The neutron porosity is usually abbreviated NPHI or PHIN  on log panels and denoted as   in equations.

N_n = \phi N_f + V_{sh} N_{sh} + V_m N_m

which can be re-arranged as:

N_n = N_m  + V_{sh} \cdot (N_{sh} -N_m) + \phi \cdot (N_f - V_{sh} N_m)

The key measurement is compensated neutron log   (log name CNL) from Compensated Neutron Tool.

The key model parameters are:

The values of  and  are calibrated for each lithofacies individually and can be assessed as vertical axis cut-off on  cross-plot against the lab core porosity  and shaliness . 

The model also accounts for saturating rock fluids with fluid CNL value .

In overbalance drilling across permeable rocks the saturating fluid is usually mud filtrate. 

In underbalance drilling the saturating fluid is identified from resistivity logs.  

The total neutron porosity  equation is:

\phi_n = \frac{N_n - N_m}{N_f-V_{sh}N_m}

The effective neutron porosity  equation is:

\phi_{en} = \phi_n -  \frac{N_{sh}-N_m}{N_f - V_{sh}N_m} \cdot V_{sh}

The fluid density  is calculated in-situ using the following equation:

N_f = s_{xo} \rho_{mf} + (1-s_{xo}) ( s_w N_w + s_o N_o + s_g N_g )

The matrix CNL is calculated from the following equation:

N_m = \sum_i V_{m,i} N_{m,i}

where 

 – volume share of the i-th matrix component,

 – density of the i-th matrix component,

.