validation and uncertainty quantification of a high ......validation and uncertainty quantification...
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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