Validation and Uncertainty Quantification of a High-Fidelity Model of a MEA-Based CO2 Capture System

Anderson Soares Chinena, Benjamin Omella, Debangsu Bhattacharyyaa, Charles Tongb, David C. Millerc

a Department of Chemical Engineering, West Virginia University, Morgantown, WV 26506, USA b Lawrence Livermore National Laboratory, Livermore, CA 94550, USA

cNational Energy Technology Laboratory, 626 Cochrans Mill Rd, Pittsburgh, PA 15236, USA

AICHE Annual Meeting 2014 Atlanta, GA

Outline

• Motivation • Approach

• Deterministic model • Uncertainty Quantification

• Results • Holdup • Pressure Drop • Interfacial Area • Mass Transfer Coefficients • Uncertainty Propagation

• Conclusion

Motivation

3

Properties Models

Process Models

Kinetic Models

Process Simulation

% CO2 Capture

Energy Requirement

Other Key Variables

Joshua Morgan Thursday

3:15 at Marriott 101

• Hydraulic Model • Holdup • Pressure Drop

• Mass Transfer Model

• Interfacial Area • Mass Transfer Coefficients

• Heat Transfer Model

• Heat Transfer Coefficients

Process Model

0

100

200

300

400

500

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9

Pres

sure

dro

p (P

a/m

)

Fv (Pa0.5)

experimental Stichlmair Billet and Schultes

A Close Look on Uncertainty in Modeling: Pressure Drop Model

• Evaluation of literature models

• Billet and Schultes • Stichlmair

Discrepancy is observed

Packing Type Liquid/gas system

Operating Conditions

Parameter range and probabilities

Parametric Uncertainty Propagation

CO2 removal: 77.95% - 80.05%

Models from Plaza (2012)1: Phoenix Model

1. Jorge Mario Plaza, Ph.D. Dissertation, UT Austin, May 2012

• Deterministic Model Identification • Identification of Model and Data • Parameter Calibration (with model form correction) • Implementation in Aspen Plus® (Fortran User Models)

• Parametric Uncertainty Quantification • Uncertainty Propagation Through Process Model

Overall Approach to UQ

Physical Properties, Hydraulic, and Mass Transfer Models

Full Process model

Holdup Model

Interfacial Model

Mass Transfer Coefficient

Model

Priors P(X1)

Priors P(X2)

Priors P(X3)

Inference

data

Inference

data

Inference

data

Posteriors π(X1)

π(X3)

Posteriors π(X2) Key variables uncertainty

MEA mass % Temperature CO2 loading

Properties Model

Priors P(X4)

Stochastic Modelling Approach

Holdup Sub-model Uncertainty Quantification

Step 1 – Model Parameter Calibration: Holdup

• 2 Parameters Calibrated

ℎ𝐿𝐿 = A11

𝑆𝑆2𝑔𝑔2 3�

𝜇𝜇𝐿𝐿𝜌𝜌𝐿𝐿

13� 𝑄𝑄𝐿𝐿𝑃𝑃

A2

Tsai (2010)2 Holdup Correlation:

Parameter Initial Calibrated A1 6.94 11.450

A2 0.573 0.647 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

9 13 17 21 25

hold

up

Liquid load (m3/m2 . h)

experimental RGR Stichlmair

RGR Billet and Schultes RGR Tsai

2. Robert Edison Tsai, Ph.D. Dissertation, UT Austin, 2010

Step 2 - Response Surface Model:Holdup

• 69 Sets of Process Variables • Uniform Prior Distribution (Monte Carlo

Simulation) • Sample size = 100 • ± 20% range assumption from calibrated values

• Results obtained from the deterministic model (6900 points)

• Multivariate Adaptive Regression Splines (MARS) method to fit a response surface

Step 2 - Response Surface Model: Holdup

Step 3 – Bayesian Inference

• Posterior distribution of the parameters are generated by maximizing expectation of finding the experimental data given the uncertainty in observation and initial guess of parametric uncertainty

• Method: Markov Chain Monte Carlo • Software: PSUADE

Step 3 – Bayesian Inference

A2

Pressure Drop

• Billet and Schultes’ correlation was evaluated • Calibration of 1 Parameter • For holdup, modified Tsai (2010) model was

considered

0

100

200

300

400

500

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9

Pres

sure

dro

p (P

a/m

)

Fv (Pa0.5)

experimental Stichlmair Billet and Schultes

Interfacial Area

• Tsai (2010) correlation was selected • No calibration was performed • Uncertainty considered in 2 Parameters

Liquid Side Mass Transfer Coefficient

• None of the existing correlations that were evaluated gave satisfactory result in comparison to the experimental data

• Wang (2013)3 was selected for being a complementary study to Tsai (2010)

• Calibration of 2 Parameters • Uncertainty considered in 2 Parameters

2.8 3 3.2 3.4 3.6 3.8x 10-4

0

0.05

0.1

0.15

0.2

C1

Prob

abili

ties

2.8 3 3.2 3.4 3.6 3.8x 10-4

0.13

0.14

0.15

0.16

0.17

0.18

C1

C2

0.13 0.14 0.15 0.16 0.17 0.180

0.05

0.1

0.15

C2

Prob

abili

ties

3. Wang, C.B., Perry, M., Rochelle, G.T., Seibert, A. F., 2013. Characterization of Novel Structured Packings for CO2 Capture. Energy Procedia 37, 2145-2153.

Parametric Uncertainty Propagation

• Posterior distributions from Bayesian Inference are considered

• User models developed in FORTRAN, compiled and used in Aspen Plus environment

• For each set of parameters and process variables, Aspen Workbook was used to run the Aspen simulations

Initial vs Final Results (Hold up, interfacial area, and liquid-side mass transfer coefficient only)

Final CO2 removal:

84.01% - 84.77%

Lean solvent : Flowrate = 6000 kg/h T = 44 oC P = 101.3 kPa 29.65% MEA

Flue gas : Flowrate = 2260 kg/h T = 43.4 oC P = 111.7 kPa 16% CO2

Initial CO2 removal:

77.95% - 80.05%

Validation: Data from Recently Conducted Test Runs at NCCC

Conclusion

• A methodology for quantification of parametric uncertainty of process models is developed.

• Starting from an initial guess, the methodology generates a more precise estimate of parametric uncertainty if the observation data and their uncertainty are known

• The methodology improves the overall estimate, both deterministic and stochastic, of the key variables.

Acknowledgment As part of the National Energy Technology Laboratory’s Regional University Alliance (NETLRUA), a collaborative initiative of the NETL, this technical effort was performed under the RES contract DE-FE0004000. The authors would like to thank Prof. Gary T. Rochelle from The University of Texas at Austin for sharing the Phoenix model. The authors sincerely acknowledge valuable discussions with Prof. Rochelle and Brent Sherman from The University of Texas at Astin.

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!

Annual AICHE meeting 2014 – Atlanta - GA