Permeability is an important parameter in the petrophysical study of a reservoir and serves as a key tool in the development of an oilfield. This is while its prediction, especially in carbonate reservoirs with their relatively lower levels of permeability compared to sandstone reservoirs, is a complicated task as it has larger contributions from heterogeneously distributed vugs and fractures. In this respect, the present research uses the data from two wells (well A for modeling and well B for assessing the generalizability of the developed models) drilled into a carbonate reservoir to estimate the permeability using composite formulations based on least square support vector machine (LSSVM) and multilayer extreme learning machine (MELM) coupled with the so-called cuckoo optimization algorithm (COA), particle swarm optimization (PSO), and genetic algorithm (GA). We further used simple forms of convolutional neural network (CNN) and LSSVM for the sake of comparison. To this end, firstly, the Tukey method was applied to identify and remove the outliers from modeling data. In the next step, the second version of the nondominated sorting genetic algorithm (NSGA-II) was applied to the training data (70% of the entire dataset, selected randomly) to select an optimal group of features that most affect the permeability. The results indicated that although including more input parameters in the modeling added to the resultant coefficient of determination (R2) while reducing the error successively, yet the slope of the latter reduction got much slow as the number of input parameters exceeded 4. In this respect, petrophysical logs of P-wave travel time, bulk density, neutron porosity, and formation resistivity were identified as the most effective parameters for estimating the permeability. Evaluation of the results of permeability modeling based on root-mean-square error (RMSE) and R2 shed light on the MELM-COA as the best-performing model in the training and testing stages, as indicated by (RMSE = 0.5600 mD, R2 = 0.9931) and (RMSE = 0.6019 mD, R2 = 0.9919), respectively. The generalizability assessment conducted on the prediction of permeability in well B confirmed the MELM-COA can provide reliable permeability predictions by achieving an RMSE of 0.9219 mD. Consequently, the mentioned methodology is strongly recommended for predicting the permeability with high accuracy in similar depth intervals at other wells in the same field should the required dataset be available.

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