Objectives
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
\rho_m | rock matrix density |
\rho_{sh} | shale density |
\rho_f | pore-saturating fluid density |
\rho_{mf} | mud filtrate density |
\{ \rho_w, \, \rho_o, \, \rho_g \} | formation water, oil, gas density |
s_{xo} | 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 |
(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.
Neutron Porosity
Part of rock volume containing the hydrogen atoms.
N_m
N_{sh}
N_f
N_{mf}
\{ N_w, \, N_o, \, N_g \}
s_{xo}
\{ s_w, \, s_o, \, s_g \} original water, oil, gas reservoir saturations
s_w + s_o + s_g = 1 The fluid density
N_f is calculated in-situ using the following equation: The matrix CNL is calculated from the following equation: where
V_{m,i} – volume share of the i-th matrix component,
N_{m,i} – density of the i-th matrix component,
\sum_i V_{mi} =1.rock matrix CNL shale CNL pore-saturating fluid CNL mud filtrate CNL formation water, oil, gas CNL a fraction of pore volume invaded by mud filtrate
(5)
\phi_n = \frac{N_{log} - N_m}{N_f-N_m}
The effective neutron porosity
\phi_{en} equation is:
(6)
\phi_{en} = \phi_n - \frac{N_{sh}-N_m}{N_f - N_m} \cdot V_{sh}
(7)
N_f = s_{xo} N_{mf} + (1-s_{xo}) ( s_w N_w + s_o N_o + s_g N_g )
(8)
N_m = \sum_i V_{m,i} N_{m,i}
Sonic Porosity
WGG Equation (Wyllie)
The WGG sonic porosity \phi_s equation is :
(9) | \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:
(10) | 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).
GGG Equation (Gardner, Gardner, Gregory)
The GGG sonic porosity \phi_s equation is :
(11) | \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:
(12) | \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:
(13) | \rho_s = (1-\phi_s)\rho_m + \phi_s \rho_f |
RHG Equation (Raymer, Hunt, Gardner)
The RHG sonic porosity \phi_s equation is :
(14) | V_{p \ log} = (1-\phi_s)^2 V_{p \ m} + \phi_s V_{p \ f} |
and only valid for \phi_s < 0.37.
Cross-Porosity Analysis
Neutron vs Density
| for oil/water saturated formations | ||
| for gas saturated formations |
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.