DISTILLATION PERFORMANCE IN THE CRITICAL REGION J. A. GERSTER, W.
H. SLACK, JR.,’ AND S. A.HARRISON*
University of Delaware, Newark, Del.
Tray efficiencies were determined for the ethyl ether-1-butanol system at pressures up to 95% of the critical pressure. A 5-inch sieve-tray column with ordinary downpipes was used; each downpipe occupied 3070 of the tower cross section. Tray efficiencies were reduced slightly with increasing throughput, but an additional reduction in efficiency was found with increasing values of reduced pressure when this variable exceeded 0.5.
G A S MIXTURE cannot be even partly liquefied a t temperatures above those encountered in the critical region (20), so that distillation of such a mixture must take place a t temperatures below the critical region. If the temperatures in the critical region lie below room temperature, refrigeration then is required to supply reflux to the distillation column. Because refrigeration costs are high and increase as the temperature level is reduced, it is usually most economical to operate such columns at temperatures not much below their critical. Separation of methane from ethane and purification of helium are two commercially important distillation processes carried out in this fashion (5, 2 3 ) . Columns operated in critical regions have many unique characteristics. At the critical point itself, the properties of the gas and liquid phases become identical, the latent heat of vaporization is zero, the relative volatility is unity, and the surface tension is zero. I n the region just below the critical point, the phase densities are similar, and latent heats of vaporization, surface tensions, and relative volatilities are small in value. Similarity in the densities of the gas and liquid phases causes hydraulic difficulties in critical columns. Liquid entrainment is more easily carried by the vapor to the tray above, and vapor entrainment in the liquid is more easily carried to the tray below. The low-density liquid requires more downflow area than would be required in more normal columns. Unfortunately, little information exists in the literature on hydraulic design of towers operated in the critical region. I t is also difficult to predict the changes which occur in tray efficiency as the pressure and temperature are raised into the critical region. The physical properties affecting efficiency, particularly diffusivity, may not be known, and other factors, such as interfacial area and degree of mixing on the tray, have not been studied. The purpose of the present research was to study the hydraulic and efficiency behavior of a distillation column when operated in the critical region.
A
Background
The maximum throughput of a fractionating tower is commonly correlated as a capacity factor, C, plotted against a n operating factor, ( L / V )( ~ ~ / p ~ with ) ‘ / ~tray , spacing and liquid Present address, E. I. du Pont de Nemours & Co., Kinston, N. C. Present address, E. I. du Pont de Nemours & Co., Old Hickory, Tenn.
seal as additional parameters ( 7 , 72, 18). The capacity factor, C, is defined as
Thus, if the tray spacing and seal are chosen, if the gas-toliquid rate ratio, L / V , is known, and if the gas and liquid densities, pV and p L , are fixed, ?I,the maximum gas rate in feet per second, may be calculated. u is commonly based upon a cross-sectional area which is that for the empty column less that for one downpipe. Smith, Dresser, and Ohlswager (22) recently developed a correlation of this type using as a basis mainly new data from 16 commercial towers known to be operating near their maximum throughputs. Some of the hydrocarbon towers had vapor densities as high as 4.8 lb. per cu. ft. and liquid densities as low as 28 lb. per cu. ft. Values of C were plotted against the operating factor with a new variable, the “settling height,” as parameter. This term was defined as tray spacing minus clear liquid depth, the latter calculated as weir height plus clear liquid overflow by the Francis formula. Their values of C increased with increasing settling height, and were independent of the operating factor u p to a value of about 0.1. From this point, C decreased more than twofold as the operating factor increased to unity. The correlation was identical regardless of whether the tower contained sieve trays, bubblecap trays, or valve trays. One of the reasons for the gradual reduction in maximum throughput as the operating factor increases above a value of 0.1 is the decreasing ability of the downpipes to handle the liquid downflow. The extent of the reduction in throughput caused by inadequate liquid downflow capacity was not determined by Smith et al. (22) nor can it be predicted by other means. A recent effort was made by Thomas and Shah (24) to determine downpipe characteristics, but their experiments were limited to studies with air and water containing varying amounts of detergent; they did show, nevertheless, that the “rules of thumb” commonly used in downpipe design (79)are conservative. Still another factor causes reduced throughput as criticality is approached. This factor is a rapidly decreasing surface tension, which promotes smaller droplet sizes and thus increased liquid entrainment. Hunt, Hanson, and Wilke demonstrated experimentally that entrainment was inversely proportional to surface tension, but did not carry their measurements into the low surface tension range found in critical columns ( 7 7). VOL. 5
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Smuck (23) also postulated that reduced surface tension was responsible for the lower tower throughput obtained in a 4.5-foot diameter de-ethanizer as the pressure was increased from 270 to 470 p.s.i.a. The value of C in Equation 1 was about 75% lower a t the higher pressure; this reduction was empirically correlated with surface tension. Smuck then used these experimental results to predict successfully the flooding point for a larger diameter propane-propylene splitter operating a t either 230 or 310 p.s.i.a. The mass transfer rate for distillation in critical regions governs the tray efficiency which is obtained. Mass transfer occurs by both molecular and convective transport, and the relative importance of these two modes of transfer is probably similar to that found in liquid-liquid extraction, where density differences of the two phases are also small. The mechanism of mass transfer for ordinary distillation and for extraction has been reviewed by Harriott (8, 9), who points out that some transfer by molecular diffusion will always occur. I t thus seems likely that the Schmidt number to some fractional power will continue to be used as an important correlating variable for tray efficiency of critical columns. Durbin and Kobayashi (7) show that the gas-phase Schmidt number varies by perhaps no more than 10% over a wide range of pressure. Other references also support this view (3, 77). The low surface tension present in critical distillation towers may affect tray efficiency in several ways: I t produces additional entrainment which lowers efficiency and also can tend to alter the magnitude of the interfacial area produced on the tray. According to Bainbridge and Sawistowski (2), the efficiency of a number of systems corrected to a common Schmidt number basis can be correlated with surface tension. These authors attributed the increase in efficiency with decreasing surface tension to an increase in interfacial area. They also considered the effect of the magnitude of the difference in surface tension of the two components upon efficiency and concluded, contrary to Zuidenveg and Harrnens (Z8), that for maximum efficiency the more volatile component should have the highest surface tension.
Experimental
Although most critical distillations of commercial interest are carried out a t low temperatures, it was decided in this study to work with a system which could be condensed with ordinary cooling water for the sake of cost and simplicity. However, because of the wide variation in pressure and temperature level involved, a high temperature heating medium, in this case an oil, was required. I t was decided to use a three-tray, conventional sieve-tray column of 5-inches diameter for these studies. Total reflux operation was employed. A binary system was chosen only after'very careful study of the literature. The system finally chosen was diethyl ether1-butanol. These substances are stable and available a t high purity and low cost. More important, their vapor-liquid and thermodynamic properties are suitable and are given in the literature in good detail u p to and including the critical region (6, 74, 75). Table I summarizes some of these data. Two factors made the ether-butanol system especially desirable for study. The first was that the relative volatility in the critical region was large enough that a reasonable precision could be obtained in determination of tray efficiency. The second factor is that the critical locus is almost linear between the critical points of the two pure components. The critical region thus is confined to a pressure-temperature range below 410
l & E C PROCESS DESIGN AND DEVELOPMENT
Table 1.
Summary of Physical Data for Diethyl Ether1-Butanol (6, 14, 15) Composition, Critic;[ Critical Pressure, Mole 7 0 Ether Temp., C. P.S.I. A .
100 74.4 47.6 27.1
193.4 219.5 247.9 266.0 289.7
0
System Pressure, P.S.I.A.
529.6 582.8 625.3 639.5 640.4
Relative Volatility, Ether- Butanol 3.48 Z!C 0.10 2.06 f 0.05 1 .OO at 65.1 mole $& ether
200 400 600 600 600 600
1.27 at 50.9 mole
1 .39 at 26.6 mole 1 .45 at 5 . 3 mole
yG ether
YGether Yoether
Proberties of Saturated Ether
Temp., O
c.
140 160 180 190 193.4
Heat of vaporiza-
Pressure, p.s.1.a.
Liquid density, g./cc.
Vapor density, g./cc.
216.5 308.8 428.9 501.2 529.6
0.544 0.495 0.430 0.369 0.265
0.045 0.070 0.115 0.169 0.265
tion,
B.t.u. Ib. 105
88 63 24 0
the critical conditions for butanol (290' C. and 640 p.s.i.a.), eliminating the need for equipment and physical property data a t conditions in excess of these values. Equipment. The column was fabricated from an 81/2-foot length of 5-inch, Schedule 90 steel pipe. Design working pressure was 700 p s i . Each of the three sieve trays rested on support rings welded to the inner shell. Each tray was 4.813 inches in diameter, and contained 42 holes of l/s-inch diameter, located on a 3/8-inch triangular spacing. The active tray area or bubbling area occupied 40% of the total tower cross section, and the remainder was occupied by conventional segmental downpipes. Each downpipe thus occupied 30% of the tower cross-sectional area, a value nearly double that used in conventional columns, but believed to be necessary for adequate handling of liquid downflow in the critical distillations to be employed. The outlet weir height was 2 inches, and the tray spacing was 18 inches except above the middle tray, which was 18 inches for some of the tests, and 30 inches for the remainder. The efficiency measurements were taken for the middle tray; it was provided with two sight glasses, each 1 inch by 4 inches high, spaced 120' apart. The test tray also contained a vertical rod fitted with washers a t 1-inch intervals for estimating froth heights through the windows. Design of the column for total reflux operation permitted the condenser and reboiler to be fastened directly to the column with no intervening piping. The condenser consisted of four vertical, 3/4-inch Schedule 90 pipes, each 37 inches long, mounted 18 inches above the top tray. The outside heat transfer area was 3.4 sq. ft. Vapors from the top tray entered the inside of these tubes from the bottom, were totally condensed, and returned by gravity directly onto the top tray liquid as in a reflux condenser operation. At the top of these tubes the inner volume was connected to a common manifold which was joined through a needle valve to a high pressure supply of nitrogen used in pressure control for the column. The reboiler liquid was contained inside of a 7-foot length of 8-inch, Schedule 90 pipe, mounted vertically directly below the column. The top of the 8-inch pipe was fastened to the
bottom of the 5-inch column through a short tapered transition piece. Inserted into the reboiler liquid was a hairpin tube bundle with tubes vertical and the 180’ return bends at the top. The bundle contained seven, 3/4-inch Schedule 90 tubes, each U-shaped, and each about 57 inches long from base to the curve of the U. The outside heat transfer area was 18.3 sq. ft. During normal operation, the tube bundle was completely covered with boiling process liquid; vapors from the liquid surface passed directly to the bottom tray which was about 18 inches above it. A level gage indicated the reboiler liquid level. The heat transfer medium which circulated through the inside of the hairpin tubes was a Mobiltherm 600 oil of low vapor pressure at temperatures up to 600’ F.; maximum inlet oil temperatures were around 500’ F. The oil was circulated by a gear pump at a rate of up to 18 gallons per minute; its flow was metered by a calibrated orifice and its temperature drop through the reboiler could be accurately measured. The oil received its heat from several electric heaters which had a combined capacity of 23 kw. Iron-constantan Conax thermocouples and Ashcroft pressure gages were located at strategic places in the apparatus. The entire equipment was well insulated. Thermocouples were located on the external surface of the insulation to assist in determination of heat loss from the unit. Operating Procedure. The reboiler was charged with about 8 gallons of ether-butanol mixture of the desired composition and the system then purged with nitrogen. Ether forms explosive peroxides with oxygen, although this reaction is repressed in the presence of iron. Vapor rate and tower pressure were controlled by variation in inlet oil temperature, oil circulation rate, cooling water rate, and amount of nitrogen admitted to the top of the condenser tubes. Inlet oil temperatures could be maintained to within 0.03’ F., and tower pressures could be maintained within 1.0 p.s.i. at steady state. Samples of the liquid were withdrawn from each tray and from the reboiler after steady state was established. The tray samples were taken from a point just upstream from the exit weir and l / * inch below the top of the weir. The samples were withdrawn through ‘/B-inch 0.d. stainless tubing run from the sample point through the walls of the column to the outside. The liquid sample lines were first water cooled, then cooled in an ice bath before passing through autoclave needle valves to the atmosphere; the samples were collected in stoppered test tubes in an ice bath. Analysis was by a PerkinElmer gas chromatograph, previously calibrated with known mixtures of ether-butanol. Scope of Experiments
The distillation tests of this study were carried out at variable composition level, system pressure, and vapor velocity under total reflux. The authors hoped to obtain as wide a variation in these conditions as possible, but the surface area of the reboiler proved to be limiting. This situation resulted partly because the reboiler heat-transfer coefficient was lower than anticipated [about 40 B.t.u./(hr.)(sq. ft.) (” F.)], but mainly because the column throughputs obtainable were considerably greater than a predicted maximum value. To offset these shortcomings, the tests were carried out with a mixture high in ether concentration: ether has the lower boiling point, so that reboiler At’s could be larger; also, a t any given temperature, latent heats of vaporization are lower in the high-ether concentration range. Reboiler compositions varied. from 28 to 89 mole 7 0 ether, but liquid compositions on the test tray (middle tray of the three-tray column) varied only from 82 to 98 mole 7 0 , and averaged 93 mole %.
The pressure level of the tests was varied from 141 to 517 p.s.i.a. ; this corresponded to a range of reduced pressure, defined as the ratio of tower pressure to the critical pressure of the liquid mixture on the test tray, of from 0.27 to 0.96. Liquid densities ranged from 38.7 to 23.5 pound per cu. ft.; the corresponding vapor densities ranged from 1.66 to 10.8 pound per cu. ft. ; and the ratio of liquid density to vapor density ranged from 23 down to 2.2. Vapor throughputs ranged from weeping to flooding, although this range of vapor rate was not obtained at each pressure level; maximum throughputs were not obtained a t the lower pressures due to reboiler limitations, A total of 60 efficiency runs and 17 throughput runs are reported ; tabulations of data and sample calculations are available (70, 76). Effect of Entrainment
Calculation of efficiencies from tray liquid compositions is straightforward under total reflux conditions in absence of entrainment. In this instance, the moles per hour of the more volatile component to and from tray n 1 is: V d , = Ln+lxn+l. Assume, however, that the vapor to tray n 1 carries with it e, moles of liquid entrainment per mole of vapor; the total input to the tray is then Vny, enVnx,. Assume further that all entrainment to tray n 1 is captured by the liquid on that tray and is returned to the tray below; assume also that this returning liquid contains no entrained vapor. I t is then possible to calculate the net moles per hour of more volatile component to tray n 1, and to define this net flow as V,Y,:
+
+
+
+
+
The term Y, is an “apparent” vapor composition to the tray, useful in defining an “apparent” tray efficiency, as first proposed : by Colburn (4)
(3) Values of E,,, often termed the “wet-tray Murphree efficiency,” are required in design to compute actual trays from theoretical trays when entrainment is present. At total reflux, V,Y, = &+I, from which it follows that Y , = L,+lx,+l and Vn x , + ~ ; thus values of E, may be directly computed from Equation 3 if experimental tray liquid compositions are available. The relationship between E,, e, and E M V , the “dry-tray Murphree efficiency” (efficiency in absence of entrainment) was first developed by Colburn ( 4 ) . He assumed that e was constant on all trays; in many of the runs of this study, however, the tray spacing was deliberately increased to 30 inches above the test tray and 18 inches elsewhere. This required the following modification to be made to the Colburn relation. First a substitution for Y , and for Y,J is made into Equation 3 from Equation 2; then each term in the numerator and denominator is divided by (yn* - ~ ~ - 1 ) . With EMvtaken as (yn Yn-l)/(Yn* Yn-l), Equation 3 then becomes
-
-
E,
=
EMV
+
c
-d
l + C
(4)
where
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I n Colburn's derivation, e,-l was taken equal to e, and ( x , xn-J was taken to be approximately equal to (%,+I x,), so that c = d, and c = e,-lEMv; this gives, for total reflux, the familiar result
-
(7) I n the case where e, # en-l, the Colburn assumption will still x , ~ )E (x,+I x n ) , which gives be made that (x,
-
-
Comparison of Equations 3 and 8 shows that E, for tray n varies depending whether the tray spacing above and below tray n is the same or different. In the present case, where the test tray always has an 18-inch spacing below it, but may have either an 18- or a 30-inch spacing above it, E, will always be greater in the latter case where e,-l > e,. T o compare the magnitude of E, and EM",divide each term in the numerator and denominator of the right-hand side of Equation 8 by EMv to obtain (9)
-
which shows that E, can be greater than EM, if en) > Eaen-l. This inequality can be satisfied in many instances when e, is small compared with en-l, and is always satisfied when e, is zero and Ea is less than unity-Le., less than 100%. A situation where E, > EM, is not commonly thought of, because in cases where the entrainment quantity is identical for all trays, Ea is always less than EMv. Calculation Procedure
Efficiencies were not calculated for trays other than the middle tray of the three-tray column. Efficiencies for the bottom tray were affected to some extent by entrainment from the reboiler, which was not known. Efficiencies for the top tray were not measurable, because a composite sample could not be obtained of the reflux which dripped directly from the reflux condenser onto the top tray. I t was not possible to determine experimentally if the liquid samples as withdrawn from the column contained appreciable quantities of entrained vapor. This problem is especially severe near the critical point where phase densities approach each other. However, efficiencies were computed assuming that the sample withdrawn from the aerated liquid mass on the tray represented the composition of the liquid on (or leaving) the tray. When the calculation is made in this manner, a t total reflux, the computed efficiency is the same whether the liquid sample is contaminated with entrained vapor or not, provided the following assumptions are met: linear equilibrium relationship, same efficiency on adjacent trays, liquid samples from adjacent trays contain the same fraction of entrained vapor, and composition of entrained vapor from adjacent trays is the same linear function of the composition of the liquid portion of the sample. Because the experiments were carried out in the high-ether composition range, the vapor-liquid equilibrium curve was nearly linear; and the other assumptions are reasonably well met. Thus, the authors believed that vapor contamination of the liquid 412
I & E C PROCESS D E S I G N A N D DEVELOPMENT
samples did not cause an undue loss of precision in the computed efficiencies. Still another factor which affected the precision of efficiency values is the rectification obtained because of heat loss through the walls of the column. The magnitude of the total heat loss in the system is the difference between the heat input to the reboiler and the heat removed a t the condenser. The former was calculated from the enthalpy loss of the heating oil to and from the reboiler; the latter was obtained by an enthalpy balance on the condenser cooler water. At the high temperatures employed in this study, heat losses averaged 24% of the heat input, but two thirds of this was heat loss from the reboiler itself. The fraction of the total heat loss dissipated from the reboiler was determined from measurement of temperatures of the outer surfaces of the insulation and from knowledge of the exposed surface areas. The rate of partial condensation of the vapor on the walls of the 30-inch section of column above the test tray was about 2% of the total vapor flow as long as the tower pressure was below about 375 p.s.i.a. (a reduced pressure of 0.7). For a reduced pressure of 0.85 (tower pressure of 464 p.s.i.a.), partial condensation was 3y0 of the total vapor flow. At a reduced pressure of 0.96, the highest value employed in these tests, the rapid decrease in latent heat of vaporization raised the fraction of vapor condensed to 6% of the total vapor flow. I n the first two instances, where the efficiency level is about 75%, the reduction in efficiency due to partial condensation is only about 2%, and corrections were not made for this effect in treatment of the data. However, where the reduced pressure was about 0.95, the efficiency level is only about 5Oy0, and the 6% partial condensation of vapor is responsible for 6 efficiency % out of the 50%. Thus, where the reduced pressure level was above 0.85, measured efficiencies were reduced accordingly before being correlated when the tray spacing was 30 inches. When the tray spacing was 18 inches, partial condensation was proportionately less, as was the efficiency correction. The enthalpy balance calculations just described were also used to calculate vapor flow rates above the test tray. Experimental enthalpies and latent heats of vaporization were available for pure ether and for pure butanol u p to their critical points. The latent heats were assumed to vary linearly with composition a t any system pressure. At any given pressure above the critical point for ether, the latent heat was assumed to vary linearly with composition between the known value for pure butanol to zero for the composition corresponding to the critical. Throughput Results
The range of throughput conditions encountered in the efficiency runs of this study is shown as open circles and triangles on Figure 1. The abscissa on this plot is the operating , for the total reflux and essenfactor, ( L / V ) ( p v / p L ) * / 2which, tially constant composition runs of this study, is directly related to the system pressure. The data shown are for the runs where stable operation and reproducible efficiencies were obtained. At the higher pressures, larger values of C could be obtained with the available reboiler because latent heats of vaporization were lower. The flooding point in the critical range was determined in a series of tests in which pure ether was employed. Each open square on Figure 1 indicates a condition of stable operation with pure ether; the solid square is the flood point. The pure-ether tests were made because thermal data, upon which the velocity calculation was based, are more firm for pure
_..
EXPERIMENTAL
0.3
I
ISPACINGABOVETESTTRAY:~
A,O
I
I
-
I
1
ETHER-BUTANOL 0 -PUREETHER
OPERATING FACTOR,
’
(+)(%)’
Figure 1 . Range of capacity factors and operating factors covered by experimental efficiency runs of this study Experimental flooding points are shown os solid points
ether than for the ether-butanol mixture. Two flooding points for butanol-ether operation, shown as solid triangles, are similar in magnitude, however, to that for pure ether. Flooding points a t lower pressures could not be obtained because of reboiler limitations. Plotted on the same figure as a solid line are the recommended values of the capacity factor, C, a t the flooding point taken from the commercial tower data of Smith, Dresser, and Ohlswager (22). The line shown is for a settling height of 16 inches which applies in this study. Figure 1 shows that a greatly increased throughput is obtainable in the experimental column of this study compared with that of the commercial columns used in the SmithDresser-Ohlswager correlation. The large downpipes employed in the experimental column are probably an important reason for the increased throughput; each downpipe had a cross section which was 30% of that for the empty column as compared with values of about 15% for commercial columns. If liquid downflow areas are too small, it is difficult to obtain adequate disengagement of vapor from the downpipe liquid when the density difference of the phases is small; the entrained or recycled vapor then limits the liquid flow capacity and also adds to the vapor loading of the tray from which it originated. Also, with a small difference in the density of the phases, less head is available to overcome friction in the downpipe. I n a private communication (27), Smith, Dresser, and Ohlswager have indicated other reasons why the 5-inch column of this study had an apparently higher throughput than their commercial columns. The first of these is that their definition of flooding was essentially where a sharp decline in efficiency occurred; in this paper, although the efficiency was low (say lo%), the tower was not considered to be flooded as long as flows to and from the column were steady. A second reason which they proposed is the lack of tower diameter (length of liquid flow) as a factor in the correlation. It does seem likely that larger diameter towers, upon which the Smith et al. correlation is based, would flood before a smaller tower. The probable mechanism of flooding in the experimental column was through excessive liquid entrainment carried by the vapor stream. Entrainment is increased as the froth height on the tray increases, and some attempt was made to obtain froth height information from the two small windows above the middle tray. At values of C less than 0.20, froth
heights were well below the bottom of the window, and were estimated to be 4 inches or less. As C was increased, froth heights increased, reaching values of around 13 inches a t C = 0.26. This height corresponded to the top of the window so that no additional information could be obtained, but flooding occurred very soon thereafter, a t C = 0.29 to 0.30. I t is also of interest to consider weep points for Figure 1. In a recent paper, Prince and Chan (73) present a careful analysis of weeping on sieve trays. These authors made predictions for the “seal point” of a perforated tray, a condition where all of the liquid flowing to the tray passes to the tray below through the perforations, but the liquid holdup on the tray (the “seal”) remains the same as during normal, nonweeping operation. Their predicted result showed that for a weir height of 2 inches and an operating factor of 0.1, the value of C required to seal the tray is 0.053. An approximation of the point where weeping would just begin would be where the dry-tray gas pressure drop equals the weir height, 2 inches. For the case of a large vapor density, the dry-tray gas pressure drop in inches of tray liquid, h, is predicted by Treybal (27) : h = 0.33
uh2
[PL Pvl
0.33
chz
(10)
For h = 2 inches, the value of Ch from the above equation is 2.46, and the corresponding value of C (where weeping begins) is 0.10. Efficiency Results
The first step in correlation of efficiency results was to consider the group of runs farthest removed from the critical region. The results were placed in order of increasing pressure, and starting with the run having the lowest pressure, 141 p.s.i.a. (corresponding to a reduced pressure, P R , of 0.27), values of apparent efficiency were plotted us. the capacity factor, C. A single correlation line resulted until the pressure level reached about 280 p.s.i.a., corresponding to a reduced pressure of 0.51, after which efficiencies were noticeably lower as the pressure level was increased a t any particular value of C. The plot of efficiency us. C for runs with reduced pressures in the range of 0.27 to 0.51 is shown as Figure 2. Runs where tray spacing was either 18 or 30 inches are included. No important effect of tray spacing is noted, indicating that entrainment effects for these runs were very small or absent.
0.08
0.10
0.10
0.14
0.16
0.18
C, CAPACITY FACTOR
Figure 2. Values of apparent efficiency, E,, vs. capacity for runs where reduced pressure, PR, did not exceed
0.5 1 Range of tower pressures is from 141 to 280 p.r.i.a.
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413
The efficiency values of Figure 2 may be compared with those of Schoenborn et al. (26) who distilled the following binary systems a t total reflux and 1 atm.: acetonebenzene, acetone-acetic acid, and benzene-acetic acid. They used a small column similar in size to the present one. Efficiencies averaged very close to 80% for each of these systems. In the present case, where Schmidt numbers are nearly the same as for Schoenborn’s systems, efficiencies would be expected to be the same as those of Schoenborn a t moderately low pressures and a t the same throughput (25). Schoenborn’s throughput corresponds to C = 0.10 on Figure 2, and the drop in efficiency with increasing throughput, as predicted by the A.1.Ch.E. procedures (25), is only from 80% a t C = 0.10 to 76y0a t C = 0.18. This result does not, however, consider the lower level of surface tension existing in the test column, which averaged 5 dynes per cm., us. the usual 20 dynes per cm. for organic liquids a t their normal boiling point (70);lower surface tension is said to increase interfacial area and thus increase efficiency ( 2 ) . The next set of efficiency data considered included those runs where throughputs were in the same range as those of Figure 2, but where the pressure level was higher, phase densities were closer to each other, and the operating factor was higher. T o show effects other than throughput, the efficiency of each of these runs, as well as the efficiency of each run on Figure 2, was corrected to a value which would be obtained a t C = 0.14. This was done using the correlation line from Figure 2, which showed that the corrected efficiency, E,(C = 0.14), was related to the measured efficiency, E,,by
E, (C = 0.14) = E,
+ 2.98 (0.14 - C)
(11)
where the two efficiencies are expressed as fractions. The corrected efficiencies are shown plotted in Figure 3 us. the reduced pressure for the test tray. Reduced pressure was chosen as the correlating variable because by indicating the extent of the approach to the critical point, it also indicates the extent to which the surface tension approaches zero, the extent to which the ratio of the phase densities approaches unity, and the extent of change of Schmidt number with pressure level. Study of Figure 3 shows that a gradual decline in efficiency occurs as reduced pressure is increased above 0.5. Observation through the windows seemed to indicate that a t higher pressures the aerated mass on the tray consisted of liquid droplets suspended in a continuous gas phase rather than vice versa as in normal columns; this could explain the observed result. Other possible factors are: the decrease in turbulence level in the vapor phase which occurs as the phase densities approach each other; and, variation of Schmidt number with
I
0.2
I 0.3
0.4
I 0.S
I 0.6
1
0.7
0.8
I 0.9
(PR
= 0.5) = Ea
+
(PR
- 0.5)(0.39)
(12)
where the two efficiencies are expressed as fractions. These corrected efficiencies are plotted us. the capacity factor, C, on Figure 4. Reference to Figure 4 shows that when C < 0.18, all of the data are correlated reasonably well by a single line. The correlation line shown is identical to that used in Figure 2 where no corrections for PRwere necessary, and where a drop in efficiency with increasing C definitely was indicated. Above C = 0.18, the efficiencies vary markedly with the spacing above the test tray. This indicates that entrainment is an important factor affecting efficiency a t the higher throughputs. T o approximate the magnitude of the entrainment a t high throughputs, a separate plot, Figure 5 , was made. In this figure, the uncorrected efficiencies (as measured) are shown plotted as points us. the capacity factor. The solid lines are the best correlation of these raw data: the dashed lines below the solid lines show the reduction in efficiency which would have been obtained if heat loss from the column had not been present (efficiencies in all previous figures already included this correction). T o estimate entrainment, it is necessary to employ Equations 7 and 8 which require knowledge of EMv,the efficiency obtained in absence of entrainment. These dry-tray efficiencies were obtained by extending the correlation line of Figure 4 into the high-throughput range ; this procedure is very approximate, but it does permit an idea to be obtained as to the magnitude of the entrainment. Before plotting this line onto Figure 5, it was corrected by Equation 12 from PR= 0.5 over to P R = 0.90, the average value of reduced pressure for the runs shown
0’
0.10
0.12
I
I
I
I
0.14
0.16
0.18
0.20
I
I
I
0.22
0.24
0.28
I
I
I
0.28
C, CAPACITY FACTOR
Figure 3. Values of apparent efficiency, corrected to the condition where capacity factor, C, is 0.1 4, as a function of fR, the reduced pressure
414
E,
I
1.0
PR, REDUCED PRESSURE
Data plotted only for runs where C
pressure. As none of these factors could be evaluated separately, the use of reduced pressure as a correlating variable appeared to be reasonable. Efficiencies for both the 18- and 30-inch tray spacing are included on Figure 3, and efficiencies appear to be unaffected by tray spacing. Thus for the throughput range considered in the figure (0.10 < C < 0.18), entrainment is not a factor affecting efficiency even at reduced pressures as high as 0.73. Entrainment Effects. To compare the runs having large throughput and large reduced pressure with the other runs, it was first assumed that the effect of reduced pressure upon efficiency just developed in Figure 3 for values of C up to 0.18 would also apply a t the higher throughputs. Thus for all of the runs where PR> 0.5, the efficiencies were corrected over to a value which would be obtained if PR were less than 0.5. By Figure 3, this corrected efficiency, E,(PR = 0.5), can be calculated as:
< 0.1 8
l&EC PROCESS D E S I G N A N D DEVELOPMENT
Figure 4. Values of apparent efficiency, corrected to the condition where reduced pressure, fR, is 0.5, as a function of capacity factor Solid points are for cases where liquid entrainment Is no longer negligible
I
1
A 18 IN. 0 30 IN.
1
~
ae
I
1
I
028
030
appreciable change in the apparent efficiency, the calculated quantity of liquid entrainment would be lower. Unfortunately, it was not possible to determine the magnitude of vapor entrainment in these studies. Low Throughput Runs. Three efficiency tests were made below the incipient weep point of C = 0.10; the efficiencies of these three runs, shown on Figure 1, average 92%. The value of PR for these runs was just slightly over 0.5,so the effect of weeping can be estimated by comparing the experimental values with those from Figure 2. This figure shows that a t values of C < 0.10, efficiencies in absence of weeping should be over 95%. The experimental values are only slightly lower than 95y0, so that operation in the range 0.10 > C > 0.06 should present no difficulties.
1
I
0
I S IN RESULT
I 8 IN. RESULT ( N O HEAT LOSS) 020
022
024
026
C, CAPACITY FACTOR
Figure 5. Values of apparent efficiency, uncorrected, for cases where liquid entrainment is no longer negligible
Conclusions
Dashed lines show reduction of effkiency if heat loss from column had been negligible. Estimate of E J ~ v , efnciency in absence of entrainment, i s also shown
on the figure. The resulting values of entrainment calculated by this procedure are given in Table 11. An alternate approximate procedure was employed also to calculate entrainment. In this instance, the value of e, in Equation 8, which is the entrainment above the 30-inch tray, was taken as zero and values of e,-l and EMv then were obtained by solving Equations 7 and 8 simultaneously a t various values of C. These results are shown in Table 11 also. The purpose of the alternate procedure was to provide lower limits for the 18-inch tray entrainment and for the dry-tray efficiency. The true entrainment values lie between the two sets of values shown in Table 11. For any value of the capacity factor, e is inversely proportional to Sn,where S is the distance from the top of the froth to the tray above, and n has a value in the range 2.0 to 3.2 (77, 25). For C, between 0.21 and 0.27,the ratio o f S values for the 30- and 18-inch trays lies between 25/13 and 13/1, so that the entrainment ratio e ~ / e 3 0 , computed as (sa,)/Sla)2.6, must lie between 5.5 and 780. From Table 11, els/eao for the case where E,, was taken from Figure 5 averages only 2.2,but its value is infinity when e30 is taken as zero. Thus the entrainment ratios computed as (S3U/s18)2'6 lie between the values from Table 11, indicating that the true values lie between those shown in the table. Reference to the table shows that the amount of entrainment was considerable, especially just below the flooding point. The fact that the column was operable with such large quantities of entrainment may be due to the fact that the entrainment droplets were very small owing to the low surface tension. The calculation for liquid entrainment neglected vapor entrainment in the downflowing liquid. If the latter caused an
Table II. Calculated liquid Entrainment Values
Throughput, C EMV(Figure 5), % Entrainment, e, from above value of EMV and Eqs. 7 and 8 18-inch tray 30-inch tray Entrainment, e, from 18-inch tray assuming e from 30-inch tray is zero EMvassuming e from 30-inch tray is zero, %
0.21 48 1.8
0.24 39 3.3
0.27 30 9.2
0.6
1.6
5.4
1.2
1.8
3.8
37
24
11
For a small column operating in the critical region with each liquid downpipe having an area equal to 30% of the tower cross section, operation a t capacity factors up to 0.20 is fairly satisfactory. The main factors affecting efficiency in the critical region were : throughput, reduced pressure, and entrainment. Effects of the first two variables were determined quantitatively for a given system. The presence of large quantities of entrainment a t the higher throughputs affected efficiency markedly, but the determined values of entrainment are not too precise. Additional studies with other systems, now in progress in these laboratories, must be made before the generality of the results obtained thus far can be confirmed. Ac knowledgment
Financial support for this research was kindly supplied by The Petroleum Research Fund of the American Chemical Society. Thanks are due to Carl Steinbaum for his assistance in these studies. Nomenclature
C c h
e
E.
=
capacity factor, defined by Equation 1
= capacity factor based upon hole velocity, uh = liquid entrainment, moles/mole of vapor = apparent tray efficiency (includes effect of
liquid entrainment) E,(C = 0.14) = value of E, a t C = 0.14 E,(PR = 0.5) = value of E, a t PR = 0.5 = Murphree vapor efficiency in absence of E MV liquid entrainment h = dry-tray gas pressure drop, inches of tray liquid L = liquid rate, moles/hr. = reduced pressure, ratio of pressure a t test PR tray to critical pressure corresponding to tray liquid composition = distance from top of froth to tray above, feet S U = gas velocity, feet/sec., based upon total tower cross section less area of one downpipe = gas velocity, feet/sec., through perforations uh V = vapor rate, moles/hr. X = mole fraction ether in liquid = mole fraction ether in vapor Y = mole fraction ether in vapor in equilibrium Y* with liquid on tray Y = apparent vapor composition to tray, defined by Equation 2 = liquid density, Ib./cu. ft. PL = vapor density, Ib./cu. ft. PV
SUBSCRIPTS n = a t tray n = a t tray above tray n n+l n-1 = a t tray below tray n VOL 5
NO. 4 O C T O B E R 1 9 6 6
415
Literalure Cited
(1) Andersen, A. E., Phillips, E. M., Hydrocarbon Process. Petrol. Refiner 43, No. 8 , 159 (1964). (2) Bainbridge, G. S., Sawistowski, H., Chem. Eng. Sci. 19, 992 (1964). (3) Berry, V. J., Koeller, R. C., A.Z.Ch.E. Journal 6, 274 (1960). (4) Colburn, A. P., Znd. Eng. Chem. 28, 526 (1936). (5) Deaton, W. M., Haynes, R. D.,- Petrol. Refiner 40, No. 3, 205 (1961). ( 6 ) Donham, W. E., Kay, W. B., Chem. Eng. Sci. 4, l(1955). (7) Durbin, L., Kobayashi, R., J . Chem. Phys. 37,1643 (1962). (8) Harriott, P., Can. J . Chem. Eng. 40, 60 (1962). (9) Harriott, P., Chem. Eng. Sci. 17, 149 (1962). (10) Harrison, S. A,, Master’s thesis in Chemical Engineering, University of Delaware, Newark, Del., 1965. (11) Hunt, C., Hanson, D. H., Wilke, C. R., A.Z.Ch.E. J. 1, 441 (1955). (12) Perry, J. H., “Chemical Engineers Handbook,” p. 18-6, McGraw-Hill, New York, 1963. 113) Prince. R. G. H.. Chan,, B.,. Trans. Znst. Chem. Eners. - (London) 43, T49 (1965). ’ (14) Schnaible, H. W., Smith, J. M., Chem. Eng. Progr. 49, Symp. Series No. 7, 159 (1953). (15) Schemilt, L. W., Espen, R., Mann, R., Can. J . Chem. Eng. ‘ 37, 142 (1959). (16) Slack, W. H., Master’s thesis in Chemical Engineering, \ - - I
University of Delaware, Newark, Del., 1964. (17) Slattery, J., Bird, R., A.Z.Ch.E. J . 4, 137 (1958). (18) Smith,. B. D., “Design of Equilibrium Stage Processes,” p. 545, McGraw-Hill, New York, 1963. (19) Zbid., p. 496. (20) Smith, J. M., Van Ness, H. C., “Introduction to Chemical Thermodynamics,” p. 359-64, McGraw-Hill, New York, 1959. (21) Smith, R. B., Dresser, T., Ohlswager, S., private communication, Feb. 23, 1966. (22) Smith, R. B., Dresser, T., Ohlswager, S., Hydrocarbon Process. Petrol. Rejiner 42, No. 5, 183 (1963). (23) Smuck, W. W., Chem. Eng. Progr. 59, No. 6, 64 (1963). (24) Thomas, W. J., Shah, A., Trans. Znst. Chem. Engrs. 42, T71 (1964). (25) “Tray Efficiencies in Distillation Columns,” Final Report of University of Delaware to A.1.Ch.E. Research Committee, American Institute of Chemical Engineers, New York, 1958. (26) “Tray Efficiencies in Distillation Columns,” Final Report of North Carolina State College to A.1.Ch.E. Research Committee, American Institute of Chemical Engineers, New York, 1959
(27) Treybal, R., “Liquid Extraction,” p. 504, McGraw-Hill, New York, 1963. (28) Zuiderweg, F. G., Harmens, A,, Chem. Eng. Sci. 9, 89 (1958). RECEIVED for review January 13, 1966 ACCEPTED July 11, 1966
LONGITUDINAL MIXING IN ORIFICE PLATE GAS-LIQUID REACTORS KENNETH 6 . BISCHOFF AND JAMES 6. PHILLIPS’ Department of Chemical Engineering, The University of Texas, Austin, Tex. Residence time distribution data were obtained in orifice plate gas-liquid reactors for different plate designs and lengths, Both holdup and mixing information was determined from the data and correlated with that of other investigators. Short tubes had somewhat different characteristics than long ones, and plate design seemed to affect holdup mare than mixing. All of the reactors had more intense mixing than that obtained with single-phase liquid flow and thus would not give a very close approach to plug flow conditions.
Ottmers and Rase (9) proposed the use of multiple orifice plate contactors as an alternative to stirred tanks for gas-liquid chemical reactions. They discussed several practical advantages such as the lack of moving parts in the reactor. Another important point was the possibility that the flow patterns in the orifice reactor could be made to approach plug flow rather than perfect mixing, as is the case in stirred tanks. Plug flow is definitely preferred for certain types of reactions, particularly those with side reactions making unwanted products (6). From motion picture studies, Ottmers and Rase found that a single large hole in the center of an orifice plate produced a long jet of highly dispersed mixture in the center of the column along with considerable backmixing along the walls. With 16 small holes with the same fractional free area, a more uniform flow was observed with a finer scale of turbulent motion. O n the basis of these qualitative observations, they concluded that plate designs with one or 16 holes would tend to perfectly mixed or plug flow conditions, respectively. Mass transfer data from Ottmers and Rase (9),however, showed little difference among the various types of plates. Since a relatively small amount of mass transfer occurred in a pass through the column, this could not be used to indicate clearly any quantitative differences between the flow patterns ECENTLY,
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Present address, Humble Oil and Refining Co., Baytown, Tex. I h E C PROCESS D E S I G N A N D DEVELOPMENT
for the plates. The motion picture studies used a very much smaller gas velocity than that found useful for mass transfer, which also makes comparative interpretations difficult. The purpose of this investigation was to delineate the types of flow patterns existing by means of residence time distribution (RTD) studies using tracers. Previous Work
There has been very little previous work on RTD in cocurrent gas sparged tubular reactors of any type. Siemes and Weiss (74) presented data for a 1.65-inch tube. More recently, Argo and Cova (7) considered backmixing in 1.8-, 4,and 176/s-inch vessels under various conditions. The above works (and this one) were concerned with the “bubble flow” regime (72). Tracer data for “annular” flow (72) in helical coiled tubes have been given by Rippel, Eidt, and Jordan ( 7 7 ) but are not directly applicable. Countercurrent bubble flow RTD information has been presented by Tadaki and Maeda (75). Information on longitudinal mixing for two-phase flow in packed beds is available and some work has been done in other geometries such as distillation column plates. These studies can serve as guides to experimental procedures and give orders of magnitude of the mixing effects. Some of the work is summarized by Levenspiel and Bischoff (7).
