376
Ind. fng. Chem. Process Des. Dev. 1083, 22, 376-380
No. AC03-78ER11343by the Aerojet Energy Converslon Co., Sacramento, CA, March 1980. Geldart, D. P O W T e d m ~ I 1973, . 7,285. Gelpetbr, N. I., Alnshtein, V. G. I n “FMdlzatbn”; Davidson, J. F.; Harrison, D., Ed.; Academlc Press: New York, 1971;p 517. Gelperhr, N. I.; Ainshtein, V. 0.;Korotyanskaya, L. A. Int. Chem. Eng. 1989, 9 , 137. Wperln, N. I.; Ainshteln, V. 0.; Zalkovskl, A. V. Khim ihWt. Mashinosh. 1988, No. 3, 17. Gkksman, L. R.; Decker, N. A. Paper preeented at 6th lnternatlonal Conference on Fudlzed Bed Combustion, Atlanta, GA, 1980. Gobllrsch, G. M.; sondreal, E. A. Fluidized Combustlon of North Dakota Lignite. “Technology and use of Lignite.” Proceedings of Symposium sponw e d by the U.S. Energy Recleerch and Development Admlnistratlon and The Unlverslty of North Dakota, Grand Forks, 1977;p 82. GorosMo, V. D.; Rozenbeum, R. 6. Izv. Vuzov, Neff’ I a s , 1958, No. 1 , 125 (cited in Zabrodsky, 1966). Grewal, N. S. Ph.D. Thesis, University of Illinois at Chlcago Clrcle, IL, 1979. Grewal, N. S. P O W Teahnol. 1081, 30, 145. Grewal, N. S. Len. Heat Mass Transfer 1962, 9, 377. Grewal, N. S.;HaJlcek, D. R. 7th International Heart Transfer Conference, Paper No. HX23,MUnchen, Federal RepubHc of Qerrnany, Sept 1982. Grewal, N. S.;Saxena, S. C. Paper presented at 4th Natlonal Heat Mass Transfer Conference, Roorkee, Indla, Nov 1977,p 53. Grewal, N. S.;Saxena, S. C. Int. J. Heet Mass Transfer 1080, 23, 1505. Grewal, N. S.;Saxena, S. C. J. Heat Transfer 1979, 101, 397. Grewal, N. S.;Saxena, S.C.; Ddidovlch. A. F.; Zabrdksy, S.S.Chem. Eng. J . 1970, 18, 197. Grewai, N. S.;Saxena, S. C. Ind. Eng. Chem Rocess Des. Dev. 1061.20,
Howe, W. C.; Auiislo, C. Chem. Eng. Rog. 1977, 73,69. Krupicrka, R. Int. Chem. Eng. 1087, 7, 122. KunU, D.; Levensplel. 0. “Flukllzatbn Engineering”; Wlley: New York, 1969; Chapter 9. Martln, M. Int. Chem. €ng. 1082, 22(1), 30. Mod, S.;Wen. C. Y. A I C K J. 1975, 27(1), 109. Newby, R. A.; Keahns, D. L.; Ah&, M. M. Proceedings, DOE/WVU Conference on FlukllzedgedCombustion System Design and Operation. Morgantown, WV, 1980 p 59. Saxena, S. C.; Grewal, N. S.; Gabor, J. D.; Zabrodsky. S. S.; Gakshtein, D. M. A&. Heat Tr8nsfer 1978, 14, 149. Staub. F. W.; Canada, 0. S.I n ”Fluldlretbn”; Davldson, J. F.; Keakns, D. L., Ed.; Cambridge University Press: London, 1978;p 339. Staub, F. W. J. Heat Transfer 1979. 701, 391. Tamarln, A. I.; Zabrodsky, S. S.; Yepanov, Yu. G. Heat Tf8nSler Soviet Res. W78, 8(5), 51. Wen, C. Y.; Yu, Y. H. Chem. €ng. Rog. Symp. Ser. 1986, 62(62), 21. Xavler, A. M.;Davldson, J. F. AIChE Symp. Ser. 1981, 77(208),388. Xavier, A. M.; Davideon, J. F. I n “FMdlzatkn”; Davklson, J. F.; Keakns, D. L., Ed.; Cambridge University Press: Cambrkige, 1978 p 333. Zabrodsky, S. S. “Hydrodynamics and Heat Tranfer In Fiuldlzed Beds”; MIT Press: Cambrklge, MA, lW6; Chapter 10. Zabrodsky, S. S.; Antonishin, N. 8.; Pamas, A. L. Can. J. Chem. Eng. 1978, 54, 52. Zabrodsky, S. S.; Epnov, Yu. G.; alershtein, D. M.; Saxena, S. C.; Kolar, A. K. Int. J . Heat Mass Transfer 1981, 24. 571.
Received for review March 20, 1981 Revised manuscript received October 6, 1982 Accepted December 20, 1982
108. Gutfinger, C.; Abuef, N. A&. Heat Tr8nsfer 1974, IO, 167.
Effect of Vapor Maldistribution on Tray Efficiency Tadlnad Mohan, Krowldl K. Rae,' and D. Prahlada Rao’ Department of Chemical Engineering, Indlan Institute of Technology Kanpw, Kanpur 2080 76, India
The effect of vapor maldistribution on the Murphree tray efficiency has been studied accounting for the variation of point efficiency that arises due to vapor maldistribution. I t is found that, even in the case of perfectly mixed and plug flow models of the liquid phase, vapor maidistribution leads to considerable reduction in tray efficiency. The maximum reduction is found to occur at a Peciet number of about 5. The variation of efficiency with the liquid flow-path length of a rectangular tray of a fixed area has been studied. Tray effeciency is found to increase with the Iiquld flow-path length well up to the point where dumping is encountered, provided uniform liquid flow distribution is ensured.
Introduction Excessive liquid gradient on a tray leads to vapor maldistribution. It is known to have a detrimental effect on tray efficiency. However, only a few attempts were made to analyze this effect with a view of providing a rational basis for the design of large diameter trays. Holm (1961) was the first to make an attempt to study the effect of linear vapor-flow gradient on tray efficiency. Later, Furzer (1969) showed that the linear vapor-flow gradient has no effect on tray efficiency for the perfectly mixed and plug model of liquid phase. For the dispersed flow of liquid, he found a marginal reduction in tray efficiency which is maximum a t a Peclet number of about 10. Recently, Lockett and Dhulesia (1980) extended Furzer’s analysis for the plug flow of vapor between the trays and the liquid flow in the same direction as well as in opposite directions on successive trays. They found that tray efficiency is unaffected by the linear vapor-flow gradient in the case of the plug flow and perfectly mixed flow of liquid phase, and there is a very small effect for trays Department of Chemical Engineering, University of California, Davis, CA 95616. 0196-4305/83/1122-0376$01.50/0
with dispersed flow conditions. In contrast, Bolles (1963) reported that investigations of bubble-cap tray columns exhibiting poor performance because of high liquid gradient showed that the vapordistribution ratio was in excess of 0.5, and recommended a value of the ratio 0.5 as the design limit. To meet this condition either multipass trays or other remedial measures are recommended. Furzer (1969) and Lockett and Dhulesia (1980) analyses do not indicate that the vapor maldistribution leads to poor tray performance. However, they considered the point efficiency to be constant over the tray in spite of wide variation of vapor velocity along the liquid flow path. In the design of large diameter columns, the tray selection-whether single or multipass-should be based on a consideration of the variation of the tray efficiency with the liquid flow-path length. In the present work, equations have been obtained to relate tray efficiency to point efficiency taking into account its variation due to vapor maldistribution. A computer simulation study of the effect of various parameters on the tray efficiency is presented. The dependence of tray efficiency on the liquid flow-path length has been examined with a view of evolving a criterion for tray selection. 0 1983 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983 377
Vapor Maldistribution The vapor distribution that arises due to the liquid gradient has been referred to hereafter as vapor maldistribution. It can be estimated from the pressure drop consideration (see Bolles 1963). Rao (1978) estimated the vapor maldistribution along the liquid flow-path length for rectangular and circular trays and found that it can be represented by a linear relation G ( w ) = G(0) + AGw (1) where w is a dimensionless distance from the inlet weir, G(w) is the vapor velocity at w, and AG = G(1) - G(0). Vapor maldistribution causes variation of point efficiency. The experimental data of point efficiencies in the presence of vapor maldistribution are not available. Hence, adopting the correlations presented in the AIChE Bubble-Tray Manual (19581, the point efficiency E o ~ ( wat) a location w was estimated by use of the local hydrodynamic conditions. The method of estimation of EoG(w) and its justification are presented later. However, from a number of computer simulated runs of the bubble-cap tray operating under different conditions, it is found that the variation of E ~ G ( wwith ) w can be expressed as
EoG(w) = A
+ BW + Cw2
(2)
where A , B, and C are constants. With these relations for C(w)and Eoc(w),equations are obtained for the Murphree tray efficiency, E-, for the perfectly mixed flow, dispersed flow, and plug flow models of the liquid phase. In addition, the following assumptions are made: (1)uniform liquid flow distribution along the width of the tray; (2) perfectly mixed vapor flow between the trays; (3) constant vapor and liquid flow rates from tray to tray; (4) linear equilibrium relationship, i.e., y* = mx b, and constant transport properties throughout the tray.
+
Tray Efficiency Perfectly Mixed Model. The enrichment of vapor as it passes through the tray n can be expressed as
where V is the molar flow rate of vapor, y ( w ) is the mole fraction of vapor leaving the vapor-liquid dispersion at w on the tray n, and y n and yn-l are the average mole fractions of vapor leaving the tray n and the tray n - 1, respectively. From the definition of point efficiency
it follows that Y(W)
- yn-1 = EOG(W)cU*n - Yo-1)
(4)
since y*(w) = y*n for the perfectly mixed flow of liquid. Substituting eq 4,2, and 1in eq 3, and on integration, we get
where 0 is the average vapor velocity. If E&w) is constant (i.e., B = 0, C = 0 ) , eq 5 reduces to E m = E,; in other words, the vapor maldistribution has no effect on tray efficiency.
Plug Flow Model. Following Lewis (19361, one can obtain the material balance on a differential slice of vapor-liquid dispersion as
dx
mZL = -(G(O) x - x*,-1 L
+ AGw)(A + Bw + Cw2)dw
Integrating the above equation between the limits x = x , at w = 1 and x = x at w = w, we get
(P + Q/2
+ R / 3 + S/4) -
where X = ( x - x*,l)/(x, - x*n-,); P = L; Q = (mZL/ L)(BG(O) A AG);R = (mZL/L)(CG(0) + B AG);and S = (mZLCAG)/L. From the definition of Em, we can show that
+
ZL Em = -vl l o X E o G ( ~ ) G ( dw ~) Substituting eq 7 in eq 8 and integrating, we get 1 EM" = - [exp(P + Q/2 + R/3 + S/4) - 11
x
(9)
where X = m V / L . If EOG is constant, eq 9 reduces to the well-known Lewis relation
Dispersed Flow Model. For the dispersed flow of liquid phase, it can be shown that the differential material balance on the slice
- - d2X - - - dX Pe d ~ 2 dw
%(G(O) L
+ AGw)(A + Bw + CW2) = 0 (10)
where Pe = Peclet number. Equation 10 is solved numerically using the fourth-order Runge-Kutta method to obtain X for different values of w by use of the boundary conditions X = 1 and dX/dw = 0 at w = 1. The computed values of X vs. w are used in the integration of eq 8 to obtain E-. It may be remarked that with the constants B = 0 and C = 0, eq 10 has been solved numerically by Furzer (1969). Evaluation of Tray Efficiency Estimation of Eoaand Its Justification. Consider a thin slice of the vapor-liquid dispersion covering its entire height and width located at w on a tray with vapor maldistribution, liquid gradient, and varying liquid flow rate per unit width. Let the thickness of the slice be large enough to accommodate a few vapor bubbles. The structure of the dispersion in the slice is expected to depend on local conditions as the vapor is expected to rise vertically upward without mixing as indicated in the Bubble-Tray Manual (1958, p 27). Further, the fact that only short calming sections are provided near the inlet and outlet weirs for the collapse of the dispersion indicates that the hydrodynamic nature of the dispersion in the slice strongly depends on the local flow conditions. Hence, it may be taken to be unaffected by the smoothly varying upstream and downstream vapor and liquid flow rates. It is known that the "froth" or dispersion density (i.e., the ratio of the clear liquid height to the height of dispersion) depends on the velocity of vapor and its density. Then it is reasonable to expect that the gas and liquid holdups
378
Ind. Eng. Chem. ProcessDes. Dev., Vol. 22, No. 3, 1983
depend on local conditions. More specifiGelly stated, it can be assumed that the interfacial area, gas-side, and liquidside mass transfer coefficients, gas and liquid holdups in the slice, and hence EOG(w)are determined by the local hydrodynamic variables only. The basic hydrodynamic variables which determine all the stated important parameters are vapor velocity, liquid flow rate per unit width and the clear liquid height. Thus, the value of Eoc(w) at the slice would be the same as the E m of a tray processing the same mixture but without vapor maldistribution and liquid gradient, and with uniform liquid flow rate, provided the vapor and liquid flow rates and the clear liquid height on the tray are the same as those prevailing in the slice. Hence in this work Eoc(w) was calculated using the formula given in the Bubble-Tray Manual employing the local values namely F(w)(= G(w) P " ' / ~ ) ,the liquid flow rate per unit width, L(w),and the clear liquid height at w. Only one further comment in justification of the method adopted for estimation of EO&) is required. The clear liquid height is equal to the sum of weir height, h,, the height of the crest over the weir, and the liquid gradient at w, A(w). The correlations presented in the manual do not account for the crest height explicitly. It can be presumed that the effect of crest height on E m is included in L which is the variable that affects it greatly. As far as h, and A b ) are concerned, it may be said that liquid at the top of the tray or the portion contained in A(w) is more effective for mass transfer than the liquid contained in h, since some clear liquid flow exists at the bottom of the tray. To account for this, we have adopted the correlations given in the "calculation form sheet" of the manual which includes the effect of the liquid gradient (for comment on this see Holland, 1975,and also Van Winkle, 1967). The method of evaluation of F(w),L(w),A(w), the values of which are needed to compute EOG(w)and E-, is discussed in the following section. Estimation of EM". A computer program has been developed to generate the tray layout and to determine tray hydraulics for a specified active area, tray geometry, and vapor and liquid flow rates. The studies reported here are limited to the bubble-cap tray with a 4in. carbon steel bubble cap of the specifications given by Bolles (1963,p 509). The correlations employed for determining tray hydraulics (which include A b ) ) are those given by Bolles (1963). He presented a plot of the "vapor-distribution ratio", Rvd vs. cap vapor load as percent slot capacity for the 4-in. carbon steel bubble caps loaded with benzene vapor at a pressure of 1 atm. The vapor flux G(w)was evaluated with the equations obtained by curve fitting the above mentioned plot to facilitate calculations on computer. The local value L(w) was calculated from a knowledge of L and tray width at
W. The values of F(w),L(w),and A(w) were evaluated a t an interval of 6.5 cm along the length of liquid flow path. Then the values of Em(w) vs. w were computed and the constants A, B, and C in eq 2 were found by the regression analysis. The tray efficiencies were evaluated from eq 5, 9, and 10 for the mixed flow, plug flow, and dispersed flow models, respectively. In the case of dispersed flow model the Peclet number was estimated ignoring vapor maldistribution.
Results and Discussion For a typical case, the estimated point efficiencies, number of gas transfer units, NG,and number of liquid transfer units, NL,at different values of 2 are shown in Figure 1. It can be seen that while NL goes through a
Vapor flow rate = 1 0 3 x IOLm3h-' Liquid tlow rate = 130 6 m3 h-' Acl!ve areoz83m2
G(OVG.0563
-10 0
Rvd= 1105
0 83-
-30 - 9 8 - 2 8 -96
-26 -91
9 -24
2
-92
-22 -90
-20 - 8 8 -18
0
05
10
15
20
'
25
-56
16 -81
hEOG
Figure 2. Tray efficiency in presence of vapor maldistribution. Table I. Hydrodynamic Variables and the Tray Details vapor flow rate 2.1 x lo4 m3 h-l liquid flow rate 68.1 m3 h-I transport properties of benzene-toluene system at 1 atm active area 9.3 mz 2.44 m ZL bubble cap 4 in standard carbon steel bubble cap (see Boles, 1963) weir height 7.5 cm pitch triangular cap spacing 25% cap diameter
maximum, NG varies linearly with Z. Since the gas-phase resistance is the controlling one, Eoc(w) closely follows the trend of NO. There is a considerable variation of point efficiency with 2. While the average point efficiency is 0.688,the point efficiency estimated ignoring vapor maldistribution is 9.733. Using G(O)/G and Pe as parameters, the E m are estimated for a single-pass rectangular tray. The tray details and operating conditions are given in Table I. The results are shown in Figurea 2 and 3. The values of the term were varied by varying m. The curvea denoted by "AIChE" in these figures refer to the tray efficiency estimated according to the procedure outlined in the "calculation form sheet" of the manual. It may be noted that even for the plug flow and perfectly mixed flow models, the vapor maldistribution has a detrimental effect on E- when E m
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983 379 Table 11. Variation of Tray Efficiency with Liquid Flow-Path Lengtha EMV
considering vapor maldistr
ignoring vapor distr
Pe 55 58 62 67 69
ZL, m
1.52 1.69 1.90 2.34 2.77
mixed 0.804 0.823 0.844 0.880 0.908
Rvd
0.89 1.07 1.28 1.74 2.25
Plug 1.239 1.283 1.333 1.420 1.489
dispersed 1.213 1.268 1.300 1.390 1.460
mixed 0.784 0.801 0.819 0.848 0.868
Plug 1.196 1,231 1.274 1.342 1.388
dispersed 1.193 1.228 1.269 1.330 1.372
Vapor flow rate 5.1 x lo5 m 3 h - l , liquid flow rate 392 m3 h" , active area 18.6 m a , m = 2.0. LO
Pe:30
15
"I
.'I /4
L9
20
10
I
W
10
0
10 08 0
1
2
3
4
5
6
7
8
(EMV) AlChE
1
2
3
4 AEOG
5
6
Figure 4. Percent error in tray efficiency estimation on ignoring vapor maldistribution.
Figure 3. Tray efficiency in presence of vapor maldistribution.
is varying, unlike in the case of constant Em The percent reduction, R ' in E- defined as
is plotted against ( E ~ ) A I cin~Figures E 4 and 5. From Figure 4 it can be seen that R'is about 10% for the tray efficiency in the range of 0.8 to 1.0. For different Peclet numbers R' vs. E- is shown in Figure 5. It can be observed that R' is maximum for Pe about 5. Similar observations were made by Furzer (1969) and Lockett and Dhulesia (1980). A comparative study of the effect of vapor maldistribution on E- of circular and rectangular trays revealed no noticeable effect of tray geometry. Since the variation of Em(w)with Z depends on the type of tray and the mixture properties (for instance, if the liquid film resistance is controlling, the trend of Eoo(w) vs. Z in Figure 1would have been similar to that of NL), the resulta presented in Figures 2 and 3 do not cover all the cases. However, rough estimates of the effect of vapor maldistribution on E m can be obtained from these plots, because generally the controlling resistance is the gas-side resistance, and the square root of Schmidt number of the vapor mixture is close to unity. In view af the design limit, Rd = 0.5, it is expected that E- should exhibit a maximum about Rd = 0.5. To check this contention, E W was estimated changing the length/width ratio of a rectangular tray with a fixed active area. For a typical case the results along with the operating conditions and tray details are given in Table 11. The other tray details are the same as those given in Table I. For the sake of comparison, the estimated E- for uniform vapor distribution and vapdr maldistribution for the three models are given. It can be seen that E- increases with 2, even though R d is far beyond the recommended limit.
35
-
30
-
25
-
20
-
15
-
a
///
G(O)/ 6:0 001
1 5 ° V
0" 0
'
1
I
I
2
3 E MV
I
4
5
Figure 5. Percent error in tray efficiency estimation on ignoring vapor maldistribution.
The detrimental effect of vapor distribution on E- has been far outweighed by the increase in point efficiencies and to a minor extent, due to the increased Pe. The increase in Em can be traced to the increased liquid depth with ZLand the liquid flow rate per unit width of weir. Since the longer path length results in higher tray efficiency, in spite of vapor maldistribution, we can conclude that the single-pass tray with twice the liquid flow path length is preferable to the expensive double-p&s tray, provided dumping of liquid is not encountered. However, it is known that the longer liquid flow path length can lead to severe nonuniform flow distribution. The recent developments in tray design aimed at ensuring uniform liquid distribution have been cited by Lockett and Satekourdi (1976).
380
Ind. Eng. Chem. Process Des. Dev. 1983, 22, 380-385
NL = number of liquid transfer units Nc = number of vapor transfer units Pe = Peclet number P, Q, R, S = constants defined by eq 7 R‘ = defined by eq 11 Rvd = vapor-distribution ratio V = vapor flow rate w = dimensionless distance from inlet weir, Z/ZL x = liquid mole fraction X = defined by eq 7 y = vapor mole fraction y(w) = vapor mole fraction at w Z = distance from inlet weir, m ZL = liquid flow-path length A(w) = liquid gradient at w A G = G(l) - G(0) y = mV/L pv = vapor density Subscripts AIChE = evaluated as per AIChE Bubble-Tray Manual n = tray n n - 1 = tray n - 1
It may be emphasized that the above inferences rest on the validity of the correlations used in the presence of vapor maldistribution. Care was excercised to check if the flow conditions are within the ranges of the correlations recommended in the Bubblenay Manual. When the flow conditions are too close to the dumping point, over a small fraction of ZLthe conditions were beyond the ranges of the correlations used. However, it is expected that this will not influence the results significantly. The likely effect of entrainment under these conditions has been explored in a companion paper. Conclusions A method of estimation of tray efficiency in the presence of vapor maldistribution is presented. It is shown that vapor maldistribution has a detrimental effect even in the case of perfectly mixed and plug models. However, tray efficiency is found to increase with the liquid flow-path length well up to the point of dumping as a result of increase in point efficiencies. A rational design of tray layout of large diameter columns should also consider the effect of vapor maldistribution on tray efficiency. Nomenclature A , B, C = constants in eq 2 b = constant by the equation y* = mx + b E- = Murphree tray efficiency E ~ ( w=)point efficiency at w Em = average point efficiency F(w) = G(w)p,’/Z G = average vapor flux, mol m-2 h-’ G(w) = vapor flux at w ,mol m-2 h-’ G(0) = vapor flux at the inlet weir, mol mb2h-’ h, = weir height, cm L = liquid flow rate, mol h-’ L(w) = liquid flow rate per unit width, mol m-l h-l m = slope of the equilibrium curve
Effect of Vapor
Ma
Literature Cited Bobs, W. L. In Smith, B. D. “Design of Equilibrium Stage Processes”; McQraw-HIII: New York, 1963; Chapter 14. “Bubble-Tray Design Manual”; American Institute of Chemical Engineers: New York, 1956. Furzer. I. A. A I C M J . 1989, 15, 235. Holland, C. D. “Fundamentals end Modeling of Separation Processes”; Prentice-Hall Inc: Englewood Cliffs, NJ, 1975; pp 356. Holm, R. A. A I C M J . 1981, 7 , 346. Lockett. M. J.; Dhulesla, H. A. Chem. Eng. J . 1980, 19, 183. Lockett, M. J.; Satekwrdi, A. Chem. Eng. J . 1978, 1 1 , 111. Rao, K. K. M. Tech. b s l s I.I.T., Kanpur, India, 1976. Van Winkle. M. ”Distillation”, m a w - H i l i Book Co: New York, 1967; p 553.
Received for review May 27, 1981 Revised manuscript received October 21, 1982 Accepted December 16, 1982
rtbution and Entrainment on Tray Efficiency
Tadlnad Mohan, Krovvldl K. Rao,t and D. Prahlada Rao’ D e p a m n t of Chemical Eng/nwIng, Indian Institute of Technology Kanpur, Kanpw 2080 16, India
The well-known Colburn model used for correcting tray efficiency for entrainment gives an underestimate in the case of dispersed and plug flow models of the iiquM phase. For these models, equations for tray efficiency have been obtained considering the variation of entrained liquid mole fractlon along the liquid flow path length. A parametric study of the composite effect of entralnment and vapor maldistributlon on tray efficiency has been presented. By chenging the length to width ratio of a rectangular tray of a fixed area, the dependence of tray efficiency on the liquid f k w path length has been studied. The results indicate that tray efflciency increases with the liquid flow path length well up to the point of liquid dumping.
In the design of large diameter trays the composite effect of entrainment and vapor maldistribution has to be considered. In a companion paper, we have reported studies of the effect of vapor maldistribution on tray efficiency. In this paper, the composite effect of entrainment and
vapor maldistribution has been studied. In general, the Colburn model is used for correcting tray efficiency for entrainment. In this model it is assumed that the mole fraction of the entrained liquid is the same as that of the liquid leaving the tray. This leads to an underestimation of the tray efficiency. The Lewis relation and the dispersed model equation for tray efficiency presented in the AIChE Bubble-Tray Manual (1958)have been extended to include the effect of entrainment. The effect of liquid flow path
?Departmentof Chemical Engineering,University of California, Davis, CA 95616. 0198-4305/83/1122-0380$01.50/0
0
1983 American Chemical Society
