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## Tier III Open-ended problem

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**Tier IIIOpen-ended problem**Module 5 – Controllability Analysis**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 Module 5 – Controllability Analysis**3.1 Doukas 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. Module 5 – Controllability Analysis**Distillation column with a side stream product.**RR (Ratio) XDT (mole fraction) XSB (mole fraction) Feed flow rate LS (lb mol/ hr) XSX (mole fraction) QB (BTU/ hr) XBT Determine the best loop pairing and calculate the Niederlinski Index for each subsystem considered. Module 5 – Controllability Analysis**3.2 The 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): Module 5 – Controllability Analysis**Distillation column used in separating ethanol and water**Overhead mole fraction ethanol (y1) Overhead reflux flow rate (u1) Temperature on tray #19 (y3) Feed flow rate (d) Mole fraction of ethanol in the side stream (y2) Reboiler steam pressure (u2) Designa steadystatedecouplerusing the generalizedapproach, withGR(0) chosenasDiag[G(0)]. Module 5 – Controllability Analysis**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 f1, f4, f5 , f7and f8 should be used to control the outlets temperature TC1,TH1,TH2. H1 T6 T1 395 K 575 K f5 TH1 m5 HE 1 Q1 A1 TD1 HE 3 Q3 A3 TD3 C1A1 365 K C1A f4 m4 C2 T3 C1 400 K f1 m1 TC1 300 K T5 C3 T4 C1B HE 2 Q2 A2 TD2 m7 f7 HE 4 Q4 A4 TD4 C1B1 358 K m8 f8 TH2 T7 718 K T2 398 K H2 Module 5 – Controllability Analysis**The gain array obtained for the system is:**TC1 TH1 TH2 f1 f8 f7 f4 f5 Choosethebestpairing, usingtheRGAandSVD. Module 5 – Controllability Analysis**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). Module 5 – Controllability Analysis