The sonic porosity is usually abbreviated SPHI or PHIS on log panels and denoted as in equations. The key measurement is the p-wave velocity sonic log from sonic tool readings.The key model parameter is rock matrix sonic velocity which is calibrated for each facies individually and can be can be assessed as vertical axis cut-off on cross-plot against the core-data porosity . The model also accounts for saturating rock fluids with p-wave velocity 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.
WGG Equation (Wyllie) The WGG sonic porosity equation is : | LaTeX Math Block |
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| \frac{1}{V_{p \ log}} = \frac{1-\phi_s \ C_p}{V_{p \ m}} + \frac{\phi_s \ C_p}{V_{p \ f}}
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where is compaction factor, accounting for the shaliness specifics and calculated as:| LaTeX Math Block |
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| C_p = \frac{V_{shс}}{V_{sh}} |
where – p-wave velocity for adjacent shales, – p-wave velocity reference value for tight shales (usually 0.003 ft/μs).
GGG Equation (Gardner, Gardner, Gregory)
The GGG sonic porosity equation is : | LaTeX Math Block |
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| \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: | LaTeX Math Block |
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| \rho_s = 171 \cdot V_{p \ m}^{1/4} |
where is measured in | LaTeX Math Inline |
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| body | \rm \big[ \frac{m^3}{kg} \big] |
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and is measured in | LaTeX Math Inline |
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| body | \rm \big[ \frac{m}{\mu s} \big] |
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and mass balance equation:
| LaTeX Math Block |
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| \rho_s = (1-\phi_s)\rho_m + \phi_s \rho_f |
RHG Equation (Raymer, Hunt, Gardner)
The RHG sonic porosity equation is : | LaTeX Math Block |
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| V_{p \ log} = (1-\phi_s)^2 V_{p \ m} + \phi_s V_{p \ f} |
and only valid for . | 