Improved estimation of two-phase capillary pressure with nuclear magnetic resonance measurements via machine learning

Capillary pressure plays a crucial role in determining the spatial distribution of oil and gas, particularly in medium-to-low permeability reservoirs, where it is closely linked to the rock's pore structure and wettability. In these environments, pore structure is the primary factor influencing capillary pressure, with different pore types affecting fluid transport through varying degrees of hydrocarbon saturation. One of the main challenges in characterizing pore structure is how to use data from core plugs to establish a relationship with microscopic pore and throat properties, enabling more accurate predictions of capillary pressure. While special core analysis laboratory experiments are effective, they are time-consuming and expensive. In contrast, nuclear magnetic resonance (NMR) measurements, which provide information on pore body size distribution, are faster and can be leveraged to estimate capillary pressure using machine learning algorithms. Recently, artificial intelligence methods have also been applied to capillary pressure prediction (Qi et al., 2024).

Currently, no readily applicable predictive model exists for estimating an entire capillary pressure curve directly from standard petrophysical logs and core data. Although porescale imaging and network modeling techniques can compute capillary pressure from micro-CT rock images (Øren and Bakke, 2003; Valvatne and Blunt, 2004), these approaches are time-consuming, limited to small sample volumes, and not yet practical for routine reservoir evaluation. In this study, we introduce rock classification techniques and implement a data-driven machine learning (ML) method to estimate saturation-dependent capillary pressure from core petrophysical properties. The new model integrates cumulative NMR data and densely resampled core measurements as training data, with prediction errors quantified throughout the process. To approach the common condition of sparsely sampled training data, we transformed the prediction problem into an overdetermined one by applying composite fitting to both capillary pressure and pore throat size distribution, and Gaussian cumulative distribution fitting to the NMR $T_2$ measurements, generating evenly sampled data points. Using these preprocessed input features, we performed classification based on the natural logarithm of the permeability-to-porosity ratio $\left(\ln \left(k/\varphi \right)\right)$ to cluster distinct rock types. For each rock class, we applied regression techniques—such as random forest (RF), k-nearest neighbors (k-NN), extreme gradient boosting (XGB), and artificial neural networks (ANN)—to estimate the logarithm of capillary pressure. The methods were tested on blind core samples, and performance comparisons among different estimation methods were based on the relative standard error of predictions.

Results indicate that NMR data are sensitive to the pore structure of rocks and significantly improve the prediction of capillary pressure and pore throat size distribution. Extreme Gradient Boosting and Random Forest models performed the best, with average estimation errors of 5 % and 10 %, respectively, for capillary pressure and pore throat size distribution. In contrast, prediction errors increased to 25 % when NMR $T_2$ data were excluded as an input feature. The use of traditional Gaussian model fitting, and higher-resolution resampling ensured that the training data covered a broad range of variability. Including NMR $T_2$ data as an input feature enhanced the model's ability to capture multimodal peaks in unconventional rocks, making the prediction problem overdetermined. By predicting vector functions from vector input features, we effectively reduced prediction errors. This interpretation workflow can be used to construct representative classification models and estimate capillary pressure across a wide saturation range.