The identification of lithology, fluid types, and total organic carbon content are of great priority in the exploration of unconventional hydrocarbons. As a new alternative, a further developed K-means type clustering method is suggested for the evaluation of shale gas formations. The traditional approach of cluster analysis is mainly based on the use of the Euclidean distance for grouping the objects of multivariate observations into different clusters. The high sensitivity of the L2 norm applied to non-Gaussian distributed measurement noises is well-known, which can be reduced by selecting a more suitable norm as distance metrics. To suppress the harmful effect of non-systematic errors and outlying data, the Most Frequent Value method as a robust statistical estimator is combined with the K-means clustering algorithm. The Cauchy-Steiner weights calculated by the Most Frequent Value procedure is applied to measure the weighted distance between the objects, which improves the performance of cluster analysis compared to the Euclidean norm. At the same time, the centroids are also calculated as a weighted average (using the Most Frequent Value method), instead of applying arithmetic mean. The suggested statistical method is tested using synthetic datasets as well as observed wireline logs, mud-logging data and core samples collected from the Barnett Shale Formation, USA. The synthetic experiment using extremely noisy well logs demonstrates that the newly developed robust clustering procedure is able to separate the geological-lithological units in hydrocarbon formations and provide additional information to standard well log analysis. It is also shown that the Cauchy-Steiner weighted cluster analysis is affected less by outliers, which allows a more efficient processing of poor-quality wireline logs and an improved evaluation of shale gas reservoirs.
Hydraulic conductivity is one of the crucial parameters used to identify the potentiality and productivity of groundwater aquifers. This research employs an integrated approach using geophysical well logging, exploratory factor analysis and surface electrical resistivity methods to detect the vertical and horizontal variation of hydraulic conductivity in Bahri city, Sudan. Based on the geophysical well logs of Spontaneous potential (SP), natural gamma ray (GR), and electrical resistivity (RS), Csókás method is used to determine the continuous variation of hydraulic conductivity along the aquifer. Csókás method is an experimentally modified version of the Kozeny–Carman equation and is based on the formation factor of the groundwater aquifer and the effective grain size. This approach is performed in three groundwater boreholes, and the obtained hydraulic conductivities showed a close agreement with that of the pumping test analysis. Furthermore, the hydraulic conductivity is measured using multivariate statistical factor analysis. This statistical approach relies on the correlation between the extracted factors and petrophysical and hydrogeological parameters. In this research, a strong negative linear correlation between the first factor and hydraulic conductivity is indicated. Consequently, a site-specific equation is suggested for continuous estimation of hydraulic conductivity along the aquifer. In the last stage, the results obtained from the Csókás method are interpolated with vertical electrical sounding (VES) measurements using to detect the horizontal variation of hydraulic conductivity throughout the studied area. This was achieved by combining the hydraulic conductivities of geophysical well logging and vertical electrical soundings to obtain a consistent estimation. As a result, the variation of hydraulic conductivity is obtained, and the average was 1.9 m/day which shows a close agreement with the average of the previous investigations (1.5 m/day). This approach is highly recommended since it can enhance data coverage, cutting down the expense of hydrogeological investigations and lowering the uncertainty of the hydrogeological models.
Well logging inversion was carried out using Levenberg-Marquardt (LM) and Singular Value Decomposition (SVD) techniques for the determination of petrophysical parameters, respectively. In this research, synthetic data contaminated with 5% Gaussian noise, and field data were used to compare the results from the two inversion methods. MATLAB software has been developed to solve the overdetermined inverse problem. The estimated petrophysical parameters from both inversion methods had been compared to one another in terms of robustness to noise, rock interface differentiation, different fluid prediction, and the accuracy of the estimated parameters. This research returns the reason to the inner iterative loop which is considered more about the Jacobian matrix sensitivity. The inversion results showed that both methods can be used in petrophysical data estimation for a reliable well-log data interpretation.
This paper shows the availability of using the Bayesian classification method to predict class membership probabilities in one of the deep tight reservoirs in Western Desert, Egypt. The workflow of our project that using the Bayesian method used the deterministic petrophysical results of three training wells to train the data and extract the classifiers. The classified data were modeled using Gaussian distribution for each lithofacies. The used wells were acquired from a deep Jurassic gas reservoir in the Western Desert of Egypt. The fitting between actual and modeled data has been reached by minimizing the L2 norm. Besides, a cross-validation process was used for validating the resulted classifiers. Finally, the Bayesian classification method can predict the GWC with an accuracy of 4 m. To avoid probability interference caused by the compacted shale more data should be added to the initial model.
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