(1)	$\begin{array}{l}\displaystyle \epsilon_f(T) = 0.25 \cdot \left[ 1+ 9 \cdot P_f + 3 \cdot \sqrt{ 9 P_f^2 + 2 P_f +1} \right]\end{array}$

(2)	$\begin{array}{l}\displaystyle P_f(T) = s_w \cdot P_w + s_o \cdot P_o + s_g \cdot P_g\end{array}$

(3)	$\begin{array}{l}\displaystyle P_w(T) = \frac{(\epsilon_w-1)(2\epsilon_w+1)}{9 \, \epsilon_w}\end{array}$

(4)	$\begin{array}{l}\displaystyle \epsilon_w(T) = 87.74 - 0.40008 \cdot T + 9.398 \cdot 10^{-4} \cdot T^2 - 1.41 \cdot 10^{-6} \cdot T^3\end{array}$

(5)	$\begin{array}{l}\displaystyle P_o(T) = \frac{\epsilon_o-1}{\epsilon_o+2}\end{array}$

(6)	$\begin{array}{l}\displaystyle P_g(T) = = \frac{\epsilon_g-1}{\epsilon_g+2}\end{array}$

where

$\begin{array}{l}s_w, \, s_o, \, s_g\end{array}$	volumetric fractions of water, oil and gas phases: $\begin{array}{l}s_w + s_o + s_g = 1\end{array}$
$\begin{array}{l}P_w, \, P_o, \, P_g\end{array}$	electrical polarization of water, oil and gas phases
$\begin{array}{l}\epsilon_w, \, \epsilon_o, \, \epsilon_g\end{array}$	relative dielectric permittivity of water, oil and gas phases
$\begin{array}{l}T\end{array}$	fluid temperature

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See also