Fluid
    substitution is one of the important means for analyzing the impact of fluid on
    reservoir rock physical parameters. During fluid substitution, Wood’s equation
    is widely used to determine bulk modulus of mixed-phase fluid. But for
    carbonate reservoirs, because of the low porosity of the matrix, heterogeneous
    filling exists in rocks, so Wood’s equation is not suitable any more. Instead, Patchy
    saturation model can be applied under this situation. Through the study of an
    extreme case of Patchy saturation model, an equation for calculating bulk
    modulus of the mixed-phase fluid filled with patchy saturation is given.
    Homogenous filled (Wood’s equation) and fully patchy saturation model are two
    extreme cases of fluid saturation, and the corresponding equations for the two
    model corresponding to the upper and lower limit of the bulk modulus of
    mixed-phase fluid.