be rectified aiid the system brought back to steady state within a reasonable period of time. The rare earth ch1or:ide (feed) flow rate in the extractor is by far tlie most imliortant 1-ariable to be coritrolled. The other variables in order of their importance are the HC1 flow rate (scrub solution), the I-IIIEHP flow rate (organic phase), and the settler interface positions. In tlie stripper>the flow of the pregiiaiit HDEHP (organic phase) was found to he the most important variable to be controlled in order to maintain steady state followed in order of irnportaiice by the H('1 flow rate (strippiiig solution) and the settler interface positioiis. literature Cited Casto. &I.'2.. 11,s. Thehis;. Iowa State UniverPitv. iimes. Iowa.
Fritz, J. S., Oliver, R. J., Pietrzyk, D. J., Anal. Chem., 30, 1111 (1958).
Hoh, Y. C., &,f.S. Thesis, Iowa State Universit'y, Ames, Iowa, 1971. Knisely, R. N., Fassel, V. A,, Butler, C. C., in "Analytical Flame Spectroscopy," It. Marrodineau, Ed., Philips Technical Library, 1970, pp 379-410. Peppard, 1). F., Ferraro, J. R., Mason, G. W.j J . Znorg. I\'ucZ. Chem., 7, 231 (1958). Rahn, R. Vi'., 3I.S.Thesis, Iowa State University, Ames, Iowa, 1967. Rahn, R. W., Smutz, M., Z n d . Etsg. Chem., Process Des. Develop., 8, 289 (1969). Seemann, It. C., Ph.11. Thesis, Iowa State University, Ames, Iowa. 1973. Seemann, It. C., Burkhart, L. E., Can. J . Chem. Engr., wbmitted for publication (1974). Rhatley, hl. C., Ph.D. Thesis, Iowa State University, Arne>, Iowa, 19d3.
1970.
RECEIVED for review September 25, 1972 ACCEPTEDMay 29, 1973
Cnsto, 31. G., Smutz, LI., Bautista, R. G., Trans. SOC.JIzning
ETzgr. AZJIE, 250, 42 (1971).
Gas Absorption by Alkaline Solutions in a Venturi Scrubber S. Uchida and C. Y. Wen* Department of Chemical Engineering, West Virginia Cniaersity, Xorgantown, TT-est Virginia 26606
Simulations of SO?absorption in various venturi scrubbers have been performed using a mathematical model which describmes mass transfer and fluid flows in the scrubbers for SOz-HgO and SOz-alkaline solution system. In order to construct and test the mathematical model of venturi scrubber performance, the various correlations available in the literature for estimation of the mean drop diameter were reviewed. From momentum, heat and mass balances in the scrubber, a set of first-order, non-linear ordinary differential equations relating the liquid velocity, the SO2 concentration in the liquid, the SO2 partial pressure, etc., along the axial direction in the scrubber were formulated. These relationships were numerically solved to give performance profiles. The calculated results based on this model were compared with experimental data obtained in several types of venturi scrubbers and showed satisfactory agreement.
I n recent year,; atomizing scrubbers have received much interest as gas absorber? as n-ell as their use in the capture of small solid particles in the gas, since this type of scrubbers can perform both duties ~rliichare necessary for pollution abatement'. Their operation is based on a gas st'ream atomizing liquid which i; lirokeii into small droplets upon which the small particles are collected or into n-hich the pollutant gas is absorbed. Venturi and flooded disk scrubbers are examples of t h e ntoiniziiig scrubber.. There are several advantages i i i this type of >?rubber.The design is quite ,simple and the unit' is very flexible in its operatioii. -1 high scrubbing; a i i d collection efficiency caii be ohtniiied, but this increaeed efficiency must be paid for by large l)o\ver costs to overcoiiie tlie correspondiiigly large pressure d r o l ~through the uii'it. Scaling aiid plugging teiidencj- in these w u b h e r s h:is lieeii demoiistmteti to be much less in comp:uiwii to the coiireiitioiial scrubbers such as packed iiii1)licity of desigii makes these scrubbers relatively iiieqiensive t o build,
Despite the growing importance of this kiiid of scrubber there has not been an adequate ratioual design method from the gas absorption point of view. In design and simulation of venturi scrubhers, it is iiecessarjto knoiv the mechanism of atomization and tlie operating characteristics such as the pressure drop acroqs the venturi scrubber: the amount of heat and mass transferred between liquid and gas, etc. This paper preseiits a model Ivhich can be used to predict the pressure drop aiid rates of heat and mass transfer in venturi-type scrubbers. Previous Studies
The pressure drop across the venturi scrubber is one of the major factors in design coiisideratioiis, because the energy requirement in operatirig the fails to overcome the venturi's relatively high pressure drop is a significant operating expense . Several experimentally derived correlations for pressure Ind. Eng. Chem. Process Des. Develop., Vol. 1 2 , No. 4, 1973
437
Table 1. Empirical Equations for Droplet Diameter a n d Their Applicable Ranges Applicable range Investigator
Sukiyama and Tanasawa (1939) Llugele (1960)
=
_ -
0 8 2
Dn Gretzinger and Marshall (1961) Wigg (1964) Kin1 and Marshall (1971)
Dm
=
D,
=
Dm
=
vrO, crn/sec
M,IML*
PL, p
10,000 to sonic velocity
1.8-15
0.01-0 46
10,000 to sonic velocity
1 8-15
10,000 to sonic
1-15
0 01-0 30
8000-35,000
0 5-20.2
0.032-0 45
7500 to sonic
0.06-40
0.01-0,50
velocity
velocity
m= m= (L
-411 units are in cgs units as listed in the nomenclature.
* Dimensionless.
drop have been presented by llatrozov (1958), Gieseke (1963), Boothroyd (1966), Volgin (1968), and Gleason (1971). However, these correlations were obtained by using smallscale equipments and contain several esperimentallj- determined constants. In 1971, Calvert (1970) and Boll (1973) developed equations for pressure drop which seem t o be applicable to the most types of venturi scrubbers. By using Sewton's IaLv Calvert derived an equation for the force required t'o change the momentum of the liquid foxing in a venturi a t a given rate. His equation, however, does not contain bhe t'erm associated with the frictional loss on the wall of the venturi. 13011's equation is substantially the same as the equation theoretically derived by Gieseke (1963) from the momentum balance of gas and liquid except that Bo11 took wall friction into consideration. The estimation of t h e diameter of liquid droplets produced in the venturi is important in calculating t'he rates of heat and mass transfer. Various correlations are available in the literature to estimate the mean diameter of the liquid droplets from different types of atomizers under different operating conditions. These correlations are applicable only to each specific type of atomizer and the specified propert'ies of the fluids: volume ratio of gas to liquid, relative velocity of gas to liquid, etc. The correlations directly applicable to the venturitype atomizers are therefore few. These are summarized in Table I. The ranges of applicabilities of various correlations in terms of the mass ratio of gas to liquid, the relative velocity of gas t o liquid, and the viscosity of liquid are very important and are also listed in Table I. Since Comings' study (1948) on the heat transfer in a venturi scrubber many studies on the venturi-type scrubbers have appeared in the literature (Anderson and Johnstone, 1955; Boyadzhiev, 1964; Elenkov and Boyadzhiev, 1967; Feild, 1950; Gleason, 1971; Harris, 1971; Johnstone, et al., 1954; Johnstone and Robert, 1949; Kuznetsov and Oratovskii, 1962; Markant, etal. 1962; Tassler, 1952; Volgin, et al. 1968). Johnstone and Robert (1949), Feild (1950), and Johnstone, et al. (1954), iiivestigated the absorption of sulfur dioxide in wat'er and alkaline solut'ioris and measured t h e amount of sulfur dioxide absorbed in the liquid a t various distances from the point of liquid injection in a venturi scrubber. 438
Ind. Eng. Chern. Process Des. Develop., Vol. 12, No.
4, 1973
Kuznetsov and Oratovskii (1962) obtained a correlation for the rat'e of gas absorption with chemical reaction in the throat and the divergent section of a venturi scrubber, relating the number of transfer units and the degree of absorption to the principal operating and design parameters of t,he apparatus. Their correlation was used by Boyadzhiev (1964) to determine the optimal conditions for gas absorption Jvith chemical reaction. Xarkant, et al. (1962), Eleiikov and Royadzhiev (1967), and Volgin, et al. (1968), also studied absorption of SOn from dilut'e gas streams by various solutions. Gleason (1971) obtained estensive esperimental data on the SOn absorption by sodium carbonate solutions and calcium hydroxide solutions in a flooded disk scrubber which is considered in this paper as a type of atomizing scrubbers. Reaction Mechanism
When sulfur dioxide is absorbed into water, the following reactions occur in the liquid phase.
The equilibrium constants for reactions 1 and 2 a t 25' are = l.T X and K n = 6.2 X lo-' M, respectively. Therefore, the latter reaction can be neglected under normal conditions. The forsard and backnard reaction rate constants for reaction 1 are kf = 3.4 X lo6 1.1see and k b = 2 X lo8 -If-' see (Onda, et al., 1971). In t h e light of the data obtained by Lbnn, et al (1955), Onda, et al. (1971), and Hikita, et al (1969), it appears that the rate of the hydrolysis reaction of SOn in mater is rapid relative to the diffusion process and t h a t the surface of the mater film 13 instantly saturated a t the equilibrium coiicentration upon eqiosure to gaseous SOZ. Therefore. the absorption of SO2 In water may be treated as a physical mechanism. In the case of the absorption of SO?by alkaline solutions, t n o additional reactions mal occur
K,
S02(aq)
HS03-
+ OH-
HSOI-
+ O W @ SOP2- + H 2 0
(3) (4)
and the equilibrium constants for reactions 3 and 4 are K s = 1.7 X 1012JI-1andK~= 6.2 X 1O6J1-',respectively. Experimeiital data obtained from the absorption of SOz in water and sodium 1i:;droxide solutions by liquid-jet type (Hikita, et al., 1969) and stop-cock type (Onda, et al., 1971) absorbers have been correlated in t h e present study by the penetration theory based on the assumption of a n instantaneous irreversible reaction as shown in Figure 1. The fact t h a t the rate of SO2 absorption into sodium hydroxide solution can be represented by t h e penetration theory with an iiistailtaneous reaction allows these two react'ions to be considered as occuririg instantaneously. Thus, from the values of equilibrium constants for these reactions SO2 can be considered t o react with hydroxyl ioii irreversibly with the overall reaction scheme of
SO2
+ 20H-
+
SOa2-
+ HzO
(5)
This reaction has t h e stoichiometric factor (number of OHions reacting with one molecule of S02(aq))of two. Performance Equation's
When liquid is injected into the high-velocity gas stream iii a venturi scrubber, it is atomized by the formatioil arid subsequent shattering of attenuated, twisted filaments and thin, cuplike films. These initial filaments and films have extremely large surface areas available for heat and mass transfer. Later nearly spherical droplets are formed which have less surface area per unit volume of liquid than do t h e attenuated films and filaments. Although the actual process of the atomization of t h e liquid is very complex, the following assumptions are made to simplify the model but they are still realistic enough so that theoretical treatment can be applied. (a) Every droplet v;hich is formed a t t h e poiiit of liquid injection will have the same diameter xhich can be calculated by the correlation for mean drop diamet>er,aiid there will be no change iii this diameter caused by coalescence or shattering during the passage of the droplet through the venturi scrubber. Epstein (1971) studied the effect of drop size distribution on t h e rate of SO2 absorption and showed t h a t it could be neglected. (b) The shape of the drop is spherical and there is no internal motion in the drop, so the drop can be represented by a rigid sphere (Hughes arid Gilliland, 1952). (c) The compressibil.ity effect of t h e gas is negligibly small. (d) There is no deposition or reeiitrainment of t h e liquid on or from t h e wall of the scrubber vessel. (e) The variatioii in gas flow rate due t o liquid vaporization is negligibly small. (f) Heats of reaction and heats of solution are negligible. (g) Temperature withiri the liquid drop is uniform. Pressure Drop. h differential equation for pressure drop in a venturi scrubber with respect t o t h e axial distance is derived by making a momentum balance in a n incremental section of t h e scrubber.
+ d(-lfLzlL) + Sg,
d(JfKugj
dPf
+ Sg,d p
=
Lsing the relationship
-11,=
S~rp,z~, = pgGo = constant
-1fL = S(1 --
E)PLVL = p ~ L 0=
eq 6 is reduced t o the following form
constant
0
(6)
Figure 1. Comparison of experimental data on rate of SO2 absorption with values based on penetration theory
The last term on the right-hand side of eq 7 relates to the friction loss which is generally expressed by the following form under turbulent flow conditions
where f is a friction factor which depends on t h e roughness of the wall of t h e venturi scrubber and the Reynolds number of the gas. Equation of Motion of Liquid Droplet. Assuming t h a t the liquid atomizes instantly into the droplet form with a cons t a n t mean diameter a t the point of entry t o the highvelocity gas stream, the force balance for the vertically moving droplet yields pL(
F)2
= pL(
g
) + r
-
pg
g
(T+)
+
where c d is the drag coefficient. Recently Ingebo (1956) obtained the drag coefficients for droplets and solid spheres in clouds accelerating in airstreams Cd =
(10)
27/'VR,03'
Equation 10 is applicable for a Reynolds number range 6-400 and a sphere diameter range 20-120 p . The second term on the right-hand side of eq 9 is usually negligible in comparison to the other terms if the droplet is in the gas-phase under normal pressure. K h e n motion is in the vertical direction eq 9 can be reduced t o g L
dz
= -g + -3-cd -
P~
4 dp
p~
VL
(uK -
VL)iVg
- ~4
(11)
Z'L
If the motion is in the horizontal direction, the term due to gravity can be eliminated aiid the relationship simplified. The average gas velocity a t any point in the venturi scrubber is calculated by the following relation (12)
vg = Go/&
where e is a voidage in the scrubber and is related by the following relationship to the velocity of the droplet VL =
LO,'(l
-
e)S
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
(13) 439
M a s s and H e a t Transfer in a Venturi. T h e relationships for t h e mass and heat balances between gas and liquid in a n incremental section of the venturi scrubber are
(L,
- dL,)(z
+ dz) - L,z
= U . ~ AdV =
-(G,/p)dp~
G m dyw = kgwap(yw1 - yw) dV = dLm
hga(tg- t ~ dV )
=
(L, - dL,)CpLdtL
(14) (15)
+
Bkgwap(ywi
-
~ w d )T'
GmCpgdtg = h,a(t~ - tg) dV
(16) (17)
Using the relationships, z = C A / P ~dTV, = S dz, NA = ~ L A C A , and a = 6(1 - e)/dp and neglecting dL, in eq 14 and 16 in comparison with the other terms, the following set of differential equations are obtained.
dCA/dz dp.4/d2 dtgldz
=
[apMkL/(Lm/S)IACA
(18)
= - [apkL/(Gm/S) IACA
(19)
[hga/(Gm/S)C~gl(t~ -
(20)
=
tg)
This set of differential equations is numerically solved by Runge-Kutta-Gill method using given initial conditions a t the nozzle point. The heat and mass transfer coefficients and equilibrium relations needed to solve the above set of equations are estimated as discussed below. H e a t and M a s s Transfer Coefficients and Equilibrium Relations. Gas-phase mass transfer to or from a single sphere placed in a moving fluid has been studied by many investigators (Froessling, 1938; Langmuir, 1918; Ranz and Marshall, 1952). X correlation having the same form as the Ranz-Marshall equation obtained by Steinberger and Treybal (1960) can be used to calculate the gas-phase mass transfer coefficient of the individual droplet in a venturi scrubber.
The applicable ranges of this correlation are 1 < - V R ~< 30,000 and 0.6 < A'sc < 30,000. Equation 25 is also used to compute the mass transfer coefficient of water vapor from t h e surface of a liquid drop into the gas phase. The heat transfer coefficient in the gas phase is estimated from the following Ranz-Marshall correlation (1952).
The mass transfer coefficient in a stagnant liquid drop for physical absorption can be obtained by solving the following differential equation expressing the material balance in the drop with initial and boundary conditions
att=O,O 0; bCA/dr = 0 a t r = ro, t
This equation can be solved analytically to obtain the rate of absorption a t time t as
The mass transfer coefficient for the physical absorption into the drop k ~ may p be defined as
For gas absorption with an instantaneous reaction, the liquid-phase mass transfer coefficient is given as follows if both the diffusivity of the gas and that' of the reactant in the liquid are nearly the same (Brunson and Wellek, 1970) kL =
[I f (CB0ICAi)IkLP
(30)
where C Ais~the interfacial concentration calculated by CAi = (CA*
- CBOR)/(1 + R)
(31)
where R = kLpH/kg. The rate of absorption in this case d l be
L V =~ k ~ C a i
(32)
The equilibrium concentration of SO2 in water is calculated by CA* = H ~ A CAO (33
+
+
where H = 1.688 X 1 0 - 6 t ~ 2 1.90 X l O P 4 t ~ 6.38 X l o F 3 and C A ~= 1.125 X 1 0 - g t ~ 2 1.375 X l O P 7 t ~ 6.263 X 440
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
+
5.0
-
-8
liquid velocity velocity
...... gar
3
sulfur concentration in liquid
.-
-__,
L
.-
'-
I
a2
0.4
-
.-.-.-.-.-.-. I
I
0.6
0.8
1.0
dimengionlasa distance Imm W X z I O , 2
Figure 2. (a) Dimensions of venturi scrubber used by Harris, et a/. (OAP venturi scrubber). (b) Dimensions of flooded disk scrubber used by Gleason, et a/. (FDS)
Figure 4. Velocity and sulfur concentration profiles along axial distance in OAP venturi scrubber
---_--
liquid temperature gas lemperature
C Inlet gas temperature. 154 ' 0 Flooded disk scrubber 80.6
Od
0.h
0.k
0.;2
0.16
O.!O
dimensionless distance from nozzle, Z
30
40
50
Figure 5. Temperature profiles of gas and liquid along axial distance in OAP venturi scrubber
1
erpcrimanloi pressure drop, Ap ( cm-HeO)
Figure 3. Comparison of calculated pressure drop in OAP venturi scrubber and flooded disk scrubber with experimental data
-
-
The applicable raiiges of this correlation are p a = 0.0005 0.002 atni and f~ = 10 50". Thc natcr vapor preswre a t the interface, p,, = py,,, call 1w e.;timatecl from Aiitoine's correlation (1954) log
psi
=
A -
B
(34)
~
fL 4-
219
where A = 7.7423 and B = 1554.16 for t~ = 35
-
55".
Results and Discussiori 111 the following, the results of simulation of various venturi scrubbers based oii the model presented in the previous sectioii are discussed. The simulations presented below are performed on a priori I1a.e without use of adjustable parameters. Simulation of t h e Experiments of Office of Air Programs, Environmental Protection Agency (Harris, 1971). A series oi experiments of SO?absorption with water and SaOH solution l r a s performed by the Office of -1ir Programs, Eiivironmental Froteetion .IgelicF-:using a venturi scrubber of the decipii slio1i11 i i i Figure 2:3 ( O a r venturi scrubber). Simulations of the performance of -their esperiments are conducted based on their operating conditions.
Esamples of the calculated results of tlie prewure tlrol), tlie velocity profiles of the gas and liquid, the concentration profile of sulfur dioxide absorbed in the liquid phase, and the temperature profiles of the gas and the liquid are show~iin Figures 3-5. The operating conditions and experimental data in this case are a:: folloivs: gas flon- rate = 30.3 ma 'Iiiiii, liquid rate = 37.85 l.,'min; inlet gas temperature = 1 M 0 , outlet gas temperature = 43'; inlet SO2 coiiceiitratioii = 2000 ppm, outlet SO2 concentratioii = 1160 ppni; pressure drop = 21 cmHzO. The liquid concentration profile presetited ill Figure 4 shows that a large amount of absorptioii is observed iiear tlie point of liquid injection. - 1 1 ~ 0 the temperature profile.; i i i Figure 5 indicate that the temperatures of both liquid and gas approach the same value rather quickly The overall result's of this simulation of tlie experiments of the Office of h i r Programs are .hon-ii in Figure 7 . Simulation of Experiments Performed by Johnstone, et a/. (1954). Johnstone, et al., reported a veiituri scrubber study iii which SO?xva.: absorbed i l l 0.6 S S n O H ;olutioiir. The diniensioiis of the 1-eiituri scrubber aiid the o!)eratiiig conditions used in their experiment> are fomid in tlie references (Feild, 1950; Johiistoiie, et al. 1954). ?'lie siniulatioii results of this system are compared with the actual esperimental data in Figures 6 and i . Simulation of Experiment Performed by Cottrell Environmental Systems, Incorporated (Gleason, 1971). T h e Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
441
Goa veloclty at throat
1.12-
- calculated
152m/xc
value
0 experimental dolo obtained by Feild(1950)
yl
--
kl.08
-0 0
''8
0
0.2 0.4 a6 0.8 dimenrlonlers distance from nanle 2
.
IO
Figure 6. Pressure profile in venturi scrubber used by Feild
(1 950)
/
0 OAP venturi ( NaOH-SOz-H20) e OAP venturi ( S O t - H ( r 0 ) A FOS (CaO-SOI-yO) A FOS (SOz-HzO) 9 Venturi of Johnstone et ai. (NaOH-SOI-hO)
I n designing a venturi scrubber, eq 7, 11, and 18-24 are simultaneously solved to give the relations among the operating and design variables. An it'eration method of solution is required since a simple analytical solution to the set of equations does not seem possible. I n what is to follow, a practical design procedure is given that may be applied t'o the design of a venturi scrubber when the gas flow rate, the gas temperature, the SO,removal efficiency, the concentration of alkali in t'he liquid, and the maximum allowable pressure drop are given. (a) Select a type of the venturi scrubber, Le., fixed or variable throat, circular or rectangular duct, etc. (b) Assume the cross-sectional area of the throat and the liquid rate. Using the given operating conditions, calculate the mean droplet diamet'er by an appropriate correlation given in Table I. ( e ) Using equations 7 , 11, and 18-24, calculate the pressure drop, the SO,removal efficiency,etc., along the axial distance and find the length of the venturi vvhich gives the maximum allowable pressure drop. (d) Compare the calculated SO, removal efficiency with the required value. If the former is lower than the latter, repeat step b through d until the required SO,removal efficiency is attained with the tolerable pressure drop. This design procedure will yield a workable vent'uri scrubber but not' necessarily the most efficient and/or economical. The optimal design of a venturi scrubber is a comples problem due to the number of independent variables and other factors such as the equipment cost and the energy requirement. Nomenclature a
contact area per unit volume, cm2/cm3 = concentration of -1and B, respectively, g-mol/
=
CA,CB
em3
Ca' Figure 7. Comparison of calculated with experimental data
SO, removal
per cent
experimental dat'a obtained by Cottrell Environmental Systems, Inc., for the SO,-lime solution system, using a flooded disk scrubber (FDS), are compared with the results obtained from the simulation of SOz absorption. The dimensions of the equipment are shown in Figure 2h. The results of the simulations are given in Figure 7 . Conclusions
A mathematical model has been developed representing the mechanism of SO,absorption into water and alkali solutions. I n spite of simplifying assumpt'ions made in the analysis, the results of the simulat'ions show good agreement with the experimental results. The model is not only useful for simulatioii but also provides a guide to the design of venturi scrubbers. From the results obtained here, the following conclusions can be drawn. (1) A% significantly large amount of mass and heat transfer takes place near the nozzle. This is primarily due to the small transfer resistances, large driving forces, and relatively long residence time of the liquid droplets in this region. (2) The operation of the venturi scrubber can be considered as isothermal except, in the zone extendiiig a few centimeters from t,he nozzle. A high heat transfer efficiency is observed in this type of equipment. (3) Concentrations of SOz close t o equilibrium values in the liquid were observed in the case of S02-H20 system a t the exit of the scrubber. 442
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No.
4, 1973
=
liquid,
dimensionless concentration of total -1absorbed in
+
CAI(CAO* CRO)
C A ~= concentration of A a t interface, g-mol/cni3 C,Q = constant in eq 33, g-mol,/cm3 CA* = concentration of h in equilibrium with partial pressure of A in gas phase, g-mol/cm3 CBO = initial concentration of B, g-mol/cm3 Cd = drag coefficient C p g , C p ~ = specific heats of gas and liquid, respectively, call g-mol O C D.k,D*, = diffusivity of A in liquid and gas, respectively, cm2/sec = mass mean diameter of droplet, p D , = nozzle diameter, em D3, = surface-volume mean diameter of droplet, p De = equivalent diameter, em dp = diameter of droplet, ern f = friction factor G, = molar gas f l o rate, ~ g-moljsec Go = volume gas flow rate, cm3/sec g = gravitational acceleration, cm/sec2 gc = unit conversion factor, g i a t m em sec2 H = Henry's larr constant, g-mol/atm em3 h, = heat transfer coefficient in gas phase, cal/cm2 see "C k,,,k,, = mass transfer coefficients for A and water vapor in gas phase, respectively, g-mol/cm2 see a t m kL = mass transfer coefficient for gas absorption with instantaneous reaction, cm/sec kLp - mass transfer coefficient for gas absorption without reaction, cmlsec L , = molar liquid flow rate, g-moljsec LEI' = dimensionless liquid flow rate, L,/L,o LO = volume liquid f l o rate, ~ [cm3/sec] JI,,JIL = mass flow rates of gas and liquid, respectively, g/sec h'A = absorption rate of g-mol,/cm2 see SRe= Reynolds number, dpLpg; p g S s C = Schmidt number, p g l p g D ~ g 'Vsh = Sherwood numher, RTk,dp/Da,
D,
P
= dimensionless t,otal pressure, p / p o p = total pressure, atm p a = partial pressure of A, a t m pi = pressure drop due to friction, a t m p,,. = partial pressure of water vapor, a t m R = ratio of gas-side resistance to liquid-side resistance, kLPI2:Ikg r = radius of droplet, cni S = cross-sectioiial area of venturi scrubber, em2 So = cross-sectional area of throat of venturi scrubber, cni2 T = dimensionless time, v g o f / z 3 T , = dinleiisionless gas temperature, f g l t g o T L = dimensionless liquid temperature, fL/’f,o t = contact time, sei: f,.tL = temperature:; of gas and liquid, respectively, “ C T’ = voluilie of venturi scrubber, cm3 ~*,,T’L = diniensioiiless velocities of gas and liquid, respectivel>-,~ , / i ~and , ~v ~ j r , o cg,cL = velocities of gas and liquid, cmjsec f gas a t iiozzle point and a t throat’,
z ’ , ~ = relative velocitj- of pas arid liquid a t t’hroat, cm/sec z = mole fraction of in liquid
yu-
=
yni
=
2
=
iiiole fraction of water vapor in gas phase iiiole fraction of x t t e r vapor a t interface dimeiisionless distance from iiozzle point, z / x o distance from iiozzle point, cm
GREEKLETTERS
p
=
4C.k
heat of vaporization, cal/g-mol driving force based 011 liquid concentration, g-mol/
=
cni3 = dimeiisioiiless driving force based on liquid coiicentrat ion E = voidage pg,p~ = viscosities of gas and liquid, respect’ively,P p g , p ~ = densities of gas and liquid, ,respectively, g/cm3 p11 = molar density of liquid, g-mol: cni3 pm = nieun density of gas niised with liquid droplets, g, cn13 Q = surface tension, dynjcni
AC.4‘
literature Cited
Anderson, L. B., Johnstone, H. F., AZChE J., 1, 135 (1955). Antoine, T. E., “Vapor-Pressure of Organic Compounds,” Interscience, S e w York, N. Y., 1954. Boll, R. H., Znd. Eng. Chem., Fundam., 12,40 (1973). Boothroyd, R. G., Trans. Znst. Chem. Eng., 44, T306 (1966). Boyadzhiev, Kh., Zn,t. Chem. Eng., 4, 22 (1964). Brunson, R. J., Wellek, R. >I., Chem. Eng. Sei., 2 5 , 904 (1970). Calvert, S., AZChE J . , 16, 392 (1970). Comings, E. W.,Adams, C. H., Shippe, E. I]., Znd. Eng. Chem., 40, 75 (1948). Elenkov, D., Boyadzhiev, K., Int. Chem. Eng., 7, 191 (1967). Epstein, AI., Progress Report to EP.4 (Feb), Bechtel Corp., (1971). Feild, R. B., 11,s.Thesis, University of Illinois, 1950. Froessling, X., Gerlunds Beitr. Geophys., 52, 170 (1938). Gieseke, J . A,, Ph.D. Thesis, Cniversity of Washington, 1963. Gleason, R. J., “Pilot Scale Investigation of a Venturi-type Contactor for removal of SO2 by the Limestone Wet Scrubbing Process” (Final report draft), 1971. Gretzinger, J., Marshall, W. R., Jr., AZChE J., 7, 312 (1961). Harris, D. B., private communication, 1971. Hikita, IT., ;isai, S., Tsuji, J., Proc. Annu. X e e t . SOC.Chem. Eng., Jap., 34th, 8207 (1969). Hughes, R. R., Gilliland, E. R., Chem. Eng. Progr., 48,497 (1952). Ingebo, It. I)., YACA4Technical Note No. 3762, Sept (1956). Johnstone, H. F., Feilds, T. B., Tassler, 11.C., Ind. Eng. Chem., 46, 1601 (1954). Johnstone, H. F., Robert, 11. H., Znd. Eng. Chem., 41, 2417 (1949). Kim, K . Y., Llarshall, W.R., AIChE J . , 17, 575 (1971). Kuznetsov, 11. D., Oratovskii, \7. I., Int. Chem. Eng., 2 , 185 11962). Langmuir, I., Phy. Rev., 12, 368 (1918). Lynn, S., Straatemeir, R., Krainers, H., Chem. Eng. Sei., 4, 49 (1955). lIarkant, H. P., LIcIroy, R. A , , lIatty, R. E., I’appi, 45, 849 (1962). llatrozov, V. I., Soobschcheniya o Sauchno-Teknicheskikh Rabotkh S I U I F No. 6 7 , 152 (1958). lIugele, R. A, AIChE J., 6, 3 (1960). Sukiyama, S., Tanarawa, Y., Trans. Soc. Jlech. Eng. Jap., 4-6, Report No. 1-6 (1938-1940). Onda, K., Sada, E., llaeda, Y., Kagaku Kogaku, 35,345 (1971). Pigford, 11. E., Pyle, C., Znd. Eng. Chent., 43, 1949 (1951). Ram, W.E., Marshall, W.R., Chem. Eng. Progr., 48, 141, 173 11952).
SUPERSCRIPT
’
=
dimensionless value
SCBSCRIPT -1 = coniponeiit to be absorbed 13 = coniponent to react with -1in liquid phase
P
gas interface L = liquid 0 = initial I
= =
Steinberger, R. L., Treybal, R. E., AIChE J . , 6,227 (1960). Tassler, 11.C., Ph.L). Thesis, University of Illinois, 1952. Volgin, B. P., Efimova, T. F., Gofman, 11. S., Int. Chem. Eng., 8, 113 (1968). Wigg, L. I)., J . Znst. Fuel, 37, 286, 500 (1964). RECEIVED for review October 2, 1972 &kLCEPTEDJune 18, 1973 The work upon which this publication is based was performed pursuant to Contract No. EHSD 71-20 with the Environmental Protection Agency.
Ind. Eng. Chem. Process Des. Develop., Vol. 1 2 , No. 4, 1973
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