3) OBJECTIVE FUNCTION & DISTURBANCES Objective function:

1. N T N U N T N U QC,LP (D/F)s LC PC x LTLP DLP XC Comparison of energy savings (V ) of different systems (compared to the best of the non-integrated min LC a (A) (B) direct or indirect sequence), sharp split: propane-butane-pentane, = [7.98 3.99 1.00]. (A) (A) (AB) (AB) (ABC) (ABC) (ABC) Petlyuk (B) Z DS IS DSF DSB ISF ISB PF PB F (%) (BC) (BC) DHP (%) LTHP (%) (%) (%) (%) (%) (%) (%) [1/3 1/3 1/3] -0.44 0.00 34.86 34.86 34.86 36.54 42.31 51.77 60.70 [0.7 0.15 0.15] 0.00 -4.05 13.87 13.87 13.87 14.11 43.05 16.11 49.71 [0.1 0.45 0.45] -3.79 0.00 39.20 46.47 46.47 39.20 39.20 66.66 66.66 (C) (B) (C) (C) XC [0.15 0.7 0.15] -0 . 05 0.00 42.47 49.13 49.13 42.47 42.47 70.17 70.37 [0.45 0.1 0.45] -1.29 0.00 20.85 20.85 20.85 22.00 42.90 28.89 50.39 [0.15 0.15 0.7] -10.70 0.00 35.08 40.08 40.08 35.08 35.08 57.64 58.20 LP HP SLP [0.45 0.45 0.1] 0.00 -2.41 31.83 31.83 31.83 32.22 42.78 49.02 60.54 F (A) (B) (A) (AB) (AB) (A) (ABC) BHP (ABC) LP LP HP HP (ABC) LP HP (B) (BC) (BC) LC LC (B) (C) (C) (C) QB,HP A XC BLP • H.K. Engelien and S. Skogestad • Norwegian University of Science and Technology, Department of Chemical Engineering, Trondheim, Norway Selecting Appropriate Control Variables for a Heat Integrated Distillation System with Prefractionator • INTRODUCTION • Classical separation schemes • ENERGY SAVINGS • Shortcut calculations for minimum vapour flowrate indicates that integrated prefractionator arrangements can have high energy savings- up to 70 %. • Direct split (DS) Indirect split (IS) Prefractionator • Examples of integrated separation schemes • DSF ISF PF • CASE STUDIED • Separation process: forward integrated prefractionator (PF) Separation: propane/butane/pentane • Feed data: zF = [0.15 0.70 0.15] Column Stages: NHP = 20 • F = 300 mol/s NLP = 40 • q = 1 • Aim: Identify good control variables CAN THESE SAVINGS BE ACHIEVED IN PRACTICE ? • 4) OPTIMIZATION RESULTS • 4 active constraints: PLP = 1 bar xB,S = 0.99 xC,B = 0.99 A = Amax • 4 levels with no steady state effect • 1 match heat duty in integrated reboiler/condenser •  Implement active constraint control for these variables •  Leaves a system with (11-9) = 2 DOF for which the choice of control variable is not clear • Fix concentration in top of LP column (xA,D = 0.99)  leaves 1 DOF for self-optimizing control • SELF-OPTIMIZING CONTROL: • The method of self-optimizing control involves a search for the variables that, when kept constant, indirectly lead to near-optimal operation with acceptableloss. • 1) DOF ANALYSIS & CONSTRAINTS • 11 DOF’s:HP columnLP column • boilup (QB,HP) boilup (QB,LP) • condensation rate (QC,HP) condensation rate (QC,LP) • reflux (LTHP) reflux (LTLP) • distillate (DHP) distillate (DLP) • bottom flowrate (BHP) bottom flowrate (BLP) • sidestream flowrate (SLP) • Process Constraints: • The pressure in the LP column should be  1 bar. • The pressure in the HP column should be  15 bar. • The reboiler duty in the LP column (QB,LP) = condenser duty in the HP column (QC,HP) • The product purities (xA,D), (xB,S) and (xC,B) should be  99 mol%. • The area in the combined reboiler/condenser should be  Amax. 5) LOSS CALCULATIONS Calculate loss: L = (Jopt - J) for a number of variables at the selected disturbances and identify the best variable(s) for control, where the loss is small. Keeping different control variables constant at the nominal value will increase the duty required when there are disturbances. The table shows the extra duty as a percentage of the optimal duty at the various disturbances. 1 % extra duty cost corresponds to about $ 25 000 per year Best control variable: DHP/F (or BHP/F) Implementation error for DHP/F is 2.9 % • 2) SIMULATIONS • Main assumptions behind model: • Simple equilibrium relationship: K-values • Partial pressure calculated from Antoine equation • Amax calculated from optimal steady state solution when (Tcond,HP - Treb,LP) = 5oC • Constant pressure in each column Optimization is done in Matlab/Tomlab, using SOL optimization routines. 6) PROPOSED CONTROL STRUCTURE Suggested control structure (for illustration): Control: Distillate composition (xD,LP) Sidestream composition (xS,LP) Bottom stream composition (xB,LP) Pressure in LP column (PLP) Self-optimizing variable: Ratio of distillate to feed flow DHP/F • 3) OBJECTIVE FUNCTION & DISTURBANCES • Objective function: • Assuming product prices are the same, pD = pS = pB and (p-pF) = p’, with F given and Q = H·V, gives: • Disturbances: • Feedrate disturbances, F± 20 % • Composition disturbances, zB,F ± 0.1 (mole fraction) • REFERENCES • Bildea, C.S., Dimian, A.C., 1999, Interaction between design and control of a heat-integrated distillation system with prefractionator, Tans IChemE, Vol. 77, Part A, 597-608. • Cheng, H. C., Luyben, W., 1985, Heat-integrated distillation columns for ternary separations, Ind. Eng. Chem. Process Des. Dev., 24, 707-713. • Ding, S.S., Luyben, W., 1990, Control of a heat-integrated complex distillation configuration, Ind. Eng. Chem. Res.¸ 29, 1240-1249. • Halvorsen, I.J., 1999, Optimal operation of Petlyuk distillation: steady-state behavior, J. Process Control, 9, 407-424. • King, C.J., 1980, Separation Processes, McGraw-Hill Book Co. • Rev, E., Emtir, M., Szitkai, Z., Mizsey, P., Fonyo, Z, 'Energy savings of integrated and coupled distillation systems', Computers and Chemical Engineering, 2001, 25, pp. 119-140 • Skogestad, S., 2000, Plantwide control: the search for the self-optimizing control structure, J. Proc. Control, Vol.10, 487-507. • CONCLUSIONS • The integrated prefractionator arrangement can give high energy savings compared with non- integrated arrangements. • Good control systems are important in order to achieve the expected energy savings. • The self-optimization method has been used as a method for selecting the control variables. • Control variables were identifies that will give low energy losses during operation • CONTACT INFORMATION • Prof.. Sigurd Skogestad Hilde K. Engelien • Department of Chemical Engineering Department of Chemical Engineering • NTNU NTNU • Sigurd.Skogestad@chemeng.ntnu.no Hilde.Engelien@chemeng.ntnu.no • http://www.nt.ntnu.no/users/skoge/