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## Electrical Conductivity of the Soil / Reservoir

Date: March 27, 2010

The electrical conductivity of the soil varies with the amount of water in the pore space, the salinity of the water, and the temperature.  I like to use a slightly modified form of the Archie's equation to provide a nice correlation of water saturation and temperature to the soil's electrical conductivity.  Dr. Vermeulen and Dr. Chute performed a number of experiments to measure the effect of temperature on the electrical conductivity of oil sands.  McMillan-McGee has done the same for numerous sites where ET-DSP™ is used for in-situ thermal remediation.  Typically the electrical conductivity will increase by a factor of three over a temperature range of 20 to 100 °C for all these sites.  The equation I use is:  The latex code for the equation is:

\begin{equation}
\sigma \left( {S_w ,T} \right) = \underbrace {\sigma _w \frac{{\phi ^m }}
{a}S_w ^2 }_{Salinity\,Effects} \cdot {\kern 1pt}
\underbrace {{\kern 1pt} \sum\limits_{i = 0}^N {a_i  \cdot
\left( {T - T_o } \right)^i } }_{Temperature\,Effects}
\label{eqn:Archie01}
\end{equation}