Growth of correlated pore-scale structures in sedimentary rocks: A dynamical model

Recent laboratory measurements have shown that pore surfaces of most sedimentary rocks have a fractal dimension ranging mostly between 2.6 and 2.8. The lower and upper cutoffs for fractal behavior are 10^-2 and 10² μm, respectively. Moreover, qualitative observations indicate that the fractal dimension increases with diagenetic alteration. To explain these measurements and observations, we construct a physical model of mineral deposition and dissolution on a substrate. We propose that when formation dynamics are reaction controlled, the forming pore-grain interface can be described by a nonlinear partial differential equation for interface growth. We construct a discrete particle deposition model corresponding to these dynamics. Three-dimensional computer simulations of the model show that resulting pore-grain interfaces are fractal, with a fractal dimension that depends on interface growth conditions and varies between D ≈ 2.63 and D ≈ 2.84, in close agreement with observations. Additionally, our model predicts an increase of the amplitude of interface undulations with dissolution and fractal dimension. We conclude that geometrical measures of pore-grain interfaces, such as the fractal dimension and the roughness amplitude, are an indicator of the diagenetic history of sedimentary rocks.