The sonic porosity is usually abbreviated SPHI or PHIS on log panels and denoted as
\phi_s in equations.
The key measurement is the p-wave velocity
V_{p \ log} from sonic tool readings.
The key model parameter is rock matrix sonic velocity
V_{p \ m} which is calibrated for each facies individually and can be can be assessed as vertical axis cut-off on
V_{p \ log} cross-plot against the core-data porosity
\phi_{\rm air}.
The model also accounts for saturating rock fluids with p-wave velocity
V_{p \ f} value.
In overbalance drilling across permeable rocks the saturating fluid is usually mud filtrate.
In underbalance drilling this the saturating fluid is identified from resistivity logs.
The WGG sonic porosity
\phi_s equation is :
| (1) |
\frac{1}{V_{p \ log}} = \frac{1-\phi_s \ C_p}{V_{p \ m}} + \frac{\phi_s \ C_p}{V_{p \ f}}
|
where
C_p is compaction factor, accounting for the shaliness specifics and calculated as:
| (2) |
C_p = \frac{V_{shс}}{V_{sh}} |
where
V_{sh} – p-wave velocity for adjacent shales,
V_{shc} – p-wave velocity reference value for tight shales (usually 0.003 ft/μs).
The GGG sonic porosity
\phi_s equation is :
| (3) |
\frac{1}{V^{1/4}_{p \ log}} = \frac{(1-\phi_s)}{V^{1/4}_{p \ m}} + \frac{\phi_s}{V^{1/4}_{p \ f}} |
The above equation is based on the Gardner correlation for sonic density:
| (4) |
\rho_s = 171 \cdot V_{p \ m}^{1/4} |
where
\rho_s is measured in
\rm \big[ \frac{m^3}{kg} \big] and
V_{p \ m} is measured in
\rm \big[ \frac{m}{\mu s} \big]
and mass balance equation:
| (5) |
\rho_s = (1-\phi_s)\rho_m + \phi_s \rho_f |
The RHG sonic porosity
\phi_s equation is :
| (6) |
V_{p \ log} = (1-\phi_s)^2 V_{p \ m} + \phi_s V_{p \ f} |
and only valid for
\phi_s < 0.37.
