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Sulphur dioxide absorption into sodium sulphite solutions in a cable contactor
Sulphur dioxide absorption into sodium sulphite solutions in a cable contactor P. Lorent, P. Gerard and J. Vanderschuren Chemical Engineering Department, Facult6 Polytechnique de Mons, 56, rue de I'Epargne, 7 0 0 0 Mons, Belgium An experimental investigation of the rate of sulphur dioxide absorption into sodium sulphite solutions in a cable contactor was made at room temperature for several gas velocities, liquid flow rates and pH values. Correlations were derived giving the overall gas mass transfer coefficients, enhancement factors and heights of transfer units for a cable-bundle scrubber. It was found that the enhancement factors are very high and that the absorption rate is mainly controlled by the gas film mass transfer resistance. Modelling of the operation according to the two-film theory of absorption with chemical reaction allowed the calculation of theoretical values of the overall mass transfer coefficient, which were found to be in good agreement with experimental results.
Keywords: flue gas desulphurization; SO2 absorption; sodium sulphite; cable contactor
Nomenclature Ar d D~ Fa G h H H0 Ht~; I K K~ K2 kG K~;
kL L m n
Archimedes number = (2R)3g/v 2 Diameter of the liquid sheath around the yarn (m) Diffusivity of component i (m 2 s -I ) Enhancement factor Gas flow rate (mol s -I) Height of the contactor (m) Henry's law constant (atm kg mol -t) Solubility coefficient of sulphur dioxide in water (atm kg tool -I) Height of a transfer unit (m) Ionic strength (mol kg -~) Equilibrium constant of reaction (22) Dissociation constant (mol kg -I) = [H+I IHSO;I/IH2SOd Dissociation constant (mol kg -I) =
Nso, P Pso, P~o~ R Re s SO,T T v Yl,Y2 y* Zi
IH+I ISO~-I/IHSO;!
[I
Gas-phase mass transfer coefficient (tool s -j m -2 bar -t ) Apparent overall gas mass transfer coefficient (mol s -t m --~ bar -I) Liquid-phase mass transfer coefficient (m s -I) Liquid flow rate on the cable (m -~s -t) Dttso~/Dso~ D.so;/Dso~-
?'i
Introduction The steadily increasing severity of the European regulations for emission of sulphur dioxide from combustion plants provides a growing need for purification units for flue gases.
0950-4214/92/030125-07 © 1992 Sutterworth-HeinemannLtd
v
Flux of sulphur dioxide (mol s -~ m--') Total pressure (bar = 105 Pa) Partial pressure of sulphur dioxide (bar) Equilibrium pressure of sulphur dioxide (bar) Radius of the cable (m) Liquid Reynolds number = 4L/2nRv Liquid sheath thickness (m) Total S(IV) = [SO_,] + IHSO;I + lSO~-I Temperature (K) Gas velocity ( m s -I) Inlet and outlet molar fraction of sulphur dioxide in the gas Equilibrium molar fraction of sulphur dioxide Ion valency Molality (mol kg -I) Activity coefficient of component i Kinematic viscosity (m-" s -I)
Subscripts i Gas-liquid interface w Water I Bulk solution Im Logarithmic mean sol Absorbent solution
The most widely used methods for flue gas desulphurization ~ are the limestone wet scrubbing process, spraydry scrubbing systems operating with slaked lime, the Wellman-Lord process using sodium sulphite regenerable by heat treatment and the dual-alkali process in which the sorbent is also a sodium sulphite solution.
Gas Separation 8" Purification 1 9 9 2 Vol 6 No 3
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SO2 absorption into Na$TO, solutions in a cable contactor: P. Lorent et al. Two plants, a commercial plant (capacity 60 000 NmZ h-’ ) and a large pilot plant (capacity 26 000 NmZ h-‘). both equipped with a three-stage cable-bundle scrubber (Amazonem), were recently started in Belgium for cleaning the gaseous effluents of a garbage combustor and an oiltiled boile?. Desulphurization is achieved by the dual-alkali process running in the dilute mode. with sodium carbonate softening, in the first unit and in the concentrated mode in the second. Amazone is a gas-liquid contactor. patented first in Belgium in 19702 and later in 21 other countries including the UK4, in which the liquid flows down a bundle of synthetic cables of small diameter(Figure I ). In most cases the gas is blown in cross-flow to the liquid though, in some applications. it may flow counter-currently with it. Single and multi-staged scrubbers are made of standard modules (width 0.6 m, depth 0.5 m and height 2 m) packed side by side and one behind another in a casing. The dual-alkali process was selected for the Amazone plants because of its high efficiency and its particular ability to prevent scaling in the scrubbers. A full description of this process is given in the literatureTex. The scrubbing liquid is an aqueous solution of sodium sulphite in which bisulphite is formed as sulphur dioxide is absorbed: NaSO?
+ SO? + H20 = 2NaHS0,
(1)
The absorbent flows out of the scrubber at pH 6.5-7. It is then regenerated in a separate reactor with lime or limestone: 2NaHS0,
+ Ca(OH),
-_* Na2S03 + CaSO,
. 0.5Hz0
+ 1.5HZ0
(2)
and produces a precipitate of calcium sulphite, which is generally oxidized to gypsum. Some oxidation of sulphite to sulphate occurs in the scrubber due to residual oxygen in the flue gas: Na,SO,
+ 0.50, + Na2S03
(3)
The sodium bound to S(Vl) is lost as reactant and is called ‘inactive’ sodium. In the concentrated active alkali mode. the sulphate ions can be removed from the solution by coprecipitation of calcium sulphate with calcium sulphite in the regenerator. The design of the Amazone scrubber requires knowledge of equilibrium contents and absorption rates of sulphur dioxide into sodium sulphite solutions.
Calculation of the equilibrium pressure sulphur dioxide over sulphite-bisulphite solutions The equilibrium sulphite-bisulphite law:
of
pressures of sulphur dioxide over the solutions were obtained by Henry’s (4)
PCob?= H[SO?I in which
Liquid
(5)
H = HOYSO, Rabe and Harris” gave the solubility water:
coefficient
H,, = exp(9.3795 - 2851.1/T)
for pure
(6)
and the activity coefficient of dissolved sulphur dioxide was estimated from the salting-out parameter determined by Hikita et al. “’ logyso~ = 0.0741
Bundle of cables
(7)
The concentration of free sulphur dioxide dissolved in the liquid was computed from pH and total S(W) by means of a model describing the equilibria between ionic and non-ionic species in the solution. together with electroneutrality and mass balance. The two dissociation constants of the sulphurous acid used in this model are taken from Johnstone and Leppla” and Naumov”. respectively: K, = exp( 1972.5/T - 10.967)
(8)
Kz = exp(3.523 - 2433.8/T - 0.0399967)
(9)
The dissociation constants of water and bisulphate ions are also taken from Naumov”. The activity coefficients of individual ions are estimated by modified Debye-Htickel laws: _[I/’
log yi = z4(T)Z;
Figure 1
126
Et Purification
+ c,+
1
in which ,4(T) and B(T) are functions of temperature as given in standard books”. The specific parameters Cji and C4i for the ions are taken from the Bechtel-Radian programme (see Table 1).
Standard Amazone module
Gas Separation
1 + B(T)CJ”
1992
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SO, absorption into Na2S03 solutions in a cable contactor: P. Lorent et al.
Table 1
Parameters of the modified Debye-HCickel equation
H+ OHHSO; so;HSO; so:-
G,
c‘?,
6 3 4.5 4.5 3 3
0.4 0.3 : 0.3 0
The activity coefficients of the non-ionic species are related to the ionic strength in this programme by logy, = U,I
(11)
in which Ui is an expe~mental constant, equal to 0.076 for sulphur dioxide. This value confirms that given by Hikita et al. “’ To check the validity of this model. the solubiiities of sulphur dioxide in water and in two solutions containing 0.225 mol Na,SO, kg-’ and either 0 or 0.225 mol Na,SO, kg-’ were determined at 20°C and increasing pressures up to I atmi4. Pressures of sulphur dioxide were measured with a strain-gauge probe and equilibrium quantities of sulphur dioxide absorbed determined by a volumetric method. Figure2 shows that.except for high S(IV)contents in water, there is a very good agreement between experimental and calculated values. Hence. we may infer that the Debye-Htickel model allows a more than adequate description of the ionic interactions in that range of concentrations.
Desulphurizstion in a single-cable laboratory absorber To study mechanisms and obtain kinetic data required for the design of Amazone scrubbers, absorption rates of sulphur dioxide in sodium sulphite-bisulphite solutions were measured in a small single-cable laboratory absorber.
Figure 3
Experimental equipment
The experimental equipment is shown in Figure 3. The absorption column is an insulated vertical glass tube of small diameter (20 mm) in the axis ofwhich is stretched a single twisted polyester yarn (with a diameter equal to 1.45 mm) identical to those used in standard Amazone absorbers. The height of this micro-contactor is 0.95 m. The absorbent solution is fed to the top distributing chamber with a small pump. The liquid flowing down the cable is collected at the bottom in a small stainless steel tube and comes out by overflowing. The gas phase is nitrogen, humidified in a saturator, in which sulphur dioxide is added to obtain concentrations of about 1200 ppm. To prevent any oxidation of the solution. the absorbent vessel and the collecting flask are flushed out continuously with nitrogen. Inlet and outlet gas concentrations are measured with a Beckman model 880 non-dispersive infrared analyser. Iodometric titration is used to determine the total S(W) contents of the liquids, simultaneously with pH measurement, Apparent overall gas-phase mass transfer coefficients are computed as follows: G
Yi -.I?
(12)
Kci = Pndh (y - y*),,,, The diameter
A Water 0.4 -
sheath
around
the yarn
d = 2(R + s)
0 Sulphite
(13)
is calculated from the liquid film thickness, correlation of Lefebvre et af. Is
D Sulphite-suiphate
‘;‘
of the liquid
given by the
0.3-
(14)
$
Experimental
0
0.2
0.4 S02T
0.6 (mol
kg-’
0.8
1.0
1 2
water)
Figure 2 Solubiiities of sulphur dioxide in water and solutions of 0.225 molal sodium sulphite and 0.225 molal sodium sulphite/ 0.225 molal sodium sulphate mixture: lines, calculated; symbols, experimental
results
Experiments were made at room temperature for three liquid flow rates on the cable, four gas velocities and different vaiues of pH of the absorbent. Solutions of various pH were prepared by absorbing gaseous sulphur dioxide into sodium sulphite solutions. Sodium hydroxide solutions (I mol kg-‘) were also used. All the runs were made with a sodium concentration of to that used in the about 0.45 mol kg-‘, corresponding Amazone dual-alkali pilot plant. The overall gas mass transfer coefficients K’, are presented in Figures 4-6 for the three liquid flow rates investigated. It can be seen that they are increasing
Gas Separation
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1992
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SO2 absorption into l&SO, 1.0
‘;
sohtions
in a cable contactoc P. Lorent et al,
v(ms-‘) 0 1.0
0.7 9
u) z 2
0.6
a.41
5
6
7
I 8
9 Mean
Figure4 Evolution of (L = 0.18 X 10-s m3 s-l)
KG
10
1 11
12
I 13
1 14
pH
with
PH
and
gas
velocity
functions of pH and gas velocity. As the coefficients KC; obtained al highest pH values{ 13.6)with sodium hydroxide solutions are obviously the gas film mass transfer coefficients kf,, it can be noted that the ratio KC,lk,,, giving the contribution of the gas film resistance. increases with pH. This ratio is very high and reaches about 95% at pH 7, revealing that the absorption of sulphur dioxide into sodium sulphite solutions of experimental concentration in the cable contactor is mainly controlled by gas-phase diffusion. The liquid-phase resistance has only a significant influence at lower than pH 6-6.5. The rise of liquid flow rate. at constant gas velocity, also increasesthe overall mass transfer coefficient, as shown in F&O-~ 7. The increase of outer liquid velocities on the cable due to higher flow rates thus enhances turbulence in the gas phase. The influences of pH. gas velocity and liquid flow rate were well depicted by the following regression correlation: Kc, = 0.57 pH” 12+I.&(~~“~)“.‘” (15)
in the range 5.5 < pH < 9, with a mean relative deviation of 2%. Determination
of enhancement
factors
The chemical reaction in liquid phase between absorbed sulphur dioxide and sulphite ions enhances the absorption rate. If the enhancement factor is assumed to remain constant along the cable. it can be calculated from the classical relation E 0.6r”
0
0.5
v(ms-‘)
0.4 5
Figure 6 (L = 0.35
L 6
7
I 9
10
Mean
pH
8
Evolution of X 10F6 m3 sc’)
(16)
0
”
ou
KG
with
1.0
I v
1.5
A
2.0
t 0
2.5 , 12
11
pH
and
gas
I 13
14
velocity
This requires knowledge of both gas and liquid film mass transfer coefficients kG and k,_ for physical absorption under the same conditions. Gas-side mass transfer coefficients were obtained by absorption runs made with I molal sodium hydroxide solutions. The reaction between sufphur dioxide and hydroxyl ions OH- is an instantaneous irreversible reaction. Referring to the two-film model. the liquid mass transfer resistance is completely cancelled in this case if the reactant concentration lies above a minimum value’!
9
7
cl L
0.8
‘;” _EO71.
,1
I
4
2 a.6 -
E)
n
cl”
z
v(m se’)
QV 0.5
0.4.
5
1 6
7
1
,
8
9 Mean
0
1.0
v
1.5
a
2.0
0
2.5
I 10
11
12
13 7
pH
8
9 Mean
Figure 6 EvokJtion of (L = 0.52 X 10e6 m3 a-+)
KG
728
8 Purification
Gas Separation
with
pH
and
gas
10
11
12
13
pH
velocity Figure 7
1992 Vol 6 No 3
Effect of the liquid flow rate on KG (v = 2 m s-+)
14
SO2 absorption into Na.$O, 1.01
solutions in a cable contactor: P. Lorent et al.
250
1
200-
7; :0.6-
2
;
::I 50
Y
0 0
0.5-
I
i.0 0.41 0
0.1
0.2
0.3
0.4
0.5
7.0
101 =
h.
co,. JDso,.
in which. according
8.5
I
9.0
Enhancement factors (v = 2 m s-l)
Fa = , ,O9 PH’.” “0 77 (
lOhL)-“.“?
(21)
(17)
\o,l&o>.
wj2’j
(18)
to Hikita et al.“’
r,,,lDsox u ) = -0.1291HS0,
I
Theoretical
(20)
mechanisms
and discussion
To explain the observed variations, theoretical expressions of the enhancement factor must be considered. In the range pH 7-10. equilibrium computations give negligible concentrations of physically dissolved sulphur dioxide in the solution. The global reaction in the liquid phase SO, + SO;- + H20 -t 2HS0,
(22)
is considered to be instantaneous and irreversible’” and takes place in a reaction plane. For the film model, the enhancement factor is given by
(19)
kL = 0.175 x IO-“( IO’L.)“”
Fa
=
,
+
Dsoj- PO:-1I
(23)
IS021 i
402
At lower pH. the reaction steps are hydrolysis of absorbed SO2 followed by proton transfer to the sulphite ion:
0*14*
SO2 + H,O = HSO,
0.12
+ H+
(24)
H+ + SO;- = HSO,
2 m 0.08 I 2 x 0.06 A * 0.04
v(ms-') a v
0.02
(25)
These reactions are considered to be instantaneous and reversible and the overall reaction is still represented by Equation (22). written now in a reversible way. The absorption rates can be predicted by the theory of mass transfer with instantaneous reversible reaction17. lx. The enhancement factor given by the film theory can be writtenI as
0.10
1.0 1.5
D Fa = I + 0.5 2
[HSO,], - [HSOY], Iso21i
0.1
0.2 L (x
10-Y?
0.4
0.5
0
s-1)
Liquid-film mass transfer coefficients
-
Iso?ll
or Fa=l+-
Figure 9
8.0
Enhancement factors are presented in Figure 10 for a constant gas velocity (2 m s-l). For all runs. these factors are very high. in the range 60 to 300. which confirms the low values of the liquid mass transfer resistance. Enhancement factors increase with pH. gas velocity and decreasing liquid flow rate. as shown by the correlation
The coefficient k, does not depend on the gas velocity. It increases with the liquid flow rate on the cable (Figure 9) as
0
7.5
Gas-film mass transfer coefficients
The strong influence of the liquid velocity. as well as the low exponent of v, is due to the flow regime occurring in the gas phase, the Reynolds number varying in the range 1200-3000 as the gas velocity increases from I to 2.5 m SC’. Liquid-phase mass transfer coefficients were estimated by absorbing pure carbon dioxide in water. They were corrected with diffusion coefficients as follows:
"
6.5
1
Mean pH Figure 10
k,; = 0.75 ““.Jh(lrjhL)“.‘4
WD,,,.
6.0
s
1
Experiments made with increasing sodium hydroxide concentrations showed that the critical concentration is lower than 0.5 mol kg-‘. The gas tilm mass transfer coefficients. given in Figure& increase with the gas velocity and the liquid flow rate according to the correlation
k L so:.
5.5
0.6
L (x 1o-6 In3 5-'I
Figure 8
m 0.18 0.35 0.52
A
Dsoi- ISOf40,
Gas Separation
[WI
- [SO:-]i i -
& Purification
I%1
(26)
I
1992
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129
SO2 absorption into NasO,
solutions in a cable contactor: P. Lorent et al.
A rise in pH or liquid molarityincreases the concentration of sulphite ion in the bulk liquid [SO:-] , and consequently leads to an increase of the enhancement factor. as shown by Equations (23) and (26). The relative influences of gas velocity and liquid flow rate on [SOzli at the interface and Fu are more complex. Both parameters increase simultaneously the overall mass transfer rate and the gas-side transfer coefficient. and the liquid flow rate greatly increases the liquid film coefficient. It appears from our results that the enhancement effect due to the chemical reaction is lower at higher liquid flowrates, which seems reasonable because of the decrease of the diffusional resistance in the liquid. The experimental mass transfer coefficients KG were then compared with transfer coefficients calculated by means of the two-film theory of Danckwerts for absorption with instantaneous chemical reactionIh. For that purpose. a program was written to compute by finite differences the evolution of concentrations along the cable contactor. Equations were derived to calculate the absorption rate of sulphur dioxide in each elemental volume of the contactor, taking into account the reaction (22) and assuming that equilibrium between gas and liquid is reached at the interface and also between all dissolved species everywhere in the liquid. These rate equations depend on the local pH of the liquid: for 7 < pH < IO (irreversible
reaction) (27)
wth 40: < kcpso, for 3 < pH < 7 (reversible N SO:
=
reaction)
k,(ISOzli- [SO?ll) ’+
[SO,]i”
[SO*],
x{;E+,(T+~)l”‘-B-;}] in which K = K,IK, (22)
(28)
[SO,]i = (pso?- &,&k~)lH is the equilibrium
constant
of the reaction
I
Figure 11 Overall mass transfer coefficients (V = 2 m s-l): lines, calculated; symbols, experimental
transfer coefficients (continuous curves) together with experimental ones, for a typical gas velocity. Similar graphs were obtained for other gas flow rates. Though the differences are small. it can be seen that the theoretical coefficients are somewhat higher than the experimental values and that they decrease more slowly with pH. These deviations are confirmed by the higher values of the enhancement factor computed by the simulation program according to the model (Equations (23) and (26)). The assumption that the chemical reaction (22) is not really infinitely rapid may be proposed to explain the discrepancy between observed and theoretical mass transfer coefficients. Nevertheless. as the gas-phase mass transfer resistance is a main fraction of the total transfer resistance. the deviations in overall K,; never exceed 4% and the agreement between predicted values and experimental results appears to be good, as shown in Figure 12.
Heights of transfer scrubber
units of Amazone
By using the correlation (15) for overall mass transfer coefficients and the interfacial area calculated from
A = nK[SO,]i B = :(K[SO,],[SO;-],)” The ratios of diffusion et al. “: 3Dsoz- = 0.614 D SO?
coefficients
were taken from Hikita
D ,,, = x = 0.705 D so2
D n = HSOl = 1.15 Dso;Equation (28) was solved by trial and error simultaneously with equilibrium calculations. For every experimental condition, a theoretical simulation of sulphur dioxide absorption was made by means of this model and a mean overall mass transfer coefficient was then derived from Equation (12). Figure I1 shows the evolution of the theoretical mass
130
Gas Separation
8 Purification
1992
Vol 6 No 3
Calculated
Figure 12 Comparison values of KG
KC
(mot s-’
between
me2 bar-’
experimental
)
and calculated
SO, absorption into NasO,
”
,.lC
(m
s-1)
I
2.5
l.O-
solutions in a cable contactor: P. Lorent et al.
range of low contents, which are likely to increase the liquid film resistance and give more accuracy to the enhancement factors. It w-ill also be worthwhile investigating the possible effect of sodium sulphate on the absorption rate of sulphur dioxide.
2.0 z -”
References
0.9 -
P
I
1.5 0.8 -
2
0.7 -
3
1 .o 0.61
7
6
0 Mean
9
I 10
4
pH
5 Figure 13
Heights of transfer units of Amazone scrubber 6
Equations (13) and (14) and the number of cables per square metre of horizontal cross section. heights of transfer units of standard Amazone modules were estimated as follows: Ho,; = 2.0, pH-“r?
“054
L,“’
7
(29)
They are presented in Figure 13 for the more usual superficial liquid flow rate L, = 33 mi h-’ rn-?. Desulphurization efficiencies measured on the three-stage Amazone scrubber in the dual-alkali pilot plant at pH 6.5-7 and for gas velocities ranging from 0.6 to I .X m s-’ confirmed the validity of this correlation.
Conclusions This experimental investigation of sulphur dioxide absorption into sodium sulphite-bisulphite solutions in a cable contactor showed that the operation is mainly controlled by the gas-phase mass transfer. Enhancement factors due to the chemical reaction in the liquid are very high in the pH range 6-9. for a sodium concentration of 0.45 mol kg-‘. which strongly decreases the liquid film transfer resistance. Overall mass transfer coefficients increase with the gas velocity and the liquid flow rate and slowly with the pH. Simulation of the experiments according to the two-film model for absorption accompanied by an instantaneous reaction allowed the computation of mass transfer coefticients that are in good agreement with measured ones. though a little higher. Further work will be done to study the influence ofthe sodium concentration in the sorbent. especially in the
8 9
Met-tick, D. and Vernon, J. Review of flue gas desulphurisation systems Chemhmty and fndustn, (6 February 1989) 55-58 Lorent, P., Gerard, P. and Vanderschuren, J. Flue gas desulphurisation by the Amazone dual-alkali process 4&h Canad Chem Enp Conf Halifax (I S-21 Julv 1990) Lefebvre, S. and A.K.Z.O. SA Procede etappareillage pour la mise en contact de fluides et le transfert de matiere et de chaleur entre ceux-ci Belgian Parents 758.570 (1970) and 767.730 (1971) Lefebvre, S. and A.K.Z.O. SA Process and device for contacting two or more continuously flowing fluids Brirish Patent 1363523 (21 October 1971) Kaplan, N. Sodium/calcium double alkali systems TheMcIlvaine Scrubber Manual (1985) Vol IV. 7-78. 156.01-156.06 Epstein. M. EPA alkali scrubbing test facilitv: Summary of testing through October 1974 EPiRep @O/2-75-047 Bechtel Cornoration. NTIS. US Deot of Commerce (June 1975) La Mantia, C.R., Lunt, R.*R., Oberholtzer,XJ.E., Field, E.L. and Valentine, J.R. Final report dual alkali test and evaluation program: Vol 1 Executive Summary EPA Rep 600/7-77-050 a (1977) 45pp: Vol II Laboratory and pilot plant program EPA Rep 600/7-77%0 6 (1977) 678pp: Vol~111 Prototype-test program nlant EPA Reo @O/7-77-050 c (19771 163~~ Van Den B&eke, W.F., Kettdlarij; A. and Lefers, J.B. The double-alkali gypsum flue-gas desulphurisation process Kema Sci Tech Reps (1988) 6 163-I 78 Rabe, A.E. and Harris, J.F. Vapour-liquid equilibrium data for the binary system sulphur dioxide and water J Chem Eng Data (1963) 8 333-336
Hikita, H., Asai, S. and Tsuji, T. Absorption of sulphur dioxide into aqueous sodium hydroxide and sodium sulphite solutions AIChE J (1977) 23b 538-544 H.F. and Leppla, P.W. The solubility of II Johnstone, sulphur dioxide at low pressures. The ionization constant and heat of ionization of sulphurous acid J Am Chem Sot (1934) 56 2233 B.N. and Kbodakorsky, I.L. 12 Naumov, G.B., Ryzhenko, Handbook ofThermo&namic Data NTIS. US Dept of Commerce (1974) 257-259 13 Robinson, R.A. and Stokes, R.H. Electrol_vte Solutions 2nd Edn. Butterworths. London (1959) I4 Frere, M., Lorent, P., Jadot, R., Gerard, P. and Vanderschuren, J. Equilibrium contents of sulphur dioxide absorbed into Na,SO,-Na,SO, aqueous solutions Fluid Phase Equilibtia (submitted April 1992) IS Lefebvre, S., Vanderschuren, J., Verheve, D. and Onyejekwe, F. Hydrodynamic characteristics of the flow of thin cylindrical liquid films on vertical solid support Chem Ig Technik (1979) 51 Ill
330-331
16 I7 18
Danckwerts, P.V. Gas-Liquid Reuctions McGraw-Hill. New York (1970) Chang, C.S. and Rochelle, G.T. SO, absorption into aqueous solutions AIChE .I (1981) 27 292-298 Van Den Broeke,‘W.F: and Lefers, J.B. Absorption of SO, into Na,SO,/NaHSO, solutions Electrotechniek (1983) 61 48-51
Gas Separation
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Keywords: flue gas desulphurization; SO2 absorption; sodium sulphite; cable contactor
Nomenclature Ar d D~ Fa G h H H0 Ht~; I K K~ K2 kG K~;
kL L m n
Archimedes number = (2R)3g/v 2 Diameter of the liquid sheath around the yarn (m) Diffusivity of component i (m 2 s -I ) Enhancement factor Gas flow rate (mol s -I) Height of the contactor (m) Henry's law constant (atm kg mol -t) Solubility coefficient of sulphur dioxide in water (atm kg tool -I) Height of a transfer unit (m) Ionic strength (mol kg -~) Equilibrium constant of reaction (22) Dissociation constant (mol kg -I) = [H+I IHSO;I/IH2SOd Dissociation constant (mol kg -I) =
Nso, P Pso, P~o~ R Re s SO,T T v Yl,Y2 y* Zi
IH+I ISO~-I/IHSO;!
[I
Gas-phase mass transfer coefficient (tool s -j m -2 bar -t ) Apparent overall gas mass transfer coefficient (mol s -t m --~ bar -I) Liquid-phase mass transfer coefficient (m s -I) Liquid flow rate on the cable (m -~s -t) Dttso~/Dso~ D.so;/Dso~-
?'i
Introduction The steadily increasing severity of the European regulations for emission of sulphur dioxide from combustion plants provides a growing need for purification units for flue gases.
0950-4214/92/030125-07 © 1992 Sutterworth-HeinemannLtd
v
Flux of sulphur dioxide (mol s -~ m--') Total pressure (bar = 105 Pa) Partial pressure of sulphur dioxide (bar) Equilibrium pressure of sulphur dioxide (bar) Radius of the cable (m) Liquid Reynolds number = 4L/2nRv Liquid sheath thickness (m) Total S(IV) = [SO_,] + IHSO;I + lSO~-I Temperature (K) Gas velocity ( m s -I) Inlet and outlet molar fraction of sulphur dioxide in the gas Equilibrium molar fraction of sulphur dioxide Ion valency Molality (mol kg -I) Activity coefficient of component i Kinematic viscosity (m-" s -I)
Subscripts i Gas-liquid interface w Water I Bulk solution Im Logarithmic mean sol Absorbent solution
The most widely used methods for flue gas desulphurization ~ are the limestone wet scrubbing process, spraydry scrubbing systems operating with slaked lime, the Wellman-Lord process using sodium sulphite regenerable by heat treatment and the dual-alkali process in which the sorbent is also a sodium sulphite solution.
Gas Separation 8" Purification 1 9 9 2 Vol 6 No 3
125
SO2 absorption into Na$TO, solutions in a cable contactor: P. Lorent et al. Two plants, a commercial plant (capacity 60 000 NmZ h-’ ) and a large pilot plant (capacity 26 000 NmZ h-‘). both equipped with a three-stage cable-bundle scrubber (Amazonem), were recently started in Belgium for cleaning the gaseous effluents of a garbage combustor and an oiltiled boile?. Desulphurization is achieved by the dual-alkali process running in the dilute mode. with sodium carbonate softening, in the first unit and in the concentrated mode in the second. Amazone is a gas-liquid contactor. patented first in Belgium in 19702 and later in 21 other countries including the UK4, in which the liquid flows down a bundle of synthetic cables of small diameter(Figure I ). In most cases the gas is blown in cross-flow to the liquid though, in some applications. it may flow counter-currently with it. Single and multi-staged scrubbers are made of standard modules (width 0.6 m, depth 0.5 m and height 2 m) packed side by side and one behind another in a casing. The dual-alkali process was selected for the Amazone plants because of its high efficiency and its particular ability to prevent scaling in the scrubbers. A full description of this process is given in the literatureTex. The scrubbing liquid is an aqueous solution of sodium sulphite in which bisulphite is formed as sulphur dioxide is absorbed: NaSO?
+ SO? + H20 = 2NaHS0,
(1)
The absorbent flows out of the scrubber at pH 6.5-7. It is then regenerated in a separate reactor with lime or limestone: 2NaHS0,
+ Ca(OH),
-_* Na2S03 + CaSO,
. 0.5Hz0
+ 1.5HZ0
(2)
and produces a precipitate of calcium sulphite, which is generally oxidized to gypsum. Some oxidation of sulphite to sulphate occurs in the scrubber due to residual oxygen in the flue gas: Na,SO,
+ 0.50, + Na2S03
(3)
The sodium bound to S(Vl) is lost as reactant and is called ‘inactive’ sodium. In the concentrated active alkali mode. the sulphate ions can be removed from the solution by coprecipitation of calcium sulphate with calcium sulphite in the regenerator. The design of the Amazone scrubber requires knowledge of equilibrium contents and absorption rates of sulphur dioxide into sodium sulphite solutions.
Calculation of the equilibrium pressure sulphur dioxide over sulphite-bisulphite solutions The equilibrium sulphite-bisulphite law:
of
pressures of sulphur dioxide over the solutions were obtained by Henry’s (4)
PCob?= H[SO?I in which
Liquid
(5)
H = HOYSO, Rabe and Harris” gave the solubility water:
coefficient
H,, = exp(9.3795 - 2851.1/T)
for pure
(6)
and the activity coefficient of dissolved sulphur dioxide was estimated from the salting-out parameter determined by Hikita et al. “’ logyso~ = 0.0741
Bundle of cables
(7)
The concentration of free sulphur dioxide dissolved in the liquid was computed from pH and total S(W) by means of a model describing the equilibria between ionic and non-ionic species in the solution. together with electroneutrality and mass balance. The two dissociation constants of the sulphurous acid used in this model are taken from Johnstone and Leppla” and Naumov”. respectively: K, = exp( 1972.5/T - 10.967)
(8)
Kz = exp(3.523 - 2433.8/T - 0.0399967)
(9)
The dissociation constants of water and bisulphate ions are also taken from Naumov”. The activity coefficients of individual ions are estimated by modified Debye-Htickel laws: _[I/’
log yi = z4(T)Z;
Figure 1
126
Et Purification
+ c,+
1
in which ,4(T) and B(T) are functions of temperature as given in standard books”. The specific parameters Cji and C4i for the ions are taken from the Bechtel-Radian programme (see Table 1).
Standard Amazone module
Gas Separation
1 + B(T)CJ”
1992
Vol 6 No 3
SO, absorption into Na2S03 solutions in a cable contactor: P. Lorent et al.
Table 1
Parameters of the modified Debye-HCickel equation
H+ OHHSO; so;HSO; so:-
G,
c‘?,
6 3 4.5 4.5 3 3
0.4 0.3 : 0.3 0
The activity coefficients of the non-ionic species are related to the ionic strength in this programme by logy, = U,I
(11)
in which Ui is an expe~mental constant, equal to 0.076 for sulphur dioxide. This value confirms that given by Hikita et al. “’ To check the validity of this model. the solubiiities of sulphur dioxide in water and in two solutions containing 0.225 mol Na,SO, kg-’ and either 0 or 0.225 mol Na,SO, kg-’ were determined at 20°C and increasing pressures up to I atmi4. Pressures of sulphur dioxide were measured with a strain-gauge probe and equilibrium quantities of sulphur dioxide absorbed determined by a volumetric method. Figure2 shows that.except for high S(IV)contents in water, there is a very good agreement between experimental and calculated values. Hence. we may infer that the Debye-Htickel model allows a more than adequate description of the ionic interactions in that range of concentrations.
Desulphurizstion in a single-cable laboratory absorber To study mechanisms and obtain kinetic data required for the design of Amazone scrubbers, absorption rates of sulphur dioxide in sodium sulphite-bisulphite solutions were measured in a small single-cable laboratory absorber.
Figure 3
Experimental equipment
The experimental equipment is shown in Figure 3. The absorption column is an insulated vertical glass tube of small diameter (20 mm) in the axis ofwhich is stretched a single twisted polyester yarn (with a diameter equal to 1.45 mm) identical to those used in standard Amazone absorbers. The height of this micro-contactor is 0.95 m. The absorbent solution is fed to the top distributing chamber with a small pump. The liquid flowing down the cable is collected at the bottom in a small stainless steel tube and comes out by overflowing. The gas phase is nitrogen, humidified in a saturator, in which sulphur dioxide is added to obtain concentrations of about 1200 ppm. To prevent any oxidation of the solution. the absorbent vessel and the collecting flask are flushed out continuously with nitrogen. Inlet and outlet gas concentrations are measured with a Beckman model 880 non-dispersive infrared analyser. Iodometric titration is used to determine the total S(W) contents of the liquids, simultaneously with pH measurement, Apparent overall gas-phase mass transfer coefficients are computed as follows: G
Yi -.I?
(12)
Kci = Pndh (y - y*),,,, The diameter
A Water 0.4 -
sheath
around
the yarn
d = 2(R + s)
0 Sulphite
(13)
is calculated from the liquid film thickness, correlation of Lefebvre et af. Is
D Sulphite-suiphate
‘;‘
of the liquid
given by the
0.3-
(14)
$
Experimental
0
0.2
0.4 S02T
0.6 (mol
kg-’
0.8
1.0
1 2
water)
Figure 2 Solubiiities of sulphur dioxide in water and solutions of 0.225 molal sodium sulphite and 0.225 molal sodium sulphite/ 0.225 molal sodium sulphate mixture: lines, calculated; symbols, experimental
results
Experiments were made at room temperature for three liquid flow rates on the cable, four gas velocities and different vaiues of pH of the absorbent. Solutions of various pH were prepared by absorbing gaseous sulphur dioxide into sodium sulphite solutions. Sodium hydroxide solutions (I mol kg-‘) were also used. All the runs were made with a sodium concentration of to that used in the about 0.45 mol kg-‘, corresponding Amazone dual-alkali pilot plant. The overall gas mass transfer coefficients K’, are presented in Figures 4-6 for the three liquid flow rates investigated. It can be seen that they are increasing
Gas Separation
& Purification
1992
Vol 6 No 3
127
SO2 absorption into l&SO, 1.0
‘;
sohtions
in a cable contactoc P. Lorent et al,
v(ms-‘) 0 1.0
0.7 9
u) z 2
0.6
a.41
5
6
7
I 8
9 Mean
Figure4 Evolution of (L = 0.18 X 10-s m3 s-l)
KG
10
1 11
12
I 13
1 14
pH
with
PH
and
gas
velocity
functions of pH and gas velocity. As the coefficients KC; obtained al highest pH values{ 13.6)with sodium hydroxide solutions are obviously the gas film mass transfer coefficients kf,, it can be noted that the ratio KC,lk,,, giving the contribution of the gas film resistance. increases with pH. This ratio is very high and reaches about 95% at pH 7, revealing that the absorption of sulphur dioxide into sodium sulphite solutions of experimental concentration in the cable contactor is mainly controlled by gas-phase diffusion. The liquid-phase resistance has only a significant influence at lower than pH 6-6.5. The rise of liquid flow rate. at constant gas velocity, also increasesthe overall mass transfer coefficient, as shown in F&O-~ 7. The increase of outer liquid velocities on the cable due to higher flow rates thus enhances turbulence in the gas phase. The influences of pH. gas velocity and liquid flow rate were well depicted by the following regression correlation: Kc, = 0.57 pH” 12+I.&(~~“~)“.‘” (15)
in the range 5.5 < pH < 9, with a mean relative deviation of 2%. Determination
of enhancement
factors
The chemical reaction in liquid phase between absorbed sulphur dioxide and sulphite ions enhances the absorption rate. If the enhancement factor is assumed to remain constant along the cable. it can be calculated from the classical relation E 0.6r”
0
0.5
v(ms-‘)
0.4 5
Figure 6 (L = 0.35
L 6
7
I 9
10
Mean
pH
8
Evolution of X 10F6 m3 sc’)
(16)
0
”
ou
KG
with
1.0
I v
1.5
A
2.0
t 0
2.5 , 12
11
pH
and
gas
I 13
14
velocity
This requires knowledge of both gas and liquid film mass transfer coefficients kG and k,_ for physical absorption under the same conditions. Gas-side mass transfer coefficients were obtained by absorption runs made with I molal sodium hydroxide solutions. The reaction between sufphur dioxide and hydroxyl ions OH- is an instantaneous irreversible reaction. Referring to the two-film model. the liquid mass transfer resistance is completely cancelled in this case if the reactant concentration lies above a minimum value’!
9
7
cl L
0.8
‘;” _EO71.
,1
I
4
2 a.6 -
E)
n
cl”
z
v(m se’)
QV 0.5
0.4.
5
1 6
7
1
,
8
9 Mean
0
1.0
v
1.5
a
2.0
0
2.5
I 10
11
12
13 7
pH
8
9 Mean
Figure 6 EvokJtion of (L = 0.52 X 10e6 m3 a-+)
KG
728
8 Purification
Gas Separation
with
pH
and
gas
10
11
12
13
pH
velocity Figure 7
1992 Vol 6 No 3
Effect of the liquid flow rate on KG (v = 2 m s-+)
14
SO2 absorption into Na.$O, 1.01
solutions in a cable contactor: P. Lorent et al.
250
1
200-
7; :0.6-
2
;
::I 50
Y
0 0
0.5-
I
i.0 0.41 0
0.1
0.2
0.3
0.4
0.5
7.0
101 =
h.
co,. JDso,.
in which. according
8.5
I
9.0
Enhancement factors (v = 2 m s-l)
Fa = , ,O9 PH’.” “0 77 (
lOhL)-“.“?
(21)
(17)
\o,l&o>.
wj2’j
(18)
to Hikita et al.“’
r,,,lDsox u ) = -0.1291HS0,
I
Theoretical
(20)
mechanisms
and discussion
To explain the observed variations, theoretical expressions of the enhancement factor must be considered. In the range pH 7-10. equilibrium computations give negligible concentrations of physically dissolved sulphur dioxide in the solution. The global reaction in the liquid phase SO, + SO;- + H20 -t 2HS0,
(22)
is considered to be instantaneous and irreversible’” and takes place in a reaction plane. For the film model, the enhancement factor is given by
(19)
kL = 0.175 x IO-“( IO’L.)“”
Fa
=
,
+
Dsoj- PO:-1I
(23)
IS021 i
402
At lower pH. the reaction steps are hydrolysis of absorbed SO2 followed by proton transfer to the sulphite ion:
0*14*
SO2 + H,O = HSO,
0.12
+ H+
(24)
H+ + SO;- = HSO,
2 m 0.08 I 2 x 0.06 A * 0.04
v(ms-') a v
0.02
(25)
These reactions are considered to be instantaneous and reversible and the overall reaction is still represented by Equation (22). written now in a reversible way. The absorption rates can be predicted by the theory of mass transfer with instantaneous reversible reaction17. lx. The enhancement factor given by the film theory can be writtenI as
0.10
1.0 1.5
D Fa = I + 0.5 2
[HSO,], - [HSOY], Iso21i
0.1
0.2 L (x
10-Y?
0.4
0.5
0
s-1)
Liquid-film mass transfer coefficients
-
Iso?ll
or Fa=l+-
Figure 9
8.0
Enhancement factors are presented in Figure 10 for a constant gas velocity (2 m s-l). For all runs. these factors are very high. in the range 60 to 300. which confirms the low values of the liquid mass transfer resistance. Enhancement factors increase with pH. gas velocity and decreasing liquid flow rate. as shown by the correlation
The coefficient k, does not depend on the gas velocity. It increases with the liquid flow rate on the cable (Figure 9) as
0
7.5
Gas-film mass transfer coefficients
The strong influence of the liquid velocity. as well as the low exponent of v, is due to the flow regime occurring in the gas phase, the Reynolds number varying in the range 1200-3000 as the gas velocity increases from I to 2.5 m SC’. Liquid-phase mass transfer coefficients were estimated by absorbing pure carbon dioxide in water. They were corrected with diffusion coefficients as follows:
"
6.5
1
Mean pH Figure 10
k,; = 0.75 ““.Jh(lrjhL)“.‘4
WD,,,.
6.0
s
1
Experiments made with increasing sodium hydroxide concentrations showed that the critical concentration is lower than 0.5 mol kg-‘. The gas tilm mass transfer coefficients. given in Figure& increase with the gas velocity and the liquid flow rate according to the correlation
k L so:.
5.5
0.6
L (x 1o-6 In3 5-'I
Figure 8
m 0.18 0.35 0.52
A
Dsoi- ISOf40,
Gas Separation
[WI
- [SO:-]i i -
& Purification
I%1
(26)
I
1992
Vol6No3
129
SO2 absorption into NasO,
solutions in a cable contactor: P. Lorent et al.
A rise in pH or liquid molarityincreases the concentration of sulphite ion in the bulk liquid [SO:-] , and consequently leads to an increase of the enhancement factor. as shown by Equations (23) and (26). The relative influences of gas velocity and liquid flow rate on [SOzli at the interface and Fu are more complex. Both parameters increase simultaneously the overall mass transfer rate and the gas-side transfer coefficient. and the liquid flow rate greatly increases the liquid film coefficient. It appears from our results that the enhancement effect due to the chemical reaction is lower at higher liquid flowrates, which seems reasonable because of the decrease of the diffusional resistance in the liquid. The experimental mass transfer coefficients KG were then compared with transfer coefficients calculated by means of the two-film theory of Danckwerts for absorption with instantaneous chemical reactionIh. For that purpose. a program was written to compute by finite differences the evolution of concentrations along the cable contactor. Equations were derived to calculate the absorption rate of sulphur dioxide in each elemental volume of the contactor, taking into account the reaction (22) and assuming that equilibrium between gas and liquid is reached at the interface and also between all dissolved species everywhere in the liquid. These rate equations depend on the local pH of the liquid: for 7 < pH < IO (irreversible
reaction) (27)
wth 40: < kcpso, for 3 < pH < 7 (reversible N SO:
=
reaction)
k,(ISOzli- [SO?ll) ’+
[SO,]i”
[SO*],
x{;E+,(T+~)l”‘-B-;}] in which K = K,IK, (22)
(28)
[SO,]i = (pso?- &,&k~)lH is the equilibrium
constant
of the reaction
I
Figure 11 Overall mass transfer coefficients (V = 2 m s-l): lines, calculated; symbols, experimental
transfer coefficients (continuous curves) together with experimental ones, for a typical gas velocity. Similar graphs were obtained for other gas flow rates. Though the differences are small. it can be seen that the theoretical coefficients are somewhat higher than the experimental values and that they decrease more slowly with pH. These deviations are confirmed by the higher values of the enhancement factor computed by the simulation program according to the model (Equations (23) and (26)). The assumption that the chemical reaction (22) is not really infinitely rapid may be proposed to explain the discrepancy between observed and theoretical mass transfer coefficients. Nevertheless. as the gas-phase mass transfer resistance is a main fraction of the total transfer resistance. the deviations in overall K,; never exceed 4% and the agreement between predicted values and experimental results appears to be good, as shown in Figure 12.
Heights of transfer scrubber
units of Amazone
By using the correlation (15) for overall mass transfer coefficients and the interfacial area calculated from
A = nK[SO,]i B = :(K[SO,],[SO;-],)” The ratios of diffusion et al. “: 3Dsoz- = 0.614 D SO?
coefficients
were taken from Hikita
D ,,, = x = 0.705 D so2
D n = HSOl = 1.15 Dso;Equation (28) was solved by trial and error simultaneously with equilibrium calculations. For every experimental condition, a theoretical simulation of sulphur dioxide absorption was made by means of this model and a mean overall mass transfer coefficient was then derived from Equation (12). Figure I1 shows the evolution of the theoretical mass
130
Gas Separation
8 Purification
1992
Vol 6 No 3
Calculated
Figure 12 Comparison values of KG
KC
(mot s-’
between
me2 bar-’
experimental
)
and calculated
SO, absorption into NasO,
”
,.lC
(m
s-1)
I
2.5
l.O-
solutions in a cable contactor: P. Lorent et al.
range of low contents, which are likely to increase the liquid film resistance and give more accuracy to the enhancement factors. It w-ill also be worthwhile investigating the possible effect of sodium sulphate on the absorption rate of sulphur dioxide.
2.0 z -”
References
0.9 -
P
I
1.5 0.8 -
2
0.7 -
3
1 .o 0.61
7
6
0 Mean
9
I 10
4
pH
5 Figure 13
Heights of transfer units of Amazone scrubber 6
Equations (13) and (14) and the number of cables per square metre of horizontal cross section. heights of transfer units of standard Amazone modules were estimated as follows: Ho,; = 2.0, pH-“r?
“054
L,“’
7
(29)
They are presented in Figure 13 for the more usual superficial liquid flow rate L, = 33 mi h-’ rn-?. Desulphurization efficiencies measured on the three-stage Amazone scrubber in the dual-alkali pilot plant at pH 6.5-7 and for gas velocities ranging from 0.6 to I .X m s-’ confirmed the validity of this correlation.
Conclusions This experimental investigation of sulphur dioxide absorption into sodium sulphite-bisulphite solutions in a cable contactor showed that the operation is mainly controlled by the gas-phase mass transfer. Enhancement factors due to the chemical reaction in the liquid are very high in the pH range 6-9. for a sodium concentration of 0.45 mol kg-‘. which strongly decreases the liquid film transfer resistance. Overall mass transfer coefficients increase with the gas velocity and the liquid flow rate and slowly with the pH. Simulation of the experiments according to the two-film model for absorption accompanied by an instantaneous reaction allowed the computation of mass transfer coefticients that are in good agreement with measured ones. though a little higher. Further work will be done to study the influence ofthe sodium concentration in the sorbent. especially in the
8 9
Met-tick, D. and Vernon, J. Review of flue gas desulphurisation systems Chemhmty and fndustn, (6 February 1989) 55-58 Lorent, P., Gerard, P. and Vanderschuren, J. Flue gas desulphurisation by the Amazone dual-alkali process 4&h Canad Chem Enp Conf Halifax (I S-21 Julv 1990) Lefebvre, S. and A.K.Z.O. SA Procede etappareillage pour la mise en contact de fluides et le transfert de matiere et de chaleur entre ceux-ci Belgian Parents 758.570 (1970) and 767.730 (1971) Lefebvre, S. and A.K.Z.O. SA Process and device for contacting two or more continuously flowing fluids Brirish Patent 1363523 (21 October 1971) Kaplan, N. Sodium/calcium double alkali systems TheMcIlvaine Scrubber Manual (1985) Vol IV. 7-78. 156.01-156.06 Epstein. M. EPA alkali scrubbing test facilitv: Summary of testing through October 1974 EPiRep @O/2-75-047 Bechtel Cornoration. NTIS. US Deot of Commerce (June 1975) La Mantia, C.R., Lunt, R.*R., Oberholtzer,XJ.E., Field, E.L. and Valentine, J.R. Final report dual alkali test and evaluation program: Vol 1 Executive Summary EPA Rep 600/7-77-050 a (1977) 45pp: Vol II Laboratory and pilot plant program EPA Rep 600/7-77%0 6 (1977) 678pp: Vol~111 Prototype-test program nlant EPA Reo @O/7-77-050 c (19771 163~~ Van Den B&eke, W.F., Kettdlarij; A. and Lefers, J.B. The double-alkali gypsum flue-gas desulphurisation process Kema Sci Tech Reps (1988) 6 163-I 78 Rabe, A.E. and Harris, J.F. Vapour-liquid equilibrium data for the binary system sulphur dioxide and water J Chem Eng Data (1963) 8 333-336
Hikita, H., Asai, S. and Tsuji, T. Absorption of sulphur dioxide into aqueous sodium hydroxide and sodium sulphite solutions AIChE J (1977) 23b 538-544 H.F. and Leppla, P.W. The solubility of II Johnstone, sulphur dioxide at low pressures. The ionization constant and heat of ionization of sulphurous acid J Am Chem Sot (1934) 56 2233 B.N. and Kbodakorsky, I.L. 12 Naumov, G.B., Ryzhenko, Handbook ofThermo&namic Data NTIS. US Dept of Commerce (1974) 257-259 13 Robinson, R.A. and Stokes, R.H. Electrol_vte Solutions 2nd Edn. Butterworths. London (1959) I4 Frere, M., Lorent, P., Jadot, R., Gerard, P. and Vanderschuren, J. Equilibrium contents of sulphur dioxide absorbed into Na,SO,-Na,SO, aqueous solutions Fluid Phase Equilibtia (submitted April 1992) IS Lefebvre, S., Vanderschuren, J., Verheve, D. and Onyejekwe, F. Hydrodynamic characteristics of the flow of thin cylindrical liquid films on vertical solid support Chem Ig Technik (1979) 51 Ill
330-331
16 I7 18
Danckwerts, P.V. Gas-Liquid Reuctions McGraw-Hill. New York (1970) Chang, C.S. and Rochelle, G.T. SO, absorption into aqueous solutions AIChE .I (1981) 27 292-298 Van Den Broeke,‘W.F: and Lefers, J.B. Absorption of SO, into Na,SO,/NaHSO, solutions Electrotechniek (1983) 61 48-51
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8 Purification
1992
Vol 6 No 3
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