Efficient sonic log estimations by geostatistics, empirical petrophysical relations, and their combination: Two case studies from Iranian hydrocarbon reservoirs

Abstract

In this study, the potential of geostatistical (GS) methods in estimating petrophysical logs (Vp sonic logs here), independently and in combination with empirical petrophysical relations (PRs) was evaluated. Moreover, the efficiencies of these two methods were compared with each other and with that of a simple PR which was Gardner's Relation (GR) here. The GS-GR method combines GS with GR to acquire a higher accuracy beyond a simple geostatistical prediction which is already expected to have a higher accuracy than that of GR. For this purpose, two different data-sets from Iranian hydrocarbon reservoirs were used. In the first case, three adjacent wells from a reservoir consisting dominantly of carbonate rocks with a rather high hydrocarbon saturation were used. To evaluate the generalizability of the propsed techniques, they were assessed on another data-set from a well in a different hydrocarbon reservoir, mainly consisting of the sandstone-carbonate lithology (with a lower hydrocarbon saturation). To estimate the sonic logs of compressional wave velocities (Vp), Gardner's Relation (GR) was implemented here using the existing density logs in the wells. Then, several univariate and bivariate geostatistical methods (the latter combined with GR) were used to assess the capabilities of the GS and the combined GS-GR methods. To evaluate the efficiencies of the GS and GS-GR methods, Cross-Validation (CV) and Jackknife (JK) techniques were employed here. Based on the CV and JK assessments, for the both reservoirs, the GS and methods especially those combined with GR (i.e. GS-GR), generally provided considerably higher accuracies than those of the GR method. GS-GR framework facilitated the integration of the secondary variable of density (ρ) here to further increase the accuracy of Vp estimations. Hence, geostatistics (GS), especially combined with the petrophysical relations (GS-PR) could be suggested as an accurate and functional tool in estimating the missing logs, having some logs from the same or the other neighboring wells.