TEM-function

In petroleum engineering, TEM (True Effective Mobility), also called TEM-function, is a criterion to characterize dynamic fluid-flow characteristics of rocks (or dynamic rock quality). TEM is a function of Relative permeability, Porosity, absolute Permeability and fluid Viscosity, and can be determined for each fluid phase separately. TEM-function has been derived from Darcy's law for multiphase flow.

$TEM={\frac {kk_{\mathit {r}}}{\phi \mu }}$

in which k is the absolute Permeability, kr is the Relative permeability, φ is the Porosity, and μ is the fluid Viscosity. Rocks with better fluid dynamics (i.e., experiencing a lower pressure drop in conducting a fluid phase) have higher TEM versus saturation curves. Rocks with lower TEM versus saturation curves resemble low quality systems.

TEM-function in analyzing Relative permeability data is analogous with Leverett J-function in analyzing Capillary pressure data.

Also, TEM-function can be used for averaging relative permeability curves (for each fluid phase, separately (i.e., water, oil, gas, CO2)).

${\text{Average kr}}={\frac {\sum _{i=1}^{n}TEM_{i}}{\sum _{i=1}^{n}({\frac {k}{\phi \mu }})_{i}}}={\frac {\sum _{i=1}^{n}({\frac {kk_{\mathit {r}}}{\phi \mu }})_{i}}{\sum _{i=1}^{n}({\frac {k}{\phi \mu }})_{i}}}$