Analysis of permeability based on petrophysical logs: comparison between heuristic numerical and analytical methods

Abstract

A series of novel heuristic numerical tools were adopted to tackle the setback of permeability estimation in carbonate reservoirs compared to the classical methods. To that end, a comprehensive data set of petrophysical data including core and log in two wells was situated in Marun Oil Field. Both wells, Well#1 and Well#2, were completed in the Bangestan reservoir, having a broad diversity of carbonate facies. In the light of high Lorenz coefficients, 0.762 and 0.75 in Well#1 and Well#2, respectively, an extensive heterogeneity has been expected in reservoir properties, namely permeability. Despite Well#1, Well#2 was used as a blinded well, which had no influence on model learning and just contributed to assess the validation of the proposed model. An HFU model with the aim of discerning the sophistication of permeability and net porosity interrelation has been developed in the framework of Amaefule’s technique which has been modified by newly introduced classification and clustering conceptions. Eventually, seven distinct pore geometrical units have been distinguished through implementing the hybridized genetic algorithm and k-means algorithm. Furthermore, a K-nearest neighbors (KNN) algorithm has been carried out to divide log data into the flow units and assigns them to the pre-identified FZI values. Besides, a cross between the ε-SVR model, a supervised learning machine, and the Harmony Search algorithm has been used to estimate directly permeability. To select the optimum combination of the involved logging parameters in the ε-SVR model and reduce the dimensionality problem, a principle component analysis (PCA) has been implemented on Well#1 data set. The result of PCA illustrates parameters, such as permeability, the transit time of sonic wave, resistivity of the unflashed zone, neutron porosity, photoelectric index, spectral gamma-ray, and bulk density, which possess the highest correlation coefficient with first derived PC. In line with previous studies, the findings will be compared with empirical methods, Coates–Dumanior, and Timur methods, which both have been launched into these wells. Overall, it is obvious to conclude that the ε -SVR model is undeniably the superior method with the lowest mean square error, nearly 4.91, and the highest R-squared of approximately 0.721. On the contrary, the transform relationship of porosity and permeability has remarkably the worst results in comparison with other models in error (MSE) and accuracy (R2) of 128.73 and 0.116, respectively.