Page tree

Versions Compared

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.
LaTeX Math Block
anchorepsilonf
alignmentleft
\epsilon_f(T) = 0.25
s_w \, V_{mw} \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( s_o \, V_{mo} + s_g \, V_{mg} \right) \cdot \frac{\epsilon-1}{\epsilon+2} = P = 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)
 = V_{mw} \cdot \frac{(\epsilon_w-1)(2\epsilon_w+1)}{9 \, \epsilon_w}
LaTeX Math Block
anchorsigma_f
alignmentleft
P_o(T) = V_{mw} \cdot \frac{\epsilon_o-1}{\epsilon_o+2}
LaTeX Math Block
anchorsigma_f
alignmentleft
P_g(T) = V_{mw} \cdot\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}
3
LaTeX Math Block
anchor
sigma
epsilon_
f
g
alignmentleft
P
\epsilon_
g
o(T) = 
\frac{\epsilon_g-1}{\epsilon_g+
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

...