265
Ind. Eng. Chem. Fundam. 1986, 2 5 , 265-269
[,] = inner product defined by eq 24 or eq 44
Registry No. o-Xylene,95-47-6;m-xylene, 108-38-3; p-xylene, 106-42-3.
Literature Cited Allen, R. H.; Yats, L. D. J. Am. Chem. SOC. 1981, 8 3 , 2799. Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. “Transport Phenomena”; Wiley: New York, 1960; p 510. Papoutsakis, E.; Ramkrishna, D. J. Heet Transfer 1981, 703, 429. Ramkrishna, D. I n “Advances in Transport Processes”; Majumdar, A. S., Mashelkar, R. A,, Eds.; Wiley: New York, 1983; Voi. 4. Ramkrishna, D.; Amundson, N. R. Chem. Eng. Sci. 1973, 28, 601. Ramkrishna, D.: Amundson, N. R. Chem. Eng. Sci. 1974, 2 9 , 1353.
Ramkrishna, D.; Amundson, N. R. “Linear Operator Methods in Chemical Engineering with Applications to Transport and Chemical Reaction Systems”; Prentice-Hall: Engiewood Cliffs, NJ, 1985; p 255. Solomon, R. L.; Hudson, J. L. AIChE J. 1971, 77, 371, 379. Turner, B. G. M.S. Thesis, Purdue University, West Lafayette, IN, 1982. Wei, J.; Prater, C. D. Adv. Catal. 1962, 73, 203. Wei, J. J. Catal. 1962, 7 , 527, 538. Wei, J. Can. J. Chem. Eng. 1968, 4 4 , 31. Wel, J. J . &tal. 1982, 76, 433. Young, L. E.;Butter, S. A,; Kaeding, W. W. J. Catal. 1982, 76, 418.
Received for review July 30, 1984
Revised manuscript received February 25, 1985 Accepted May 28, 1985
Heterogeneous and Homogeneous Effects of H,S on Light-Hydrocarbon Pyrolysis John H. Kolts Research and Development, Phillips Petroleum Company, Bartlesville, Oklahoma 74004
The pyrolysis of ethane, propane, isobutane, n-butane, and ndecane has been studied with H,S added in the 0-10% range under conditions in which the surfaceholume ( S N )ratio was varied over approximately 6 orders of magnitude. In the absence of H,S the pyrolysis rates and product selectivities remained virtually constant over large changes In S / V ratio. At low S/V ratios HS , can either inhibit or accelerate the rate of hydrocarbon decomposition depending upon the nature of the intermediate radicals. Under high S/V conditions, H,S caused an increase in pyrolysis rate for all hydrocarbons tested. The results are consistent with a mechanism and kinetic analysis in which the effect of high surface area is to catalyze the decomposition of HS , into intermediate radicals. The effects of HS , on product selectivity appear as a large increase in propylene yield from n-butane feed, increased isobutene from isobutane feed, and little or no change in selectivity with n-decane, propane, or ethane feed.
or with H2S present as
Introduction The ability of hydrogen sulfide to homogeneously accelerate or inhibit the rate of hydrocarbon pyrolysis reactions and to alter the selectivity to various products has been known for several years. These changes in conversion rate and selectivity have been well documented for ethane (Scacchi et al., 1970; McLean and McKenney, 1970), propane (Porchey and Royer, 1974; Tischler and Wing, 1973), isobutane (Niclause et al., 1976), n-butane (Large et al., 1972), and neopentane (Scacchi et al., 1968). Niclause et al. (1976) have reviewed the data and presented a mechanism to explain the effects of H2S. Rebick (1980, 1981) has also reviewed the effects of H2S on light hydrocarbons and has extended the data base and interpretation to heavier alkanes and alkenes. According to the mechanism of Niclause et al. (19761, H2S or some other hydrogenated additive can alter hydrocarbon pyrolysis in two ways. H2S can increase the rate of hydrogen transfer by substituting a more facile set of reactions for the normal propagation steps. If one uses the notation of Niclause, this can be represented with no additive present as p.
--L k k-i
8. + p H
+ 8.
(1)
@H+ p.
(2)
m
k2
0196-4313/86/1025-0265$01.50/0
-- + 0. m
(1)
k + H2S -3, PH + HS.
(3)
p-
p.
A k k-i
k-3
HS.
+ pH
e k
H2S
+ p*
(4)
where p- represents hydrocarbon radicals that decompose unimolecularly, P- are hydrocarbon radicals that decompose via bimolecular hydrogen abstraction, and pH and PH are the hydrogenated form of the respective radicals. PH and m will be the major reaction products where m is any stable decomposition product, for example, ethylene from unimolecular decomposition of 1-C3H,- or propylene from decomposition of 2-C4H9.. The second way H2Scan alter pyrolysis reactions is via introduction of new termination steps that occur between HS- and other radicals formed during the pyrolysis. Under this mechanism an accelerated decomposition rate may be expected when hydrogen transfer is rate limiting (k2< k,) or can be inhibited when unimolecular decomposition is rate limiting (k, < k 2 ) via introduction of the new termination steps. The above mechanism assumes that H2S does not play an active role during the initiation steps of the radical chain reaction. This is based on the larger H-SH bond dissociation energy (-90 kcal mol-l) when compared to 0
1986 American Chemical Society
266
Ind. Eng. Chem. Fundam., Vol. 25, No. 2, 1986
Table I. Selectivities to Products over Quartz Chips and Silica (185 m2 g-') a t - 2 5 % Conversion" propane n-butane isobutane quartz silica quartz silica quartz silica 792 "C 793 "C 741 "c 737 "C 749°C 745'C Ci 17.8 19.5 16.1 16.9 13.5 14.7 c2 1.7 0.2 6.1 5.7 0.8 0.3 Czb 34.8 36.0 32.1 29.7 2.7 2.9 C3 3.8 0.9 2.1 0.8 C3b 44.9 43.2 40.2 43.2 35.5 36.9 c, 0.2 0.1 C,b 1.9 1.1 2.1 3.6 45.4 45.2 ~
I
QUARTZ
I REACTOR
BLEND
TO VENT OR WET
f--
TEST METER SAMPLE
I
"Reactor space-time = 0.11 s. bAlkene Table 11. Conversions over Quartz Chips and Silica Gel (185 m2al)with and without 1% H2Sn hydroquartz chips silica gel carbon temo. "C no H,S 1% H,S no H,S 1% H,S 48 36 46 69 ethane 800 24 28 24 48 propane 780 n-butane 750 ou 44 30 79 isobutane 756 38 45 37 61 16 24 22 54 n-decane 670 ~~
Figure 1. Schematic diagram of pyrolysis flow system.
typical C-C bonds (80-86 kcal mol-') and that long chain lengths in hydrocarbon pyrolysis would overwhelm any small changes in the initiation steps. The present study will investigate the effects of H2Son hydrocarbon pyrolysis under conditions that may show the effects of
H2S
k5
Ha
+ HS.
(5)
as an initiation step. Specifically, hydrocarbon pyrolysis experiments were conducted over silica surfaces in which the surface to volume ratio (S/V) ranged from 1to lo6 cm-I. The S / V ratios reported in the literature for similar experiments are typically less than 10 cm-'.
-
Experimental Section Experiments were conducted using 6-mm-i.d. quartz reactors in a downflow configuration (see Figure 1). Preheating of the feed stream was accomplished in zone one. Zone two, which was 8-9 cm in length, was maintained at the desired reaction temperature. The temperature in zone 2 was constant to within f3 "C. Zone three was not used in the present set of experiments. Temperature measurements were made in a quartz thermocouple well centered in the reactor. All gases used in the experiments were either Phillips pure grade or Matheson research grade and were used without further purification. H2Swas typically added to the reactor as a 20% blend in nitrogen. Flows were set by using gas metering valves and were continuously monitored with electronic mass flow indicators. Reactor space-times quoted do not take into account volume expansion with hydrocarbon conversion. Effluent from the reactor was snap sampled and analyzed by using the HP5880 chromatograph with 18 f t of 27% Bis 2-EEA, 6 f t of 80% Porapak N + 20% Porapak Q, and 7 f t of 13X molecular sieve. Hydrogen analysis was done on a Carle BGC using nitrogen carrier gas. The chromatographs were calibrated with a certified standard blend from Air Products. Absolute material balances were checked for each feed tested and were better than 96%. Reported selectivities are based on normalized moles of feed converted to particular products, excluding hydrogen. Results Two sets of pyrolysis experiments were conducted with C2 through C, alkanes and n-decane. The first set was to determine the effects of large changes in the surface/ volume ratio. The second was to measure the effects of small quantities of H2Son pyrolysis when the surface-to-
"Reactor pressure was 1 atm at a constant space-time of 0.11 s. Table 111. Pyrolysis of n-Butane over Quartz Chips and Silica Gel (185 m2g-') as a Function of H2S" H,S Dartial Dress., atm 0.0 0.005 0.01 0.02 0.04b Conversion, % 7.5 (7.8) 11.9 (16.0) 12.6 (31.7) 16.0 (35.3) 20.1 (40.0) Selectivity CH, 14.5 (16.1) 17.3 (18.7) 18.8 (18.9) 19.0 (18.1) 19.2 (19.0) CZH, 22.8 (24.8) 17.9 (11.4) 15.8 (11.5) 13.6 (11.0) 11.9 (10.9) 9.8 (9.9) 11.3 (9.9) 9.6 (10.0) 9.6 (10.2) C2HO 8.2 (7.0) CSH, 46.2 (44.9) 51.6 (53.3) 52.1 (55.0) 53.0 (56.4) 55.1 (56.2) Temperature was 650 OC, total pressure was 1 atm, and partial pressure of n-butane was 0.5 atm, with the balance being N,. Values in parentheses are for silica. bAt [H2S]= 0.1 atm the conversion over silica was 6170.
volume ratio was changed over several orders of magnitude. Figure 2 shows conversion data obtained for n-butane pyrolysis at widely different S/V ratios, using an empty quartz reactor, one containing quartz chips, and one with high surface area silica gel. As shown, conversion of nbutane was virtually constant when space-time is held constant (assuming silica gel to be a solid particle). Similar experiments using propane and isobutane feeds also showed no discernible difference in conversion under widely varying S/V ratios. Ethane did show a 3-6% decrease in conversion over silica gel when compared to quartz chips at temperatures between 700 and 825 "C, whereas n-decane showed a small increase in conversion over silica gel. As shown in Table I, the product selectivities observed over quartz chips or silica gel did not differ appreciably. There are small but consistent trends that show increased selectivity to ethane, propane, and butane in the presence of quartz chips and a slight increase in methane yield over silica. Pyrolysis of n-decane showed a small increase in C,-C, hydrocarbons over quartz chips as compared to data taken over silica. From the data presented it appeared that the S / V ratio has very little effect on pure hydrocarbon pyrolysis; however, as shown in Table 11, small amounts of H2S in conjunction with high S/V ratios can have large effects on the pyrolysis rate. The changes observed with H,S under low S / V conditions follow closely trends reported in the lit-
Ind. Eng. Chem. Fundam., Vol. 25, No. 2, 1986 100
4
TEMP. " C Figure 2. Conversion of n-butane as a function of temperature over different silica materials: 0, empty quartz reactor; A,quartz reactor packed with 5 cm3 of 16-40-mesh quartz chips; a, quartz reactor packed with 5 cm3 of American Cyanamid silica gel (185 m2 g-'), space-time calculated on the basis of silica being a solid particle (Le., same void volume as quartz); m, same as previous except space-time calculated around true void volume of silica particle. Gas composition in all cases was 50% C4and 50% NP.Gas flows were adjusted to give a space-time of 0.11 s at 750 OC.
675
700
725
750
775
800
825
TEMP. ' C
Figure 3. Conversion of n-butane under different S/V ratios: 0 , quartz chips (no H2S);V,empty reactor; A,quartz chips; 0, silica gel (56.8 m2 g-'); 0, silica gel (84.7 m2 g-'); m, silica gel (185 m2 g-'); A, silica gel (314m2 g-'). Total pressure was 1atm; H2Sconcentration was 1%in each case, except base data where no H,S was added. All packing materials were 16-40 mesh.
erature (Rebick, 1980). However, at high S/V ratios the observed conversions were much larger than expected. The effects of H2S concentration are summarized in Table 111. Conversion of n-butane as a function of silica gel surface area is shown in Figure 3. Experiments conducted over quartz chips of different mesh sizes between 10 and 40 did not show the effects of increased S/V ratio. The observed trends in product selectivity with and without H2S can be seen in Table I11 for n-butane pyrolysis. Over both quartz and silica, methane, ethane, and propylene increased, while ethylene selectivity decreased. Ethylene and propylene showed the greatest changes in selectivity. Changes observed with ethane and propane feeds were very similar with and without H2S. Isobutane showed a 1&13% increase in isobutene selectivity and a corresponding decrease in propylene in the presence of H2S. Sulfur analysis using Drager tubes indicated that no H2S, within experimental error (*lo%), was being consumed during the reaction. In addition, no sulfur compounds were detected in the liquid products.
267
Discussion Surface-to-VolumeEffects. The data obtained with no H2Spresent indicate for propane, butane, and isobutane that over silicon materials large changes in S/V ratio had little or no effect on conversion or selectivity and only small effects with ethane and n-decane feeds. Pyrolysis data in the literature relating to the effects of S/V ratio over silicas have produced some conflicting results. Pratt and Rogers (1979a-c, 1980) in wall-less reactor studies found no surface effects using ethane, propane, and n-butane but indicated surface area effects were present with isobutane. Laidler et al. (1962) and Voerodsky (1959) found that increasing the S/V of quartz inhibited the rate of propane pyrolysis. Fusy et al. (1965, 1966) found that for pure alkanes the pyrolysis rates were nearly independent of S/V ratio when using silica packing materials (slightly dependent for ethane and isobutane and independent for n-butane and isopentane). The general consensus at present is that silica surfaces have only minor effects on alkane pyrolysis, especially at high conversion levels (>20%). Data reported here certainly substantiate this. Many of the inconsistencies reported in the literature may have been a result of trace amounts of oxygen being present (Corcoran, 1983). Homogeneous and Heterogeneous Effects of HzS. As has been shown, pyrolysis data obtained in this study with added H2S and low-S/V conditions conform very closely to those reported in the literature. The mechanism of Niclause et al. (1976) predicts the effects of H2S on hydrocarbon conversion rate quite reliably, and in those cases which are rate limited by unimolecular decomposition (e.g., C,H,., 2-C3H7.,etc.), the trends in product selectivity can also be predicted. The data and the mechanism also imply that H2S interacts homogeneously. Rebick (1980) has derived rate equations which describe the changes in product selectivity for those hydrocarbons that are rate limited by hydrogen transfer. The data for several hydrocarbons show that HS. radicals tend to remove hydrogen from positions on the hydrocarbon molecule that are different from typical hydrocarbon radicals. n-Butane pyrolysis data show the change in hydrogen abstraction selectivity quite dramatically via the substantial increase in propylene selectivity and reduced ethylene selectivity. These results imply that HS. abstracts a larger percentage of hydrogen at the secondary carbon, where propylene is formed from 2-C4H9-. Data for isobutane are also consistent with this interpretation. On a microscopic scale the reasons for this preference are unknown. One explanation may be the fact that HS. has a diffuse electron cloud that is highly polarizable. Hydrocarbon radicals have relatively tight electron clouds with lower polarizabilities. This would allow HS. to adapt to the incoming hydrocarbon, forming a more stable and longer lived complex. Traditionally, the more stable complex has been found to form, preferentially, the thermodynamicallyfavored product, 2-C4H9.in the butane example. If this explanation holds true, one might expect that H atoms may give higher than expected rates of ethylene formation from n-butane. In this case H.is highly reactive and would abstract hydrogen from n-butane much closer to the statistical distribution. The higher relative rate of 1-C4H9-formation would result in increased rates of ethylene formation. Data in the literature for alkane (Hirato, 1968) and olefin (Taniewski et al., 1981) hydropyrolysis do show enhanced ethylene formation rates. Much more detailed experiments with known H atom sources are needed, however, to prove the proposed differences in abstraction selectivity.
268
Ind. Eng. Chem. Fundam., Vol. 25, No. 2, 1986
/
0.5
/8
1
i
c
$ 2
0.41-
Y
y
0.3-
z 9 ," 0.2: 0.1
i
c
-0
I
'
OL-
/ f -
-
31
0
'e/
*
1
650
a-•
1
- 1 - L
750
700
800
TEMP. " C
0.02
0.01
Figure 4. H2S decomposition a t 1-atm pressure: 0,silica gel (185 m2 g-l); 0 , quartz chips. Feed to reactor was 1.5% H2S in nitrogen at a space-time of 0.11 s.
Table I1 and Figure 3 indicate heterogeneous effects of H2S at high S/V ratios, in contrast to HzS data taken under low-S/V conditions, that indicated homogeneous reactions. All hydrocarbons tested showed large increases in conversion; the most striking was ethane, which showed an inhibition with H2S a t low S/V and a substantial enhancement in conversion at high S/V. Changes in product selectivity for all the hydrocarbons tested at high-S/V conditions closely followed those observed a t low-S/V conditions and were about equal when compared on a constant-conversion basis. Figure 4 shows data obtained when H2S is passed over quartz chips and silica gel in the absence of hydrocarbon. The results show a significant increase in the decomposition rate of H2S,independent of hydrocarbon, most likely as a result of weak rather than strong interactions of H2S with silica gel. Order-dependence measurements using n-butane, a t a temperature of 725 "C, showed that [H2S] varied to the 0.33 power over quartz chips and to the 0.54 power over silica gel having a surface area of 185 m2 g-'. Rebick (1980) also found a 0.3 power dependence at 650 "C for n-butane pyrolysis. As the above results indicate, silica gel appears to catalyze the decomposition of H2S. Assuming the decomposition involves formation of Ha and HS., the effect on hydrocarbon pyrolysis would be to add an additional initiation step. Using ethane pyrolysis as an example, we can represent the homogeneous chain radical mechanism in the presence of H2S as (Muller et al., 1977)
0.03
0.04
[HzSl / [cz H6] Figure 5. Variation of ethylene formation rates as a function of [H2S]/[C2H6] ratio: 0 , silica gel having surface area of 56.8 m2 g-l; 0,silica gel having a surface area of 185 m2 8'.
ditions will add the following initiation step, where SS is some site that catalyzes H2S decomposition. H2S + [SS] -% Ha
+ HS.
(13)
At steady state the ratio of initial rates of ethylene formation in the presence or absence of heterogeneous initiation has the following form: ( R O ) surface,HzS
(RO)H2S
(
+
k5[H2S] '/' k6[c2H6])
(I4)
where k5 = kl3[SS]. The heterogeneous decomposition of H2S can only have an accelerating effect on the decomposition rate when compared to the homogeneous reaction. Equation 14 can be rearranged to (15) and has been plotted in Figure 5 for ethane pyrolysis.
(11)
From the slopes, k5 = 134k6 for silica gel having a surface area of 56.8 m2 8-l and k5 = 319k6 for silica gel having a surface area of 185 m2 g-'. Similar results obtained for silica gel having a surface area of 320 m2 g-' were only slightly higher than that taken a t 185 m2 g-l. The increased rate of initiation will have little or no effect on product selectivity. Data for propane, isobutane, and n-butane at low and high S/V ratios show this is true when compared at constant conversion. The mechanism by which silica gel catalyzes the decomposition of H2S has been assumed to be via (13), H. and HS. reacting with gas-phase hydrocarbons. From a purely thermodynamic standpoint a concerted reaction of the following type H,S H, + S (16) would be more favorable. Sulfur atoms would then abstract successive hydrogen atoms, re-forming H2S and initiating the chain reaction. In either case each heterogeneous decomposition of H2Swill result in formation of two intermediate radicals.
CZH,y + HS. (12) The rate-limiting step is unimolecular decomposition (8), and H2S can have only an inhibiting effect (Niclause et al., 1976). Heterogeneous initiation under high-S/V con-
Conclusions Results of the present study have shown that (1)large changes in S / V ratio of silica materials have little or no effect on the pyrolysis rate and product selectivity with propane, isobutane, and n-butane and only minor effects
initiation
k6
+
propagation
-
C2H5H.
HS. termination
--
2CH3. C2H6 CH,. + CzH6 CH, CzH5. CH3. H2S -.+ CH, HS. k8
+ H2S
+ C2H6
(6) (74 (7b)
+ +
C2H4+ H.
--- + kg
Hz
k k-K
2C2H5.
H,S
(8)
HS.
+~
(9) 2
~
5
.
(10)
kii --+
kn
-
269
Ind. Eng. Chem. Fundam. 1986, 25, 269-279
on ethane and n-decane pyrolysis, (2) under pyrolysis conditions with H2S present and low S/V ratios, the data have confirmed results in the literature, and (3) with H2S over silica gel with high S/V ratios the pyrolysis rate was increased with all feeds tested. The effects of H2S under high S/V ratios are consistent with a mechanism in which the silica gel catalyzes the decomposition of H2S into intermediate radicals. The heterogeneous decomposition of H2Sappears as an additional initiation step and can only accelerate hydrocarbon pyrolysis rates. This is in contrast to the homogeneous mechanism which can accelerate or inhibit the pyrolysis rates in the presence of H2S. The observed changes in product selectivity with added H2S are the same in both the heterogeneous and homogeneous reactions.
Acknowledgment I thank Dr. A. M. Schaffer for many helpful discussions and Mrs. H. B. Vanderveen for her excellent technical assistance. Registry No. H a , 7783-06-4; ethane, 7484-0; propane, 74986; isobutane, 75-28-5; n-butane, 106-97-8; n-decane, 124-18-5.
Fusy, J.; Martin, R.; Dzierjynskl, M.; Nlclause, M. Buii. SOC.Chim. Fr. 1986, 3783. Fusy, J.; Scacchi, 0.;Martin, R.; Combes, A.; Niclause, M. C . R . H e w . Seances Acad. Scl. 1985. 261, 2223. Hirato, M. J . Pet. SOC.Jpn. 1068, 1 1 , 934. Laidler, K. J.; Sagert. N. H.; WoJclechowskl,0. W. Proc. R . SOC.London, A 1962, 270, 242. Large, J. F.; Martin, R.; Niclause, M. C . R. Hebd. Seances Acad. Sci., Ser. C 1972, 274, 322. McLean, P. R.; McKenney, D. J. Can. J . Chem. 1970, 48, 1782. Muller, J.; Baronnet, F.; Scacchl, G.; Dzrerzynski, M.; Niclause, M. I n f . J . Chem. Kinet. 1977, 9 , 425. Niclause, M.; Earonnet, F.; Scacchi, G.; Muller, J.; Pezequel, J. Y. ACS Symp. Ser. lg76, No. 3 2 , 17-36. Pratt, G.; Rogers, D. J . Chem. Soc., Faraday Trans. 1 1979a, 75, 1089. Pratt, G.; Rogers, D. J . Chem. SOC.,Faraday Trans. 1 1979b, 75, 1101. Pratt, G.; Rogers, D. J . Chem. Soc., Faraday Trans. 1 1979c, 75, 2688. Pratt, G.; Rogers, D. J . Chem. SOC.,Faraday Trans I 1980. 76, 1694. Porchey, D. V.; Royer, D. J. U.S. Patent 3803260, 1974. Rebick, C. “Frontiers of Free Radical Chemistry”; Academic Press: New York, 1980. Rebick, C. Ind. Eng. Chem. Fundam. 1881, 2 0 , 54. Scacchl, G.; Baronnet, F.; Martin, R.; Niclause, M. J . Chim. Phys. Phys.Chim. Bioi. 1988, 6 5 , 1671. Sacchl, G.; Dzlerzynski, M.; Martin, R.; Niclause, M. Int. J . Chem. Kinet. 1970, 2 , 115. Tanlewski. M.; Zachowicz, A.; Skutil, K.; Maciejko, D. Ind. Eng. Chem. Rod. Res. Dev. 1081, 2 0 , 746. Tlschler, L. G.; Wing, M. W. U S . Patent 3773850, 1973. Voerodsky, V. V. Trans. Faraday Soc. 1959, 55, 65.
Literature Cited
Received for review August 23, 1984 Accepted M a y 28, 1985
Corcoran, W. H. “Pyrolysis: Theory and Industrial Practice”; Academic Press: New York, 1983.
Design and Synthesis of Homogeneous Azeotropic Distillations. 4. Minimum Reflux Calculations for Multiple-Feed Columns Sanford G. Levy and Michael F. Doherty’ Department of Chemical Engineering, Goessmann Laboratow, University of Massachusetts, Amherst, Massachusetts 0 1003
A general method for calculating minimum reflux ratios in double-feed columns has been derived. The method applies to ideal, nonideal, and homogeneous azeotropic distillations. In addition, algebraic criteria have been developed for finding the best feed alignment. Some counterlntultlve cases are described.
Introduction The aim of this series of papers is to produce an automated method for the design and synthesis of azeotropic distillation sequences. The procedure, when completed, will allow for the rapid evaluation of many alternative entrainers. After each column sequence has been designed and optimized, a small set of economically attractive schemes can then be examined more closely. In the first part of this series (Van Dongen and Doherty, 1985), the problem formulation is presented. Levy et al. (1985) and Doherty and Caldarola (1985) (which will be referred to as parts 2 and 3, respectively) describe the design method for single-feed columns and the relationship between the simple distillation residue curve map and possible sequence structures. The purpose of this paper is to extend the design procedure of part 2 to double-feed distillation columns. Two-feed columns are used widely in extractive distillations (Benedictand Rubin, 1945) where a heavy entrainer feed is used to aid in the purification of either an azeotropic or a close-boiling mixture. Such columns would also be used for the more general homogeneous azeotropic dis0196-4313/86/1025-0269$01.50/0
tillations proposed in part 3. Another important use for double-feed columns occurs when identical separations are required of two streams of different composition. In this case, the separations should be performed in one column with the feed streams introduced at two different points. In the past, engineers have used three types of design procedures for these columns. For ideal mixtures, Underwood’s (1946) method of calculating the minimum reflux ratio has been extended by King (1980) and Barnes et al. (1972) to allow for multiple feed streams and side products. A McCabe-Thiele method of design for nonideal systems has been used by Dunn et al. (1945), Sheibel (1948), Smith and Dresser (1948), Atkins and Boyer (1949), and Chambers (1951). This method involves plotting a pseudobinaryx-y diagram assuming a constant nonvolatile entrainer concentration in the liquid phase. These methods can supply a relatively good estimate of r- if the entrainer is very heavy. However, this technique does not lend itself to algebraic calculations and fails when the third component (whether it be an entrainer or otherwise) is volatile to any extent. Hoffman’s (1977) method is much 0
1986 American Chemical Society
