Volumetric Rock Model

@wikipedia

The rock volume  $//<![CDATA[ \begin{array}{l}\Omega_R\end{array} //]]>$ is split into three major components: effective pore volume  $//<![CDATA[ \begin{array}{l}\Omega_e\end{array} //]]>$, shale volume  $//<![CDATA[ \begin{array}{l}\Omega_{sh}\end{array} //]]>$ and rock martix  $//<![CDATA[ \begin{array}{l}\Omega_m\end{array} //]]>$:

The usual practice is to use relative volumes:

which are measured in V/V units (or fracs) and honor the following constraint:

The relative effective pore volume  $//<![CDATA[ \begin{array}{l}\phi_e\end{array} //]]>$ contains free or connate fluids (water, oil , gas) and called effective porosity.

The log name is PHIE.

It corresponds to air porosity of the dried laboratory cores:  $//<![CDATA[ \begin{array}{l}\phi_e = V_{\rm air \, core}\end{array} //]]>$. 

The relative shale volume  $//<![CDATA[ \begin{array}{l}V_{sh}\end{array} //]]>$ is called shaliness and contains three major components: silt   $//<![CDATA[ \begin{array}{l}V_{\rm silt}\end{array} //]]>$, clay  $//<![CDATA[ \begin{array}{l}V_c\end{array} //]]>$ and clay bound water  $//<![CDATA[ \begin{array}{l}V_{\rm cbw}\end{array} //]]>$:

The log name is VSH.

The clay bound water  $//<![CDATA[ \begin{array}{l}V_{\rm cbw}\end{array} //]]>$ is usually measured as the fraction of shale volume:

where  $//<![CDATA[ \begin{array}{l}s_{\rm cbw}\end{array} //]]>$ is called bulk volume water of shale (BVWSH).

The total porosity is defined as the sum of effective porosity  $//<![CDATA[ \begin{array}{l}\phi_e\end{array} //]]>$ and clay bound water  $//<![CDATA[ \begin{array}{l}V_{\rm cbw}\end{array} //]]>$:

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. 

Nevertheles, 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.

On the other hand, the effective porosity itself is also not the final measure of the volume available for flow.

It includes the unconnected pores which do not contribute to flow:

Besides the connected effective porosity includes the connate fluids which may be not flowing in the practical range of subsurface temperatures, pressure gradients and sweeping agents:

Finally, the useful porosity which represents a volume available for flow can be 

where  $//<![CDATA[ \begin{array}{l}s_{irr}\end{array} //]]>$ represents a fraction of pore volume, occupied by irreducible fluid (usually water).