\epsilon_f(T) = 0.25 \cdot \left[ 1+ 9 \cdot P_f + 3 \cdot \sqrt{ 9 P_f^2 + 2 P_f +1} \right]
P_f(T) = s_w \cdot P_w + s_o \cdot P_o + s_g \cdot P_g
P_w(T) =  \frac{(\epsilon_w-1)(2\epsilon_w+1)}{9 \, \epsilon_w}
 \epsilon_w(T) = 87.74 - 0.40008 \cdot T + 9.398 \cdot  10^{-4} \cdot T^2
- 1.41  \cdot  10^{-6} \cdot T^3
P_o(T) = \frac{\epsilon_o-1}{\epsilon_o+2}

P_g(T) =  = \frac{\epsilon_g-1}{\epsilon_g+2}

where

volumetric fractions of water, oil and gas phases: 

electrical polarization of water, oil and gas phases

relative dielectric permittivity of water, oil and gas phases

fluid temperature


See also


Petroleum Industry /  Upstream / Subsurface E&P Disciplines / Fluid Analysis / Fluid Capacitance

Dielectric permittivity of water @model ]


References


https://www.dropbox.com/s/7haygqxdc7bzmu9/Harvey-Lemmon-50062.pdf?dl=0