Determination of permeability index using Stoneley slowness analysis, NMR models, and formation evaluations: a case study from a gas reservoir, south of Iran

• The bisection method was used for permeability determination by Stoneley slowness.
• The least squares method was used for calibration of the empirical models.
• The XPT data were used to demonstrate the validity of the results.
• The calibration has reduced the RMSE for the empirical models.
• The calibration had more effect on the intrinsic permeability than other models.

In hydrocarbon reservoirs, permeability is one of the most critical parameters with a significant role in the production of hydrocarbon resources. Direct determination of permeability using Stoneley waves has always had some difficulties. In addition, some un-calibrated empirical models such as Nuclear Magnetic Resonance (NMR) models and petrophysical evaluation model (intrinsic permeability) do not provide reliable estimates of permeability in carbonate formations. Therefore, utilizing an appropriate numerical method for direct determination of permeability using Stoneley waves as well as an appropriate calibration method for the empirical models is necessary to have reliable results.This paper shows the application of a numerical method, called bisection method, in the direct determination of permeability from Stoneley wave slowness. In addition, a linear regression (least squares) method was used to calibrate the NMR models including Schlumberger Doll Research (SDR) and Timur–Coates models as well as the intrinsic permeability equation (permeability from petrophysical evaluations). The Express Pressure Tester (XPT) permeability was considered as an option for the reference permeability. Therefore, all permeability models were validated for the Stoneley permeability and calibrated for the empirical models with the XPT permeability. In order to have a quantitative assessment on the results and compare the results before and after the calibration, the Root Mean Squares Error (RMSE) was calculated for each of the used models. The results for the Stoneley permeability showed that, in many points there was not much difference between the Stoneley permeability calculated by the bisection method and the XPT permeability. Comparing the results showed that the calibration of the empirical models reduced their RMSE values. As a result of the calibration, the RMSE was decreased by about 39% for the SDR model, 18% for the Timur–Coates model, and 91% for the petrophysical evaluations model. Presented bisection method calculates permeability directly without of any inversion or external calibration.