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

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

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.

Flowsheet of the amine scrubbing process

pressure

reboiler

duty

flue gas

rate recirculation

rate

Optional

intercooler

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

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

Focus on column model

• Same base models for both absorber and stripper

MEA solution

steam

and

CO2

flue

gas

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

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

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

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

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

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.

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

System boundary reduced model

Detailed: stripper unit Simplified: absorber & HX

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

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

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

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

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) − ᶯ𝑟𝑒𝑓2+ 𝛽

𝑑𝑢

𝑑𝑡

2

𝑑𝑡𝐻𝑝

0

• Constraint on reboiler pressure

𝑝𝑟𝑒𝑏𝑜𝑖𝑙𝑒𝑟 𝑡 ≤ 𝑝𝑚𝑎𝑥

Reboiler

Desorber

From

Absorber

To

Absorber

To

Storage

Condenser

Pressure

control

Heat injection

G

desorberL

G L

reb?

LV

F

conden?

r?

r?

valvegasSink

T_gs

k=313p_gs

k=1.3e5

p_set

k=1?

valve.p?

headPressure

T_c?

T=3?K

leanSolut?

richSolut?

f low sou?

T_so?

k=356Vflo?

k=16.?

liquidSink

T_ls

k=313p_ls

k=2e5

summary

Q_reb?

k=2e6

gain

pI1

vol2

vol1

dQ

heat_der

I

k=1

1s

• 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

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

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;

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

Results: 2 DOF

• Prediction horizon: 1000s

• Sampling: 100s

• NLP: 38536 equations for 2 DOF

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

Acknowledgements

• This work was partly funded by Vinnova