This document summarizes research on developing a nonlinear model predictive control (NMPC) strategy for optimizing the operation of a post-combustion carbon capture unit. Key points: 1) Researchers created a detailed Modelica model of an amine-based carbon capture process but reduced it to improve computational efficiency for real-time optimization. 2) The reduced model was validated against experimental plant data and found to accurately capture system dynamics and behavior. 3) JModelica.org was used to perform offline optimizations of the reduced model, minimizing costs while satisfying operational constraints. 4) Preliminary results showed the NMPC approach was able to optimize reboiler duty and maintain a target carbon

1. NONLINEAR MODEL PREDICTIVE CONTROL FOR
OPERATION OF A POST COMBUSTION
ABSORPTION UNIT
J. Åkessona,b, G. Lavedana, K. Prölßa,
H. Tummescheita, S. Veluta
a) Modelon AB
b) Department of Automatic Control, Lund University
ICEPE Conference 2011, Frankfurt

2. Motivation: Optimal control for CCS
• Carbon dioxide separation reduces power plant efficiency significantly
• Find control strategy that handles dynamically changing boundary
conditions, and changing regulatory conditions while minimizing
operational costs
• Solve this task with non-linear model-predictive control (NMPC)
• Challenge: model needs to be sufficiently accurate, yet simple enough
to be optimized in real time!
power plant
legal restrictions
emission costs
dynamic load demands
electricity market price
fluegas
process steam
post-combustion
carbon capture
cleaned gas

3. Overview
Detailed model
development
Model reduction
Formulation of the
optimal control problem
State estimation from
measurements
Solution of the optimal
control problem
Application of control
signal to process
offline
online
Process toward NMPC Used tools
Dymola
Dymola/
JModelica.org
JModelica.org
JModelica.org
Presentation outline
1
2
3
4
Example
Offline
example
Modelica is modeling language for physical
systems modeling, simulation and
optimization defined by an open specification.
Both Dymola and JModelica.org use
Modelica for describing the model.

4. Flowsheet of the amine scrubbing process
pressure
reboiler
duty
flue gas
rate
recirculation
rate
Optional
intercooler

5. Model development
1. Medium properties and reactions
 MEA-water-CO2 system incl. ions (electrolyte solution)
 Gas mixture, flue gas (absorber) and water/CO2 (stripper)
 Phase equilibrium at liquid/gas interface and in reboiler
2. Distributed bulk flow with dynamic mass and energy
balances, algebraic flow correlation (pressure drop and
hold-up)
3. Heat and mass transfer, semi-empirical correlations
 liquid/gas, liquid/liquid, liquid/solid
 enhancement due to reactions

6. Assumptions and dynamics
• Discretization only in bulk flow direction
• Gas/Liquid mass transfer with transfer coefficents and
enhancement factors instead of discretized multi-
component diffusion
• Instantaneous reactions in the liquid phase reduce the
number of states to four per liquid volume (amounts of
carbon dioxide, MEA and water, temperature)
• Incompressible liquid and ideal gas yield index 1 system

7. Focus on column model
• Same base models for both absorber and stripper
MEA solution
steam
and
CO2
flue
gas

8. Chemical system in liquid phase
Ion speciation in the liquid phase
missing in the plot:
H2O, OH-, H3O+, CO3--
• Chemical equilibrium
 :activity coefficient
x : mole fraction
 : stoichiometry coeffficient
T: temperature
• Assumed because of
 relatively fast reactions
 limited amount of literature
data available for kinetics
 trade-off in order to cut
down the number of
numerical states

9. Model validation – Complete system
• Experimental data from pilot plant in Esbjerg, also presented in Faber et al. ,
Proceedings of GHGT 10
Constant boundary
conditions(open loop):
• Solution recirculation
rate
• Reboiler duty
• Flue gas temperature
and composition
• Gas exit pressures
• 30% MEA solution
Step variation: Flue gas flow rate

10. Model validation – Complete system
Removal rate (absorber)
• Very good agreement in
lower load case
• Experimental data
apparently not in steady-
state
Temperatures (stripper)
• good overall agreement
• simulation model reveals
faster dynamics
• total liquid system volume
was unknown and
probably underestimated
Not measured: Liquid
composition

11. Model validation – Complete system
Gas temperature profile in
absorber
• two (steady-state) operating
points
• assumption: even distribution
of measurement points
• good agreement of simulation
with measurements
• conclusions on model quality
possible concerning
 heat of sorption
 heat and mass transport

12. Model validation - stripper
Experimental data from: Tobiesen et al., Chem. Eng. Sci., 63 (2008) 2641-2656
Given:
• Solution flow rate
• Inlet temperature
• Inlet loading
• Reboiler duty
• Packing and
packing height
Caution:
• Extremely small
loading range,
usually larger

13. Model reduction – Ion speciation
• Computing the speciation in the liquid phase results in
large non-linear equation systems
• Eliminating ion speciation increases robustness and
simulation speed
• Liquid solution consists of
three species only: total CO2,
total H2O, total MEA
• Mole fraction of molecular
CO2, is computed from a
spline interpolation of the
speciation map:
xCO2 = f (T, NCO2/NMEA)Xmea=const.

14. Model reduction
Further assumptions
• Heat of sorption
 Important for correct reboiler duty
 Simplification: concentration independent
• Heat and mass transfer
 Constant transfer coefficients, incl. enhancement
• Constant heat capacities for each species in system
• Constant density of liquid phase
• Simplified model of absorber (desorber more important for energy savings)
• Overall effect: simulation time reduced by factor of 200

15. System boundary reduced model
Detailed: stripper unitSimplified: absorber & HX

16. Stripper unit
• Stripper + reboiler, comparison of detailed and reduced
model, steady-state cases
• Given reboiler duty and inlet solvent loading
Conclusion:
• phase and chemical
equilibrium and heat of
sorption are captured
sufficiently well in
reduced model

17. Optimization
Problem
 Goal: minimize the separation and emission cost while satisfying
operation and regulatory constraints
 Potential degrees of freedom: reboiler duty, circulation rate,
(stripper pressure)
 Constraints: pump capacity, reboiler pressure, CO2 emission...
 Boundary conditions: flue gas rate and composition, electricity
price
Solution
 Method: Nonlinear Model Predictive Control
 Tool: JModelica.org platform

18. Towards NMPC
NMPC=sequence of open loop control problems
1. Estimate process states from measurements
2. Solve optimal control problem on the prediction horizon
3. Apply the first sample of the optimal input
4. Update internal data, go back to step 1 and repeat sequence
Current project status
 Solve the NMPC problem offline, using detailed simulation model
instead of real process
 Using an extended Kalman filter for state estimation
 Using one or two degrees of freedom (control signals to optimize)
 On a simplified system

19. Interaction Structure
CCS Plant or
Simulation model
State observer:
Extended
Kalman Filter
Optimization problem,
simplified model
Local linearized
model
uk yk
1
2
3
4
1. Estimate states from
measurements
2. Solve optimal control problem on
the prediction horizon
3. Apply the first sample of the
optimal input
4. Update linear part of Kalman filter,
go back to step 1 and repeat
sequence

20. Simplified problem
• Stripper unit:1493 equ., 50 states
• Absorber: equilibrium with flue gas
• Fixed circulation rate
• Pressure control at top
• DOF=reboiler duty
• Target removal efficiency ᶯ
• Minimize quadratic cost
𝐽 𝑢, 𝑥0 = 𝛼 ᶯ(𝑡) − ᶯ 𝑟𝑒𝑓
2
+ 𝛽
𝑑𝑢
𝑑𝑡
2
𝑑𝑡
𝐻 𝑝
0
• Constraint on reboiler pressure
𝑝 𝑟𝑒𝑏𝑜𝑖𝑙𝑒𝑟 𝑡 ≤ 𝑝 𝑚𝑎𝑥
Reboiler
Desorber
From
Absorber
To
Absorber
To
Storage
Condenser
Pressure
control
Heat injection
G
desorber
L
G L
reb?
LV
F
conden?
r?
r?
valve
gasSink
T_gs
k=313
p_gs
k=1.3e5
p_set
k=1?
valve.p?
headPressure
T_c?
T=3?
K
leanSolut?
richSolut?
flow sou?
T_so?
k=356
Vflo?
k=16.?
liquidSink
T_ls
k=313
p_ls
k=2e5
summary
Q_reb?
k=2e6
gain
pI1
vol2
vol1
dQ
heat_der
I
k=1
1
s
• Overall model: 1600 equations, 55 states
• Simplified absorber, interpolating for different L/G ratios.
• Pressure control at top of column
• 1 DOF: reboiler duty (DOF: degree of freedom)
• 2 DOF: reboiler duty and circulation rate
• Given target removal efficiency

21. Jmodelica.org
Extensible open-source platform for simulation and
optimization of Modelica models
• Dynamic optimization
• Modelica extension: Optimica
• Direct collocation method
• Large scale NLP
• Solver: IPOPT
• Python interface

22. Optimizing with JModelica.org
optimization
desorber_opt(objective=cost(finalTime),startTime=0.0,finalTime=1000)
extends desorber;
parameter Real alpha=1 “output weight”;
parameter Real beta=1 “input weight”;
parameter Real eta_r “target efficiency”;
parameter Real p_max “maximal reboiler pressure”;
Real cost “cost function”;
equation
der(cost)=alpha*(desorber.eta-desorber.eta_r)^2+beta*du^2;
constraint
desorber.p_reb<=p_max;
end desorber_opt;

23. Results: 1 DOF
• Prediction horizon: 1000s
• Sampling: 100s
• NLP: 29824 equations
• Initialization with constant
trajectories
• Solved in 73 iterations, less
than 100 s
• Consistency between
Jmodelica.org and Dymola

24. Results: 2 DOF
• Prediction horizon: 1000s
• Sampling: 100s
• NLP: 38536 equations for 2 DOF

25. Summary
• Results and Conclusions
 A validated Modelica model library for transient simulation of amine-
based post-combustion capture
 The plant model was able to capture measured behavior of
absorption process
 Physical model reduction leads to a model suitable for optimization
 JModelica.org was used to perform optimization on this model with
1600 equations and 55 state variables
• Future work
 Consider parts of power generation in model/cost function (LP turbines)
 Moving horizon estimation instead of Extended Kalman Filter for state
estimation
 Stripper pressure as degree of freedom
 Higher discretization of stripper column
 Maintain real-time for more complex model (input blocking, sampling,
initialization, Hessian...)
• New evaluation framework CasADi
• Methods for real-time NMPC, e.g., Advanced step method by V. Zavala

26. Acknowledgements
• This work was partly funded by Vinnova