Ind. Eng. Chem. Res. 1989, 28, 870-873
870
COMMUNICATIONS Absorption of Carbonyl Sulfide in Aqueous Alkaline Solutions: New Strategies T h e absorption of carbonyl sulfide in aqueous alkaline solutions, containing toluene as a second emulsified liquid phase, was studied. T h e experimental results have been analyzed based on a n unsteady-state mass-transfer model. At a 20% (v/v) holdup of toluene, a n enhancement factor of 2.5 was obtained, which agrees well with the theoretical prediction. T h e use of an aqueous alkaline solution of 2-propanol (50%,w/w) enhanced the specific rate of absorption by a factor of 4, primarily due to the higher solubility in such a solution. The strategy of using an emulsified nonvolatile second liquid phase to intensify the specific rate of absorption of a sparingly soluble gas in liquid where it reacts was originally suggested by Sharma (1983). The suggested role of the second liquid phase was probed by Mehra and Sharma (1985) for the absorption of propylene, but-1-ene, and isobutylene into emulsions of chlorobenzene in aqueous solutions of sulfuric acid. Mehra et al. (1988) have given a comprehensive account of this subject and have analyzed experimental data on the basis of the unsteadystate mass-transfer model (Mehra, 1988). The present work was undertaken to examine the effect of a second emulsified liquid phase on the specific rates of absorption of carbonyl sulfide (COS) in aqueous alkaline solutions. Carbonyl sulfide is an undesirable impurity in a variety of industrial gases. The refinery and synthesis gases may also contain significant amount of COS. It is necessary to remove COS down to the ppm level for reasons of either catalyst sensitivity to COS in subsequent operations or statutory regulations. A common absorbent for COS, in the absence of C02, is an aqueous sodium hydroxide solution in which carbonyl sulfide is sparingly soluble. The reaction is as follows:
COS
+ 40H-
-
C 0 3 2 -+ S2- + H20
Therefore, absorption studies, using emulsified toluene as a second liquid phase, were carried out to assess the effect of the additional phase on the specific rates of absorption. It was also thought that aqueous alkaline solutions containing 2-propanol may prove to be useful in view of higher solubility in such solutions.
Experimental Section The specific rates of absorption of COS in emulsions of toluene in aqueous alkaline solutions were measured by m i.d. glass stirred cell the up-take method in a 9.5 X (Danckwerts, 1970). The effective gas-liquid interfacial m2. The solute gas was stored in a area was 59.8 X balloon a t atmospheric pressure after purification by passing through an aqueous caustic potash solution (40% w/w). The procedure for conducting any run was similar to that followed by Mehra and Sharma (1985). The fractional holdup of the dispersed liquid phase was varied from 0.1 to 0.2 (v/v, of the total liquid phase). Stable homogeneous emulsions were made by adding the desired amount of the aqueous alkaline solution, toluene, m i.d. mechanically and a selected emulsifier in a 9.5 X 0888-5885/89/2628-0870$01.50/0
agitated contactor. This was stirred vigorously at 25 rev/s for a period of 480 s. The emulsions thus obtained were milky white in appearance, and there was no change in the total liquid-phase volume upon emulsification. The prepared emulsions were stable even after the cessation of stirring for an extended period of about an hour. The emulsions thus obtained were used for the absorption of COS. Ultrasound was also used for emulsification, and the resulting emulsions were comparable in stability and average droplet size to those prepared by mechanical agitation. Sharma (1965) has reported a D (COS-water) value of 1.94 x m2/s at 25 "C; Versteeg and Van Swaaij (1988) have reported a D (C02-water) value of 2.22 X m2/s a t 30 "C. The diffusivity of COS in different aqueous solutions containing sodium hydroxide was corrected for the effect of viscosity using the Stokes-Einstein equation, Dp/T = constant. The value of the mass-transfer coefficient, k~ (2.85 X lo4 m/s), was obtained for the C02-water system a t 303 K using an 9.5 x m i.d. glass stirred cell a t 1.33 rev/s by previous workers in our laboratory. The value of 121, was corrected for the effect of viscosity and diffusivity when used for COS-NaOH and COS-2-propanol systems by multiplying the value of kL for C02-water by the following correlation:
The second-order rate constant, k2, of the COS-NaOH system was estimated in the present work from data on the specific rate of absorption of COS in aqueous NaOH at 30 OC; the vapor pressure of water was duly accounted for while computing the value of [A*]. The solubility data of COS in water have been reported (Seidell, 1941; Sharma, 1965). The solubility of COS in toluene and aqueous 2-propanol solutions was measured experimentally; the concentration of dissolved COS was determined iodometrically. The solubility of COS in electrolyte solutions was corrected based on data provided by Sharma (1964). For every run, it was ensured that no bubbles or foam remained a t the gas-liquid interface. The specific rate of absorption remained steady over a long period, exceeding 900 s, and successive runs gave reasonable reproducibility, with an average deviation of less than 5 %, as long as the conditions of emulsification were maintained. The droplet 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 871 Table I. Physicochemical Data: Absorption of COS at 30 OC" [BOIN~OH,
kmol/m3 0.10 0.10 0.25
NaC1, kmol/m3 4.0
109DA, m2/s 1.37 1.97 1.83
106kL, m/s 2.24 2.66 2.58
'Solubility of COS in water (1 atm) = 1.73 X
lo-'
1OZ[A*], kmol/m3 0.51 1.59 1.51
mA, &mol/ m3 mic)/ (kmol/m3 cont) 104 33 35
kz, m3/ (kmol s) 18.5 6.69 7.38
1O7RA, kmol/(m2 s) 2.69 7.12 9.60
kmol/m3; solubility of COS in toluene (1 atm) = 53.28 x
kl, s-l 1.85 0.669 1.845
kmol/m3.
Table 11. Experimental Enhancement Factor for the Absorption of COS in the Emulsion of Toluene in Aqueous Alkaline Solutionsn NaOH, NaCl, i07RA,exp, kmol/m3 kmol/m3 10 S surfactant kmol/(m2 s) 6A.aXo 6A.th 0.10 4.0 2.69 0.2 1 TWEEN-4Ob 6.73 2.50 2.19 0.10 4.0 0.10 4.0 0.1 1 TWEEN-40 4.16 1.55 1.71 7.12 0.10 0.10 0.2 1 LAE-7' 14.18 1.99 1.77 0.25 9.60 1 LAE-7 14.20 1.48 1.39 0.25 0.2
T = 30 f 1 "C; P = 1 atm; stirrer speed = 1.33 rev/s; V,, = 2.5 X lo4 m3; d, = 1 X lo4 m; a = 59.8 poly(oxy ethylene) sorbitan fatty acid. Lauryl alcohol ethoxylate (7 mol ethylene oxide/mol of alcohol).
X
lo4
mz. *Palmitate ester of
-
Table 111. Absorution of COS in Aaueous Alkaline Solution of 2-Prooanol" [BOINaOH~
solvent water aqueous 2-propanol (25%, w/w) aqueous 2-propanol (50%, w/w) aqueous 2-propanol (80%, w/w)
kmol/m3 0.25 0.25 0.25 0.25
109~, m2/s 1.83 1.65 1.37 1.10
T = 30 f 1 "C; P = 1 atm; stirrer speed = 1.33 rev/s; a = 22
X
size of the microphase was measured by an optical microscope. The average droplet size was l x lo4 m. The advantage of employing organic solvents containing dissolved NaOH for the removal of COS was also examined. For this purpose, aqueous 2-propanol was used as the solvent. All the experiments were carried out at room temperature (30 f 1 "C) and a t atmospheric pressure. The required materials were obtained from commercial firms. The COS gas cylinder was obtained from B.O.C. Ltd., U.K. Results and Discussion The experimental results are given in Tables 1-111. The results of absorption experiments in 1 M NaOH solution agree well with the pertinent data of Sharma (1965); the value of the second-order rate constant of 11.9 m3/(kmol s) at 30 "C may be compared with the value 12 m3/(kmol s) a t 25 "C reported by Sharma. Effect of Second Liquid Phase. The experimental results show that the specific rate of absorption increases with the suggested strategy. The enhancement factor, defined as the ratio of specific rate of absorption in the presence of the emulsified second liquid phase to that in its absence (base case), decreases with a reduction in the holdup of the second liquid phase. The extent of the enhancement decreases with an increase in the concentration of sodium hydroxide. These results are in consonance with the predictions. Experiments with only aqueous alkaline solutions containing the relevant emulsifer (that is, in the absence of the second liquid phase, toluene) did not show an increase in the specific rate of absorption. Thus, it appears that the effect of micelles on the specific rate of absorption is negligible, presumably due to low values of the distribution coefficient of COS between water and the micellar phase.
105kL, m/s 2.58 2.46 2.15 2.01 m2; V = 0.7
1OZ[A*], kmol/m3 1.51 3.52 6.78 8.11 X
10IRA,ex 7 kmol/(mB s) 9.6 19.8 41.0 42.4
6A,exp
2.1 4.3 4.4
IO4 m3,
Effect of Organic Solvent. An alcoholic solution of caustic soda (0.25 kmol/m3) containing 2-propanol (50%, w/w) intensified the specific rate of absorption of COS by a factor 4. This is due to the higher solubility of COS in such a solution. The experimental conditions were selected such that there was no depletion of hydroxyl ion concentration in the diffusion film in the liquid phase, near the gas-liquid, interface, as the condition given by eq 4 (see below) was satisfied. The speed of stirring had a very nominal effect on the specific rate of absorption in the range 1-1.33 rev/s. Theory The reaction involved in the present work is first order with respect to the solute gas concentration as well as with respect to hydroxyl ion concentration (Sharma, 1965). The reaction under operating conditions in this study conforms to the regime between slow and fast pseudofirst-order regime for the base case (that is, in the absence of the emulsified second liquid phase) and the following equation, based on Danckwerts' surface renewal theory, holds (Doraiswamy and Sharma, 1984):
The conditions given below should be satisfied: q>M1/2>1 where
(2)
872 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989
In the above regime, a considerable amount of solute gas is consumed in the diffusion film. So, the suggested mechanism of enhancement of specific rate of absorption will occur when the droplet size of the dispersed second liquid phase is smaller than the diffusion film thickness (Sharma, 1983). Mehra (1988) has presented an analytical solution, based on Danckwerts’ surface renewal theory, of the unsteadystate differential species balance equations for both the continuous and microdispersed phases, with an assumption that the droplets are stationary, and there is no reaction within the emulsified organic phase, which is as follows: RA,th
= [A*J[(l- ~ O ) ~ A I ~ ] (3) ”~
where
I=[
+ a(kL2/oA) + P (kL2/oA) + W
(kL2/oA)’
a =
wo
KO
1-10
m A
I
kl + -+ KO w=-
p = - klK0 mA
m A
carbonyl sulfide compared to solutions where 2-propanol was not used. Acknowledgment S.K.C. is thankful to the University Grants Commission, New Delhi, India, for an award of senior research fellowship. Nomenclature [A*] = concentration of solute gas A at the gas-liquid interface, kmol/m3 a = gas-liquid interfacial area, m2 [Bo]= concentration of liquid-phase reactant B in the bulk continuous phase, kmol/m3 of continuous phase D A = diffusivity of A in the continuous phase, m2/s D B = diffusivity of B in the continuous phase, mz/s d p = average microphase droplet size, m G = constant defined in eq 4, dimensionless I = constant defined in eq 3, s-1/2 KO = transport coefficient in continuous phase, s-l k L = mass-transfer coefficient (gas-liquid, liquid side), m/s kl = pseudo-fiist-order rate constant for the reaction A + ZB products in the continuous phase, 9-l k2 = second-order rate constant for the reaction A + ZB products in the continuous phase, m3/(kmol s) lo = volumetric holdup of microphase, m3 of microphase/m3 of total m A = distribution coefficients of A between microphase and continuous phase, (kmol/m3 of microphase)/(kmol/m3 of continuous phase) RA,th = specific rate of absorption of A, kmol/(m2 s) R A b = specific rate of absorption of A for base case, kmol/(m2
-
120~
KO=-d,2
Equation 3 was used to calculate the specific rate of absorption in the presence of the emulsified second liquid phase. For the case when there is no reaction within the microphase, the condition for no depletion of B in the continuous phase, near the gas-liquid interface, is (Mehra, 1988)
-
9)
S = volume of surfactant, m3/m3 of total x 100 V = volume of the continuous phase, m3 w = constant, defined in eq 3, s-l t = time, s 2 = stoichiometricnumber in the reaction A + ZB products, 2 = 4 in present work
-
where
G =
Greek Symbols
P(1- 20)DB
a = constant defined in eq 3, s-l B = constant defined in eq 3, sW2
kL2
gA = enhancement factor, dimensionless
This condition was found to hold. The theoretical enhancement factor, 4A,th,is defined as the ratio of the predicted specific rate of absorption in the presence of emulsified second liquid phase to that in its absence (the base case): @A,*
= RA,th/RA,b
(5)
where R A b and R A t h are specific rates of absorption as defined by eq 1and 3, respectively. A comparison of the experimental enhancement factor, @A,er ,and that of theoretical one, @A,th, has shown very gooi agreement. Conclusions The suggested strategy of using an emulsified second liquid phase to enhance the specific rate of absorption of COS in the aqueous alkaline medium, where it reads, was found to be successful, and the highest enhancement factor was 2.5. The theory of mass transfer with chemical reaction in the presence of a microphase, based on Danckwerts’ surface renewal approach, can be used satisfacturilyto explain the extent of enhancement. An aqueous solution containing 2-propanol and dissolved NaOH gave an enhanced specific rate of absorption of
Subscripts cont = continuous exp = experimental
mic = microphase sol = solution th = theoretical tot = total (continuous phase plus microphase) Registry No. 2-Propanol, 67-63-0;toluene, 108-88-3;sodium hydroxide, 1310-73-2. Literature Cited Danckwerts, P. V. Gas-Liquid Reactions; McGraw-Hill: New York, 1970. Doraiswamy, L. K.; Sharma, M. M. Heterogeneous Reactions; Wiley: New York, 1984; Vol. 11. Mehra, A. Intensification of Multiphase Reactions Through the use of a Microphase-1 Theoretical. Chem. Eng. Sci. 1988, 43, 899-912. Mehra, A.; Sharma, M. M. Absorption with Reaction: Effect of Emulsified Second Liquid Phase. Chem. Eng. Sci. 1985, 40, 2382-2385. Mehra, A.; Pandit, A.; Sharma, M. M. Intensification of Multiphase Reactions Through the use of a Microphase-I1 Experimental. Chem. Eng. Sci. 1988,43,913-927. Seidell, A. Solubilities of Inorganic and Metal Organic Compounds, 3rd ed.; D. van Nostrand Co.: New York, 1941; Vol. 1, p 238.
Ind. Eng. Chem. Res. 1989,28, 873-875 Sharma, M. M. Kinetics of Gas Absorption: Absorption of C02 and COS in Alkaline and Amine Solutions. Ph.D. Thesis, The University of Cambridge, Cambridge, U.K., 1964. Sharma, M. M. Kinetics of Reactions of Carbonyl Sulfide and Carbon Dioxide with Amine and Catalysis by Brbnsted Bases of the Hydrolysis of COS. Trans. Faraday SOC.1966,61,681-687. Sharma, M. M. Perspectives in Gas-Liquid Reactions. Chem. Eng. Sci. 1983,38,21-28. Versteeg, G.F.; Van Swaaij, W. P. M. Solubility and Diffusivity of Acid Gases (COz, NzO) in Aqueous Alkanolamine Solutions. J.
873
Chem. Eng. Data. 1988,33,29-34.
Swades Kumar Chaudhuri, Man Mohan Sharma* Department of Chemical Technology University of Bombay Matunga, Bombay 400 019, India Received for review June 13, 1988 Accepted January 17, 1989
Optimal Thermodynamic Heat Transfer This paper presents a set of heuristics useful for optimal design of heat-exchange networks and integrated heat and power systems. These heuristics consolidate other approaches reported in the literature in a formalism useful for design purposes. Introduction For a given fixed transfer area, minimization of the system entropy generation is an interesting approach because it yields optimal solutions in some economic sense. The general problem is a minimization of entropy generation under certain set of constraints. The question is which are the general rules or the general principles to achieve this objective. This problem was analyzed for generalized transfer operations (mass, momentum, and heat transfer) by Tondeur and Kvaalen (1987). For heat-exchange network synthesis, a systematic procedure was developed in Irazoqui (1986) using this same basic idea. This methodology was also utilized for thermal desalination system synthesis (Scenna, 1987; Aguirre and Scenna, 1988) and for power cycle design (Aguirre, 1987). This paper presents a set of heuristics useful for optimal design of heat-exchange networks and integrated heat and power generation systems. These heuristics consolidate the approaches reported in the literature in a formalism useful for design purposes. Optimal Criteria for Minimum Entropy Generation If we want to develop a criterion to minimize entropy generation in any heat-transfer operation, we need to adopt a set of assumptions and a set of decision variables such as gradient or temperature field. Nevertheless, care must be taken with the assumptions in order to find adequate solutions for conventional problems of heat-exchange systems design. In fact, one criterion for the functional construction is to utilize linear nonequilibrium thermodynamic analysis and Onsager’s reciprocity relations. That is, to utilize a set of flux or driving force definitions to express the usual thermodynamic relationships (Onsager, 1931a,b; Gyamarti, 1970; Wisniewski et al., 1976). Following this line of thinking, the local rate of entropy production is expressed as u = Lu,
du = X L f 2 dV
(1)
Then, for a system with a finite size V, the optimization problem is min
Q
= min I L L
f2
dV1
(2)
If our interest is a driving force or a gradient field, f, and we assume that L is not a function off, the solution for this problem is the homogeneous distribution of the gradient field, f , throughout the system. That is, f is a con-
stant value. But for design purposes, our interest is to clearly define f. So, if we want to find an expression of f through the determination of the temperature field, expression 2 must be written as a functional of this field. If we assume that the basic assumptions of continuum mechanics are valid in our system (Slattery, 1972), assume stationary state, and omit the dissipations due to momentum- and mass-transfer fluxes (because our attention is focalized only on heat-transfer phenomena), the expression of the tqtal entropy generation is u
=
u, d V =
-( $
( J V T )d V
1
=
where we assume that the heat flux (Fourier law) is
J = -XVT
(4)
where X is assumed to be a constant. It must be remarked that this assumption does not necessarily agree with the assumption of L as a constant value. Then, the problem to be solved is min
Q
= min
I-( LA(7) VTVT dV))
(5)
where u is a function of the temperature field. In the Appendix section, it is demonstrated that
V T / V l r c r=, constant
(6)
is the condition for the minimization of entropy generation. { ( x ) is a vector normal to the heat-exchange area. This is in the direction in which temperature distribution becomes outstanding. The condition given by eq 6 must be understood as the goal to be achieved by adequate designs. It must be remarked that this solution implies that the driving force must be uniformly distributed and then, from eq 3, a, too. Therefore, the term “driving force” is strictly defined as V T / T. On the other hand, if we consider that V T f T is a constant value, from eq 4, J / T (the entropy flux) is a constant value too (if h is a constant). Moreover, from the previous conclusions and eq 3, it is easy to show that a, (the entropy generation per unit of area) must be a constant value throughout the system. Then, a,, us, VTf T , or Jf T uniformly distributed can be used as the thermodynamic optimality criterion. The relationship between thermodynamic optimal solutions and economical optimal ones is analyzed according to all
0888-5885f 8912628-0873$01.50 f 0 0 1989 American Chemical Society
