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

From explorationto production, the permeability of reservoirrocksis essential for various stages of all types of hydrocarbon fielddevelopment. In the absence of costly reservoir rock samples, havinga reliable correlation to predict rock permeability in the zone(s)of interest is crucial. To predict permeability conventionally, petrophysicalrock typing is done. This method divides the reservoir into zonesof similar petrophysical properties, and the permeability correlationfor each zone is independently developed. The challenge of this approachis that the success depends upon the reservoir's complexityand heterogeneity and the methods and parameters used for rock typing.As a result, in the case of heterogeneous reservoirs, conventionalrock typing methods and indices fail to predict the permeability accurately.The target area is a heterogeneous carbonate reservoir in southwesternIran 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 classifiedinto two petrophysical zones, and then, permeability for each zonewas estimated. Due to the heterogeneous nature of the formation, thepredicted permeability results needed to be more accurate. In thesecond part, we applied novel machine learning algorithms, modifiedgroup modeling data handling (GMDH), and genetic programming (GP)to develop one universal permeability equation for the whole reservoirof interest as a function of porosity, the radius of pore throatsat mercury saturation of 35% (r35), and connate watersaturation (S (wc)). The novelty of the currentapproach is that despite being universal, the models developed usingGP 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 andGP resulted in accurate prediction with R (2) of 0.99 and 0.95, respectively, in the heterogeneous reservoir ofinterest. Moreover, as this study aimed to develop an explainablemodel, different parameter importance analyses were also applied tothe developed permeability models, and r35 was foundto be the most impactful feature.