The rock volume  is split into three major components: pore volume , shale volume  and rock martix :

\Omega_r = \Omega_e +\Omega_{sh} + \Omega_m

The usual practice is to use relative volumes:

\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:

\phi_e +V_{sh} + V_m = 1

The relative pore volume  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: . 

The relative shale volume  is called shaliness and contains three major components: silt  , clay  and clay bound water :

V_{sh} = V_{\rm silt} + V_c + V_{\rm cbw}

The log name is VSH.

The clay bound water  is usually measured as the fraction of shale volume:

V_{\rm cbw} = s_{\rm cbw} \cdot V_{sh} 

where  is called bulk volume water of shale (BVWSH).

The total porosity is defined as the sum of effective porosity  and clay bound water :

\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:

\phi_e  = \phi_{\rm connected} + \phi_{\rm closed}

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

\phi_{\rm connected} = \phi_{\rm free} + \phi_{\rm connate}

Finally, the pore volume available for flow is represented by the following formula: 

\phi_{\rm flow} = \phi_e \cdot (1 - s_{\rm connate})

where 

s_{\rm connate}=\frac{\phi_{\rm connate}}{\phi_{\rm open}}

As one may expect the value has the most linear correlation with permeability.