A hierarchical,network-type,dynamic simulator of the immiscible displacement in heterogeneous porous media is developed to simulate the rate-controlled displacement of two fluids at two scales,from the pore network to the core scale.A cubic network is constructed,where each node is assigned a permeability which is chosen randomly from a distribution function.Moreover,heterogeneities in wettability can be entered as randomly or non-randomly distributed contact angles.The degree of heterogeneity is quantified by the width of the distribution function of the corresponding property(permeability,contact angle).The capillary pressure at each node is calculated by combining a generalized Leverett J-function with a Corey type model.The simulator is used to examine the sensitivity of the transient responses of the axial distribution of fluid saturation and total pressure drop across the network to the heterogeneity as expressed by the permeability/ wettability distribution functions,and the capillary number.Moreover the effects of heterogeneity on the overall(up-scaled) relative permeability functions are elucidated. Input parameters are obtained from either quasi-static simulations of pressure-controlled immiscible displacement in pore networks,or inverse modeling of flow tests on heterogeneous soil columns with the aid a multi-flow path model.
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