Dependence of critical porosity on pore geometry and pore structure and its use in estimating porosity and permeability

Abstract

It is well recognized that the wave velocity is not only influenced by its constituent materials but also by the details of the rock bulk. This situation may bring about data points of P-wave velocity Vp measured on a large number of rock samples against either porosity or permeability of the frequently scattered although certain trends may exist. This paper presents the results of a study by employing rock samples on which ϕ, k, and Vp are measured in attempt to characterize critical porosity ϕc and its relation to other rock properties. The approach used in this study is the use of Kozeny equation. The equation is believed to account for all parameters influencing absolute permeability of porous media. A mathematical manipulation done on the equation has resulted in a power law equation that relates pore geometry √(k/ϕ) to pore structure k/ϕ3. Three different sets of sandstone amounting totally to as many as 716 samples were provided in this study. The properties measured are ϕ, k, and Vp, and grain size. For each sandstone data set, at least there are nine groups of the rock samples obtained. When Vp is plotted against ϕ, it is found that each group of each sandstone data set has both its own ϕc and an excellent relation of ϕ, Vp, and ϕc. Furthermore, combining all the basic equation for Vp, Kozeny equation, and the empirical relation for porosity results in a model equation to predict permeability. In conclusion, for the sandstones employed, ϕc is a specific property of a group of rocks having a similar pore geometry.