\sigma_f = s_w \cdot \sigma_w(T) + s_o \cdot \sigma_o(T) + s_g \cdot \sigma_g(T)

where

volumetric fractions of water, oil and gas phases: 

electrical conductivity of water, oil and gas phases

fluid temperature


In many practical applications the 
electrical conductivity of hydrocarbons is much less than that of produced water  so that  can be approximated as:

\sigma_f \approx s_w \cdot \sigma_w(T)


Fluid Resistivity of the miltiphase fluid mix can be found as:

\rho_f = \sigma_f^{-1}

See also


Petroleum Industry /  Upstream / Subsurface E&P Disciplines / Fluid Analysis /  Fluid Conductivity & Fluid Resistivity