Origin of fractional flow dimension to a partially penetrating well in stratified fractured reservoirs. New results based on the study of synthetic fracture networks

To determine the origin of fractional flow dimensions identified from the results of pumping tests in fractured reservoir, the geometric specificities of synthetic networks are compared to flow dimensions obtained from simulated pumping tests. The modeled reservoirs studied in this paper constitute a system of orthogonal fractures generated by using a pseudo-random process controlled by simple mechanical rules. Flow induced by pumping is simulated while considering the intersections between discontinuities as pipes with various apertures. In many cases, the simulations result in fractional flow dimension although the flow-path network is not self-similar at different scales. We also show that the range of pipe conductance can affect early-time flow behavior although late-time flow behavior appears to be insensitive to the latter. Finally we propose an explanation for the fractional dimension of flow while considering the spatial distribution of interconnections between flow paths.