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 EngineeringThe 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 NegevILASS Europe, Como 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
Ben-Gurion University of the Negev
Scavenging of air pollutionsAbsorbers
– 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)
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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
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 NegevILASS 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 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
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Description of the model
Ben-Gurion University of the Negev
sinkUv cos2
yR
kUr v
2
2cos2sin
Y
X
Y
XY
XPe
X iiii
i
i
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)
.Ry where k = 0.009 0.044 for different Re, and
where
,2010
2011
bb
b
mxx
mxxX
,2010
2022
bb
b
mxx
xxX
ii D
RkUPe ,
2R
tDii ,
R
yY
xi– molar fraction of i-th species;
xb10– initial molar fraction of absorbate in
a droplet;
xb20– molar fraction of absorbate in a gas
phase at height H ;
m– dimensionless Henry constant
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Description of the model
Ben-Gurion University of the Negev
Boundary conditions:
wherey
xCDN i
iii
)( 222 bXX at Y
)( 111 bXX at Y
21 XmX at 0Y
21 NN at 0Y
(3)
(4)
(5)
(6)
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Method of the solution
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Method of the solution
Ben-Gurion University of the Negev
Integral material balance over the droplet yields:
dNRtd
xdVC Y
b sin20
0121
1 (8)
Expression for absorbate concentration in the bulk of a droplet is the following :
0 10
211
1 ),(
sin)()(
)1(
31)( d
TXmX
DmPeTX
T
bbb (9a)
For the linear vertical distribution of absorbate in the gaseous phase:
0 10
11
1 ),(
sin)(
)1(
31)( d
T
dBX
DmPeTX
T
bb (9b)
ground on the absorbatean ofion concentrat is,)(
)(200
2010
20200b
bx
Hkmxx
RxxmB
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where
Method of the solution
Ben-Gurion University of the NegevILASS 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
],[1
FRFdF Ni
N
ii
b
a
,,bai ,,...,2,1 Ni
where FRN – remainder of the series after the N-th term.
,0 ihTTi N
TTh N 0
NigfKfKhfKh
gf
i
i
jjjiiiii ,,1,)
2
1()
2
11(
),0()0(1
100
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Results and discussion
Ben-Gurion University of the Negev
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).
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Results and discussion
Ben-Gurion University of the Negev
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.
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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.
Results and discussion
Ben-Gurion University of the Negev
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
water in the atmosphere, xb10 = 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. gradxb2 for absorption of SO2 by water droplet, xb10 = 0, xb20 =
0.01 ppm.
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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.
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