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).{{cite journal

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}} 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.

:$\backslash mathit\{TEM\}\; =\; \backslash frac\{k\; k\_\{\backslash mathit\{r\}\}\}\{\backslash phi\; \backslash mu\}$

in which $k$ is the absolute permeability, $k\_\backslash mathit\{r\}$ 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. Furthermore, TEM-function in two-phase flow systems is an extension of RQI (rock quality index) for single-phase systems.

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

:$\backslash text\{Average\; kr\}\; =\; \backslash frac\{\backslash sum\_\{i=1\}^n\backslash mathit\{TEM\}\_i\}\{\backslash sum\_\{i=1\}^n\backslash left(\backslash frac\{k\}\{\backslash phi\; \backslash mu\}\backslash right)\_i\}\; =\; \backslash frac\{\backslash sum\_\{i=1\}^n\backslash left(\backslash frac\{k\; k\_\{\backslash mathit\{r\}\}\}\{\backslash phi\; \backslash mu\}\backslash right)\_i\}\{\backslash sum\_\{i=1\}^n\backslash left(\backslash frac\{k\}\{\backslash phi\; \backslash mu\}\backslash right)\_i\}$