712
Ind. Eng. Chem. Res. 1987, 26, 712-718
Dispersed-Phase Hydrodynamic Characteristics and Mass Transfer in Three-phase (Liquid-Liquid) Fluidized Beds Tai-Ming Chiu, Ying-Chu Hoh,* and Wei-Ko Wang Chemical Engineering Division, Institute of Nuclear Energy Research, Lung-Tan, Taiwan, R.O.C.
The dispersed-phase holdup, axial mixing, and mass transfer in a three-phase (liquid-liquid) fluidized bed have been studied experimentally. The test system used was kerosene-acetic acid (solute)-NaOH solution-solid particles. The indicator color change method was employed to obtain the solute concentration profile. The Peclet number and volumetric mass-transfer coefficient were estimated from the concentration profile along the column height with the aid of a axial dispersed plug-flow model and nonlinear optimization method. The results show that the dispersed-phase holdup, axial dispersion coefficient, and volumetric mass-transfer coefficient are dependent on the dispersed-phase flow rate and particle size. The continuous-phase flow-rate effect is not significant. Complementary measurements have also performed on two-phase (liquid-liquid) systems. Liquid-liquid extraction is carried out in industry principally in countercurrent flow through columns or in mixer-settlers. Recently, there has been interest in finding the possibilities of operating a liquid-liquid extraction contactor in cocurrent flow. Godfrey and Slater (1978) have reviewed the cocurrent flow system for liquid-liquid extraction. Acharjee et al. (1978) have studied the cocurrent flow liquid-liquid ternary mass transfer in ejectors. Takahashi et al. (1983) have pointed out that in solvent extraction processes, the multistage contact in upward cocurrent flow is also favorable for obtaining the high extracted fraction of solute. The cocurrent extraction in a reciprocating plate column has been studied by Noh and Baird (1984). It is only in more recent years that a few papers have become available on the topic of cocurrent three-phase fluidized bed extraction. Roszak and Gawronski (1979) have pointed out that cocurrent liquid-liquid flow in a column with fluidized beds of solid particles is promising in catalytic, leaching, and extraction processes. Two liquid phases flowing cocurrently through a fluidized bed provide compact, efficient, and inexpensive mixing and good dispersion contact. The power required for dispersion and mixing is supplied by the pressure drop rather than by the density difference; hence, very high throughputs are possible. Mass-transfer coefficients and drop size distributions in cocurrent liquid-liquid-solid fluidized beds have been reported by Roszak and Gawronski (1979) for the systems toluene-acetic acid-water and toluene-benzoic acid-water, and by Kim et al. (1983) for the system toluene-acetic acid-water at relative low dispersed-phase flow rates. Dakshinamurty et al. (1980) reported the mass-transfer data for the extraction of propionic and butyric acids from the dispersed phase to the continuous phase in three-phase cocurrent fluidized beds. The extraction of nicotine from water to kerosene in a three-phase (liquid-liquid) fluidized bed has been reported by Dakshinamurty et al. (1983). The individual fluid-phase resistances for the systems of isobutyl alcohol-water, methyl isobutyl ketone-water and n-butyl acetate-water have been measured by Dakshinamurty et al. (1984). Most of the previous studies on liquid-liquid mass transfer in three-phase cocurrent fluidized beds are confined to low dispersed-phase flow rates and based on the plug-flow model. The purpose of the present study is to obtain the experimental data of the holdup, axial mixing, and mass transfer for the dispersed phase in a cocurrent liquid-liquid-solid fluidized bed. The indicator color 0888-5885/87/2626-0712$01.50/0
change method (Baird, 1974) was employed to measure the necessary data. This method can avoid the additional mass transfer during the sampling because no sampling is required in this method. In addition, the mixing characteristics of the continuous phase need not be known for calculation since the acidic solute in the continuous phase is zero.
Method of Analysis The indicator color change technique was developed by Baird (1974) for the measurement of axial mixing in a pulsed plate column. Recently, Noh and Baird (1984) modified the method to determine the mass-transfer rate based on the plug-flow model in a cocurrent reciprocating plate column. The principle of the method is based on an instantaneous chemical reaction between acid and base allowed to take place in the continuous phase. The neutralization zone height may be detected from the color change of the suitable trace indicator, such as phenolphthalein. In operation, an acid solute transfers from the dispersed phase to the continuous phase which contains a free base. The details should be referred to the work of Noh and Baird (1984). If perfect radial mixing and steady state are assumed, for the one-dimensional dispersion model, the solute balance across an infinitesimal column element yields the following differential equation for mass transfer from the dispersed phase into the continuous phase:
The solute concentration in the continuous phase is equal to zero because an instantaneous reaction occurs in that phase. Hence eq 1 can be written as d2Co uo dCo Koa Ed------co =0 (2) dZ2 60 dZ 60 The dispersion coefficient, Ed, is a probabilistic term accounting primarily for velocity distribution effects, including eddy mixing and interphase entrainment. Instead of the dispersed-phase dispersion coefficient, the column Peclet number, PedH, is frequently used as an axial mixing parameter. It is defined as (3) Equation 2 is normally written in dimensionless form 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 713
where Co = Co/(Co)in, 2 = Z / H , and Nod= KoaH/uo. The boundary conditions are (5)
The solution for eq 4 with the boundary conditions as shown in eq 5 and 6 is m2paemiZ
- mlemiem2Z
C, =
(7)
where pedH(
m, = 2
1-
[ [
1+-
(8)
PedH
m2 = “dH( - 1 + 1 + -4N0d]”2) 2 PedH
(9)
Equation 7 can be used to calculate the concentration profiles when PedHand Nodor Koa are known and vice versa. The overall mass balance across the bed leads to (10) uO[(cO)in- c01 = UA[(CA)in - CAI The value of CA becomes zero at the neutralization zone height, Z,, and it follows from eq 10 that
where
The relationship between eo and 2, was obtained by varying the height of the neutralization zone in the column for the bed of constant height and voidage. Changes in the height of the neutralization zone in the column were realized by varying the concentration of the base in the continuous phase at a constant concentration of acid in the dispersed phase. It should be noted that the values of 6 must be equal to or less than 1.0 if neutrality is to be achieved within the bed. For plug flow, eq 4 can be reduced to
or dCo = -KoaCo dZ If Koa is constant, then Uo
7
-U0
Koa = - In Co
H
If Koa is not constant, then the local values of Koa are calculated from
Table I. Properties of Solid Particles type diameter, m glass beads 0.00227 glass beads 0.00436 Table 11. Properties of Fluids water density, kg/m3 kerosene density, kg/m3 interfacial tension, mN/m
density, kg/m3 2500 2380
1000 784 21
The equilibrium distribution of acetic acid strongly favors the continuous phase (Noh and Baird, 1984) and KOwill be nearly equal to the dispersed-phase-fiim mass-transfer coefficient. In addition, Losev and Zheleznyak (1976) have pointed out that with an instantaneous chemical reaction in the continuous phase, the mass transfer from the controlling dispersed phase remains the same as in the absence of a chemical reaction and that only the magnitude of the motivating force varies. The column Peclet number and average volumetric mass-transfer coefficient of the dispersed phase were calculated via a nonlinear optimization procedure from the measured concentration profiles with the aid of eq 7 until the sum of the squares of the difference between the measured and calculated solute concentrations was minimized. The value of the average volumetric mass-transfer coefficient based on the plug-flow model was used as the initial search value of Koa. The method proposed by Chang (1984) was employed to calculate the initial guess value for the Peclet number.
Experimental Section The experiments were carried out in a cylindrical Plexiglas column so that the solid behavior could be observed. The diameter of the column was 0.042 m, and the length was 1.6 m. The column was equipped with nine pressure taps at 0.15-m intervals and seven sampling points at 0.2-m intervals. The top of the column protruded into a concentrically mounted outlet header, acting as an overflow weir to maintain an approximately constant head in the column. The calming section, 0.3-m long, was packed with 6-mm-diameter glass beads in 0.1-m height. Between the calming section and the bed, a gasket attached with 1.47 X and 7.4 X m clear opening stainless steel screen was placed between the flanges to support the bed. The extraction system was kerosene-acetic acid-NaOH solution. Glass beads of two different sizes were used as the solid particles. The properties of solid particles are shown in Table I. In operation, acetic acid transfers from the dispersed phase which is kerosene to the continuous phase which is the diluted NaOH solution containing trace phenolphthalein. The inlet acetic acid concentration was in the range 0.05-0.08 kmol/m3. The dispersed phase was pumped from a storage tank through a rotameter and entered into the bed via a distributor which was located 1.0 cm below the bed support. The inlet NaOH concentration was in the range 0.002-0.03 kmol/m3. The continuous phase was pumped from a storage tank through a rotameter and entered into the bed via the calming section. The fluid properties are shown in Table 11. The bed height was determined either by pressure drop profiles or by visual observation. The neutralization zone height was measured by visual observation. The reproducibility was quite well. The holdup of dispersed phase was measured by drawing out a sample through a sampling point and measuring the phase volumes after separation in a graduated cylinder. The dispersed-phase holdup
714
Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987
SETTLER
TO
?-
7 w
v
t
O3I
i i
m
ROTAMETER P
0'4
/'
a
3
P
1
a P
l O L E W S PHASE
W
RLP
o.2
ORGWC PHASE
STORAW T A M
STOWE T A M
Figure 1. Experimental setup. U,
V
u, = 0,073 "S/
u, '
= 0.043 m/s
A
= 0.092 m/r
0
0
/
0.02
0.03
0.04
suprtiid Dicp.ru6
Phase
W i r y
0
0.01
0.05 U.
0.06
, msI
Figure 3. Holdup of dispersed phase in bed with 0.00227-m particles. 0.2
t
/ / 0.4
c
03
d d, = 0.00436m I
0 0
0.01
I
I
0.02
Superhclal
0.03
Oispersed
I
0.04 Phose
I
0.05 Velocify
I
I
0.06 uo
0.07
, m /s
Figure 2. Holdup of dispersed phase in bed with 0.00436-m particles.
profile was obtained by sampling from different vertical levels along the length of the bed. Care must be taken in drawing the sample in order to maintain the steady-state operation. The holdup of the dispersed phase in the two-phase system was also measured by quickly closing the organic and aqueous inlet valves simultaneously after steady state was reached and measuring the interface position after the phase separation was completed. The concentration of NaOH in the aqueous phase was determined by titration with standard HC1 solution. The concentration of acetic acid in kerosene was determined by titration of the raffinate after the phase separation. The flow diagram of the present work is shown in Figure 1.
Results and Discussion Holdup of the Dispersed Phase. The plots of holdup of the dispersed phase in three-phase (liquid-liquid) fluidized beds as a function of the dispersed-phase flow rate are shown in Figures 2 and 3. Figure 4 shows the relationship between holdup of the dispersed phase and the dispersed-phase flow rate in the absence of solid particles. The results show that the dispersed holdup increases with increasing the dispersed-phase flow rate in both two-phase and three-phase systems. The increasing holdup of the dispersed phase can be attributed to the fact
t
0.2
E
P f B B
0 U, A
= 0.033 "/S = 0.056 m/c
U,
0 U, = 0.073 "/s
0.I
0
U,
= 0.092 m/s
d, = 0
I
0
0.01
I
I
002
Suwrficiol
003 Di-ced
I
0.04
Phaud
I
I
I
0.05
0.06
Volocity
U.
, m /s
Figure 4. Holdup of dispersed phase in two-phase system.
that an increase in the flow of the dispersed phase results in an increase in the drop population density. A similar trend was observed for the gas holdup in gas-liquid-solid fluidized beds. It was found that the gas holdup in gasliquid-solid fluidized beds increases with increasing the gas velocity for a particular liquid velocity (Epstein, 1981; Chiu, 1982). The effect of the continuous-phase flow rate on the holdup of the dispersed phase can be deduced from Figures 2-4. It can be seen that for a particular flow of a dispersed phase, its holdup decreases with increasing the continuous-phase velocity. An increase in the flow of the continuous phase causes an increase in turbulent force as well
Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 715
s
003
-
0.6
A
=
d,
0.00436
0
U.
V
U,
A A
U,
.
X V
m
n
0.5
-
' I d,=O
0.4
-
@
0.3
-
c
d.
= 0.00227 m
U,
= 0.073 m/s
002
-
0
= 0033 %
0 0 4 3 "/. = 0.086 mh ~ U, = 0.073 "% u, = 0.092 "/*
=
v
d.. , 0 00227 m
u, = 0.10e "/'
/./' ' / ' A
I
'//.A*/'/
ai
0
D
'
~
I
I
I
a2
0.3
0.4
M ROW
uuaup
e.
Figure 6. Relationship between drift flux and holdup of dispersed phase. I
0 0
0.01
I 0.02
U. Suprrflciol
I
I 0.03
0.04
I 0.05
I 0.06
, m!
Dlcprrred
Phase
Velocity
Figure 5. Comparison of solid-free dispersed-phase holdup in particulate systems with two-phase systems.
0.04
-
0.03
-
1%-
d,.
0.00436 m
0.02
I-
V
0
as conveying drops faster. The observed decrease in the dispersed-phase holdup suggested that the effect of faster conveyance of drops by the continuous phase is relatively larger than that of the decrease of drop size. The effect of particle size on the dispersed-phaseholdup can also be detected from Figures 2 and 3. It appears that for given continuous-phaseand dispersed-phase flow rates, the dispersed-phase holdup increases with increasing particle diameter. This could be explained by the increase of inertial force which caused drop breakup as the particle size increased. From Figures 2-4, it can be seen that the dispersed-phase holdup in beds with the presence of solid particles is smaller than that of the one without particles. This may be due to the decrease of the available crosssectional area for the flow. The typical plots of the solid-free dispersed-phase holdup, i.e., the ratio of the dispersed-phase holdup to the bed porosity, as a function of the dispersed-phasevelocity for three-phase and two-phase systems are shown in Figure 5. It appears that the solid-free dispersed-phase holdup in the bed with 0.00436-m solid particles is larger than that of the one without solid particles. However, a reverse trend appeared when the particle diameter is 0.00227 m. This means that the bed with 0.00436-m-glassbeads is characterized by the drop breakup and the bed with 0.00227-m-glass beads is characterized by drop coalescence. A similar trend was observed in gas-liquid-solid fluidized beds (Epstein, 1981; Chiu, 1982). It should be noted that the steady-state dispersed-phase holdup is not equal to the flow ratio of the dispersed phase to the total flow. This could be inferred that there is a slip between the two phases. The slip velocity or drift flux concept has been correlated with the dispersed-phase holdup successfully and has been used to predict the holdup in countercurrent extractors. According to the results of Wallis (1969), the drift flux of the dispersed phase is defined as
According to the above equation, the drift flux, VcD, calculated from the present data is plotted as a function of
0
j 2
0
---
0.01
5
Dalahinomuny et. at. ( I O I O )
0
3
0.-
1
'*-
1 rs i
U, = 0.056 m/r U, = 0.073 "/r U, = 0.106 %
-
t 6 P
0.W
0.01
o
-
0 0
---
UA = 0.033 m/r U, = 0.043 m/s u, = 0.056 m/s UA = 0 . 0 7 3 U, = 0 . 0 9 2
% mka/g
/'
I
I
I
d,
/
= 0.00227 m
I '
I I 8+ -'
/ -
Da*rl*Mmny et. at. ( I O I O )
I
d'=o
I
I
716 Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987
culation within the droplets when they collide with solid particles. From Figure 7, it can be seen that the effect of the continuous-phase velocity on Koa is not significant. The values of Koa decrease very slightly with increasing the continuous-phase velocity. An increase in the continuous-phase velocity leads to the decrease in the dispersed-phase holdup as well as the drop size resulting from the increase of turbulence. The first consequence causes a decrease in interfacial area; thus, Koa decreases. The latter consequence leads to an increase in interfacial area; thus, Koa increases. The slight effect of the continuousphase velocity on Koa may be due to the offset of both consequences. According to the literature, the effect of the continuous-phase velocity on Koa in three-phase (liquid-liquid) fluidized beds is not consistent among the previous studies. Roszak and Gawronski (1979) found that Koa decreases with increasing the continuous velocity for the system of toluene-acetic acid-water at uo = 0.0011 m/s. Dakshinamurty et al. (1980) found that Koa is independent of the continuous-phase velocity in the case of extraction of propionic and butyric acids from the dispersed kerosene phase to the continuous water phase. Later, Dakshinamurty et al. (1983) reported that Koa increases with increasing the continuous-phase velocity for the extraction of nicotine from the continuous water phase to the dispersed kerosene. The decrease of Koa as the continuous-phase velocity is increased can be detected from the correlation of Noh and Baird (1984). They studied the mass transfer of acetic acid from the dispersed kerosene phase to the continuous dilute NaOH solution in a cocurrent reciprocating plate column. The effect of the particle size on Koa can be detected from Figure 7. The results show that the larger the particle size, the larger the value of Koa is. This can attribute to the increase of inertial force as the particle size increases. Bailes et ai. (1976) pointed out that the presence of the solid particles will promote mass transfer by breaking any large dispersed-phase drops and by promoting mixing in drops either by distorting them or by producing a coalescence-redispersion cycle as well as reducing axial mixing. From Figure 7, it can also be seen that the value of Koa in the particulate system is larger than that in the twophase system. A similar trend was observed by Dakshinamurty et al. (1980, 1983). The dashed lines shown in Figure 7 represent the calculated values of Koa by using the correlation equation proposed by Dakshinamurty et al. (1980) in the extraction of propionic and butyric acids from the dispersed phase to the continuous phase. Dakshinamurty et al. (1980) reported that the height of the transfer unit is equal to 1.54 and 3.15 m for the three-phase system with 0.0044-m porcelain beads and the two-phase system, respectively. It can be seen that the data obtained in the present work for the two-phase system are in agreement with the correlation equation proposed by Dakshinamurty et al. (1980) except a t the higher dispersed-phase flow rates. In addition, the present data for the three-phase system with 0.00436-m glass beads are relatively higher than those calculated from the correlation equation reported by Dakshinamurty et al. (1980). This may be due to the different solute used and the different method employed for the data treatment. The values of Koa reported by Dakshinamurty et al. (1980) were calculated based on the plug-flow model and by using logarithmic mean concentration of the solute as the concentration driving force. Dispersed-Phase Axial Mixing. A knowledge of the value of the dispersion coefficient or Peclet number is essential to the design of a column-type extractor. The
'? t
0.2
j$ 0.I
I 1 1
0 0
0.01 Superficial
I
I
0.02 Dirpsrwd
Phase
0.04
I
I
1
0.03
0.05
Velocity
Uo
0.06
, m /s
0.03
n &
2
.
0.02
L-0.01
0
U A = 0 . 0 9 2 "/I
f
0
0
0.01
Suptrficial
0.02
M8pm.d
0.03
Phase
0.04
v.locity
0.05
U.
0.06
, m/r
Figure 8. Relationship between particle Peclet number and fluid flow rates in particulate systems.
particle Peclet number is equal to the product of the column Peclet number and the ratio of the particle diameter to the bed height. The plots of the particle Peclet number in a three-phase (liquid-liquid) fluidized bed as a function of the dispersed-phase velocity a t the various continuous phase velocities are shown in Figure 8. It can be seen that for the bed with smaller particles, the particle Peclet number initially increases, passes a maximum value, and then decreases. The particle Peclet number initially increases and then levels off for beds with larger particles. Figure 9 shows the effect of the dispersed-phase velocity on the dispersion coefficient in three-phase (liquid-liquid) fluidized beds at the various continuous-phase velocities. For the bed with small particles and an increase in the dispersed-phase velocity at a fixed continuous-phase velocity, the dispersion coefficient initially decreases, passes a minimum value, and then begins to increase. For the bed with larger particles, the dispersion coefficient initially decreases with increasing the dispersed-phase velocity and then levels off. There is scarce data on dispersed-phase mixing for cocurrent liquid-liquid-solid fluidized beds in the literature. With an increase in the dispersed-phase velocity, the axial dispersion coefficient decreases in countercurrent extractors. This phenomena has been reported by Komasawa and Ingham (1978), Husung et al. (1981),and Jancic et al. (1984) for conventional and other types of columns. All of them have pointed out that the decreasing dispersed-phase dispersion coefficient is due to the effects of higher coalescence and redispersion frequency resulting from higher dispersed-phase holdup as the dispersed-phase velocity increased. Schugerl (1967) reported that the gas-phase axial mixing in cocurrent bubble columns and gas-liquid-solid fluidized beds is caused by nonuniformity of the bubble velocities. The increasing coalescence and redispersion diminish the
Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 717 U, = 0.043 m/s
U, = 0.056 m/s
0
0.03 -
0.00436 m U, = 0.092
V
9
U, = 0.106 m/s
V
u
z E
0.02
-
0.01
-
0
W
E
E c
8
0
.-su
si
8
01
I 0.02
I
0.0 I
0
Supertlcia~
o i s p ~ ~ Phose ~ d
I 0.04
I
0.03 vclociry
I
I
0.05
0.06
, m/s
U.
Figure 9. Effect of fluid flow rates on the dispersion coefficient in particulate systems.
I
.4
u, * 0.073 m h v uA= 0.092 m/s
0
.2
0' 0
I
I
I
I
I
I
0.01
0.02
0.03
0.04
0.05
0.06
Supwflcial
Dispersed
Phoie
Voloclty
m 1s
Figure 10. Relationship between Peclet number based on column diameter and dispersed-phase flow rate.
nonuniformity of the bubble velocity and the intensity of the axial mixing. From Figure 9, it can be seen that the dispersion coefficient increases with increasing the continuous-phase velocity at a fixed flow of dispersed phase. The increasing dispersion coefficient may be due to the decrease of the dispersed-phase holdup. It is also found that the dispersion coefficient of the dispersed phase increases with decreasing particle size. As indicated before, drop size and its rising velocity decreased with increasing particle size in a three-phase (liquid-liquid) fluidized bed. This could explain why the smaller the particle size, the larger the dispersion coefficient that results. It is recognized that the presence of solid particles leads to narrow the drop size distribution and to a corresponding narrowing of the drop rising velocity distribution. It is expected that the dispersed-phase axial dispersion coefficient in a liquid-liquid two-phase system is higher than that in a particulate system. Figure 10 shows the relationship between the Peclet number based on column diameter and dispersed-phase velocity. It can be seen that
0
-
- Dir#rrion 0
.
MOM
EIWmvnMlDotcr
UA = 0.073 m/s U* '
= 0.03 I
I
m/s '
1
1
I
I
I
I
718
I n d . Eng. Chem. Res. 1987,26, 718-726
1. The dispersed-phase holdup increases with increasing the dispersed-phase velocity and particle size and with decreasing the continuous-phase velocity in a three-phase (liquid-liquid) fluidized bed. A similar trend was observed in the two-phase (liquid-liquid) system. 2 . The presence of solid particles leads to an increase in the volumetric mass-transfer coefficient and a decrease in mixing intensity. 3. The bed with larger particles (0.00436 m) is characterized by drop breakup and that with smaller particles (0.00227 m) is characterized by drop coalescence. 4. The volumetric mass-transfer coefficient increases with increasing the dispersed-phase velocity and particle size and slightly decreasing the continuous-phase velocity. 5. The dispersion coefficient in the bed with smaller particles initially decreases, passes a minimum value, and then increases as the dispersed-phase velocity is progressively increased. However, in the bed with larger particles, the dispersion coefficient initially decreases and then levels off. In the two-phase system, the Peclet number based on the column diameter is constant with a value of 0.1152 f 0.005.
Nomenclature a = interfacial area per unit volume, l / m CA = concentration of NaOH in the continuous phase, kmol/m3 Cn = concentration of acetic acid in the dispersed phase, kmol/m3 = CO/(Co)jn Co* = equilibrium concentration of acetic acid in the con-
tinuous phase, kmol/m3 Ed = dispersion coefficient of the dispersed phase, mz/s H = bed height, m KO= overall mass-transfer coefficient, mj s Nod = number of transfer units Ped, = Peclet number based on column diameter, (u$)/(&) PedH= column Peclet number, (u,$f)/(EdcO) Ped, = particle Peclet number, (uOdp)/(+O) uA = continuous-phase superficial velocity, mj s
uo = dispersed-phase superficial velocity, m/s V,, = drift flux, m/s = axial length, m Z = Z/H
z
Greek Symbols q, = the dispersed-phase holdup
Literature Cited Acharjee, D. K.; Mitra, A. K.; Roy, A. N. Indian J . Technol. 1978, 16, 262. Bailes, P. J.; Huges, M. A. Chem. Eng. 1976, 86. Baird, M. H. I. Can. J. Chem. Eng. 1974, 33, 341. Chang, S. S.Master Thesis, National Taiwan Institute of Technology, Taipei, Taiwan, R.O.C., 1984. Chiu, T. M. Ph.D. Thesis, Polytechnic Institute of New York, Brooklyn, 1982. Dakshinamurty, P.; Krishnamurty, R.; Prasad, M. S. S.S.; Rajasekhar, P. B. Indian J . Technol. 1983, 21, 20. Dakshinamurty, P.; Subrahmanyam, V.; Rao, R. V. P.; Vijayaaradhi, P.; Ind. Eng. Chem. Process Des. Dev. 1984,23, 132. Dakshinamurty, P.; Subrahmanyam, V.; Seshagirirao, V. V. B.; Prasad, M. S.S.S. Indian J . Technol. 1980, 18, 501. Epstein, N. Can. J . Chem. Eng. 1981, 59, 649. Godfrey, J. C.; Slater, M. J. Chem. Znd. 1978, 745. Husung, G.; Marr, R.; Wolschner, B. Proc. World Congr. Chem. Eng., 2nd 1981,4, 439. Jancic, S.J.; Zuiderweg, F. J.; Streiff, F. AZChE Symp. 1984,80(238), 139. Kim, B. K.; Kim, K.; Ryu, M. S.Proc. Pac. Chem. Eng. Congr., 3rd 1983, 1 , 124. Komasawa, I.; Ingham, J. Chem. Eng. Sci. 1978, 33, 341. Losev, B. D.; Zheleznyak, A. S. J. Appl. Chem. USSR (Engl. Transl.) 1976, 49, 1593. Noh, S.H.; Baird, M. H. I. AZChE J . 1984, 30, 120. Roszak, J.; Gawronski, R. Chem. Eng. J. 1979, 17, 101. Schugerl, K. Proc. Znt. Symp. Fluid. 1967, 9.4, 782. Takahashi, K.; Kamiha, H.; Uchida, S.;Takeuchi, H. Soluent Extr. Zon Exch. 1983, I , 311. Wallis, G. B. One-dimensional Two Phase Flow; McGraw-Hill, New York, 1969; Chapter 6.
Received for review November 20, 1985 Revised manuscript received October 21, 1986 Accepted December 6, 1986
Optimal Retrofit Design of Multiproduct Batch Plants Jane A. Vaselenak,+Ignacio E. Grossmann,* and Arthur W. Westerberg Department of Chemical Engineering, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213
The problem of retrofit design of multiproduct batch plants is considered in which the optimal addition of equipment to an existing plant must be determined in view of changes in the product demands. I n order t o circumvent the combinatorial problem requiring the analysis of many alternatives, the problem is formulated as a mixed-integer nonlinear program (MINLP) and solved with the outer-approximation algorithm of Duran and Grossmann. It is shown that by using suitable variable transformations and approximations, the global optimum solution is guaranteed. Two numerical examples are presented. This paper will address the problem of optimal retrofit design of multiproduct batch plants. In this problem, the sizes and types of equipment for an existing multiproduct batch plant are given. Due to the changing market conditions, it is assumed that new production targets and selling prices are specified for a given set of products. The problem then consists in finding those design modifications that involve purchase of new equipment for the existing *Author to whom correspondence should be addressed. 'Current address: Shell Development Co., Houston, TX 77001.
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plant to maximize the profit. The production targets that are given for the retrofit problem could be fixed or be given as upper limits. In this work the production levels are treated as upper limits to account for the following possibility. If the cost of the new equipment to operate at these new production levels is more than the revenue from the increased production, then either no new equipment should be purchased or else limited additions of equipment should be made at lower production levels. Therefore, the production levels must be optimized as part of the retrofit design problem. 0 1987 American Chemical Society
