Integrated metaheuristic approaches for estimation of fracture porosity derived from fullbore formation micro-imager logs: Reaping the benefits of stand-alone and ensemble machine learning models

Fracture porosity is one of the most effective parameters for reservoir productivity and recovery efficiency. This study aims to predict and improve the accuracy of fracture porosity estimation through the application of advanced machine learning (ML) algorithms. A novel approach was introduced for the first time to estimate fracture porosity by reaping the benefits of petrophysical and fullbore formation micro-imager (FMI) data based on employing various stand-alone, ensemble, optimisation and multi-variable linear regression (MVLR) algorithms. This study proposes a ground-breaking two-step committee machine (CM) model. Petrophysical data containing compressional sonic-log travel time, deep resistivity, neutron porosity and bulk density (inputs), along with FMI-derived fracture porosity values (outputs), were employed. Nine stand-alone ML algorithms, including back-propagation neural network, Takagi and Sugeno fuzzy system, adaptive neuro-fuzzy inference system, decision tree, radial basis function, extreme gradient boosting, least-squares boosting, least squares support vector regression and k-nearest neighbours, were trained for initial estimation. To improve the efficacy of stand-alone algorithms, their outputs were combined in CM structures using optimisation algorithms. This integration was applied through five optimisation algorithms, including genetic algorithm, ant colony, particle swarm, covariance matrix adaptation evolution strategy (CMA-ES) and Coyote optimisation algorithm. Considering the lowest error, the CM with CMA-ES showed superior performance. Subsequently, MVLR was employed to improve the CMs further. Employing MVLR to combine the CMs yielded a 57.85% decline in mean squared error and a 4.502% improvement in the correlation coefficient compared to the stand-alone algorithms. The results of the benchmark analysis validated the efficacy of this approach.