An application of a multiindex, time-fractional differential equation to evaluate heterogeneous, fractured rocks

A multiindex, distributed fractional differential equation is derived and solved in terms of the Laplace transformation. Potential applications proposed model include study fluid flow heterogeneous rocks, examination bimodal exchange between mobile-immobile regions groundwater systems, incorporation existence liesegang bands fractured addressing influences faulted other skin at interfaces, among others. Asymptotic solutions that reveal structure resulting are presented; addition, they provide for ensuring accuracy numerical computations. Fractional flux laws based on Continuous Time Random Walks (CTRW) serve as a linchpin to account complex geological considerations arise fluids rocks. Results intended be applied Theis scale when combined with geological/geophysical models production statistics all aspects subsurface flow: geothermal hydrocarbon fluids, injection into aquifers, geologic sequestration hazardous waste disposal. may extended role wellbores such horizontal wells more systems.