Pore structure characterization and permeability estimation with a modified multimodal Thomeer pore size distribution function for carbonate reservoirs

Abstract

Pore structure of carbonate reservoirs is complex and multimodal. In order to characterize the pore structure of complex carbonate, a modified multimodal Thomeer pore size distribution (PSD) function was developed, which was based on the multimodal Gaussian density function and three controlling parameters including peak position, peak height and full width at half maximum (FWHM). The Expectation-Maximization algorithm for Gaussian mixture model was utilized to obtain three controlling parameters for the calculation of Thomeer parameters, namely the extrapolated displacement pressure, the percent bulk volume occupied by mercury at infinite capillary pressure and the pore geometrical factor. Three permeability models were proposed based on the Thomeer parameters and compared with the previous models. The results show that PSD curve of 55% samples need more than two Gaussian density function, which illustrates the multimodal characteristic. Thomeer parameters relate to the controlling parameters of Gaussian density function. The peak position moved toward larger capillary pressure with the increase of extrapolated displacement pressure and pore geometrical factor. The peak height has positive correlation with the percent bulk volume occupied by mercury at infinite capillary pressure and negative correlation with pore geometrical factor respectively. FWHM has positive correlation with pore geometrical factor. The extrapolated displacement pressure derived from the first Gaussian density function has a high correlation with permeability, which demonstrates that permeability is mainly controlled by the maximum pore throat radius. We found that when the sample has the percentage occupied by the first porous system larger enough than 21.64%, its permeability is dominated by the first porous system with the maximum pore throat radius; otherwise, it would be influenced by the second porous system. The comparative study shows that permeability models that has considered the influence of second porous system could improve the accuracy of permeability estimation for the complicated carbonate samples.