Pore System Characterization and Petrophysical Rock Classification Using a Bimodal Gaussian Density Function

Abstract

This paper introduces a bimodal Gaussian density function to characterize pore-size distributions in terms of incremental pore volume versus logarithmic pore-throat radius. An inverse problem is formulated and solved to reconstruct mercury injection capillary pressure curves by enforcing a bimodal Gaussian pore-size distribution. The bimodal Gaussian model generates six petrophysically interpretable attributes which provide a quantitative basis for petrophysical modeling and rock typing. Correlations between these attributes and their associated petrophysical properties are investigated to verify interpretations. In the field case, the correlation coefficient (R2) between absolute permeability, end-point gas relative permeability and the mean value of large pore-throat size mode are 0.93 and 0.715, respectively. Correlation (R2=0.613) is also observed between critical water saturation and pore volume connected by small pore-throat sizes. Petrophysical modeling based on the bimodal Gaussian pore-size distribution with sufficient core data calibration predicts static and dynamic petrophysical properties that are in agreement with laboratory core measurements. The quantitative pore-system description underlies a new petrophysical rock typing method that combines all relevant pore-system attributes. Verification of the method was performed with field data from two key wells in the Hugoton carbonate gas field, Kansas.