A permeability–porosity relationship for mudstones

The relationship between permeability and porosity for fine-grained clastic sediments (“mudstones”) is a key constitutive equation for modelling subsurface fluid flow and is fundamental to the quantification of a range of geological processes. For a given porosity, mudstone permeability varies over a range of 2–5 orders of magnitude. We show here that much of the range can be explained by variations in lithology, which we define simply and pragmatically by clay content (mass fraction of particles less than 2 microns in diameter). Using clay content as the quantitative lithology descriptor, we have used a dataset (clay content range of 12–97%; porosity range of 0.04–0.78; six orders of magnitude permeability range) comprising 376 data points to derive a new bedding perpendicular permeability (K, m2) – void ratio (e = porosity/(1-porosity)) relationship as a function of clay content (CF):ln(K)=−69.59−26.79⋅CF+44.07⋅CF0.5+(−53.61−80.03⋅CF+132.78⋅CF0.5)⋅ⅇ+(86.61+81.91⋅CF−163.61⋅CF0.5)⋅ⅇ0.5ln(K)=−69.59−26.79⋅CF+44.07⋅CF0.5+(−53.61−80.03⋅CF+132.78⋅CF0.5)⋅ⅇ+(86.61+81.91⋅CF−163.61⋅CF0.5)⋅ⅇ0.5The coefficient of regression (r2) = 0.93. At a given porosity, the inclusion of the quantitative lithological descriptor, clay content reduces the predicted range of permeability from 2 to 5 orders of magnitude to one order.