Sulfur Dioxide Removal in Venturi Scrubbers Clayton P. Kerr' Confrol Systems Laboratory, Office of Research and Development, Environmenfa/,Protecfion Agency, Research Triangle Park, North Carolina 2771 7
A theoretical model for overall gas-phase volumetric mass transfer coefficients in venturi scrubbers has been developed and used for presentation of experimental data from small pilot scale power plant flue gas scrubbing installations. Correlations are presented for limestone, lime, and magnesia slurries and sodium carbonate solutions as scrubbing liquid. The model includes gas-phase, liquid-phase, and solids dissolution resistance to mass transfer. Conclusions regarding the importance of the various resistances to mass transfer are drawn from the fitted constants obtained by least-squares fit.
Venturi scrubbers, because of reduced scaling and plugging tendency and demonstrated capability for removal of particulate material, are being considered as part of the gas scrubbing equipment in various power plant stack gas scrubbing processes for sulfur dioxide removal. In some proposed scrubbing operations, sulfur dioxide is absorbed in a scrubbing liquor containing sparingly soluble reactants and converted to both sulfite and sulfate metal salts which are also sparingly soluble. This sparing solubility of the reactant and product salts requires in most cases that the scrubbing liquor be a slurry with the resulting scaling, plugging, and salt entrainment problems. The overall resistance to mass transfer, in general, is dependent upon four separate resistances: gas-phase resistance, liquid-phase resistance, chemical reaction resistance, and if the scrubbing liquor contains a solid reactant then a solids dissolution resistance. If one or more of these resistances are negligible, then the theoretical analysis required for developing the correlation and the type of experimental data required for determination of fitted constants will be simplified. Experimental data, obtained from demonstration-size pilot plants, have been used to obtain fitted constants for the correlations developed for predicting sulfur dioxide removal in venturi scrubbers (Downs and Kubasco, 1970; Gleason, 1971). These publications contain all of the data used in this study and descriptions of the equipment and the test programs. From the correlations developed, conclusions have been drawn regarding the magnitude of the various resistances to mass transfer.
chaotic. This development is based upon a mobile liquid interface. The rate expression for sulfur dioxide removal is based upon the following simplifying assumptions. (1) All chemical reactions are fast. (2) Solids present in the scrubbing liquor are sparingly soluble. (3) Solids dissolution in the liquid film adjacent to the gas-liquid interface is unimportant. (4) The internal pore area of the solids is much larger than the external area of the solid particles, and the rate of dissolution of solids is proportional to the product of the mass of solids and the concentration difference between dissolved sulfur dioxide and the equilibrium value. With these assumptions, the volumetric molar mass transfer rate for the gas phase may be written as
Theoretical Development In a venturi scrubber, the high gas velocity in the throat atomizes the liquid into drops, increasing the area for mass transfer and accelerating the liquid drops to the exit gas velocity. At Reynolds numbers greater than 200 (where the Reynolds number is defined in terms of the drop diameter, relative gas velocity, gas density, and gas viscosity), the liquid in the drop is characterized by chaotic internal motion (Lode and Heideger, 1970; Makino and Takashima, 1969). The mobility of the liquid interface continues a t least as long as the liquid drops and gas are a t different velocities, and the mass transfer rates will be higher in the liquid phase because of convective transport rather than molecular diffusion. The presence of surfactants or fine dusts can reduce or eliminate internal drop motion a t low Reynolds numbers. For this application where the Reynolds numbers a t the throat are large (about 500), the drop motion probably remains highly
where hla is the liquid-phase mass transfer coefficient per unit volume, (hr)-I, and c1 is the dissolved sulfur dioxide concentration near the gas-liquid interface, lb mol/cu ft, and for the rate of solids dissolution written in terms of the concentration of sulfur species using assumption 4
'
Present address, Department of Chemical Engineering, Tennessee Technological University, Cookeville, Tenn 38501
222
Ind. Eng. Chern., Process Des. Develop., Vol. 13, No. 3,1974
N
- &c,)
= k,&
(1)
where N is the volumetric molar mass transfer rate, lb mol/(hr cu ft), k,a is the gas-phase mass transfer coefficient per unit volume of scrubber, lb mol/(hr cu ft), y is the gas-phase mole fraction, 6 is the Henry's law constant, (lb mol/cu ft)- I, and cI is the liquid-phase composition a t the gas-liquid interface, lb mol/cu ft (dissolved sulfur dioxide). (EPA policy requires the use of metric units for quantification. This paper, however, uses nonmetric units to reflect the literature cited. Readers more familiar with metric units may use the conversion factors given in Table I for convenience.) For the liquid adjacent to the gas liquid interface
N
kla(c,
- CJ
(2)
(3) where k, is the dissolution rate constant. ft/hr, s is the is the equilibrium solids area per cu ft of gas, ft- I, and dissolved sulfur dioxide concentration. lb mol/cu ft. Equations 1, 2 , and 3 can be combined to yield an expression for the overall resistance to mass transfer
1-=
KGa
1 k,a
+ -kla+ 01
81
k,s
(4)
Similar expressions have been proposed by Ramachandran and Sharma (1969). The average gas-phase mass transfer coefficient, h,, is adopted from Sherwood and Pigford (1952) as
N S h = 2.0
+ bNReNS~.'"
(5)
where the average relative velocity between gas and liquid is used to characterize the Reynolds number. With the molecular diffusion term dropped, the gas-phase mass transfer coefficient can be expressed as
where b is a constant, D, is the molar diffusivity, 6 is the gas density, Nsc is the gas-phase Schmidt number, pLnis the gas viscosity, and ut is the throat velocity (all quantities in consistent units). The liquid-phase mass transfer coefficient, k , , is obtained using the turbulent sphere model of Handlos and Baron (1957) with an average circulation time of 2d/vt (Higbie, 1935). This result, with an average relative velocity of half the throat velocity, is
k1
0.Ol~t
(7)
The gas-liquid interfacial area, a, can be obtained from a = O.OoBL’/d’
(8) where a is the specific interfacial area, sq ft/cu ft, L’ is the liquid/gas ratio, gal of liquid/1000 cu ft of gas, and d’ is the drop diameter, ft. The drop diameter is obtained using the NukiyamaTanasawa (1938) correlation
where d is the drop diameter in microns and ut is throat velocity in ft/sec. Combining eq 4, 6, 7, 8: and 9 yields
The first term in eq 10 represents the contribution of solids dissolution to the overall resistance to mass transfer, and the second term represents the contribution of the gas and liquid phases to the overall resistance. Treating s as constant should not introduce appreciable error if excess solid reactant is used, if the dissolution constant k, is not too small, and if the Henry’s law constant 8 1 is not too large. Equation 10 is a resistance in series model which means the moles of sulfur dioxide absorbed and the moles of sulfite precipitated are equal, and the dissolved sulfur dioxide in the liquid remains approximately constant. If there are no solids or if the solids do not dissolve significantly, then the term Ol/k,s should be deleted from eq 10, and if the dissolved sulfur dioxide concentration changes significantly, then 8 1 does not remain constant and some suitably averaged value should be used.
Evaluation of the Experimental Overall Mass Transfer Coefficient The terms in braces in eq 10 have been treated as constants and determined by a least-squares fit which requires experimental values of &u. These values of &a have been determined in the following fashion. For a differential element of venturi throat, the rate of mass transfer can be expressed as
- y*)A
d~ (11) where u is velocity, A is the cross sectional area, 6 , is the molar gas density, y is the mole fraction of sulfur dioxide, y* is the equilibrium mole fraction of sulfur dioxide, and z - ~ A b , d y = KGa(y
is length (all quantities in consistent units). Rearranging and integrating yields (12) The term z is the effective length of the venturi for mass transfer. Since all of z consists essentially of a straight throat, u is equal to the throat velocity, ut. If a stoichiometric amount of reactant is used, then y* is probably constant and *much less than either y1 or yz, and the integral term in eq 12 becomes (13) The terms y1 and yz are the inlet and outlet sulfur dioxide mole fractions. The term y* can be calculated by considering the appropriate chemical equilibria present in the liquid phase. This development can be found in the Appendix of this article in the microfilm edition of this journal. (See paragraph a t end of paper regarding supplementary material.) If there are no solids or if the solids do not dissolve, then the material balance equation for the dissolved sulfur dioxide is CI
= c11
- (y - Y l )7480 L’6,
(14)
Since y* = 01 CI, eq 14 can be combined with-eq 12 and integrated to yield
Where there is adequate dissolved reactant (low values of 15 becomes equivalent to eq 12 and 13, and the resistance in series model with rapid solids dissolution and sparing solubility will yield the same values of fitted constants as those obtained by using eq 15 and 10 with solids dissolution excluded.
el), eq
Discussion of Results Pilot plant data (Gleason, 1971) with strong sodium carbonate solutions as scrubbing liquor were used to determine the effective length of the scrubber. In this system, there is no solids dissolution resistance or liquidphase resistance, and an effective length of the scrubber of 2.50 in. yields experimental overall mass transfer coefficients equal to those calculated from eq 6 with the constant term, b, equal to 1. As indicated in Figure 1, the intercept is approximately zero, corresponding to zero solid dissolution resistance. Johnstone, et al. (1954), report effective lengths of 3 in. when liquid-phase diffusion controls. It would be desirable to be able to calculate z theoretically rather than treating it as an experimentally determined constant. However, for a pulsating, deformed drop, z calculated from a force balance on the drop involves considerable difficulties and uncertainties (Levich, 1962). Using an effective scrubber length of 2.50 in. and eq 13 for determining the number of transfer units, pilot plant data with lime slurries (Gleason, 1971) and magnesium oxide slurries (Downs and Kubasco, 1970) as scrubbing liquor have been adequately fitted with the solids dissolution resistance excluded. Both of these systems were fitted Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 3, 1974 223
.
25 a lom4
lo
I
eo
IO-'
I.o
0.5
[yy+d] "t
Figure 1. Comparison of model with experimental data (magnesium oxide and lime slurries).
Figure 2. Comparison of model with experimental data (limestone slurries).
20 x I O',
Table I. Nonmetric Conversion Factors -i
The nonmetric
Multiply by
Yields metric
atm cu f t
760 28.32 5/9('F - 32)
mm Hg liter OC
O F
ft $81 in. sq ft
c
L
I
m
0.30
3.79 25 4 0.09
liter cm sq m
with a common regression line since physical and transport properties for both gas phases are the same (temperatures for both systems were approximately the same). The expression for the liquid-phase mass transfer coefficient is independent of physical and transport properties, and only those experimental data where reactant stoichiometries were approximately 1.O were used. Apparently the Henry's law coefficients for these systems are approximately the same. The equilibrium calculations outlined in the Appendix indicate that limestone slurries are only sparingly soluble, and if the liquid compositions remain close to the dilute equilibrium compositions, then the resistance in series model should be adequate for presentation of data. The resistance in series model should not be used under the following conditions: coarse ground stone, hard stone rather than soft stone, and low stoichiometry. These conditions do not represent anticipated design conditions. The pilot plant data with limestone slurries (Gleason, 1971) was fitted with the solids dissolution resistance included. It is of interest to compare the value of the intercept obtained from the least-squares fit with that obtained from some order of magnitude calculations. Ramachandran and Sharma (1969) have indicated that typical values for the dissolution constant, &, in general vary from 6.5 X to 26.0 X 10-5 ft/sec. Depending upon the porosity of the limestone, the quantity s can vary from
.5
1.0
1.5
0
Figure 3. Comparison of model with experimental data (soda ash solutions). 0.7 to about 4.0 ft-1 (limestone stoichiometry of 1). If a Henry's law constant of 0.00087 (lb mol/cu f t ) - l is used (the compositions used are shown in the Appendix), the intercept should vary from about 2.3 x loF4 to 52.5 x 10-4 (lb mol/hr cu f t ) - l compared with 5.0 x obtained from the regression analysis. Table I1 summarizes the fitted constants with 99% confidence limits, the correlation coefficient @*), and the F levels. Figures 1-3 show the experimental data and leastsquares fit. All fitted constants are based upon an effective venturi length of 2.50 in. Most of the scatter in Figures 1-3 is probably due to experimental error in determining the inlet and outlet compositions required for determining the number of transfer units from eq 13. A combined analytical and sampling error of 15% which is reasonable, will account for the scatter in Figures 1-3. The exit gas composition from the venturi is particularly
Table 11. Summary of Fitted Constants
System Sodium carbonate Magnesium oxide or lime Limestone 224
Intercept
5.091 X
lo-'
&
5.159 X
Slope
lo-'
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 3, 1974
1.044 X 2.361 x 7.15 X
lo-'
f 0.103 X f 0.963 X f 3.85 X
lo-*
R2
F
92% 68% 45 %
724 81
31
Table 111. Relative Magnitude of the Resistances to Mass Transfera
System Sodium carbonate Magnesium oxide or lime Limestone
d' = drop diameter, ft k, = average gas-phase mass transfer coefficient, lb mol/
Solids dissolution
Gas phase
Liquid phase
0%
100%
0%
0% 33 %
44 % 10%
56% 57 %
Table values are based on a throat velocity of 100 ft/sec and a liquid/gas ratio of 20 ga1/1000 cu ft. prone to error because of the difficulty of obtaining a sample without further contacting of gas and liquid in the sampling device. With the fitted constants and values of physical properties, eq 10 can be used to determine the relative magnitudes of the various resistances to mass transfer. Table I11 lists these values. As expected, the more soluble systems, magnesium oxide or lime, have less liquid-side resistance that the less soluble limestone system (corrected for solids dissolution). Acknowledgments The author wishes to acknowledge the use of the facilities of the D. W. Mattson Computer Center of Tennessee Technological University. Nomenclature A = area, sqft Dm = molar diffusivity, lb mol/(ft hr) or lb mol/(ft sec) &a = overall gas-phase mass transfer coefficient per unit volume of scrubber, lb mol/(hr cu f t ) or lb mol/ (sec cu ft) L' = liquid gas ratio, gal of liquid/1000 cu ft of gas N = mass transfer per unit volume of scrubber, lb mol/ (hr cu ft) NRe = Reynolds number NsC = Schmidtnumber N s ~= Sherwood number a = gas-liquid interfacial area, sq ft of liquid surface per cu ft of gas b = constant q, = dissolved sulfur dioxide composition near the solid surface, lb mollcu ft c1 = dissolved sulfur dioxide composition a t the gas-liquid interface, lb mol/cu ft cI,c11 = dissolved sulfur dioxide composition near the gas-liquid interface, lb mol/cu ft, and a t entrance d = drop diameter, microns
(hr sqft) k,a = gas-phase mass transfer coefficient per unit volume of scrubber lb mol/(hr cu ft) or lb mol/(sec cu ft) 121 = liquid-phase mass transfer coefficient, ft/sec or ft/hr kla = liquid-phase mass transfer coefficient per volume of scrubber, (hr)-lor (sec)-l k , = dissolution rate constant, ft/hr or ft/sec s = solids area per unit volume of gas, (ft)u = velocity, ft/sec ut = throat velocity, ft/sec y = mole fraction of sulfur dioxide, gas phase y* = equilibrium mole fraction of sulfur dioxide gas phase y1,yz = inlet, outlet sulfur dioxide mole fractions z = effective length of venturi, f t
Greek Letters 81 = Henry's law constant, (lb mol/cu ft)-l 6, = gas density, lb/cu ft 6m = gas density, lb mol/cu ft p,,, = gas viscosity, consistent units
Literature Cited Downs, W., Kubasco, A. J., "Magnesia Base Wet Scrubbing of Pulverized Coal Generated Flue Gas-Pilot Demonstration," (NAPCA Contract CPA 22-69-162), NTlS No. PB198-074 and PB198-075 (1970). Gleason, R . J., "Pilot Scale Investigation of a Venturi-Type Contactor for Removal of Sulfur Dioxide by the Limestone Wet-Scrubbing Process," (EPA Contract EHSD 71-24), NTlS No. PB209-023 (1971). Handlos, A. E.. BaronT.,A./.Ch.E.J., 3, 127 (1957). Higbie. R . , Trans. A./.Ch.€., 31,365 (1935). Johnstone, H. F., Field, R. E., Tassler, M. C., Ind. Eng. Chem., 46, 1601 (1954). Levich, V. G., "Physicochemical Hydrodynamics," p 431, Prentice-Hall, Englewood Cliffs, N. J . , 1962. Lode, T., Heideger, W. J.. Chem. Eng. Sci., 25, 1081 (1970). Makino. M., Takashima. Y., Bull. Tokyo Inst. Techno/., No. 90, 151 (1969). Nukiyama, S., Tanassawa, Y., Trans. SOC.Mech. Eng. (Jap.), 4 (14), 86, (1938). Ramachandran, P. A.. Sharma, M . M., Chem. Eng. Sci., 24, 1681 (1969). Sherwood, T. K., Pigford, R . L., "Absorption and Extraction," p 73, McGraw-Hill, New York, N. Y.. 1952.
Received for review January 29, 1973 Accepted April 5, 1974
Supplementary Material Available. An Appendix to this article will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (105 X 148 mm, 24X reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. C. 20036. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche, referring -to code number PROC -74-222.
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 3, 1974
225
