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LaTeX Math Block
anchor1sigma_f
alignmentleft
\sigma_f = s_w \cdot \sigma_w(T) + s_o \cdot \sigma_o(T) + s_g \cdot \sigma_g(T)

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\sigma_w(T), \, \sigma_o(T), \, \sigma_g(T)

electrical conductivity
of the water
 of water, oil and gas phases

LaTeX Math Inline
bodyT

fluid temperature


In many practical applications the 
electrical conductivity of hydrocarbons is much less than that of produced water 

LaTeX Math Inline
body\sigma_w(T) \gg \sigma_o(T) \gg \sigma_g(T)
so that 
LaTeX Math Block Reference
anchorsigma_f
 can be approximated as:

LaTeX Math Block
anchorZZ7WU
alignmentleft
\sigma_f \approx s_w \cdot \sigma_w(T)

...


Fluid Resistivity of the miltiphase fluid mix can be found as:

LaTeX Math Block
anchorrhof
alignmentleft
\rho_f = \sigma_f^{-1}

See also

...

Petroleum Industry /   Upstream /  Data Acquisition / Well & Reservoir Surveillance Subsurface E&P Disciplines / Well loggingFluid Analysis / Cased-Hole Logging / Production Logging (PLT) Borehole Flow Profile (BFP) / Fluid Conductivity Log (FCOND)  Fluid Conductivity & Fluid Resistivity