New Approaches of Porosity-Permeability Estimations and Quality Factor Q Characterization based on Sonic Velocity, Critical Porosity, and Rock Typing

Abstract

Many investigations have been discussed and it is a well-recognized fact that sonic wave velocity is not only influenced by its rock matrix and the fluids occupying the pores but also by the pore architecture details of the rock bulk. This situation still brings a lack of understanding, and this study is purposed to clearly explain how acoustic velocity and quality factor correlate with porosity, permeability and details internal pore structure in porous rocks. This study employs 67 sandstone and 120 carbonate core samples collected from several countries in Europe, Australia, Asia, and USA. The measured values are available for porosity ϕ, permeability k, clay content Vcl, compressional velocity Vp, and quality factor Qp in saturated and pressurized conditions. Then, a proposed method is developed by re-arrangement on Kozeny equation to perform rock typing based on pore structure similarity which called as pore geometry-structure (PGS). The proposed rock typing method allows investigating the influential primary factors that control acoustic velocity and quality factor. Besides that, basic rock physics equations for sonic velocity and critical porosity concepts are also involved and derived to obtain a new solution to predict porosity and permeability. At least eight rock groups are established from rock typing with its Kozeny constant. This constant is a product of pore shape factor Fs and tortuosity τ. Then, the relations of velocity and quality factor versus porosity, permeability, pore geometry (k/ϕ)0.5, and pore structure (k/ϕ3) are constructed. One can find that each relation among the rock groups of each lithology is clearly separated and produce high correlations. Velocity and quality factor tend to be high with an increase in Kozeny constant. However, for a given porosity for all the groups, velocity and quality factor increase remarkably with a decrease in Kozeny constant. These all mean that velocity and quality factor increase with either an increase in the complexity of pore systems or, at the same pore complexity, a decrease in specific internal surface area. On the other hand, each rock group for both sandstone and carbonate has its critical porosity and it strongly correlates with velocity and porosity. Finally, critical porosity becomes a specific property of rock groups having similar pore geometry and structure. As a novelty, the empirical equations are derived to estimate compressional velocity and quality factor based on petrophysical parameters. Furthermore, this study also establishes empirical equations for predicting porosity and permeability by using compressional wave velocity, critical porosity, and PGS rock typing.