Physics informed convolutional neural network for TOC estimation in heterogeneous Barren Measures Shales

The total organic carbon content is one of the key controls on hydrocarbon potential in unconventional shale systems. In the Indian Barren Measures Shales, TOC estimation from wireline logs remains challenging due to the strong heterogeneity, variable mineralogy, and limited core-calibrated geochemical measurements of shales. Standard empirical methods, such as the ΔlogR technique, capture first-order trends but often fail to generalise across mineral compositions. Purely data-driven machine learning models improve flexibility but may produce physically inconsistent predictions when sample sizes are small or when petrophysical responses are nonlinear.

This work presents a Physics Informed Convolutional Neural Network designed to estimate TOC from gamma ray, bulk density, and resistivity logs while embedding rock physics behaviour directly into the learning process. The network uses one dimensional convolutional filters to learn depth dependent patterns associated with organic richness, and incorporates the ΔlogR principle as a soft constraint in the loss function. The training workflow includes depth windowing and a hybrid loss function that balances data fidelity with physics consistency, which stabilises learning under limited sample availability.

Using 104 depth-indexed TOC measurements, the model was trained with five-fold cross-validation and a range of physics weighting factors. The final configuration achieved a mean absolute error (MAE) of 0.3, a root mean square error (RMSE) of 0.4, and a Pearson correlation coefficient (r) of 0.9, representing an improvement over both a standard multilayer perceptron (MAE = 0.6, RMSE =1, r =0.6) and the classical ΔlogR approach (MAE = 0.9, RMSE =1.3, r =0.4). These results show that physics informed learning provides a reliable and physically consistent framework for petrophysical characterisation in heterogeneous unconventional reservoirs, offering a generalizable workflow that integrates geological knowledge with machine intelligence to support improved formation evaluation and reduce uncertainty in reservoir assessment.