A subterranean reservoir where the pore space of media or formation rock is multimodal, and the media may have imbedded multiple scales of fracture networks, is simulated. The modes of the pore system and the scale of fracture networks are each represented as a separate, but interactive continuum with the other. A matrix solution with arrangement of the reservoir data adapted for parallel computation is utilized. The simulation allows multiple continua to be co-located and multi-interacting, in that each continuum may have current and counter-current multiple multiphase exchanges with other continua.
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