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LaTeX Math Block
anchorsigma_fepsilonf
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\epsilon_f = 0.25 \cdot \left[ 1+ 9 \cdot P_f + 3 \cdot \sqrt{ 9 P_f^2 + 2 P_f +1} \right]
LaTeX Math Block
anchorPf
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\epsilonP_f = s_w \cdot \epsilonP_w(T) + s_o \cdot \epsilonP_o(T) + s_g \cdot \epsilonP_g(T)
LaTeX Math Block
anchorsigma_f
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\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
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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