1 M. Panahi ’Plantwide Control for Economically Optimal Operation of Chemical Plants’ Plantwide...

1M. Panahi ’Plantwide Control for Economically Optimal Operation of Chemical Plants’

Plantwide Control for Economically Optimal Operation of Chemical Plants

- Applications to GTL plants and CO2 capturing processes

Mehdi PanahiPhD defense presentation

December 1st, 2011Trondheim


Outline

Ch.2 Introduction

Ch.4 Economically optimal operation of CO2 capturing process; selection of controlled variables

Ch.5 Economically optimal operation of CO2 capturing process; design control layers

Ch.6 Modeling and optimization of natural gas to liquids (GTL) process

Ch.7 Self-optimizing method for selection of controlled variables for GTL process

Ch.8 Conclusions and future works


Outline

Ch.2 Introduction







Skogestad plantwide control procedure

I Top Down • Step 1: Identify degrees of freedom (MVs)• Step 2: Define operational objectives (optimal operation)

– Cost function J (to be minimized)– Operational constraints

• Step 3: Select primary controlled variables CV1s (Self-optimizing) • Step 4: Where set the production rate? (Inventory control)

II Bottom Up

• Step 5: Regulatory / stabilizing control (PID layer)– What more to control (CV2s; local CVs)?– Pairing of inputs and outputs

• Step 6: Supervisory control (MPC layer)• Step 7: Real-time optimization


Mode I: maximize efficiency

Mode II: maximize throughput

Optimal Operation

Self-optimizing control is when we can achieve acceptable loss with constant setpoint values for the controlled variables without the need to reoptimize the plant when disturbances occur


Selection of CVs: Self-optimizing control procedure

Step 3-1: Define an objective function and constraints

Step 3-2: Degrees of freedom (DOFs)

Step 3-3: Disturbances

Step 3-4: Optimization (nominally and with disturbances)

Step 3-5: Identification of controlled variables (CVs) for

unconstrained DOFs

Step 3-6: Evaluation of loss


Maximum gain rule for selection the best CVs

Let G denote the steady-state gain matrix from inputs u (unconstrained degrees of freedom) to outputs z (candidate controlled variables). Scale the outputs using S1

1i

1S =diag

span(z )

i i i,opt i,opt id,e d e

span(z )= max z -z = max e (d)+ max e

max 2 -1/21 uu

1 1L =

2 σ (S GJ )

For scalar case, which usually happens in many cases, the maximum expected loss is:

uumax 2

1

J 1L =

2 S G

Maximum gain rule is useful for prescreening the sets of best controlled variables


Exact local method for selection the best CVs

21max. Loss= σ(M)

2-11/2 y

uu nM=J G (FW W )d

y -1 yuu ud dF=G J J -G

opt.ΔyF=

ΔdF is optimal sensitivity of the measurements with respect to disturbances;


Applications of plantwide procedure to two important processes

1. Post-combustion CO2 capturing processes (Chapters 3, 4 and 5)

2. Converting of natural gas to liquid hydrocarbons (Chapters 6 and 7)


An amine absorption/stripping CO2 capturing process*

Dependency of equivalent energy in CO2 capture plant verses recycle amine flowrate

*Figure from: Toshiba (2008). Toshiba to Build Pilot Plant to Test CO2 Capture Technology. http://www.japanfs.org/en/pages/028843.html.

Importance of optimal operation for CO2 capturing process


Gas commercialization options and situation of GTL processes

A simple flowsheet of a GTL process


Outline

Ch.2 Introduction







Economically optimal operation of CO2 capturing

Absorber

Stripper

Pump 1 Reboiler

V-6

Rich/Lean Exchanger

Surge TankPump 2

V-8Condenser

Cooler

V-5

V-2

V-4

V-9

V-3

Steam

Cooling Water in

Amine Makeup

Water Make up

Flue Gas from Power

Plant

V-7

To Stack

CO2

Condensate

Cooling Water out

Cooling Water out

Cooling Water in

n=1n=1

n=15

n=20

V-1

V-10

Step 1. Objective function:

min. (energy cost + cost of released CO2 to the air)

Steps 5&6. Exact Local method: The candidate CV set that imposes the minimum worst case loss to the objective function

Step 2. 10 steady-state degrees of freedom

Step 3. 3 main disturbances

Step 4. Optimization4 equality constraints and 2 inequality

2 unconstrained degrees of freedom;10-4-4=2


Exact local method for selection of the best CVs

39 candidate CVs- 15 possible tray temperature in the absorber- 20 possible tray temperature in the stripper- CO2 recovery in the absorber and CO2 content at the bottom of the stripper- Recycle amine flowrate and reboiler duty

The best self-optimizing CV set in region I: CO2 recovery (95.26%) and temperature of tray no. 16 in the stripper

These CVs are not necessarily the best when new constraints meet

Applying a bidirectional branch and bound algorithm for finding the best CVs


Optimal operational regions as function of feedrate

Region I. Nominal feedrate

Region II. Feedrate >+20%: Max. Heat constraint

Region III. Feedrate >+51%: Min. CO2 recovery constraint


Proposed control structure with given flue gas flowrate (region I)


Region II: in presence of large flowrates of flue gas (+30%)

Flowrateof flue gas (kmol/hr)

Pumpsduty

(kW)

Self-optimizing CVs in region I CoolerDuty(kW)

Reboilerduty(kW)

Objectivefunction

(USD/ton)CO2 recovery

%

Temperatureof

tray no. 16°C

Optimal nominal point

219.3 3.85 95.26 106.9 321.90 1161 2.49

+5% feedrate 230.3 4.24 95.26 106.9 347.3 1222 2.49

+10% feedrate 241.2 4.22 95.26 106.9 371.0 1279 2.49

+15% feedrate 252.2 4.64 95.26 106.9 473.3 1339 2.49

+19.38% feedrate,reboiler duty

saturates

261.8 4.56(+18.44%)

95.26 106.9 419.4 (+30.29%)

1393(+20%)

2.50

+30% feedrate (reoptimized)

285.1 4.61 91.60 103.3 359.3 1393 2.65

Saturation of reboiler duty (new operations region, region II); one unconstrained degree of freedom left

Maximum gain rule for finding the best CV: 37 candidates

Temp. of tray no. 13 in the stripper: the largest scaled gain


Proposed control structure with given flue gas flowrate (region I)


Proposed control structure with given flue gas flowrate (region II)

Reboiler duty at the maximum


Region III: reaching the minimum allowable CO2 recovery

Flowrateof

flue gas (kmol/hr)

Pumps Duty(kW)

CO2

recovery %

Self-optimizingCV

in region II

Cooler Duty(kW)

Reboiler Duty(kW)

Objective function

(USD/ton)

Temperatureof tray 13

°C

Optimal nominal case in +30% feedrate

285.1 4.61 91.60 109 359.3 1393 2.65

+40% feedrate 307.02 4.58 86.46 109 315.5 1393 2.97

+50% feedrate 328.95 4.55 81.31 109 290.3 1393 3.31

+52.78% feedrate,reach to minimum

CO2 recovery

335.1 4.54 80 109 284.6 1393 3.39

A controller needed to set the flue gas flowrate


Outline

Ch.2 Introduction







Design of the control layers

Regulatory layer: Control of secondary (stabilizing) CVs (CV2s), PID loops • Absorber bottom level,

• Stripper (distillation column) temperature,

• Stripper bottom level,

• Stripper top level,

• Stripper pressure,

• Recycle surge tank: inventories of water and amine,

• Absorber liquid feed temperature.

Supervisory (economic) control layer: Control of the primary (economic) CVs (CV1s), MPC

• CO2 recovery in the absorber,• Temperature at tray 16 in the stripper,• Condenser temperature.


RGA analysis for selection of pairings

2 2

dyn. -2s

2 2

6.85s+1.74 -0.76s 0.038

2400s +107s+119.7s +11.4s+1G (s)=(-9.51s-1.02)e 0.45s+0.0754

218s +17.3s+1 205s +18.8s+1

dyn.RGA (0)=0.77 0.23

0.23 0.77

10-3

10-2

10-1

100

101

102

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Frequency [rad/min]

||RG

A -

I|| su

m

Diagonal pairing alt.1

Off-diagonal pairing alt.2Recycle amine

Reboiler

dutyCO2 recovery

Temp. no.16 in the stripper

2SS

0.5232 1.48G 10

8.47 5.17

SSRGA =0.27 1.27

1.27 0.27

1. Dynamic RGA

2. Steady-State RGA


”Break through” of CO2 at the top of the absorber (UniSim simulation)

Liquid mole fraction of CO2 in trays of the Absorber

0,015

0,02

0,025

0,03

0,035

0,04

0,045

0,05

0,055

0 50 100 150 200 250 300 350 400 450

Time (min)

mo

le f

rac

tio

n

tray 15

tray 14

tray 13

tray 12

tray 11

tray 10

tray 9

tray 8

tray 7

tray 6

tray 5

tray 4

tray 3

tray 2

tray 1

tray 1

tray 15


Proposed control structure with given flue gas flowrate, Alternative 1


Proposed control structure with given flue gas flowrate,Alternative 2 (reverse pairing)


Proposed control structure in region II,Alternative 3


Modified alternative 2 Modified Alternative 2: Alternative 4


Control of self-optimizing CVs using a multivariable controller


Performance of the proposed control structure, Alternative 1






Performance of the proposed control structure, MPC


• Alternative 1 is optimal in region I, but fails in region II

• Alternative 2 handles regions I (optimal) and II (close to optimal), but more interactions in region I compare to Alternative 1. No need for switching

• Alternative 3 is optimal in region II. Need for switching

• Alternative 4 is modified Alternative 2 ,results in less interactions. No need for switching

• MPC, similar performance to Alternatives 2 & 4

Comparison of different alternatives

Alternative 4 is recommended for implementation in practice


Outline

Ch.2 Introduction







A simple flowsheet of GTL process

CH4 CO+H2(CH2)n

CO+H2+CH4

CO2

(CH2)n


Auto-thermal reformer (ATR) reactions

2n

Oxidation of methane:

Steam reforming of methane:

Shift Reaction:

4 2 2

32

2CH O CO H O

4 2 23CH H O CO H

2 2 2CO H O CO H

( )2n m 2 2

mC H +nH O n H +nCO

2 4 2CO+3H CH +H O

2 2 2CO+H O CO +H

Pre-reformer reactionsConverting higher hydrocarbons

than methane, For

Methanation

Shift Reaction

Fischer-Tropsch (FT) reactions

2 2 22 (- -)nnCO nH CH nH O


Fischer-Tropsch (FT) reactor

2 2 22 (- -)nnCO nH CH nH O

Simulation of a slurry bubble column reactor (SBCR)

Reactions:

Kinetics (the model developed by Iglesia et al):

2 4

4

8 0.05

5

1.08 10( )g-atom surface metal. s1 3.3 10

H CO CH

CHCO

P P molr

P

2

8 0.6 0.65

5

1.96 10( )g-atom surface metal. s1 3.3 10

H CO COCO

CO

P P molr

P

FT products distribution (ASF model): 2 1(1 ) nnw n

41 reactions: 21 reactions for CnH2n+2 and 20 reactions for CnH2n

FT products: C1, C2, C3-C4 (LPG), C5-C11 (Naphtha, Gasoline), C12-C20 (Diesel), C21+ (wax)


Detailed flowsheet of GTL process (UniSim)

Heater

Natural Gas8195 kmol/hr3000 kPa, 40 °CCH4:0.955C2H6:0.030C3H8:0.005n-C4H10:0.004N2:0.006

Pre-Reformer

Sep

ara

tor

CO

2

Rem

ov

al

Steam

Pure Oxygen(from ASU)5236 kmol/hr

Water8589 kmol/hr

Fired Heater

Autothermal Reformer

(ATR)

FT Reactor

3-Phase Separator

Compressor

MP Saturated Steam

48887 kmol/hr252 °C, 4000 kPa

MP Steam Light Ends

Purge to fired heater (as fuel)

392 kmol/hr

Water38°C

4743 koml/hr

Tail Gas12673 kmol/hrCH4: 0.3587CO: 0.1454H2: 0.2142N2: 0.1173CO2: 0.0838H2O: 0.0024Other: 0.0782

MP Steam

Syngas35100 kmol/hr

Vapor

Liquid

CO2

936 kmol/hr

To Upgrading Unit721 kmol/hr, 30°C(141.4 m3/hr)vol. mole fractionLPG: 0.0468

Naphtha/Gasoline: 0.3839

Diesel: 0.3216

Wax: 0.2242

Other: 0.0235

To fired heater (not shown) to produce superheat steam

ASU Turbines

Superheated Steam

Extra Steam

27020 kmol/hr

Water

Natural Gas (fuel)

2937 kmol/hr3000 kPa

200 °C

675 °C

5204 kmol/hr455 °C, 3000 kPa

1030 °C

16663 kmol/hr400 °C, 4000 kPa 10 kPa

210°C2000 kPa

210°C

Water9736 kmol/hr


4 2

0.4

10.6

12 25

2

22 2 19 2

20000.55

1 1 1 1 1 116 [ 2 ( ) ... 25 ( )]

16 1 30 1 28 1 352 1 350

(1 ) 2000(1 ) 1 1 1 1 1 1

16 [ 2(2 (1 ) )( ) ... 25(1 2 3 ...20 )(1 ) ( )]16 1 30 1 28 1 352 1 350

CH H

CO CO

r P wwr P w w

0.02 0.03 0.04 0.05 0.06 0.070.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

Left hand side value in 6.12

Val

ue

of

real

ro

ots

Real roots α as a function of the selectivity (1.2 ≤ H2/CO ≤ 2.15)

1) α1

2) α2

3) Constant α = 0.9 (α3)

2

(0.2332 0.633)[1 0.0039( 533)]CO

CO H

yT

y y

Different methods for calculation of α


FT reactor performance (single pass) at H2/CO=2 feed for

α1, α2 and α3

parameter α1 α2 α3

CO conversion, % 83.56 86.52 86.97

H2 conversion, % 90.98 91.82 91.97

CH4 formation (kg/kgcat.hr) 0.0106 0.011 0.011

Other hydrocarbons formation (kg/kgcat.hr)

0.1877 0.1924 0.1924


FT Products distribution when α1 is used






Dependency of different α calculation methods vs. feed H2/CO


Optimization formulation

Objective function

Variable income (P): sales revenue – variable costs

Steady-state degrees of freedom1. H2O/C (fresh + recycled hydrocarbons to pre-reformer)

2. O2/C (hydrocarbons into ATR)

3. Fired heater duty

4. CO2 recovery percentage

5. Purge ratio

6. Recycle ratio to FT reactor

Operational constraints1. Molar ratio H2O/C ≥ 0.3

2. ATR exit temperature ≤ 1030ºC, active at the max.

3. Inlet temperature to ATR ≤ 675ºC, active at the max.

4. The purge ratio is optimally around 2%, it is bounded at a higher value, active at the min.


Optimality of objective function (α2 model) with respect to decision variables and active constraints, wax price= 0.63 USD/kg


Outline

Ch.2 Introduction







Optimal Operation of GTL process

- Mode I: Natural gas is given

- Mode II: Natural gas is also a degree of freedom (maximum throughput)


Process flowsheet of GTL process with data for optimal nominal point (mode I)

Heater

Natural Gas8195 kmol/hrCH4:0.955C2H6:0.030C3H8:0.005n-C4H10:0.004N2:0.006

Pre-Reformer

Se

pa

rato

r

CO

2

Re

mo

va

l

Steam

Oxygen(from ASU)5190 kmol/hr

Water8560 kmol/hr

Fired Heater


(ATR)

FT Reactor

3-Phase Separator

Compressor I0.47 MW

HP Saturatied Steam

Light Ends

Purge to fired heater (as fuel)325 kmol/hr

Water906 kmol/hr

Tail Gas10846 kmol/hr

MP Steam

Syngas34627 kmol/hr

Vapor210°C

2500 kPa

Liquid

CO2906 kmol/hr

Liquid fuels to upgrading unit: 751 kmol/hr (144 m3/hr)vol. mole fractions:LPG: 0.0525Naphtha/Gasoline: 0.3759Diesel: 0.3156 Wax: 0.2257


ASU TurbinesSuperheated Steam

Extra Steam

Water

Natural Gas (fuel)

455°C

4896 kmol/hr 455°C, 3000 kPa

200°C

675°C

1030°C

Compressor II0.55 MW

V-1∆P=f(Q)

Recycle Tail gas to FT7762 kmol/hr

2700 kPa

2500kPa3000kPa

210°C2700 kPa3000 kPa

Steam Drum

Water


Mode I: Natural gas flowrate is given

Step 1: Define the objective function and constraintsVariables income

Inequality ConstraintsThree inequality constraints + capacity constraints on the variable units; fired heater

(duty +40% compared to nominal), CO2 recovery unit (+20% feedrate), oxygen plant (+20% oxygen flowrate).

Equality Constraints (Specs:9)

Step 2: Identify degrees of freedom (DOFs) for optimization15 degrees of freedom


Step 3: Identification of important disturbances

Natural gas flowrate,

Natural gas composition,

Natural gas price,

FT reactions kinetic parameter,

Change in active constraints value.


Step 4: Optimization

MIXED method: combines the advantage of global optimization of BOX and efficiency of SQP method

15 degrees of freedom, 9 equality constraints and 3 active constraints:

unconstrained degrees of freedom: 15 – 9 – 3 = 3, which may be viewed as:

H2O/C, CO2 recovery, tail gas recycle ratio to FT reactor

Step 5. Identification of candidate controlled variables

18 candidate measurements including the three unconstrained degrees of freedom 18 18!

8163 3!15!

Step 6. Selection of CVs

Exact local method for selection of the best CVs


no. Sets Loss (USD/hr)

1 y3:CO2 recoveryy9: CO mole

fractionin fresh syngas

y12: CO mole

fractionin tail gas

1393

2 y3:CO2 recovery y2: H2O/Cy6: H2/CO

in tail gas1457

3 y3:CO2 recovery y2: H2O/Cy5: H2/CO

in fresh syngas1698

4 y3:CO2 recoveryy6: H2/CO

in tail gas

y5: H2/CO

in fresh syngas2594

5y10:CH4 mole


y6: H2/CO

in tail gas

y5: H2/CO

in fresh syngas2643

Individual measurements (mode I)

worst-case loss for the best 5 individual measurement sets


Control structure for mode I of operation with proposed CVs and possible pairings with MVs (red lines are by-pass streams)

Heater

Natural Gas

Pre-Reformer

Se

par

ato

r

CO

2 R

emo

va

l

Steam

Oxygen(from ASU)

Water

Fired Heater


(ATR)

FT Reactor

3-Phase Separator

Compressor I

HP Saturated Steam

Light Ends


Water

Tail Gas

MP Steam

Syngas

Vapor

Liquid

CO2

Liquid fuels to upgrading unit


ASU Turbines

Superheated Steam

Extra Steam

Water

Natural Gas (fuel)

SP=455°C

SP=200°C

SP=675°C SP=1030°C

Compressor II

V-1∆P=f(Q)

Recycle Tail gas to FT

Steam Drum

Water

TC

TC

TC

TC

TC

TC

PC

TC

PC

PC

SP=30 bar

SP=38°C

SP=210°C

SP=12.5bar

SP=30°C

SP=27bar

CCSP (H2O/C)

CC

Self-optimizing CV1 SP (CO%)=25.67

SP=455°CTC

CC

Self-optimizing CV2SP (CO2 recovery%)=

75.73

RCCC

Self-optimizing CV3 SP (CO%)=12.96

RC

SP=3% purge

SP (splitter ratio)


Mode II: Natural gas feedrate is also a degree of freedom

Point A: oxygen flowrate saturates

1 extra DOF, 1 new active constraint


Optimal values in: nominal point, saturation of oxygen flowrate and maximum throughput

H2O/C O2/CCO2

recovery

Recycle ratio to FT

Purge of

tail gas

H2/CO

fresh

H2/CO

into FT

CO conversion % H2 conversion %

Carbonefficiency

Objective function(USD/hr)

per pass

overallper pass

overall

opt. nominal

0.6010 0.523 75.73% 73.79% 3% 2.1 2.03 85.74 95.50 89.93 96.92 0.87 74.59% 49293

max. oxygen

0.5357 0.516 76.80% 90% 3% 2.092 1.91 67.08 94.14 74.705 95.88 0.86 74.30% 59246

max. through

put0.4084 0.504 76.04% 97.13% 3% 2.095 1.80 51.25 94.79 60.69 96.39 0.87 74.31% 59634

FT reactor volume is the bottleneck


no. SetsLoss

(USD/hr)

1y3:CO2

recoveryy2: H2O/C

y7: H2/CO

into FT reactor3022

2y3:CO2

recoveryy2: H2O/C

y6: H2/CO

in tail gas3316

3y3:CO2

recoveryy2: H2O/C

y5: H2/CO

in fresh syngas3495

4y3:CO2

recoveryy2: H2O/C

y17: tail gas

flowrate to syngas unit

4179

5y3:CO2

recovery

y9: CO mole


y15: CO mole

fractioninto FT reactor

4419

Individual measurements (mode II)

worst-case loss for the best 5 individual measurement sets


Control structure for mode II of operation with proposed CVs and possible pairings with MVs (red lines are by-pass streams)

Heater

Natural Gas

Pre-Reformer

Se

par

ato

r

CO

2 R

em

ov

al

Steam

Oxygen(from ASU) flowrate is at max.

Water

Fired Heater


(ATR)

FT Reactor

3-Phase Separator

Compressor I

HP Saturated Steam

Light Ends


Water

Tail Gas

MP Steam

Syngas

Vapor

Liquid

CO2

Liquid fuels to upgrading unit


ASU Turbines

Superheated Steam

Extra Steam

Water

Natural Gas (fuel)

SP=455°C

SP=200°C

SP=675°C SP=1030°C

Compressor II

V-1∆P=f(Q)

Recycle Tail gas to FT

Steam Drum

Water

TC

TC

TC

TC

TC

TC

PC

TC

PC

PCSP=30 bar

SP=38°C

SP=210°C

SP=12.5bar

SP=30°C

SP=27bar

CCSP (H2O/C=0.4084)

Self-optimizing CV1

SP=455°CTC

CC

Self-optimizing CV2SP (CO2 recovery%)=

76.04

RC

CC

Self-optimizing CV3SP (H2/CO)=1.8

RC

SP=3% purge

SP (splitter ratio)


• Self-optimizing method was applied for selection of the CVs for GTL

• There are 3 unconstrained DOFs in both modes of operation

• One common set in the list of the best individual measurements in two modes:

CO2 recovery

H2/CO in fresh syngas

H2O/C setpoint reduces from 0.6 to o.4

• Operation in Snowballing region should be avoided

• Saturation point of oxygen plant capacity is recommended for operation in practice

Concluding remarks of self-optimizing application for GTL process


Outline

Ch.2 Introduction







Conclusions and future works

Systematic plantwide procedure of Skogestad was applied for a post-combustion CO2 capturing process; a simple control configuration was achieved, which works close to optimum in the entire throughput range without the need for switching the control loops or re-optimization of the process

A GTL process model suitable for optimal operation studies was modeled and optimized. This model describes properly dependencies of important parameters in this process

Self-optimizing method was applied to select the right measurements for the GTL process in two modes of operation

UniSim/Hysys linked with MATLAB showed to be a very good tool for optimal operation studies


Conclusions and future works

Implementation of the final control structure for CO2 capture plant is recommended for implementation in practice

Dynamic simulation of the GTL process should be done to validate the proposed control structures

The application of plantwide control procedure is strongly recommended for other newer energy-intensive processes

Developing a systematic method for arriving at a simple/single control structure, which works close to optimum in all operational regions can be a good topic for future work

Thank you for your attention!

Date post:	23-Dec-2015
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