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

Abstract

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 3.5h 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. The parametric bootstrap method provides a promising alternative to the MCMC approach for fast uncertainty quantification of the underlying geophysical inverse problems.