400
Ind. Eng. Chem. Process Des. Dev. 1904, 23, 400-406
Srinivasan, D.; Lakshmanan, C. M.; Degaleesan, T. E.; Laddha, G. S. Ind. Chem. Manuf. 1978, 16, 30. Suhnel. Von K.; Messow, U.; Salomon, M. Z . Phys. Chem. (Leiprig) 1979, 260, 142. Touhara, H.; Ikeda, M.; Nakanishi, K.; Watanabe, N. J . Chem. Thermodyn. 1975, 7, 887. Valero, J.; Gracia, M.; Gutierrez Losa, C. J . Chem. Thermodyn. 1980. 72, 621. Van Ness, H. C.;Soczek, C. A.; Peloquin, G. L.; Machado, R . L. J . Chem. Eng. Data 1987a, 12, 217. Van Ness, H. C.; Soczek, C. A.; Kochar. N. K. J . Chem. Eng. Data 1967b. 12, 346.
VelaSCO, I.; Otin, S.; Gutlerrez Losa, C. J . Chim. Phys. 1978, 75, 706. Woydckl, W. J . Chem. Thermodyn. 1975, 7 , 7 7 . Woyclckl, W. J . Chem. Thermodyn. 1975, 7 . 77. Woycickl, W. J . Chem. Thermodyn. 1980, 12, 165. Woyclckl, W.; Rhensius, P. J . Chem. Thermodyn. 1979, 1 1 , 153.
Received for review July 8, 1982 Accepted June 16, 1983
Some Aspects of Process Design of Liquid-Liquid Reactors T. V. Vasudevan and Man Mohan Sharma' Department of Chemical Technology, Universtiy of Bombay, Matunga, Bombay-400 0 19, India
Some aspects of the process design of liquid-liquid reactors where extraction is accompanied by fast reaction in the immediate vicinity of the interface have been considered. In a large number of cases of practical relevance analytical expressions can be deriied to obtain the pertinent design parameter. In the case of mechanically agitated contactors, operated batchwise, it can be shown that even a 10% excess of the reactant can bring down the batch time very substantially. The height of packed columns, for different controlling regimes, c a n be calculated analytically. Even in the case of plate columns the number of plates can be calculated analytically.
Introduction A variety of industrially important reactions, such as nitration, sulfonation, alkylation, reduction, etc., involve two liquid phases. In some cases where a choice can be exercised, the liquid-liquid mode of operation may be preferred over gas-liquid operation, due to the possibilities of obtaining much higher values of interfacial area in the former case. Consider the removal of COS from a C3 stream where both gas-liquid and liquid-liquid modes of operation can be considered; some advantages may be realized by adopting the liquid-liquid mode of operation (Sharma, 1983). The design of liquid-liquid reactors has received very limited attention and this paper will consider some aspects of process design of such reactors. Some aspects of the process design of gas-liquid reactors have been considered by Juvekar and Sharma (1977), and their paper may be considered as background information. Depending on the circumstances, the reaction can be carried out in the following modes of operation: batch, "semi-batch", and continuous. Mechanically agitated contactors are used for batch and "semi-batch" operations and spray columns, packed columns, plate columns, multistage mechanically agitated contactors, centrifugal extractors, etc., are usually used for continuous operation. The important design parameter is the time of reaction for a specified level of conversion in the case of batch and "semi-batch" operations and volume/height of reactor for the continuous mode of operation. A variety of cases of possible practical relevance have been considered and analytical expressions are given for most of the cases; in some cases numerical solutions are required. Some typical cases reported in Table I will be considered. Equations for design parameters are derived based on the assumption that the reaction is isothermal. This assumption is well justified because of the ease of heat re0196-4305/84/1123-0400$01.50/0
Table I. Design of Liquid-Liquid Reactors case no.
statement
(i) The concentration of solute in the dispersed phase is low so that there is no change in the dispersed phase flow rate and hence in the holdup and effective interfacial area. (ii) The molar volumes of reactant and product (soluble in the dispersed phase) are equal so that there is no change in the dispersed phase flow rate and hence in the holdup and effective interfacial area; there is no resistance in the dispersed phase. (iii) The dispersed phase is pure and the product is insoluble in the dispersed phase; time/height required for complete disappearance of droplets to be calculated.
moval in liquid-liquid reactors, and hence possibilities of maintaining isothermal conditions exist.
Batch Reactors In the design of batch reactors all the cases mentioned in Table I and subcases a and b mentioned in Table I1 have been considered. The analytical expressions for the different cases considered are given in Table 111. We assume that: (i) both the liquid phases are completely backmixed; (ii) the physical properties of liquids remain unchanged during the operation; and (iii) temperature remains constant throughout the period of operation. Considering case (i) of Table I with subcase (a) of Table 11, the material balance a t any time can be written as
= NAaV
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reactant over the stoichiometric amount brings down the batch time or height of the reactor by a considerable extent. This happens due to a shift in the regime of reaction as the reaction proceeds, when stoichiometric quantities are used. Semi-Batch Reactors The specific rate of mass transfer across the film of the dispersed phase is given by
(5) NA= kd([AoI - [Ail) Substituting eq 5 into eq 2 and rearranging, we get
In this type of reactor one of the reactants (say A) is added at discrete intervals into the reaction mixture either to achieve a better yield or to have a better control over heat transfer or for safety. The total number of intervals (N) is fixed with the same level of conversion for each interval. The assumptions mentioned in the analysis of design of batch reactors hold here as well. Proceeding on the same lines as in the case of batch reactors, the time for Nth interval can be obtained as
Integrating eq 1 and rearranging, we get zvd
(7) [Bo1 = [Boli - -([Aoli - [An]) VC Substituting eq 6 and 7 into eq 4 and rearranging we get
d[AoI + P(Y + dt
6
[AoI"2[AoIi)
+ (y +
tN
(8)
where P = a Vkd/ v d
k:VC
Vc[Boli
y=--
[Aoli vd
and
(9)
DAkZzVd
"(
6=
+-
mA
vc
DAkZz
)"2
vd
The initial and final conditions are a t t = 0:
[A01 =
[Aoli
(loa)
at t = t g :
[A01 =
Wolf
(lob)
The solution of eq 8 using initial and final conditions as per eq 10 gives the batch time
and
The total time can be obtained by the addition of time of individual intervals. The analytical expressions for the different cases considered are given in Table IV.
For the design of continuous plug-flow reactors (packed column, pipeline reactors, etc.) with cocurrent operation, the same analytical expressions as given for the batch reactor can be used for evaluating the height/length ratio of the reador with the modification that the volume of the reactor, V , will be replaced by the cross-sectional area of the contactor, S , and batch time, t b , will be replaced by the heightllength of the contactor, h,/L. In the case of countercurrent operation the parameter y will be
1
v c [Bo vd
0
+ [Aoli +
k,2 VC ~
DAkZzVd
and arctan in the design equation will be replaced by arcsin. An interesting observation in the design of batch and continuous plugflow reactors is that a 10% excess of
Plate Column Contactors In plate column contactors the main consideration is the calculation of the number of plates required to achieve a specified level of conversion. We assume t h a t (i) temperature is the same on all plates of the column; (ii) physical properties of the liquid phases do not change as they traverse through the column; (iii) on each plate the continuous phase is completely backmixed while the dispersed phase moves in a plug-flow manner. Equations are derived for obtaining the number of plates for cases (i) and (ii) of Table I and subcases (b) and (c) of Table I1 and are reported in Table V. Considering case (i) of Table I and sub-case (c) of Table I1 the rate of reaction can be written as Also
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 2, 1984
Eliminating [Ai] from eq 13 and substituting in eq 12, we get
405
Table I and subcases (a) and (b) of Table I1 have been considered. The analytical expressions for the various cases considered are given in Table VI. Considering case (i) of Table I with subcase (a) of Table 11, the material balance around the reactor can be written as Vd([Ao]i - [Aolo) = NAaV = aVm~[Ai],x kC2)'l2 (26)
Also kd([Ao] - [Ail) = m~[Ai]oX (D~kz[Bo]o+ k:)l12
(27)
Eliminating [Ai] from eq 27 and substituting it in eq 26, we get Vd([AoIi - [AoIo) = (aVmAkd[Ao]o X (DAk2[BoIo + k:)112)/(kd + mA x (DA~~[B,], + k:)'/') (28) where, [A,] = ([Ao]n+l+ [A,],)/2, the average concentration of A over the plate. Rearranging eq 16, we get
From material balance of two components around the reactor we also have
where
Substituting eq 29 and 30 in eq 28 we get the volume of reactor V=
P(6
+ (Y - x)'/? (y - x)W
x 1- x
(31)
where = Vd/akd
and
=
1-6
6-1
5T-i + a g [ B o l n The above procedures for the different cases considered in this paper will also be applicable when the reaction takes place in the dispersed phase, with the dispersed phase quantities associating themselves with B and continuous phase quantities with A (that is-the dispersed phase quantities like v,, kd, etc., will take the place of continuous phase quantities and vice versa). When the organic phase is present in excess all the design equations will be in terms of B, and y will be (zvd[A0li/V,) - [BOli;other constants will change accordingly. (In -a) 1 + 6 1-6
Multistage Mechanically Agitated Contactors Operated Continuously (Cocurrent or Countercurrent) In the design of this type of reactors the main parameter to be evaluated is the volume of reactor required for the specified level of conversion. The assumptions made in the design of batch reactors are valid. Case (i) and (ii) of
Fast Reaction in Both Phases A number of examples of practical relevance fall in this category, and Mhaskar and Sharma (1975) and Rod (1974) have discussed some typical cases. Backmixing in the ContinuoudDispersed Phase In the above exercise, although aspects of backmixing have not been taken into consideration, in the case of packed column or multistage contactors, these can also be considered with suitable modifications of constituent differential equations (Sarkar et al., 1980).
406
Ind. Eng. Chem. Process Des. Dev. 1984, 23, 406-409
Conclusions In a number of cases of practical importance the appropriate design parameter can be calculated by using an analytical expression, and this has been illustrated with some typical examples. In particular, it has been shown that: (1)analytical equations can be obtained for the time of reaction in the case of mechanically agitated contactors operated in batch or semibatch manner; (2) height/length of a packed column/plug-flow pipeline contactor, operated cocurrently and countercurrently, can be obtained by using analytical equations; (3) analytical equations can be derived for the calculation of number of plates in plate column contactors, thus avoiding the tedious graphical procedure or plate to plate calculations; (4)the volume of a continuously operated stirred tank reactor can be calculated from simple analytical equations for a variety of important cases. Nomenclature a = interfacial area of mass transfer, m2/m3 dispersion or
m2/m3contactor volume a' = interfacial area of mass transfer, m2/m2(cross-sectional area of plate)
[Ai] = concentration of solute A at the interface, mol/m3 [AJ= concentration of A in the bulk of organic phase, mol/m3 [A*] = solubility of solute in the aqueous phase, mol/m3 [Bo]= concentration of B in the bulk of aqueous (B) phase, mol/m3 DA = diffusivity of species A in B phase, m2/s h, = total height of the column, m k, = true continuous phase mass transfer coefficient, m/s kd = true dispersed phase mass transfer coefficient, m/s' k, = pseudo-first-order rate constant, s-l k2 = second-order rate constant, m3/mol s
L
= total length of the contactor, m = distribution coefficient of solute between aqueous and
mA
organic phases N = number of intervals or number of plates in a plate column contactor NA = specific rate of reaction, mol/m2 s S = cross-sectional area of column or pipeline contactor, m2 t B = total batch time, s V , = volume or volumetric flow rate of continuous phase, m3 or m3/s Vd = volume or volumetric flow rate of dispersed phase, m3 or m3/s V = total volume of reactor, m3 z = stoichiometric factor Subscripts i = inlet or initial condition f = final condition o = outlet condition N = Nth interval for semibatch operation n = nth plate
Literature Cited Juvekar, V. A.; Sharma, M. M. Trans. Inst. Chem. Eng. 1977, 55, 77. Mhaskar, R. D.;Sharma, M. M. Chem. Eng. Sci. 1975, 30, 011. Rod, V. Chem. Eng. J. 1974, 7 , 137. Sarkar, S.;Mumford, C. J.: Phillips, C. R. Ind. Eng. Chem. Process Des. Dev. 1980, 79, 665-671. Sharma, M. M. I n "Handbook of Solvent Extraction"; Chapter 2.1, Lo, T.C.; Baird, M. H. I.; Hanson, C., Ed.; Wiley: New York, 1983; p 37.
Received for review October 13, 1981 Revised manuscript received September 8, 1982 Accepted May 10, 1983
This paper was presented a t the 181st National Meeting of the American Chemical Society,Atlanta, GA, April 1981; INDE 87.
COMMUNICATIONS Improved Technique for Monitoring Balling Circuitst Control of balling circuits tends to be a subjective operation based on operator experience and intuition. Cumulative sum techniques have been applied to output data from a balling system to yield more informative control charts. It has been observed that these cusum plots allow prediction of process upsets, caused by changes in moisture content or feed characteristics, before they become apparent in the pelletized product. Results indicate that the deviation (AW) of the output rate from the expected value can be used to estimate the changes in moisture content required to correct the situation. A universal correlation between change in moisture content and AW has been observed for a number of different feed materials.
Introduction The control of industrial balling circuits tends to be a subjective operation based largely on operator experience and intuition. An operator uses a record of either recycle or product load variation, together with a visual apparaisal of the surface condition (wet or dry) of the pelletized product, to determine what control action to take. In most plants adjustment of the liquid bonding phase is the primary mechanism used to control pellet size. However, drifting and surging effects, coupled with long delay times, NRCC No. 22465
make efficient operation of pelletizing plants a complicated and difficult problem (Sherrington, 1968). During some recent work with a laboratory scale conical balling drum (Meadus and Sparks, 1983), it was determined that changes in the rate of production of pellets could be graphically represented in a way that allowed prediction of out of control changes in granule size before they were physically observable in the product. Such advance warning of impending process upsets materially reduces the delay time before implementation of corrective action and can result in overall improvement in process control and product quality.
0196-4305/84/1123-0406$01.50/0Published 1984 by the
American Chemical Society
