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Gas absorption accompanied by fast chemical reaction in water-in-oil emulsions
Shorter Communications
Pergamoa
3331
Chemtecll E~~ine.?ri~
Sctmce. Vol. 49, No. 19. pp. 3331-3334 1994 Copyriahi0 195’4 Ekwim Science Ltd Printed in Great Britain. AU ri&ta rewrved mm-2509/w 57.00 + 0.00
ooo9-2509(94)00137-5
Gas absorption
accompanied
(First received
by fast chemical
7 June 1993; accepted
The rates of multiphase reactions, where the reacting species
reside in different phases [A(g) and B(1)], are usually limited by the diffusion of one of the species from its original phase into the other [A(g) --) A(I)] where diffusion and reaction [A(I) + zB(9 + products] proceed simultaneously. The use of microheterogeneous media (in lieu of the reactive liquid p,ba.u), such as micellar solutions, microemulsions and macroemulsions, for conducting such diffusion limited multiphase reactions has been investigated for a variety of systems over the last decade (Janakiraman and Shanna, 1985; Bruining et aZ., 1986; Bhagwat and Sharma, 1988; Mehra et al., 1988). The advantages that accrue from the use of such media include the intensification of the specific rate of reaction (implying smaller reactor sixes and/or shorter processing times), modification of selectivity (Pradhan et al., 1992) product distribution and even autocatalytic effects on the reaction rate (Mehra and Sharma, 1988). For most of the systems that have been reported in the literature, the original, reactive liquid was retained as the continuous phase while an immiscible additional liquid, or a surfactant bearing phase was microdispersed in it. The essential mechanistic feature in bringing about the rate intensification, in these systems, is the role of the microdispersed phase acting as a sink for the rate limiting diffusant (A). This happens when the microdispersed constituents have physical or chemical affinity for the solute relative to the continuous liquid phase where the solute is usually sparingly soluble. A necessary condition for the rate enhancement to occur is that the size of the microdispersed constituents must be smaller than the diffusional length scales of the diffusant. In such a situation, the microdispersed sinks essentially interact with the diffusing solute, either by reacting with or solubilizing it, so as to remove it from the vicinity of the interface formed by the original phases. The concentration gradients near this interface thus become steeper leading to enhanced interphase mass transfer rates. The solute taken up by the microdisparsed phase is either consumed within it or discharged into the A-deficient bulk phase (Mehra, 1988). An alternative strategy to increase the efficacy of processing rates involves the use of “inverted” media, wherein the original reactive liquid phase is microdispersed in another liquid which is immiscible with it and which shows a high physical affinity for the rate-limiting diffusant (A), This strategy was first suggested by Mehra (1989), along with a preliminary theoretical analysis demonstrating its feaaibility. Therefore, it was thought desirable to experimentally investigate the idea of conducting a gas-liquid reaction in the gas-“inverted” emulsion mode. In this paper we wish to report the results of our study on the absorption of carbon dioxide into emulsions of aqueous sodium hydroxide in a-ethyl hexanol, along with some theoretical considerations to establish the upper bounds on the specific rates for such a situation. This model system of carbon dioxide absorption was chosen because it is well characterized in terms of physicochemical properties and the reaction is known to be very fast
reaction in water-in-oil
in revised fawn 23 April
emulsions
1994)
(instantaneous) since the rate constant values are extremely high [k2 = 104 m3/kmol; Danckwerts (1970)]. Also, 2-ethyl hexanol is a cheap solvent and easily available in bulk quantities. Figure 1 gives a schematic picture for a single penetration element located at the gas-emulsion interface. The gas phase consists of pure carbon dioxide whereas the emulsion phase is made up of a microdispersed aqueous solution of sodium hydroxide in the continuous 2-ethyl hexanol phase. The aqueous phase microdrops act as “microreactors” located at different points along the concentration gradients of the diffusing carbon dioxide in the non-reactive organic phase. EXPERIMENTAL
Stable emulsions of aqueous sodium hydroxide solutions, of a given strength, in 2-ethyl hexanol were prepared by mechanical stirring in a glass vessel of 60mm diameter, equipped with a six bladed glass turbine impeller (diameter, 25 mm). The speed of stirring was 15 rev/s and the emulsion preparation time was kept around 900s. Brij 52 (polyoxyetbylene cetyl ether) was used as the surfactant to aid emulsification. The volume of the emulsion, prepared for a given absorption run, was fixed at 2 x 10V4 ms while the
r continuous\phase
GAS
0
(oil)
EMULSION (penetration element)
BULK
Fig. 1. Schematic sketch of mass transfer accompanied by a chemical reaction in the microdispersed phase, at the gasemulsion interface.
Shorter Communications
3332
dispersed phase fractional bold-up ranged from 0.05 to 0.2. The concentration of the surfactant ranged between 2 and 10 wt % of the dispersed phase (being on the higher side for larger hold-ups of the microdispersed phase and higher conconcentrations of sodium hydroxide). The stability of the emulsion was checked visually by ascertaining that no phase separation occurred in an unstirred sample within the first 1800 s of making the emulsion (the absorption runs were carried out for a period not exceeding 360 s). Also, stable emulsions were milky white and “homogeneous” in appearance. An optical microscope was used to determine the microdispersed phase droplet size. (radius) which ranged between 8 and 5 q, the number average size being about 6.5flm. It was found that emulsions having an aqueous concentration of sodium hydroxide exceeding 0.12 kmol/m” were unstable since these sedimented very rapidly. All the absorption measurements were made at a temperature of 28°C and atmospheric pressure and were carried out at in a glass stirred cell of internal diameter 90 mm equipped with a mercury seal and provided with a four bladed (flat, vertical) impeller (diameter 60 mm) which could be rotated at speeds between 0.17 and 20 rev/s. The speed of stirring was kept low enough to avoid rippling on the flat interface of the stirred cell. A typical run mvolved charging of the stirred cell with the absorbent liquid/emulsion followed by purging of the gas space in the reactor for about 15 s (at high gas flow rates). The stirrer was then started and the carbon dioxide flow rate out of a balloon, maintained essentially at atmospheric pressure, was monitored as a function of time with the help of soap film meter. This equipment and procedure is similar to what has been used in some of the earlier studies (Mehra et al., 1988). Absorption runs were also carried out for pure water and 2-ethyl hcxanol as well as for plain aqueous sodium hydroxide solutions in order to determine the values of the physical mass transfer coefficients in water and oil and to ensure that the reactor was operating satisfactorily (such that the match between the experimental and calculated values of the classical enhancement factor was reasonable). Some emulsions were also made in the stirred cell itself at a stirring speed of about 15 rev/s the preparation time being kept around 900 s. The microdrop sixes measured with an optical microscope were found to be similar to the ones obtained with the earlier described procedure. RESULTS AND OBSERVATIONS The specific rates of absorption for various operating conditions are shown in Table 1. The rates declined very slowly over the period of observation which was about 300 to 360 s. For the runs at higher hoId-ups of the microdispersed phase (1.) and concentrations of the aqueous phase
reagent (4). the decline in the rate was negligible whereas for less loaded emulsions the decrease in rate was of the order of 10%. The relevant physieo-chemical data for the system are also shown in this table. For the case of physical absorption, the specific rate declined significantly with time on account of saturation of the bulk liquid phase. The rates were higher for Z-ethyl hexanol than for water because of the higher solubility of carbon dioxide in the former. For absorption into.emulsions, the specific rates increased with increasing microdispersed phase hold-up (1.:0.05 to 0.2), aqueous phase concentration of sodium hydroxide (q: 1 and 2), and speed of stirring (N: 0.417 to 1 rev/s), respectively. There was no effect of the procedure by which the emulsion was made on the specific rate of absorption. THEORY
The development of rigorous theory for absorption in water-in-oil emulsions accompanied by an instantaneous reaction in the microdispersed phase is expected to be raasonably complex and will involve a population balance ap preach in order to account for the aqueous phase reagent distribution in different drops which have reacted to diRerent extents. However, it is relatively simple to obtain expressions for the specific rate in the limiting situation when the reao tion is “fast” and the microdrops are “small”. In the limit, fast reactions may be deemed to be instantaneous: An instantaneous reaction is characterized by the existence of a reaction plane at which the two reacting species destroy each other. Thus, when a stagnant spherical drop containing reagent B is immersed in a phase bearing solute A., a reaction front will form which, to begin with, will be coincident with the drop surface and then move inwards into the drop as A penetrates into it and a Bdepleted shell appears. Since the microdrops are small (in the micron size range) and the emulsions are stabilized by a surfactant, the microdrops may be taken to be rigid, spherical objects within which the reactant(B) diffuses towards the reaction front and reacts instantaneously with the solute A. For the ease when the rCactiOn front moves “slowly” (high concentration of B in the microdrops, high hold-up of the microdrops) it may be taken to be coincident with the microdrop surface and the rate of reaction for any microdrop will be controlled only by the diffusion of B from the internal parts of the microdrop to its surface. The unsteady state diffusion equation for B, in a single microdrop, may thus be written as
Table 1. Specific rates of absorption
(R, x 10’ kmol/mr s) of carbon dioxide into emulsions of aqueous sodium hydroxide in 2-ethy hexanol, at various conditions
4
1.0 2.0
N = 0.417 rev/s 15.00 17.40
1.0 2.0
N = 1.0 rev/s 21.00 23.00
VL= 3.15 x lo-’ 15.20 18.10
m/s
I$ = 3.62 x 10-s m/s 21.443 24.20
ti‘ = 217 x 10-s m/s 17.00 19.60 &,=2.4Ox1O-sm/s 24.00 26.00
Property values z = 2,’ c, = 2.85 x lo-* kmol/m”. WA= 1.98 x 10m9 mn/s,r Dfi z PA, We = 3.35 x 10m9 ma/s,* ml-1.9, Y=2x10-4m’,a=6.36x10-sm2 ‘Taken from Perry and Chiiton (1973); t taken from Danckwerts (1970).
Shofier Commtmications with the initial and boundary
conditions
e=
0:
R
C;=C&,
e>
0:
r = 0,
aC; -_=O ar
r = R,
q-0.
12)
The species balance for the diffusion of solute A in the continuous organic phase, in a surface element, is given by
3333
accounts for the zero-order behaviour in that the solute is completely consumed within the surf&e element at a distance S, from the gas-emulsion interface. In keeping with the pseudohomogeneous assumption, the effect of inter-drop interactions of any kind un Fa has not been considered. Also, the external (organic) phase resistance to the transport of A towards a microdrop has been neglected because of higher soiubitity in the oil phase relative to the aqueous phase. Solving the transformed versions of eqs (3) and (4) gives the expression for the specific rate of absorption, averaged over the gas-emulsion interface, into the emulsion
(3) along with the conditions e = 0: 0 > 0:
W
a,,
x =
to be imposed cl;=cI,=o cl: = c;,
(4) = mlC;,
and
ac;
c;=c&=o.
ax=o +1)/J?.
where Fa is the molar flux of 3, at the microdrop surface, summed over all the microdrops located between x and x + dx, per unit volume of the emulsion. The superscripts a and o denote the aqueous and the organic phases, respectively. Equation (3) is written on the assumption that the emulsion can be viewed as a pseudohomogeneous phase wherein the diffusivity of solute A can be approximated by that in the continuous phase (i.e. no diffusivity retardation due to microdrop “barriers” or enhancement due to close packing of the microdrops); this is generally true at “low” hold-ups of the microdispersed phase. Microdrop coalescenti has been neglected. Transforming eqs (1) and (2) into the Luplace domain and solving for the flux of B from a single drop, yields
The last results are obtained from application of the surface renewal theory due to Danckwerts (1970), where the age distribution of penetration elements at the gas-emulsion interface is simply given by S exp( -SO) (fraction of elements between age 0 and B + do) so that the specific rate averaged ouer the whole inte+x is given by j,” - Dl;(X;/ax)rX,,, S exp( -.%I) dS = S( -D~(dt?~/dx)),,O. Here, S is the surface renewal frequency and may be related to the liquid (emtdsion) side mass transfer coei%cient by k”‘ E a. Substituting this de6nition and the expression for FB from eq. (S), into eqs (6) and (7), the resulting expression is given by RA = J-
Lq 3 CManh do - 11 WA -L) 4=
k; C;,m,
~
Ml
where 4 = mnR and the symbols with an overbar denote Luplace domain variables, It is also assumed that all the microdrops have a tied radius, R. For the set of assumptions made, it can be seen that Fa does not depend upon C; and hence the rate of uptake by a microdrop is independent of its location with respect to the gas-emulsion interface. Thus, in this limit of the reaction front being coincident with the microdrop surface, Fx behaves as a t&edependent, zero-order reaction term. The condition at x --t S,
Table
- U
1.9
3[d/tanh
x sinh
cash(
Expt.
1
N= 1.0 2.0
1)
+1
(9)
into
G
I. = 0.1
1. = 0.2
Theo.
Expt.
Theo.
Expt.
Theo.
Expt.
Theo.
2.82 2.43
291 2.83
293 2.46
3.06 291
2.75 3.17
3.41 3.10
1.89 -
2.07 3.37
3.07 3.36
2.94 3.02
3.13 3.54
3.03 3.18
3.15 3.80
3.22 3.54
1.92
2.07 3.37
N = 0.417 rev/s :::
4 -
(
ELA
4
d2
where d = kER/,&@ and q = C&,j(zC’&). In the limiting case when # + 0 (around d = 0.2) eq. (8) reduces to
2. Enhancements factors in the speciiic rates of absorption of carbon dioxide emulsions of aqueous sodium hydroxide in ðyl hexanol, at various conditions
l_ = 0.05
(7)
l.Orev/s
3334
Shorter
Communications
This represents the maximum possible specific rate that can be obtained for such systems and is based on the instantaneous discharge of the dispersed-phase reactant into the continuous phase. Dividing eq. (9) by the maximum rate for pure physical absorption in water, i.e. k”,C;,, the expression for the limiting maximum enhancement factor is obtained as mA sinh (Gosh-’
(Q + l))/Q
(10)
Therefore, under these conditions, the rate is simply sustained at the maximum valuefor physical absorption in the oil phase, provided the reaction is able to keep the value of the bulk concentration near zero. Figure 2 shows the variation of
and the extent of penetration of solute A, as given by a simplification of eq. (7), becomes
+6,=cosh-‘(Q+l)
s
de-xl
= sinh [cash-’
(11) 6; =
where Q = m,(l -1.,)/&q) and 6 = 0:/k;. It is important to note that for situations where transient effects are important, such as accumulation in the continuous and/or microdispersed phase (as represented by terms containing mA) or time-dependent reaction terms (those containing Q), it is not possible to use the simpler film model of mass transfer.
&/ji=?j
(12)
40-
(16)
30-
20-
(17)
,’ ’ 5.0
1
*! ,’
\ \ \
,’
‘\ ---
are also shown in this table. The relevant physico-chemical data used in computing the enhancement factors are given in Table 1. The value of mA was approximated by using the initial rate for physical absorption of carbon dioxide in 2-ethyl hexanol = ktC;,ml
j-1)
sr = 1 + l/Q.
Table 2 shows I the experimental and theoretical (limiting) values req. (lo)] of the enhancement factors in the specific rates of absorption of carbon dioxide in different emulsions characterized by volumetric, fractional hold-up of the microdispersed phase (13 and the concentration of sodium hydroxide in it (q), for two stirring speeds. The classical enhancement factor values, experimental as well as those computed from (Doraiswamy and Sharma, 1984)
R: = ktC&
= cash-‘(Q
(15)
[derived from eqs (10) and (11). respectively] vs the group Q. For ST to become equal to four, which is approximately the penetration depth for pure physical absorption, Q is about 26. In other words, the assumption that Co, is zero is likely to be violated for Q > 26 (this is not a suflicient condition as some A still goes into the bulk phase with the surface elements returning from the gas-emulsion interface to the bulk, though under typical operating conditions this amount is likely to be “small”). A line showing another enhancement factor ¬ed as es and given by the expression below is also shown in Fig. 2:
DISCUSSION
E:=(~+&)
(Q +l)]/Q
, \ \
,’
61 &.J
,’
/’ ’
,’
,’
,’
>’
40
3.0
2.0
(13)
where the values of ki and Cj,, (solubility of carbon dioxide in water) are known independently. The value thus obtained was m, = 1.9 and compares well with the values of around 2 that may be calculated from literature data on the solubility of carbon dioxide in various organic solvents (Stephen and Stephen, 1962). Equation (13) and condition (4) assume that the distribution coefficient mA can be approximated as the ratio of solubilities of carbon dioxide in 2-ethyl hexanol to that in water. The solubility value for the aqueous phase has been taken to be identical to that in pure water since the correction factors arising due to the presence of ions (Danckwerts, 1970) were negligible at the low concentrations of sodium hydroxide used in this study. No viscosity effects have been considered in this study except those implicitly included in the measured values of the mass transfer coefficients for the aqueous and the oil phases. The viscosity did not vary appreciably with a change in the hold-up of the aqueous phase or the sodium hydroxide concentration in it. For pure Z-ethyl hexanol the measured viscosity was about 4.0 x 10-s kg/ms whereas for the heaviest emulsion was around 4.3 x 10-s kg/m s. Before analysing the absorption data, with the help of the proposed theory, it is worthwhile examining some implications of eq. (10). When Q 9 1, the sinh and cash-’ terms cancel each other and the expression for the limiting value of the enhancement factor reduces to
Fig. 2. Plot of enhancement factors sr and es as well as penetration depth of diffusant ST vs group Q.
This line signifies an enhancement factor that would be obtained if all the B currently immobilized within the microdrops were available in free (di&sive, with di@sivity equal to D$) form to react instantaneously with the A dij’using in the oil phase. Therefore, the effect of immobilizing B is to lower the enhancements to values given by .sl from ss. The significance of 4 in the proposed model arises from the fact that it represents the square root of the ratio of microdrop conversion time to the surface element contact PADi = J Rz/D~D~PL) tune (4 = k”,R/ and appears in the expression r or Fs to account for its time-dependent behaviour. Also, for the extreme case, namely, 4 4 1, the assumption of the reaction plane and the microdrop surface coinciding becomes redundant since now the discharge of B into the continuous phase may be considered to be instantaneous and the term Fs behaves like a point source. Therefore, the microdrops within a penetration element which are exposed
3335
Shorter Communications to a non-rero concentration of A are expected to deplete completely during their residence at the gas-emulsion interface, for this limit. In terms of dimensional estimates, the typical contact time of a penetration element is about 2 s whereas the time for complete conversion of a microdrop, according to rigorous calculations (Dutta et al., 1988), will range from about 0.25 to 0.6 times R2/D& i.e. 3.0 x lo-’ to 7.5 x lo-’ s, for the most highly loaded microdrop (using q = 2 and 20, for a microdrop close to the gas-emulsion interface and that away from it which is exposed to a tenth of the interfacial concentration, respectively). For typical operating conditions, 4 cannot be greater than unity since 4 reduces to R/(Dz/kO,) for 0: sz 4, and the condition for the emulsifiedphase microdrops to act as microreactors within a penetration element is R < (0:/k:). In this study, Q c 0.12. Therefore, eq. (10) may be expected to be obeyed closely. The size of the microdrops is not expected to influence the specific absorption rates in any significant manner as long as the condition of 4 being small is not violated, which is indeed the case for this study. In any ease, since the two procedures for making stable emulsions did not yield any significant difference in the microdrop sixes, it is not possible to test for any microdrop size effects. It may now be seen from Table 2 that the experimentally observed enhancement factors show excellent agreement with the corresponding values computed from eq. (10). The fact that for the stirring speed of N = 1 rev/s, the experimental values are consistently, slightly higher than the upper bound calculated from theory, probably reflect the measurement errors associated with the determination of the mass transfer coethcients and consequently the value of mA through eq. (13). For instance, mA = 2.1 (instead of 1.9) will make the theoretical enhancement factors slightly exceed the experimentally observed values. Thus, the microdrops exposed to A, near the gas-emulsion interface, deplete fully and this state of depletion percolates to more and more microdrops gradually; meanwhile the specific rate of absorption is sustained near the value for physical absorption into a pure oil phase.
CONCLUSIONS The strategy of absorption in water-in-oil emulsions accompanied by a fast chemical reaction in the emulsified phase has been experimentally explored along with a theoretical analysis. A common system, namely, carbon dioxide absorption in emulsions of aqueous sodium hydroxide in 2-ethyl hexanol has been used as a model system. The purpose of this study has been primarily to explore and test the strategy rather than demonstrate any significant enhancements. The experiments are limited by the difficulty in obtaining stable emulsions at high concentrations of the internal-phase reagent. This limitation is system specific and excellent enhancements may be obtained for chemical systems which have a large value of the distribution coefBetent m, (oil/water) for the solute A partitioning between the oil and the aqueous phases. Typically, industrial systems in which the absorbing solute has a high relative afinity for an organic phase will stand to benefit in terms of increased rates of absorption, such as absorption of olefinic gases (Mehra et al., 1988), carbonyl sulfide (Choudhuri and Sharma, 1989). etc. As compared to a pure aqueous, reactive phase it will become beneficial to use this strategy for absorption, in order to get higher rates, when E’, c Efi [as given by eq. (lo)]. Figure 3 shows plots of EC”and Efi (with mA as parameter) vs q for a typical set of conditions. The xones where I!& < E$ is satisfied denote the operating points where this benefit is likely to be achieved (along with the desired minivalue of rn”).
60
m”=50 .. ,
50/ --~
40-t
/
EA'
EAL
ccl
-
+T crl
30-
,
/
/
/
,
/
/
/
/’ mA=25
Fig. 3. Variation of enhancement factors .?Ii and E> versus concentration ratio 4 with distribution coe&cient mA as parameter; Data used: 1. = 0.1, kg/k”, = 1, D;/D> = 1.
In comparison to oil-in-water emulsions (Mehra, 1988) where the enhancement effects are proportional to the square root of m,,, here for the case of water-m-oil emulsions, these are directly in proportion to m, (Mehra, 1989). B. V. VENUGOPAL ANURAG MEHRA’ Department of Chemical Engineering Indian Institute of Technology, Bombay Powai, Bombay 400 076
NOTATION
concentration of solute A, kmol/m3 concentration of reactant B, kmol/m” diffusivity of A, ml/s diffusivity of B, m2/s enhancement factor in specific rate of absorption, dimensionless molar flux of B at (total) surface area of microdrops, located at distance x from the gas-emulsion interface, per unit volume of continuous phase, kmol/ms s liquid (emulsion) mass transfer coethcient for gasemulsion mass transfer, m/s second-order rate constant, ml/km01 s volumetric fractional hold-up of the microdispersed phase, dimensionless distribution coef6cient for solute A partitioning between the organic and aqueous phase [organic/aqueous], dimensionless speed of agitator rotation, rev/s ratio defined in eq. (7) (q = CG/zC;,), dimensionless group deiined in eq. (10) [Q = m,(l - lJ/(l,q)], dimensionless radial coordinate for a spherical microdrop, m radius of a microdrop, m specitic rate of absorption, kmol/ma s Laplace domain symbol and surface renewal freW==Y,
l/s
distance from the gas-emulsion interface in a surface element, m stoichiometric factor in the reaction A + HB + products, dimensionless (z = 2, in this study)
‘Author
to whom correspondence
should be addressed.
3336
Shorter Corn lmunications
Greek symbols d thickness of gas-emulsion 4 g s1 s1
e 3
diffusion film, emulsion
side (8 = Dz/k”d, m penetration thickness of diffusant k, m ratio of 4 to 6, dimensionless product of a, and Jmi dimensionless enhancement factor defined by eq. (16), dimensionless enhancement factor defined by eq. (17). dimensionless time (surface element contact time scale), s position of reaction front within a single drop, m Thiele modulus for diffusion of B in microdrop (4 = &R/m),
dimensionless
denotes (for A)
initial concentration
Superscripts a pertaining c g
i
L 0
A.1.Ch.E. J 34, 694-697. lanakiraman, B. and Sharma, M. M., 1985, Oximation of cycle-alkanones (cyclododecanone and 4-tert-butylcyclohexanone): micellar catalysis in slow and fast solid-liquid and liquid-liquid reaction systems. Chem.
Engng Sci. 40.223-233.
Subscripts denotes bulk value b 0
Danckwerts, P. V., 1970, Ga.+Liquid Reactions. McGraw Hill, London. Choudhuri. S. K. and Sharma, M. M., 1989, Absomtion of carbonyl sulfide in aqueous alkaline solutions: new strategies. Znd. Engng Chem. Res. Zs, 870-873. Do&wamy, L. K. and Sharma, M. M., 1984, Heterogeneous Reactions, Vol. 2. Wiley, New York. Dutta. B. K.. Middva. U. and Rav. P.. Mass transfer accompa&d by an &&taneous -r&&ion in a rigid drop.
(for B) or solubility
Mehra, A., 1988, Intensification of heterogeneous reactions through the use of a microphase - I. Theoretical. Chem. Engng Sci. 43, 899-912. Mehra, A., 1989, Intensification of heterogeneous reactions through the use of water-in-oil media, Chem. Engng Sci.
44,448-452. to aqueous phase to classical theory for plain
pertaining phase pertaining to gas phase initial value limiting value pertaining to organic phase
reactive
REFERENCES Bhagwat, S. S. and Sharma, M. M., 1988, Intensification of solid-liquid reactions: microemulsions. Chem. Engng Sci.
43, 195-205. Bruining, W. .I., Joosten, G. E. H., Beenackers, A. A. C. M. and Hofrnan, H., 1986, Enhancement of gas-liquid mass transfer by a dispersed second liquid phase. Chem. Engng Sci. 41, 1873-1877.
Mehra. A.. Pandit, A. and Sharma, M. M., 1988, Intensification bf heterogeneous reactions ihrough the L& of microDhases -IL. Experimental. Chem. Enarur Sci. 43,913-927. Mehra, A. and Sh&na, M. M., 1988, Absorption of hydrogen sulfide in aqueous solutions of iodides containing dissolved iodine: enhancements in rate due to DrcciDitated _ sulfur. Chem. Engng Sci. 43, 1071-1081. Perry, H. P. and Chilton. C. H., 1973, Chemical Engineers’ Handbook, pp. 3-93. Mcgraw Hill Kogakusha, Tokyo. Pradhan. N. C., Mehra, A. and Sharma, M. M., 1992, Intensification and selectivity modification through the use of a microphase: simultaneous absorption of two gases with chemi&l reaction. Chem. Engng Sci. 47, 493-498. Stephen, P. and Stephen, H., 1962, Solubilities orfZnorg~@c and Organic Compounds, pp. 107 1- 1075. Pergamon Press, London.
Pergamoa
3331
Chemtecll E~~ine.?ri~
Sctmce. Vol. 49, No. 19. pp. 3331-3334 1994 Copyriahi0 195’4 Ekwim Science Ltd Printed in Great Britain. AU ri&ta rewrved mm-2509/w 57.00 + 0.00
ooo9-2509(94)00137-5
Gas absorption
accompanied
(First received
by fast chemical
7 June 1993; accepted
The rates of multiphase reactions, where the reacting species
reside in different phases [A(g) and B(1)], are usually limited by the diffusion of one of the species from its original phase into the other [A(g) --) A(I)] where diffusion and reaction [A(I) + zB(9 + products] proceed simultaneously. The use of microheterogeneous media (in lieu of the reactive liquid p,ba.u), such as micellar solutions, microemulsions and macroemulsions, for conducting such diffusion limited multiphase reactions has been investigated for a variety of systems over the last decade (Janakiraman and Shanna, 1985; Bruining et aZ., 1986; Bhagwat and Sharma, 1988; Mehra et al., 1988). The advantages that accrue from the use of such media include the intensification of the specific rate of reaction (implying smaller reactor sixes and/or shorter processing times), modification of selectivity (Pradhan et al., 1992) product distribution and even autocatalytic effects on the reaction rate (Mehra and Sharma, 1988). For most of the systems that have been reported in the literature, the original, reactive liquid was retained as the continuous phase while an immiscible additional liquid, or a surfactant bearing phase was microdispersed in it. The essential mechanistic feature in bringing about the rate intensification, in these systems, is the role of the microdispersed phase acting as a sink for the rate limiting diffusant (A). This happens when the microdispersed constituents have physical or chemical affinity for the solute relative to the continuous liquid phase where the solute is usually sparingly soluble. A necessary condition for the rate enhancement to occur is that the size of the microdispersed constituents must be smaller than the diffusional length scales of the diffusant. In such a situation, the microdispersed sinks essentially interact with the diffusing solute, either by reacting with or solubilizing it, so as to remove it from the vicinity of the interface formed by the original phases. The concentration gradients near this interface thus become steeper leading to enhanced interphase mass transfer rates. The solute taken up by the microdisparsed phase is either consumed within it or discharged into the A-deficient bulk phase (Mehra, 1988). An alternative strategy to increase the efficacy of processing rates involves the use of “inverted” media, wherein the original reactive liquid phase is microdispersed in another liquid which is immiscible with it and which shows a high physical affinity for the rate-limiting diffusant (A), This strategy was first suggested by Mehra (1989), along with a preliminary theoretical analysis demonstrating its feaaibility. Therefore, it was thought desirable to experimentally investigate the idea of conducting a gas-liquid reaction in the gas-“inverted” emulsion mode. In this paper we wish to report the results of our study on the absorption of carbon dioxide into emulsions of aqueous sodium hydroxide in a-ethyl hexanol, along with some theoretical considerations to establish the upper bounds on the specific rates for such a situation. This model system of carbon dioxide absorption was chosen because it is well characterized in terms of physicochemical properties and the reaction is known to be very fast
reaction in water-in-oil
in revised fawn 23 April
emulsions
1994)
(instantaneous) since the rate constant values are extremely high [k2 = 104 m3/kmol; Danckwerts (1970)]. Also, 2-ethyl hexanol is a cheap solvent and easily available in bulk quantities. Figure 1 gives a schematic picture for a single penetration element located at the gas-emulsion interface. The gas phase consists of pure carbon dioxide whereas the emulsion phase is made up of a microdispersed aqueous solution of sodium hydroxide in the continuous 2-ethyl hexanol phase. The aqueous phase microdrops act as “microreactors” located at different points along the concentration gradients of the diffusing carbon dioxide in the non-reactive organic phase. EXPERIMENTAL
Stable emulsions of aqueous sodium hydroxide solutions, of a given strength, in 2-ethyl hexanol were prepared by mechanical stirring in a glass vessel of 60mm diameter, equipped with a six bladed glass turbine impeller (diameter, 25 mm). The speed of stirring was 15 rev/s and the emulsion preparation time was kept around 900s. Brij 52 (polyoxyetbylene cetyl ether) was used as the surfactant to aid emulsification. The volume of the emulsion, prepared for a given absorption run, was fixed at 2 x 10V4 ms while the
r continuous\phase
GAS
0
(oil)
EMULSION (penetration element)
BULK
Fig. 1. Schematic sketch of mass transfer accompanied by a chemical reaction in the microdispersed phase, at the gasemulsion interface.
Shorter Communications
3332
dispersed phase fractional bold-up ranged from 0.05 to 0.2. The concentration of the surfactant ranged between 2 and 10 wt % of the dispersed phase (being on the higher side for larger hold-ups of the microdispersed phase and higher conconcentrations of sodium hydroxide). The stability of the emulsion was checked visually by ascertaining that no phase separation occurred in an unstirred sample within the first 1800 s of making the emulsion (the absorption runs were carried out for a period not exceeding 360 s). Also, stable emulsions were milky white and “homogeneous” in appearance. An optical microscope was used to determine the microdispersed phase droplet size. (radius) which ranged between 8 and 5 q, the number average size being about 6.5flm. It was found that emulsions having an aqueous concentration of sodium hydroxide exceeding 0.12 kmol/m” were unstable since these sedimented very rapidly. All the absorption measurements were made at a temperature of 28°C and atmospheric pressure and were carried out at in a glass stirred cell of internal diameter 90 mm equipped with a mercury seal and provided with a four bladed (flat, vertical) impeller (diameter 60 mm) which could be rotated at speeds between 0.17 and 20 rev/s. The speed of stirring was kept low enough to avoid rippling on the flat interface of the stirred cell. A typical run mvolved charging of the stirred cell with the absorbent liquid/emulsion followed by purging of the gas space in the reactor for about 15 s (at high gas flow rates). The stirrer was then started and the carbon dioxide flow rate out of a balloon, maintained essentially at atmospheric pressure, was monitored as a function of time with the help of soap film meter. This equipment and procedure is similar to what has been used in some of the earlier studies (Mehra et al., 1988). Absorption runs were also carried out for pure water and 2-ethyl hcxanol as well as for plain aqueous sodium hydroxide solutions in order to determine the values of the physical mass transfer coefficients in water and oil and to ensure that the reactor was operating satisfactorily (such that the match between the experimental and calculated values of the classical enhancement factor was reasonable). Some emulsions were also made in the stirred cell itself at a stirring speed of about 15 rev/s the preparation time being kept around 900 s. The microdrop sixes measured with an optical microscope were found to be similar to the ones obtained with the earlier described procedure. RESULTS AND OBSERVATIONS The specific rates of absorption for various operating conditions are shown in Table 1. The rates declined very slowly over the period of observation which was about 300 to 360 s. For the runs at higher hoId-ups of the microdispersed phase (1.) and concentrations of the aqueous phase
reagent (4). the decline in the rate was negligible whereas for less loaded emulsions the decrease in rate was of the order of 10%. The relevant physieo-chemical data for the system are also shown in this table. For the case of physical absorption, the specific rate declined significantly with time on account of saturation of the bulk liquid phase. The rates were higher for Z-ethyl hexanol than for water because of the higher solubility of carbon dioxide in the former. For absorption into.emulsions, the specific rates increased with increasing microdispersed phase hold-up (1.:0.05 to 0.2), aqueous phase concentration of sodium hydroxide (q: 1 and 2), and speed of stirring (N: 0.417 to 1 rev/s), respectively. There was no effect of the procedure by which the emulsion was made on the specific rate of absorption. THEORY
The development of rigorous theory for absorption in water-in-oil emulsions accompanied by an instantaneous reaction in the microdispersed phase is expected to be raasonably complex and will involve a population balance ap preach in order to account for the aqueous phase reagent distribution in different drops which have reacted to diRerent extents. However, it is relatively simple to obtain expressions for the specific rate in the limiting situation when the reao tion is “fast” and the microdrops are “small”. In the limit, fast reactions may be deemed to be instantaneous: An instantaneous reaction is characterized by the existence of a reaction plane at which the two reacting species destroy each other. Thus, when a stagnant spherical drop containing reagent B is immersed in a phase bearing solute A., a reaction front will form which, to begin with, will be coincident with the drop surface and then move inwards into the drop as A penetrates into it and a Bdepleted shell appears. Since the microdrops are small (in the micron size range) and the emulsions are stabilized by a surfactant, the microdrops may be taken to be rigid, spherical objects within which the reactant(B) diffuses towards the reaction front and reacts instantaneously with the solute A. For the ease when the rCactiOn front moves “slowly” (high concentration of B in the microdrops, high hold-up of the microdrops) it may be taken to be coincident with the microdrop surface and the rate of reaction for any microdrop will be controlled only by the diffusion of B from the internal parts of the microdrop to its surface. The unsteady state diffusion equation for B, in a single microdrop, may thus be written as
Table 1. Specific rates of absorption
(R, x 10’ kmol/mr s) of carbon dioxide into emulsions of aqueous sodium hydroxide in 2-ethy hexanol, at various conditions
4
1.0 2.0
N = 0.417 rev/s 15.00 17.40
1.0 2.0
N = 1.0 rev/s 21.00 23.00
VL= 3.15 x lo-’ 15.20 18.10
m/s
I$ = 3.62 x 10-s m/s 21.443 24.20
ti‘ = 217 x 10-s m/s 17.00 19.60 &,=2.4Ox1O-sm/s 24.00 26.00
Property values z = 2,’ c, = 2.85 x lo-* kmol/m”. WA= 1.98 x 10m9 mn/s,r Dfi z PA, We = 3.35 x 10m9 ma/s,* ml-1.9, Y=2x10-4m’,a=6.36x10-sm2 ‘Taken from Perry and Chiiton (1973); t taken from Danckwerts (1970).
Shofier Commtmications with the initial and boundary
conditions
e=
0:
R
C;=C&,
e>
0:
r = 0,
aC; -_=O ar
r = R,
q-0.
12)
The species balance for the diffusion of solute A in the continuous organic phase, in a surface element, is given by
3333
accounts for the zero-order behaviour in that the solute is completely consumed within the surf&e element at a distance S, from the gas-emulsion interface. In keeping with the pseudohomogeneous assumption, the effect of inter-drop interactions of any kind un Fa has not been considered. Also, the external (organic) phase resistance to the transport of A towards a microdrop has been neglected because of higher soiubitity in the oil phase relative to the aqueous phase. Solving the transformed versions of eqs (3) and (4) gives the expression for the specific rate of absorption, averaged over the gas-emulsion interface, into the emulsion
(3) along with the conditions e = 0: 0 > 0:
W
a,,
x =
to be imposed cl;=cI,=o cl: = c;,
(4) = mlC;,
and
ac;
c;=c&=o.
ax=o +1)/J?.
where Fa is the molar flux of 3, at the microdrop surface, summed over all the microdrops located between x and x + dx, per unit volume of the emulsion. The superscripts a and o denote the aqueous and the organic phases, respectively. Equation (3) is written on the assumption that the emulsion can be viewed as a pseudohomogeneous phase wherein the diffusivity of solute A can be approximated by that in the continuous phase (i.e. no diffusivity retardation due to microdrop “barriers” or enhancement due to close packing of the microdrops); this is generally true at “low” hold-ups of the microdispersed phase. Microdrop coalescenti has been neglected. Transforming eqs (1) and (2) into the Luplace domain and solving for the flux of B from a single drop, yields
The last results are obtained from application of the surface renewal theory due to Danckwerts (1970), where the age distribution of penetration elements at the gas-emulsion interface is simply given by S exp( -SO) (fraction of elements between age 0 and B + do) so that the specific rate averaged ouer the whole inte+x is given by j,” - Dl;(X;/ax)rX,,, S exp( -.%I) dS = S( -D~(dt?~/dx)),,O. Here, S is the surface renewal frequency and may be related to the liquid (emtdsion) side mass transfer coei%cient by k”‘ E a. Substituting this de6nition and the expression for FB from eq. (S), into eqs (6) and (7), the resulting expression is given by RA = J-
Lq 3 CManh do - 11 WA -L) 4=
k; C;,m,
~
Ml
where 4 = mnR and the symbols with an overbar denote Luplace domain variables, It is also assumed that all the microdrops have a tied radius, R. For the set of assumptions made, it can be seen that Fa does not depend upon C; and hence the rate of uptake by a microdrop is independent of its location with respect to the gas-emulsion interface. Thus, in this limit of the reaction front being coincident with the microdrop surface, Fx behaves as a t&edependent, zero-order reaction term. The condition at x --t S,
Table
- U
1.9
3[d/tanh
x sinh
cash(
Expt.
1
N= 1.0 2.0
1)
+1
(9)
into
G
I. = 0.1
1. = 0.2
Theo.
Expt.
Theo.
Expt.
Theo.
Expt.
Theo.
2.82 2.43
291 2.83
293 2.46
3.06 291
2.75 3.17
3.41 3.10
1.89 -
2.07 3.37
3.07 3.36
2.94 3.02
3.13 3.54
3.03 3.18
3.15 3.80
3.22 3.54
1.92
2.07 3.37
N = 0.417 rev/s :::
4 -
(
ELA
4
d2
where d = kER/,&@ and q = C&,j(zC’&). In the limiting case when # + 0 (around d = 0.2) eq. (8) reduces to
2. Enhancements factors in the speciiic rates of absorption of carbon dioxide emulsions of aqueous sodium hydroxide in ðyl hexanol, at various conditions
l_ = 0.05
(7)
l.Orev/s
3334
Shorter
Communications
This represents the maximum possible specific rate that can be obtained for such systems and is based on the instantaneous discharge of the dispersed-phase reactant into the continuous phase. Dividing eq. (9) by the maximum rate for pure physical absorption in water, i.e. k”,C;,, the expression for the limiting maximum enhancement factor is obtained as mA sinh (Gosh-’
(Q + l))/Q
(10)
Therefore, under these conditions, the rate is simply sustained at the maximum valuefor physical absorption in the oil phase, provided the reaction is able to keep the value of the bulk concentration near zero. Figure 2 shows the variation of
and the extent of penetration of solute A, as given by a simplification of eq. (7), becomes
+6,=cosh-‘(Q+l)
s
de-xl
= sinh [cash-’
(11) 6; =
where Q = m,(l -1.,)/&q) and 6 = 0:/k;. It is important to note that for situations where transient effects are important, such as accumulation in the continuous and/or microdispersed phase (as represented by terms containing mA) or time-dependent reaction terms (those containing Q), it is not possible to use the simpler film model of mass transfer.
&/ji=?j
(12)
40-
(16)
30-
20-
(17)
,’ ’ 5.0
1
*! ,’
\ \ \
,’
‘\ ---
are also shown in this table. The relevant physico-chemical data used in computing the enhancement factors are given in Table 1. The value of mA was approximated by using the initial rate for physical absorption of carbon dioxide in 2-ethyl hexanol = ktC;,ml
j-1)
sr = 1 + l/Q.
Table 2 shows I the experimental and theoretical (limiting) values req. (lo)] of the enhancement factors in the specific rates of absorption of carbon dioxide in different emulsions characterized by volumetric, fractional hold-up of the microdispersed phase (13 and the concentration of sodium hydroxide in it (q), for two stirring speeds. The classical enhancement factor values, experimental as well as those computed from (Doraiswamy and Sharma, 1984)
R: = ktC&
= cash-‘(Q
(15)
[derived from eqs (10) and (11). respectively] vs the group Q. For ST to become equal to four, which is approximately the penetration depth for pure physical absorption, Q is about 26. In other words, the assumption that Co, is zero is likely to be violated for Q > 26 (this is not a suflicient condition as some A still goes into the bulk phase with the surface elements returning from the gas-emulsion interface to the bulk, though under typical operating conditions this amount is likely to be “small”). A line showing another enhancement factor ¬ed as es and given by the expression below is also shown in Fig. 2:
DISCUSSION
E:=(~+&)
(Q +l)]/Q
, \ \
,’
61 &.J
,’
/’ ’
,’
,’
,’
>’
40
3.0
2.0
(13)
where the values of ki and Cj,, (solubility of carbon dioxide in water) are known independently. The value thus obtained was m, = 1.9 and compares well with the values of around 2 that may be calculated from literature data on the solubility of carbon dioxide in various organic solvents (Stephen and Stephen, 1962). Equation (13) and condition (4) assume that the distribution coefficient mA can be approximated as the ratio of solubilities of carbon dioxide in 2-ethyl hexanol to that in water. The solubility value for the aqueous phase has been taken to be identical to that in pure water since the correction factors arising due to the presence of ions (Danckwerts, 1970) were negligible at the low concentrations of sodium hydroxide used in this study. No viscosity effects have been considered in this study except those implicitly included in the measured values of the mass transfer coefficients for the aqueous and the oil phases. The viscosity did not vary appreciably with a change in the hold-up of the aqueous phase or the sodium hydroxide concentration in it. For pure Z-ethyl hexanol the measured viscosity was about 4.0 x 10-s kg/ms whereas for the heaviest emulsion was around 4.3 x 10-s kg/m s. Before analysing the absorption data, with the help of the proposed theory, it is worthwhile examining some implications of eq. (10). When Q 9 1, the sinh and cash-’ terms cancel each other and the expression for the limiting value of the enhancement factor reduces to
Fig. 2. Plot of enhancement factors sr and es as well as penetration depth of diffusant ST vs group Q.
This line signifies an enhancement factor that would be obtained if all the B currently immobilized within the microdrops were available in free (di&sive, with di@sivity equal to D$) form to react instantaneously with the A dij’using in the oil phase. Therefore, the effect of immobilizing B is to lower the enhancements to values given by .sl from ss. The significance of 4 in the proposed model arises from the fact that it represents the square root of the ratio of microdrop conversion time to the surface element contact PADi = J Rz/D~D~PL) tune (4 = k”,R/ and appears in the expression r or Fs to account for its time-dependent behaviour. Also, for the extreme case, namely, 4 4 1, the assumption of the reaction plane and the microdrop surface coinciding becomes redundant since now the discharge of B into the continuous phase may be considered to be instantaneous and the term Fs behaves like a point source. Therefore, the microdrops within a penetration element which are exposed
3335
Shorter Communications to a non-rero concentration of A are expected to deplete completely during their residence at the gas-emulsion interface, for this limit. In terms of dimensional estimates, the typical contact time of a penetration element is about 2 s whereas the time for complete conversion of a microdrop, according to rigorous calculations (Dutta et al., 1988), will range from about 0.25 to 0.6 times R2/D& i.e. 3.0 x lo-’ to 7.5 x lo-’ s, for the most highly loaded microdrop (using q = 2 and 20, for a microdrop close to the gas-emulsion interface and that away from it which is exposed to a tenth of the interfacial concentration, respectively). For typical operating conditions, 4 cannot be greater than unity since 4 reduces to R/(Dz/kO,) for 0: sz 4, and the condition for the emulsifiedphase microdrops to act as microreactors within a penetration element is R < (0:/k:). In this study, Q c 0.12. Therefore, eq. (10) may be expected to be obeyed closely. The size of the microdrops is not expected to influence the specific absorption rates in any significant manner as long as the condition of 4 being small is not violated, which is indeed the case for this study. In any ease, since the two procedures for making stable emulsions did not yield any significant difference in the microdrop sixes, it is not possible to test for any microdrop size effects. It may now be seen from Table 2 that the experimentally observed enhancement factors show excellent agreement with the corresponding values computed from eq. (10). The fact that for the stirring speed of N = 1 rev/s, the experimental values are consistently, slightly higher than the upper bound calculated from theory, probably reflect the measurement errors associated with the determination of the mass transfer coethcients and consequently the value of mA through eq. (13). For instance, mA = 2.1 (instead of 1.9) will make the theoretical enhancement factors slightly exceed the experimentally observed values. Thus, the microdrops exposed to A, near the gas-emulsion interface, deplete fully and this state of depletion percolates to more and more microdrops gradually; meanwhile the specific rate of absorption is sustained near the value for physical absorption into a pure oil phase.
CONCLUSIONS The strategy of absorption in water-in-oil emulsions accompanied by a fast chemical reaction in the emulsified phase has been experimentally explored along with a theoretical analysis. A common system, namely, carbon dioxide absorption in emulsions of aqueous sodium hydroxide in 2-ethyl hexanol has been used as a model system. The purpose of this study has been primarily to explore and test the strategy rather than demonstrate any significant enhancements. The experiments are limited by the difficulty in obtaining stable emulsions at high concentrations of the internal-phase reagent. This limitation is system specific and excellent enhancements may be obtained for chemical systems which have a large value of the distribution coefBetent m, (oil/water) for the solute A partitioning between the oil and the aqueous phases. Typically, industrial systems in which the absorbing solute has a high relative afinity for an organic phase will stand to benefit in terms of increased rates of absorption, such as absorption of olefinic gases (Mehra et al., 1988), carbonyl sulfide (Choudhuri and Sharma, 1989). etc. As compared to a pure aqueous, reactive phase it will become beneficial to use this strategy for absorption, in order to get higher rates, when E’, c Efi [as given by eq. (lo)]. Figure 3 shows plots of EC”and Efi (with mA as parameter) vs q for a typical set of conditions. The xones where I!& < E$ is satisfied denote the operating points where this benefit is likely to be achieved (along with the desired minivalue of rn”).
60
m”=50 .. ,
50/ --~
40-t
/
EA'
EAL
ccl
-
+T crl
30-
,
/
/
/
,
/
/
/
/’ mA=25
Fig. 3. Variation of enhancement factors .?Ii and E> versus concentration ratio 4 with distribution coe&cient mA as parameter; Data used: 1. = 0.1, kg/k”, = 1, D;/D> = 1.
In comparison to oil-in-water emulsions (Mehra, 1988) where the enhancement effects are proportional to the square root of m,,, here for the case of water-m-oil emulsions, these are directly in proportion to m, (Mehra, 1989). B. V. VENUGOPAL ANURAG MEHRA’ Department of Chemical Engineering Indian Institute of Technology, Bombay Powai, Bombay 400 076
NOTATION
concentration of solute A, kmol/m3 concentration of reactant B, kmol/m” diffusivity of A, ml/s diffusivity of B, m2/s enhancement factor in specific rate of absorption, dimensionless molar flux of B at (total) surface area of microdrops, located at distance x from the gas-emulsion interface, per unit volume of continuous phase, kmol/ms s liquid (emulsion) mass transfer coethcient for gasemulsion mass transfer, m/s second-order rate constant, ml/km01 s volumetric fractional hold-up of the microdispersed phase, dimensionless distribution coef6cient for solute A partitioning between the organic and aqueous phase [organic/aqueous], dimensionless speed of agitator rotation, rev/s ratio defined in eq. (7) (q = CG/zC;,), dimensionless group deiined in eq. (10) [Q = m,(l - lJ/(l,q)], dimensionless radial coordinate for a spherical microdrop, m radius of a microdrop, m specitic rate of absorption, kmol/ma s Laplace domain symbol and surface renewal freW==Y,
l/s
distance from the gas-emulsion interface in a surface element, m stoichiometric factor in the reaction A + HB + products, dimensionless (z = 2, in this study)
‘Author
to whom correspondence
should be addressed.
3336
Shorter Corn lmunications
Greek symbols d thickness of gas-emulsion 4 g s1 s1
e 3
diffusion film, emulsion
side (8 = Dz/k”d, m penetration thickness of diffusant k, m ratio of 4 to 6, dimensionless product of a, and Jmi dimensionless enhancement factor defined by eq. (16), dimensionless enhancement factor defined by eq. (17). dimensionless time (surface element contact time scale), s position of reaction front within a single drop, m Thiele modulus for diffusion of B in microdrop (4 = &R/m),
dimensionless
denotes (for A)
initial concentration
Superscripts a pertaining c g
i
L 0
A.1.Ch.E. J 34, 694-697. lanakiraman, B. and Sharma, M. M., 1985, Oximation of cycle-alkanones (cyclododecanone and 4-tert-butylcyclohexanone): micellar catalysis in slow and fast solid-liquid and liquid-liquid reaction systems. Chem.
Engng Sci. 40.223-233.
Subscripts denotes bulk value b 0
Danckwerts, P. V., 1970, Ga.+Liquid Reactions. McGraw Hill, London. Choudhuri. S. K. and Sharma, M. M., 1989, Absomtion of carbonyl sulfide in aqueous alkaline solutions: new strategies. Znd. Engng Chem. Res. Zs, 870-873. Do&wamy, L. K. and Sharma, M. M., 1984, Heterogeneous Reactions, Vol. 2. Wiley, New York. Dutta. B. K.. Middva. U. and Rav. P.. Mass transfer accompa&d by an &&taneous -r&&ion in a rigid drop.
(for B) or solubility
Mehra, A., 1988, Intensification of heterogeneous reactions through the use of a microphase - I. Theoretical. Chem. Engng Sci. 43, 899-912. Mehra, A., 1989, Intensification of heterogeneous reactions through the use of water-in-oil media, Chem. Engng Sci.
44,448-452. to aqueous phase to classical theory for plain
pertaining phase pertaining to gas phase initial value limiting value pertaining to organic phase
reactive
REFERENCES Bhagwat, S. S. and Sharma, M. M., 1988, Intensification of solid-liquid reactions: microemulsions. Chem. Engng Sci.
43, 195-205. Bruining, W. .I., Joosten, G. E. H., Beenackers, A. A. C. M. and Hofrnan, H., 1986, Enhancement of gas-liquid mass transfer by a dispersed second liquid phase. Chem. Engng Sci. 41, 1873-1877.
Mehra. A.. Pandit, A. and Sharma, M. M., 1988, Intensification bf heterogeneous reactions ihrough the L& of microDhases -IL. Experimental. Chem. Enarur Sci. 43,913-927. Mehra, A. and Sh&na, M. M., 1988, Absorption of hydrogen sulfide in aqueous solutions of iodides containing dissolved iodine: enhancements in rate due to DrcciDitated _ sulfur. Chem. Engng Sci. 43, 1071-1081. Perry, H. P. and Chilton. C. H., 1973, Chemical Engineers’ Handbook, pp. 3-93. Mcgraw Hill Kogakusha, Tokyo. Pradhan. N. C., Mehra, A. and Sharma, M. M., 1992, Intensification and selectivity modification through the use of a microphase: simultaneous absorption of two gases with chemi&l reaction. Chem. Engng Sci. 47, 493-498. Stephen, P. and Stephen, H., 1962, Solubilities orfZnorg~@c and Organic Compounds, pp. 107 1- 1075. Pergamon Press, London.