Selecting Appropriate Control Variables for a
Heat Integrated Distillation System with Prefractionator
H.K. Engelien and S. Skogestad
NTNU
NTNU
Norwegian University of Science and Technology, Department of Chemical Engineering, Trondheim, Norway
INTRODUCTION
ENERGY SAVINGS
Classical separation schemes
Direct split (DS)
Indirect split (IS)
Prefractionator
(A)
(B)
(A)
Shortcut calculations for minimum vapour flowrate indicates that integrated prefractionator arrangements can
have high energy savings- up to 70 %.
Comparison of energy savings (V min) of different systems (compared to the best of the non-integrated
direct or indirect sequence), sharp split: propane-butane-pentane, a = [7.98 3.99 1.00].
(A)
(AB)
(AB)
(ABC)
(ABC)
(ABC)
(C)
(C)
(B)
[1/3 1/3 1/3]
[0.7 0.15 0.15]
[0.1 0.45 0.45]
[0.15 0.7 0.15]
[0.45 0.1 0.45]
[0.15 0.15 0.7]
[0.45 0.45 0.1]
(C)
Examples of integrated separation schemes
DSF
ISF
PF
Petlyuk
DSF
DSB
ISF
ISB
(%)
(%)
(%)
(%)
(%)
(%)
(%)
-0.44
0.00
-3.79
-0.05
-1.29
-10.70
0.00
0.00
-4.05
0.00
0.00
0.00
0.00
-2.41
34.86
13.87
39.20
42.47
20.85
35.08
31.83
34.86
13.87
46.47
49.13
20.85
40.08
31.83
34.86
13.87
46.47
49.13
20.85
40.08
31.83
36.54
14.11
39.20
42.47
22.00
35.08
32.22
42.31
43.05
39.20
42.47
42.90
35.08
42.78
(ABC)
LP
(ABC)
LP
HP
LP
HP
(%)
60.70
49.71
66.66
70.37
50.39
58.20
60.54
(C)
(B)
(C)
Separation process:
forward integrated prefractionator (PF)
Feed data:
zF
F
q
Aim:
Identify good control variables
Separation:
propane/butane/pentane
(B)
(BC)
(BC)
(C)
51.77
16.11
66.66
70.17
28.89
57.64
49.02
PB
(AB)
(AB)
(A)
PF
(%)
CASE STUDIED
(A)
(A)
(B)
HP
IS
(BC)
(BC)
(ABC)
DS
ZF
(B)
= [0.15 0.70 0.15]
= 300 mol/s
=1
Column Stages:
NHP
NLP
= 20
= 40
CAN THESE SAVINGS BE ACHIEVED IN PRACTICE ?
SELF-OPTIMIZING CONTROL:
4) OPTIMIZATION RESULTS
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.
4 active constraints:
PLP = 1 bar
4 levels with no steady state effect
1 match heat duty in integrated reboiler/condenser
1) DOF ANALYSIS & CONSTRAINTS
 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
11 DOF’s:
HP column
boilup (QB,HP)
condensation rate (QC,HP)
reflux (LTHP)
distillate (DHP)
bottom flowrate (BHP)
LP column
boilup (QB,LP)
condensation rate (QC,LP)
reflux (LTLP)
distillate (DLP)
bottom flowrate (BLP)
sidestream flowrate (SLP)
A = 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
Extra cost of duty as the percentage of the optimal duty for each of the disturbances
nominal value will increase the duty required when
Control variable, c
Percent of optimal duty
Percent of optimal duty
there are disturbances. The table shows the extra duty
(feedrate disturbance)
(composition disturbance)
F + 20 %
F - 20%
z + 0.1
z - 0.1
as a percentage of the optimal duty at the various
P
2.50
0.95
21.94
71.70
disturbances.
LT /F
0.02
0.01
0.99
Infeasible
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.
F,B
F,B
HP
HP
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
xC,B = 0.99
Fix concentration in top of LP column (xA,D = 0.99)  leaves 1 DOF for self-optimizing control
Process Constraints:





xB,S = 0.99
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
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 %
6) PROPOSED CONTROL STRUCTURE
Optimization is done in Matlab/Tomlab, using SOL optimization routines.
QC,LP
Suggested control structure (for illustration):
(D/F)s
3) OBJECTIVE FUNCTION & DISTURBANCES
LC
PC
x
LTLP
DLP
XC
LC
Objective function:
J = pD D + pS S + pB B - pF F - pQQ
LTHP
XC
Assuming product prices are the same, pD = pS = pB and (p-pF) = p’, with F given and Q = H·V, gives:
J '= - V
DHP
LP
HP
Control:
Distillate composition (xD,LP)
Sidestream composition (xS,LP)
Bottom stream composition (xB,LP)
Pressure in LP column (PLP)
SLP
F
Self-optimizing variable:
Ratio of distillate to feed flow DHP/F
BHP
LC
LC
Disturbances:
QB,HP
A


Feedrate disturbances, F± 20 %
Composition disturbances, zB,F ± 0.1 (mole fraction)
BLP
REFERENCES
CONCLUSIONS




The integrated prefractionator arrangement can give high energy savings compared with nonintegrated 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
Department of Chemical Engineering
NTNU
Sigurd.Skogestad@chemeng.ntnu.no
http://www.nt.ntnu.no/users/skoge/
XC
Hilde K. Engelien
Department of Chemical Engineering
NTNU
Hilde.Engelien@chemeng.ntnu.no
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, 407424.
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.