Uncertainty assessment of porosity and permeability by clustering algorithm and fuzzy arithmetic

Abstract

A hybrid clustering-fuzzy arithmetic algorithm is here proposed, which uses cluster analysis to quantify porosity uncertainty, then the uncertainty is projected to the irreducible water saturation and permeability by the means of fuzzy arithmetic. The proposed method is applied to five wells of the carbonate Sarvak Formation, in an Iranian onshore oil-field. First, cluster analysis is applied to the porosity logs including neutron porosity, bulk density and sonic transit time. The uncertainty range of porosity is defined by the range of neutron porosity in each cluster. In order to estimate the core porosity, neutron porosity is calibrated to the core porosity in each cluster. Due to the average of error, the calibrated clustering-based porosity is at least 33% more accurate than the conventional methods. Based on the generalization ability of porosity estimators, a homogeneous porosity zone is determined northward. Irreducible water saturation, analyzed by the proposed method, has less overestimation, compared to the conventional evaluation of irreducible water saturation. Permeability fuzzy number is compatible with core tests, except in well S1, which is drilled in a location, compressed by two stress regimes (N-S and NW-SE). Two criteria are defined for validating the fuzzy numbers by core data: (i) Crit1 finds an average α-cut of core values; (ii) Crit2 finds the best α-cut to optimize uncertainty interval of the fuzzy number. The α > 0.90 is the most appropriate for porosity and permeability studies.