The density porosity is usually abbreviated DPHI or PHID on log panels and denoted as
\phi_d in equations.
The key measurement is the bulk rock density
\rho_B (log name RHOB) from Litho-Density Tool.
The key model parameters are:
| rock matrix density |
| shale density |
| pore-saturating fluid density |
| mud filtrate density |
\{ \rho_w, \, \rho_o, \, \rho_g \} | formation water, oil, gas density |
| a fraction of pore volume invaded by mud filtrate |
\{ s_w, \, s_o, \, s_g \} | original water, oil, gas reservoir saturations
s_w + s_o + s_g = 1 |
The values of
\rho_m and
\rho_{sh} are calibrated for each lithofacies individually and can be assessed as vertical axis cut-off on
\rho_B cross-plot against the lab core porosity
\phi_{\rm air} and shaliness
V_{sh}.
The model also accounts for saturating rock fluids with fluid density
\rho_f.
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 density porosity
\phi_d equation is:
| (1) |
\phi_d = \frac{\rho_B - \rho_m}{\rho_{fl}-\rho_m} |
The effective density porosity
\phi_{ed} equation is:
| (2) |
\phi_{ed} = \phi_d - \frac{\rho_{sh}-\rho_m}{\rho_{fl}-\rho_m} \cdot V_{sh} |
The fluid density
\rho_f is calculated in-situ using the following equation:
| (3) |
\rho_f = s_{xo} \rho_{mf} + (1-s_{xo}) ( s_w \rho_w + s_o \rho_o + s_g \rho_g ) |
The matrix density is calculated from the following equation:
| (4) |
\rho_m = \sum_i V_{m,i} \rho_{m,i} |
where
V_{m,i} – volume share of the i-th matrix component,
\rho_{m,i} – density of the i-th matrix component,
\sum_i V_{mi} =1.
