APR 15. 2009

1. Separation Progress ReportSeon B. Kim APR 15. 2009 LPPD

2. Objectives • Long-term Objectives • Short-term Objectives • Developing a robust computer algorithm for synthesis of optimal separation networks with fully automatic process • Finding highly precise distillation model • Investigation of the sensitivities of composition profiles with different mathematical or column models • 2. Finding simple but robust algorithm of feasibility test • 3. Finding fast and accurate optimization method to find an optimal column network.

3. Previous work Composition profiles of 3 and 4 component mixtures • Constant relative volatility and Ideal mixture • Tray-by-tray, Underwood, and Continuous models Feasibility test • Total screening • Bracket and secant method Pinch Point Calculation • Pinch point equations • Finding stable nodes from each model • Direct calculation with Linninger’s method Profile transformation into rectangular coordinate • Continuous model • Arc-length and bubble point temperature(BPT) 

4. Outline • Find a robust column design algorithm • Column profile model • Continuous differential Equations with temperature as an independent variable • Tray-by-tray model • Underwood model • Mathematical solution method • Implicit Euler method • Helper algorithm • Pinch Point calculation • Attainable Temperature Window • Bubble Point Distance

5. Composition profiles • Continuous model • Equilibrium eq. (ideal mixture) • Mass balance • Numerical Integration • Implicit Euler integration • Composition Equations At total reflux At finite reflux

6. Composition profiles • Quaternary Mixture Stripping section D Rectifying section

7. Composition profiles • Underwood model • Mass conservation • BPT Parameter τp,r B B Bubble point temperature τp,s τp,s D D

8. Composition profiles • Quaternary mixture B Rectifying section Stripping section ATW of Rectifying section ATW of Stripping section Design Specification Feed Composition = [.3 .2 .25 .25] Relative Volatility = [8 3 2 1] Distillate Composition = [.95 .039 .01 .001] Reflux Ratio = 10 C

9. Feasibility test τp,r • Temperature changes monotonically in distillation column • Temperature is should be bounded between distillate or bottom temperature to the pinch points - ATW is necessary condition for feasible design dA dB B TA Feasible design Min(BPD) = 0 dB dA τB τA TB Attainable Temperature Window B B τp,s D D D

10. Feasibility test • Quaternary mixture BPD D xd3

11. Pinch Point Calculation • Pinch point equation (rectifying section) • Constant volatility • By replacing with d: distillation : unstable point : saddle point : pinch point β γ α

12. Pinch Point Calculation UW composition profile (rectifying section) Pinch point Loci By PPE ←β as r→ ∞ ←α ←γ Converge to stable node Converge to stable and unstable node

13. Reversibility of composition profiles • The composition profiles departing from distillate or bottom product can be computed depending of the specific reflux ratio, and they always converge near to the stationary concentrations. • The stationary points are equivalent to pinch points • Backward computation algorithm finds composition profiles from the pinch points to distillate or bottom product requirements. • A robust backward computation from the pinch point could be helpful to find a feasible separation because the trajectories traced from the product specifications have difficult to achieve the last composition point of the path. • Usually the pinch points are close to the interception point in a feasible system

14. Forward algorithm

15. Backward algorithm

16. Composition profile • Backward profile from exact pinch point • is not possible •  driving force of the trajectory • to escape from the stationary • point is not enough because the pinch • point is a stable point • A point near the pinch point • can be an alternative • starting point of the • backward computation

17. Future work • Find or improve robust column design algorithms • Column profile model • Continuous differential Equations with temperature as an independent variable • Mathematical solution model • Finite Element Collocation on Orthogonal Polynomials • Helper algorithm • Coordinate transformation • Pinch Point calculation • Attainable Temperature Window • Bubble Point Distance