Murphree Point Efficiencies in Multicomponent Systems Gary C. Young1 and James H. Weber2 Department of Chemical Engineering, University of Nebraska, Lincoln, N B 68508
Murphree vapor point efficiencies were determined for the systems n-hexane-methylcyclopentane, nhexane-methylcyclopentane-ethanol, and n-hexane-methylcyclopentane-ethanol-benzene, The results obtained on the binary system are in agreemeni with efficiencies calculated by the AlChE correlation. For the ternary, surface-tension negative systems had higher efficiencies than positive ones, as expected for operations in the spray regime. A mathemaiical model was developed for the prediction of efficiencies in ihe systems investigated. The work on the multicomponent systems confirms the concept that the efficiencies of all components may not b e equal. In all cases, the major resistance to mass transfer was in the vapor phase. The data were obtained in a sieve tray column of 1 17/8-in. diam.
T r a y efficiencies are recognized as a n important factor in distillation column design. While there have been many investigations of tray efficiencies for binary systems-the AIChE made a major research effort in this area (Gerster et al., 1958; blalakoff, 1955; Schoenborn et al., 1959; and Williams et al., 1 9 6 G t h e investigations of multicomponent systems have been few in number (Diener and Gerster, 1968; Haselden and Thorogood, 1964; S o r d , 1946; and Qureshi and Smith, 1958). The reasons for these developments are obvious. Nonetheless, efficiencies obtained on a binary system have a serious limitation-Le., the efficiencies of the two components must be identical. Consequently, the question immediately arises, do the efficiencies obtained under these conditions indeed reflect the behavior in multicomponent systems? The latter are of more practical significance. Normally, for calculation and design purposes, the efficiencies of the con~ponentsin a multicomponent system have been assumed equal. This has been done knowingly, but often with some feeling of trepidation. Years ago, Walter and Sherwood (1941) pointed out the unlikelihood of identical values of these efficiencies. With these thoughts in mind, this investigation of Murphree point efficiencies in multicomponent systems was initiated, and the purpose here is to present our results. Clearly, much more work needs to be done, but hopefully this work will be of some assistance to the individuals interested in this field. First, a few definitions and a n explanation of the reason that point efficiencies rather than plate efficiencies were measured. The Murphree point efficiency, E O G , is defined as:
This contrasts with the tray efficiency, which is defined as:
The major difference is in the first term in the denominator. I n Equation 1, y t , ? * represents the vapor mol fraction
1
Present address, Continental Oil Co., Ponoa City, OK 74601. To whom correspondence should be addressed.
440 Ind. Eng.
Chem. Process Des. Develop., Vol. 1 1 , No. 3, 1972
of the i component in equilibrium with the liquid a t some particular point on the tray, while in Equation 2, Y ~ , ~ * represents the vapor composition in equilibrium with the liquid leaving the tray. Similar expressions may be written for the liquid phase. I n addition, relationships between point and plate efficiencies can be developed, but the pattern of liquid mixing on the tray must be taken into account. Alternately, a number of point efficiencies on a given tray may be measured, and a value for the overall efficiency obtained by integration. For design purposes the plate efficiency is the more useful. For predictive and correlative purposes, the point efficiency is possibly more useful because it presumably is not dependent on the mechanical features of the contacting device but only on the physical properties of the system and the flow regimes. Consequently, we set out to measure point efficiencies. Finally, since wall effects are known to be significant in small columns, and scaling-up, therefore, difficult, an l17/8-in. diam column was used. Experimental Equipment and Operating Procedure
Complete details of the experimental equipment and operating procedure are presented elsewhere (Young, 1971). The flow scheme in Figure 1 permits the unit to be operated as a rectifier or as a stripper. The column contains three sieve trays of identical design. The center one was the test tray. The column sections above and below the test tray were glass; this permitted observation of the action on the two lower trays. The sieve trays, 1 1 7 / 8 in. in diam, had 8% free area, 21/2-in. weir, and '/*-in. liquid seals. The holes were 3/8 in. in diameter and located on the apexes of equilateral triangles with sides of 13/16 in. Tray spacing was 153/8in. One sampling device mas located below the test tray for the rising vapors. The other was located above the test tray for the vapor and liquid. Samples could be obtained on or at any distance above the test tray and a t radii of 0.0, 0.75, 1.50, 2.25, 3.00, and 3.75 in. through a 360' angular rotation. The sampling tubes, hypodermic needles-0.047 in. i.d., when not in use were kept clear by bleeding nitrogen through them. When sampling the vapor, there always exists the possibility that entrained liquid may be included. To reduce this possibility, the thermocouples were placed immediately
in front of the tube ends. As a check, on the initial runs a number of vapor samples was obtained from different points in the vapor space, and in some cases duplicate runs were made. I n neither instance were differences detected in the compositions of the vapor. These are clear indications t h a t the vapor samples mere representative. The column was operated a t atmospheric pressure.
DlSTlLLATlOll COLURH
Selection of System
The range of a number of important variables was, a t least partially if not completely, fixed by the design of the equipment. The selection of the system, however, is still a matter of importance and offers almost infinite possibilities. And, the final decision involves compromises. I n this particular case, the n-hexane-ethanol-methylcyclopentane-benzene system was chosen. The boiling range, 68.7-8O.l0C, is small. This makes separation difficult, but does minimize any thermal distillation effect. There is some variation in properties, such as surface tension, liquid-phase viscosity, and gas-phase diffusion coefficients. With the variation of surface tension, the possibility of operating, in surface tension, positive and negative regimes existed. Also, differences in gas-phase diffusion coefficients may cause different efficiencies in gas-phase-controlled mass transfer operations (Toor and Sebulsky, 1961). Consequently, these considerations were important. Last, and by no means insignificant, were the facts that vapor-liquid equilibrium data were available for this quaternary system-and for the constituent binary and ternary systems-and that the ternary and quaternary equilibrium relationships can be predicted accurately using the Wilson equation (Wilson, 1964), as shown by Prausnitz et al. (1967). This latter fact meant t h a t a convenient and accurate method of interpolation was available. Because the quaternary vapor-liquid equilibrium data are so important in this work, additional measurements were made on the system. These data are available (Young, 1971) and were in good agreement with previous work. Analytical Technique and Accuracy of Experimental Measurements
Methods of analysis and accuracy of the experimental measurements are matters of interest. Compositions were determined by gas-liquid chromatography. A Perkin-Elmer 880 chromatograph, equipped with a hot wire detector, a 194B printing integrator, and a Leeds & Xorthrup Speedomax G strip chart recorder, was used. The instrument was calibrated using 20 samples of different, but known, compositions. Using mean values of calibration factors defined as: (3) and back-calculating compositions and comparing with the compositions determined by weighing, the average absolute deviation in analysis is h 0 . 2 mol yo. Temperature-measuring equipment, as well as flowrators and pumps were calibrated, and degrees of precision determined (Young, 1971). Since experimental errors exist, and predicted equilibrium compositions may deviate from the true values, a range was determined for each experimental value of the efficiency. Using Equation 1, the minimum value was obtained by assuming the experimental errors to yield a minimum difference in the numerator and a maximum difference in the denominator, while the maximum value was obtained by
VEliT
1
STEAM
I
I
IrREBOILER
Figure 1. Overall flow diagram of distillation apparatus 1. Top section of column, calming section 2. Glass section
3. Glass section 4. Bottom section of column, calming section 5. Sampling devices Troy 2 i s the test tray
assuming the reverse conditions. The range does, indeed, reflect the extreme conditions. Confidence limits on the sample estimate of the population mean for the Murphree vapor point efficiency were determined. To do this, the point efficiency was measured five times over an interval of 15-20 min. These data combined with the t-distribution were used to compute confidence limits since the population variance is not known. For 99% confidence limits, the t-distribution value a t the 99.5 percentile was used, and the value of the 97.5 percentile for the 95% confidence limits. Discussion
I n a n investigation of this type, a great amount of data is obtained. These are reported by Young (1971), and illustrating the point, the experimental data and calculated results for one of the runs employing the quaternary system are included as Table I. I n Table 11, the most significant results for all the runs are reported. Point efficiencies for the binary system n-hexane-methylcyclopentane, the ternary system n-hexane-methylcyclopentane-ethanol, and the quaternary system n-hexanemethylcyclopentane-ethanol-benzene, were obtained. Runs were made under conditions of total reflux, and absorbing and stripping conditions. The vapor velocity, based on the tray bubbling area, varied from 1.13 to 2.56 ft/sec. This was the range of observed stable operation-minimal weeping, not a n excessive amount of entrainment, and good vaporliquid contacting and liquid mixing on the tray. If one accepts the definition t h a t the ratio of the froth height to the plate spacing ( x100) is a rough measure of the percentage of flooding, then our maximum was 30%. The correlation of Hunt et al. (1955) predicts the amount of entrainment as 0.0019 lb of liquids/lb of vapor a t the higher vapor rates. Initially, point efficiencies were obtained on the binary system. The purpose was twofold: one, to develop a familiarity with the operation of the equipment, and two, to obtain data which could be checked against the AIChE correlation (Bubble-Tray Design Manual, 1958). The mean values of the point efficiencies were 68, 71, and 68%, while the comparable Ind. Eng. Chem. Process Des. Develop., Vol. 11, No. 3, 1972
441
Table 1. Murphree Vapor Point Efficiencies (Run 29)
System operating as stripping column Flaw . .- .. rate . -. -
Flow streom
n-Hexone
Composition, mol fraction EtOH MCP
Benzene
Accumulator stream 0.425 0.296 0.128 0.151 Feed stream (top) 0.471 0.155 0.159 0.215 Bottom product stream 0.502 0.076 0.171 0.251 Reboiler feed stream 0.502 0.076 0.171 0.251 Reboiler liquid 0,501 0.005 0.190 0.304 Vapor leaving top of column Steam to reboiler, 100.4°C, 0.0 p i g , 2.09 lb/min Pressure drop across tray, 2.1 mm Hg, froth height 4.9 in., clear liquid height, 5 / * in. Pressure above tray, 730.5 mm Hg or 0.961 atm Liquid flow rate, 0.423 lb mol/min or 32.9 lb/min Vapor flow rate, 0.145 lb mol/min or 10.6 lb/min L/V ratio, 2.91 lb mol/lb mol; L/B ratio, 1.52 lb mol/lb mol Temperature drop across tray, 2.1°C
Temp, OC
49.5 56.2 60.8 60.8 63.3 59.6
Ib mol/ gaI/min
1.82 5.72 3.92 2.10
min
0.145 0.423 0.277 0.149
At tray condition Vapor load, 1.07 fta/sec Liquid load, 5.76 gal/min Linear vapor velocity based on tray bubbling area, 1.77 ft/sec Vapor density, 0.00226 lb mol/ft3 or 0.168 lb/ft3 Liquid densit,y, 0.549 lb mol/ft3 or 42.9 lb/ft3 95 and 99% confidence limits on sample estimate of population mean Murphree vapor point efficiency, point location on tray 270°, radius 0.75 in., 5 samples taken during 15-min interval 95%
99%
0.46 0.58 0.6 0.59
0.43 0.58 0.5 0.57
< EOG, n-Hexane < Eo', Ethanol < EoG,MCP < E O G , Benzene
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