Equivalent permeability of shale rocks: Simple and accurate empirical coupling of organic and inorganic matter

•A new permeability model of shale coupling organic/inorganic matrix is established.•Effects of permeability contrast, TOC (vol) and random distribution are considered.•The model is simple but accurate for all contrast and TOC (vol) after validation. Coupling the organic/inorganic permeabilities in shale is fundamental. Simple treatments, including the arithmetic/geometric average methods, are problematic and can lead to large errors. More complicated methods can generate reasonable results but are much more expensive. In this work, a simple and accurate empirical model for the equivalent permeability of shale considering permeability contrast between organic and inorganic matter and TOC is established. Geometric explanation of the parameters in the model is also provided. Afterwards, model validation against numerical data demonstrates the accuracy of the model in all realistic scenarios. Moreover, model comparison with arithmetic/geometric average methods shows the superiority of the model in accurate calculation while keeping the form simple. Finally, the model is applied to liquid flow in shale, and the results are analyzed. The model is highly recommended for theoretical studies in shale gas/oil that need coupling of the organic and inorganic permeabilities, including single-phase and multi-phase flows.