Accurate permeability estimation in tight carbonates is a key reservoir characterization challenge, more pronounced with heterogeneous pore structures. Experiments on large volumes of core samples are required to precisely characterize permeability in such reservoirs which means investment of large amounts of time and capital. Therefore, it is imperative that an integrated model exists that can predict field-wide permeability for un-cored sections to optimize reservoir strategies. Various studies exist with a scope to address this challenge, however, most of them lack universality in application or do not consider important carbonate geometrical features. Accordingly, this work presents a novel correlation to determine permeability of tight carbonates as a function of carbonate pore geometry utilizing a combination of machine learning and optimization algorithms.

Primarily, a Deep Learning Neural Network (NN) is constructed and further optimized to produce a data-driven permeability predictor. Customization of the model to tight-heterogenous pore-scale features is accomplished by considering key geometrical carbonate topologies, porosity, formation resistivity, pore cementation representation, characteristic pore throat diameter, pore diameter, and grain diameter. Multiple realizations are conducted spanning from a perceptron-based model to a multi-layered neural net with varying degrees of activation and transfer functions. Next, a physical equation is derived from the optimized model to provide a stand-alone equation for permeability estimation. Validation of the proposed model is conducted by graphical and statistical error analysis of model testing on unseen dataset.

A major outcome of this study is the development of a physical mathematical equation which can be used without diving into the intricacy of artificial intelligence algorithms. To evaluate performance of the new correlation, an error metric comprising of average absolute percentage error (AAPE), root mean squared error (RMSE), and correlation coefficient (CC) was used. The proposed correlation performs with low error values and gives CC more than 0.95. A possible reason for this outcome is that the machine learning algorithms can construct relationship between various non-linear inputs (for e.g., carbonate heterogeneity) and output (permeability) parameters through its inbuilt complex interaction of transfer and activation function methodologies.