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The rock volume
\Omega_r is split into three major components: pore volume
\Omega_e, shale volume
\Omega_{sh} and rock martix
\Omega_m:
| (1) |
\Omega_r = \Omega_e +\Omega_{sh} + \Omega_m |
The usual practice is to use relative volumes:
| (2) |
\phi_e = \frac{\Omega_e}{\Omega_r}, \quad V_{sh} = \frac{\Omega_{sh}}{\Omega_r}, \quad V_m = \frac{\Omega_m}{\Omega_r} |
which are measured in V/V units (or fracs) and honor the following constraint:
| (3) |
\phi_e +V_{sh} + V_m = 1 |
The relative pore volume
\phi_e is also called effective porosity (PHIE) and contains free and connate fluids (water, oil , gas).
It corresponds to air porosity of the dried laboratory cores:
\phi_e = V_{\rm air \, core}.
The relative shale volume
V_{sh} is called shaliness and contains three major components: silt
V_{\rm silt}, clay
V_c and clay bound water
V_{\rm cbw}:
| (4) |
V_{sh} = V_{\rm silt} + V_c + V_{\rm cbw} |
The log name is VSH.
The clay bound water
V_{\rm cbw} is usually measured as the fraction of shale volume:
| (5) |
V_{\rm cbw} = s_{\rm cbw} \cdot V_{sh} |
where
s_{\rm cbw} is called bulk volume water of shale (BVWSH).
The total porosity is defined as the sum of effective porosity
\phi_e and clay bound water
V_{\rm cbw}:
| (6) |
\phi_t = \phi_e + V_{\rm cbw} = \phi_e + s_{\rm cbw} V_{sh} |
The log name is PHIT.
The term total porosity is more of a misnomer as it actually does not represent a pore volume for free flow as the clay bound water is essential part of the rock solids.
Nevertheless, the total porosity property has been adopted by petrophysics as a part of interpretation workflow where the intermediate value of total porosity from various sensors leads not only to effective porosity but also to lithofacies analysis.
The effective porosity is not a final measure of the volume available for flow.
It includes the unconnected pores which do not contribute to flow:
| (7) |
\phi_e = \phi_{\rm connected} + \phi_{\rm closed} |
Besides the connected effective pore volume
\phi_{\rm open} includes the connate fluids which may be not flowing in the practical range of subsurface temperatures, pressure gradients and sweeping agents:
| (8) |
\phi_{\rm connected} = \phi_{\rm free} + \phi_{\rm connate} |
Finally, the pore volume available for flow is represented by the following formula:
| (9) |
\phi_{\rm flow} = \phi_e \cdot (1 - s_{\rm connate}) |
where
| |
s_{\rm connate}=\frac{\phi_{\rm connate}}{\phi_{\rm open}} |
|
a fraction of pore volume, occupied by connate fluid (usually water or oil) and estimated in laboratory Special Core Analysis (SCAL) |
As one may expect the
\phi_{\rm flow} value has the most linear correlation with permeability.
