Multi-scale modeling with generalized dynamic discrepancy

Transcription

1 Multi-scale modeling with generalized dynamic discrepancy David S. Mebane,*, K. Sham Bhat and Curtis B. Storlie National Energy Technology Laboratory *Department of Mechanical and Aerospace Engineering, West Virginia University Statistical Sciences Group, Los Alamos National Laboratory SIAM Annual Meeting, July 2013

2 multi-scale modeling Multi-scale modeling is an inherently statistical problem. What information will be propagated to the next scale? What is the role of experimental data? How do we account for uncertainty in parameters and models? How do we handicap (or prevent) extrapolation? 2

3 equilibrium problems wt.-% CO % CO 2 7.5% 10% 18.5% 100% temperature (K) Fig. 2 TGA output for a sample exposed to 18.5% CO 2,balance N 2 Like many data sets, this one has some shortcomings that should be acknowledged, but should not otherwise discourage the effort to derive useful information from the data. The gap in the data between 65 and 92 Carises from a desire to focus on temperatures likely to be encountered in the adsorber and regenerator of an actual capturesystem. It isclear from several studies of PEI-impregnated sorbents of this type 11,13,14,18,42 Fig. 3 Equilibrium TGA data for the sorbent exposed to CO 2 at various concentrations, balance N 2 barrier) deprotonated by a second amine. However, anot possibility is the formation of carbamic acid, by a trans of a proton from the nitrogen atom of the encounter co plex to one of the oxygens of the CO 2 molecule. This can accomplished either by a bending of the encounter comp or through a catalytic proton exchange with water or anot 3

4 equilibrium problems wt.-% CO % CO 2 7.5% 10% 18.5% 100% temperature (K) Fig. 2 TGA output for a sample exposed to 18.5% CO 2,balance N 2 Like many data sets, this one has some shortcomings that should be acknowledged, but should not otherwise discourage the effort to derive useful information from the data. The gap in the data between 65 and 92 Carises from a desire to focus on temperatures likely to be encountered in the adsorber and regenerator of an actual capturesystem. It isclear from several studies of PEI-impregnated sorbents of this type 11,13,14,18,42 Fig. 3 Equilibrium TGA data for the sorbent exposed to CO 2 at various concentrations, balance N 2 barrier) deprotonated by a second amine. However, anot possibility is the formation of carbamic acid, by a trans of a proton from the nitrogen atom of the encounter co plex to one of the oxygens of the CO 2 molecule. This can accomplished either by a bending of the encounter comp or through a catalytic proton exchange with water or anot 4

5 equilibrium problems DS Mebane, KS Bhat, JD Kress, et al., Phys. Chem. Chem. Phys. 15 (2013)

6 application in amine-based CO 2 sorbents bivariate ΔH-ΔS posterior (left) with and (right) without ab initio priors DS Mebane, KS Bhat, JD Kress, et al., Phys. Chem. Chem. Phys. 15 (2013)

7 equilibrium problems (left) model + discrepancy predictions (right) model-only predictions, with 95% confidence bounds DS Mebane, KS Bhat, JD Kress, et al., Phys. Chem. Chem. Phys. 15 (2013)

8 weight fraction temperature (K) dynamic problems weight fraction temperature time (s) x 10 4 Fig. 2 TGA output for a sample exposed to 18.5% CO 2,balance N Like many data sets, this one has some shortcomings tha should be acknowledged, but should not otherwise discourag the effort to derive useful information from the data. The ga in the data between 65 and 92 Carises from a desire to focu on temperatures likely to be encountered in the adsorber an regenerator of an actual capturesystem. It isclear from severa studies of PEI-impregnated sorbents of this type 11,13,14,18,4 8

9 weight fraction temperature (K) dynamic problems weight fraction temperature time (s) x 10 4 Fig. 2 TGA output for a sample exposed to 18.5% CO 2,balance N Like many data sets, this one has some shortcomings tha should be acknowledged, but should not otherwise discourag the effort to derive useful information from the data. The ga in the data between 65 and 92 Carises from a desire to focu on temperatures likely to be encountered in the adsorber an regenerator of an actual capturesystem. It isclear from severa studies of PEI-impregnated sorbents of this type 11,13,14,18,4 9

10 dynamic problems 10

11 dynamic problems 11

12 dynamic problems 12

13 dynamic discrepancy Bayesian smoothing spline analysis of variance (BSS-ANOVA) BJ Reich, CB Storlie and HD Bondell, Technometrics 51 (2009)

14 dynamic discrepancy Input domain for the GP drastically reduced. Computational complexity of the GP evaluation reduced. Integration of the SDE takes place in the course of the MCMC routine. 14

15 dynamic discrepancy Proof-of-concept with reality (left) creating data for calibration of a simpler model with dynamic discrepancy (below). 15

16 dynamic discrepancy Bivariate posteriors for two of the parameters in t. Left is a case with informative priors, and right with uninformative priors. The blue dot is reality. 16

17 Temperature (K) Temperature (K) dynamic discrepancy Extrapolated Temperature Profile Extrapolated Temperature Profile Time (s) Time (s) Extrapolative predictions in the case of upscaling to a steady-state process model. Left is a case with informative priors, and right with uninformative priors. The black line is reality. 17

18 dynamic discrepancy 18

19 conclusions A novel, Bayesian perspective on multi-scale modeling is introduced. A new framework for Bayesian calibration in dynamic contexts has been demonstrated. The dynamic discrepancy leads to the possibility of an iterative process that can prevent extrapolation. 19

20 thanks David Miller Juan Morinelly Dan Fauth Mac Gray Andrew Lee Joel Kress Contact: David S. Mebane 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. 20