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 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.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 1201550
- Journal Information:
- International Journal of Greenhouse Gas Control, Vol. 27, Issue C; ISSN 1750-5836
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Uncertainty analysis and probabilistic segmentation of electrical resistivity images: the 2D inverse problem: Uncertainty Analysis of 2D-ERT
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journal | September 2017 |
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