(1)	$\begin{array}{l}\displaystyle s_w \, V_{mw} \cdot \frac{(\epsilon -1)(2\epsilon+1)}{9\epsilon} + \left( s_o \, V_{mo} + s_g \, V_{mg} \right) \cdot \frac{\epsilon-1}{\epsilon+2} = P = s_w P_w + s_o P_g + s_g P_g\end{array}$

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

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

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

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

(6)	$\begin{array}{l}\displaystyle \epsilon_o(T) = 3\end{array}$

(7)	$\begin{array}{l}\displaystyle \epsilon_o(T) = 2\end{array}$

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