Design of Sideatream Dlstlllation Columns

columns are emmined for a ternary mixture. more than four-component Ideal mixtures. Introduction. A sidestream distillation column can be used to sepa...
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Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 822-828

Design of Sideatream Dlstlllation Columns Konetanilnoa N. Gllnos and Mlchael F. Malone' Department of Chemical Engineering, Unhws& of Massachusetts, Amherst, Massachusetts 0 1003

A shortcut procedwe to design sidestream dlstlllatiOn columns Is presented. Shnpie expressions are obtained for the number of trays, the minlmum vapor rate, and for the bounds imposed by thermodynamics on the sldestream composition. Degrees of freedom and feaslMe design spdfkations are also discussed. Three types of sidestream columns are emmined for a ternary mixture. Wealso suggest a procedure for quaternarlesand extensions to more than four-component Ideal mixtures.

Introduction A sidestream distillation column can be used to separate any nonazeotropic multicomponent mixture into three products. Therefore, it can often substitute for a sequence of two columns. However, the purity of the sidestream product is restricted by thermodynamics and by the nature of the distillation process. Hence, these columns are appropriate either as prefractionators (the sidestream is fed to another column for further separation) or to generate recycle streams when there is no strict requirement of the recycle composition. They are also broadly used in the petroleum industry, where blends are produced rather than pure products. We examine three types of columns, depending on whether the sidestream is below or above the feed tray and on whether it is taken off as a vapor or as a liquid. Obviously, the liquid above and the vapor below the feed are the richest in the middle component, but there is also incentive for taking a liquid sidestream below the feed. We may lose in purity but the vapor rate required is drastically reduced and therefore the column is cheaper. Of course, a fourth possibility is a vapor sidestream above the feed. Since there are no savings in vapor rate, a lower maximum concentration of middle component and few applications we are aware of, this alternative is not considered. An evaluation of these alternatives as well as a quantitative comparison of sidestream columns with simple sequences was the original motivation for this investigation. Here, we focus only on results for the design of sidestream colunns. Shortcut Design We consider a sidestream column (Figure 1) where a nonazeotropic ternary mixture consisting of components A, B, and C is distilled. We present here the case of a column with a sidestream above the feed. Columns with sidestreams below the feed can be treated in an analogous way and results for those cases are presented in the Appendix. Design specifications often require a relatively pure top and bottoms product and a high fractional recovery of B in the sidestream. However, there is a maximum concentration of B we can achieve in the sidestream which is not known a priori, and this sidestream purity constraint limits the feasible design specifications. We also are interested in approximate expressions for the vapor rate and the number of trays. These topics are addresed below. Mass Balances. Since we are interested in sharp separations between A and C, we assume that essentially no A appears in the bottom product and no C in the top. This is a reasonable assumption in material balances necessary

for preliminary design purposes, and it ale0 introduces little error into the calculation of vapor rates. Of course, the number of trays is much more sensitive to distillate and bottoms composition. For this sidestream column six independent equations can be written, one mass balance for each component plus three mole fractions that sum to unity. If the flow rate and composition of the feed are specified, 12 unknowns remain, that is the three flow rates of streams D, P, W and nine mole fractions in the above streams. We therefore need six design specifications. As stated above, we set X A ,=~0 and XC,D= 0, so that four more specifications remain. There are no limitations on the purity of D and W we can achieve and it is convenient to choose X, and Xc,w. We can also specify the recovery of component B in the sidestream and there is no limitation on this value. Alternatively, we can specify X B , although ~ we must first calculate (XB3)- to make sure that our choice is feasible. Estimation of this limiting sidestream composition is done below. The fractional recovery of A in the distillate can also be chosen, but if we specifyjm (or D)it is possible to violate the thermodynamic constraint on XA,p For instance, if we specify jAD to be near unity, this means that nearly no A leaves the column with the sidestream and this may not be feasible. It therefore is more convenient to specify j , , which is not constrained. Summarizing, the specifications we prefer to make are: D 0,X u , Xc,w, h , W , and either XB,Por j B p , XA,W= X ~ , = the latter in the range from zero to unity. These specifications may or may not be compatible with actual needs in most designs. If, for instance, B is a reactant and P is recycled, we may want to recover most of our reactant but we may not require a high purity of the recycle stream. But when B is a product, the sidestream column may not be appropriate since the purity of B is limited. If A is the primary product, it can be obtained in high purity, but it will also be recycled because of the upper limit on ita fractional recovery. For this case, a column with the sidestream below the feed may be more economical. There are no constraints on XC,W and jc,w and a sidestream above the feed is thus appropriate if C is the main product. Vapor Rate. The main advantage of a sidestream column is that while performing the primary separation, say B/C, we take advantage of the vapor rate needed for this split in order to effect an additional separation at small incremental cost, say A from B. This secondary separation A/B can be done economically only to the extent that the vapor rate required for the primary separation permits. For a sidestream column separating A, B, and C, B/C is

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Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985 823

For a sidestream column we can define two reflux ratios. One of them is the reflux ratio at the top of section 2 of the column and corresponds to the primary B/C separation (see Figure 1)and the other is the reflux ratio at the top and corresponds to the secondary separation. We denote them by the subscripts 2 and 1, respectively

arction

V L1 - - 1= D D

R 1 =

I I

R2=-- V

P+D

*e:ion

I=-

L2

P+D

(4) (5)

Glinos and Malone (1984) have presented equations to estimate the minimum reflux ratio for sharp splits of multicomponent mixtures which hold for sidestream columns as well. Their expression for the AB/C split is

Figure 1. Sidestream distillation column with a liquid sidestream above the feed.

the primary separation if the sidestream is above the feed and A/B is the primary separation if the sidestream is below the feed. At this point a thermodynamic constraint on the sidestream composition arises. In general, we are able to achieve any purity we wish in the sidestream (assuming that enough trays are available) provided that we increase the reflux ratio accordingly. But this may be far above what the primary separation requires. Obviously, this is not desirable and instead we should consider some other type of column. In what follows, we base the minimum reflux (or vapor) rate calculation on the primary separation and then evaluate the limiting composition in the sidestream. This composition will rarely turn out to be very high (except if the A/B split is very easy and the B/C split very difficult, of if the amount of component A present in the feed is very small) because only one column section is provided for the secondary separation. Also, note that there are not any distributed non-keys that we must take into account in the minimum vapor rate evaluation: the split is of the AB/C type, and there are not any non-keys intermediate in volatility; on the other hand, light non-key A does not distribute, since its relative volatility must be well above the volatility of component B in order to choose to use a sidestream column. Underwood's equation for the minimum vapor rate can be written (see King, 1980)

v,,

=

aAIDXA,D

aA

+ PXA,P) - 51

+ aB(DXBJl

aB

+ PxB,P) - 51

(DxC,D

+

+ PxC,Pl 1- 51

(1)

where V is the vapor flow above the feed plate and t1 is the root of the following equation for which aB> t1 > 1

For sharp separations (Xc,w= jc,y = 1)and a saturated liquid feed to the column, eq 1with the help of (2) simplifies to W Vmin= (3) t1 - 1

This equation allows straightforward calculation of R, and gives values which are usually less than 4% in error compared to the exact Underwood solutions. It holds for sharp splits and saturated liquid feeds. If the split is not sharp (components C and B appear in the sidestream and bottoms, respectively, in significant amounts) Glinos and Malone (1984) also give a method to calculate R, based on the value given by eq 6. Furthermore, if CYA >> CYB(say a ratio 1O:l) and the split is sharp (e.g., a pasteurization column), eq 3 or 6 greatly simplify to (7)

Minimum and Theoretical Number of Plates. For the column section above the sidestream (column section 1 in Figure l), Fenske's equation gives the minimum number of plates l n ( 2 E ) (8) In (aAB) where (NJmin includes the sidestream tray. For column sections 2 and 3, Fenske's equation gives again (N1)min

=

In(%$) (9) In ((YB) To estimate the theoretical number of plates in the column section below the sidestream, we can use the rule of thumb N2,3 = 2W2,Jmin (10) or if we want high accuracy we can use Eduljee's approximation to Gilliland's graphical correlation (King, 1980) (Ndmin

=

For the upper part of the column (above the sidestream), these approximations are not satisfactory. In this column section the mixture is essentially a binary and the mole fraction of component A at the top will often be high. Based on these assumptions, we simplified Underwood's equation for the theoretical number of trays (Underwood, 1946) to get (for a proof of eq 12 see Glinos, 1984)

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824

N1 =

(12) Equation 12 is Satisfactory for Xu greater than about 0.98. Exactly the same equation was found by Jafarey et al. (1979), using Smoker’s equations for a binary separation in a simple column. Note that for large R, eq 12 reduces to Fenske’s formula. Minimum Mole Fraction of A in the Sidestream. The minimum XA,Pis obtained for an infinite number of stages in column section 1 (pinch zone composition). Then we have (Underwood, 1946)

where is the smallest root of Underwood’s equation for the rectifying section. If we rearrange this equation to a quadratic for 5, we find (R1

+ 1)t2 - ((am+ 1)Ri + ~ A B X B+, D X A , D+~ R l a D = 0 (14)

Note that (XA,P)min and are functions of R1, and R1 depends on D through eq 4. Therefore, a mass balance on A has to be solved along with eq 13 and 14. (15) FXA,F= DXA,D + PXA,P If we assume that R2 or the vapor rate V is already fixed, the system of eq 13 to 15 seems to contain one independent parameter and that we have to fix either R1 (and then D through eq 4) or XA,D. However, this is not true, and by algebraically manipulating this system of equations we can show that XAD cancels out everywhere. In other words, (XA,p),, is independent of X, and is fixed once we have fixed the vapor rate throughout the column. Also, one might think that (XA,P)min can go to zero if R1 in eq 14 approaches infinity. This is not true because in this case D in eq 4 should go to zero (V is considered fixed), which is not allowed by the mass balance, eq 15. Since (XA,P)min is independent of XA,D, and in order to simplify the calculations,we can set X, = 1. In this case, the smallest root of eq 14 is = 1, and the system of eq 13 to 15 reduces to the following quadratic equation

The minimum composition of A in the sidestream depends on the value of the reflux ratio (vapor rate). If R2 in eq 16 is equal to ita operating value (for instance from the rule of thumb R2 = l.2(RJmin,with the latter calculated from eq l ) , then we obtain the true absolute minimum value for XA,pand infinite trays are needed to reach that value under these given internal flows. Then we have to pick a value for XA,p somewhat bigger than (XA,p)min to operate. On the other hand, we can set Rz = (RZ)- in eq 16 and this yields a value for the sidestream composition always ~~. bigger than (X,p),i?, which we will call ( X A , ~ )The meaning of this “critical” composition is the following. If we choose X u such that ( X A , P (XA,p)cr, then for R2 = (R2)- pinches will appear only near the feed tray. In the first case above, where XA,p < (XA,p)cr, the secondary A/B separation has become primary and (R2)min is not the true minimum reflux ratio. The latter should rather be calculated from eq 13. In order to avoid this, the sidestream composition is chosen such that

> (xA,P)cr

(17) If a A >> (YB and the top product is highly pure, the expression for the limiting mole fraction of A in the sidestream simplifies to this very handy relationship XA,P

Equation 18 can be used for pasteurization columns. We see that it is possible to obtain essentially pure component B at the sidestream, if XA,F is small enough. To find the maximum mole fraction of B in the sidestream, Xc,pis found through a mass balance on C and then (19) (XB,P)max = 1 - (XA,P)min- x C , P An alternate method to estimate the limiting sidestream composition has been suggested to us by Hooper (1983) as follows: (1) Calculate or estimate the distribution coefficients Ki, i = A, B, C, at the temperature and pressure corresponding to the side draw location. (2) Evaluate the vapor rate V at the side draw location by setting the stripping factor for component C, KcV/L, equal to 0.9 (roughly equivalent to R = 1.2Rb). It follows that: V = (F - W)/(1- Kc/O.9). (3) A mass balance on component A for the section above the sidestream along with the equilibrium relationship YA = KAXA gives the desired limiting composition: X, = FX,,F/(V(KA - 1) + W - F). This method involves two main steps: evaluation of the vapor rate needed for the primary (B/C) separation and the calculation of the sidestream composition. However, there is uncertainty about the value of Kc we should use. The equilibrium constant depends on temperature and pressure and therefore it varies with column height much more than the relative volatilities. The correct location to calculate the stripping factor is the upper pinch zone (King, 1980). For instance, if the pinch occurs at the feed plate, KHKshould be calculated a t feed plate conditions. Evaluation of the K value a t the side draw location will give satisfactory results if the upper pinch is located far away from the feed and near the sidestream, but it will result in very poor estimates of the vapor rate if the pinch occurs near the feed (as it does for the AB/C split we are talking about, regardless of the feed compositions). In step 3, KA should be evaluated at the sidestream location, as suggested. An accurate estimate unfortunately requires the solution of a quadratic even for constant a systems since KA C Y ~ / ( C Y+~XB). X A Thus, an accurate estimate for V and the sidestream purity will require Kc at the upper pinch near the feed plate and KA at the sidestream. Of course, the great strength of this method is for highly nonideal systems, where eq 16 and 18 do not apply, and the Kivalues must be calculated as a function of composition. Example. Consider an ideal ternary mixture A, B, C with relative volatilities 5,2, and 1, and feed compositions 0.10, 0.45, and 0.45, respectively. To recover B from a

Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985

sidestream we would like to know the minimum mole fraction of A in this stream. The separation is sharp and W = 45 mol/h. We assume that KB = 1 at the side draw location and with Hooper’s method we find that V = 124 m/h and (XAp),, = 0.042. With our method we calculate that V= 145 m/h, V = 163 m/h, and (XA,p)- = 0.036. We see that the assumption that KB = 1is approximately correct, and the estimation for the limiting composition found by Hooper’s method is satisfactory and conservative due to the underestimation of V. This will often be the case. However, the estimation of Vis 24% in error and with the value of 124 m/h found the separation cannot be acheived, since this vapor rate is below the minimum. However, when K values are known a priori, even in nonideal systems, the alternate method is satisfactory for many purposes. Accuracy of the Design A sidestream column, separating a mixture of benzene, toluene, and xylene, was designed first by the above method and then by using the computer aided design program ASCEND-I1 (Locke, 1981). This rigorous program is a simultaneous equation solver and is capable of evaluating the reflux ratio required for a separation, the number of trays, and also does optimizations. Constant molal overflows in each column section and constant relative volatilities were assumed. Although the design equations presented above are supposed to be shortcut expressions for preliminary design, they proved surprisingly accurate for the caaes we examined. The maximum error in the calculated stream compositions did not exceed 0.17%, and the error in the reflux ratio was about 0.08%. The limiting sidestream composition of component A was only 1.0% different from the value calculated with eq 16. For composition specifications being below this value the computer-aided analysis did not converge without violating constraints for positivity of the mole fractions. Therefore, for ideal systems and sharp separations, the design method proposed seems to be quite accurate and simple. Generalizations The analysis above was for a ternary mixture. If the mixture to be separated has more components, the detailed equations differ, but the basic concepts and the design procedure remain the same. We outline below the analysis of a column with a sidestream above the feed separating a quaternary mixture, and then a generalization for more components. For four-component mixtures, there are 3 possible splits in a sidestream column which are shown in Figure 2. We denote them by A/B/CD, AB/C/D, and A/BC/D split. We examine them one by one, in comparison to the ternary mixture. A/B/CD Split. For sharp splits XD,D = XD,p = 0 and the set of specifications and the mass balance solution remain exactly the same as for the ternary case. The minimum reflux ratio for the primary separation AB/CD can be found from Underwood’s equations or from an explicit approximate expression (Glinos and Malone, 1984)

825

rA’”

TSA A , B d

(a) A/B/CD

split

Figure 2. Three possible splits of a quaternary mixture in a column with a sidestream above the feed.

The minimum and theoretical number of trays can be found from eq 8 to 12. The limiting sidestream composition is also found from eq 16. AB/C/D Split. If the (primary) separation is sharp, then no A and B and nearly no C appear in the bottoms and no component D appears in the distillate. We can then calculate the minimum vapor rate or R, without specification of the top and sidestream compositions. Underwood’s equations for the ABC/D split can be used or alternatively the approximate expression (Glinos and Malone, 1984)

The number of trays is given by Fenske’s and Gilliland’s equations or eq 10. Equation 12 does not apply since the mixture in the top section is not a binary. The limiting sidestream composition can be found allowing infinite trays in column section l. The ternary mixture ABC is essentially distilled in this section and under limiting flow conditions the pinch will occur exactly at the sidestream tray since all three components are present in significant amounts in the upper pinch zone (Underwood, 1946; Shiras et al., 1950). Hence, the limiting composition will coincide with the pinch composition. We find (Underwood, 1946)

and

R1depends on the distillate flow through eq 4 and then the above equations contain 5 unknowns (4 compositions and D). They can easily be solved along with the four mass balance equations P+D+W=F

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Id.Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985

DXB,D+ PXB,P= FXB,F XA,D+ XB,D= 1

(24)

to give the minimum compositions of A and B in the sidestream, the distillate composition, and the corresponding distillate and sidestream flow rates (a total of 6 unknowns). Actually, the sidestream limiting composition is independent of these flows and of the distillate composition, but because we assumed that no C appears at the top when we wrote eq 22 and 23, we have to evaluate values for D and P consistent with this assumption. A mass balance on component D yields XD,pand then the maximum Xc,p can be found by difference. A/BC/D Split. The variable specifications that are feasible, the number of trays and the minimum reflux ratio required for the primary separation ABC/D, are exactly the same as the previous case. However, the evaluation of the limiting sidestream composition is different. The upper part of the column performs the separation A/BC and under limiting flow conditions in column section 1, the upper pinch zone will be located some trays above the sidestream tray (Shiras et al., 1950),because some plates are needed to wash out the heavy non-key C. The sidestream composition therefore does not coincide with the pinch composition. Alternatively, Underwood's equations can be written for the rectifying column section 1considering the sidestream as a feed with negative flow (King, 1980). This case requires solution of an equation similar to (1)for the appropriate root CYAC < f < CYBCand using thi? in an equation like (2) gives the sidestream composition. A simipler way, valid for sharp splits (nearly no B in the distillate), is to use the approximate expression for the minimum reflux ratio for the split A/BC (Glinosand Malone, 1984) written in terms of the sidestream compositions

This equation has three unknowns (since R1 depends on D, V is considered fEed). Therefore, it has to be combined with mass balances on components B and C

__

FxC,F

and simultaneous solution of the above 4 equations for the three mole fractions and D yields the desired limiting sidestream composition. Note that by substituting the three compositions in terms of D, from the mass balances above, into eq 25, a quadratic with D as the only unknown is obtained. Therefore, an analytical solution for this case is possible. It should not be surprising that we use expressions for minimum reflux to calculate compositions. If these equations are satisfied for some value of R, this means that limiting conditions prevail in the column section these equations apply to. Besides, eq 13 is the minimum reflux expression for a sharp binary split (XA,D = 1; t1 = l), and using eq 22 and 23 we find for R1

which gives exactly the minimum reflux for the sharp split

1 3 1

v3FFX i,w

Figure 3. Sidestream distillation column with a liquid (or vapor) sidestream below the feed.

between A and C where B is distributed (see Glinos and Malone, 1984). The compositions found from minimum reflux expressions coincide with those found at pinch zones when the pinches occurr at the sidestream plate, as it happens for all but the last previous cases. This simple analysis for the preliminary design of sidestream columns is easy to extend to other cases. It may be convenient to reduce mixtures with more than 4 components to quaternaries by lumping. Lumping rules are suggested by Glinos and Malone (1984). We also note that the method presented does not assume saturated liquid feed into the column and we can use Underwood's equations with q # l. However, eq 6,20,21, and 25 are derived on the basis of q = 1 and should not be used for other cases.

Design Algorithm 1. Specify the desired split for the primary separation by setting fractional recoveries, flows or mole fractions. Do not specify the sidestream composition or the recoveries of the products withdrawn closest to the sidestream. 2. Based on 1 evaluate V,, or Rminfor the primary separation with eq 1or 6 or the analogous equations from the Appendix. 3. Calculate the limiting sidestream compositions with eq 16 or A-5 and 19. 4. Choose R = 1.2R- and a sidestream composition 5 to 10% above the minimum (or below the maximum). 5. Complete the mass balances on the column. 6. Find the number of theoretical trays with eq 9,10, and 12 or A-2 from the Appendix. (In the column section performing the secondary separation don't forget to use the appropriate R.) Conclusions Although sidestream columns are not rare in industry, shortcut methods were not available for their design. Whenever such columns were designed by hand, completely arbitrary values were assigned to the number of trays required and the sidestream composition, which could be far from the correct or optimal values. The equations we presented here are simple to use and provide the design engineer with accurate estimations of the vapor rate, the number of trays, and the sidestream composition, provided that the mixture exhibits a nearly ideal behavior.

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This design method will also allow incorporation of sidestream columns in the synthesis of liquid separation systems and to compare designs with traditional sequences of simple columns.

2 and for column section 3 from the following expressions

Acknowledgment

I-

This work was supported from the U.S. Department of Energy (Grant DE-AC02-81ER10938). We are thankful to J. M. Douglas and F. E. Marquez for their help. We also thank Dr. W. B. Hooper of Monsanto Corp. for an interesting and stimulating dialogue. Appendix Columns with a Sidestream below the Feed. There are several reasons to take a sidestream below the feed. In general, we want the difficult split to be done by the main part of the column (primary separation), and leave the easier split for the single column section near the sidestream. If we are separating the ternary mixture A, B, and C and the A/B separation is much more difficult than the B/C separation, we want to recover B with a sidestream drawoff below the feed. On the other hand, if we demand both a high fractional recovery and a high purity of component A at the top product, the only way to get those is to withdraw the sidestream from the lower part of the column. We can take a sidestream as a vapor or as a liquid. Obviously, the vapor will be the richest in component B, which we want to recover, and therfore the cost of further separation of a vapor sidestream and/or the recycle costs will be less compared to a liquid sidestream. But if we use a liquid sidestream, the vapor rate and the operating costs of the column are drastically reduced. This is a tradeoff we have to take into account when we design a separation system. The liquid sidestream often turns out to be a much more economical solution. For a final product, however, a vapor sidestream is often taken for another reason. When scaling or heavy impurities are present, they may be allowed to accumulate in the reboiler with the sidestream product taken as a vapor. In what follows we will briefly present equat; 11s to design columns with a liquid or vapor sidestream selow the feed. Equations holding for liquid sidestream have an “L” in their number and equations for a vapor sidestream have a “V”. Vapor sidestream compositions are denoted by Yih; Design. The limitations on the specifications we can make concern the fractional recovery of C at the bottom, which cannot be specified as high as we want, and the sidestream composition. For given vapor rate (or reflux) in the upper part of the column, there is a minimum mole fraction of C in the sidestream. To find the minimum reflux ratio we can use Underwood’s equations or the following approximation (Glinos and Malone, 1984)

Rm =

~ B ( X A+ , FX B ~ ) XC,F X A ~ (-~ A X A ~ (-~1)A

+

(A-1)

This equation is good only for sharp splits ( X B ,1~ 0.99) and saturated liquid feeds and predicta R,,, with an average error of about 3% in comparison to the exact Underwood‘s solution. The minimum number of trays can be found from Fenske’s equations if we consider A and B the key components for sections 1and 2 (see Figure 3) and B and C the key components for section 3. The theoretical number of trays can be found from eq 9 or 10 for sections 1 and

xB,p

(S+

xB,W

(S +

- 1)xC,W - a B - 1)xCJ’- a B (A-1L)

(A-1V) These equations are derived by use of Underwood’s expressions (Underwood, 1946) and are based on the assumptions that the separation is sharp (Xc,w I0.99) and the mixture distilled in section 3 of the column is binary. The limiting composition of C in the sidestream is the pinch composition under conditions of limiting flow and infinite trays in column section 3. We find that

where E2 is the biggest root of Underwood’s equation for a stripping section. If we write this equation in a quadratic form we find Sf2 - [aBXB,w + Xc,w + S(aB +I)][ + (S + 1 ) a B = 0 (A-3) Both S and 5 depend on the bottom and sidestream flow rates and therefore the above equations have to be solved along with a mass balance on component C. The bottom composition Xc,wis supposed to be fmed and the absolute minimum value of (XCp)- is taken for Xc,w = 1. If Xc,w is near unity, then eq A-3 shows that E2 equals approximately to aB. Substituting this value into eq A-2 and solving together with the mass balance we find the approximations ((YB -

U(RXA,F+ q)(Xc,p)min2- {(“B - 1) X + 4) - x ~ p + l)(Xcp)mh+ X c p =~ 0 (A-4L)

(Rx~p + Xcp

I

l(R + ~ ) X A ,+Fq - 1l(Yc,p)mi,2- RXA, + 4 - XC,F+

The above equations are written in terms of R (instead of S)because R is supposed to be fixed by the primary separation A/B, and they hold only for relatively sharp splits. If we set R = R- we will get the “critical” limiting composition, as explained in the case of the column with a sidestream above the feed. We then have to pick an Xcp value somewhat bigger than that to operate. For distillation of 4 or more component mixtures in sidestream columns, with the sidestream below the feed, we can easily derive expressions in the way we did that when the sidestream was above the feed. We do not present them here for reasons of space.

I&. ~ n gctwm. . Process DBS.

02s

Nomenclature D = distillate flow rate, mol/h P = sidestream flow rate, mol/h W = bottom flow rate, mol/h F = feed flow rate, mol/h V = vapor internal flow rate, mol/h Li= liquid internal flow rate in column section i, mol/h Ri= reflux ratio at the top of section i , defined either by eq 5 or 6 S = reboil ratio defined by S = V / W q = feed quality Xi$ = mole fraction of component i in stream j Yi = mole fraction of component i in the sidestream if the later is taken below the feed as a saturated vapor j i k = fractional recovery of component i in stre& k ki = equilibrium distribution coefficient of component i, defined as Y i / X i Ni = number of plates in column section i = minimum mole fraction of component i we can acheive in the sidestream, for given vapor rate and infinite number of trays in column section 1

DBV.

i9s5, 24, 828-831

(X,p), = mole fraction of i in the sidestream under conditions of minimum reflux and infinite trays around both the sidestream and the feed tray Greek Letters aij = relative volatility of component i with respect to j ; if j does not appear, it is assumed to be the heaviest component = parameter in Underwood's equations Literature Cited Gllnos, K.; Maione, M. F. Ind. €ng. Chem. Process Des. Dev. 1984, 23,

764. Glinos, K. h . D . Dissertetlon. Unkrerslty of Massachusetts, Amherst. MA,

1984. Moper, W. B. Monsanto Co.,St. Louis, MO, personal communication, 1983. Jafarey, A.; McAvoy, T. J.; Douglas, J. M. Ind. Eng . Chem . Fundam. 1979, 78. 181. King. C. J. "Separation Processes", 2nd ed.;McGraw-Hill: New York, 1980. Lmke, M. H. W.D. Thesis, Carnegle-Mekn Unkrerslty, Pmsburgh. PA, 19~1. Shkas, R. N.; Henson, D. N.; Gibson, C. H. Ind. Eng. Chem. 1950, 42, 871. Underwood, A. J. V. J . Inst. Pet. 1948, 32,598.

Received for review July 25, 1983 Revised manuscript received October 15, 1984 Accepted November 1, 1984

Dimerization of Acetaldehyde to Crotonaldehyde over Silica-Alumina Bed Operating in Reaction-Regeneration Cycles Joo6 M. Arandeo;

Arluro Romero, and Javler Bltbao

Department of Technical Chemistry, Univwsity of Wasque Country, Apdo. 644, Bilbao, S p i n

The operation in reaction-regeneration cycles of isothermal fixed bed reactors wlth decaying catalyst was studied. The case where the regeneration tlme is dependent on reaction time was treated. The effect of cleaning time between two cycles and of space time on the optimum length of operation time and initial activity of regenerated catalyst to maximize the production was analyzed. The calculation procedure was applied to dimerization of acetaldehyde to crotonakiehyde on a siiica-alumina catalyst.

Introduction Several design strategies (Douglas et al., 1980) can be considered to solve the problems caused by catalyst deactivation. The election of one of them depends on the throughput and on the kinetic and deactivation characteristics. One of the feasible strategies is the operation of the reactor by reaction-regeneration cycles. The optimum design for a reactor-regenerator system operating by cycles consists in the calculation of the length of operation, initial activity of catalyst, and temperature policy that maximizes the production. When several reactors in parallel are used (operating on different part of the cycle to keep continuous the production), the calculation of the optimum is the same thing as the computation of all three factors for one of those reactors. Earlier works that studied this design problem (Smith and Dresser, 1957; Walton, 1961; Kramers and Westerterp, 1963) consider that the operation time is much larger than the regeneration time; thus it is not treated as a variable. This circumstance will be true when the time to prepare the reactor between cycles, cleaning time or dead time, is much larger than the regeneration time, or when the regeneration is not carried out in situ. 0196-4305/85/1124-0828$01.50/0

If the operation and regeneration times are of similar magnitude, the determination of the optimum cycle will be difficult. The catalyst will be replaced when the operation time leads to the maximum production. The production, P, can be defined as

P=

(

mol of product ( t + t,) W / F b time X cat. weight XAt

)

(1)

To calculate the optimum operation time, top$,it will be necessary to compute firstly the time between two cycles, t,, which will be t , = t, t d (2)

+

The dead time, t d , will be independent of the operation time, but the regeneration time, t,, will increase as the content of coke on the catalyst is increased, i.e., as the operation time is increased. Thus, in order to set the relationship between the regeneration and operation times, it is necessary to have the following expressions: kinetic equation at zero time (-rA)O

= f(xA,T)

kinetic equation of deactivation 0 1985 Amerlcan Chemlcal Society

(3)