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Analysis of well log data using time series models and geostatistical methods

Xenaki Anastasia

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Summary

This thesis focuses on the statistical analysis of well log data from two hydrocarbon reservoirs located in Labrador Island, Western Newfoundland (Canada). The data is obtained from two onshore wells (Finnegan and Seamus). We focus on the analysis of four logs (spontaneous potential, Gamma radiation and two induction logs) from six different formations. The thesis has three main objectives: (i) to estimate the probability distributions and spatial correlations in data obtained from the same well, (ii) to evaluate cross-correlations between logs across the two different wells, and (iii) to explore methods for the reconstruction of missing well log data.With respect to the first objective, the exploratory statistical analysis indicates that the majority of the respective properties do not follow the Gaussian distribution. However, after removing an empirically determined trend function, the residuals are closer to the Gaussian distribution. The spontaneous potential and Gamma radiation indicators can be described by Cauchy and Gumbel distributions, while the induction indicators by means of the Gamma and Weibull distributions. Variogram analysis suggests that spontaneous potential and Gamma Radiation conform to the same type of theoretical variogram model with similar sill and range values.In reference to the second objective, the statistical analysis indicates weak cross correlations between log data measured at the two different wells. The Gamma radiation logs show both positive and negative cross correlations which are overall higher (in magnitude) than for the respective correlations for the other three logs.Regarding the third objective, the comparison of the performance of different imputation, interpolation and time series algorithms for gap filling indicates that linear interpolation, linear weighted moving average and less often the Kalman-ARIMA methods are the top-performing algorithms for well log gap filling.

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