TEM-function

In petroleum engineering, TEM (True Effective Mobility), also called TEM-function, is a criterion to characterize dynamic two-phase flow characteristics of rocks (or dynamic rock quality). [1][2][3][4][5][6][7][8][9][10] 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. [1]

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

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.[1]

TEM-function in analyzing Relative permeability data is analogous with Leverett J-function in analyzing Capillary pressure data. Furthermore, TEM-function in two-phase flow systems is extension of RQI (Rock Quality Index) for single-phase systems. [1]

Also, TEM-function can be used for averaging relative permeability curves (for each fluid phase, separately (i.e., water, oil, gas, CO2)).[1]

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