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Flue gas desulphurization by spray dry absorption
Chemical Engineering and Processing 39 (2000) 45 – 52 www.elsevier.com/locate/cep
Flue gas desulphurization by spray dry absorption F.F. Hill a,*, J. Zank b b
a BASF AG, Ludwigshafen, Germany Institut fu¨r Thermische Verfahrenstechnik, Uni6ersita¨t Karlsruhe (TH), 76128, Karlsruhe, Germany
Received 10 May 1999; accepted 10 May 1999
Abstract Absorption efficiency of sulphur dioxide in spray dry absorption depends on the superposition of the absorption process with the drying process. A model has been established considering heat and mass transfer processes for a single droplet and the two phase flow inside the spray dryer. Model predictions are compared with experimental data showing the influence of drying conditions and stoichiometric ratio on the absorption efficiency. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Sulphur dioxide; Spray dryer; Stoichiometric ratio
1. Introduction In spray dry absorption a fine spray of lime slurry is brought into contact with flue gas inside a spray dryer in order to remove sulphur dioxide by chemical absorption. Simultaneously the water evaporates from the droplets leaving a dry powder, consisting of unreacted calciumhydroxide and the reaction product of sulphur dioxide and calciumhydroxide as the final product. The powder is separated from the cleaned flue gas by a fabric filter or an electrostatic precipitator and is usually used for landfill. To obtain a high absorption efficiency an excess of calciumhydroxide is required. Consequently the conversion of calciumhydroxide in the process is incomplete. A first theoretical investigation on spray dry absorption was done by Getler et al. [3]. They concluded from the distribution of elements inside the particles, that absorption remains incomplete because of the formation of a product layer on an unreacted core. Kinzey [6] and Newton [8] derived a model for
spray dry absorption taking into account the gas and liquid phase mass transfer resistances. They considered sulphur dioxide removal only during the wet droplet stage. These models underestimate the absorption efficiency observed at a coal fired plant which Shih [13] interpreted as an additional reaction of sulphur dioxide with the final (dried) product. It is well known [12] that drying of aqueous solutions containing particles strongly depends on the solubility of these particles. In case the flue gas contains various acid components such as hydrogen chloride, the reaction products with calcium hydroxide can be highly soluble. Since the drying of droplets strongly influences the absorption efficiency, the experiments in this work are performed with an artificial flue gas which contains only sulphur dioxide as an acid component in order to determine the influence of operating parameters on absorption efficiency systematically. The experimental data are compared with the prediction of a mechanistically based model.
2. Model
Dedicated to Prof em. Dr.-Ing. E.-U. Schlu¨nder on the occasion of his 70th birthday. * Corresponding author. Tel.: + 49-621-6051729; fax: + 49-6216074795. E-mail address: [email protected] (F.F. Hill)
The model derived for spray dry absorption [5] is based on the combination of a model for the heat and mass transfer processes for a single droplet with a simple model for the two phase flow of gas and droplets inside the spray dryer.
0255-2701/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S 0 2 5 5 - 2 7 0 1 ( 9 9 ) 0 0 0 7 7 - X
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F.F. Hill, J. Zank / Chemical Engineering and Processing 39 (2000) 45–52
2.1. Processes inside a single droplet As shown by Reinhart [10] and Constan and Calvert [2] no internal circulation occurs in free falling water droplets with diameters smaller than 1 mm. Since the viscosity of lime suspension is higher and the typical droplet diameter is significantly smaller than 1 mm, droplets in spray dry absorption can be treated as rigid spheres. The reaction of sulphur dioxide with calciumhydroxide in an aqueous phase provides predominantly calciumsulphite–hemihydrate corresponding to the overall mass transfer and reaction equation: SO2 (g) + Ca(OH)2 CaSO*3 1/2 H2O + 1/2 H2O (1) Since the reaction of the dissolved reactants is instantaneous a spherical surface exists where the reaction takes place and where the calciumsulphite – hemihydrate precipitates due to its low solubility. With regard to the large particle concentration inside a droplet and assuming an infinite dissolution rate of calciumhydroxide particles the spherical reaction front recedes into the droplet as calciumhydroxide is converted. As a result the droplet consists of an outer shell of reaction product and a core of calciumhydroxide. The resulting distribution of components inside a droplet is depicted in Fig. 1. Simultaneous with absorption, diffusion and reaction the evaporation of water takes place and the droplet shrinks, which in the model is assumed to happen homogeneously. When a critical moisture content is reached, the aqueous phase recedes into the solid agglomerate and the falling rate period begins.
Fig. 2. Mass transfer and reaction model for simultaneous absorption, reaction and evaporation.
2.1.1. Mass transfer and reaction The mass transfer and reaction model for a single droplet is depicted in Fig. 2. For the absorption process, the gas phase and the liquid phase mass transfer are considered, for the drying process only the gas phase mass transfer must be taken into account. The overall mass transfer and reaction equation Eq. (1) for sulphur dioxide absorption can be subdivided into the following steps: (a) Gas phase mass transfer of sulphur dioxide: N: SO2,dr/g = r˜ g kg,SO2 Adr (y˜SO2,g − y˜SO2,I) ,
(2)
where the overall mass transfer coefficient is:
!
kg,SO2 = (bSO2) − 1 +
"
dSO2/air Sd I,dag m Aag
−1
−1
.
(3)
The second term in brackets is headed only for the falling rate period to take into account the additional mass transfer resistance of the dry porous outer shell. The gas phase mass transfer coefficient bSO2is calculated according to the correlation of Ranz and Marshall [11]. It can be shown [15], that the simultaneous diffusion of sulphur dioxide and water has no significant influence to the mole fluxes of the single species. (b) Absorption of sulphur dioxide at the interface of gas phase and aqueous phase: SO2(g)l SO2(aq)
(4)
and formation of sulphurous acid: SO2(aq)+ H2O H2SO3.
(5)
Rabe and Harris [9] related the total amount of undissociated sulphur dioxide to the partial pressure of sulphur dioxide in the gas phase. (c) Dissociation of sulphurous acid: H2SO3 + H2O Fig. 1. Distribution of components inside a spray droplet.
H3O+ + HSO− 3 ,
HSO-3 + H2O H3O+ + SO23 − .
(6) (7)
F.F. Hill, J. Zank / Chemical Engineering and Processing 39 (2000) 45–52
The dissociation constants K1,.dis, K2,dis were determined by Hikita et. al [4] and Tartar and Garretson [14], respectively. (d) Mass transfer of sulphur species inside the droplet:
N: SO2,dr/g = dH2SO3 + dHSO− 3
K1,dis
c˜H2SO3,I
× Sdrf,dIc˜H2SO3,I.
N: H2O,dr/g = r˜ g kg,H2O Aag ln
47
1− y˜H2O,g . 1− y˜*H2O,I
(14)
With regard to the low solubility of the dissolved components the interfacial mole fraction of water is calculated from the vapour pressure of pure water. The mass transfer coefficient is: kg,H2O =
!
(bH2O) − 1 +
(8)
"
dH2O/air SdI,dag m Aag
−1
−1
. (15)
The diffusion flux of the sulphur species consists of the fluxes of undissociated sulphurous acid and hydrogen sulphite. Since the second dissociation constant is small the flux of sulphuric acid is negligible. (e) Dissolution of calciumhydroxide at the outer shell of the unreacted core:
Again, the second term in brackets accounts for the additional mass transfer resistance of the dry porous outer shell.
Ca(OH)2 (s) Ca2 + + 2 OH−
Q: = a KA Adr (Tg − Tdr) .
(9)
and diffusion outward to the reaction front: N: Ca(OH)2 = dCa(OH)2 Sdc,drf c˜*Ca(OH)2 .
(10)
H2SO3 + 2 OH− SO23 − + 2 H2O,
(11)
HSO− + OH− SO23 − + H2O, 3
(12)
and reaction to calciumsulphite – hemihydrate: (13)
Since the solubility of calciumsulphite – hemihydrate is extremely low, the reaction product can be assumed to precipitate at the reaction front. In general, ionic reactions are instantaneous in aqueous phase, but extremely slow in the absence of water. Therefore and with regard to own experimental results the reaction of sulphur dioxide with the dried product is not taken into account. (g) Drying Since the solubility of calciumhydroxide and calciumsulphite–hemihydrate is low, drying of droplets in spray dry absorption is similar to the drying of aqueous droplets with suspended inert particles. As shown by Schlu¨nder [12], the drying behavior of aqueous suspension droplets can be described as the drying of water droplets. The drying begins with the constant rate period during which the drying rate is controlled by gas phase resistance for heat and mass transfer only. While water evaporates homogenous shrinking of droplets is assumed until the solid particles touch. Afterwards the water recedes into the porous matrix of solid calciumsulphite–hemihydrate and the falling rate period starts. In this period an additional resistance to the diffusion of vapour in the porous particle from the wet core to the surface of the agglomerate lowers the drying rate. Neglecting the counter diffusion of sulphur dioxide, the evaporation rate of a single droplet is calculated by:
(16)
Gas phase heat transfer coefficient a is calculated according to Ranz and Marshall [11]: Nu = 2 + 0.6 Re0.5 Pr1/3.
(f) Neutralisation at the reaction front:
2Ca2 + +2SO23 − + H2O 2CaSO3 1/2H2O.
2.1.2. Heat transfer Heat transfer to a single droplet is calculated by:
(17)
The Ackermann-factor [1] is calculated according to Marshall [7]: N: dr/g c˜p , (18) 4p l 1 1 − Rdr Rbl where the diameter of the gas phase boundary layer is:
KA =
Rbl =
u , eu − 1
u =
Nu R . Nu− 2 dr
(19)
As can be shown by the Biot-number for the droplet, temperature gradients inside a single droplet of a diameter smaller than 100 mm can be neglected.
2.2. Two phase flow The two-phase flow of gas and droplet phase is described with a simple one-dimensional model, which only accounts for changes in axial direction. Therefore the gas phase flow is set as being a plug flow or backmixed. The balance equations for mass and energy are solved separately for each phase. The momentum balance is solved only for the droplet phase. While the continuous gas phase is described with the Eularian approach the Lagrangian approach is used for the dispersed phase. Concerning a multidisperse spray, different droplet sizes are balanced separately. Interaction between the droplets like coalescence or collision is not considered. Interaction between the phases consist of momentum (aerodynamic drag), mass transfer (absorption, evaporation) and convective heat transfer. Coupling for heat and mass transfer is bidirectional while momentum transfer only accounts for the effects of the
F.F. Hill, J. Zank / Chemical Engineering and Processing 39 (2000) 45–52
48
gas phase on the droplets. Therefore, the gas phase velocity is calculated from mass balance. For a detailed description of the two-phase flow modeling consult [5].
The exponent n for the ratio of diffusion coefficients is derived from the Ranz–Marshall correlation: Sh= C RemScn
2.3. Absorption efficiency at high stoichiometric ratio A simple equation for the absorption efficiency can be derived for a high stoichiometric ratio assuming a vanishing absorption rate during the falling rate period. At high stoichiometric ratio, the conversion of calciumhydroxide is extremely low. Therefore the reaction front remains at the droplet surface and liquid phase mass transfer resistance for sulphur dioxide is neglectable. Since absorption and reaction of sulphur dioxide only occurs in the presence of water the absorption efficiency only depends on the initial water concentration inside the droplet and the ratio v of absorption to evaporation rate: v
N: H2O,dr/g . N: SO2,dr/g
(20)
The rate ratio v can be calculated from Eq. (15) and Eq. (2): v=
dH2O,g dSO2,g
= const
1−n
1 1 −y˜H2O,g ln y˜SO2,g −y˜SO2,I 1 −y˜*H2O,I –( Tdr –)
(22)
and characterises the two phase flow pattern: no relative motion, n= 0; turbulence: n=0.4. Mole fluxes of water and sulphur dioxide are transferred over the same interfacial area. Consequently the rate ratio v is independent of the interfacial area and therefore of the droplet diameter. Assuming constant droplet temperature, X, and back mixed gas phase, the rate ratio v is constant and can be expressed by the mole fluxes of water and sulphur dioxide at the inlet and outlet of the spray dryer: v=
N: H2O,sus N: H2O,sus = . N: SO2,a − N: SO2,v N: SO2,a − N: gY0 SO2,g,v
(23)
The sulphur dioxide absorption efficiency for a backmixed gas phase: hSO2,backmixed
N: SO2,a − N: SO2,v N: SO2,a
(24)
is calculated using Eq. (21) and Eq. (23): (21)
Since the reaction front remains at the droplet surface, the interfacial sulphur dioxide mole fraction y˜SO2,I equals zero.
hSO2,backmixed
1
= 1+
1−y˜H2O,g,a dH2O,g y˜H2O,g,v − y˜H2O,g,a dSO2,g
1−n
ln
1− y˜H2O,g,v 1− y˜*H2O,I
.
(25)
Fig. 3. Set-up: 1, orifice flow meter; 2, condensate trap; 3, electrical heater; 4, static mixer; 5, tube pump; 6, storage tank; 7, gas distributor; 8, two fluid nozzle; 9, spray dryer; 10, cyclone; 11, fan.
F.F. Hill, J. Zank / Chemical Engineering and Processing 39 (2000) 45–52
49
3. Experimental set-up The experimental set-up is shown in Fig. 3. The spray dry absorption experiments are performed with a laboratory scale spray dryer with an inner diameter of 0.16 m and variable length. Most of the experiments are conducted with a spray dryer length of 1.5 m. In order to examine the influence of the residence time on the absorption efficiency some experiments are performed with lengths of 0.75 and 1 m. An artificial flue gas is generated by mixing steam and sulphur dioxide into a flow of heated ambient air. The concentration of sulphur dioxide and water is varied between 100 and 900 ppm and 10 and 20 vol%, respectively. An even distribution of the gas flow held constant at 16 m3/h is ensured by a perforated plate at the inlet of the spray dryer. The slurry used contained 2.5 – 10 wt% lime with 5 wt% lime in the standard run. For atomization, a two-fluid nozzle producing a spray with 25 mm mean diameter is used. At the outlet of the spray dryer the reaction product is separated from the gas stream by a cyclone. The sulphur dioxide and water concentrations are determined at the inlet of the spray dryer and after the cyclone with a heated infrared photometer (MCS100 HW, Perkin Elmer).
4. Results and discussion Experiments were performed to demonstrate the influences of calciumhydroxide excess, gas temperature, residence time, initial droplet size and particle size of lime. The experimental results are discussed in terms of stoichiometric ratio and absorption efficiency. The stoichiometric ratio is defined as the ratio of calciumhydroxide mole flux to sulphur dioxide mole flux at the inlet of the spray dryer: l
N: Ca(OH)2,a . N: SO2,a
(26)
Fig. 4. Influence of stoichiometric ratio on absorption efficiency, calc. calculated curves T calc. g,a =110°C and T g,a =131°C.
The stoichiometric ratio is set by the gas phase sulphur dioxide concentration. Therefore, the amount of evaporated water and consequently the drying conditions are constant for a run. The influence of the stoichiometric ratio on the absorption efficiency for various gas phase temperatures is illustrated in Fig. 4. The symbols indicate experimental data, the lines are model predictions. Considering heat losses, the gas inlet temperature for calculation is slightly lower than the experimental inlet temperature, so that calculated gas outlet temperature equals measured gas outlet temperature. In principle, all measured and calculated curves show a similar tendency. At high stoichiometric ratio the absorption rate reaches its maximum value, since internal mass transfer resistances for sulphur dioxide are neglectable. With decreasing stoichiometric ratio the absorption efficiency is decreasing. That is because calciumhydroxide conversion (Fig. 5) increases and therefore additional liquid phase mass transfer resistances for sulphur dioxide lower the absorption rate. Verifying the assumption of a neglectable reaction rate in the dry stage Fig. 6 shows the influence of the
The absorption efficiency is defined as the ratio of sulphur dioxide mole flux absorbed inside the spray dryer to the sulphur dioxide mole flux at the inlet of the spray dryer: h
N: SO2,a −N: SO2,v . N: SO2,a
(27)
The conversion efficiency of calciumhydroxide is defined as the ratio of converted calciumhydroxide mole flux to calciumhydroxide mole flux at the inlet of the spray dryer and is related to the stoichiometric ratio and absorption efficiency as follows: UCa(OH)2
N: Ca(OH)2,a −N: Ca(OH)2,v h = . N: Ca(OH)2,a l
(28)
Fig. 5. Influence of stoichiometric ratio on calciumhydroxid convercalc. sion, calculated curves T calc. g,a =110°C and T g,a =131°C.
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F.F. Hill, J. Zank / Chemical Engineering and Processing 39 (2000) 45–52
Fig. 6. Influence of mean residence time on absorption efficiency for two gas inlet temperatures.
mean residence time on the absorption efficiency. The residence time of the droplets is varied between 2.5 and 5 s when the length is 0.75 and 1.5 m. No significant influence on the absorption efficiency is observed indicating a very low reaction rate in the dry stage. The influence of the gas phase temperature for three different stoichiometric ratios is illustrated in Fig. 7. An increase in the gas phase temperature causes a decrease in absorption efficiency because the drying rate is increased with gas phase temperature and therefore the time period for absorption is decreased. Absorption efficiencies calculated from Eq. (25) agree well with the experimental data at high stoichiometric ratio. Calculation assuming a turbulent flow pattern provide slightly higher absorption efficiencies than those assuming no relative motion between droplets and gas phase. That is because of the decreasing influence of the diffusion coefficients. Again, the experimental results show a decrease in absorption efficiency with decreasing stoichiometric ratio due to additional liquid phase mass transfer resistances. As shown in Fig. 8, maximum absorption
Fig. 7. Influence of gas inlet temperature on absorption efficiency for various stoichiometric ratios.
Fig. 8. Comparison of analytically (Eq. (25)) and experimentally determined absorption efficiency at high stoichiometric ratio (l =3) assuming turbulent two phase flow.
efficiency is determined by the ratio of absorption rate to evaporation rate which can be calculated according to Eq. (25). Several experiments were performed to determine the influence of initial droplet size on absorption efficiency (Fig. 9). Initial droplet size distribution is determined by nozzle gas and was measured separately with a light scattering instrument (Malvern 2600). Assuming the influence of the nozzle gas on the flow pattern inside the spray dryer can by neglected, there is no influence of initial droplet size on absorption efficiency. For high stoichiometric ratios, this is also indicated by Eq. (25). Considering moderate stoichiometric ratios, model predictions also indicate that there is only a small influence of droplet diameter on absorption efficiency. The influence of calciumhydroxide particle size on absorption efficiency is illustrated in Fig. 10. As expected, there is no influence of particle size distribution at high stoichiometric ratios, since gas phase resistance controls absorption rate. Whereas at moderate stoichiometric ratios, smaller calciumhydroxide particles yield higher absorption rates. This may be caused by higher mass transfer coefficients and the higher specific surface of smaller particles.
Fig. 9. Influence of initial mean droplet size on absorption efficiency.
F.F. Hill, J. Zank / Chemical Engineering and Processing 39 (2000) 45–52
Y y a r b d l h m v
temperature difference between gas temperature and adiabatic saturation temperature loading fraction heat transfer coefficient density mass transfer coefficient diffusion coefficient stoichiometric ratio absorption efficiency tortuosity factor rate ratio
Subscripts ag bl dis dr d g I rf sus a v
agglomerate boundary layer dissociation droplet diameter gas phase interface reaction front suspension inlet outlet
Superscripts *
equilibrium molar
T DTas
Fig. 10. Influence of lime particle size on absorption efficiency.
5. Conclusions At high excess of calciumhydroxide the absorption efficiency of sulphur dioxide is limited by the drying conditions. Since significant absorption and reaction occurs only in the presence of water, the absorption efficiency strongly depends on the ratio of the evaporation rate to the absorption rate. At moderate excess of calciumhydroxide, the absorption efficiency is lowered by additional liquid phase mass transfer resistances for sulphur dioxide. The model proposed shows good agreement with experimental results. Model predictions and experimental results also indicate, that the influence of the initial droplet diameter on the absorption efficiency is negligible. At moderate stoichiometric ratios the absorption efficiency can be increased using a lime suspension with smaller calciumhydroxide particles.
Acknowledgements The authors gratefully acknowledge the financial support of the DFG (Deutsche Forschungsgemeinschaft).
Appendix A. Nomenclature surface area concentration constant Ackermann-factor first dissociation constant second dissociation constant gas phase overall mass transfer coefficient mole flux exponent Sc-number heat flux
A c C KA K1,diss K2,diss kg N: n Q: Sd1,d2 =
2p 1 1 geometry − d1 d2 factor
51
References [1] G. Ackermann, Wa¨rmeu¨bertragung und molekulare Stoffu¨ber tragung im gleichen Feld bei großen Temperatur- und Partial druckdifferenzen, VDI-Forschungsheft 382 (1937) S.1/6. [2] G.L. Constan, S. Calvert, Mass transfer in drops under condi tions that promote internal circulation, AIChE J. 6 (1) (1960) 9 – 22. [3] J.L. Getler, H.L. Shelton, D.A. Furlong, Modeling the spray absorption process for SO2 removal, APCA J. 29 (1979) 1270– 1274. [4] H. Hikita, S. Asai, H. Nose, Absorption of sulfurdioxide into water, AIChE J. 24 (1) (1978) 147 – 149. [5] F.F. Hill, Schwefeldioxidabscheidung aus Rauchgasen mit der Spru¨habsorptions-trocknung, Fortschritt-Berichte VDI, VDIVerlag Du¨sseldorf, Dissertation Universita¨t Karlsruhe (TH), 1998. [6] J.R. Kinzey, M.K. Kinzey, Modeling the Gas and Liquid-Phase Resistances in the Dry Scrubbing Process for Sulfur-Dioxide Removal, Dissertation, Cornell University Pittsburgh, PA, 1988. [7] W.R. Marshall, Heat and mass transfer in spray drying, Trans. ASME 77 (1966) 1377 – 1385. [8] G.H. Newton, J. Kramlich, R. Payne, Modeling the SO2-slurry droplet reaction, AIChE J. 36 (12) (1990) 1865 – 1872. [9] A.E. Rabe, J.F. Harris, Vapor liquid equilibrium data for the binary system, sulfur dioxide and water, J. Chem. Eng. Data 8 (3) (1963) 333 – 336. [10] A. Reinhart, Das Verhalten fallender Tropfen, Chem. Ing. Tech. 36 (7) (1964) 740 – 746.
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[11] W.E. Ranz, W.R. Marshall, Evaporation from drops, Part I, II, Chem. Eng. Prog. 48 (91952) 141–146; 173–180. [12] E.-U. Schlu¨nder, U8 ber die Trocknung ruhender Einzeltropfen und fallender Spru¨hnebel, Dissertation Technische Hochschule Darmstadt, 1962. [13] H.-S. Shih, Simulation of Sulfur-Dioxide Removal via Hy drated Lime Slurries in a Spray Dryer Absorber Flue Gas Desulfurization System, Theses, University of Alabama,
.
Tuscaloosa, 1989. [14] H.V. Tartar, H.H. Garretson, The thermodynamic ionization constants of sulfuric acid at 25°C, J. Am. Chem. Soc. 63 (1941) 808 – 816. [15] J. Zank, Theoretische und experimentelle Untersuchungen zur Schwefeldioxid-abscheidung bei der Spru¨habsorptionstrock nung, Diplomarbeit Universita¨t Karlsruhe (TH), 1996.
Flue gas desulphurization by spray dry absorption F.F. Hill a,*, J. Zank b b
a BASF AG, Ludwigshafen, Germany Institut fu¨r Thermische Verfahrenstechnik, Uni6ersita¨t Karlsruhe (TH), 76128, Karlsruhe, Germany
Received 10 May 1999; accepted 10 May 1999
Abstract Absorption efficiency of sulphur dioxide in spray dry absorption depends on the superposition of the absorption process with the drying process. A model has been established considering heat and mass transfer processes for a single droplet and the two phase flow inside the spray dryer. Model predictions are compared with experimental data showing the influence of drying conditions and stoichiometric ratio on the absorption efficiency. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Sulphur dioxide; Spray dryer; Stoichiometric ratio
1. Introduction In spray dry absorption a fine spray of lime slurry is brought into contact with flue gas inside a spray dryer in order to remove sulphur dioxide by chemical absorption. Simultaneously the water evaporates from the droplets leaving a dry powder, consisting of unreacted calciumhydroxide and the reaction product of sulphur dioxide and calciumhydroxide as the final product. The powder is separated from the cleaned flue gas by a fabric filter or an electrostatic precipitator and is usually used for landfill. To obtain a high absorption efficiency an excess of calciumhydroxide is required. Consequently the conversion of calciumhydroxide in the process is incomplete. A first theoretical investigation on spray dry absorption was done by Getler et al. [3]. They concluded from the distribution of elements inside the particles, that absorption remains incomplete because of the formation of a product layer on an unreacted core. Kinzey [6] and Newton [8] derived a model for
spray dry absorption taking into account the gas and liquid phase mass transfer resistances. They considered sulphur dioxide removal only during the wet droplet stage. These models underestimate the absorption efficiency observed at a coal fired plant which Shih [13] interpreted as an additional reaction of sulphur dioxide with the final (dried) product. It is well known [12] that drying of aqueous solutions containing particles strongly depends on the solubility of these particles. In case the flue gas contains various acid components such as hydrogen chloride, the reaction products with calcium hydroxide can be highly soluble. Since the drying of droplets strongly influences the absorption efficiency, the experiments in this work are performed with an artificial flue gas which contains only sulphur dioxide as an acid component in order to determine the influence of operating parameters on absorption efficiency systematically. The experimental data are compared with the prediction of a mechanistically based model.
2. Model
Dedicated to Prof em. Dr.-Ing. E.-U. Schlu¨nder on the occasion of his 70th birthday. * Corresponding author. Tel.: + 49-621-6051729; fax: + 49-6216074795. E-mail address: [email protected] (F.F. Hill)
The model derived for spray dry absorption [5] is based on the combination of a model for the heat and mass transfer processes for a single droplet with a simple model for the two phase flow of gas and droplets inside the spray dryer.
0255-2701/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S 0 2 5 5 - 2 7 0 1 ( 9 9 ) 0 0 0 7 7 - X
46
F.F. Hill, J. Zank / Chemical Engineering and Processing 39 (2000) 45–52
2.1. Processes inside a single droplet As shown by Reinhart [10] and Constan and Calvert [2] no internal circulation occurs in free falling water droplets with diameters smaller than 1 mm. Since the viscosity of lime suspension is higher and the typical droplet diameter is significantly smaller than 1 mm, droplets in spray dry absorption can be treated as rigid spheres. The reaction of sulphur dioxide with calciumhydroxide in an aqueous phase provides predominantly calciumsulphite–hemihydrate corresponding to the overall mass transfer and reaction equation: SO2 (g) + Ca(OH)2 CaSO*3 1/2 H2O + 1/2 H2O (1) Since the reaction of the dissolved reactants is instantaneous a spherical surface exists where the reaction takes place and where the calciumsulphite – hemihydrate precipitates due to its low solubility. With regard to the large particle concentration inside a droplet and assuming an infinite dissolution rate of calciumhydroxide particles the spherical reaction front recedes into the droplet as calciumhydroxide is converted. As a result the droplet consists of an outer shell of reaction product and a core of calciumhydroxide. The resulting distribution of components inside a droplet is depicted in Fig. 1. Simultaneous with absorption, diffusion and reaction the evaporation of water takes place and the droplet shrinks, which in the model is assumed to happen homogeneously. When a critical moisture content is reached, the aqueous phase recedes into the solid agglomerate and the falling rate period begins.
Fig. 2. Mass transfer and reaction model for simultaneous absorption, reaction and evaporation.
2.1.1. Mass transfer and reaction The mass transfer and reaction model for a single droplet is depicted in Fig. 2. For the absorption process, the gas phase and the liquid phase mass transfer are considered, for the drying process only the gas phase mass transfer must be taken into account. The overall mass transfer and reaction equation Eq. (1) for sulphur dioxide absorption can be subdivided into the following steps: (a) Gas phase mass transfer of sulphur dioxide: N: SO2,dr/g = r˜ g kg,SO2 Adr (y˜SO2,g − y˜SO2,I) ,
(2)
where the overall mass transfer coefficient is:
!
kg,SO2 = (bSO2) − 1 +
"
dSO2/air Sd I,dag m Aag
−1
−1
.
(3)
The second term in brackets is headed only for the falling rate period to take into account the additional mass transfer resistance of the dry porous outer shell. The gas phase mass transfer coefficient bSO2is calculated according to the correlation of Ranz and Marshall [11]. It can be shown [15], that the simultaneous diffusion of sulphur dioxide and water has no significant influence to the mole fluxes of the single species. (b) Absorption of sulphur dioxide at the interface of gas phase and aqueous phase: SO2(g)l SO2(aq)
(4)
and formation of sulphurous acid: SO2(aq)+ H2O H2SO3.
(5)
Rabe and Harris [9] related the total amount of undissociated sulphur dioxide to the partial pressure of sulphur dioxide in the gas phase. (c) Dissociation of sulphurous acid: H2SO3 + H2O Fig. 1. Distribution of components inside a spray droplet.
H3O+ + HSO− 3 ,
HSO-3 + H2O H3O+ + SO23 − .
(6) (7)
F.F. Hill, J. Zank / Chemical Engineering and Processing 39 (2000) 45–52
The dissociation constants K1,.dis, K2,dis were determined by Hikita et. al [4] and Tartar and Garretson [14], respectively. (d) Mass transfer of sulphur species inside the droplet:
N: SO2,dr/g = dH2SO3 + dHSO− 3
K1,dis
c˜H2SO3,I
× Sdrf,dIc˜H2SO3,I.
N: H2O,dr/g = r˜ g kg,H2O Aag ln
47
1− y˜H2O,g . 1− y˜*H2O,I
(14)
With regard to the low solubility of the dissolved components the interfacial mole fraction of water is calculated from the vapour pressure of pure water. The mass transfer coefficient is: kg,H2O =
!
(bH2O) − 1 +
(8)
"
dH2O/air SdI,dag m Aag
−1
−1
. (15)
The diffusion flux of the sulphur species consists of the fluxes of undissociated sulphurous acid and hydrogen sulphite. Since the second dissociation constant is small the flux of sulphuric acid is negligible. (e) Dissolution of calciumhydroxide at the outer shell of the unreacted core:
Again, the second term in brackets accounts for the additional mass transfer resistance of the dry porous outer shell.
Ca(OH)2 (s) Ca2 + + 2 OH−
Q: = a KA Adr (Tg − Tdr) .
(9)
and diffusion outward to the reaction front: N: Ca(OH)2 = dCa(OH)2 Sdc,drf c˜*Ca(OH)2 .
(10)
H2SO3 + 2 OH− SO23 − + 2 H2O,
(11)
HSO− + OH− SO23 − + H2O, 3
(12)
and reaction to calciumsulphite – hemihydrate: (13)
Since the solubility of calciumsulphite – hemihydrate is extremely low, the reaction product can be assumed to precipitate at the reaction front. In general, ionic reactions are instantaneous in aqueous phase, but extremely slow in the absence of water. Therefore and with regard to own experimental results the reaction of sulphur dioxide with the dried product is not taken into account. (g) Drying Since the solubility of calciumhydroxide and calciumsulphite–hemihydrate is low, drying of droplets in spray dry absorption is similar to the drying of aqueous droplets with suspended inert particles. As shown by Schlu¨nder [12], the drying behavior of aqueous suspension droplets can be described as the drying of water droplets. The drying begins with the constant rate period during which the drying rate is controlled by gas phase resistance for heat and mass transfer only. While water evaporates homogenous shrinking of droplets is assumed until the solid particles touch. Afterwards the water recedes into the porous matrix of solid calciumsulphite–hemihydrate and the falling rate period starts. In this period an additional resistance to the diffusion of vapour in the porous particle from the wet core to the surface of the agglomerate lowers the drying rate. Neglecting the counter diffusion of sulphur dioxide, the evaporation rate of a single droplet is calculated by:
(16)
Gas phase heat transfer coefficient a is calculated according to Ranz and Marshall [11]: Nu = 2 + 0.6 Re0.5 Pr1/3.
(f) Neutralisation at the reaction front:
2Ca2 + +2SO23 − + H2O 2CaSO3 1/2H2O.
2.1.2. Heat transfer Heat transfer to a single droplet is calculated by:
(17)
The Ackermann-factor [1] is calculated according to Marshall [7]: N: dr/g c˜p , (18) 4p l 1 1 − Rdr Rbl where the diameter of the gas phase boundary layer is:
KA =
Rbl =
u , eu − 1
u =
Nu R . Nu− 2 dr
(19)
As can be shown by the Biot-number for the droplet, temperature gradients inside a single droplet of a diameter smaller than 100 mm can be neglected.
2.2. Two phase flow The two-phase flow of gas and droplet phase is described with a simple one-dimensional model, which only accounts for changes in axial direction. Therefore the gas phase flow is set as being a plug flow or backmixed. The balance equations for mass and energy are solved separately for each phase. The momentum balance is solved only for the droplet phase. While the continuous gas phase is described with the Eularian approach the Lagrangian approach is used for the dispersed phase. Concerning a multidisperse spray, different droplet sizes are balanced separately. Interaction between the droplets like coalescence or collision is not considered. Interaction between the phases consist of momentum (aerodynamic drag), mass transfer (absorption, evaporation) and convective heat transfer. Coupling for heat and mass transfer is bidirectional while momentum transfer only accounts for the effects of the
F.F. Hill, J. Zank / Chemical Engineering and Processing 39 (2000) 45–52
48
gas phase on the droplets. Therefore, the gas phase velocity is calculated from mass balance. For a detailed description of the two-phase flow modeling consult [5].
The exponent n for the ratio of diffusion coefficients is derived from the Ranz–Marshall correlation: Sh= C RemScn
2.3. Absorption efficiency at high stoichiometric ratio A simple equation for the absorption efficiency can be derived for a high stoichiometric ratio assuming a vanishing absorption rate during the falling rate period. At high stoichiometric ratio, the conversion of calciumhydroxide is extremely low. Therefore the reaction front remains at the droplet surface and liquid phase mass transfer resistance for sulphur dioxide is neglectable. Since absorption and reaction of sulphur dioxide only occurs in the presence of water the absorption efficiency only depends on the initial water concentration inside the droplet and the ratio v of absorption to evaporation rate: v
N: H2O,dr/g . N: SO2,dr/g
(20)
The rate ratio v can be calculated from Eq. (15) and Eq. (2): v=
dH2O,g dSO2,g
= const
1−n
1 1 −y˜H2O,g ln y˜SO2,g −y˜SO2,I 1 −y˜*H2O,I –( Tdr –)
(22)
and characterises the two phase flow pattern: no relative motion, n= 0; turbulence: n=0.4. Mole fluxes of water and sulphur dioxide are transferred over the same interfacial area. Consequently the rate ratio v is independent of the interfacial area and therefore of the droplet diameter. Assuming constant droplet temperature, X, and back mixed gas phase, the rate ratio v is constant and can be expressed by the mole fluxes of water and sulphur dioxide at the inlet and outlet of the spray dryer: v=
N: H2O,sus N: H2O,sus = . N: SO2,a − N: SO2,v N: SO2,a − N: gY0 SO2,g,v
(23)
The sulphur dioxide absorption efficiency for a backmixed gas phase: hSO2,backmixed
N: SO2,a − N: SO2,v N: SO2,a
(24)
is calculated using Eq. (21) and Eq. (23): (21)
Since the reaction front remains at the droplet surface, the interfacial sulphur dioxide mole fraction y˜SO2,I equals zero.
hSO2,backmixed
1
= 1+
1−y˜H2O,g,a dH2O,g y˜H2O,g,v − y˜H2O,g,a dSO2,g
1−n
ln
1− y˜H2O,g,v 1− y˜*H2O,I
.
(25)
Fig. 3. Set-up: 1, orifice flow meter; 2, condensate trap; 3, electrical heater; 4, static mixer; 5, tube pump; 6, storage tank; 7, gas distributor; 8, two fluid nozzle; 9, spray dryer; 10, cyclone; 11, fan.
F.F. Hill, J. Zank / Chemical Engineering and Processing 39 (2000) 45–52
49
3. Experimental set-up The experimental set-up is shown in Fig. 3. The spray dry absorption experiments are performed with a laboratory scale spray dryer with an inner diameter of 0.16 m and variable length. Most of the experiments are conducted with a spray dryer length of 1.5 m. In order to examine the influence of the residence time on the absorption efficiency some experiments are performed with lengths of 0.75 and 1 m. An artificial flue gas is generated by mixing steam and sulphur dioxide into a flow of heated ambient air. The concentration of sulphur dioxide and water is varied between 100 and 900 ppm and 10 and 20 vol%, respectively. An even distribution of the gas flow held constant at 16 m3/h is ensured by a perforated plate at the inlet of the spray dryer. The slurry used contained 2.5 – 10 wt% lime with 5 wt% lime in the standard run. For atomization, a two-fluid nozzle producing a spray with 25 mm mean diameter is used. At the outlet of the spray dryer the reaction product is separated from the gas stream by a cyclone. The sulphur dioxide and water concentrations are determined at the inlet of the spray dryer and after the cyclone with a heated infrared photometer (MCS100 HW, Perkin Elmer).
4. Results and discussion Experiments were performed to demonstrate the influences of calciumhydroxide excess, gas temperature, residence time, initial droplet size and particle size of lime. The experimental results are discussed in terms of stoichiometric ratio and absorption efficiency. The stoichiometric ratio is defined as the ratio of calciumhydroxide mole flux to sulphur dioxide mole flux at the inlet of the spray dryer: l
N: Ca(OH)2,a . N: SO2,a
(26)
Fig. 4. Influence of stoichiometric ratio on absorption efficiency, calc. calculated curves T calc. g,a =110°C and T g,a =131°C.
The stoichiometric ratio is set by the gas phase sulphur dioxide concentration. Therefore, the amount of evaporated water and consequently the drying conditions are constant for a run. The influence of the stoichiometric ratio on the absorption efficiency for various gas phase temperatures is illustrated in Fig. 4. The symbols indicate experimental data, the lines are model predictions. Considering heat losses, the gas inlet temperature for calculation is slightly lower than the experimental inlet temperature, so that calculated gas outlet temperature equals measured gas outlet temperature. In principle, all measured and calculated curves show a similar tendency. At high stoichiometric ratio the absorption rate reaches its maximum value, since internal mass transfer resistances for sulphur dioxide are neglectable. With decreasing stoichiometric ratio the absorption efficiency is decreasing. That is because calciumhydroxide conversion (Fig. 5) increases and therefore additional liquid phase mass transfer resistances for sulphur dioxide lower the absorption rate. Verifying the assumption of a neglectable reaction rate in the dry stage Fig. 6 shows the influence of the
The absorption efficiency is defined as the ratio of sulphur dioxide mole flux absorbed inside the spray dryer to the sulphur dioxide mole flux at the inlet of the spray dryer: h
N: SO2,a −N: SO2,v . N: SO2,a
(27)
The conversion efficiency of calciumhydroxide is defined as the ratio of converted calciumhydroxide mole flux to calciumhydroxide mole flux at the inlet of the spray dryer and is related to the stoichiometric ratio and absorption efficiency as follows: UCa(OH)2
N: Ca(OH)2,a −N: Ca(OH)2,v h = . N: Ca(OH)2,a l
(28)
Fig. 5. Influence of stoichiometric ratio on calciumhydroxid convercalc. sion, calculated curves T calc. g,a =110°C and T g,a =131°C.
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Fig. 6. Influence of mean residence time on absorption efficiency for two gas inlet temperatures.
mean residence time on the absorption efficiency. The residence time of the droplets is varied between 2.5 and 5 s when the length is 0.75 and 1.5 m. No significant influence on the absorption efficiency is observed indicating a very low reaction rate in the dry stage. The influence of the gas phase temperature for three different stoichiometric ratios is illustrated in Fig. 7. An increase in the gas phase temperature causes a decrease in absorption efficiency because the drying rate is increased with gas phase temperature and therefore the time period for absorption is decreased. Absorption efficiencies calculated from Eq. (25) agree well with the experimental data at high stoichiometric ratio. Calculation assuming a turbulent flow pattern provide slightly higher absorption efficiencies than those assuming no relative motion between droplets and gas phase. That is because of the decreasing influence of the diffusion coefficients. Again, the experimental results show a decrease in absorption efficiency with decreasing stoichiometric ratio due to additional liquid phase mass transfer resistances. As shown in Fig. 8, maximum absorption
Fig. 7. Influence of gas inlet temperature on absorption efficiency for various stoichiometric ratios.
Fig. 8. Comparison of analytically (Eq. (25)) and experimentally determined absorption efficiency at high stoichiometric ratio (l =3) assuming turbulent two phase flow.
efficiency is determined by the ratio of absorption rate to evaporation rate which can be calculated according to Eq. (25). Several experiments were performed to determine the influence of initial droplet size on absorption efficiency (Fig. 9). Initial droplet size distribution is determined by nozzle gas and was measured separately with a light scattering instrument (Malvern 2600). Assuming the influence of the nozzle gas on the flow pattern inside the spray dryer can by neglected, there is no influence of initial droplet size on absorption efficiency. For high stoichiometric ratios, this is also indicated by Eq. (25). Considering moderate stoichiometric ratios, model predictions also indicate that there is only a small influence of droplet diameter on absorption efficiency. The influence of calciumhydroxide particle size on absorption efficiency is illustrated in Fig. 10. As expected, there is no influence of particle size distribution at high stoichiometric ratios, since gas phase resistance controls absorption rate. Whereas at moderate stoichiometric ratios, smaller calciumhydroxide particles yield higher absorption rates. This may be caused by higher mass transfer coefficients and the higher specific surface of smaller particles.
Fig. 9. Influence of initial mean droplet size on absorption efficiency.
F.F. Hill, J. Zank / Chemical Engineering and Processing 39 (2000) 45–52
Y y a r b d l h m v
temperature difference between gas temperature and adiabatic saturation temperature loading fraction heat transfer coefficient density mass transfer coefficient diffusion coefficient stoichiometric ratio absorption efficiency tortuosity factor rate ratio
Subscripts ag bl dis dr d g I rf sus a v
agglomerate boundary layer dissociation droplet diameter gas phase interface reaction front suspension inlet outlet
Superscripts *
equilibrium molar
T DTas
Fig. 10. Influence of lime particle size on absorption efficiency.
5. Conclusions At high excess of calciumhydroxide the absorption efficiency of sulphur dioxide is limited by the drying conditions. Since significant absorption and reaction occurs only in the presence of water, the absorption efficiency strongly depends on the ratio of the evaporation rate to the absorption rate. At moderate excess of calciumhydroxide, the absorption efficiency is lowered by additional liquid phase mass transfer resistances for sulphur dioxide. The model proposed shows good agreement with experimental results. Model predictions and experimental results also indicate, that the influence of the initial droplet diameter on the absorption efficiency is negligible. At moderate stoichiometric ratios the absorption efficiency can be increased using a lime suspension with smaller calciumhydroxide particles.
Acknowledgements The authors gratefully acknowledge the financial support of the DFG (Deutsche Forschungsgemeinschaft).
Appendix A. Nomenclature surface area concentration constant Ackermann-factor first dissociation constant second dissociation constant gas phase overall mass transfer coefficient mole flux exponent Sc-number heat flux
A c C KA K1,diss K2,diss kg N: n Q: Sd1,d2 =
2p 1 1 geometry − d1 d2 factor
51
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