in(R) describes the initial state of the particles, fed as slurry, to the batch reactor at batch time, θ ) 0. Solution Strategy. To solve the population balance equation, the method described by Mehra1 is used, in which a new variable w(R, x, t) ) (η(R, x, t))/R is defined. This reduces the population balance equation to

∂w ∂w + G(R, x, t) ) 0 (R > 0) ∂t ∂R

(39)


Figure 3. Variation of concentration of (a) SO2 and OH-, (b) SO32-, (c) magnified image of a, (d) magnified image of b, and (e) HSO3- with distance from the gas-liquid interface at t ) 0.1tc, to illustrate the position of reaction planes. Other parameter values are from Table 3. Table 3. Parameters Used in the Model for Dissolution of Mg(OH)2 Particlesa parameters C/A CsD DA DD aGL/VL Fp Mw a

value

units

source

0.9 × 100 154 × 10-3 1.49 × 10-9 2.68 × 10-9 50 2360 58.33

kmol/m3 kmol/m3 m2/s m2/s m2/m3 kg/m3 kg/kmol

Perry and Chilton19 Perry and Chilton19 Dagaonkar et al.11 Dagaonkar et al.11 measured manufacturer's specifications

Setting the derivative to zero, gives w(R, x, t) ) constant which implies w(R, x, t) ) w(R0, x, 0). Thus b η(R, x, t) η(R0, x, 0) η (R0) ) (R > 0) ) R R0 R0

In order to eliminate the dummy variable R0, eq 7 is integrated with the initial condition R ) R0 at t ) 0 and we get

Also, DB ) DC ) DD.

Using the method of characteristics, the left-hand side of the above equation can be taken as the total derivative, dw/dt.

(40)

R02 ) R2 +

2ShRDDMw Fp

∫0t(CsD - CD)dt1

(R > 0) (41)

1910


Figure 4. Variation of average particle size, Rmean, with distance from the gas-liquid interface at t ) tc. Other parameter values are from Table 3.

Figure 7. Variation of average particle size at the gas-liquid interface, R/mean, with contact time, t ) tc. Other parameter values are from Table 3.

Figure 5. Variation of solid holdup, l, with distance from the gas-liquid interface at t ) tc. Other parameter values are from Table 3.

Figure 8. Enhancement factor, φA, versus batch time, θ. The following data were used: lo ) 0.020, stirring speed ) 125 rpm, ShR ) 375. Other parameter values are from Table 3.

Figure 6. Variation of instantaneous rate of absorption, RiA, with contact time, t ) tc. Other parameter values are from Table 3.

On substituting the above in eq 40, we get

ηb η(R, x, t) )

[x

R2 +

2ShRDBMw Fp

R2 +

2ShRDBMw Fp

x

]

∫0t(CsD - CD)dt1 R

∫0t(CsD - CD)dt1 (42)

for R0 e Rmax. Otherwise, η(R, x, t) ) 0. The species balance equations along with the population balance equation are solved across the penetration time. The

Figure 9. Average particle size, Rbmean, and holdup, lb, versus batch time, θ. The following data were used: lo ) 0.020, stirring speed ) 125 rpm, ShR ) 375. Other parameter values are from Table 3.

bulk values are calculated at the end of each penetration time. As only discrete values of ηb(R, θ) are known, a cubic spline is fitted at all bulk values to get the intermediate values. The Crank Nicholson method is used to discretize the concentration and the population balance equation. The various operating parameters and relevant physiochemical data are given in Table 3 below. All the rate constants have been taken to be equal to or greater than 106 m3/kmol‚s, such that these values emulate the behavior of an instantaneous reaction, i.e., the computed outputs are insenitive to the chosen rate constant values. The initial


Figure 10. Evolution of bulk particle size distribution with batch time. The following data were used: lo ) 0.020, stirring speed ) 125 rpm, ShR ) 375. Other parameter values are from Table 3.

Figure 11. Evolution of bulk particle size distribution with batch time The following data were used: lo ) 0.020, stirring speed ) 150 rpm, ShR ) 450. Other parameter values are from Table 3.

distribution, which is the input to the proposed model, has been taken from experiments. Results and Discussion Penetration Element Profiles. The concentration profiles at the gas-liquid interface for all the four species are shown in Figure 3. The position of the reaction zone is guided by the value of q (q ) CsD/zC/A). A low q value suggests faster penetration of the gas, SO2, than the penetration of dissolved solid, i.e., OH-, in the reverse direction. Hence, the reaction front is far from the gas-liquid interface as shown in Figure 3a. The variations of mean particle size, Rmean, and holdup, l, from the gas-liquid interface, at t ) tc are shown in Figures 4 and 5, respectively. The particle size and holdup initially

decrease rapidly as one moves toward the gas-liquid interface and, then, acquire a flat profile indicating that all particles in this zone dissolve to the same extent. The variation of an instantaneous specific rate of gas absorption, RiA, with contact time is shown in Figure 6. Very fine particles dissolve instantaneously leaving behind large particles leading to a flat profile of RiA at higher times. The variation of average particle size at the gas-liquid interface, Rmean(0, t) (denoted by R/mean) is shown in Figure 7. The size decreases with increasing contact time. Bulk Liquid Profiles. The variation of the enhancement factor (defined as a dimensionless average specific rate of absorption, i.e., φA ) RA/kLC/A) with batch time is shown in Figure 8, and the variation of mean particle size and solid holdup with batch time is shown in Figure 9. The decreasing flat curve of

1912




Rbmean is due to similar and slow rates of dissolution of particles. The solid holdup decreases smoothly over the batch time. Particle Size Distributions (PSDs). Figures 10-13 show experimental as well as theoretical PSDs, at different holdups and stirring speeds. The input for the initial particle size distribution was taken from experiments. A least-squares regression was used to find the best value of the Sherwood number at which the proposed model best fits the experimental data for every run, by summing the error across all the batch times. An inset shows the initial PSD if the values are much greater than for the distributions at other times. The Sherwood number increases with increasing stirring speeds, due to faster dissolution of the reactant particles. The Sherwood number also decreases with increasing holdups, indicating that the interparticle distance decreases, which lowers the driving force for

Table 4. Fitted Values of Sherwood Number, ShR, at Different Operating Conditions stirring speed

lo ) 0.02

lo ) 0.05

125 (rpm) 150 (rpm)

375 450

120 250

dissolution in the liquid phase. Given the tremendous complexity of the experiments, the match between theory and experimental results looks very reasonable. Table 4 shows the “best” fit values of Sherwood number. These fitted Sherwood number values are perhaps too high to be realistic, because these imply unusually large slip velocities; therefore, these may be treated as “apparent” values, that possibly represent the enhancing effect of reaction on the dissolution rate, as described by Uchida et al.3 This effect has not been considered explicitly in the model proposed here.


Conclusions This study shows that sparingly soluble, fine reactant particles dissolve significantly and undergo a substantial change in size, near the gas-liquid interface, when used to absorb a reactive gas. A rigorous, population balance-based model, using the complex three-step reaction mechanism for absorption of sulfur dioxide in slurries of fine magnesium hydroxide particles, is developed which includes the effect of change in particle size. The model is validated using experimental PSD data, obtained at different magnesium hydroxide holdups and stirring speeds. The particle dissolution Sherwood number is used to “match” the experimental data with the model estimates. The results suggests that the Sherwood number increases with increasing stirring speeds and decreasing magnesium hydroxide holdups. Nomenclature

ShR ) Sherwood number for particle dissolution, t ) time, s tc ) contact time, s x ) distance from gas-liquid interface within penetration element, m Greek Letters η ) particle size distribution function, m-4 Fp ) density of solid reactant, kg/m3 θ ) batch time, s φA ) enhancement factor, λ ) position of reaction plane from the gas-liquid interface, m Subscripts b ) bulk in ) initial

English

Literature Cited

A ) gas being absorbed or the concentration of species A, SO2 B ) SO32C ) HSO-3 C/A ) soncentration of A at the gas-liquid interface, kmol/m3 CsD ) solubility of D in liquid phase, kmol/m3 Ci ) concentration of species i in the liquid phase, kmol/m3 D ) solid species or concentration of dissolved solid in liquid, OHDi ) diffusivity of species i in liquid phase, m2/s G ) growth rate for single particle, m/s K ) equilibrium constant, k1 ) second-order rate constant in liquid phase for reaction between A and D, m3/kmol‚s k2 ) second-order rate constant in liquid phase for reaction between A and B, m3/kmol‚s k3 ) second-order rate constant in liquid phase for reaction between C and D, m3/kmol‚s kL ) liquid side mass transfer coefficient for gas-liquid (slurry) contact, m/s ksl ) liquid side mass transfer coefficient for (single) particle dissolution, m/s l ) solid loading (volumetric), lo ) initial solid loading (volumetric), Mw ) molecular weight of solid reactant, kg/kmol N ) number concentration of solid reactant particle, m-3 No ) initial value of number concentration of solid reactant particle, m-3 R ) radius of the particle, m RA ) average specific rate of absorption, kmol/m3‚s RiA ) instantaneous specific rate of absorption, kmol/m3‚s Rmax ) maximum radius of the particle in distribution, m Rmean ) mean radius of the particle in distribution, m

(1) Mehra, A. Chem. Eng. Sci. 1996, 51, 461-477. (2) Ramchandran, P. A.; Sharma, M. M. Chem. Eng. Sci. 1969, 24, 1681-1686. (3) Uchida, S.; Koide, K.; Shindo, M. Chem. Eng. Sci. 1975, 30, 644646. (4) Sada, E.; Kumazawa, H.; Butt, M. A.; Sumi, T. Chem. Eng. Sci. 1977, 32, 972-974. (5) Sada, E.; Kumazawa, H.; Butt, M. A. Chem. Eng. Sci. 1979, 34, 715-718. (6) Sada, E.; Kumazawa, H.; Butt, M. A. Chem. Eng. Sci. 1980, 35, 771-777. (7) Sada, E.; Kumazawa, H.; Butt, M. A. Chem. Eng. Sci. 1977, 32, 1165-1170. (8) Uchida, S.; Moriguchi, H.; Maejima, H.; Koide, K.; Kageyama, S. Can. J. Chem. Eng. 1978, 56, 690-697. (9) Uchida, S.; Miyachi, M.; Ariga, O. Can. J. Chem. Eng. 1981, 59, 560-561. (10) Yagi, H.; Hikita, H. Chem. Eng. J. 1987, 36, 169-174. (11) Dagaonkar, M. V.; Beenackers, A. A. C. M.; Pangarkar, V. G. Chem. Eng. J. 2001, 81, 203-212. (12) Dagaonkar, M. V.; Beenackers, A. A. C. M.; Pangarkar, V. G. Chem. Eng. Sci. 2001, 56, 1095-1101. (13) Dagaonkar, M. V.; Beenackers, A. A. C. M.; Pangarkar, V. G. Catal. Today 2001, 66, 495-501. (14) Scala, F.; D’Ascenzo, M. AIChE J. 2002, 48, 1719-1726. (15) Scala, F. Ind. Eng. Chem. Res. 2002, 41, 5187-5195. (16) Akbar, M. K.; Yan, J.; Ghiaasiaan, S. M. Int. J. Heat Mass Trans. 2003, 46, 4561-4571. (17) Akbar, J.; Ghiaasiaan, S. M. Chem. Eng. Sci. 2004, 59, 967-976. (18) Mehra, A.; Rao, P. T.; Suresh, A. K. Chem. Eng. Sci. 1997, 52, 3311-3319. (19) Perry, H. P.; Chilton, C. H. Chemical Engineers’ Handbook; McGraw Hill: Tokyo, 1973.

ReceiVed for reView November 15, 2006 ReVised manuscript receiVed January 19, 2007 Accepted February 2, 2007 IE061461H

SO2âMg(OH) - American Chemical Society

Recommend Documents

SO2âMg(OH) - American Chemical Society