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

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

Gas absorption by falling droplets Ben-Gurion University of the Negev Single Droplet SO 2 absorption of boiler flue gas HF absorption in the aluminum industry In-cloud scavenging of polluted gases (SO 2, CO 2, CO, NOx, NH 3 ) Air Soluble gas Scavenging of air pollutions by cloud and rain droplets is the species in dissolved state Henry’s Law: Spray tower absorbers Spray scrubbers

Vertical concentration gradient of soluble gases Ben-Gurion University of the Negev Scavenging of air pollutions Absorbers –different rates of gas absorption by droplets at the inlet and outlet of the absober Gaseous pollutions in atmosphere –SO 2 and NH 3 – anthropogenic emission – CO 2 – competition between photosynthesis, respiration and thermally driven buoyant mixing Fig. 1. Aircraft observation of vertical profiles of CO 2 concentration (by Perez-Landa et al., 2007) 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: SO 2 – Gravenhorst et al., 1978 NH 3 – Georgii and Müller, 1974 CO 2 – 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 Scientific background Ben-Gurion University of the Negev ILASS Europe, Como 2008

Description of the model Ben-Gurion University of the Negev In the analysis we used the following assumptions:  c << 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 0.1 mm R 0.5 mm 10 Re U 4.5 m/s ILASS Europe, Como 2008

Description of the model Ben-Gurion University of the Negev 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: (2) (i = 1, 2) where k = for different Re, and where – molar fraction of i-th species; xixi – initial molar fraction of absorbate in a droplet; x b10 – molar fraction of absorbate in a gas phase at height H ; x b20 – dimensionless Henry constant m ILASS Europe, Como 2008

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

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

Method of the solution Ben-Gurion University of the Negev 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) ILASS Europe, Como 2008 where

Method of the solution Ben-Gurion University of the Negev 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: Method of numerical solution Ben-Gurion University of the Negev where – remainder of the series after the N-th term. ILASS Europe, Como 2008

Results and discussion Ben-Gurion University of the Negev. Fig. 2. Dependence of the concentration of CO 2 in the bulk of a water droplet vs. time (average concentration of CO 2 in the atmosphere is 300 ppm), x b10 = 0. Fig. 3. Dependence of the concentrattion of CO 2 in the bulk of a water droplet vs. time (average concentration of CO 2 in spray absorber is 600 ppm). ILASS Europe, Como 2008

Results and discussion Ben-Gurion University of the Negev Fig. 5. Dependence of the concentration of CO 2 in the bulk of a water droplet vs. time (average concentration of CO 2 in the atmosphere is 300 ppm), x b10 = mx b20.. ILASS Europe, Como 2008 Fig. 4. Dependence of the concentration of the dissolved gas in the bulk of a water droplet vs. time for absorption of SO 2 by water in the atmosphere, x b10 = 0.

Results and discussion Ben-Gurion University of the Negev Fig. 6. Aircraft observation of vertical profiles of CO 2 concentration (by Perez-Landa et al., 2007) Fig. 7a. Dependence of concentration in the atmosphere on the altitude in the morning Fig. 7b. Dependence of concentration in the atmosphere on the altitude in the afternoon. Fig. 8. Dependence of the concentration of the dissolved gas in the bulk of a water droplet vs. time for absorption of CO 2 by water in the atmosphere, x b10 = 0.

Results and discussion Ben-Gurion University of the Negev Fig. 9. Dependence of the relative concentration of the dissolved gas at a ground vs. gradx b2 for absorption of SO 2 by water droplet, x b10 = 0, x b20 = 0.01 ppm. ILASS Europe, Como 2008

Conclusion Ben-Gurion University of the Negev 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. ILASS Europe, Como 2008