Dynamic Modeling of a Solid-Sorbent CO2

Capture System

Srinivasarao Modekurti, Debangsu Bhattacharyya

West Virginia University, Morgantown, WV

Stephen E. Zitney

National Energy Technology Laboratory, Morgantown, WV

David C. Miller

National Energy Technology Laboratory, Pittsburgh, WV

1

AIChE 2013 Annual Meeting

San Francisco, CA, USA, November 3-8, 2013

OUTLINE

Motivation

Dynamic Model Development

Results and Discussions

Conclusions

2

MOTIVATION

Under the auspices of US DOE’s Carbon Capture

Simulation Initiative (CCSI), we are developing

computational models of various post-combustion CO2

capture technologies

As part of this project, our current focus is on the

development of dynamic models and control systems for

solid-sorbent CO2 capture and compression system.

3

4

Optimized Process Developed using CCSI Toolset

GHX-001

CPR-001

ADS-001

RGN-001

BLR-001

Flue Gas from Plant

Clean Gas to Stack

CO2 to Sequestration SHX-01

SHX-02

CPR-002

LP/IP Steam from Power Plant

CPP-002

ELE-002

ELE-001

Flue Gas

Clean Gas

Rich Sorbent

LP Steam

HX Fluid

Legend

Rich CO2 Gas

Lean Sorbent

Parallel ADS Units

Parallel RGN Units

Parallel ADS Units

GHX-002

CPP-000

Cooling Water

Injected Steam

Cooling Water

Saturated Steam Return to Power Plant

Mild SteamDirectly Injected into Reactor

Compression Train

Co

nd

en

sed

W

ate

r

Co

nd

en

sed

W

ate

r

Solid Sorbent MEA27

(D10°C HX) MEA27

(D5°C HX) Q_Rxn (GJ/tonne CO2) 1.82 1.48 1.48

Q_Vap (GJ/tonne CO2) 0 0.61 0.74

Q_Sen (GJ/tonne CO2) 0.97 1.35 0.68

Total Q 2.79 3.44 2.90

ADS-001A ADS-001B

Diameter (m) 9.748

Bed Depth (m) 7.232 4.854

Total HX Area (m2) 1733.7 941.3

RGN-001

Diameter (m) 7.147

Height (m) 4.592

Total HX Area (m2) 1573.1

Solid Sorbent:

NETL 32D,

a mesoporous

amine-impregnated

silica substrate

Modeling Domain

5

Bubbling Fluidized Bed Model

Development

6

• 1-D two-phase pressure-driven non-isothermal dynamic model of a solid-

sorbent CO2 capture in a two-stage bubbling fluidized bed reactor system.

• Models are flexible such that it can be used as an adsorber or regenerator

• Embedded cooler/heater depending on the application

• Flexible configuration- solids can enter/leave at/from the top or bottom

• A 2-stage adsorption model with customized variables for uncertainty

quantification capabilities has been developed

DYNAMIC MODEL – BUBBLING

FLUIDIZED BED

Model Assumptions 1. Each BFB consists of bubble, emulsion and

cloud-wake regions.

2. Bubble region is free of solids.

3. Constant average particle properties

throughout the bed

4. Adsorption-reaction takes place in solid-phase.

5. Solids leave at the top of the bed (Overflow-

type configuration).

6. Transients of the immersed heat exchangers

are neglected

*Lee, A.; Miller, D. A 1-D Three Region Model for a Bubbling Fluidized Bed Adsorber. Ind. Eng. Chem. Res. , 52, 469-484, 2013

* Modekurti, S.; Bhattacharyya, D., Zitney, S. E., Dynamic modeling and control studies of a two-stage bubbling fluidized bed

adsorber-reactor for solid sorbent CO2 capture, Ind. Eng. Chem. Res. , 52, 10250-120260, 2013

7

MODEL DEVELOPMENT

• Gaseous species : CO2, N2, H2O

• Solid phase components: bicarbonate, carbamate, and

physisorbed water.

• Transient species conservation and energy balance

equations for both gas and solid phases in all three

regions. *Lee, A.; Miller, D. A 1-D Three Region Model for a Bubbling Fluidized Bed Adsorber. Submitted to Ind. Eng. Chem. Res. 2012

8

CONSERVATION EQUATIONS Bubble Region :

Cloud-wake Region :

Gaseous Components

Gaseous Components

9

CONSERVATION EQUATIONS Cloud Wake Region :

Adsorbed Species

10

Emulsion Region :

CONSERVATION EQUATIONS CONTD.

Gaseous Components

11

Emulsion Region :

CONSERVATION EQUATIONS CONTD.

Adsorbed Species

12

Adsorber

Clean

Gas

Flue

Gas

Fresh

Sorbent

CO2 Rich

Sorbent

HYDRODYNAMIC MODEL

Mori and

Wen (1975)

Sit and Grace (1981)

13

REACTION KINETICS

𝐻2𝑂 𝑔 ↔ 𝐻2𝑂 𝑝ℎ𝑦𝑠

2𝑅2𝑁𝐻 + 𝐶𝑂2,(𝑔) ↔ 𝑅2𝑁𝐻2+ + 2𝑅2𝑁𝐶𝑂2

−

𝑅2𝑁𝐻 + 𝐶𝑂2,(𝑔) + 𝐻2𝑂 𝑝ℎ𝑦𝑠 ↔ 𝑅2𝑁𝐻2+ + 𝐻𝐶𝑂3

−

2 2

2

2

, , , ,

1, , 1, ,

, , 1, ,

, , , ,

, ,

, ,, , , ,

2, , 2, , , ,

, , 2, ,

1 2

i r H O i r H O i

r i r i

r t i r i

r carb i r bicarb i

r bicarb i

i r CO ir carb i r bicarb i v v

r i r i r H O i

v v r t i r i

PC nr k

C K

n nn

PCn n n nr k n

n n C K

2

, , , ,2 , ,

, ,, , , ,

3, , 3, ,

, , 3, ,

1 2

r carb i r bicarb i

r carb i

i r CO ir carb i r bicarb i v v

r i r i

v v r t i r i

n nn

PCn n n nr k

n n C K

1/25/2014 14

*Lee et al. A model for the Adsorption Kinetics of CO2 on Amine-Impregnated Mesoporous Sorbents in the Presence of Water, 28th

International Pittsburgh Coal Conference 2011, Pittsburgh, PA, USA.

Dynamic Model–Moving Bed Reactor

1-D two-phase pressure-driven non-isothermal dynamic

model of a moving bed reactor mainly for the

regenerator application

Model Assumptions Vertical shell & tube type reactor

Gas and solids flows are modeled by plug flow

model with axial dispersion.

Particles are uniformly dispersed through the

reactor with constant voidage

Particle attrition ignored

Temperature is uniform within the particles

Solid In

Solid Out

Gas In

Gas Out

Utility In

Utility Out

• Gaseous species : CO2, N2, H2O

• Solid phase components: bicarbonate,

carbamate, and physisorbed water.

15

Integrated pre and post-heat exchangers are considered for

heat recovery

Gas and solids flows are modeled by plug flow model

with axial dispersion

For pressure drop calculation, a modified Ergun equation by using

the slip velocity between the solids and gas is used instead of the superficial fluid

velocity

Energy balance equations consider heat transfer between solid

and gas and tube wall and the mixed phase

Heat transfer coefficient between the mixed phase and the tube

wall is calculated by a modified packet-renewal theory

Bed hydrodynamics are described by analogy to fixed bed and

fluidized bed systems

Reaction kinetics are similar to the bubbling bed model

Development of Moving Bed Model

16

Pneumatic Transport Modeling

Assumptions

• Isothermal

• Ideal separation of gases and solids. Therefore, transport gas is free of solids after

separation.

• No mass transfer and reactions during the transport

Options considered for the transport medium

• Unclean flue gas from the adsorber inlet

• Clean flue gas from the adsorber outlet

• A recycling transport medium with makeup from the clean gas

• CO2 from the outlet of the regenerator

Calculation of the overall pressure drop in the vertical pipe

• Pressure drop due to gas acceleration

• Pressure drop due to solids acceleration

• Pressure drop due to gas to pipe friction

• Pressure drop due to solids to pipe friction

• Pressure drop due to static head of the solids

17

Pneumatic Transport Modeling: Regenerator to Adsorber

P ip e

B 1

Fe e d _ H o p p e rB 3

Co m p re sso r

Co o le r

S o lid s_ In

S 2

S 1

S 3

S 5

S 6

S 4

S 1 3

S 1 4

S 1 5

Solids from the regenerator

Solids to the adsorber

ΔP (bar) 0.56

Pipe Dia (m) 0.3

Pipe Length (m) 25

Load Ratio (S/G) 40

Choking Velocity (m/s) 20.1

Superficial Velocity (m/s) 24.2

18

Solids from the adsorber

Solids to the regenerator

Pneumatic Transport Modeling: Adsorber to Regenerator

ΔP (bar) 0.18

Pipe Dia (m) 0.45

Pipe Length (m) 15

Load Ratio (S/G) 28.3

Choking Velocity (m/s) 19.1

Superficial Velocity (m/s) 22.9

19

Dynamic model of a multi-stage integral gear compressor system with inter-stage

coolers, knock-out drums, and TEG absorption system has been developed.

Performance curves obtained from a commercial vendor has been used for

calculating off-design performance.

CO2 Compression System Model

20

0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.240.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Psi3

Ps

i s

-15

0

15

30

40

50

60

70

75

CO2 Compression System Model Dimensionless Exit Flow Coefficient

Dimensionless Isentropic Head Coefficient

= Isentropic head =

21

CO2 Compressor Load Control

Surge Detection and Control

00 if

if

0

0

( ) ( ) ( )

( ) ( )

(0)

u t k t y t u

k t y y

k k

Gain Scheduling Controller

22

IGV Model

Modeling of Balance of the Plant

1. Pressure flow-network along with the control

valves

2. Gas and Solid distributors

3. Downcomer and Exit-hopper

4. Other components such as flue-gas stack etc.

5. Pre-heater, post-heat exchanger, post-cooler,

steam and BFW system for heat recovery

23

SOLUTION METHODOLOGY

All models are set up in Aspen Custom

Modeler

The dynamic model is solved by using the

Method of Lines

ACM model is embedded in Simulink for

LMPC implementation.

24

Bubbling Bed Model : Results from Single Stage

0 0.2 0.4 0.6 0.8 10.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

Z/L

Mo

le F

racti

on

H2O

CO2

Flue Gas

Inlet

Flue Gas

Outlet

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

1.4

Z/L

Mo

lar

Lo

ad

ing

(m

ol/kg

so

lid

s)

Solids overflow exit type configuration

Bic

Car

H2O

Solids

Inlet

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Z/L

Mo

le F

ract

ion

H2O

CO2

Gas Inlet Gas Outlet0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Z/L

Mo

lar

Lo

ad

ing

(m

ol/kg

so

lid

s)

Bic

Car

H2O

Solids Outlet Solids Inlet

Adsorber

Regenerator

25

Moving Bed Regenerator: Results

26

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Z/L

Mo

le F

racti

on

CO2

H2O

Gas OutletGas Inlet

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Z/L

Mo

lar

Lo

adin

g (

mo

l/kg

so

lids)

Bic

Car

H2O

Solids InletSolids Outlet

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9110

112

114

116

118

120

122

124

126

128

130

Z/L

So

lids

Tem

per

atu

re (C

)

Solids Outlet Solids Inlet 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9900

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

Z/L

Gas

Flo

w R

ate

(km

ol/h

r)

Gas Inlet Gas Outlet

84

85

86

87

88

89

0 1000 2000 3000 4000 5000

CO

2 C

ap

ture

(%

)

Simulation Time (s)

SP PV

• PID controller for controlling CO2 capture by manipulating the

solid sorbent flowrate.

• Note the large undershoot and long settling time.

Configuration and Performance of the PID Controller

CONTROLLER DESIGNS FOR MAINTINING

CO2 CAPTURE – ADSORBER-ONLY (20% step

increase in flue gas flowrate) 1. PID CONTROLLER

27

• Data for the process and disturbance models are generated by

implementing step changes in the sorbent flowrate and the flue gas

flowrate, respectively.

• Process and disturbance models are identified in MATLAB as first-order

and pure-gain-plus-second–order models, respectively.

CONTROLLER DESIGN CONTD. 2.FEEDBACK-AUGMENTED FEEDFORWARD CONTROLLER

Comparison of the process model

to the data from ACM®

28

84

85

86

87

88

89

0 1000 2000 3000 4000 5000

CO

2 C

ap

ture

(%

)

Simulation Time (s)

SP PV

• Note the smaller/shorter undershoot with large overshoot and

settling time

Configuration and Performance of the Feedback-Augmented

Feedforward Controller

CONTROLLER DESIGN CONTD. 2.FEEDBACK-AUGMENTED FEEDFORWARD CONTROLLER

29

0 1000 2000 3000 4000 5000-2

-1.5

-1

-0.5

0

0.5

Time (s)

De

via

tio

n f

rom

th

e s

tea

dy

sta

te C

O2 c

ap

ture

(%

)

Measured and simulated model output

Estimated using ARX on data set t

Discrete-time IDPOLY model: A(q)y(t) = B(q)u(t) + e(t)

A(q) = 1 - 1.473 q^-1 + 0.2636 q^-2 + 0.2923 q^-3 - 0.08314 q^-4

B1(q) = -0.03877 q^-1 + 0.1641 q^-2 + 0.05974 q^-3 - 0.1471 q^-4

B2(q) = -4.348 q^-1 + 0.03616 q^-2 - 21.36 q^-3 + 20.11 q^-4

ARX model as the disturbance model

CONTROLLER DESIGN CONTD. 3.LINEAR MODEL PREDICTIVE CONTROLLER

30

Simulink block diagram for LMPC implementation 31

Manipulated variable is sorbent

flowrate.

ACM model is embedded in

SIMULINK for MPC

implementation.

20% step increase in flue gas

flowrate as disturbance.

Configuration of LMPC with

Additional Integrator

CONTROLLER DESIGN CONTD. 3.1 Offset-free LMPC Using an Integrator

32

Estimation of unmeasured disturbance

using advanced Controllers of MPC

toolbox in MATLAB ®.

The ACM model is embedded in

SIMULINK for MPC implementation.

20% step increase in flue gas flowrate.

Performance is satisfactory even for

other disturbances.

Configuration and performance

of LMPC with

estimation of unmeasured

disturbance

CONTROLLER DESIGN CONTD. 3.2 Offset-free LMPC Using Unmeasured Disturbance

33

CONTROLLER PERFORMANCE COMPARISON

Control performances of

LMPC-I and LMPC-II are

superior to others

Control Performance Table

CONTROLLER IAE ISE ITAE

(hr) (hr) (hr2)

(1) PID 0.8111 1.7551 1.12E-04

(2) FBAUGFF 0.4751 0.5502 6.60E-05

(3) LMPC-I 0.3913 0.6138 5.57E-05

(4) LMPC-II 0.4007 0.6386 6.30E-05

34

Control Configuration of the Regenerator System

R GN

B 1

B 2

S H X 1

S H X 2

B 3B 5

P U M P

B 7

S te a m _ H e a d e r

B 6

B 8

B 1 0

B 1 1

B 1 2

R xS T In

CO 2 R ic h

H xS T In

H xS T O u t

S 2

S 1 2

S 1 6

S 5

S 1 5

S 1 8

S 1 3

S 1

S 6

S 9

S 1 4

S 1 0S 1 1

S 1 7

S 2 0

Steam Header

Temperature

Controller

Split-Range

Level Controller

Schematic of the ACM flow sheet of the moving bed regenerator with

steam/BFW system

Integrated Adsorber-Regenerator Dynamic

Model: PID Controller

36

Integrated Adsorber-Regenerator Dynamic

Model: PID Controller

37

Pressure Dynamics in CO2 Compression System: 10%

Ramp Change in flowrate

PRESSURE

Time Hours

Com

p_sta

ge7.o

_port

.P b

ar

Com

p_S

tage6.o

_port

.P b

ar

Com

p_S

tage5.o

_port

.P b

ar

Com

p_S

tage4.o

_port

.P b

ar

Com

p_sta

ge3.o

_port

.P b

ar

Com

p_sta

ge2.o

_port

.P b

ar

Com

p_sta

ge1.o

_port

.P b

ar

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0

96.0

98.0

100.0

102.0

58.0

60.5

63.0

65.5

68.0

36.0

38.0

40.0

42.0

20.0

21.0

22.0

23.0

24.0

11.0

11.5

12.0

12.5

5.4

5.6

55.9

6.1

5

2.4

2.4

52.5

2.5

52.6

2.6

52.7

38

Time Hours

Co

mp_

sta

ge

8.e

lec

_po

w k

W

Co

mp_

sta

ge

7.e

lec

_po

w k

W

Co

mp_

Sta

ge

6.e

lec_

pow

kW

Co

mp_

Sta

ge

5.e

lec_

pow

kW

Co

mp_

Sta

ge

4.e

lec_

pow

kW

Co

mp_

sta

ge

3.e

lec

_po

w k

W

Co

mp_

sta

ge

2.e

lec

_po

w k

W

Co

mp_

sta

ge

1.e

lec

_po

w k

W

0.0 20.0 40.0 60.0

162

0.0

164

0.0

166

0.0

164

0.0

168

0.0

172

0.0

176

0.0

260

0.0

270

0.0

280

0.0

290

0.0

240

0.0

250

0.0

260

0.0

270

0.0

300

0.0

310

0.0

320

0.0

330

0.0

340

0.0

340

0.0

360

0.0

380

0.0

400

0.0

420

0.0

440

0.0

460

0.0

480

0.0

500

0.0

440

0.0

460

0.0

480

0.0

500

0.0

39

Power Dynamics in CO2 Compression System: 10% Ramp

Change in flowrate

CONCLUSIONS 1. One-dimensional, non-isothermal, pressure-driven dynamic

models of a two-stage BFB adsorber-reactor, a moving bed

regenerator, an integral gear CO2 compression system along

with the balance of the plant has been developed in ACM for

solid-sorbent CO2 capture.

2. For adsorber-only case, the performances of both LMPC

strategies are satisfactory and superior to other control

strategies.

3. The response of the coupled adsorber-regenerator system is

slow and oscillatory due to interactions between the systems.

Advanced control strategies should be considered for

satisfying the overall CO2 capture target over a period of

time.

40

Acknowledgements: • As part of the National Energy Technology Laboratory’s

Regional University Alliance (NETL-RUA), a collaborative

initiative of the NETL, this technical effort was performed under

the RES contract DEFE0004000.

Disclaimer: This presentation was prepared as an account of work sponsored by an

agency of the United States Government. Neither the United States

Government nor any agency thereof, nor any of their employees, makes

any warranty, express or implied, or assumes any legal liability or

responsibility for the accuracy, completeness, or usefulness of any

information, apparatus, product, or process disclosed, or represents that

its use would not infringe privately owned rights. Reference herein to any

specific commercial product, process, or service by trade name,

trademark, manufacturer, or otherwise does not necessarily constitute or

imply its endorsement, recommendation, or favoring by the United States

Government or any agency thereof. The views and opinions of authors

expressed herein do not necessarily state or reflect those of the United

States Government or any agency thereof.

Thank you

1/25/2014 42

1/25/2014 43

Pneumatic Transport Modeling

Terminal Velocity of the particles:

Choking Velocity, Voidage at Choking, and Superficial Velocity

44

Pneumatic Transport Modeling

Load Ratio, Gas and Solid Velocities

Reynold’s Number and Gas Friction Factor

45