APPLICATION OF REACTION KINETICS TO PROCESS DESIGN Hydrogenation of Isooctene LOUIS S. KASSEL Universal Oil Products Company, Chicago, Ill.
The kinetics of catalytic hydrogenation such as that of isooctene is developed both for ordinary flow conditions, and for twostage or three-stage operation with countercurrent flow between stages. The case of ideal countercurrent flow is also developed, since it represents the limit of many-stage operation. The general conclusion reached is that two-stage operation is clearly justified by the increased capacity, but that only minor increases are produced by still more stages. Curves are given which show the effect of changing the hydrogen ratio as well as the number of stages.
HE principal component of high-octane aviation fuel is the so-called isooctane. This substance is prepared by the polymerization of isobutene, or the cross polymerization of isobutene and n-butenes, using as catalysts either solid phosphoric acid preparations or liquid sulfuric acid. The polymer is hydrogenated with a nickel catalyst to give a product containing large amounts of 2,2,4-trimethylpentane and having an octane number of 93 to 99.5, depending upon various operating conditions. The following calculations indicate the application of reaction kinetics to design problems in a process of this type. The reaction being considered may be written
T
O + H = P
where 0 represents a n olefin, P a paraffin, and H hydrogen. The following type of equation has been found satisfactory as a kinetic representation of certain catalytic hydrogenations:
FIGURE 2. TWO-STAGE VOLUYES, R = 1.2; F = 0.99
The equation in this form is applicable to a static system a t constant volume. When a flowing system is used and the reaction is carried out a t constant pressure, the kinetics be0:
-
/
I- f
/- f
f
FIGURE 3.
CONCENTRATION FOR COUNTERCURRENT
FLOW
come somewhat more complex. The above equation gives the rate of change of concentrations due directly to the reaction, but not that caused indirectly on account of the change in density. That is, 0
FIGURE 1. TWO-STAGE HYDROGENATION FLOWCHART
MARCH, 1939
where u is the volume of any fixed quantity of reactants. It is convenient to define:
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vH v0 = = A B
UP =
orvdt
vn-l
B
___
B
+ mC
*
dC
B
The total volume occupied during the contact time, t , is V = vdt. The octene space velocity is S
=
k
Gvo
A"(;)"
(R + I),
dC
% XYDROO€NAT/ON
1
I
R PO
Gvo/T/
where G depends upon the exact definition of space velocity. Hence,
The kinetic equation now becomes:
-- k - A n
k (z)" A
c
where u is the volume of the quantity of reactants Charged in unit time. At the inlet, A = Ao,B = BO,C = 0 , v = 210. We define further Ao/Bo= R, C/& = F. Then, F
dC _ dt
=
When n
=
+ 1(m- F- 1)F d F
1, this may be integrated to give: R
1 1 log -1-F R-llog ~
/. 6
-1
R SY R R - F g [ F =log R _-- R 1 __ R -F R - 1 log-]
/. 6
/.4
+
+
where y = 1 - m /.z
Experimental data show that in the present case it is satisfactory to take n = 1, m = 1.
1.0
I
1 -log
.a
R - 1
-1
R R-F
.6
One important design question is whether operation in several stages with countercur.+ rent flow of hydrogen and octene is advantageous. For two-stage operation represented schematically in Figure 1, the above analysis 0 .OE .04 .OG .Ob ./O ./Z . SPA c E Y F L O c ir Y is modified as follows: The fraction of the octene hydrogenated in the first stage is taken FIGURE 4. REQUIRED VALUESOF R AS A FU~WTIOX OF 8 FOR VALUESOF F as F,, and the total hydrogenation as F. Then F .99 .9a 5-98 ,995 .995.99 F1 moles of H are reR moved per mole of 0 P reaching the second /./e reactor; hence the composition charged to the /.I6 first stage is R - F F I moles of H per mole of 0. The composition charged /.I4 8t to the second stage is R moles of HI 1 - F1 moles L/2 of 0, and F1 moles of P; se this c o m p o s i t i o n c o u l d 1/0 have been reached by parE tial hydrogenation of a mixture of R F1 moles /. 08 of H per mole of 0. The reciprocal space velocity L 04 in the second stage is, then, the reciprocal space 404 velocity required to give a partial hydrogenation of L 0.2 F with this mixture minus the reciprocal space velocity required to give a /.00 5PACd YCLOClTY partial hydrogenation of F1. That is, VALUESOF R AS A FUNCTION OF S FOR VALUESOB F FIGURE 5. REQUIRED
+
+
f
+
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1
R -F
log + 3'1 - 1
1
R
;A]
" 1
+ F 1 - 1 log R + F1 - F
Figure 2 shows the reciprocal space velocities for two-stage operation with R = 1.2 and F = 0.99 for various values of Fl. The maximum space velocity is reached a t F1 = 0.6565 and a ratio of second-stage volume to first-stage volume of 1.98 to 1. The increase in space velocity permissible due to two-stage operation is 72.5 per cent. If the two reactor volumes are made equal, the value of F1 is about 0.81, and the permissible space velocity is 66 per cent greater than with single-stage operation. The same type of calculation may be made for a three-stage system. It is found that a t R = 1.2 and F = 0.99, the minimum total volume is reached when the volumes of the stages are in the ratio of 1 to 1.377 to 2.533, giving F1 = 0.43, FZ = 0.84, and Fa = 0.99. With this arrangement the space velocity may be increased an additional 6.6 per cent beyond that for two stages. If the volumes are the same in the three stages, the degrees of hydrogenation are FI = 0.64, Fz = 0.935, and Fa = 0.99, and the space velocity can be about 8 per cent larger than for two stages of equal volume. When it is considered that each additional stage requires a condenser, a liquid receiver, and a pump, i t is clear that three-stage operation could not be justified for these conditions. Since rather laborious trial-and-error calculations are required to determine the space velocity for three-stage operation, i t is convenient to develop the kinetics for hypothetical countercurrent flow, which is the limiting case of infinite stage operation. It can then be concluded that whenever this
case shows no large advantage over two-stage operation, there is no need to make calculations for three stages. We consider only the special case m = 1, n = 1. Let F be the fraction of 0 which reacts in the entire system, and f the fraction which has reacted a t any point. For every mole of 0 and R moles of H entering the system, we have at that point 1 f moles of 0,f moles of P, and R - F f moles of H, as showrl f 1). in Figure 3. Thevolumeis then v = vo ( R - F Then,
+
+ +
Figures 4 and 5 show calculated required values of R as a function of S for various values of F for single-stage, twostage, and infinite-stage operation. These figures provide information needed for economic study of optimum operating conditions, with respect to both number of stages and hydrogen excess. No such study can be attempted here, but i t is possible to suggest as general conclusions that two-stage operation is desirable for high degrees of hydrogenation at low values of the hydrogen ratio, and that three- or more stage operation is probably never justified. R E C E I V E DNovember 2 , 1938.
Courtesy, Paczfic Pulp and Paper Industry
OPERATIKG FLOOR OF THE DIGESTER BUILDING.THEREIs AN INSTRUMEKT PAKEL AND PIPIXGARE OF STAINLESS STEEL FOR EACHDIGESTER;TOPRELIEFVALVES (See article by Kobe a n d Doumrtni, page 257.)
MARCH. 1939
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