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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}


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.

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