HUNGARIAN JOURNAL OF INDUSTRIAL CHEMISTRY VESZPREM Vol. 30. pp. 171- 176 (2002) DIRECT CALCULATION OF SULFUR DIOXIDE ABSORPTION BY WATER DROPS * t A A t A. SABONI, S. ALEXANDROVA, • SSENOV (Groupe Ecoulements Transferts de Matiere et de Chaleur, LTP, Universite de Caen, Dept GTE, 120 rue de l'Exode, 50 000 Saint Lo, FRANCE 1Department of Chemical Engineering, University of Chemical Technology and Metallurgy, 8 K. Ohridski Blvd, 1756 Sofia, BULGARIA) Received: July 21, 2000; Revised: March 11,2002 Absorption of pollutant gases into water drops is one of the major removal mechanism i~ clouds: ra~n a~d scrubbers. The aim of this article is to present a new model for prediction of the mass transfer m gas-hqmd di.spersed. sy~ten:s encountered in scrubber or atmospheric systems. In the liquid phase, a model based on local scales, mterfactal hqmd friction velocity and drop size diameter is used. In the continuous gas phase the well known Beard and_Pruppache~ model is applied. Data obtained by the modelling of the S02 absorption in a single_ drop are c?mpared to pu~hs~ed expenmental results and a fairly good agreement was found. Finally, we present a partiCular ~d 1IDportant application of the abo~e model as an illustration of its use. As an example, sulfur dioxide washout by ram, falling through a polluted plume, IS considered. Key words: absorption, sulfur dioxide, modelling, drops Introduction Removal of sulfur oxides plays an important role in the air pollution control. In the atmosphere, chemical reactions occur between sulfur oxides, aerosol particles, and trace gases, such as nitrogen oxides. Some products of the reactions, absorbed by the cloud and rain drops, render the acidic precipitation. A knowledge of the mass transfer mechanism in the case of gas absorption (from I into) drops is necessary to understand the scavenging of trace gases in clouds, rain and wet scrubbers. Mass transfer between gas phase and water drops depends on the physical and chemical properties of the diffusing gas, the drop size and the hydrodynamics around and inside the moving drops. The transport of trace gases from the air into the falling drop is controlled by molecular diffusion, as well as by the convective mass transfer outside and inside the falling drops. The internal circulation, generated by the aerodynamic drag on the drop surface, facilitates the redistribution of the absorbed gas [3, 19, 7}. For instance, the short residence time of some gases in the atmosphere is due to the fact that these gases are preferentially absorbed by cloud and rain droplets and removed in this way from the air. As a consequence the acidic precipitations are strongly affecting the aquatic ·corresponding author deterioration and material degradation, resulting in agricultural productivity, forest growth and known or anticipated effect on human health . A number of mathematical models have been proposed and many experimental investigations have been carried out in the area of air-pollution control in order to provide better understanding of the scavenging of trace gases in clouds, rain drops, and industrial wet scrubbers. For drops, falling in a well soluble gas medium (in this case the transfer resistance is located in the gas phase), the survey of the published works [4, l, 11, 19] show that a number of good numerical n:o~els exist, as well as experimental correlations for predtctlon of the mass transfer coefficients in the gas film. For liquid phase controlled resistance, [16] proposed a model based on local scales, interfacial liquid friction velocity and drop diameter. The model were validated experimentally by Amokrane et al. (2] compared literature models with the experimental data of Gamer and Lane [9}, Kaji et al. [11] Walcek et al. [19] and Lindhjem [lJ. They found considerable discrepancies between the experimental data and the published models. On the contrary, they observed that the Saboni model {16] fits the experimental data very well. The experimental study and model validation in _the case of sulfur dioxide absorption by water drops faUmg through 172 high gas concentration (few%) has been described in details by Amok:rane et al. [2]. The purpose of this article is to test a new model to predict the S02 absorption and desorption by falling drops in air containing traces of sulfur dioxide. If absorption is to be modeled as local process, based on the overall simulation of the two phase flows , two approaches are possible ; a) To compute the hydrodynamics and the mass transfer at each point in the system as a function of the local conditions. b) Using the experimental results together, with a complete numerical simulation, to develop and refine approximate· models for the mass transfer between the two phases. At the present time option (a) is completely excluded by limitations in computational power. The calculations will be prohibitively expensive and impractical for routine application to the description of scrubber and atmospheric systems. An example of option (b), similar to that used by Walcek et al. [17, 18, 19}, is presented in this article. The authors proposed a simplified theoretical approach which was validated by experimental data. They applied it to describe the scavenging of trace gases by drops. Their simplified theory has an important advantage over the rigorous ·model (Navier-Stokes and diffusion-convection equations), as it is computationally much faster, since the two dimensional problem is transformed into a !- dimensional one. However calculations remain too slow for routine application (in cloud models and mesoscale pollution transport models, as mentioned by Mitra et al., [14]). In this study, an application, which simplify considerably the computati0ns, is presented. Model formulation Starting from the expression for mass flux across the interface, we can write : (1) where S1 and Vi are the surface area and the droplets volume respectively, where k 1 is the local liquid mass transfer coefficient, Cu is the equilibrium concentration at the interface and C1is the average concentration in the Jrop. According to Saboni {16] and Amokrane et al. [2], the liquid mass transfer coefficient is given as : with k1 =o.sJD~u· u* :::U~Pg CD Pt 2 (2) {3) where Dt is the liquid phase molecular diffusivity, u * is the interfacial liquid friction velocity, p is the gas g density and p is the liquid density. l The total drag coefficient, Cv can be deduced from the equation proposed by Berry and Pranger [6]: ln(Re)= -3.126 + 1.013 *ln(C0 Re 2 )- + 0.01912 * [ln(c v Re 2 )] 2 (4) In this relation the Reynolds number range between 1 and 3550 and the term CvRe2 between 2.4 and 10 7 Mass transfer across the interface reduces the concentration of the diffusing specie in one of the phases and increases it in the other. The change in each of the two phases is given by: (5) Where Vg and V 1 are the volume of the gas and the liquid phase, respectively and tis the time. cg and cl are the concentration of the diffusing specie in the continuous and the dispersed phase, respectively. Local equilibrium is supposed at the interface between liquid and gas phase concentration. For this reason and supposing that the pH value does not exceed 5.5 we can wtite : (6) where KH and K 1 are the equilibrium constants and C . is gl the gas concentration at the interface. In addition to equilibrium, mass flux continuity across the interface give the gas concentration at the interface: with 8 = 2a g Sh (8) where C8= is the bulk gas concentration, where k8 is the local gas mass transfer coefficient. The gas concentration boundary layer, 8g, is calculated from the expression for the Sherwood number in the gas phase (Beard and Pruppacher [5]; Pruppacher and Rasmussen [15]): Sh =L61+0.718Re05 Sc()33 (9) where Sc is the Schmidt number. Only results for the total sulfur concentration will be presented. C = [H2S03] + [HS03-l + [S03=J, the concentrations of the individual species being obtained from the total concentrations by simple relations (Appendix). 2.5 2 ~ 0 1.5 .s ~ 0 ~ . u <> Experlm ents of Mitra et al (1992} 0.5 50 100 150 200 250 300 Time (s) Fig. I Concentration within a drop as a function of time of exposure to S02 (for a 2.88 mm drop radius, drop temperature =10 °C, [S02] = 1035 ppbv) .. = 0 1.5 .s • ;! . -u 0.5 20 40 --Present model <> Experiments of Mitra et al (1992) ~a Time (o) 80 • 100 120 Fig.2 Concentration within a drop as a function of time of exposure to S02 (for a 2.88 mm drop radius, drop temperature =12.5 oc, [S02] = 97 ppm) Results and discussion Comparison with Laboratory Studies For a constant gas concentration , which is the typical case for laboratory studies, the Eqs.(l), (2), (6) and (7) are sufficient to describe sulfur dioxide absorption by individual freely falling large water drops. In order to evaluate the model adequacy, we test the model for the case of low and intermediate gas concentration (the mass transfer resistance is located both in the gas and the aqueous phase). The comparison is made between the model and the experimental results for sulfur dioxide absorption from individual large water drops. The model is compared to the Mitra et al. [13] and Mitra et al. [14] experimental results concerning two broad categories of sulfur dioxide absorption. The experiments were carried out in a vertical wind tunnel which allows to freely suspend a single drop in the vertical air stream of the tunnel. In the first category a 2.88 mm radius drop were exposed to sulfur dioxide- air mixture. Fig.l shows the evolution 173 0.8 --Present model <> Experiments of Mftra & Hannemann (1993) ~ 0.6 e= u 0.4 0.2 20 40 60 80 100 120 Time (s) Fig.3 The variation of the rate CvCinitial of S(IV) desorption with time exposure S02 (for a 2.88 tnm drop radius, drop temperature= 15 °C, C;nitial = 3.39 10'3 mole liter' 1 ) of the average total sulfur dioxide concentration vs. the time exposure in the case of 1035 ppbv S02 concentration in the gas phase. In Fig.2 results are reported for the absorption in the case of 97 ppm so2 concentration in the gas phase. From Fig.l and Fig.2, we observe that the values predicted by the present model are in good agreement with the experimental results. In the second category of experiments (Mitra et al., [14]), a drop initially containing S(IV) was exposed to sulfur-free air to determine the rate of sulfur dioxide desorption. Fig.3 shows the evolution of the average total sulfur dioxide concentration vs. the time exposure for a 3.39 10·3 mol liter·1 drop initial concentration. The results obtained from the model agree well with those from experiments. Example of Model application A brief illustration of the proposed model, applied to the sulfur dioxide washout by rain falling through a polluted plume, is shown below. This case is of growing interest, because the precipitation scavenging constitutes an important sink for gases in the atmosphere and can influence their local, regional and global distributions. A similar attempt was first made by Barrie [4J extended by Walcek et al. [17, 18, 191 and Hannemann et al. [10]. The Walcek et al. [17, 18, 19] procedure, adapted to the present model, may be summarized by the following: Let us consider a vertical column containing of air and sulfur dioxide. We suppose ·gaussian concentration distribution in the plume with a peak centered 200 m above the ground. Assuming the absence of S02 initially, the drops are supposed to fall sequentially in the air column that is devised into 300 layers, each of one meter in height. The drops enters a given layer of air with concentration Ctop and exit at its bottom with concentration Cbot· Cbo! is calculated from Eqs.(l), (2), (6) and (7), and represents the C1op value for the next layer. 174 300 250 200 .§. .. 150 .s:; "' ;; :1: 100 "' --lnitl~i Plume ~ .... /: '• I --Plume after 1 em rain '• I I 50 i\ I I I -----Plume after2 em rain ......... Plume after 3 em rain I ., I ~ 0 0 0.2 0.4 0.6 0.8 Concentration, C /C g gmax FigAVariation of S02 concentration with height in pollution layer after specified amounts of raindrops have fallen through. Initial concentration is 500 ppb (v). Rainfall rate, R = 1 mmlh The gas phase concentration is calculated from Eq.(5) which is rewritten in discrete form as: vd (cbot -ctop) vg ru (10) where C 8 n and C 8 n+l are the concentration in the layer before and after the drops have passed trough . Vg is the air volume and Vd is the volume of raindrops falling through the layer. The same equatien was applied to each layer as the drop progress through the entire column. From Eq.(JO) the gas concentration in each layer is determined according to, c;+l = c; - (cbo, - c,op )AQ (11) Az where AQ is the rainfall increment and Az is the layer height (respectively 0.1 rum and 1m, in this study). The gas profile will be modified after each AQ, (corresponding to a given set of drops falling through the column). Another set of drops is allowed to fall through this new profile and the procedure is repeated until the trace gas reaches a certain gas concentration. For further simplification, we consider the mean raindrop radius, r m representative for this distribution: (12) where r m is given in rum and the rainfall rate, R, in mmlh. Plume washout results Plume washout was calculated for 'precipitation intensity, R, of 1 mmlh and 15 mmlb. Fig.4 shows the time evolution of the specified gaussian distribution of sulfur dioxide concentration as a population of drops faits the plume pollution with an initial peak profile concentration of 500 ppb (v). In the case of 300 250 200 ~: .§. E 150 ~ " :1: 100 50 0 0 . t' '( 'I 'I : I I \ {: ! ,, :J tl il ,: 0.2 0.4 --lnil!al Plume -- Plume after 1 em rain -----Plume after 2 em rain · · · ·-Plume after 3 em rain ......... Plume after 4 em rain 0.6 0.8 Concentration, C /C g gmax Fig.5 Variation of S02 concentration with height in pollution layer after specified amounts of raindrops have fallen throngh. Initial concentration is 500 ppb (v). Rainfall rate, R = 15 mm/h 1 mmlh rainfall rate , corresponding to small drop size ( = 1.1 rum), the drops absorb and desorb the sulfur dioxide rapidly. We see that the gas concentration have a maximum and that the corresponding heightmax depends on rainfall quantity passed through the plume. The maximum gas concentration is displaced to shorter height with increasing rainfall quantity. For rainfall rate of 15 mmlh (Fig.5), corresponding to larger raindrop ( = 2.06 rom), the average concentration is reduced, while the height of the plume remains roughly constant To. explain the difference between these two cases, combination of the following two effects has to be considered : residence time (drop terminal velocity) and the absorption ability (drop diameter and gas concentration). From FigA and 5, we can note also that the scavenging is mainly controlled both by the total amount and intensity of the rainfall, which is in agreement with some in situ observations (see for example Durana et al. [8]). Conclusion In the first part of this paper, a simple analytical model was used to determine the sulfur dioxide absorption/desorption by freely falling drops. Data obtained by the model of the so2 absorption/desorption by single drop are compared with published experimental data and a fairly good harmony was found. In the second part, a particular important application of the above model is presented as an illustration of its predictive ability. As an example, sulfur dioxide washout by rain, falling through a pollution plume, is considered. The model predicts the redistribution of the plume through which the raindrops had fallen as function of the rainfall rate. Although the observed agreement between model and experimental results, from which some useful predictions on the atmospheric scavenging can be drawn, further investigations are needed for the initial rate under realistic conditions. Effects as multi- component gas phase, oxidation, break-up and/or coalescence, evaporation, air motions, have to be considered. SYMBOLS a radius of drop c dimensionless concentration Cg bulk gas concentration c interface gas concentration gi CD drag coefficient (z concentration of drop eli equilibrium concentration of drop d drop diameter D molecular diffusivity gas/liquid phase g,l kt liquid mass transfer coefficient kg gas mass transfer coefficient R Rainfall rate Re Reynolds number r radial coordinate Tm mean drop radius s surface area Sc Schmidt number Sh Sherwood number t dimensional time u Terminal velocity * Interfacial liquid friction velocity u v drop volume p g,l fluid density ( gas/liquid) REFERENCES 1. ALTWICKER E. R. and LlNDIDEM C. E.: AIChE J., 1988, 34(2), 329-332 2. AMOKRANE H., SABONI A. and CAUSSADE B.: AIChE J., 1994, 40, 1950-1960 3. BABOOLAL L. A., PRUPPACHER H. R. and TOPALIAN J. H.: J. atmos. Sci, 1981, 38, 856-870 4. BARRIE L. A.: Atmospheric Environment, 1978, 12, 407-412 5. BEARD K. V. and PRUPPACHER H. R.: J. Atm. Sci., 1971,28,1455-1464 6. BERRY E. X. and PRANGER M. R.: J. Appl Meteor., 1974, 13, 108-113 7. CAUSSADE B. and SABONI A.: in S. E. Schwartz and W. G. N. Slinn {eds.), Precipitation Scavenging and Atmosphere-Surface Exchange, Vol. 1 Hemisphere Publishing Corp., Washington, 29-40, 1992 8. DURANA N., CASADO H., EZCCURA A., GARCIA C., LACAUX J.P., and DINH P. V.: Experimental study of the scavenging process by mean of sequential precipitation collector: preliminary results. Atmospheric Environment Part A: General topics 26A(13), 2437-2443, 1992 9. GARNER F. H. and LANE J. J.: Tran. Inst. Cbem. Eng., 1959, 37, 162 10. HANNEMANN A. U., MITRA S. K. and PRUPPACHER H. R.: J. Atm. Chern., 1996,24,271-284 175 11. KAJI R., HISHINUMAY. and KURODA H.: J. Chern. Eng. Japan, 1985, 18(2),169 12. MAAHS H. G.: Sulfur dioxide water equilibria between 0 an 50 °C. In D. R. Schryer (ed.). Heterogenous Atmospheric Chemistry. Am. Geophy. Union., 187-195,1982 13. MITRA S. K., W ALTROP A. HANNEMANN A. U., FLOSSMANN and PRUPPACHER H. R.: in S. E. Schwartz and W. G. N. Slinn (eds.), Precipitation Scavenging and Atmosphere-Surface Exchange, Vol. 1 Hemisphere Publishing Corp., Washington, 123-141, 1992 14. MITRA S. K. and HANNEMANN A. U.: J. Atm. Chern., 1993, 16, 201-218 15. PRUPPACHER and RASMUSSEN: J. Atmos. Sci, 1979, 36, 1255-1260 16. SABONI A.: These de doctorat de l'INP de Toulouse, 1991 17. WALCEK C. J. and PRUPPACHER H. R.: J. Atm. Chern., 1984, 1, 269-289 18. W ALCEK C. J., PRUPPACHER H. R., TOPALIAN J. H. and MITRA S. K.: J. Atm. Chern., 1984, l, 290-306 19. W ALCEK C. J. and PRUPPACHER H. R.: J. Atm. Chern., 1984, 1, 291-306 APPENDIX Equilibrium relations for sulfur dioxide in water When sulfur dioxide is absorbed into water, the resulting equilibrium relations (Walcek et al. [17, 18, 19}, Amokrane et al.,[2]) are written us: (Al) HSO~ + H 2 0 ¢::? H 3 0+ +SO; (A3) The values of the equilibrium constants K8 , K 1 and K2 , of the reactions AI, A2 and A3 are respectively (Maahs [121, Mitra et aL [131): [H SO J {~-6.sz1) K H ::: 2 3 = 10 r RT (moles/moles) (A4) [S02 ] [HSO;J[H30+] =10( 8 :-·m) (moles/liter) (A5) [H 2S03 ] rso=JrH o+J (621.91_9.278) K1 = 3 3 == 10 T (moles/liter) (A6} [HSO;] Where T is the absolute temperature expressed in Kelvin. The total sulfur concentration [S} is written as {SJ={H2S03 ]+[HS0i]+[SO~] (A7) After several manipulations from Eqs.(A4}-(A6), together with the following conditions. 176 • Condition of electroneutrality: (A8) • Condition of water ionization: • The equilibrium constant of the ionization of water is defined by: Kw =[H3 0+][0H-] (thatisKw =10- 14 at25 ·c) (AlO) • The total sulfur concentration as function of pH of the solution is given by: _( + -~J[H3 0+] 2 +K1[H 30+]+K!Kz (All) [S]-l[H30 ] [H30+] Kl[H30+]+2K!Kz For pH< 5.5, reaction A3 may be neglected. Thus the total S concentration is then given by: [H o+f +K [H o+] [SJ = [H 2 S0 3 1 + [Hso; J = 3 K 1 3 (Al2) l Which may be written in this form: [S]=[H 2S0 3]+[HSO;J=KH[S0 2 ] 8 +~K1 KH[S02 ] 8 (Al3) Page 174 Page 175 Page 176 Page 177 Page 178 Page 179