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 10(2) mu m, 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 approximate to 2.63 and D approximate to 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.