Inversion of pore aspect ratio distribution based on effective medium theories

The pore aspect ratio is an important parameter to describe pore structure characteristics of porous rocks. At present, the most classical model used to obtain complete pore aspect ratio distribution of rocks is the David-Zimmerman (D-Z) pore structure model. The model assumes that the rock is composed of solid mineral matrix, a group of stiff pores having the same aspect ratio and a distribution of micro-cracks with different aspect ratios, in which the material matrix and stiff pores are pressure-independent. Based on the assumptions, the pore aspect ratio and porosity of stiff pores and micro-cracks are extracted from the pressure dependence of ultrasonic velocities. The key point of this method is that the cumulative crack density is taken as a bridge to establish the intrinsic relationship between rock elastic modulus and pore aspect ratio through effective medium theory. However, in the D-Z model, the cumulative fracture density of multi-porosity rock is directly calculated using the formula of crack density theoretically only applicable for rock with a single pore type, which makes it difficult to achieve good inversion accuracy in many cases. In order to improve the classical D-Z model, this paper proposes an inversion method for calculating pore aspect ratio distribution using thought experiment. In this method, the cumulative crack density is accurately computed through a fictitious unloading path, and the classical D-Z model based on DEM and MT is extended to the case of KT and SCA. As a result, a detailed inversion workflow combining with four effective medium theories is established. This workflow is applied in the aspect ratio distribution extraction for a set of sandstones and carbonate samples to illustrate the capability of the method. The results show that the proposed method is in better agreement with the actual data as compared to the D-Z model, and can be applied to both sandstone and carbonate samples. In addition, the proposed method is almost independent of the selection of the effective medium theories. The pore structure parameter obtained from the four theories changes with pressure in a similar way. Although there is a slight difference in these results, it gradually disappears with increasing pressure. Our method is an important supplement to the classical D-Z pore structure model. It is of great significance in the characterization of rock pore structure, prediction of fluid saturated rock velocity and simulation of pore-scale squirt flow.

Automated summary

A method for calculating pore aspect ratio distribution using thought experiment was proposed to improve the classical D-Z pore structure model, resulting in a detailed inversion workflow incorporating four effective medium theories. The proposed method showed better agreement with actual data compared to the D-Z model, and was almost independent of the selection of effective medium theories.