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LaTeX Math Block
anchorsigma_f
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P_w =  \frac{(\epsilon_w-1)(2\epsilon_w+1)}{9 \, \epsilon_w}
LaTeX Math Block
anchor1
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 \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\epsilon_f 

where

LaTeX Math Inline
bodys_w, \, s_o, \, s_g

volumetric fractions of water, oil and gas phases: 

LaTeX Math Inline
bodys_w + s_o + s_g = 1

LaTeX Math Inline
bodyP_w(T), \, P_o(T), \, P_g(T)

electrical polarization of water, oil and gas phases

LaTeX Math Inline
body\epsilon_w(T), \, \epsilon_o(T), \, \epsilon_g(T)

relative dielectric permittivity of water, oil and gas phases

LaTeX Math Inline
bodyT

fluid temperature

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