Best Practices in Automatic Permeability Estimation: Machine-Learning Methods vs. Conventional Petrophysical Models

Multiple physics-based and empirical models have been introduced 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 complex rocks. This paper documents best practices for permeability estimation by comparing results obtained with both machine-learning methods and conventional petrophysical models. Furthermore, comparisons are performed of different salient statistical and petrophysical features obtained with the two approaches. 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. Dimensionality reduction techniques were implemented, such as principal component analysis (PCA), singular value decomposition (SVD), discrete wavelet transforms (DWT), and deep-learning-based autoencoders to generate latent-space well logs, 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 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. Results were compared 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 neural networks best estimate permeability from triple-combo well logs across a wide range of variation (0.001 to 2,000 md) with an average of 16% relative standard error when using the original well logs. Estimations improved using latent-space well logs with discrete wavelet transforms. Machine-learning algorithms reduced the estimation error to less than 13% while implementing a fully connected autoencoder resulted in less than 10% error. The Timur-Coates model is the most reliable for data sets with a priori information about irreducible water saturation, yielding less than 22% relative standard error, yet it requires prior data classification to improve estimation accuracy. Estimation workflows proved to be generalizable, as they can be used for permeability estimation in both conventional and unconventional reservoirs. The new procedure is computationally efficient, with estimations obtained in less than 2 minutes of CPU time. Uncertainty estimates show that permeability calculations are accurate, as their distributions border the true values within ± 5 md. However, it is important to note that training wells must cover the widest possible range of measurements and petrophysical and fluid properties to improve the estimation of permeability in test wells. Data normalization does not always improve machine-learning estimations, especially across very low (0.0001 to 20 md) or high (150 to 2,000 md) permeability ranges, where it resulted in a 25% increase in permeability estimation error compared to non-normalized data.