Near-exponential relationship between effective stress and permeability of porous rocks revealed in Gangi's phenomenological models and application to gas shales

• Gangi's phenomenological permeability models for intact and fractured rocks revisited.
• The power law permeability models can be approximated by exponential equations.
• Ranges of effective pressure under which the approximations hold are defined.
• Semi-empirical compressibilities that are related to rock properties are obtained.
• The models have been applied to the experimental permeability data for six gas shales.

A number of theoretical models, as well as empirical equations obtained by fitting specific experimental data, have been developed to describe the relationship between effective stress and permeability of intact and fractured porous rocks. It has been found that most experimental data can be fitted using exponential equations. In this study the modified power law equations by Gangi for intact and fractured rocks are revisited to evaluate their applicability for modeling experimental permeability data which display exponential or near-exponential effective stress dependency. It has been shown that Gangi's power law equations for both intact and fractured rocks can be approximated, over the range of effective stresses of practical interest, by exponential equations with compressibilities that are related to the physical properties of the rock. The significance of this work is that it has provided further theoretical evidence for the apparent exponential relationship between effective stress and permeability. Moreover, it allows for more vigorous theoretical equations to be applied with the easiness of empirical exponential equations. This is demonstrated by applying the models to the experimental permeability data for six gas shales reported recently.