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)

Selecting Appropriate Control Variables for a Heat Integrated Distillation System with Prefractionator

INTRODUCTION

Classical separation schemes

H.K. Engelien and S. Skogestad

Norwegian University of Science and Technology, Department of Chemical Engineering, Trondheim, Norway

ENERGY SAVINGS

Shortcut calculations for minimum vapour flowrate indicates that integrated prefractionator arrangements can have high energy savings- up to 70 %.

CASE STUDIED

Separation process: forward integrated prefractionator (PF) Separation: propane/butane/pentane

Feed data: zF = [0.15 0.70 0.15] Column Stages: NHP= 20F = 300 mol/s NLP = 40q = 1

Aim: Identify good control variables

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 acceptable loss.

1) DOF ANALYSIS & CONSTRAINTS

11 DOF’s: HP column LP columnboilup (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.

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.

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. EngelienDepartment of Chemical Engineering Department of Chemical EngineeringNTNU NTNUSigurd.Skogestad@chemeng.ntnu.no Hilde.Engelien@chemeng.ntnu.nohttp://www.nt.ntnu.no/users/skoge/

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.

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.

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 effect1 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

6) PROPOSED CONTROL STRUCTURE

N T N U N T N U

Examples of integrated separation schemes

Direct split (DS) Indirect split (IS) Prefractionator

(ABC)

(A)

(B)

(C)

(BC)

(AB)(B)

(C)

(BC)

(A)

(ABC)

HP LP

(B)

(C)

(BC)

(A)

(ABC)

(A)

(B)

(ABC) HP LP

(C)

(AB)

(ABC)

(A)

(B)(C)

(AB)

Comparison of energy savings (Vmin) of different systems (compared to the best of the non-integrateddirect or indirect sequence), sharp split: propane-butane-pentane, = [7.98 3.99 1.00].

ZF DS

(%)

IS

(%)

Petlyuk

(%)

DSF

(%)

DSB

(%)

ISF

(%)

ISB

(%)

PF(%)

PB

(%)[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[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[0.45 0.45 0.1] 0.00 -2.41 31.83 31.83 31.83 32.22 42.78 49.02 60.54

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

(A)

HP LP(B)

(C)

(BC)

(AB)

(ABC)

DSF ISF PF

D S B F QJ p D p S p B p F p Q= + + - -

'J V=-

DLP

SLP

QB,HP

LPHP

PC LC

XC

XC

LTHPDHP

BHP

BLP

QC,LP

A

LC

x

(D/F)s

LC

XC

LC

LTLP

F

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 %

Extra cost of duty as the percentage of the optimal duty for each of the disturbances

Percent of optimal duty

(feedrate disturbance)

Percent of optimal duty

(composition disturbance)

Control variable, c

F + 20 % F - 20% zF,B + 0.1 zF,B - 0.1

PHP 2.50 0.95 21.94 71.70

LTHP/F 0.02 0.01 0.99 Infeasible

DHP/F 0.03 0.02 1.3 1.47

xBD,HP 0.02 0.06 26.96 38.71

QB,HP Infeasible 24.55 Infeasible 2.44

DHP 8.40 19.14 1.33 1.41

BHP 20.80 28.11 1.33 1.41

QB,HP/F Infeasible Infeasible Infeasible Infeasible

BHP/F 0.03 0.02 1.30 1.47

xBB,HP 0.02 0.14 40.92 Infeasible

LTHP Infeasible 1.99 0.97 Infeasible

T4,HP 3.88 1.09 26.49 Infeasible

CAN THESE SAVINGS BE ACHIEVED IN PRACTICE ?