820 Ind. Eng. Chem. Process Des. Dev. 1984, 23, 820-827

Prediction of Point Efficiencies on Sieve Trays. 2. Multicomponent Systems

Hong Chan and James R. Fair'

Department of Chemical Engineering, The University of Texas, Austin, Texas 78712

Multicomponent mass transfer theory has been used to develop working models for the predictton of component efficiencies in sieve tray distillation columns. The models have been valiited by special laboratory experiments, themselves related to equlvalent experiments at the commercial scale. Two model versions have been explored: a rigorous matrix model and a simplified psewbbhmry model. I t appears that for most cases of practical interest the latter model, applied to the dominating species in the mixture, gives reasonable results. This supports the approach often taken by engineers not having access to, or computing capability for, the more exact matrix approach.

Part 1 of this paper (Chan and Fair, 1984) deals with the prediction of point efficiencies of binary distillation systems. For a binary system, the efficiency of each com- ponent is the same and thus there is a single efficiency value for a given set of operating conditions. For a mul- ticomponent system, however, it is possible to have as many efficiency values as there are components of the mixture being processed. It has been common practice to assume that a binary efficiency, based on the key com- ponents, could be applied to all members of the multi- component mixture. Such an approach can surely be questioned because of unusual interaction phenomena such as osmotic diffusion, diffusion barriers, and reverse dif- fusion (Toor, 1957) that can occur in mass transfer pro- cesses. This part of the paper covers development and application of rigorous models for multicomponent point efficiencies. I t includes also an analysis of a situation in which the use of a simple pseudo-binary efficiency appears to be an adequate substitute for a rigorously derived array of multicomponent efficiencies. Previous Work

Toor (1964a) first developed the solution of the Iinear- ized equations of multicomponent mass transfer by matrix methods. He then applied the methods to the prediction of component efficiencies in multicomponent distillation (Toor, 1964b). However, no experimental data were taken to test the predictive model.

Diener and Gerster (1968) reported point efficiencies for the acetonemethanol-water system and proposed a binary method as well as a ternary method (which included mass transfer interactions) for the prediction of efficiencies in the ternary system. The correlation developed in their work for the number of vapor phase transfer units, N,, was valid only for the system studied (as pointed out by the authors). Medina, McDermott, and Ashton (1979) mod- ified the ternary method of Diener and Gerster to permit prediction of the efficiencies of the cyclohexaneln-hep- tane/toluene system. Experiments on the ternary system and the three pairs of binary systems were all carried out at the same vapor loading. For the test system, the three binary-pair vapor diffusion coefficients are almost the same, so interaction phenomena caused by widely differing sizes and nature could not be observed. Also, the method proposed has certain limitations as discussed by Krishna (1980).

Young and Weber (1972) studied point efficiencies for binary, ternary, and quaternary systems. In their pre- diction model liquid phase diffusional resistance was ne-

0196-4305/84/1123-0820$01.50/0

glected, and the .method used to compute the multicom- ponent effective diffusion coefficients was limited to the case of only one component diffusing through a mixture of stagnant gases (Wilke, 1950).

Krishna and Standart (1976a) developed a general ma- trix method of solution to the Maxwell-Stefan equations for multicomponent mass transfer. They later applied the method to predict the efficiencies of the system ethyl al- coholltert-butyl alcohol/water (Krishna et al., 1977). All of the experiments with the ternary system and the binary pairs were performed under similar hydrodynamic con- ditions, and the liquid diffusional resistance was neglected in the efficiency prediction.

Since multicomponent mass transfer models can be built from binary pair information, a reliable method for binary efficiency prediction is necessary. Such a method has been described in part 1 of this paper (Chan and Fair, 1984). Multicomponent Mass Transfer Theory

Krishna and Standart (1976a) developed a film model solution for solving the Maxwell-Stefan equations (Bird et al., 1960) for mass transfer in an n-component ideal gas mixture. The solution can be summarized as

Ni = J i + YiN, (i = 1, n) (1)

N T = CNi (2)

(4 = [kl(Ay) (3)

[m = [KI[El (4)

[K] = [B]-' (5)

(6)

(7)

(8)

*I i = Ni/kin + "/ki, (i = 1, n - 1) (9)

n

i= l

[El = [@I{exp[@l - [111-1 n

m = l m # i

Bii = yi/kin + c Ym/kim ( i = 1, n - 1)

B , . LJ = -yiaij ( i , j = 1, n-1; i # j )

n

m = l m # i

11 = -Niaij (i, j = 1, n - 1; i# j ) (10)

(i, j = 1, n - 1; i # j ) (11)

where brackets [ 3 represent a square matrix of dimensions n - 1 by n - 1, and parentheses 0, for example (J), rep-

aij = l / k i j - l / k i n

0 1984 American Chemical Society

Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 821

nents. I t is more common to define individual component efficiencies for each of the species of a multicomponent system in the form

(22)

Only n - 1 independent efficiencies can be defined since the mole fractions add to unity. Equations 22 can be rewritten in the matrix form as

b o u t - yin) = @ov~ (Y* - yin) (23) where (EoV] indicates a diagonal matrix. And from eq 15 and 23, the relation between the two efficiency definitions can be expressed as

fiov,i = (Yi,out - Yi,in) / (Yi* - Yi,in)

n

fi,,, = CEov,l,(Ay,/Ayl) (i = 1, n - 1) (24)

where Ayi is the constituent driving force for component

Experimental Work A five-tray, 1 in. i.d. Oldershaw glass column was used

in the experimental work. All tests were made at total reflux. After steady state was reached, liquid samples were taken at the total condenser and the downflow from the bottom tray. Samples were then analyzed by using gas chromatography to determine the compositions. Two highly nonideal ternary systems were tested methyl acetate-chloroform-benzene and methanol-methyl ace- tate-chloroform. The reasons for choosing these systems were the following. (1) Vapor-liquid equilibrium data were available (Bushmakin and Kish, 1957; Holmes and Van Winkle, 1970; Hudson and Van Winkle, 1969; Hudson, 1969; Hudson and Van Winkle, 1970; Nagata, 1962a; Na- gata, 1962b). Wilson equations (Wilson, 1964) were used to express VLE relations and they could be entered into the computer program. This is important since modeling multicomponent distillation requires tray-to-tray calcula- tions. (2) The two ternary systems are nonideal, and the effeds of mass transfer interactions could be studied. (3) The surface tensions for the individual components at their boiling points are all within 20 f 1.5 mN/m, so the surface tension effects on the mass transfer rates (Zuiderweg and Harmens, 1958) could be avoided.

Useful information about Oldershaw testing equipment can be found in many articles (e.g., Biribauer et al., 1957; Collins and Lantz, 1946, Oldershaw, 1941). Further details of the experimental setup, operating procedure, and data reduction are available (Chan, 1983). Scale-down Correlation

Since efficiencies were measured in a bench scale 01- dershaw column, therefore it was necessary to develop a corresponding scale-down model. The recent work by Fair et al. (1983) showed a consistent relationship between efficiencies of Oldershaw columns and efficiencies of com- mercial scale columns. Figures 1 and 2 show the efficiency comparisons for the cyclohexaneln-heptane system and the isobutane / n-butane system, where the data of Frac- tionation Research, Inc. (FRI) (Sakata and Yanagi, 1979) were the basis of commercial scale sieve tray distillation efficiency data. I t is important to note that in order to correlate the small and large column throughputs, the efficiencies were plotted against "approach to flooding", and all the test results showed that over the range of practical interest (50 to 85% of flood) the commercial point efficiency was always higher than the Oldershaw column efficiency.

In order to improve the equivalence of the efficiencies for the two scales of operation, the effect of weir height

J = 1

1.

resent a column matrix of dimension n - 1. Only n - 1 independent equations for the diffusive fluxes

J, can be written from eq 3, since we have from eq 1 and 2

n EJ, = 0 (12) 1=1

For eq 6,9, and 10, a prior knowledge of the molar fluxes Ni is required in the calculation of the correction factor matrix [E], and from that the finite flux mass transfer coefficient matrix [q. Thus, the determination of the diffusive fluxes J, and the molar fluxes Ni is not explicit, and iteration calculations are required. Also, an additional determinancy condition is needed to obtain the molar fluxes from eq 1 and 2. Such a determinancy condition is usually obtained by considering the energy balance (Krishna and Standart, 1976b) or by assuming special conditions such as equimolar counter transfer or mass transfer through a stagnant component, i.e., inert carrier (Krishna, 1977).

For mass transfer in the liquid phase, additional ther- modynamic factors must be considered because of system nonidealities. Generalized Maxwell-Stefan equations have been developed (Lightfoot et al., 1962; Slattery, 1972) to describe molecular diffusion phenomena in the case of nonideal n-component mixtures, and Krishna's matrix method can be used to solve the equations with some small modifications (Krishna, 1977). The suggested method to handle the system nonidealities was to estimate an activ- ity-corrected mass transfer coefficient matrix [Ka] based on generalized Maxwell-Stefan (or activity-corrected) diffusion coefficients D, instead of the Fick's law diffusion coefficients 33,. Then [K] was obtained simply by

[KI = [KaI[Gl (13) where [GI is a "thermodynamic factor matrix" defined as

G,, = 4, + (x,/x,)(~ In r l / d In xJ) (14)

Multicomponent Distillation Modeling Efficiencies for multicomponent distillation were ana-

lyzed by the matrix method (Krishna et al., 1977; Toor, 1964b), and summarized as

b o u t - yin) = [Eovl(Y* - in) (15) [ E O V I = [Cl - exPHNov1l (16)

(17)

[Nvl = (18)

where matrices [&I and [kL] can be calculated in the same manner as in eq 1 to 11. Matrix [m] is the matrix of equilibrium constants defined as

(20)

The matrices [@,I and IoL] are "bootstrap" solution matrices which allow calculation of the molar fluxes from the diffusive fluxes based on an additional determinancy condition. The elements of these matrices can be obtained from the determinancy condition such as taking the in- terphase energy balances (Krishna and Standart, 1976b). Or if equimolar counter transfer is assumed, then [@I matrices reduce to identity matrices and eq 17 becomes

[~; ' ,v]-~[@v]-~ = [fiv1-'[@vl-' +[m]GM/LM[2\j,l-'[@L1-'

W L 1 = [E i , l%tL (19)

m, = dy,*/dx, (i, j = 1, n - 1)

[NOv]-' = [fiv]-' + [ ~ ] G M / L M [ ~ ~ L ] - ' (21) It can be seen from eq 15 that the mass transfer effi-

ciency for component i is affected by the other compo-

822 Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984

e 'JA - A

Figure 1. Efficiency of Oldershaw column compared with point efficiency of FRI column (5.1-cm weir); cyclohexane/n-heptane at 21 to 28 kPa.

L ;- nL,c?s-kw L -

um JM

Figure 2. Efficiency of Oldershaw column compared with point efficiency of FRI column (5.1-cm weir); isobutaneln-butane at 1138 kPa.

7 ,! I

"0.0 C.2 0.4 0.G 1.9 y . 3 'bF

f -

Figure 3. Efficiency of Oldershaw column compared with projected point efficiency of FRI column (2.5-cm weir); cyclohexaneln-heptane at 21 to 28 kPa.

on the commercial scale data was studied. For the same vapor and liquid flow conditions, and on the basis of the model given in part 1

N, 0: hL0.5 (25)

NL hL (26) Since hL decreases as h, (weir height) is decreased, it

follows that a downward adjustment in weir height, had it been made during the FRI tests, would have given a lower efficiency.

The FRI data were obtained from a column with a 5-cm outlet weir. Equations 25 and 26, with the liquid holdup calculated by the method of Bennett et al. (1983), can be used to project the efficiency profiles for weir heights other than those used experimentally. The projected efficiency profiles can then be compared with Oldershaw efficiencies to obtain a better fit. Results for the 2.5-cm outlet weir are shown in Figures 3 and 4 for cyclohexane/n-heptane and isobutaneln-butane, respectively. The lack of fit of the cyclohexane/n-heptane system could be explained by differences in the operating pressure levels and effects of surface tension on mass transfer rates (Zuiderweg and Harmens, 1958) in a small column such as the Oldershaw. (Cyclohexaneln-heptane is a surface tension negative system.)

I I 2LDERShAW

A F R I . 2 . 5 CU. W E I R r P I I O . E C T E D >

I

T L "0.0 0.2 0 . 4 0.6 0.8 1 . 0

f = u, 1 u,,

Figure 4. Efficiency of Oldershaw column compared with projected point efficiency of FRI column (2.5-cm weir); isobutaneln-butane at 1138 kPa.

~ -

1 - r - P r - ' W j

L J

Figure 6. Scale-up correlation (see Figure 5 for identification of symbols).

To examine further the scale-down correlation, five binary systems were tested in the Oldershaw equipment. Care was taken to select the systems so that surface tension effects were avoided. Figure 5 shows the plots of point efficiencies vs. fractional flooding for the five systems. The scale-down correlation could be examined by predicting the efficiencies of the five binary systems for the FRI column with a 2.5-cm outlet weir and comparing the pre- dicted efficiency profiles with the experimental Oldershaw results. Or, as another alternative, one can assume that the FRI column with a 2.5-cm weir has the same efficiency plot as Figure 5 and then back-calculate the mass transfer coefficients and compare them with the general mass transfer correlation (part 1) to verify the assumption.

The second approach was adopted since the mass transfer coefficient ( k p J is much more sensitive than the point efficiency E,. Fair's correlation (Fair and Matthews, 1958; Fair, 1961; Smith, 1963) was used to estimate the flooding capacity for the FRI column in order that the operating velocities for the data points could be deter- mined. The results are given in Figure 6 which shows that the fit of data with the general mass transfer correlation is quite good.

Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 823

Table I. Experimental Data for Ternary System T1 [Methyl Acetate (l)/Chloroform (2)/Benzene (3)]; Total Reflux; Oldershaw

run no. T1-2A T1-2B T1-2C T1-2D T1-3A T1-3B T1-3C T1-3D Tl-3E

top tray Y1 0.7986 0.7657 0.7412 0.7289 0.7381 0.6979 0.6622 0.6366 0.6191 top tray Yz 0.1083 0.1304 0.1483 0.1605 0.1312 0.1557 0.1800 0.1983 0.2147

bottom tray x1 0.3685 0.3488 0.3310 0.3019 0.2616 0.2469 0.2299 0.2157 0.2031 bottom tray x 2 0.3129 0.3216 0.3296 0.3408 0.2906 0.2953 0.3011 0.3057 0.3096 bottom tray T, K 339.2 339.6 339.8 340.4 341.5 341.7 342.1 342.3 342.6 boilup rate, mL/s 0.5747 0.7205 0.8130 0.9709 0.5435 0.6281 0.7375 0.8591 0.9804 Pvt kg/m3 3.14 3.16 3.19 3.21 3.16 3.17 3.19 3.21 3.24 PL9 k / m 3 979 983 992 996 971 979 983 988 992 un, m/s 0.328 0.404 0.465 0.554 0.306 0.354 0.416 0.484 0.551 f = un/ud 0.493 0.619 0.698 0.832 0.463 0.535 0.628 0.731 0.833

top tray T, K 332.5 333.0 333.3 333.5 333.5 334.1 334.6 335.0 335.3

Table 11. ExDerimental Data for Ternary System T2 [Methanol (l)/Methyl Acetate (%)/Chloroform (3)]; Total Reflux; . .

Oldershaw T2-1A T2-1B T2-IC T2-1D T2-2A T2-2B T2-2C T2-2D T2-2E

top tray YI 0.4126 0.4179 0.4252 0.4305 0.4570 0.4668 0.4762 0.4837 0.4900 top tray YZ 0.5344 0.5185 0.4998 0.4867 0.4579 0.4423 0.4233 0.4062 0.3928 top tray T, K 327.3 327.4 327.6 327.7 327.7 327.8 327.9 328.0 328.1 bottom tray xl 0.4942 0.4966 0.5013 0.5022 0.7310 0.4719 0.7460 0.7591 0.7653 bottom tray x2 0.3524 0.3462 0.3382 0.3334 0.1753 0.1649 0.1594 0.1477 0.1417 bottom trav. T. K 328.6 328.7 328.7 328.8 boilup rate; m i l s 0.3636 0.4545 0.5556 0.6631 P”9 k / m 3 2.28 2.28 2.28 2.29 PL9 k / m 3 919 923 927 931 un, m/s 0.280 0.351 0.430 0.513 f = un/ud 0.369 0.462 0.566 0.676

From the above evidence, it can be concluded that the FRI column with a 2.5-cm outlet weir has the same point efficiency as the Oldershaw column. With this as a basis, the mass transfer model of part 1 can be used to simulate the Oldershaw point efficiency. Multicomponent Rigorous Modeling,

The number of transfer units matrix [N,] (or [&I) can be related to the binary pair Nv,ij (or NL,J in the same manner as in eq 1 to 11, with “diffusive moles transfered per unit volume of froth” replacing “diffusive flux J“, “total moles transfered per unit volume of froth” replacing “molar flux N”, and “number of transfer units” replacing “mass transfer coefficient k”. The mass transfer model given in part 1 can be used to estimate the binary pair Nv,ij and

$0 estimate the transfer units in the liquid phase, the approach suggested by Krishna (eq 13 and 14) was not adopted. This was mainly because the liquid diffusion coefficient in the correlation of Foss and Gerster (1956) is the Fick’s law diffusion coefficient, and it would not be justified to say that the activity-corrected diffusion coef- ficient could be used when applying the correlation. Thus, the Fick’s law diffusion coefficient was evaluated and used to obtain the transfer units of the liquid phase.

Burchard and Toor (1962) suggested that in ternary systems the binary pair could be evaluated at com- positions of x i / ( x i + x j ) and x j / ( x i + x . ) , where x i and x j are the mole fractions of species i and j in the mixture. The system studied by Burchard and Toor was a rather ideal one, but the method at least provided an estimation even for nonideal systems. Use of this method to estimate the binary pair D , i j in nonideal systems could not be verified at this point. However, since the mass transfer resistance in the liquid phase is normally much lower than that in the vapor phase for distillation, the error caused by estimation of D , , is not likely to be serious.

Three design equations were tested based on several assumptions or simplifications: (I) Assume equimolar counter transfer and neglect the effect of finite flux mass transfer rates on the mass transfer coefficients. (11) As-

NL i’.

330.1 330.2 330.3 330.5 330.6 0.2976 0.3463 0.4119 0.4789 0.5405 2.00 2.00 2.00 1.99 1.99 895 896 899 901 902 0.272 0.319 0.381 0.447 0.508 0.340 0.399 0.476 0.559 0.635

sume equimolar counter transfer and use the finite flux mass transfer correction factor matrix [E] for this special case (Krishna, 1977). (111) Consider the interphase energy balance, and obtain the [/3] and [E] matrices accordingly (Krishna and Standart, 1976b).

The modeling takes the following steps: (1) Start with the compositions of liquid on the bottom tray. (2) Use the binary mass transfer models, the scale-down correlation and the multicomponept equations to calculate the effi- ciency matrix [E,,] or (E,,,). (3) Calculate the composition of the vapor leaving the tray from eq 15 or 23. Because of total reflux and steady state operation, this composition is the same as the liquid composition on the tray above. (4) Repeat steps 2 and 3 until the top tray is reached.

No significant difference was found in the results from the three design equations. This indicated that, at least for the systems studied, the assumption of equimolar counter transfer is valid for distillation, and also the effect of finite transfer rates can be neglected. Pseudo-Binary Model

To handle multicomponent distillation in an approxi- mate fashion, two components were chosen to represent the entire system. Efficiency was calculated based on the vapor and liquid diffusion coefficients of the chosen pair and then used for all components. The choice of the binary pair could either be the two dominating species in the mixture a t the point of consideration or the key compo- nents of the separation. The binary pairs chosen were methyl acetate-chloroform for system T1, and metha- nol-methyl acetate for system T2. Results and Discussion

Experimental results for the two ternary systems are given in Tables I and 11. Runs T1-3D and T2-2E were selected to show typical modeling results as given in Tables I11 and IV. (A complete listing of the results is available (Chan, 1983)). The y values represent the coqposition of the vapor leaving a particular tray n, and the E,,‘s are the component efficiencies from the rigorous model on the tray. The term EovP represents the single efficiency pre-

024 Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984

57r- Table 111. Multicomponent Modeling for System T1" [Methyl Acetate (l)/Chloroform (Z)/Benzene(3)]

Experimental Liquid Compositions (Mole Fraction)

liauid on trav 1 liauid from condenser (1) 0.2157 0.6366

0.3057 0.1983 (3) 0.4786 0.1651

Multicomponent Modeling rigorous model pseudo-binary model

(1) (2) (3) (1) (2) (3) Tray 5

0.1775 y 0.6256 E,P

Tray 4 0.2192 y 0.6309 E ,

Tray 3 0.2695 y 0.6343 Eov*

Tray 2 0.3295 y 0.6359 EovP

Tray 1 0.3996 y 0.6359 EovP

r, 0.5783 E,, 0.6505

0.2442 0.6829

0.5937 0.2420 0.6778 0.6778

0.1644 0.6778 'VAPOR C O N C E Y T R A T I O N

0 - METHYLACETATE - R I G C R O U S MOOEL A P - CHLOROFORM _ _ _ P S E U D O - B l h A R Y MODE x 3 - B E N Z E N E

Figure 7. Predicted vapor composition profiles for methyl ace- tate/chloroform/benzene; run T1-3D.

r, 0.5016 E , 0.6482

0.2792 0.6847

0.5146 0.2783 0.6754 0.6754

0.2071 0.6754

y, 0.4255 E,, 0.6456

0.3050 0.6992

0.4358 0.3053 0.6740 0.6740

0.2589 0.6740 --Ti- 7

r, 0.3517 E, 0.6424

0.3188 -0.4391

0.3589 0.3199 0.6737 0.6737

0.3213 0.6737

r, 0.2813 E,, 0.6384

"Run T1-3D.

0.3191 0.6241

0.2849 0.3202 0.6742 0.6742

0.3949 0.6742

Table IV. Multicomponent Modeling for System T2" [Methanol (l)/Methyl Acetate (t)/Chloroform(3)]

Experimental Liquid Compositions (Mole Fraction)

liauid on trav 1 liauid from condenser

1' ', 0

d . 0 012 0.4 0.G c1. YAPOR C O N C E N T R A T I O N , V

- R I a O R O L S MODEL 0 1 HETHANGL A 2 M I T H I L A C E - A 7 E _._ PSEUOO 3 l h A - V YO-EL n 3 - H L ~ Q O F F . R M

Figure 8. Predicted vapor composition profiles for methanol/ methyl acetate/chloroform; run T2-2E.

predicted by the pseudo-binary approach. The solid symbols on tray 5 show the experimental composition of the liquid from condenser.

Both models predicted the experimental data quite well for all the runs. The pseudo-binary approach did a slightly better job for some cases. It is important to note that in some runs the efficiencies predicted from the rigorous model did show the interaction phenomena (point effi- ciency not bounded between 0 an+ 1); for example, in run T2-2E, efficiency for chloroform (Eov,3) on tray 4 was -9.9. The predicted profiles for chloroform in run T2-2E from the two different models started deviation from tray 1, and there was no drastic change on tray 4 as would be expected since the two predicted efficiencies had different signs (0.675 from pseudo-binary, -9.9 from rigorous model). The s p e situation could be found in run T1-3D (tray 2), where Eov,2 (chloroform) was -0.439 and E o v P was 0.674; but the two predicted composition profiles for chloroform almost coincided.

-@ov,l = E o v , l l + EOV,lZ/R

Eov,2 = Eov,22 + EOV,Zl(R)

-@ov,3 = (R-@ov,i + -@Ov,z)/(R + 1) R= (Yl* - YI, ,d / (Y2* - Y2,m)

For a ternary system, eq 24 can be simplified as (27) (28) (29)

(30) Multicomponent interaction phenomena can occur un-

= AY 1 / AY 2

der the following cases.

(1) 0.7653 0.4900 (2) 0.1417 0.3928 (3) 0.0930 0.1172

Multicomponent Modeling rigorous model pseudo-binary model

(1) (2) (3) (1) (2) (3) Tray 5

y 0.4616 0.3709 0.1675 y 0.4610 0.3968 0.1422 E,, 0.6869 0.6519 0.5313 EovP 0.6794 0.6794 0.6794

Tray 4 r, 0.4860 0.3410 0.1730 y 0.4887 0.3611 0.1502

Tray 3 r, 0.5233 0.3055 0.1712 y 0.5294 0.3192 0.1515 E , 0.6860 0.6476 0.8687 E,P 0.6662 0.6662 0.6662

Tray 2 r, 0.5805 0.2608 0.1586 y 0.5890 0.2681 0.1429 E, 0.6848 0.6356 0.8174 E,P 0.6524 0.6524 0.6524

Tray 1 r, 0.6634 0.2047 0.1319 y 0.6702 0.2071 0.1227 E,, 0.6761 0.6081 0.8259 Eo,P 0.6310 0.6310 0.6310

"Run T2-2E.

Eov 0.6864 0.6519 -9.880 EovP 0.6745 0.6745 0.6745

dicted from the pseudo-binary model. Because of total reflux operation, the liquid from the total condenser should have the same composition as the vapor leaving the top tray (tray 5). Comparing the predicted composition of vapor leaving tray 5 with the measured composition of liquid from the condenser would indicate the accuracy of the model. Predicted composition profiles are plotted in Figures 7 and 8; the solid lines show the prediction from the rigorous model while the dashed lines are the profiles

Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 825

Table V. Six-Component Deethanizer Case Study [Predicted Composition of Vapor Leaving a Plate (Mole Fraction)]

plate 1 (bottom) rigorous model pseudo- binary

(2-3 pair) pseudo- binary

(3-4 pair) plate 2 rigorous model

pseudo- binary (2-3 pair)

pseudo- binary (3-4 pair)

plate 7 rigorous model pseudo- binary

(2-3 pair) plate 13 rigorous model

pseudo- binary (2-3 pair)

plate 14 (top) rigorous model pseudo- binary

(2-3 pair) pseudo-binary

(1-2 pair)

5.865(10-6) 0.1998 6.851(10-6) 0.2019

6.668(10-6) 0.1991

1.924(10-') 0.2871 2.225(104) 0.2889

2.154(10-4) 0.2856

5.107(10-2) 0.5773 5.741(10-2) 0.5786

6.143(10-2) 0.8450 6.425(10-2) 0.8448

0.1295 0.8299 0.1201 0.8341

0.1248 0.8324

"Components: (1) methane; (2) ethane; (3) propylene; (4) propane:

Case 1. R - 0, i.e., Ay, - 0; then bounded (eq 27).

Case 2. R - f -, i.e., Ay2 - 0; then bounded (eq 28).

Case 3. R - -1, Le., Ay3 - 0 (Ay, + Ay2 - 0); then can be unbounded (eq 29).

By examining the modeling r-sults, one can find: for run T1-3D, on tray 2 (case 2), = -0.439, R = $56.6, Ay, = 0.0007. For run T2-2E, on tray 4 (case 3), E0v,3 =

From eq 24 and the above evidence, it is clear that multicomponent interactions are important for species when the constituent driving forces for those species are very small compared to the other constituent driving forces. The interaction cases reported by ,Krishna et al. (1977) for distillation of ethyl alcohol/tert-butyl alcohol- /water also confirmed this fact.

From the definition of individual component efficiency, the mole fraction of component i in the exit vapor is

Yi,out = Yi,in + gov,iAyi (31)

Consider the case of Ayi - 0, and the rigorous model predicts a negative efficiency for component i; the pseu- do-binary approach predicts a single efficiency (which is well bounded between 0 and 1) for all the components. The difference in predicted yi,out from the two models is negligible because the driving force Ayi is small. In other words, the net effect of mass transfer of component i is not significant.

The problem of not being able to predict the multicom- ponent interactions by the pseudo-binary model is not severe. The important question is how to choose the bi- nary pair components to represent the whole system or how to determine a single effective diffusion coefficient to use in the calculation of mass transfer efficiency. Burchard and Toor (1962) had some success using a single diffusion coefficient in the ternary system they studied. However, more studies are necessary for such a method to be validated.

Six-Component Simulation Case Study A six-component deethanizer distillation simulation was

presented by Bolles and Fair (19821, where ideal stages

can be un-

can be un-

-9.880, R = -0.998, Ay3 = -0.0001.

0.2847 0.3406 0.2858 0.3419

0.2854 0.3422

0.2713 0.3102 0.2723 0.3114

0.2729 0.3126

0.1409 0.1557 0.1415 0.1564

7.947(10-2) 8.025(10-2)

8.138(10-2)

6.060(10-2) 6.1 11 (

6.180(

3.110( 3.126(10-2)

2.019(104) 2.573( lo4)

4.942( 6.785(10")

5.823(10-5)

9.537( lo-') 9.009 (1 0-2)

9.183(10-2)

7.061(10-2) 6.601(10-2)

6.685 ( 1 0-2)

4.393( 3.488(10-2)

8.978(10-3) 7.567(

1.060( 1.589(10-5)

1.322(10-6)

(5) isobutane; (6) n-butane.

were assumed in the tray-to-tray calculations. The ma- terial balance, temperature and pressure profiles, and vapor-liquid equilibria were given. The multicomponent rigorous model and the pseudo-binary model were applied for efficiency predictions. To calculate the number of transfer units, some typical values of vapor and liquid holdup and approach to flood were taken from the FRI data for isobutaneln-butane at 2758 kPa, to generate binary efficiencies. This was reasonable, since the oper- ating pressure in the simulation study was also 2758 kPa. The resulting transfer units were

N, = 75 aV1l2 (32)

NL = 344a)L1I2 (33) The key components in the mixture were ethane (com-

ponent 2) and propylene (component 3), and they were used in the pseudo-binary model to represent the system. However, at the bottom section of the column propylene and propane (components 3 and 4) became the dominating species, and at the very top of the column methane and ethane (1 and 2) were the major components. To examine the effects of these components, they were also chosen as the binary pair in the pseudo-binary model a t locations where they were indeed the dominating species. The re- sults are given in Table v. It can be seen that the de- viation between the rigorous model and the pseudo-binary approach was not significant. Also, the results from the pseudo-binary approach (by choosing 3-4 pair a t bottom section of the column and 1-2 pair a t the very top of the column) were even closer to the rigorous prediction. Summary and Conclusions

The scale-down relationship between a commercial size distillation column and a bench-type Oldershaw column has been studied. Surface tension effects play an impor- tant role in the mass transfer in a small column such as the Oldershaw, while such effects are not as important in commercial scale columns. For surface tension neutral systems, the Oldershaw column was found to have the same separation efficiency as the large FRI test column with a 2.5-cm outlet weir. The scale-down correlation can be used for large scale design directly from Oldershaw data (Fair et al., 1983) and is especially useful for complex

826

mixtures or when VLE data are not well-defined. How- ever, surface tension effects must be considered during the scale-up procedure.

For predicting multicomponent distillation efficiencies, two models have been used: a general matrix model and a simplified approach which considers the whole system as a pseudo-binary. The rigorous model required certain lengthy and complex iteration calculations, while the pseudo-binary approach was straightforward and easy to implement. Two nonideal ternary systems were tested through the use of Oldershaw equipment, and both models predicted the experimental data quite well.

Departures of multicomponent efficiencies from those obtained on the pseudo-binary basis were evaluated. It was concluded that for most separations the pseudo-binary approach is satisfactory and gives results within the limits of accuracy imposed by the general mass transfer model (Chan and Fair, 1984). This conclusion holds especially if the key components dominate the feed mixture to the column.

Future Work A considerable amount of research in the area of mul-

ticomponent mass transfer is currently being carried out (e.g., Weiland and Taylor, 1982). Besides the Toor and the Krishna models, two new methods have recently been proposed to predict mass transfer phenomena in multi- component mixtures (Krishna, 1981; Taylor and Smith, 1982). The main advantage of the new methods is that they are both explicit in the fluxes and do not require iterative calculations. Because they are considerably easier to be incorporated with design procedures, it is possible that the new methods can provide means to deal with multicomponent mass transfer without excessive compli- cations. A statistical comparison between several proposed methods was recently reported (Smith and Taylor, 1983), this should give some guidelines for future applications of these methods.

For rigorous multicomponent efficiency prediction, a stepwise procedure, coupled with a well-documented com- puter program on file, would aid in the complex calcula- tions required. This is especially true for systems with a large number of components.

On the basis of this work, the pseudo-binary efficiency approach appears to be useful for most multicomponent separations. However, such a conclusion is based on a limited amount of evidence. A more exhaustive compar- ison between pseudo-binary efficiencies and rigorously calculated efficiencies would be welcome. Nomenclature ai = interfacial area for mass transfer, m2/m3 [B] = matrix with elements defined by eq 7 and 8, [kg-mol/(s

Dij = activity-corrected binary diffusion coefficient of i-j pair,

Dij = binary diffusion coefficient of i-j pair, cm2/s DL,ij = diffusion coefficient of i-j pair in multicomponent

D, = diffusion coefficient, vapor, cm2/s [E] = matrix of correction factor, defined by eq 6 E,, = point efficiency, vapor concentration basis, fractional [E,,] = point efficiency matrix, defined by eq 16 E,+. = element of matrix [E,] {E,.,( = individual point efficiency matrix, defined by eq 22

= individual point efficiency of component i, fractional E o v P = pseudo-binary point efficiency in multicomponent

f = fractional approach to flooding [GI = thermodynamic factor matrix, defined by eq 14 GM = molar velocity of vapor, kg mol/(s m2)

Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984

m2)]-’

cm2/s

system, liquid, cm2/s

system, fractional

hL = liquid holdup on tray, cm h, = weir height, cm [a = identity matrix (J) = diffusive flux matrix, kg mol/(s m2) Ji = diffusive flux of component i , kg-mol/(s m2) ki j = mass transfer coefficient of i-j pair in multicomponent

system, kg-mol/ (s m2) k , = mass transfer coefficient of binary system, vapor, m/s [K,] = matrix of activity-corrected multicomponent mass

transfer coefficients, kg mol/ (s m2) [ItL] = matrix of finite flux multicomponent mass transfer

coefficients, liquid, m/s [R,] = matrix of finite flux multicomponent mass transfer

coefficients, vapor, m/s LM = molar velocity of liquid, kg mol/(s m2) [m] = matrix of equilibrium constants, defined by eq 20 n = number of components Ni = molar flux of component i , kg mol/(s m2) [NL] = finite flux number of transfer units matrix, liquid NL,i. = number of transfer units of the i-j pair in a multim-

[fiOv] = finite flux overall number of transfer units matrix NT = total molar flux, kg mol/(s m2) N y = number of transfer units, vapor [N,] = finite flux number of transfer units matrix, vapor Nv,ij = number of transfer units of the i-j pair in a multi-

R = ratio of vapor driving forces defined by eq 30 tL = average liquid residence time, s t , = average vapor residence time, s U, = vapor velocity through active area of tray, m/s Uaf = vapor velocity through active area of tray at flood, m/s x i = mole fraction of component i, liquid y i = mole fraction of component i, vapor yi* = equilibrium vapor mole fraction of component i yi,in = mole fraction of component i in the entering vapor yi,out = mole fraction of component i in the exiting vapor Greek Letters aij = coefficient defined by eq 11 [PL] = “bootstrap” solution matrix, liquid [P,] = “bootstrap” solution matrix, vapor yi = activity coefficient of component i 6ij = Kronecker delta Matrix Notation ( ) = column matrix with n - 1 elements [ ] = matrix of dimension n - 1 by n - 1 { ] = diagonal matrix of dimension n - 1 by n - 1

Literature Cited Bennett, D. L.; Agrawal, R.; Cook, P. J. AIChE J. 1083, 29, 434. Blrd, R. B.; Stewart, W. E.; Lightfoot, E. N. “Transport Phenomena”; Why:

New York, 1960. Biribauer, F. A,; Oakley, H. T.; Porter, C. E.; Staib, J. H.; Stewart, J. Ind.

Eng. Chem. 1057, 49(10) 1673. Boiles, W. L.; Fair, J. R. I n “Encyclopedia of Chemical Processing and

Design”, J. J. McKetta, Ed.; Marcel Dekker: New York, 1982; p 42 ff. Burchard, J. K.: Toor, H. L. J. phvs. Chem. 1082, 66, 2015. Bushmakin, I. N.; Klsh, I. N. Zh. Prikl. Khim. 1957, (30), 200. Chan, H.; Fair, J. R. Ind. Eng. Chem. Process Des. Dev. 1984, preceding

Chan, H. Ph.D. Dlssertation, The University of Texas at Austin. May 1983. Collins, F. C.; Lantz. V. Anal. Chem. 1046, f6, 673. Diener, D. A,; Gerster, J. A. Ind. Eng. Chem. Process Des. Dev. 1988, 7,

Fair, J. R., Matthews, R. L. Pet. Refiner 1058, 37(4) 153. Fair, J. R. PetroIChem. Eng. 1081, 33(10) 211. Fair, J. R.; Null, H. R.; Bolles, W. L. Ind. Eng. Chem. Process Des. Dev.

Foss, A. S.; Gerster, J. A. Chem. Eng. frog. 1056. 52, 284. Holmes, M. J.; Van Winkle, M. Ind. Eng. Chem. 1070, 62, 21. Hudson, J. W.; Van Winkle, M. J. Chem. Eng. Data 1080, 74, 310. Hudson, J. W. Ph.D. Dissertation, University of Texas at Austin, 1969. Hudson, J. W.; Van Winkle, M. Ind. Eng. Chem. Process Des. Dev. 1070.

Krishna, R.; Standart, G. L. AIChE J . 1976a, 22, 383. Krishna, R.; Standart, G. L. Lett. Heat Mass Transfer I976b. 3, 173. Krishna, R.; Martinez, H. F.; Sreedhar, R.; Standart, G. L. Trans. Inst. Chem.

Krishna, R. Chem. Eng. Sci. 1077, 32, 659. Krishna, R. Chem. Eng. Sci. 1080, 35, 2371. Lightfoot, E. N.; Cussler, E. L.; Rettig, R. L. AIChE J . 1982, 6, 708.

ukicomponent system, liquid

component system, vapor

article in this issue.

339.

1083, 22, 53.

9 , 466.

Eng. 1077. 55, 178.

Ind. Eng. Chem. Process Des. Dev. 7004, 23, 827-833 027

Medina, A. G.; Mccermott, C.; Ashton. N. Chem. Eng. Sci. 1979, 34, 861. Nagata, I. J . Chem. Eng. Data 1982~1, 7 , 360. Nagata. I. J . Chem. Eng. Data 1982b, 7 , 367. Oldershaw. C. F. Ind. €ng. Chem. 1941, 13, 265. Sakata, M.; Yanagi. T. I . Chem. E. Symp. Ser. No. 56, 1979. 3.2121. Slattery, J. C. “Momentum, Energy and Mass Transfer in Continua”; McOraw-

Smith, E. D. “Design of Equilibrium Stage Processes”: McGraw-Hill: New

Smith. L. W.; Taylor, R. Ind. Eng. Chem. Fundam. 1983, 22, 97. Taylor, R.; Smith, L. W. Chem. Eng. Commun. 1982, 14, 361. Toor, H. L. AIChE J . 1957, 3 , 198.

Hili: New York, 1972.

York, 1963; Chapter 15 by Fair, J. R.

Toor, H. L. AIChE J . 1984~1, 10, 448, 460. Toor, H. L. AIChE J . 1984b, IO, 545. Weiiand, R. H.; Taylor, R. Chem. Eng. Educ. 1982, 16(4) 158. Wilke, C. R. Chem. €ng. Prog. 1950, 46(2) 95. Wilson, G. M. J . Am. Chem. Soc. 1984, 86, 127. Young, G. C.; Weber, J. H. Ind. Eng. Chem. Rocess Des. Dev. 1972, 1 1 ,

Zuiderweg, F. J.; Harmens, A. Chem. Eng. Sci. 1958, 9 , 89. 440.

Received for review June 2, 1983 Accepted November 28, 1983

Slmulation of Catalytic Reactions in Shale Oil Refining

Tek Sutlkno’

Midwest Research Institute, Kansas City, Missouri 64 110

Stanely M. Walas

Department of Chemical and Petroleum Engineering, University of Kansas, Lawrence, Kansas 66044

Process yield data from advanced catalytic reaction of Paraho shale oil have been simulated. The properties and the required refining severity of shale 011 are different from those of petroleum crudes. The simulation was made to evaluate if mathematical models developed for hydrotreating, hydrocracking, and fluid catalytic cracking of petroleum-based oils can be applied for simulation of these reaction processes used for shale oils. Preliminary results indicate that refining of shale oil by these processes can be adequately simulated by the models derived for petroleum-based oils. However, further process data at several reaction conditions of a variety of shale oils are needed to confirm the applicabilities of these models.

Introduction The use of shale oil as an alternate feedstocks for the

production of transportation fuels has been the subject of several investigations (Frost and Cottingham, 1974; Lovell et al., 1981; Sullivan et al., 1978). It is generally concluded that surface-retorted shale oil such as Paraho shale oil can be refined to various specification-grade transportation fuels-diesel fuel, gasoline, and jet fuel. The properties of shale oil are, however, significantly different from pe- troleum crudes, and the refining of shale oil is more com- plex and severe than that of petroleum. Advanced cata- lytic reaction processes are required to convert shale oil to transportation fuels.

Most of the published models for simulations of ad- vanced catalytic reaction processes in oil refining are de- veloped from and verified with experimental data on pe- troleum-based feedstocks. These models can be used for the development of designs, operations, and refining strategy development. Because of the specific properties of shale oil and the refining severity required, this paper evaluates the applicabilities of the readily developed models for simulation of catalytic reaction processes in shale oil refining. This applicability evaluation is necessary if any of the petroleum refining reaction models is to be used for designs, yield predictions, or optimization of the respective reaction process in shale oil refining.

Process models for catalytic reactions in oil refining are generally complex and involve several parameters. The values of these parameters must be known if the model is used for simulation or yield prediction purposes. Al-

though several research investigations of shale oil refining have been conducted, these investigations are feasibility studies in nature, and experimental yield data from cat- alytic reaction processes of shale oil refining are very lim- ited. A literature survey indicated that the pilot plant refining data reported by Sullivan et al. (1978) are the most comprehensive at present; three pilot refining schemes shown in Figures 1 to 3 were used in this pilot plant study of shale oil refining. In light of their comprehensiveness, those pilot plant data are used as the bases for present simulation study.

As shown in Figures 1 to 3, the major catalytic reaction processes in shale oil refining are hydrotreating, hydro- cracking, fluid catalytic cracking, and reforming. Only hydrotreating, hydrocracking, and fluid catalytic cracking data are simulated in this study; the reforming process is not included because shale oil-derived naphtha is report- edly identical with petroleum-based naphtha (Lovell et al., 1981; Sullivan et al., 1978). Hydrotreating, hydrocracking, and fluid catalytic cracking processes in shale oil refining perform different functions, and simulation of each of these processes requires specific mathematical framework. The mathematical models for simulations of these processes have been selected from the literature; these models and the results of simulations are described next in the order of hydrotreating, hydrocracking, and fluid catalytic cracking. A. Hydrotreating

In refining shale oil to transportation fuels, the main purpose of hydrotreating is removal of nitrogen; therefore,

0196-4305/84/1123-0827$01.50/0 0 1984 American Chemical Society