The Kinetics of lsobutane Alkylation in Sulfuric Acid Lien-mow Lee and Peter Harriott' School of Chemical Engineering, Cornell University, Ithaca, New York 74853
The acid-catalyzed reaction of isobutane with 1-butene and the oligomerization of 1-butene were studied using uniform hydrocarbon drops and short contact times in an unstirred reactor. Kinetic constants for a simplified model were calculated using a theory for simultaneous mass transfer and chemical reaction.
Introduction The acid-catalyzed alkylation of isobutane with butenes is an important process in the production of high octane gasoline. The product is a complex mixture containing about 20% Cs to C7 compounds, 60 to 65% octanes, and 15 to 20% higher boiling compounds. According to Zimmerman et al. (1962), the trimethylpentanes, with octane numbers in the 100-110 range, make up 80 to 85% of the octane fraction, and the remainder is dimethylhexanes, with an average octane number of only 70. The product distribution and the yield, in pounds of alkylate per pound of olefin fed, are affected by many reaction variables, and there has been a great deal of work directed to understanding the mechanism of reaction and improving the yield and quality of the alkylate. The reaction system is a suspension of hydrocarbon droplets in sulfuric acid, and the reactions are believed to take place only in the acid phase. A mechanism based on the carbonium ion principles of Whitmore (1934) was presented by Schmerling (1944-1946), and some of the basic reactions are given below. chain initiation:
+ HzSO4 +C4+ + HS04ki
C4=
(1)
k-1
main chain:
+
CS+ i-C4
k3
i-C4+
+ Cs
k -3
by-product reactions:
+c5++ k5
c12+
c7=
ec7++ c5= k7
c12+
(7)
k-7
Octanes are produced by a chain reaction in which a tertbutyl cation adds to a butene molecule to form a C-8 carbonium ion, followed by hydride abstraction from isobutane to form isooctane and regenerate the tert- butyl cation. The C-8 ions can add more butene to form C-12 or C-16 ions, which crack to give smaller carbonium ions and other olefins, leading to a variety of light and heavy ends (Hoffmann and Schriesheim, 1962).Butyl cations are also formed by direct addition of a proton to butene, which leads to C-8 and larger carbonium ions formed entirely from butene, lowering the yield of alkylate as well as the quality. Both these routes to the formation 282
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 3, 1977
of by-products, the polymerization of butene and the addition of butene to C-8 carbonium ions, are minimized by maintaining a high ratio of isobutane to butene in the reaction zone. Several mechanisms have been suggested for the formation of dimethylhexane. They may be formed by the reaction of tert-butyl cations with 1-butene, which is in the feed or formed by isomerization of 2-butene. The amount of dimethylhexane formed is only slightly greater when using 1butene instead of 2-butene, which indicates rapid isomerization. Isomerization of isobutylene is relatively slow, yet about the same amount of dimethylhexanes are formed (Zimmerman et al., 1962).The dimethylhexane may be produced from isobutylene via an allylic carbonium ion (Hoffmann and Schriesheim, 1962), which could be formed by hydride abstraction from isobutylene. Albright and Li (1970)suggest that acid-soluble hydrocarbons or red oil cations contribute to the formation of allylic carbonium ions. The isomerization of trimethylpentyl carbonium ions to dimethylhexyl ions is probably not a major route to dimethylhexanes, since the amount of dimethylhexanes in the octane fraction varies appreciably with residence time and agitation conditions (Mosby and Albright, 1966). Mass transfer effects are important in both plant and laboratory reactors, as shown by the effect of agitation on the yield and quality of the alkylate. Li et al. (1970) found a steady increase in octane number with stirrer speed for a small reactor operating a t 1000-4000 rpm, which corresponds to a much greater power consumption than in commercial reactors. They concluded that mass transfer of isobutane from hydrocarbon droplets to the acid phase is the controlling step in the alkylation reaction. Sprow (1969) showed how the droplet size in a small reactor varied with agitation conditions and also concluded that isobutane mass transfer was an important limitation. However, the effect of agitation on product quality may be partly due to increased droplet coalescence, which lowers the average concentration of butene in the organic phase and thus increases the ratio of isobutane to butene. The total amount of butene in the reactor is very small, but the drops have a distribution of butene concentration ranging up to that of the feed, and coalescence must take place several times to lower the butene concentration to the average value. More rapid coalescence decreases the fraction of drops with a high butene concentration. The products formed in alkylation come partly from rapid primary reactions, in which all of the olefin and much of the isobutane is consumed, and partly from slow reactions of the primary products with themselves or with additional isobutane. Using laboratory reactors with residence times of 15 to 60 s, much less than the several minutes used industrially, Mosby and Albright (1966) found no unreacted butenes, but the amount of isooctanes still increased appreciably and the heavy ends decreased as residence time was increased fourfold. Tests by Li et al. (1970) showed a further rise in octane num-
Table I. Solubilities (wt 970) of Isobutane in Sulfuric Acid 15 "C Saturated 90% HzS04 94% H2S04 98% H2S04
0.075 0.081 0.089
1 atm
0.035 0.039 0.046
ber and in alkylate yield as the time was increased from 1 to 5 min, indicating more incorporation of isobutane in the product mixture. These slow reactions are very important and deserve more detailed study, since the effects of temperature, agitation, and acid strength may differ from the effects of these variables on the primary reactions. However, only the primary reactions were investigated in this work, and the goal was to get kinetic measurements a t short contact times and only moderate butene conversions, using a system of known contact area so that mass-transfer effects could be accounted for. The low solubilities of the reactants in sulfuric acid and the high reaction rates indicated that the primary reactions take place in a thin zone around the hydrocarbon droplets. The process falls in the category of simultaneous diffusion and reaction, where both diffusion rates and reaction kinetics influence the rate and neither can be said to be controlling. In a simplified view of alkylation, the reaction of isobutane with butene to form isooctane is the main reaction, and the oligomerization of butenes is the by-product reaction, or a t least the first step in the formation of less desirable products. Kinetic studies of 1-butene oligomerization in sulfuric acid in a capillary-flow reactor gave a first-order rate constant of about 3.4 X lo4 s-l a t 25 "C based on an estimated solubility and diffusivity (Naworski and Harriott, 1969). However, there was some evidence for a higher reaction order, and the second-order rate constant for oligomerization would be 8.7 X los cm3/mol s. Since the main reaction accounts for only about half of the alkylate product when the isobutane-olefin ratio is large (5-20) the effective rate constant for the main reaction is expected to be less than that for oligomerization, say of the order IOs cm3/mol s. Rate constants cannot be obtained from most other studies of alkylation, since the butenes are generally completely consumed. Relative reactivities can be inferred from the results of Zimmerman et al. (1962). Olefin was added to a semi-batch reactor over a 20-min period, and at the end of this period, the olefin conversion was 98% for 1-butene, 99.6% for Zbutene, and 100%for isobutene. The relative order of conversions agrees with earlier studies on the rate of absorption of butenes in sulfuric acid (Davis, 19281, but the contact times and areas were not measured. These results should not be interpreted just as differences in solubility of the butenes, since the solubilities of the unreacted butenes are probably nearly the same, but there may be large differences in the reaction rate constants for butenes. The results show that isomerization is not quite rapid enough to maintain equilibrium between 1-butene and %butene under alkylation conditions, when the butene is consumed in a few seconds. In this work, the mass transfer resistances for isobutane and butene in the acid phase were allowed for in determining reaction rate constants. The mass transfer area was controlled by generating hydrocarbon drops of uniform size in a reactor similar to that of Naworski and Harriott (1969). The drops did not coalesce and the contact time was kept to a few seconds so that only part of the butene was consumed. The rate constants for a simplified kinetic model were calculated from the overall rate data using a theory for simultaneous mass transfer and chemical reaction. The product distributions were analyzed, and some runs were made with l-hexene to get further evidence for the mechanism of byproduct formation.
25 "C Saturated 0.040 0.069 0.084
1 atm
0.026 0.036 0.044
35 "C Saturated 0.054 0.071 0.074
1 atm 0.018 0.031 0.025
Figure 1. Diffusion cell. A is absorption chamber made of Pyrex with 26-mm i.d. and 15-cm height. B and C are inlets for organic vapor and sulfuric acid, respectively; both are 3/8 in. in o.d. D is a three-way stopcock with a 3-mm bore size and a Teflon clad plug. E is a graduated capillary trubore tube with 1 mm. i.d.
Physical Properties The solubilities and diffusivities of isobutane and 1-butene are needed to apply the theory of simultaneous mass transfer and reaction. The solubility of isobutane was determined by bubbling the vapor through sulfuric acid until there was no further increase in weight, which took about 1 h. With longer contact times, the acid turned brown, probably because of a slow reaction in which sulfur dioxide was generated (Kramer, 1967). Tests with nitrogen showed negligible loss by vaporization. The solubilities given in Table I are for 90,94, and 98% HzS04, the other component being water. The acid used for commercial alkylation is recycled and contains as much as 5-10% organic reaction products, which are thought to enhance the solubility of isobutane. Only fresh acid was used for the tests of this study, and although some organic material accumulated in the acid, the solubilities given in Table I were used for the analysis. The rapid polymerization of butenes in sulfuric acid makes it impossible to measure their physical solubility. The solubility of 1-butene in sulfuric acid was estimated to be 2.5 times that for isobutane based on published solubilities for the two materials in various solvents. The diffusivities of isobutane and of n-butane in sulfuric acid were determined by measuring the vapor absorption rate a t constant pressure in an unstirred cell (Figure 1).The cell was placed in a temperature bath and purged with butane vapor for 5 min. Sulfuric acid a t the same temperature was quickly but carefully introduced to avoid wetting the wall above the liquid surface. A drop of water was then placed a t the open end of the capillary tube, and as absorption of butane proceeded, the decrease in gas volume was followed by movement of the water drop. Based on the penetration theory for absorption in a stagnant medium, the amount absorbed and the drop displacement should vary with the square root of the contact time, and the diffusivity can be calculated from the slope of a graph of distance vs. t1I2. The cell was used to measure the diffusivity of nitrogen in cm2/s a t 25 "C, in distilled water, giving a value of 2.6 X reasonable agreement with published data. The results for isobutane in sulfuric acid are somewhat uncertain, because there was a change in slope after about 100 s, as shown for a typical run in Figure 2. There may have been slight convection currents remaining from the introduction of the liquid, or perhaps olefin impurities in the vapor reacted with the surface to change the properties of the top layer of acid. The diffusivities were based on the initial slope of the graph, and the Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 3, 1977
283
,
,
6-
o
o
I aai
!SECI"'
Figure 2. Absorption data of isobutane in 94% sulfuric acid at 25
Y
"C.
0
1
2
3 4 Tmo,
5
6
7
6
9
1
10
5pc
Figure 4. Shrinkage of butene drops in 98%H2S04.
Table 11. Diffusivities of Isobutane and n-Butane in Sulfuric Acid D
98% Acid 94% Acid 90% Acid
'd
Figure 3. Diagram for flow reactor ( a ) and semi-batch reactor ( b ) .
values are given in Table 11. The scatter shows that the measurements are not accurate, and the diffusivities should only be used for approximate calculations. Equipment Alkylation and polymerization studies were made in a continuous flow reactor and a semi-batch reactor, shown in Figure 3. The flow reactor was a glass tube 3.5 mm i.d. and 28 cm long. Sulfuric acid passed upward through the reactor in laminar flow carrying with it a stream of hydrocarbon droplets. Mixtures of isobutane and olefins were fed from a pressurized tank through a stainless steel hypodermic needle, 0.1 mm i.d., and drops 0.55 m m in diameter were formed. The free rise velocity of the drops was only 1 cm/s, and contact times of 2 to 9 s were obtained by varying the sulfuric acid flow. The reaction was quenched with a cold saturated solution of sodium sulfate in a mixing tee, and the hydrocarbon product was collected in a pressurized settling tank. The reactor was in a water bath, and temperatures of 15 t o 35 "C were used. The semi-batch reactor was 38 cm long and 6 mm i.d., and the hydrocarbon feed unit was the same as described above. The products which collected on top of the acid layer were removed intermittently through a sample line which ended just above the acid surface, and the runs were continued for u p to 100 min. The residence time for these semi-batch runs was -6 s, because the reactor was only half-filled with acid and the drop diameter was larger than that in the flow reactor. The reaction products were analyzed with a temperature284
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 3, 1977
Isobutane n-Butane Isobutane n-Butane Isobutane n-Butane
X lo6 cm2/s
15°C
25°C
35°C
1.40 1.31 1.69 1.18 1.31
1.49 1.09 1.91 1.50 1.40
1.27
1.36
3.59 1.86 2.09 1.70 6.10 6.93
programmed gas chromatograph equipped with a flame ionization detector. Two 50-ft columns were used, and they were packed with diatomaceous earth loaded with DC-550 silicone fluid. A typical alkylate of known composition, supplied by the Exxon Company, was used t o calibrate the system. The semi-batch reactor was used for the reaction of 14Ctagged isobutane with 1-butene. The samples were allowed to flash to remove unreacted isobutane and butene (as checked by GC analyses), and the liquid product was dissolved in a scintillation solvent. The radioactivity was determined with a Packard Tri-Carb liquid scintillation spectrometer, Model 3375. The liquid product was clean and gave a counting efficiency of 95%. Tracer tests with the flow reactor were not satisfactory, since the quenched product (which was brown) gave a low counting efficiency because of complex organics extracted from the acid phase. Kinetics of 1-Butene Oligomerization The rate of 1-butene oligomerization was determined by the temperature rise method in a previous study (Naworski and Harriott, 19691, and a different approach was used here as a check. Pure 1-butene was fed t o the flow reactor, and the decrease in drop diameter with time was determined from photographs. It was assumed that none of the products formed in the acid phase returned to the drop, which may seem unlikely, since most of the products formed in alkylation do diffuse back to hydrocarbon drops and are collected in the hydrocarbon fraction. However, the butene drops in these tests were contacted with fresh acid for only a few seconds, and the acid was not saturated with hydrocarbons. Some of the oligomers formed must have diffused back to the drop, but most probably diffused further outward into the acid phase. The shrinkage data for drops in 98% HzS04 are given in Figure 4, and similar results were obtained for other acid strengths. The diameter decreased a t a constant rate, suggesting a constant mass transfer rate per unit area, but the change in drop diameter was not large enough to confirm this trend. The equations for diffusion plus chemical reaction were solved numerically assuming the reaction was second order
Table 111. Oligomerization Rate of 1-Butene in Sulfuric Acid Acid concn
Temp, "C
98% 98% 98% 94% 94%
15 25 35 15 25 35 15 25 35
kA,
--I
cm3/(mol
s)
x 108
40
94%
90% 90% 90%
3.90 9.50 10.70
I
1.80 5.30 6.00
0.17 2.30 2.80
,
go a0 €a IKEUTANE IN FEE>,%
O k
in dissolved butene. The transient terms were omitted because the time required to establish a pseudo-steady-state boundary s (Lee, 1973). Different values of the layer was only 3.0 X rate constant were tried until the calculated and experimental results agreed, and the values are given in Table 111. 1 d
(
dC D A -r -2 dr drA)
- kACA2 = 0
(8)
da dt
(2)
(11)
PA-=
dC
D A
r=n
The rate constants for oligomerization increase severalfold on going from 90 to 98% acid, and they also increase with temperature, although the change from 15 to 25 "C appears much greater than that from 25 to 35 "C. There are not enough data to show whether this is a real change in activation energy. The rate constant for 98% acid a t 25 "C is 10%higher than the value given by Naworski and Harriott (1969), corrected to the same units. A slightly lower value was expected because of back diffusion of products, but the difference is within experimental error. Kinetics of Isobutane Alkylation Preliminary alkylation tests in the flow reactor showed that not much isobutane was incorporated in the product a t contact times up to 9 s. Determination of isobutane consumption by material balance was inaccurate, and kinetic calculations were therefore based on the radioactivity of the product formed in the semi-batch reactor. The hydrocarbon droplets were in contact with the acid phase for 5-6 s, long enough to react about one-third of the butene in an equimolar feed and a smaller fraction of the isobutane. The results for several feed ratios and acid strengths are shown in Figure 5 . The amount of isobutane in the product increases approximately linearly with feed concentration a t low concen-
WAO+ 4* f a
=
Figure 5. Reaction of isobutane and 1-butenein semibatch reactor at 25 "C.
constant was shown to increase about fourfold over the same range of acid strengths (Table 111). The data in Figure 5 are for the first product samples, which were collected in about 30 min of operation. There was a gradual accumulation of organic material in the stationary acid phase, and second samples generally had less incorporation of isobutane in the product. As shown in Figure 6, the decrease in isobutane incorporation could be caused by a decrease in acid strength during operation, but the final acid strength was not measured. The change in product composition might also be due to differences in the rate of extraction of products from the acid phase. Products formed from butene alone are more soluble in acid, and a higher fraction of these materials would be left in the acid phase. A detailed kinetic analysis (Lee, 1973) showed that the consumption of isobutane and butene in primary reactions could be treated with the following simplified model, where A represents 1-butene and B represents isobutane.
A
-
+A
kA
kB
oligomers; A t B +octanes
The equations for diffusion and reaction of butene and isobutane are
s,'a2D* (2)
trations, and there is some indication of a more rapid increase a t high isobutane concentrations. The dashed lines are extended to 51%, the composition expected as the isobutaneolefin ratio approaches infinity and by-product reactions become negligible. The percentage isobutane in the product increases slightly with acid strength, indicating that the reactions consuming isobutane increase somewhat more rapidly than the by-product reactions. The oligomerization rate
dt
r=n
where subscripts A and B stand for 1-butene and isobutane, respectively, f A is the mole fraction of 1-butene in the hydrocarbon phase, and WAOand WBO are the initial amount of butene-1 and isobutane present in the hydrocarbon phase. This simplified model assumed that isobutane and butene react as they diffuse into the acid phase and does not deal with Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 3, 1977
285
OFlRSf ~
9M%ffi
OSECOND W R I N G
50-
I
i
I?
'I 0
0 %CF 'Y)BUTL\NE IN T K FEED
Figure 6. Percentage of isobutane found in the product as functions of its concentration in the feed and acid age; 98% acid, 25 "C. '
0
2
4
6
8
1
0
Time, S x
Table IV. Rate Constants for the Alkylation of Isobutane ) 1-Butene Oligomerization ( k ~a t) with 1-Butene ( k ~and 25 "C Sulfuric acid 98% 94% 90%
kB,
k A,
cm3/g-mol s
cm'3/g-mols
kA/kB
2.25 x 108 1.32 X lo8
9.5 x 108
4.2 4.0
6.64 X lo7
5.3 x 108 2.3 X lo8
3.5
the eventual diffusion of products back to the organic phase. The products are assumed to be completely recovered, which ignores the accumulation of organic material in the acid phase as well as the slow secondary reactions in the acid. Equations 12-18 were solved numerically in the same manner as for 1butene oligomerization. Using the 1-butene oligomerization rate constants which were caluclated earlier, the alkylation rate constants were calculated by a trial and error method. The detailed computer program and the calculated results were presented by Lee (1973). Table IV gives the alkylation and oligomerization rate constants obtained in this study. The ratio of the rate constant for oligomerization to that for alkylation goes up slightly as the acid strength increases, although more isobutane is incorporated in the product at high acid strengths. This anomaly may be due to the decrease in thickness of the reaction zone or butene boundary layer as the acid strength increases. The isobutane boundary layer extends further than the butene boundary layer, as unreacted isobutane diffuses into the bulk acid phase. Both boundary layers are smaller a t high acid strengths, but the average isobutane concentration in the reaction zone will be greater when the reaction takes place closer to the interface. Since the rate constant for oligomerization is about four times that for alkylation, and the butene solubility was estimated to be 2.5 times that for isobutane, very high ratios of isobutane to butene in the organic phase are needed for a good yield of alkylate. In this work, when the feed contained 80% isobutane, only 1 5 2 5 %of the product came from isobutane, which corresponds to a t most 30-50% octane in the product, the remainder being heavy ends and light ends resulting from oligomerization and some cracking. Tests in a stirred reactor at comparable feed concentrations and short residence times (Shlegeris and Albright, 1969) gave much higher alkylate yields, but coalescence probably made the average isobutane-butene ratio in the drops several times that of the feed. Using the simplified model of this study and the rate constants for 25 "C and 98% HaS04, an octane yield of about 85% is predicted for an isobutane-butene ratio of 20 in the drops. 286
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 3, 1977
Figure 7. Comparison of octanes and heavy ends compositions between fresh acid and isobutane presaturated acid as function of residence time at 25 "C in 98% acid. In the analysis of the alkylation tests, the isobutane concentration in the bulk acid phase was assumed to be zero. In commercial practice, the acid is partly saturated with isobutane, which leads to a higher average concentration of isobutane in the reaction zone around the drops and also contributes to the slow reaction of isobutane with dissolved high boilers. T o show the importance of dissolved isobutane on the primary reaction products, some tests were made in the flow reactor using sulfuric acid that had been pre-saturated with isobutane. Figure 7 shows that the amount of heavy ends in the product was decreased from about 62% to about 50% and the octane increased from 15 to 23% on going to presaturated sulfuric acid. Since these are not large changes, the average isobutane concentration in the reaction zone may be not far from saturation, even when the bulk concentration is zero. Therefore, mass transfer of isobutane should not be considered the controlling step in the normal sense of the term. The consumption of isobutane in primary reactions is determined by simultaneous diffusion and reaction near the interface, but the chief factor influencing the yield of alkylate is the olefin concentration in the drops, which depends on the feed ratio, coalescence rate, and average residence time. T h e Formation of Dimethylhexanes The products formed in the semibatch and flow reactors had less octanes than normal alkylate, and the octane fraction contained about 30% dimethylhexanes, twice the normal value. None of the previously discussed mechanisms seemed to account for this change in octane composition, and it appeared that cracking of heavy carbonium ions could be a major source of dimethylhexanes. T o explore this possibility, several runs were made using 1-hexene as the olefin, which would give some octanes as a result of oligomerization and cracking reactions. The ratios of dimethylhexanes to heptanes are shown in Table V. Heptane was chosen as a comparison because it can be produced only as a result of cracking, whether the olefin is butene or hexene. With mixtures of hexene and isobutane, the amount of dimethylhexanes was about equal to the amount of heptanes, and the octane fraction was 75% dimethylhexanes. The octanes presumably come from splitting C12, CIS, or CIS carbonium ions, with dimethylhexyl ions favored over trimethylpentyl ions. When 1-butene was used in the same reactor, the ratio of dimethylhexanes to heptanes was 1.0,about the same as with 1-hexene,although the amount
Table V. Dimethylhexane Formation with Different Olefins % Olefin
System
in feed
1-Hexene, this work 1-Hexene, this work 1-Butene, this work 1-Butene, Zimmerman 2-Butene, Zimmerman 1-Butene, Albright (1966)
33 64 49 25 25 25
of each fraction was 2-3 times larger. This indicates that most of dimethylhexanes had the same origin as heptane, that is from cracking of large carbonium ions. The data for commercial reactors and stirred laboratory reactors, in Table V, show a dimethylhexane-heptane ratio of 1.8 for 1-butene as a feed, significantly higher than the values found in this study. With vigorous agitation the olefin-isobutane ratio is reduced, and there is less cracking and oligomerization, making formation of dimethylhexanes by other mechanisms more prominent. The ratio 1.8 could mean 1 lb of dimethylhexane formed by cracking/lb of heptane formed, with the rest coming from reaction of 1-butene with tert- butyl cations or some alternate mechanism. The slightly lower yield of dimethylhexane obtained by Zimmerman when using 2-butene instead of 1-butene shows that isomerization, while rapid, is not quite fast enough to give an equilibrium distribution of butenes before alkylation occurs. In an attempt to measure the rate of isomerization, pure 1-butene drops were contacted with 94% sulfuric acid a t 15 "C for 2 s, with only 8% conversion of the butene fed. The dissolved C4 fraction contained 50% 1-butene,40% %butene, and 10%isobutane, showing appreciable isomerization, though still far from the equilibrium value of 90-95% 2-butene. The isobutane probably came from direct isomerization of secondary carbonium ions to tert- butyl cations, rather than cracking of large red oil carbonium ions, since the acid was fresh and the contact time quite small. The formation of isobutane is consistent with the results of Hoffmann and Schriesheim (1962), who found I4C-labeled isobutane when alkylating isobutane with labeled 1-butene. Nomenclature a = diameter of a droplet a t time t , cm CA = concentration of 1-butene a t time t , g-mol/cms CAO= initial concentration of 1-butene, g-mol/cm3 C g = concentration of isobutane a t time t , g-mol/cms CBO = initial concentration of isobutane, g-mol/cm3 D A = diffusivity of 1-butene in sulfuric acid, cm2/s
'
Dimethylhexane/ heptane
Dimethylhexane/ octane
1.10 0.97 1.02 1.82 1.61 1.83
0.73 0.75 0.29 0.15
0.13 0.15
D B = diffusivity of isobutane in sulfuric acid, cm2/s f~ = mole fraction of 1-butene in organic phase ~ A O = initial mole fraction of 1-butene in organic phase h~ = oligomerization constant for 1-butene in sulfuric acid, cm3/g-mol s k g = alkylation constant for isobutane with 1-butene in sulfuric acid, cm3/g-mol s r = radius, cm t = time, s WAO = initial moles of 1-butene in the droplet, g-mol WBO = initial moles of isobutane in the droplet, g-mol d = concentration boundary layer thickness, cm 6~ = concentration boundary layer thickness for 1-butene, cm 6~ = concentration boundary layer thickness for isobutane, - cm p = average molar density of organic phase, g-mol/cm" P A = molar density of 1-butene in organic phase, g-mol/ cms p~ = molar density of isobutane in organic phase, g-mol/ cm3 L i t e r a t u r e Cited Albright, L. F.. Chem. Eng., 73, 209 (1966). Albright. L. F., Li, K. W., Ind. Eng. Chem., Process Des. Dev., 9 , 447 (1970). Albright, L. F., Houle, L., Sumutka, A. M., Eckert, R. E., Ind. Eng. Chem., Process Des. Dev., 11, 446 (1972). Davis, H. S.,J. Am. Chem. SOC.,50, 2780 (1928). Hoffmann, J. E., Schriesheim, A. J.. J. Am. Chem. SOC.,84, 953 (1962). Iverson, J. O., Schmerling, L., Adv. Pet. Chem. Refin., 1, 337 (1958). Jernigan, E. C., Gwyn, J. E.. Claridge, E. K.. Chem. Eng. Prog.. 61, 74 (1965). Kramer, G. M., J. Org. Chem., 32, 1916 (1967). Lee, L. M., Ph.D. Thesis, Cornell University, Ithaca, N.Y., 1973. Li, K. W., Eckert, R. E., Albright, L. F., Ind. Eng. Chem., Process Des. Dev.. 9 , 434 (1970). Mosby, J. F., Albright, L. F., Ind. Eng. Chem., Prod. Res. Dev.. 5, 183 (1966). Naworski, J. S.,Jr., Harriott, P., Ind. Eng. Chem., Fundam.. 8, 397 (1969). Shlegeris, R. J., Albright, L. F., lnd. Eng. Chem., Process Des. Dev., 8, 92 (1969). Sprow, F. B.,Ind. Eng. Chem., Process Des. Dev., 8, 254 (1969). Whitmore, F. C., Ind. Eng. Chem., 26, 94 (1934). Zimmerman, C. A., Kelly, J. T., Dean, J. C., Ind. Eng. Chem., Prod. Res. Dev., I , 124 (1962).
Receioed f o r reuieu' February 19.1976 Accepted January 31,1977
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