Neutron count in time interval

# Neutron Porosity

 N_{near}[\tau] = \int_{\tau_1}^{\tau_2} N_{near}(t) dt

 N_{far}[\tau] = \int_{\tau_1}^{\tau_2} N_{far}(t) dt

 N2F = \frac{ N_{near}[\tau]}{N_{far}[\tau]}

Diffusion Correction

 \phi_T = N2F[\tau] + \Delta_{\tau}(\phi_N)

# Neutron Sigma

 N_{near}(t) = N_{near}(0) \exp ( - t \, \Sigma_{near} )

 N_{far}(t) = N_{far}(0) \exp ( - t \, \Sigma_{far} )

Diffusion Correction

 \Sigma_{near} = \Sigma_{frm} + \Delta_{near}(\phi)

 \Sigma_{far} = \Sigma_{frm} + \Delta_{far}(\phi)

# Neutron Saturation

 \Sigma_{frm} = (1-\phi) \, \Sigma_m + \phi \, ( \Sigma_w \, s_w + \Sigma_o \, s_o +\Sigma_g \, s_g)

 \delta \Sigma_{frm} \approx +/-1.5 c.u.

 \Sigma_m = \sum_k \Sigma_k

 \Sigma_o \approx 18 \quad 11 < \Sigma_o < 21

 \Sigma_w = 21 + 0.05 * Sal[\rm ppk]

 \Sigma_g \approx 3

 \Sigma_{sh} \approx 40 \, c.u.

 \Sigma_{ls} \approx 7 \, c.u.

In case of two-component sandstone-shale model:

 \Sigma_m = (1-V_{sh}) \, \Sigma_{snd} + V_{sh} \, \Sigma_{sh}

In case of two-component limestone-shale model:

 \Sigma_m = (1-V_{sh}) \, \Sigma_{lms} + V_{sh} \, \Sigma_{sh}

TSCN, TSCF, NPHI, SIGMA

# References

SPE162074 – Memory Pulsed Neutron-Neutron Logging