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Toward Distillation Optimization - Comparison of Tray-by-tray and Underwood Method July. 9. 2008 Seon-byeong Kim. LPPD. Research Target ㅡ. Understanding basic distillation theories

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  1. Toward Distillation Optimization- Comparison of Tray-by-tray and Underwood Method July. 9. 2008Seon-byeong Kim LPPD

  2. Research Target ㅡ • Understanding basic distillation theories • Finding optimized distillationin viewpoints of energy and cost • To approach optimized distillation, all possible methods will be explored • Starting with ternary mixtures, possibly expand the method into more multi-component mixtures

  3. Manageable Categories • Column Design • Column Size • Arrangement of column equipments • Synthesis of Complex Column • Column Configuration • Column Sequencing • Operating Condition • Tray-by-tray and Underwood Methods …….My Coverage for this Presentation

  4. Column Sequencing for simple colums • Generalized equation to find the number of sequences to separate a multi-component mixture [R W Thompson] • One simple Method to find optimum sequence is finding the sequence having minimum marginal vapor flowrate (MVF)

  5. Column Sequencing • Number of sequences required to separate a multi-component mixture

  6. Possible Sequences • Possible column sequences for 4 components mixture (2) (1) (3) (4) (5)

  7. Comparing Sequences with MVF (1) (3) A/BCD BC/D Total MVF = 15.47 AB/CD Total MVF = 7.33 Case (3) is more optimized sequence than case (1)

  8. Tray-by-tray Analysis • Mass Balance • At each stages (inlet)=(outlet) (In) = (out) 1st stage  2nd stage  ㆍ ㆍ Nth stage  After summation  Rewrite with Solving for yi,n+1 UIC LPPD

  9. From Component balance From Equilibrium UIC LPPD

  10. Underwood Method-Derivation of the equations [Rectifying Section] • The mass balance for component i in the ternary mixture (1) • Multiply this equation by (2)

  11. Underwood Method(cont’d)-Derivation of the equations • Summation for all components (3) • Choose to simplify this expression (4) (5)

  12. Underwood Method(cont’d)-Derivation of the equations • Rearrange eq.(3) (6) (7) (8) (9)

  13. Underwood Method(cont’d)-Derivation of the equations • After finding the roots , we can write two equations with two roots (10) (11) • Divide eq.(10) by eq.(11) (12)

  14. Underwood Method(cont’d)-Derivation of the equations • At the top of the colum (n=2), both numerator and denominator of the left hand side are equal to r+1 by eq.(5) (13) • 3rd stage (14)

  15. Underwood Method(cont’d)-Derivation of the equations • 4th stage (15) • nth stage (= feed stage) (16)

  16. Finding compositions by UW method Finding the compositions for each component in feed stage and the number of trays required Finding the compositions for each component in stage 2

  17. Underwood Method(cont’d)-Derivation of the equations [Stripping Section] By analogous development as rectifying section (17) (18)

  18. Cardano’s Method • To find the roots from cubic equation

  19. Derivation of Cardano’s method • Make the coefficient of cubic term from •   • The substitution eliminates the quadratic term; in fact, we get the equation called depressed cubic •   • 3. Substituting into it and multiplying both sides by y3 yields •  • Suppose that we can find numbers u and v such that •  and  t=u+v

  20. Derivation of Cardano’s method(Cont’d) 5. Substitution v in the equation of with   • We can solve above one as quadratic equation for u3   • Since and , 

  21. Comparison of Tray-by-tray and Underwood • Input Data

  22. Tray-by-tray Composition Profile UIC LPPD

  23. Underwood Composition Profile UIC LPPD

  24. UIC LPPD

  25. Marginal vapor flowlate calculation Direct sequence is more optimized than indirect sequence

  26. Future Study • Calculation and programming to find the minimum reflux by Underwood Equation • MATLAB programming calculating MVF • Approach to Complex Column Distillation • Understanding Objective function for optimization • Single variable optimization (ex. Newton Method) • Multivariable optimization • Deterministic method (direct and indirect methods) • Stochastic method (ex. genetic algorithm)

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