INFLUENCE OF VERTICAL DISTRIBUTION OF ABSORBATE IN A GASEOUS PHASE ON GAS ABSORPTION BY FALLING LIQUID DROPLET

1. INFLUENCE OF VERTICAL DISTRIBUTION OF ABSORBATE IN A GASEOUS PHASE ON GAS ABSORPTION BY FALLING LIQUID DROPLET T. Elperin, A. Fominykh and B. Krasovitov Department of Mechanical Engineering The Pearlstone Center for Aeronautical Engineering Studies Ben-Gurion University of the Negev P.O.B. 653, Beer Sheva 84105, ISRAEL

2. Outline of the presentation ILASS Europe, Como 2008 • Motivation and goals • Fundamentals • Description of the model • Results and discussion • Conclusions Ben-Gurion University of the Negev

3. Gas absorption by falling droplets Henry’s Law: Air Soluble gas is the species in dissolved state Spray tower absorbers Scavenging of air pollutions by cloud and rain droplets • SO2 absorption of boiler flue gas • HF absorption in the aluminum industry • In-cloud scavenging of polluted gases (SO2, CO2, CO, NOx, NH3) Spray scrubbers Single Droplet Ben-Gurion University of the Negev

4. Vertical concentration gradient of soluble gases ILASS Europe, Como 2008 Scavenging of air pollutions • Absorbers • different rates of gas absorption by droplets at the inlet and outlet of the absober • Gaseous pollutions in atmosphere • SO2 and NH3 – anthropogenic emission • CO2 – competition between photosynthesis, respiration and thermally driven buoyant mixing Fig. 1. Aircraft observation of vertical profiles of CO2 concentration (by Perez-Landa et al., 2007) Ben-Gurion University of the Negev

5. Scientific background ILASS Europe, Como 2008 • Gas absorption by falling droplets: • Walcek and Pruppacher, 1984 • Alexandrova et al., 2004 • Elperin and Fominykh, 2005 • Measurements of vertical distribution of trace gases in the atmosphere: • SO2 – Gravenhorst et al., 1978 • NH3 – Georgii and Müller, 1974 • CO2 – Denning et al., 1995; Perez-Landa et al., 2007 • Effect of vertical distribution of absorbate in a gaseous phase on gas absorption by falling droplet: • Elperin, Fominykh and Krasovitov 2008 Ben-Gurion University of the Negev

6. Description of the model 0.1 mm R 0.5 mm 10 Re 300 0.7 U 4.5 m/s ILASS Europe, Como 2008 In the analysis we used the following assumptions: • dc<<R • Tangential molecular mass transfer rate along the surface is small compared with a molecular mass transfer rate in the normal direction • The bulk of a droplet, beyond the diffusion boundary layer, is completely mixed by circulations inside a droplet and concentration of absorbate is homogeneous in the bulk • The droplet has a spherical shape. Fig. 1. Schematic view of a falling droplet and concentration profile Ben-Gurion University of the Negev

7. Description of the model where k = 0.009 0.044 for different Re, and ILASS Europe, Como 2008 Fluid velocity components at the gas-liquid interface are (Prippacher & Klett, 1997): (1) Transient equations of convective diffusion for the liquid and gaseous phases read: (i = 1, 2) (2) where Ben-Gurion University of the Negev

8. Description of the model at (3) at (4) at (5) at (6) ILASS Europe, Como 2008 Boundary conditions: where Ben-Gurion University of the Negev

9. Method of the solution ILASS Europe, Como 2008 Ben-Gurion University of the Negev

10. Method of the solution ILASS Europe, Como 2008 Integral material balance over the droplet yields: (8) Expression for absorbate concentration in the bulk of a droplet is the following : (9a) For the linear vertical distribution of absorbate in the gaseous phase: (9b) where Ben-Gurion University of the Negev

11. Method of the solution ILASS Europe, Como 2008 Ben-Gurion University of the Negev

12. Method of numerical solution ILASS Europe, Como 2008 • The method of solution is based on the approximate calculation of a definite integral using some quadrature formula: • The uniform mesh with an increment h was used: • Using trapezoidal integration rule we obtain a system of linear algebraic equations: where – remainder of the series after the N-th term. Ben-Gurion University of the Negev

13. Results and discussion ILASS Europe, Como 2008 Fig. 2.Dependence of the concentration of CO2 in the bulk of a water droplet vs. time (average concentration of CO2 in the atmosphere is 300 ppm), xb10 = 0. . Fig. 3. Dependence of the concentrattion of CO2 in the bulk of a water droplet vs. time (average concentration of CO2 in spray absorber is 600 ppm). Ben-Gurion University of the Negev

14. Results and discussion ILASS Europe, Como 2008 Fig. 5. Dependence of the concentration of CO2 in the bulk of a water droplet vs. time (average concentration of CO2 in the atmosphere is 300 ppm), xb10 = mxb20. . Fig. 4. Dependence of the concentration of the dissolved gas in the bulk of a water droplet vs. time for absorption of SO2 by water in the atmosphere,xb10 = 0. Ben-Gurion University of the Negev

15. Results and discussion Fig. 8. Dependence of the concentration of the dissolved gas in the bulk of a water droplet vs. time for absorption of CO2 by water in the atmosphere, xb10 = 0. Fig. 7a.Dependence of concentrationin the atmosphere on the altitude in the morning Fig. 7b.Dependence of concentrationin the atmosphere on the altitude in the afternoon. Fig. 6. Aircraft observation of vertical profiles of CO2 concentration (by Perez-Landa et al., 2007) Ben-Gurion University of the Negev

16. Results and discussion ILASS Europe, Como 2008 Fig. 9. Dependence of the relative concentration of the dissolved gas at a ground vs. gradxb2 for absorption of SO2 by water droplet, xb10 = 0, xb20 = 0.01 ppm. Ben-Gurion University of the Negev

17. Conclusion ILASS Europe, Como 2008 • Vertical inhomogenity of the soluble gas concentration in the gaseous phase strongly affects mass transfer during gas absorption by falling droplet. • When concentration of the soluble gases decreases with altitude, droplets absorb trace gases during all their fall. • When concentration of the soluble trace gases increases with altitude, beginning from some altitude gas absorption is replaced by gas desorption. • Concentration of the dissolved gas in a droplet at the ground is independent of the initial concentration of the dissolved gas in a droplet. • It is showed that when concentration of a soluble gas in a gaseous phase has a maximum on the ground, concentration of the dissolved gas in a droplet on the ground is lower than concentration of saturation in a liquid corresponding to the concentration of trace gas on the ground. On the contrary when concentration of the soluble gas in a gaseous phase has a minimum on the ground, concentration of the dissolved gas in a droplet on the ground is higher than concentration of saturation in a liquid corresponding to concentration of soluble gas on the ground. Ben-Gurion University of the Negev