Predicting permeability of tight carbonates using a hybrid machine learning approach of modified equilibrium optimizer and extreme learning machine

It is a problematic task to perform petro-physical property prediction of carbonate reservoir rocks in most cases, specifically for permeability prediction since a carbonate rock most commonly contains grains of heterogeneous size distributions. Consequently, the permeability calculation of tight rocks in laboratories is costly and very time-consuming. Therefore, this study aims to tackle this issue by developing novel hybrid models based on combination of the modified version of the equilibrium optimizer (EO), i.e., MEO, and two conventional machine learning algorithms, namely extreme learning machine (ELM) and artificial neural network (ANN). The MEO employs a mutation mechanism in order to avoid trapping in local optima of EO by increasing the search capabilities. In this study, ELM-MEO and ANN-MEO, novel metaheuristic ELM-based and ANN-based algorithms, were constructed to predict the permeability of tight carbonates. In addition, ANN, ELM, RF, RVM and MARS combined with particle swarm optimization and genetic programming algorithm have a better insight into the performances for preferably predicting the permeability carbonates. The results illustrate that the proposed ELM-MEO model with R² = 0.9323, RMSE = 0.0612 and MAE = 0.0442 in training stage and R² = 0.8743, RMSE = 0.0806 and MAE = 0.0660 in testing stage, outperformed other ELM-based and ANN-based metaheuristic models in predicting the permeability of tight carbonates at all levels.