scavenging of gaseous pollutants by falling liquid droplets in inhomogeneous atmosphere t. elperin,...

Scavenging of Gaseous Pollutants by Falling Liquid Droplets in Inhomogeneous

Atmosphere

T. Elperin, A. Fominykh and B. Krasovitov

Department of Mechanical EngineeringThe Pearlstone Center for Aeronautical

Engineering Studies Ben-Gurion University of the NegevP.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 NegevIAAR, 22st Annual Meeting, Tel-Aviv, 2008

Gas absorption by falling droplets

Ben-Gurion University of the Negev

Single Droplet

• SO2 absorption of boiler flue gas

• HF absorption in the aluminum industry

• In-cloud scavenging of polluted gases (SO2, CO2, CO, NOx, NH3)

Air

Soluble gas

Scavenging of air pollutions by cloud and rain droplets

is the species indissolved state

Henry’s Law:

Spray towerabsorbers

Sprayscrubbers

Vertical concentration gradient of soluble gases


Scavenging of air pollutionsAbsorbers

– different rates of gas absorption by droplets at the inlet and outlet of the

absober

Gaseous pollutants 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)

IAAR, 22nd Annual Meeting, Tel-Aviv, 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

Scientific background

Ben-Gurion University of the NegevIAAR, 22nd Annual Meeting, Tel-Aviv, 2008



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 bulkThe 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 300

0.7 U 4.5 m/s

¿ ¿

¿ ¿

¿ ¿




v _=_ kU sin_ v r=2kU

Rycos_

∂ X i

∂ _i

_ Pei{_ sin _∂ X i

∂ __ 2Y cos_

∂ X i

∂ Y }= ∂2 X i

∂ Y 2

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)

y << R .where k = 0.009 0.044 for different Re, and

where

X 1=x1_ mxb20

xb10_ mxb20

, X 2=x2_ xb20

xb10_ mxb20

,

Pei=RkUDi

_i=tDi

R2 , Y =yR

,

¿

– dimensionless Henry constant m

– molar fraction of absorbate in a gas phase at height H ;

xb20

– initial molar fraction of absorbate in a droplet;

xb10

– molar fraction of i-th species;xi




Boundary conditions:

where N i =_ DiC i

∂ xi

∂ y

X2=X

b2__2_ at Y _ ∞

X1=X

b1__1_ at Y _ _ ∞

X1=mX

2 at Y =0

N1=N

2 at Y =0

(3)

(4)

(5)

(6)


Method of the solution




Integral material balance over the droplet yields:

_ VC1

dx b1

dt= 2πR2 ∫

0

π

N 1_Y = 0sin __d_ (8)

Expression for absorbate concentration in the bulk of a droplet is the following :

X b1_T _=1_3

Pe1_π_1_ m_D_∫0

T

[X b1____ mX b2___]∫0

πsin__1__ ,T_ __

d_ (9a)

For the linear vertical distribution of absorbate in the gaseous phase:

X b1_T _=1_3

Pe1_π_1_ m_D_∫0

T

[X b1____ B__]∫0

πsin__d__1__ ,T_ __

d_ (9b)

B=m_x200_ x20_R

_x10_ mxb20_k_H, xb200 is concentration of an absorbate on the groundwhere


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


∫a

b

F ___d_= ∑i= 1

N

_ i F __ i__ RN [F ], _i_ [a,b], i=1, 2, ... ,N ,

where RN [F ] – remainder of the series after the N-th term.

T i=T0_ ih, h_TN_ T 0

N

f _0_=g_0_,

_1_12

h_K ii__ f i=h_12

K i0 f 0_ ∑j=1

i_ 1

K ij_ f j__ gi , i=1,_ ,N




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).




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.




Fig. 6. Aircraft observation of vertical profiles of CO2 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 CO2 by

rain droplet in the atmosphere, xb10 = 0.



Fig. 9. Dependence of the relative concentration of the dissolved gas on the ground vs. gradxb2 for absorption of SO2 by water droplet, xb10 = 0, xb20

= 0.01 ppm.


Conclusions


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.


scavenging of gaseous pollutants by falling liquid droplets in inhomogeneous atmosphere t. elperin,...

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