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A Bayesian multivariate model using Hamiltonian Monte Carlo inference to estimate total organic carbon content in shale

Prediction of total organic carbon (TOC) content using geophysical logs is one of the key steps in shale reservoir characterization. Various empirical relations have previously been utilized for the estimation of TOC content from well logs; however, uncertainty quantification in the model estimation is often ignored while performing TOC estimation in a deterministic framework. We introduce the problem of TOC estimation in a Bayesian setting with the goal of enhancing the TOC content prediction together with the quantification of the uncertainty in model prediction. In order to signify the uncertainty, we draw random samples of model parameters from the posterior distribution by realizing multi-dimensional stochastic processes within the Hamiltonian Monte Carlo (HMC) algorithm. The posterior model for the variables that influence TOC estimation is conditioned on the available well log observations and is further defined by the a priori and likelihood distributions. We demonstrate examples of applications of this approach to estimate the TOC content on two real field datasets from the well-known Devonian Duvernay shale of western Canada, and Silurian shale of the Ahnet Basin. The accuracy in the estimation is arbitrated by comparing the prediction results with those obtained using the two most widely used empirical models. Corroborating the results by the laboratory-measured TOC contents demonstrate that the Bayesian approach offers more reliable and better confidence in predictions when compared to the empirical models as it provides additional information on the prediction uncertainty. Finally, the implications of the present approach are derived in terms of depositional environments to characterize the high TOC content zone in the studied organic shale formations.