Simultaneous Chemical Reaction and Fractional Distillation ISOMERlZATI ON Bruce Longtin Illinois Institute
of Technology, Chicago, Ill.
Merle
Randall
University of California, Berkeley, CdliF.
in the still pot as fast as it can be removed by fractionation; this is practically the only way that substantially 100 per cent yield of either single isomer can be obtained. At room temperature the isomerization is slow enough so that the product is moderately stable.
A
flow sheet and design method are presented for a continuous process b y w h i c h a mixture o f t w o isomers may b e converted into the pure, more volatile isomer b y distillation. The isomeric mixture i s fed continuously into a reaction kettle from w h i c h the desired product i s removed b y The fractionation serves t w o purfractional distillation. poses-to reduce the size o f kettle needed t o carry out the reaction at the desired rate, and t o yield a product whose content of volatile isomer is greater than that of isomeric equilibrium. The process i s applicable either t o an isomerization w h i c h i s fairly r a p i d at the boiling p o i n t but incomplete at equilibrium, or t o one w h i c h is complete at equilibrium but fairly slow at the b o i l i n g point. The design method is essentially that of Ponchon and Savarit, modified t o include the effect of chemical reaction o n the plates and i n the kettle. I t indicates that the factors controlling the amount of reaction at each level i n the column are the composition of l i q u i d at that level, and the ratio ot the volume of l i q u i d i n w h i c h reaction i s occurring t o the rate of take-off OF product. The method differs from the usual one of Ponchon and Savarit i n that the net f l o w points for successive levels i n the column d o n o t coincide. It i s applicable as w e l l t o cases i n w h i c h isomerization or polymerization occurs i n the fractionating t o w e r as an unwanted by-product of distillation, and serves as the starting p o i n t for the treatment of cases involving more than t w o components.
CONTINUOUS ISOMERIZATION PROCESS
Isomerization reactions such as that studied by Winstein and Young (6) may be carried out in a continuous rather than batch fashion by the method illustrated in Figure 1. The mixture of isomers is fed continuously into a reaction kettle which serves also as the pot of a fractionating column. The fractionating column serves t o remove the more volatile isomer from the kettle, while preventing escape of the less volatile isomer. It is important that the product be rapidly chilled in the auxiliary cooler to prevent return to the equilibrium composition. This process is taken in the present paper as the simplest starting point in the study of simultaneous reaction and distillation, since it avoids the complications of more than two components and of batch operation (i. e., departure from steady state). At the same time a considerable insight into the treatment of the more complex cases may be gained from the study of this simplified case. DESIGN METHOD
The heat content vs. mole fraction design diagram ( I , 4,6) for the process of Figure 1 is presented in Figure 2. Normally the symbols L I , VI, DIwould be used to designate the liquid, vapor, and net flow, respectively, a t the first level in the column, etc. In labeling points in Figures 1 and 2, it was found that these complete symbols could not be used legibly, so only the numeral subscripts were used, with vapor and net flow points distinguished from liquid points by primes and double primes, respectively. Thus the points LD,VB, L)Bare labeled 3, 3/, and 3“, respectively. The “net flow” a t the vth level [between the nth and (n 1)th plates] consists of the net flow of heat content a t this level, together with the net flow of each component. These constituents of the net flow are defined by the equations:
I N A NUMBER
of commercial as well as laboratory processes a fractionating column is used as an aid in forcing a chemical reaction toward completion. I n accordance with the principle of LeChatelier (S), distillation is used to remove the reaction products from the reacting mixture, while the fractionating tower prevents the simultaneous removal of the reactants. The principal commercial example is the esterification process (3)in which the fractionating tower separates the ester and water as products, while retaining the alcohol and acid within that section of the column in which the reaction occurs. A typical laboratory example is the preparation of pure methyl vinyl carbinyl bromide from the equilibrium mixture with its isomer, crotyl bromide, as reported by Winstein and Young (6). At the boiling poirit the low-boiling isomer is produced
-+
VuHL
f,iuMu
DVzv= V u 3 .
- Lvcv
f)uli!
292
(Uet fl0N (Jf h a t
C;OlltCll~)
(net fiow of cornponetit U )
(1) (2)
March, 1942 Dv(1 DV
-2”)
INDUSTRIAL AND ENGINEERING CHEMISTRY = Vv(1 -
=
YV)
- Lv(1
V V - LV
-
ZY)
(net flow of component A)
(3)
(net flow of total material) (4)
The upward direction is taken as positive. In Figure 2 each set of three points representing liquid, vapor, and net flow at the same level is shown on a single straight line (e. g., the line D3V8L3,which is labeled 3”3’3) in agreement with the above equations and with the center-of-gravity principle (4). The typical design construction for a plate fractionating tower, with or without chemical reaction, is made up of alternately an equilibrium tie line LvVv+land a construction line L,V,D, through a net flow point (4, as in Figure 2. This make-up of the stepwise construction is determined by the requirement that liquid and vapor leaving the same theoretical plate must be at equilibrium. For inefficient plates an appropriate construction is substituted for the equilibrium tie line (4). The graphical construction for a particular type of operation of a plate tower is completely determined by locating the net flow points. In the present case the isomerization reaction converts some of component A carried by the net flow into B (or vice versa) as each plate is passed, changing the composition of the net flow. As will be seen later, the heat content of the net flow is unaltered by the reaction. The chief new feature introduced by the chemical reaction is that the location of each successive net flow point must be calculated from the conditions of material and heat balance, whereas in the absence of reaction the net flow points are all coincident. Once the net flow points have been located, the graphical construction is essentially the same as that for the column in which no reaction occurs. HEAT AND MATERIAL BALANCE
Isomer B is produced by the reaction A+B
(5)
a t the rate of h,i, moles per unit time on the nth plate. The rate of production of B in the reaction kettle may be calculated in the same way. As a first approximation the amount of reaction occurring a t points in the column other than the reaction kettle and liquid holdup will be neglected. The material balance for each component in the process takes the form that the net flow of any component away from the plate is the sum of the net flow of that component into the plate plus the amount produced on the plate, since
293
none may accumulate on the plate a t steady state. The thermodynamic principle that a t steady state the net flow of heat content away from any section is the sum of the net flow of heat content into the section plus the heat absorbed by the section applies as well in the presence of chemical r e a c t i o n a s i n i t s a b sence. The conditions of material and heat balance for the nth plate consequently take the form, DVZV
- z,)
= Dv-1
+ h,;,
ZV-1
-
=
Dv-i (1
DY
=
DY-I
Dvn;
=
Dv-lnu-‘j
Dv(1
ZU-I)
(component B)
(6)
- hnim (component A)
(7)
(total material) (8)
+ 4,
(heat content)
(9)
when it is assumed that the net flow Du-1 enters the plate while D, leaves the plate. The amount, h,;,, of component -4used up per unit time by the reaction is necessarily equal to the amount of B produced due to the isomerization (Equation 5 ) . For the adiabatic column the heat, 4, absorbed a t the plate per unit time is zero. Since the reaction replaces A, mole for mole, by B, the net flow of total material will be the same throughout the column as indicated by Equation 8, and D , need not be distinguished from DU- I. Considering a t the same time that the column is adiabatic, the relation between the H us. N coordinates of successive net flow points is found from Equations 6, 8, and 9 as zv
-
Z V -
1
a,”=
= h,i,/D
(10)
E;-
(11)
where D is the undistinguished value of Du,D v - 1, etc. According to Equations 10 and 11, the successive net flow points have the same molal heat content coordinates (as shown in Figure 2) while the mole fraction coordinates differ by the amount, h,r,/D, of B produced in the intervening plate per mole of net flow. QUALITATIVE FEATURES
I n the absence of adequate thermodynamic and rate data, Figure 2 was constructed to correspond as closely to a typical real problem as was possible on theoretical bases. The properties of components A and B were chosen to be consistent with the principles of thermodynamics and kinetics. The problem of obtaining 10 moles per minute of a product containing 0.98 mole fraction of B from a feed containing 0.228 mole fraction of B in a tower having 0.5 liter holdup per plate was specified. The dotted curve E& (Figure 2) represents the composition of mixture in which chemical equilibrium has been reached at each temperature corresponding to a given molal heat content. Points to the left of this curve represent mixtures in which equilibrium is approached by production of isomer B. Reaction Kettle Points to the right of represent mixtures in which isomer FIGURE 1. CONTINUOUS A must be produced in order to approach equilibrium. I n Figure 2 the liquid flowing down from each plate above FRACTIONAL DISTILLATION PROCESS FOR CONthe thirteenth level (hence the liquid on the plate) is repreVERTING A MIXTUREOF sented by a point to the right of Hence on each of these Two ISOMERSINTO PUREVOLATILEISOMER plates component A is produced; or since B is used up, the
E&
E&.
294
INDUSTRIAL AND ENGINEERING CHEMISTRY
rate, i,, of producing B is negative. The net flow leaving the plate contains a smaller mole fraction of B than that entering. Thus above the thirteenth level the net flow points progress toward smaller mole fractions of B in going up the column toward the top (zero level). All of the production of B occurs on plates below the thirteenth level and in the kettle, Below the thirteenth level, the net flow points progress toward larger mole fractions of B in going up the column. Some of the net flow points are shown with a mole fraction of B greater than unity. For example, the mole fraction z16 of B in the net flow entering the bottom of the tower from the kettle is 1.186. The mole fraction of A is necessarily -0.186. Since the net flow of total material upward is 10 moles per minute (equal to the rate of feed and of withdrawal of product), the net flow of B upward a t this level is +11.86 and of A is -1.86 as given by Equations 1, 2, 3, and 4. That the net flow of A is negative means simply that there is a net flow of A back into the kettle. This back flow of A is necessary if the A produced on plates above the thirteenth level is not to contaminate the final product.
Vol. 34, No. 3
construction is continued in the same way down the column. With minor modifications the same procedure may be followed in carrying the calculations up the column, THE CONDENSER
If the vapor from the tower is condensed and chilled too rapidly to permit any reaction in the condenser, the material and heat balance of the condenser will lead to the results already used in the ordinary case of a column without chemical reaction. I n a total condenser, the net flow into the condenser has the same composition as the product, and as the liquid and vapor streams of which it is the net flow. DoVoLois a vertical straight line whose mole fraction coordinate is that of the product stream. The heat content coordinate of Do may be calculated from Equations 1and 4 as when the reflux ratio (LO/Vo)has been specified. CAPACITY OF REACTION KETTLE
LOCATION OF NET FLOW POINTS
With the net flow point Dolocated, the stepwise calculation is carried down through the column to locate finally the point V2g (labeled 16') representing vapor entering the bottom plate. Since this vapor comes from equilibrium with liquid in the kettle, the point L17a t the liquid end of an equilibrium tie line through Vle must represent the composition of liquid
I n Equation 11 the rate, in, a t which B is produced in a liter of boiling liquid may be calculated from chemical rate laws. It is the difference between the rate a t which B is produced in the forward reaction and that a t which B is used up in the reverse reaction in boiling liquid of the given composition. Owing to the variation of boiling point with composition, this rate cannot generally be represented by a simple algebraic function of mole fraction. A plot of i, us. N, such as that of Figure 3 100 (on which the calculations for Figure 2 are based), is more convenient. Suppose that in the stepwise constructions the net flow point D1 has just been ;a0 found (x7 = 1.128, H; = 100.88 kg.-cal. L per mole), and DS must now be located, W n in progressing down the column. AcW VI cording to Equation 11, the molal heat Z 60 content coordinate, H[, of this point is -0 0 the same as that of D r n a m e l y , 100.88 0 kg.-cal. per mole. The mole fraction .Y coordinate 28 is given by Equation 10 as 40 27 - h,i,/D, since the net flow leaving the e c W plate is D1. e c The rate k , of reaction on the inter0 0 vening plate is determined by the come 20 0 position of liquid on this plate. Point W I V,, already located, represents vapor rising from equilibrium with liquid on this LlQWD -- e - 7" . 3. 0 5 plate. The desired liquid composition is hence that of point L8 a t the liquid end of ip the equilibrium tie line through V7. The jb mole fraction, 2 7 , of B in this liquid is 0 0.2 0.4 0.6 0.8 I found to be 0.668. From Figure 3 the Mol Fraction o f B rate ?, a t which B is produced per minute FIGURE 2. HEATC O N T E N T VS. COMPOSITION DESIGN per liter of boiling liquid on this plate is DIAGR.431 FOR CONTINUOUS ISO1\IERIZATION PROCESS read as -0.40 (i. e., B actually used up), corresponding to this composition of liquid on the plate. Remembering that h, and D were specified as 0.5 and 10, respectively, Equation 10 in the kettle. This point must lie to the left of curve E& gives zs = 1.128 - 0.5 (-0.40)/10 = 1.148, and point DS (Figure 2), in order that component A may be converted into has now been located. B by isomerization in the .kettle. In the present case 517 has The point LSrepresents the liquid leaving the plate, as well the value 0.171, corresponding to which a rate of production as that on the plate. Hence point V Sis next located at the of 0.149 mole of B per minute per liter of liquid in the kettle intersection of 8with the vapor curve, and the stepwise is read from Figure 3.
-
' ' L
March, 1942
INDUSTRIAL A N D ENGINEERING CHEMISTRY
The net flow F’I into the kettle consists of the feed F plus the heat supplied by the heater; it thus has the same composition as the feed and differs from F only in heat content. The material balance for the kettle leads to results analogous to Equations 10 and 11: Hb Zb
- ZF
3
= he;es/D
(14)
where subscript b refers to the net flow from the kettle into the tower and B to the liquid contents of the kettle. Equation 13 requires that the point F” have the same molal heat content coordinate as all other net flow points, as shown in Figure 2.
I
.%
‘Z
-0.5
’
0
0.2
’
’
found a surprising lack of complete data for any system (multicomponent as well as binary) which might be of interest. CONCLUSIONS ’
(13)
H!
*
0.4 0.6 Mol F!actlon of B
*
’
0.8
’
J
I .o
In a process such as that of Figure 1 the plates in the tower are divided into two groups by the plate on which the chemical equilibrium composition is reached. Above this level the plates serve to separate the desired product, and the undesired reversal of the reaction is to be suppressed by keeping the liquid holdup to a minimum. Below this level the plates serve to increase the rate of reaction in the kettle by maintaining more than the equilibrium concentration of reactant in the kettle. While the reaction does occur in the desired direction on these plates, it occurs a t a lower rate per unit volume than in the kettle, so that the greatest gain is to be obtained by placing as much of the liquid capacity as possible in the kettle. The process may evidently be used to advantage even in cases where the equilibrium lies so far in the desired direction that it is not necessary to use fractionation as a means of equilibrium shifting. In such cases the column is used only to keep the kettle contents rich in reactants so that kettle capacity may be diminished.
FIGURE3. RATEOF ISOMERIZATION IN BOILING OF Two LIQUIDISOM~RS, A AND B MIXTURES For a particular reflux ratio and number of plates (sixteen plates and Lo/VO= 110/120 in the case shown) the conditions of the problems specify zF and D while completely determining the values of 21, and iB which will be obtained from the graphical construction. In the present case z p is 0.228 and D is 10, while the construction yields the values zb = 216 = 1.186 and i, = 0.149. It is thus seen from Equation 14 that the volume of liquid, h,, in the kettle can have only the value 10 (1.1860.228)/0.149 = 61.8 liters if the column is to function in the specified way. If the kettle actually has a different capacity, the composition of product obtained will not be the specified 0.98 mole fraction B. If a column of a t e e n plates had been considered, the construction would have given point L1eas the liquid in the kettle, with a correspondingly smaller value of iBsince Lle lies closer to the equilibrium composition E&. Thus a larger volume of liquid would be needed in the kettle to produce B a t the specified rate. With 12.6 plates the reaction rate in the kettle b e comes zero (liquid in the kettle has the equilibrium composition), and a kettle of i d n i t e capacity is needed. The design of the process is thus a question of striking an economic balance between kettle capacity and number of plates in the tower. D A T A NEEDED In constructing the H us. N diagram, the heat of reaction is needed in addition to the heat content and liquid vapor equilibrium data needed in the usual case. Whereas ordinarily each pure component is assigned an arbitrary heat content (say H = 0) a t 0”C., only one of the reactants may be so treated in the present case. The heat content of the other component must be assigned such a value at 0” C. that the difference in heat content of the two gives the heat of reaction. I n addition to the above data, rates of reaction a t the boiling point are needed. The authors have
295
ACKNOWLEDGMENT
The assistance of L. H. Butterworth in preparing the diagrams is gratefully acknowledged. NOMENCLATURE net flow at designated level feed stream F’ net flow into kettle L liquid stream at designated level vapor stream at designated level V (The above symbols in an equation denote the number of moles of total material in the particular stream flowing past the designated level per unit time.)
D F
= = = = =
molal heat content of a liquid molal heat content of a vapor molal heat content of a net flow N = mole fraction of component B in general z = mole fraction of component B in a liquid y = mole fraction of component B in a vapor z = mole fraction of com onent B in a net flow h = volume of liquid holcfup i = moles of B produced by reaction per unit time in unit volume Subscripts n number of a late v = number of a Lvel in the column F = feed b = level below bottom plate B = contents of kettle Labels 0, 1, 2, etc. = Lo,L , Lz, etc., respectively 0’, l’, 2’ etc. = VO,VI, VZ,etc., respectjvely OM,I#, a b , etc. = D ~D, ~4, , etc., respectively = H’ = H” = H
=I
LITERATURE CITED (1) Gay, “Distillation et rectification”, Paris, Baillhre et Fils, 1936. (2) Groggins, “Unit Processes in Organic Synthesis”, 2nd ed., New York, McGraw-Hill Book Co., 1938. (3) LeChatelier, Compt. rend., 99,788(1889). (4) Randall and Longtin, IND.ENQ.CHEM.,30, 1063, 1188 (1938). (6)T F l e , Ibid.,27,392 (1935). (6) Winstein and Young, J. Am. Chem. SOC.,58, 109 (1936).
