Continuous Distillation 1: McCabe-Thiele Method

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1 Guidelines for the Number of Distillation Separation Stages Februar, 9 refeed Corporation Dr. Yoshio Kumagae Continuous Distillation : McCabe-Thiele Method

2 Continuous Distillation : McCabe-Thiele Method. Review of Diagram Construction Method 3 A miture of 4 mol% benzene and 6 mol% toluene (boiling point liquid) is to be separated in a distillation column. The molar fractions of benzene in the distillate and bottoms are to be set to.9 and., respectivel. Set the reflu ratio to., and find the number of required theoretical stages b the McCabe-Thiele method. Rectifing section operating line n n n D R n D R R : Steam composition leaving stage n : Liquid composition leaving stage n : Overhead product composition R : Reflu ratio Operating line for diagram : R R R D 4

3 .6.4. Reference: vapor pressures of benzene () and toluene () =^( /(.79+t)) =^( /(9.48+t)) D==

4 .6 D==.9.4. Rectifing Section Operating Line Slope=R/(R+)=/ q Line: Boiling oint Liquid.6 D==.9.4. Rectifing Section Operating Line Slope=R/(R+)=/

5 q Line: Boiling oint Liquid D== Rectifing Section Operating Line Slope=R/(R+)=/3. Stripping Section Operating Line..4.6 Bottoms Liquid Condition 9 q Line: Boiling oint Liquid D== Rectifing Section Operating Line Slope=R/(R+)=/3. Stripping Section Operating Line Number of Theoretical Stages: 9 (8 distillation stages + reboiler)..4.6 Bottoms Liquid Condition

6 Continuous Distillation : McCabe-Thiele Method. Guidelines for Number of Stages Although the number of stages is influenced b the reflu ratio and the purit at the top of the column, the difficult of distillation separation can be pictured from the diagram alpha= 5 5 系列

7 Relative volatilit (α ) = ratio of equilibrium ratios The diagram can be calculated from the relative volatilit ) ( ) ( / / / K K ) ( Useful relationship 3 In an ideal sstem Raoult s law holds o o K K o o o o K K / / In a sstem where Raoult s law holds, the relative volatilit becomes the phsicall meaningful propert value of the vapor pressure ratio. The relative volatilit is the ratio of the vapor pressures of the pure substances (ideal sstem) 4

8 Continuous Distillation : McCabe-Thiele Method 3. Eamples of Guidelines The boiling point difference between p-dichlorobenzene (DB) and o-dichlorobenzene (ODB) is 6 C. Let us consider the difficulties of separation b distillation. 6

9 . Correlate the vapor pressure data of p-dichlorobenzene (DB) and o-dichlorobenzene (ODB) with the Antoine equation. Use Log() = A - B/T as the Antoine equation.. Calculate the relative volatilit at C, draw the diagram and consider the difficult of separation b distillation. t, [ ] DB, [mmhg] ODB, [mmhg] log() Vapor ressure Correlation ODB = /T log() ODB. DB = /T DB 8

10 DB-ODB Vapor Liquid DB ODB 気液平衡 Equilibrium.6.4. α= Although it has not been determined eactl, it can be epected that the number of theoretical stages required for distillation will be ver large. Continuous Distillation : Actual lant Correlation

11 N act =35/ΔT N act :Actual number of distillation column stages ΔT:Difference in the boiling points of the components to be separated Satoru Kawai (Mitsubishi Kasei): "rocess Sekkei ni-okeru Bunshi Kagaku Kougakuteki Shuhou (in Japanese : Molecular Chemical Engineering Methods in rocess Design)", Recent rocess Design Engineering Workshop organized b the Societ of Chemical Engineers, Japan (November 7, 987) From this approimation method, it is possible to estimate the actual number of stages from the difference in the boiling points of the components ver easil. Batch Distillation: Rose Relationship

12 Guidelines for the Number of Distillation Separation Stages (Batch) In a binar sstem batch distillation, if the reflu ratio is kept constant, the concentration of the low boiling point component in the distillate decreases with time. However, ecept in special cases, it is generall sufficient to design the distillation column so that the first 4% of the distillate has a low-boiling point component concentration of 95 mol% purit or more. As a result of eamining the relationship between the theoretical number of stages and the reflu ratio in such a case, Rose obtained the following relationships. "Kagaku Kougaku Binran, Revised 3rd ed. (in Japanese)" p (8.63) Here, R is the reflu ratio, S is the number of steps, and α is the relative volatilit (if it varies within the column, an average value ma be used). If R and S are within the range of Equation (8.63), the desired separation can be roughl obtained. These relationships can be simplified as, Note that these relationships can be applied onl when the composition of the feed solution is between and 9 mol%. Rose, A. : Ind. Eng. Chem., 33, 594 (94) 3 (8.64) Rose s Relationship and Design Eamples Sstem Relative Volatilit.85/logα Number of theoretical stages Operation reflu ratio Remarks. Water / olar Solvent New column. Silane derivatives/ EDC New column 3. Olefin Column reassignment Cases and : Since new columns are involved, these case-studies are focused mainl on Rose s relationship, and the number of stages is close to Rose s relationship. However, the reflu ratio is not that important. Case 3: There were onl theoretical stages in the column to be reassigned, and as a result of increasing the reflu ratio, it became close to that calculated b Rose s relationship. Setting both the number of stages and the reflu ratio to a value obtained from Rose s relationship appears to be an over specification. In the last eample, the relative volatilit is close to that of o-dichlorobenzene and p-dichlorobenzene. Batch distillation seems to have a comparativel better separation performance than continuous distillation. 4

13 Conclusion Whether for continuous or batch operation, it is important to use guidelines before performing distillation calculations in order to do an efficient investigation. It is difficult to develop guidance skills b using onl a process simulator. It appears that these skills can be developed b comparing simulator results with methods that emplo simple guidelines. 5