(1) | \epsilon_f = 0.25 \cdot \left[ 1+ 9 \cdot P_f + 3 \cdot \sqrt{ 9 P_f^2 + 2 P_f +1} \right] |
(2) | P_f = s_w \cdot P_w(T) + s_o \cdot P_o(T) + s_g \cdot P_g(T) |
(3) | P_w = \frac{(\epsilon_w-1)(2\epsilon_w+1)}{9 \, \epsilon_w} |
(4) | \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 |
where
s_w, \, s_o, \, s_g | volumetric fractions of water, oil and gas phases: s_w + s_o + s_g = 1 |
P_w(T), \, P_o(T), \, P_g(T) | electrical polarization of water, oil and gas phases |
\epsilon_w(T), \, \epsilon_o(T), \, \epsilon_g(T) | relative dielectric permittivity of water, oil and gas phases |
T | fluid temperature |
See also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Fluid Analysis / Fluid Capacitance
[ Dielectric permittivity of water @model ]