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.

在大多数情况下，对碳酸盐岩储层岩石进行岩石物理性质预测是一项有问题的任务，特别是对于渗透率预测，因为碳酸盐岩最常包含不均匀粒度分布的颗粒。因此，实验室中致密岩石的渗透率计算成本高昂且非常耗时。因此，本研究旨在通过开发基于平衡优化器 (EO) 的修改版本（即 MEO）和两种传统机器学习算法（即极限学习机（ELM）和人工神经网络）的组合的新型混合模型来解决这个问题。网络 (ANN)。MEO 采用变异机制，通过增加搜索能力来避免陷入 EO 的局部最优。在本研究中，ELM-MEO 和 ANN-MEO，构建了基于 ELM 和 ANN 的新型元启发式算法来预测致密碳酸盐岩的渗透率。此外，ANN、ELM、RF、RVM和MARS结合粒子群优化和遗传编程算法对优选预测渗透性碳酸盐岩的性能有更好的了解。结果表明，所提出的 ELM-MEO 模型具有R ²  = 0.9323、RMSE = 0.0612 和 MAE = 0.0442 在训练阶段和R ²  = 0.8743、RMSE = 0.0806 和 MAE = 0.0660 在测试阶段，在预测致密碳酸盐岩渗透率方面优于其他基于 ELM 和基于 ANN 的元启发式模型在所有级别。