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Title: Uncertainty quantification of CO₂ saturation estimated from electrical resistance tomography data at the Cranfield site

A parametric bootstrap approach is presented for uncertainty quantification (UQ) of CO₂ saturation derived from electrical resistance tomography (ERT) data collected at the Cranfield, Mississippi (USA) carbon sequestration site. There are many sources of uncertainty in ERT-derived CO₂ saturation, but we focus on how the ERT observation errors propagate to the estimated CO₂ saturation in a nonlinear inversion process. Our UQ approach consists of three steps. We first estimated the observational errors from a large number of reciprocal ERT measurements. The second step was to invert the pre-injection baseline data and the resulting resistivity tomograph was used as the prior information for nonlinear inversion of time-lapse data. We assigned a 3% random noise to the baseline model. Finally, we used a parametric bootstrap method to obtain bootstrap CO₂ saturation samples by deterministically solving a nonlinear inverse problem many times with resampled data and resampled baseline models. Then the mean and standard deviation of CO₂ saturation were calculated from the bootstrap samples. We found that the maximum standard deviation of CO₂ saturation was around 6% with a corresponding maximum saturation of 30% for a data set collected 100 days after injection began. There was no apparent spatial correlation between the meanmore » and standard deviation of CO₂ saturation but the standard deviation values increased with time as the saturation increased. The uncertainty in CO₂ saturation also depends on the ERT reciprocal error threshold used to identify and remove noisy data and inversion constraints such as temporal roughness. Five hundred realizations requiring 3.5 h on a single 12-core node were needed for the nonlinear Monte Carlo inversion to arrive at stationary variances while the Markov Chain Monte Carlo (MCMC) stochastic inverse approach may expend days for a global search. This indicates that UQ of 2D or 3D ERT inverse problems can be performed on a laptop or desktop PC.« less
Authors:
 [1] ; ORCiD logo [1] ;  [1] ;  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Type:
Accepted Manuscript
Journal Name:
International Journal of Greenhouse Gas Control
Additional Journal Information:
Journal Volume: 27; Journal Issue: C; Journal ID: ISSN 1750-5836
Publisher:
Elsevier
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; uncertainty quantification; CO₂ saturation; electrical resistance tomography; parametric bootstrap; geophysical monitoring; nonlinear Monte Carlo inversion
OSTI Identifier:
1201550

Yang, Xianjin, Chen, Xiao, Carrigan, Charles R., and Ramirez, Abelardo L.. Uncertainty quantification of CO₂ saturation estimated from electrical resistance tomography data at the Cranfield site. United States: N. p., Web. doi:10.1016/j.ijggc.2014.05.006.
Yang, Xianjin, Chen, Xiao, Carrigan, Charles R., & Ramirez, Abelardo L.. Uncertainty quantification of CO₂ saturation estimated from electrical resistance tomography data at the Cranfield site. United States. doi:10.1016/j.ijggc.2014.05.006.
Yang, Xianjin, Chen, Xiao, Carrigan, Charles R., and Ramirez, Abelardo L.. 2014. "Uncertainty quantification of CO₂ saturation estimated from electrical resistance tomography data at the Cranfield site". United States. doi:10.1016/j.ijggc.2014.05.006. https://www.osti.gov/servlets/purl/1201550.
@article{osti_1201550,
title = {Uncertainty quantification of CO₂ saturation estimated from electrical resistance tomography data at the Cranfield site},
author = {Yang, Xianjin and Chen, Xiao and Carrigan, Charles R. and Ramirez, Abelardo L.},
abstractNote = {A parametric bootstrap approach is presented for uncertainty quantification (UQ) of CO₂ saturation derived from electrical resistance tomography (ERT) data collected at the Cranfield, Mississippi (USA) carbon sequestration site. There are many sources of uncertainty in ERT-derived CO₂ saturation, but we focus on how the ERT observation errors propagate to the estimated CO₂ saturation in a nonlinear inversion process. Our UQ approach consists of three steps. We first estimated the observational errors from a large number of reciprocal ERT measurements. The second step was to invert the pre-injection baseline data and the resulting resistivity tomograph was used as the prior information for nonlinear inversion of time-lapse data. We assigned a 3% random noise to the baseline model. Finally, we used a parametric bootstrap method to obtain bootstrap CO₂ saturation samples by deterministically solving a nonlinear inverse problem many times with resampled data and resampled baseline models. Then the mean and standard deviation of CO₂ saturation were calculated from the bootstrap samples. We found that the maximum standard deviation of CO₂ saturation was around 6% with a corresponding maximum saturation of 30% for a data set collected 100 days after injection began. There was no apparent spatial correlation between the mean and standard deviation of CO₂ saturation but the standard deviation values increased with time as the saturation increased. The uncertainty in CO₂ saturation also depends on the ERT reciprocal error threshold used to identify and remove noisy data and inversion constraints such as temporal roughness. Five hundred realizations requiring 3.5 h on a single 12-core node were needed for the nonlinear Monte Carlo inversion to arrive at stationary variances while the Markov Chain Monte Carlo (MCMC) stochastic inverse approach may expend days for a global search. This indicates that UQ of 2D or 3D ERT inverse problems can be performed on a laptop or desktop PC.},
doi = {10.1016/j.ijggc.2014.05.006},
journal = {International Journal of Greenhouse Gas Control},
number = C,
volume = 27,
place = {United States},
year = {2014},
month = {6}
}