Statistical approaches to leak detection for geological sequestration

[摘要] (cont.) Variability in the residuals translates into uncertainty in CO₂ forecasts. Thus by reducing the spread of the residuals, improving the model increases the signal to noise ratio and improves the ability to detect shifts. A least squares example using CO₂ data from Mauna Loa is used to illustrate the effect of autocorrelation due to systematic seasonal variability on the ability to detect. The issue is that ordinary least squares tends to underestimate uncertainty when data are serially correlated, implying high false positive rates. Improving the model reduces autocorrelation in the residuals by eliminating systematic trends. Because the data exhibit gaps, Lomb periodograms are used to test the residuals for systematic signals. The model chosen by DIC removes all of the growing and seasonal trends originally present at the 5% level of significance. Thus improving the model is a way to reduce autocorrelation effects on false positives. A key issue for future monitoring sites will be demonstrating the ability to detect shifts in the absence of leaks. The urban weekend weekday effect on atmospheric CO₂ is introduced to illustrate how this might happen. A seasonal detrending model is used to remove systematic trends in data at Mauna Loa, Harvard Forest and Salt Lake. Residuals indicate the presence of positive shifts at the latter sites, as expected, with the magnitude of the shift being larger at the urban site than the rural one (~ 8 ppm versus ~ 1 ppm). Normality tests indicate the residuals are non-Gaussian, so a Bayesian method based on Bayes factors is proposed for determining the amount of data needed to detect shifts in non-Gaussian data. The method is demonstrated on the Harvard and Salt Lake CO₂ data. Results obtained are sensitive to the form of the error distribution. Empirical distributions should be used to avoid false positives. The weekend weekday shift in CO₂ is detectable in 48-120 samples at the urban site. More samples are required at the rural one. Finally, back-of-the-envelope calculations suggest the weekend weekday shift in emissions detected in Salt Lake is - 0(0.01) MtCO₂km- yr- 1. This is the equivalent of 1% of 1 MtCO₂ stored belowground leaking over an area of 1 km2 The framework developed in this thesis can be used to detect shifts in atmospheric CO₂ (or other types of) data after data is already available. Further research is needed to address questions about what data to collect. For example, what sensors should be used, where should they be located, and how frequently should they be sampled? Optimal monitoring network design at a given location will require balancing the need to gather more information (for example, by adding sensors) against operational constraints including cost, safety, and regulatory requirements.

[发布机构] Massachusetts Institute of Technology