GROWTH OF CORRELATED PORE-SCALE STRUCTURES IN SEDIMENTARY-ROCKS - A DYNAMICAL MODEL

Recent laboratory measurements have shown that pore surfaces of most s edimentary rocks have a fractal dimension ranging mostly between 2.6 a nd 2.8. The lower and upper cutoffs for fractal behavior are 10(-2) an d 10(2) mu m, respectively. Moreover, qualitative observations indicat e that the fractal dimension increases with diagenetic alteration. To explain these measurements and observations, we construct a physical m odel 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 deposi tion model corresponding to these dynamics. Three-dimensional computer simulations of the model show that resulting pore-grain interfaces ar e fractal, with a fractal dimension that depends on interface growth c onditions and varies between D approximate to 2.63 and D approximate t o 2.84, in close agreement with observations. Additionally, our model predicts an increase of the amplitude of interface undulations with di ssolution and fractal dimension. We conclude that geometrical measures of pore-grain interfaces, such as the fractal dimension and the rough ness amplitude, are an indicator of the diagenetic history of sediment ary rocks.