1. PIECENAMP Module 5 – Controllability Analysis 1 Tier III Open-ended problem

2. PIECENAMP Module 5 – Controllability Analysis 2 Tier III Statement of intent The goal of this tier is to solve few real-life applications of Controllability Analysis, in which the student must interpret the results obtained from a range of Controllability Analysis tools. At the end of Tier III, the student should be able to identify the following: Benefits of the use of Controllability Analysis tools Potential cost saving opportunities from the use of Controllability Analysis tools Environmental impact reduction resulting from the application of Controllability Analysis tools How the application of Controllability Analysis tools can be used to obtain an operable process

3. PIECENAMP Module 5 – Controllability Analysis 3 3.1Doukas and Luyben reported the transfer function model for the distillation column with a side stream product. The feed contains benzene (B), toluene (T) and xylene (X), with the benzene in the side stream of much less importance than the other controlled variables. The linearized transfer function model is: The process is shown on the next slide.

4. PIECENAMP Module 5 – Controllability Analysis 4 Feed flow rate XD XD T (mole fraction) XB XB T RR (Ratio) XS B (mole fraction) Distillation column with a side stream product. LS (lb mol/ hr) QB (BTU/ hr) XS X (mole fraction) Determine the best loop pairing and calculate the Niederlinski Index for each subsystem considered.

5. PIECENAMP Module 5 – Controllability Analysis 5 3.2The transfer function model for a pilot scale binary distillation column used to separate ethanol and water was given in TIER 2, The process variables are (in terms of deviations from their respective steady state values):

6. PIECENAMP Module 5 – Controllability Analysis 6 Feed flow rate (d) Overhead mole fraction ethanol Overhead mole fraction ethanol (y 1 ) Reboiler steam pressure Reboiler steam pressure (u 2 ) Overhead reflux flow rate (u 1 ) Distillation column used in separating ethanol and water Mole fraction of ethanol in the side stream Mole fraction of ethanol in the side stream (y 2 ) Temperature on tray #19 Temperature on tray #19 (y 3 ) Design a steady state decoupler using the generalized approach, with G R ( 0 ) chosen as Diag[G(0)].

7. PIECENAMP Module 5 – Controllability Analysis 7 HE 1 Q 1 A 1 TD 1 HE 1 Q 1 A 1 TD 1 HE 3 Q 3 A 3 TD 3 HE 3 Q 3 A 3 TD 3 HE 2 Q 2 A 2 TD 2 HE 2 Q 2 A 2 TD 2 HE 4 Q 4 A 4 TD 4 HE 4 Q 4 A 4 TD 4 f1f1f1f1 m1m1m1m1 f5 f4f4f4f4 m4m4m4m4 m5m5m5m5 f7f7f7f7 m8m8m8m8 m7m7m7m7 H1H1H1H1 TH1TH1TH1TH1 575 K 718 K H2H2H2H2 TH2TH2TH2TH2 C1C1C1C1 300 K TC1TC1TC1TC1 C 1A C 1B C 1A1 C 1B1 400 K T5T5T5T5 395 K T6T6T6T6 T7T7T7T7 T3T3T3T3 365 K C2C2C2C2 T2T2T2T2 T4T4T4T4 T1T1T1T1 398 K 358 K C3C3C3C3 f8f8f8f8 3.3 S.G.Oliveira and F.S.Liporace [3] have obtained the Gain Array for the HEN showed below, where the manipulated variables are f 1, f 4, f 5, f 7 and f 8 should be used to control the outlets temperature T C1,T H1,T H2.

8. PIECENAMP Module 5 – Controllability Analysis 8 f1f1f1f1 f4f4f4f4 f8f8f8f8 T C1 T H1 T H2 f7f7f7f7 The gain array obtained for the system is: f5f5f5f5 Choose the best pairing, using the RGA and SVD.

9. PIECENAMP Module 5 – Controllability Analysis 9 References [1]Wood, R,K. and M.W. Berry, “Terminal Composition Control of a binary distillation column,” Chem. Eng. Sci., 29, 1808 (1973). [2] Ogunnaike, B. A., J.P. Lemaire, M. Morari, and W.H. Ray, “Advanced multivariable control of a pilot plant distillation column”, AICHE, 29, 632 (1983). [3]Oliveira, S.G., Lopirace, F.S., Araujo, O.Q.F. et al. The importance of control considerations for heat exchanger network synthesis: a case study. Braz. J. Chem. Eng., June 2001, vol.18, no.2, p.195-210. ISSN 0104-6632. [4]Ogunnaike, B. A. and Ray, W. H., Process Dynamics, Modeling and Control, Oxford University Press, New York (1994). [5]Marlin, T. M., Process Control Designing Processes and Control Systems for Dynamic performance, McGraw-Hill, United States of America (1995).