I n d . Eng. Chem. Res. 1988,27, 739-743 7
739
w = water 0 = initial condition = measured value
= residence time, min
-
= fat phase holdup ratio in reactor
Subscripts and Superscripts
a = fatty acid d = diglycerides e = equilibrium state f = fat phase g = glycerol m = monoglyceride t = triglyceride
Literature Cited Patil, T. A.; Butala, D. N.; Raghunathan, T. S.; Shankar, H. S. Ind. Eng. Chem. Res. 1988, preceding paper in this issue.
Received for review May 8, 1986 Revised manuscript received May 19, 1987 Accepted June 18, 1987
Thermal Hydrolysis of Vegetable Oils and Fats. 3. An Analysis of Design Alternatives P. D. Namdev, T. A. P a t i l , T. S. Raghunathan, and H. S. S h a n k a r * Department of Chemical Engineering, Indian Institute of Technology, Bombay 400 076, India
An analysis of the oil hydrolysis reactor design alternatives is performed. A model reaction t == g for oil hydrolysis is used to simulate the performance of several reactor configurations. The continuous countercurrent spray column is shown t o be superior t o others in terms of productivity and conversion. A tubular plug-flow reactor module is shown t o have promising features. 1. Introduction A number of reactor configurations can be considered for oil hydrolysis. These include batch, semicontinuous, and continuous reactors. However, commercial operations employ either batch autoclaves or continuous countercurrent spray columns. Batch operations have considerable operational flexibility but involve low productivity. The countercurrent columns have higher productivity but lower operational flexibility, thus the need for evaluation of existing as well as possible design alternatives. A three-step kinetic model for the oil hydrolysis reaction is given by Patil et al. (1988a). It is possible to simulate the performance of different reactor configurations by using this model. Since the kinetic model is nonlinear, numerical procedures are required for the solutions of resulting ordinary differential equations. Namdev (1987) has simulated the performance of a continuous countercurrent spray column by using this model. In this paper, the elementary reaction t g is used to model the oil hydrolysis reaction. The single-step kinetic model is fitted to the experimental data of Sturzenneger and Sturm (1951) to estimate the parameters. Analytical solutions of the performance equations for batch, semicontinuous, and continuous hydrolyzers are given. The procedure thus provides a quick method of understanding the performance aspects of different design alternatives and would therefore be valuable for design and operating personnel. 2. The Model Reaction
Consider the model liquid-liquid reaction k
t&g k2
(1)
under the following assumptions to be equivalent to the fat/oil hydrolysis reaction described earlier by Patil et al. (1988a,b). (a) Component t is present in phase 1, where reaction 1 occurs, while product g distributes between phases 1and 2 such that the following equation applies: y g = mxg (2)
(b) Component t has no solubility in phase 2, and phases 1 and 2 are immiscible. (c) The mass and density of each phase remain constant during the reaction. (d) Reaction 1 belongs to a very slow reaction regime. The model reaction and oil hydrolysis are equivalent. Thus, t may be assumed to represent the triglycerides or oil and g to represent glycerol. The initial level of t in phase 1 (xto)is therefore to be adjusted to correspond to the glycerol content of feed oils. Also, for this model reaction, the ratio of molecular weights M J M , is obviously unity. The extent of reaction, X , can be related to the measured acid and saponification values as - AVO x = AV -SV - AVO
(3)
Also for every mole of glycerol produced, 3 mol of fatty acids is produced. Hence, the fatty acid productivity, Pa, can be determined from the g productivity by the following relationship:
Pa = fpg
(4)
where f is 3 times the ratio of molecular weights of fatty acid to glycerol. The objective functions (X)and Pg will depend upon reactor configurations and operating conditions used. We examine a number of reactor alternatives to bring out these features in the following sections. 3. Batch Reactor The balance for component't giyes dC,/dt, = rt = kzCg- k;C, _._
(5)
The overall balance of component g in both phases'gives (Lxto/MJX + (Lxg0/Mg)+ (Gygo/Mg)= ( L x g / M g )+ ( G y g / M g )
Using eq 2 for y g gives xg = ( A / D ) X
1988 American Chemical Society
+B
(6)
740 Ind. Eng. Chem. Res., Vol. 27, No. 5, 1988
where A = 1/(1+ mG/L)
1.0
B = A(xgo+ ygoG/L) D = Mt/(Mgxto)
1
From the stoichiometry of the reaction, we have
c, = CtO(l- X )
X
(7)
Since the mass and density of each phase remain constant, we have
C, = ptxi/Mi
(8)
for any component i. Substituting for C, and C, in terms of X in eq 5 , we get dX/dt, = k,(F - EX) (9) where
F = 1 - BD/K Integrating eq 9 leads to
(10)
The product g does not dissolve in phase 1 under ambient condition so that the corrected mass fraction of g in phase 2 a t ambient conditions is
9, = y,/(AmG/L)
(11)
If the volumetric hold-up ratio 4 of phase 1 in the reactor is defined as 4 = 1/[1 + (G/L)(Pl/Pdl
= yg4pl(G/L)/(ti
+t
~ )
4. Parameter Estimation The single-step kinetic model described above involves three parameters, namely, kl, K, and m. These are estimated by fitting the model to experimental data of coconut oil hydrolysis (Sturzenneger and Sturm, 1951) with the help of a nonlinear regression technique (Ottoy and Vansteenkiste, 1985). The fit is shown in Figure 1, and the parameter estimates for coconut oil are given in Table I. Similar agreements are seen a t other temperatures. A deviation of f8-12% has been observed. Figure 1 shows that the model prediction of final conversion is always lower than the experimental value. Despite the deviation, the simplicity of this model renders it very useful for obtaining an insight into the relative performance features of the reactor alternatives. In view of this merit, the behavior of different reactor configurations is evaluated by using this model. 5. Continuous Stirred Tank Reactor The schematic view of this configuration is shown in the part 2 (Patil et al., 1988b). The mass balance of the component t gives -
c, + rt7
=0
(14)
The mass balance of component g gives Lxgo/Mg + Gygo/Mg
+ (Lxto/Mt)X
0
10
20
tr
30 min
40
50
1.0
Figure 1. Comparison of single-step model fit with experimental data for coconut oil hydrolysis at 240 O C and G / L = 0.9.
temw. " C 225 240 260 280 reaction rate constant (kJ,min" 0.9 1.5 2.4 5.0 reaction equilibrium constant (K) 0.458 0.610 0.853 1.160 glycerol distribution coeff ( m ) 27 20 14 10
eq 2 for y g with further manipulations give the expression for X as X(7) = k l ~ R F / ( l+ h17RE) where
T~
=
Lx,/M, + Gy,/Mg (15) Substituting for the rate expression (rt),concentration (Ci) and extent of reaction (X) from eq 5 , 7, and 8 and using
(16)
is the residence time, defined as 7R
= 4v@l/L
(17)
and E and F are as defined in eq 9. The g productivity is given by
(13)
where ti is the idle time and tR is the total reaction time.
c,,
(1951)
0
0
(12)
then g productivity, defined as the amount of g produced per unit reactor volume and time, can be determined from P g
;Ingle st;p mo;et Sturm clnd 5turzenragrr 0.8
Table I. Single-Step Kinetic Model Parameter Estimates for Coconut Oil
E = 1 + A/K
x(tr) = (J'/E)[1 - exp(-k,Etr)l
X
:o ,
o,2
11 P
p g
= ygpld(G/L)/7R
(18)
CSTR conversion data of Patil (1986) have been compared with single-step model prediction. A standard deviation of 0.08-0.12 for conversion has been found. 6. Semicontinuous Reactor
The reactor contains a mixture o f t (L, kg) and g (G, kg), while hot phase 2 is sprayed continuously from the top at the rate of G' (kg/min) on the reactor contents. The concentrated g in phase 2 stream is continuously removed from the bottom at G'(kg/min). The mass fraction of g in the outlet stream of phase 2 is yg. The temperature and pressure of the reaction mixture are held constant during the reaction. The reactor contents are assumed to be well mixed so that exit concentration yg is the same as that in the reactor. In addition, eq 2 for phase equilibria of g is assumed to hold. Thus, an overall component mole balance for g over a period of time gives
(Lxgo/Mg + Gyg,/Mg) + (Lxto/MJX + xt*GL,/M, d t , = (Lxg/Mg + Gy,/Mg) +
Substituting for yg from eq 2 in the above equation and subsequent differentiation with respect to time give dx,/dt, = P,(dX/dt,) + Q1xg + R1 (20) where P, = A/D
Q1 = A(-mG'/L)
R1 = ACygoG'/L)
and A and D are as defined in eq 6. Now using the overall balance of component t gives
Ind. Eng. Chem. Res., Vol. 27, No. 5, 1988 741 dC,/dt, = rt
dYg/dV =
Substituting for rt from eq 5 gives dX/dt, = Q2xg - k1X
+ kl
(21)
+ Gyg)/Mg + (Lxto/Mt)
=
(Lxt/Mt) Q2 = - k i D / K
dxg/dV = (PG/L
x=o
yg=ygo
(22)
Equations 20 and 21 with initial condition 22 are solved simultaneously by the Laplace method, and the final solution is
+ Az exp(bt,) + A3 exp(ct,) xg(tr) = A4 + A, exp(bt,) + A6 exp(ct,) X(tJ = Al
(23) (24)
and yg(tr)can be determined from eq 2. Here the constants are
A1 = - ( a k J / ( b c ) Ab = ( b + kl)A2/Q2 b, c =
+ PiQz - k i ) f ((Qi + PiQz - hi)' + 4kiQi)1'21
The average phase 2 g mass fraction after a period of operation tR is calculated from
Using eq 2 and 24 in the above equation gives
gg(tR) = ( m / t ~ ) [ A d t+~ AS(ebtR- l ) / b
+ &(ectR- l ) / C ] (25)
The productivity (Pg)is given as
Pg = YgPl@(G'/L)tR/(tR + ti)
(26)
7. The Continuous Countercurrent Spray Column Consider a tall high-pressure column in which phase 1 containing component t enters at the bottom and contacts the descending stream of phase 2 containing component g. The column operates isothermally and at steady state. Reaction 1 takes place in phase 1, and the g produced distributes between phases. The molar flux of this transfer based on phase 2 properties is given as
N g = k,(mx,
- YJ
(27)
All earlier assumptions except eq 2 are assumed to hold. The component balance for g in phase 1over a differential element AV gives
(LxJV - (Lxg)v+av- NgaAV + (-rt)MgA(4U = 0
(28)
This leads to the following differential equation for x g after substitution for N g and rt: dxg/dV = P(xt/w) - (P/K + 4 x g + cuyyg/m (29) where w = Mt/Mg
+ xgo - ygoG/L
7 = Xto/W
Equations 30 and 32 describe the performance of the column and it involves kinetic, thermodynamic, and transport parameters of the system. This set of two linear differential equations requires two conditions for its solution. These could be chosen from among the following depending on the situation on hand:
v=0 v=0 v = VR
+ kl)As/QZ
(C
a = (kiQi - R i Q z ) / k i
'/[(Qi
IC. = (1 + K ) / K
A, = (Al - l ) k , / Q , A, =
+ w / m ) y g - (PIC. + w ) x g + Pv (32)
where
A2 = ( b - a ) k , / ( b ( b- c ) }
A, = (c - a ) k l / ( c ( c- b ) }
+ (Lxg + GYgo)/Mg (31)
Substituting for xt from eq 31 in eq 29, we get
The initial conditions are
t=O
(30)
- mYxg
The overall balance for component g between V = 0 and V = V gives Gxgo
where
YYg
x g = xgo
(33)
= Ygo
(34)
= YgH
(35)
Yg Yg
The solution can be obtained by any of the known techniques such as that by Jeffreys et al. (1961). Equation 31 gives xt in terms of V, and eq 8 gives X in terms of V. The productivity (p,) is given as
Pg = $PIYgO(G/L) where
T
(36)
/TR
is the residence time defined in eq 17.
8. The Cocurrent Plug Flow Reactor Here a mixture of oil and water is pumped through a high-pressure heat exchanger. All earlier assumptions except eq 2 are assumed to hold. The equations describing the variation of x g and yg are obtained by using a similar procedure as before. The component g balance in phase 1 can be seen to be the same as eq 29. The component g balance in phase 2 gives
dYg/dV =
m v g
-
(37)
YYg
The overall balance for g between V = 0 and V gives Lxgo + GYgo
Mg
Lxto
Lxg + GYg
Mt
Mg
+-=
Lxt
+Mt
(38)
Substituting for xt from eq 38 in eq 29, we get dxg/dV = ( a r / m - PG/L)y, - (PIC. + a Y ) x g + ( w / m ) y g (39) Equations 37 and 39 describe the performance of the reactor, and it involves the kinetic, thermodynamic, and transport parameters. This system of two linear differential equations requires two conditions for its solution. These are v = 0 x g = xgo (40)
v=o
yg=ygo
The solution can be obtained by standard techniques.
mG/L y = k,a/G
a =
P = klp14/L
Similarly, component balance for g in phase 2 gives
9. Results and Discussion
The performance of different reactor alternatives is simulated for coconut oil at 240 OC and G I L = 0.9. Batch and CSTR configurations are already covered by Patil et
742 Ind. Eng. Chem. Res., Vol. 27, No. 5 , 1988 0 0
0
08
t
O,+
iI 5 ,
jo,6 I -k
p : 65
kg -
m' min
----- k y O = 1 S O A n
I 3
LO
T
I 80 Min
o0
1
120
lo,@
Coconut -011Hydrolysis 24ooc, G / L I 0.9 -Batch A CSTR Semicontinuous 0 Coutorcurrent b Coourrent V LO
80
d
1
120 .
0
--+
Figure 2. Predicted effect of k,a on countercurrent spray column performance for coconut oil hydrolysis a t 240 "C and G / L = 0.9.
al. (1988a,b); salient features of the semicontinuous, continuous countercurrent, and cocurrent reactors are covered in the discussion below. The continuous countercurrent spray column is simulated for G = 66 kg/min and k,a = 65 kg/(m3.min). The values used are similar to those of Jeffreys et al. (1961). A volumetric fat phase (phase 1)hold-up ratio (4) of 0.98 is used, which is close to the experimental value determined by Jeffreys et al. (1967). The performance is found to be a strong function of the value of 4, i.e., hydrodynamics. The effect of k,a on the variation of X against 7 is negligible as shown in Figure 2. This is to be expected since the reaction belongs to a very slow reaction regime. The performance of the cocurrent reactor is also simulated for same operating conditions as above. Here the value of @ is determined from eq 12. The k,a value used is the same as that for the countercurrent column since the reactor performance is found to be insensitive to this parameter. Most of the industries in India employ batch autoclave in the temperature range 230-240 "C. Conversion to semicontinuous mode of operation is often considered as an alternative. For simulation of the semicontinuous reactor, the phase 1 hold-up ratio (@)is determined by eq 12 and the ratio G'/L is roughly taken to be equal to l/tR, as practiced in industry. The simulation results are shown in Figures 3 and 4. As seen from Figure 4, the instantaneous-phase glycerol mass fraction goes through a maxima. Therefore, it is worthwhile to stop the operation when reasonable conversion and an average aqueous glycerol fraction are obtained. This mode thus combines flexibility of batch operation in terms of both oil and aqueous feedstock and advantages due to higher conversion. Figures 3 and 4 show relative merits of different ideal reactor configurations in terms of variation of X and yg or ggoagainst the reaction time (tR)or T ~ .Table I1 compares X,yg or ygo,Pg,and Pa for various reactor alternatives for the same operating and feed conditions. It is seen from Table 11that the continuous countercurrent spray column is superior to all other alternatives. The CSTR is found to give the lowest conversion ( X ) ,which is as expected. Semicontinuous is an improvement over batch in terms
tr
,
t min
1600
4
Figure 3. Comparison of predicted final conversion of ideal reactor configurations for oil hydrolysis.
,_;-----:" A
a
0 0
tr,T
0
Batch CSTR Semicontinuous y Countercurrent Cocurrent
BO
LO
0
A
A
0
0
min
120
60
--+
Figure 4. Comparison of predicted product aqueous glycerol mass fraction of ideal reactor configurations for oil hydrolysis. Table 11. Comparison of Performance of Different Reactor Configurations for Coconut Oil Hydrolysis at 240 "C,G I L = 0.9, Feed Water y s = 0.0, xtO= 0.1383, T~ or t , = 90 min, and t i = 270 min
reactor type batch CSTR semicontinuous cocurrent countercurrent
final conversn 0.84 0.65 0.86 0.837 0.87
product aq glycerol mass fraction 0.127 0.100 0.057 0.120 0.132
productivity, k/m3J h fatty acids glycerol 89 13 207 30 133 19 251 36 494 71
of both X and Pgbut gives a lower final average aqueous glycerol fraction, 7,. The cocurrent reactor gives nearly the same conversion as batch but higher productivity, as no idel time is involved. A stagewise cocurrent operation could give an X as high as the countercurrent column at relatively lesser
Ind. E n g . Chem. Res. 1988, 27, 743-751
743
SV = saponification value, mg of KOH/g of fat t, = reaction time, min t~ = total reaction time, min V = volume of the continuous reactor, m3 w = M,/M, X = overall conversion as defined in eq 3 x , = mass fraction of species i in phase 1 or oil phase y , = mass fraction of species in phase 2 or aqueous phase
investment and operating cost. This type of stagewise hydrolysis, with interstage separation of product glycerol, can be organized to give high thermal efficiency. Scaling up and down are relatively easy since high-pressure heat exchangers can be fabricated over a wide capacity range. It is to be borne in mind that this paper brings out the relative performance features. The predicted values of X and Pgare slightly lower than what is obtained in reality. This is the limitation of the single-step model.
Greek Symbols
4 = oil phase (phase 1) volumetric hold-up ratio p , = density of phase i, kg/m3 T = residence time, min
10. Conclusions
An elementary reaction t + g can be used to describe the oil hydrolysis in various reactor configurations. The design equations for ideal reactors have been derived, and simulation is done to bring out their relative performance features. The continuous countercurrent spray column is shown to have superior performance features but requires more investment since it requires a tall column working a t very high pressure. The cocurrent plug flow reators, operated in stages, could be a promising alternative design. This system resembles high-pressure heat exchangers and can be erected horizontally, offering possibilities of better energy integration, compactness, ease of operation, and lesser investment. Such a scheme could make continuous fat hydrolysis economically viable a t small scale.
-
Superscripts -
= at ambient condition
= average mass fraction in semicontinuous reactor
Subscripts g = component g or glycerol i = idle time 1 = oil phase or phase 1 r = reaction time R = top of the column or end of reaction t = component t or triglycerides 2 = aqueous phase or phase 2 0 = initial or feed
Literature Cited Jeffreys, G. V.; Jenson, V. G.; Edwards, R. E. Proceedings of the 36th Intnl. Congress on Industry Chemistry, Spl. T32, Vol. 111, Brussels, 1967. Jeffreys, G. V.; Jenson, V. G.; Miles, P. R. Trans. Inst. Chem. Eng. 1961,39, 389. Namdev, P. D. M.Tech. Thesis, Department of Chemical Engineering, Indian Institute of Technology, Bombay, India, 1987. Ottoy, J. P.; Vansteenkiste, G. C. In Software for Engineering Problems; Adey, R. A., Ed.; Computational Mechanics: New York, 1985; p 71. Patil, T. A. “Hydrolysis of Vegetable Oils”. Ph.D. Dissertation, Department of Chemical Engineering, Indian Institute of Technology, Bombay, India, 1986. Patil, T. A.; Butala, D. N.; Raghunathan, T. S.; Shankar, H. S. Ind. Eng. Chem. Res. 1988a,part 1 of 3 in this issue. Patil, T. A.; Raghunathan, T. S.; Shankar, H. S. Ind. Eng. Chem. Res. 1988b,part 2 of 3 in this issue. Sturzenneger, A.; Sturm, H. Znd. Eng. Chem. 1951,4 3 ( 2 ) , 510.
Nomenclature
a = interfacial area per unit reactor volume, m2/m3 AV = acid value, mg of KOH/g of fat-oil Ci = molar concentration of species i, kmol/m3 G = mass or mass flow rate of aqueous phase or phase 2, kg/min G‘ = mass flow rate of aqueous phase or phase 2 in semicontinuous reactor, kg/min K = reaction equilibrium constant k,, = mass-transfer coefficient based on aqueous phase or phase 2 properties, kmol/ (mmin) k , = specific forward reaction rate constant, min-’ L = mass or mass flow rate of oil phase or phase 2, kg/min Mi = molecular weight of species i m = equilibrium distribution coefficient for glycerol on weight basis Pi= productivity of species i, kg/m3/h ri = rate of species i production, kmol/m3/min S = interphase area available for mass transfer, m2
Received for review May 8, 1986 Revised manuscript received September 23, 1987 Accepted November 27, 1987
Coke Formation during Pyrolysis: Roles of Residence Time, Reactor Geometry, and Time of Operation Lyle F. Albright* and James C. Marekt School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907
New information has been obtained on factors affecting coke formation on solid surfaces during the pyrolysis of hydrocarbons to produce ethylene and various olefins. Coke production is affected by the amount and type of coke precursors that are produced in the gas phase. Geometrical factors affect the transfer especially of the higher molecular weight precursors t o the surfaces. Nickel and iron which catalyze coke formation are often incorporated in the coke formed on stainless steel surfaces and affect the morphology of the coke. Coke deposits in ethylene (or olefin) furnaces are generally greatest on the surfaces of the reactor coil at or near ‘Present address: E. I. du Pont de Nemours & Co., Inc., Aiken, SC 29801.
0888-5885/88/2627-0743$01.50/0
the exit end. This section of the coil is hottest, and more coke precursors are present there. Precursors include acetylene, aromatics that produce polycyclic hydrocarbons and tars, and diolefins. Coke is produced during pyrolyses by a complicated 0 1988 American Chemical Society
