Hydrocarbon-bearing shale has become a major source of energy in recent years. Assessment of rock properties is extremely important in source rocks because of pervasive heterogeneity, thin beds, and incomplete and uncertain knowledge of saturation-porosity-resistivity models. Two major interpretation challenges in hydrocarbon-bearing shale are (a) constructing a reliable petrophysical model, and (b) quantifying the uncertainty of interpretation products. Many factors impact the petrophysical model, including complex solid composition, pore structure, and porous kerogen.

This paper introduces a stochastic joint inversion method specifically developed to address the quantitative petrophysical interpretation of hydrocarbon-bearing shale. The method is based on the rapid and interactive numerical simulation of resistivity and nuclear logs. Instead of property values themselves, the estimation method delivers the posterior probability of each property. The Markov-Chain Monte Carlo (MCMC) algorithm is employed to sample the model space to quantify the posterior distribution of formation properties. This procedure optimally contends with the challenges of complex mineralogy. Compared to traditional deterministic estimation procedures, the new interpretation method explicitly quantifies the uncertainty of hydrocarbon-bearing shale properties. Additionally, it allows the use of fit for-purpose statistical correlations between water saturation, salt concentration, porosity, and electrical resistivity to implement uncertain, non-Archie resistivity models derived from core data, including those affected by total organic carbon (TOC). The estimation method also explicitly corrects for shoulder-bed effects on well logs across thin beds, thereby providing enhanced layer-by-layer values of solid composition, porosity, and fluid saturation. In the case of underdetermined estimation problems, i.e. when the number of measurements is lower than the number of unknowns, the use of a-priori information enables plausible results within pre-specified petrophysical and compositional bounds.

The developed stochastic interpretation technique is successfully verified with data acquired in the Barnett shale. Core data are combined into a-priori information for interpretation of nuclear and resistivity logs. Results consist of mineral concentrations, TOC, and porosity together with their uncertainty. The agreement between estimated mineral/fluid concentrations and core data is better than 80%.

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