Modeling Permeability Using Advanced White-Box Machine Learning Technique: Application to a Heterogeneous Carbonate Reservoir

[Image: see text] From exploration to production, the permeability of reservoir rocks is essential for various stages of all types of hydrocarbon field development. In the absence of costly reservoir rock samples, having a reliable correlation to predict rock permeability in the zone(s) of interest is crucial. To predict permeability conventionally, petrophysical rock typing is done. This method divides the reservoir into zones of similar petrophysical properties, and the permeability correlation for each zone is independently developed. The challenge of this approach is that the success depends upon the reservoir’s complexity and heterogeneity and the methods and parameters used for rock typing. As a result, in the case of heterogeneous reservoirs, conventional rock typing methods and indices fail to predict the permeability accurately. The target area is a heterogeneous carbonate reservoir in southwestern Iran with a permeability range of 0.1–127.0 md. In this work, two approaches were used. First, based on permeability, porosity, the radius of pore throats at mercury saturation of 35% (r35), and connate water saturation (S(wc)) as inputs of K-nearest neighbors, the reservoir was classified into two petrophysical zones, and then, permeability for each zone was estimated. Due to the heterogeneous nature of the formation, the predicted permeability results needed to be more accurate. In the second part, we applied novel machine learning algorithms, modified group modeling data handling (GMDH), and genetic programming (GP) to develop one universal permeability equation for the whole reservoir of interest as a function of porosity, the radius of pore throats at mercury saturation of 35% (r35), and connate water saturation (S(wc)). The novelty of the current approach is that despite being universal, the models developed using GP and GMDH performed substantially better than zone-specific permeability, index-based empirical, or data-driven models used in the literature, such as FZI and Winland. The predicted permeability using GMDH and GP resulted in accurate prediction with R(2) of 0.99 and 0.95, respectively, in the heterogeneous reservoir of interest. Moreover, as this study aimed to develop an explainable model, different parameter importance analyses were also applied to the developed permeability models, and r35 was found to be the most impactful feature.