- Email: [email protected]
Distillation Column Control Benchmarks: Four Typical Problems
Copyright © IF AC Dynamics and Control of Chemical Reactors (DYCORD+'95), Copenhagen, Denmark, 1995
DISTILLATION COLUMN CONTROL BENCHMARKS: Four Typical Problems A.
Koggersb~l
J~rgensen
and S. Bay
Department of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark.
Abstract: An industrial size distiUation plant is suggested as a benchmark for different distillation control problems. The problems range from simple one point control , via two point control over a sidestrearn control problem to optimizing control. The plant is fed with a mixture which is almost binary, but with a slight impurity. A range of industrially relevant disturbances are defined , and performance requirements are specified. The choise of model representation and method is left open to the participants. A nonlinear simulation model is made available. Keywords: Benchmark examples; Computer Simulation; Mathematical models .
CV9
1. II\'TRODUCTION
P;.
Expansion valve
Several distillation process models have been provided in the Iitterature in the form of transfer function models , e.g. the SHELL-Control Problem (P rett and Morari , 1987) . The emergence of robust control theory have demonstrated that often model uncertainty may be performance limiting in addition to limitations introduced by process dynamics such as right half plane transmission zeros and by disturbance characteristics. Since there have been little consensus thus far with proposing uncertainty models for distillation control problems it is suggested in this paper to adopt an industrial size distillation plant as a benchmark for control studies. In order to investigate the influence of different control problems upon different aspects of solution approaches four different control problems are defined.
Col
l' D
F
Secondary cve condenser B
Fig. 1. Distillation plant flowsheet.
The purpose of this paper is to concentrate on description of the four control problems problems , disturbances and control rquirements. First however th e plant is briefly introduced with available actuators and measurements .
An experimentally validated simulation model has been develop ed (Koggersb01 and J0rgensen , 1995) and used for numerous studies of column operation and column control. Koggersb01 and J crgensen (1992a+b) investigated dynamics and control configurations for the plant operated both as a two-product binary column and as a ternary sidestream column. Correa and J0rgensen (1993) looked at the column as part of a two-column heterogeneous azeotropic distillation process . They compared performance of different control strategies. Varga et al. (1995) studied model representations for control of the column.
2. PLA!'iT DESCRIPTIOI\' Figure 1 shows a flowsheet of the process. The column has 19 sieve trays , a thermosiphon reboiler , a total condenser and a reflux drum . It separates a mixture of methanol and isopropanol with a low concentration water impurity. This impurity will mainly escape the column through the bottom product . The heat pump has an expansion valve which throttles high pressure liq323
uid freon (R114) to a lower pressure (Pd suitable for evaporation in the condenser. After the condenser there is a control valve (CV9) by which the freon vapour flowrate can be manipulated . After superheating the vapour , the compressor elevates the pressure to a high pressure (PH) suitable for condensation in the reboiler. A small part of the condensation takes place in a secondary condenser which by a cooling water circuit is connected to a set of air-fan coolers. The cooling rate can be manipulated by the control valve CV8 , thus controlling PH . Through a storage tank (Rec) and the pre-compression heat exchanger the freon circuit is closed at the expansion valve.
Qw is electrical energy consumption of the heat pump compressor. XD , XB, and z are molefractions of methanol in the distillate , of isopropanol in the bottom product, and of methanol in the feed stream . Prize functions for the four terms are as follows : CD
0.31 · XD
-
0.23 [DKr/mole] (2)
CB
1.12 · XB
-
0.85 [DKr/mole] (3)
CF
0.08 - 0.05 · z [DKr/mole]
(4)
0.11 [DKr/MJ]
(5)
Cw
The control requirements are to:
For this process four distillation control problems are proposed :
• Keep the specified concentrations within specified hard limits. • Ensure zero steady state control error. • Preferably obtain fast settling . • Preferably have an over-/undershoot less than 25% of the hard limits .
1. One point control, where the top concentration should be kept. The bottom concentration should satisfy much looser limits. 2. Two point control, where both ends should satisfy equally tight limits . 3. Sidestream control problem , as case 2, but with a sidestream where also performance requirements on the sidestream should be satisfied . 4. Optimizing control of one of the above cases .
A mathematical simulation model is available by E-mail [email protected]. The code is in FORTRAN and provides a full simulation, where the controller may be introduced into the CONTROL subroutine, which is executed every 30 - 60 seconds real time on the plant. The mathematical model is under test and preliminary results therefrom are available in Koggersb!1ll and J !1lrgensen (1995) . Further results will be available , especially on delays in boil-up and reflux flowrates .
3. BENCHMARK PROBLEMS
The objectives are to:
The problem statement requests a control configuration and a control design for the selected control problem . The participants are allowed to :
• Reject disturbances in feed concentration and flowrate. Two process disturbance stress levels are specified . • Satisfy setpoint tracking requirements. On the level beneath purity control, the requirement is to be able to move the process on a smoth curve between any two points in the operating region (Fig . 2) . On the purity control level the requirement is to be able to move smoothly between different purity levels in both products independently. • The purpose of having a sidestream should be to purge water , and when manipulated , the objective should be to assist in disturbance rejection while minimizing the loss of valuable products through the sidedraw. • The objective for optimizing control should be to maximize the following function , e.g. with respect to variations in the prize of electrical power around the clock.
J
D + CB(XB) ' B cF(z)·F-cw · Qw
1. Use any design method. 2. Use different methods (or retune) for different stress levels . 3. Filter setpoint changes, as long as the hind limits are observed. 4. Add extra stimulation to the setpoint, as long as the hard limits are observed. 5. Perform identification prior to and/or during control.
Since any mathematical model contains simplifications, it may also be feasible to test a few most promising controllers in practice on the plant .
CD(XD) '
4. OPERATING CONDITIONS
(1)
where the four contributions are: Value of top product, value of bottom product , cost of feed stream (fuel value), and cost of electrical power. D , B, and F are distillate , bottom and feed flowrates in moles per second,
4.1. Operatmg point
The operating point proposed for purity-control investigations is defined as follows : 324
J
Vapour flow (m /h. condensed) 2 . 2~
They enter the process simultaneously through feed ftowrate and feed composition in the followmg manner:
-r----------r----r---=
1 .7~
F(t)
z(t)
+ AF . sin(wfast . t) Za + Az . sin(wsl ow ' t)
(8)
Fa
(9)
1.25
F( t) is volumetric feed flowrate and z( t) is feed concentration of the light key component. Three situations are considered : The nominal case and two enhanced stress levels . These are as follows .
0.75
0.25
Nominal case Stress level 1 Stress level 2
-t.,.-,~.....-+-,..,..,..~~~~~~....,...,...,....,..,...,....,..~,..,..........,...,.~"
30
50
70
90
110
Column pressure (kPa)
Fig. 2. Operating region of the plant. The region is limited by tray weeping , minimum PL, tray flooding , and maximum P L . Column pressure is measured on the top tray.
Feed ftowrate Feed composition : Methanol Isopropanol Water Product purities : Distillate Bottom , if controlled Column top pressure
3 .0
mole-% mole-% mole-%
97.5 97 .5 75 .0
mole-% mole-% kPa
5. REFERENCES Correa, R .G .; J(I!rgensen , S.B (1993); ' Dynamics and Control of Heterogeneous Azeotropic Distillation' ; Proceedings of IFAC World Congress 1993 vol. 1, pp . 55-58, Sidney , A ustralia .
Koggersb(l!l, A. ; J(I!rgensen , S.B. (1992a) ; ' Control Structures for a Sidestream Distillation Column Separating a Ternary Mixture '; Proceedings of IFAC Symposium DY-
Hard limits on product purities are ±0.5 mole-% . The feed stream is saturated liquid. When used , the sidestream is drawn as saturated liquid .
CORD+92, April 27-29'th, College Park, Maryland, USA, pp . 237- 24 2.
Koggersb(l!l , A. ; J(I!rgensen , S.B. (1992b) ; 'Dynamics and Control of a Distillation Column with a Sidestream '; Distillation and Ab-
4.2 . A ctuator limits
sorption, IChemE Symposium Series no . 128, pp .A429-A449.
Figure 2 shows the limits for boil-up in the possible range of column pressure . In addition there are the following hard limits to be observed.
Koggersb(l!l, A.; J(I!rgensen , S.B. (1995) ; ' Verification of a Distillation Column Simulation Benchmark'; Submitted for presentation at
Heat pump pressures :
PLar
p;;ar
Reflux flowrate , max . Distillate ftowrate , max . Bottom prod . ftowrate , max.
Az is low A z is high Az is high
Low and high amplitudes are defined relative to the disturbance free steady state inputs (Fa and za): Low is 5% , and high is 25%.
liters/min
49.5 49 .5 1.0
AF is low AF is low AF is high
600.0 1400.0 35 .0 8.0 8.0
kPa kPa liters/min liters/min liters/min
4.3 . Disturbances The disturbances to the process are considered to have two frequency contents : 211"/(120 min)
(6)
wfast
21T/(15 min)
(7)
Jun e 7-
Prett , D.M. ; Morari , M. (1987) ; 'Shell Process Control Workshop ', Butterworths , 1987. Varga, E.I .; Kovacs , G .Z.; J(I!rgensen , S.B.; Hangos , K.M. (1995) ; ' Robust Analysis of Distillation Column Dynamics ' ; Submitted for presentation at IFAC Symposium DYCORD+9S, June 7-9 'th , Helsingilr, Denmark.
Furthermore, the number of active cylinders in the compressor can be varied between 4 and 16 in steps of 2.
wsl ow
IFAC Symposium DYCORD+9S, 9 'th , H elsingflr, Denmark.
325
DISTILLATION COLUMN CONTROL BENCHMARKS: Four Typical Problems A.
Koggersb~l
J~rgensen
and S. Bay
Department of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark.
Abstract: An industrial size distiUation plant is suggested as a benchmark for different distillation control problems. The problems range from simple one point control , via two point control over a sidestrearn control problem to optimizing control. The plant is fed with a mixture which is almost binary, but with a slight impurity. A range of industrially relevant disturbances are defined , and performance requirements are specified. The choise of model representation and method is left open to the participants. A nonlinear simulation model is made available. Keywords: Benchmark examples; Computer Simulation; Mathematical models .
CV9
1. II\'TRODUCTION
P;.
Expansion valve
Several distillation process models have been provided in the Iitterature in the form of transfer function models , e.g. the SHELL-Control Problem (P rett and Morari , 1987) . The emergence of robust control theory have demonstrated that often model uncertainty may be performance limiting in addition to limitations introduced by process dynamics such as right half plane transmission zeros and by disturbance characteristics. Since there have been little consensus thus far with proposing uncertainty models for distillation control problems it is suggested in this paper to adopt an industrial size distillation plant as a benchmark for control studies. In order to investigate the influence of different control problems upon different aspects of solution approaches four different control problems are defined.
Col
l' D
F
Secondary cve condenser B
Fig. 1. Distillation plant flowsheet.
The purpose of this paper is to concentrate on description of the four control problems problems , disturbances and control rquirements. First however th e plant is briefly introduced with available actuators and measurements .
An experimentally validated simulation model has been develop ed (Koggersb01 and J0rgensen , 1995) and used for numerous studies of column operation and column control. Koggersb01 and J crgensen (1992a+b) investigated dynamics and control configurations for the plant operated both as a two-product binary column and as a ternary sidestream column. Correa and J0rgensen (1993) looked at the column as part of a two-column heterogeneous azeotropic distillation process . They compared performance of different control strategies. Varga et al. (1995) studied model representations for control of the column.
2. PLA!'iT DESCRIPTIOI\' Figure 1 shows a flowsheet of the process. The column has 19 sieve trays , a thermosiphon reboiler , a total condenser and a reflux drum . It separates a mixture of methanol and isopropanol with a low concentration water impurity. This impurity will mainly escape the column through the bottom product . The heat pump has an expansion valve which throttles high pressure liq323
uid freon (R114) to a lower pressure (Pd suitable for evaporation in the condenser. After the condenser there is a control valve (CV9) by which the freon vapour flowrate can be manipulated . After superheating the vapour , the compressor elevates the pressure to a high pressure (PH) suitable for condensation in the reboiler. A small part of the condensation takes place in a secondary condenser which by a cooling water circuit is connected to a set of air-fan coolers. The cooling rate can be manipulated by the control valve CV8 , thus controlling PH . Through a storage tank (Rec) and the pre-compression heat exchanger the freon circuit is closed at the expansion valve.
Qw is electrical energy consumption of the heat pump compressor. XD , XB, and z are molefractions of methanol in the distillate , of isopropanol in the bottom product, and of methanol in the feed stream . Prize functions for the four terms are as follows : CD
0.31 · XD
-
0.23 [DKr/mole] (2)
CB
1.12 · XB
-
0.85 [DKr/mole] (3)
CF
0.08 - 0.05 · z [DKr/mole]
(4)
0.11 [DKr/MJ]
(5)
Cw
The control requirements are to:
For this process four distillation control problems are proposed :
• Keep the specified concentrations within specified hard limits. • Ensure zero steady state control error. • Preferably obtain fast settling . • Preferably have an over-/undershoot less than 25% of the hard limits .
1. One point control, where the top concentration should be kept. The bottom concentration should satisfy much looser limits. 2. Two point control, where both ends should satisfy equally tight limits . 3. Sidestream control problem , as case 2, but with a sidestream where also performance requirements on the sidestream should be satisfied . 4. Optimizing control of one of the above cases .
A mathematical simulation model is available by E-mail [email protected]. The code is in FORTRAN and provides a full simulation, where the controller may be introduced into the CONTROL subroutine, which is executed every 30 - 60 seconds real time on the plant. The mathematical model is under test and preliminary results therefrom are available in Koggersb!1ll and J !1lrgensen (1995) . Further results will be available , especially on delays in boil-up and reflux flowrates .
3. BENCHMARK PROBLEMS
The objectives are to:
The problem statement requests a control configuration and a control design for the selected control problem . The participants are allowed to :
• Reject disturbances in feed concentration and flowrate. Two process disturbance stress levels are specified . • Satisfy setpoint tracking requirements. On the level beneath purity control, the requirement is to be able to move the process on a smoth curve between any two points in the operating region (Fig . 2) . On the purity control level the requirement is to be able to move smoothly between different purity levels in both products independently. • The purpose of having a sidestream should be to purge water , and when manipulated , the objective should be to assist in disturbance rejection while minimizing the loss of valuable products through the sidedraw. • The objective for optimizing control should be to maximize the following function , e.g. with respect to variations in the prize of electrical power around the clock.
J
D + CB(XB) ' B cF(z)·F-cw · Qw
1. Use any design method. 2. Use different methods (or retune) for different stress levels . 3. Filter setpoint changes, as long as the hind limits are observed. 4. Add extra stimulation to the setpoint, as long as the hard limits are observed. 5. Perform identification prior to and/or during control.
Since any mathematical model contains simplifications, it may also be feasible to test a few most promising controllers in practice on the plant .
CD(XD) '
4. OPERATING CONDITIONS
(1)
where the four contributions are: Value of top product, value of bottom product , cost of feed stream (fuel value), and cost of electrical power. D , B, and F are distillate , bottom and feed flowrates in moles per second,
4.1. Operatmg point
The operating point proposed for purity-control investigations is defined as follows : 324
J
Vapour flow (m /h. condensed) 2 . 2~
They enter the process simultaneously through feed ftowrate and feed composition in the followmg manner:
-r----------r----r---=
1 .7~
F(t)
z(t)
+ AF . sin(wfast . t) Za + Az . sin(wsl ow ' t)
(8)
Fa
(9)
1.25
F( t) is volumetric feed flowrate and z( t) is feed concentration of the light key component. Three situations are considered : The nominal case and two enhanced stress levels . These are as follows .
0.75
0.25
Nominal case Stress level 1 Stress level 2
-t.,.-,~.....-+-,..,..,..~~~~~~....,...,...,....,..,...,....,..~,..,..........,...,.~"
30
50
70
90
110
Column pressure (kPa)
Fig. 2. Operating region of the plant. The region is limited by tray weeping , minimum PL, tray flooding , and maximum P L . Column pressure is measured on the top tray.
Feed ftowrate Feed composition : Methanol Isopropanol Water Product purities : Distillate Bottom , if controlled Column top pressure
3 .0
mole-% mole-% mole-%
97.5 97 .5 75 .0
mole-% mole-% kPa
5. REFERENCES Correa, R .G .; J(I!rgensen , S.B (1993); ' Dynamics and Control of Heterogeneous Azeotropic Distillation' ; Proceedings of IFAC World Congress 1993 vol. 1, pp . 55-58, Sidney , A ustralia .
Koggersb(l!l, A. ; J(I!rgensen , S.B. (1992a) ; ' Control Structures for a Sidestream Distillation Column Separating a Ternary Mixture '; Proceedings of IFAC Symposium DY-
Hard limits on product purities are ±0.5 mole-% . The feed stream is saturated liquid. When used , the sidestream is drawn as saturated liquid .
CORD+92, April 27-29'th, College Park, Maryland, USA, pp . 237- 24 2.
Koggersb(l!l , A. ; J(I!rgensen , S.B. (1992b) ; 'Dynamics and Control of a Distillation Column with a Sidestream '; Distillation and Ab-
4.2 . A ctuator limits
sorption, IChemE Symposium Series no . 128, pp .A429-A449.
Figure 2 shows the limits for boil-up in the possible range of column pressure . In addition there are the following hard limits to be observed.
Koggersb(l!l, A.; J(I!rgensen , S.B. (1995) ; ' Verification of a Distillation Column Simulation Benchmark'; Submitted for presentation at
Heat pump pressures :
PLar
p;;ar
Reflux flowrate , max . Distillate ftowrate , max . Bottom prod . ftowrate , max.
Az is low A z is high Az is high
Low and high amplitudes are defined relative to the disturbance free steady state inputs (Fa and za): Low is 5% , and high is 25%.
liters/min
49.5 49 .5 1.0
AF is low AF is low AF is high
600.0 1400.0 35 .0 8.0 8.0
kPa kPa liters/min liters/min liters/min
4.3 . Disturbances The disturbances to the process are considered to have two frequency contents : 211"/(120 min)
(6)
wfast
21T/(15 min)
(7)
Jun e 7-
Prett , D.M. ; Morari , M. (1987) ; 'Shell Process Control Workshop ', Butterworths , 1987. Varga, E.I .; Kovacs , G .Z.; J(I!rgensen , S.B.; Hangos , K.M. (1995) ; ' Robust Analysis of Distillation Column Dynamics ' ; Submitted for presentation at IFAC Symposium DYCORD+9S, June 7-9 'th , Helsingilr, Denmark.
Furthermore, the number of active cylinders in the compressor can be varied between 4 and 16 in steps of 2.
wsl ow
IFAC Symposium DYCORD+9S, 9 'th , H elsingflr, Denmark.
325