Several physics-based and empirical models have been developed in the past to estimate permeability from well logs. Estimation of flow-related petrophysical properties from borehole geophysical measurements is challenging in the presence of spatially heterogeneous rocks. Core measurements are usually regarded as ground truth for inferring in-situ petrophysical properties but are typically sparsely sampled or non-existent. Modern machine-learning methods enable new strategies to estimate permeability from well logs and achieve accurate results, hence mitigating the lack of densely sampled core measurements.
We document best practices for permeability estimation from well logs and core data by comparing results obtained with both machine-learning (ML) methods and conventional petrophysical models. The new interpretation workflow incorporates the usage of latent-space well logs to estimate permeability at the resolution of core samples and well logs, while uncertainty is quantified as part of the process.
Data preprocessing is paramount to successfully applying ML methods to well-log interpretation. We preprocessed core data acquired in key wells that incorporate expert knowledge, depth-matched core porosity with log-calculated porosity, interpolated triple-combo well logs to core depth, and performed feature engineering on the resulting data suite. To generate latent-space well logs, dimensionality reduction techniques were implemented, such as principal component analysis (PCA), singular value decomposition (SVD), discrete wavelet transforms (DWT), and deep-learning-based autoencoders, from which models were trained to estimate permeability. From the latent-space models, we performed regression using random forest, k-nearest neighbors, artificial neural network (ANN), and the Timur-Coates model to estimate the logarithm of permeability from core porosity and well logs (gamma ray, bulk density, neutron porosity, and photoelectric factor). Finally, the uncertainty of the estimated permeability was calculated based on the validation variance function for the test set. Comparisons of performance among the various estimation methods were performed based on the relative standard error of permeability estimations. To reach general conclusions, the methods were tested on data sets from a variety of carbonate and clastic (shaly and clean) rocks, both conventional and unconventional.
Results indicate that random forest and artificial neural networks best estimate permeability from triple-combo well logs across a wide range of permeability variations (0.001 to 2,000 md) with an average of 16% relative standard error when using the original well logs. Estimations improve when using latent-space well logs with discrete wavelet transforms. ML algorithms reduced the error to less than 13%, while implementing a fully connected autoencoder resulted in less than 10% error using the core-resolved support system. We obtained 5% average permeability estimation errors at well-log resolution, a 50% further decrease compared to the core support. The Timur-Coates model/approach is the most reliable for data sets with a priori information about irreducible water saturation, yielding less than 22% relative standard error. Yet, prior data classification is required to improve estimation accuracy. Estimation workflows proved generalizable, as they can be used for permeability estimation in conventional and unconventional reservoirs.
