Geostatistical modeling of porosity and evaluating the local and global distribution

Abstract

Porosity is one of the main variables needed for reservoir characterization. For this volumetric variable, there are many methods to simulate the spatial distribution. In this article, porosity was analyzed and modeled in the local and global distribution. For simulation, Sequential Gaussian simulation (SGS) and Gaussian Random Function (GRFS) were applied. Also, kriging was used to estimate the porosity at specific locations. The main purpose of this work was to investigate the porosity to compare geostatistical simulation and estimation methods in a sandstone reservoir as a real case study. First, the data sets were normalized by the Normal Scores Transformation (NST) and stratigraphic coordinate. The model of experimental variograms was fitted in the vertical and horizontal directions. For the simulation methods, 10 realizations were generated by each method. The Q-Q plots were calculated, and both sets of quintiles (Target Porosity Distribution versus Porosity realization) came from normal distributions with the following correlation coefficients: 0.93, 0.94 and 0.97 related to GRFS, SGS and Kriging, respectively. The extracted variograms from realizations showed that the kriging couldn’t reproduce the variograms with global distribution. For local validation, the cross-validation was evaluated and three wells were omitted. The re-estimation of porosity was considered at located well logs through the well sections window where the kriging had a better performance with minimum error to estimate porosity locally. Finally, the cross-sectional models were generated by each algorithm which showed that the simple kriging tries to produce smoother distribution, whereas conditional simulations (SGS and GRFS) try to represent more global-detailed sections.