Objectives

The main objective of RDL porosity interpretation is to predict air porosity from OH logs.

The interpretation model is calibrated to air porosity on dried out lab cores.

Definition

Different OH sensors have complex correlation to effective porosity, shaliness and pore-saturating fluids.

The density, neutron, sonic and resistivity tools show a monotonous correlation to porosity and shaliness.

The density, and neutron tools exhibit a linear correlation while sonic  and resistivity tools exhibit non-linear correlation to porosity and shaliness.      

Density Porosity

Neutron Porosity

Sonic Porosity

The sonic porosity is usually abbreviated SPHI and denoted as 

The key measurement is the p-wave velocity sonic log 

The key model parameter is rock matrix sonic velocity 

The model also accounts for saturating rock fluids with p-wave velocity 

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 

\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 = \frac{V_{shс}}{V_{sh}}

where 

GGG Equation (Gardner, Gardner, Gregory)

The GGG sonic porosity 

\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:

\rho_s = 171 \cdot V_{p \ m}^{1/4}

where 

and mass balance equation:

\rho_s = (1-\phi_s)\rho_m + \phi_s \rho_f

RHG Equation (Raymer, Hunt, Gardner)

The RHG sonic porosity 

V_{p \ log} = (1-\phi_s)^2 V_{p \ m} + \phi_s V_{p \ f}

and only valid for 

Cross-Porosity Analysis

Neutron vs Density

\phi_e = \frac{ \phi_{ed} + \phi_{en}}{2}

\phi_e = \sqrt{\frac{ \phi_{ed}^2 + \phi_{en}^2}{2} \ }

Sonic vs Density

SPHI  is usually not sensitvie to second porosity development while DPHI  accounts for it proportionally.

This means formation units with secondary porosity development will show DPHI growing over SPHI.

Reference