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LaTeX Math Block
anchorepsilonf
alignmentleft
\epsilon_f(T) = 0.25
s_w  \cdot
\left[ 1+ 9 \cdot P_f + 3 \cdot \sqrt{ 9 P_f^2 + 2 P_f +1} \right] LaTeX Math Block
anchorPf
alignmentleft
P_f(T) 
\frac{(\epsilon -1)(2\epsilon+1)}{9\epsilon} + \left( 1-s_w \right) \cdot \frac{\epsilon-1}{\epsilon+2} = s_w
\cdot
 P_w + s_o
\cdot
 P_
o
g + s_g
\cdot 
P_g
LaTeX Math Block
anchorsigma_f
alignmentleft
P_w
(T)
 =  \frac{(\epsilon_w-1)(2\epsilon_w+1)}{9 \, \epsilon_w}
LaTeX Math Block
anchorsigma_f
alignmentleft
P_o(T) = \frac{\epsilon_o-1}{\epsilon_o+2}
LaTeX Math Block
anchorsigma_f
alignmentleft
P_g(T) = \frac{\epsilon_g-1}{\epsilon_g+2}
LaTeX Math Block
anchorepsilon_w
alignmentleft
\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
LaTeX Math Block
anchor
sigma
epsilon_
f
o
alignmentleft
P
\epsilon_o(T) =
\frac{\epsilon_o-1}{\epsilon_o+2}
 16 ÷ 20
LaTeX Math Block
anchor
sigma
epsilon_
f
g
alignmentleft
P
\epsilon_g(T) =
\frac{\epsilon_g-1}{\epsilon_g+2}
1 ÷ 2

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, \, P_o, \, P_g

electrical polarization of water, oil and gas phases

LaTeX Math Inline
body\epsilon_w, \, \epsilon_o, \, \epsilon_g

relative dielectric permittivity of water, oil and gas phases

LaTeX Math Inline
bodyT

fluid temperature

...

Show If
grouparax
Panel
bgColorpapayawhip
titleARAX

References

[pdf] A. H. Harvey and E. W. Lemmon, Method for Estimating the Dielectric Constant of Natural Gas Mixtures, International Journal of Thermophysics, Vol. 26, No. 1, January 2005 ,DOI: 10.1007/s10765-005-2351-5

[pdf] Eric F. May et al, Density, dielectric constant and PVT measurementsof a gas condensate fluid, Journal of Petroleum Science and Engineering 41 (2004) 297–308https://www.dropbox.com/s/7haygqxdc7bzmu9/Harvey-Lemmon-50062.pdf?dl=0