Content

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

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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

The density porosity is usually abbreviated DPHI on log panels and denoted as $\begin{array}{l}\phi_d\end{array}$ in equations.

The key measurement is the bulk rock density $\begin{array}{l}\rho_B\end{array}$ (log name RHOB) from Litho-Density Tool.

The key model parameters are:

$\begin{array}{l}\rho_m\end{array}$	rock matrix density
$\begin{array}{l}\rho_{sh}\end{array}$	shale density
$\begin{array}{l}\rho_f\end{array}$	pore-saturating fluid density
$\begin{array}{l}\rho_{mf}\end{array}$	mud filtrate density
$\begin{array}{l}\{ \rho_w, \, \rho_o, \, \rho_g \}\end{array}$	formation water, oil, gas density
$\begin{array}{l}s_{xo}\end{array}$	a fraction of pore volume invaded by mud filtrate
$\begin{array}{l}\{ s_w, \, s_o, \, s_g \}\end{array}$	original water, oil, gas reservoir saturations $\begin{array}{l}s_w + s_o + s_g = 1\end{array}$

The values of $\begin{array}{l}\rho_m\end{array}$ and $\begin{array}{l}\rho_{sh}\end{array}$ are calibrated for each lithofacies individually and can be assessed as vertical axis cut-off on $\begin{array}{l}\rho_B\end{array}$ cross-plot against the lab core porosity $\begin{array}{l}\phi_{\rm air}\end{array}$ and shaliness $\begin{array}{l}V_{sh}\end{array}$ .

The model also accounts for saturating rock fluids with fluid density $\begin{array}{l}\rho_f\end{array}$ .

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 $\begin{array}{l}\phi_d\end{array}$ equation is:

(1)	$\begin{array}{l}\displaystyle \phi_d = \frac{\rho_B - \rho_m}{\rho_{fl}-\rho_m}\end{array}$

The effective density porosity $\begin{array}{l}\phi_{ed}\end{array}$ equation is:

(2)	$\begin{array}{l}\displaystyle \phi_{ed} = \phi_d - \frac{\rho_{sh}-\rho_m}{\rho_{fl}-\rho_m} \cdot V_{sh}\end{array}$

The fluid density $\begin{array}{l}\rho_f\end{array}$ is calculated in-situ using the following equation:

(3)	$\begin{array}{l}\displaystyle \rho_f = s_{xo} \rho_{mf} + (1-s_{xo}) ( s_w \rho_w + s_o \rho_o + s_g \rho_g )\end{array}$

The matrix density is calculated from the following equation:

(4)	$\begin{array}{l}\displaystyle \rho_m = \sum_i V_{m,i} \rho_{m,i}\end{array}$

where

$\begin{array}{l}V_{m,i}\end{array}$ – volume share of the i-th matrix component,

$\begin{array}{l}\rho_{m,i}\end{array}$ – density of the i-th matrix component,

$\begin{array}{l}\sum_i V_{mi} =1\end{array}$ .

Neutron Porosity

The neutron porosity is usually abbreviated NPHI and denoted as $\begin{array}{l}\phi_n\end{array}$ in equations.

The key measurement is compensated neutron log $\begin{array}{l}N_n\end{array}$ (log name CNL) from Compensated Neutron Tool.

The key model parameters are:

$\begin{array}{l}N_m\end{array}$	rock matrix CNL
$\begin{array}{l}N_{sh}\end{array}$	shale CNL
$\begin{array}{l}N_f\end{array}$	pore-saturating fluid CNL
$\begin{array}{l}N_{mf}\end{array}$	mud filtrate CNL
$\begin{array}{l}\{ N_w, \, N_o, \, N_g \}\end{array}$	formation water, oil, gas CNL
$\begin{array}{l}s_{xo}\end{array}$	a fraction of pore volume invaded by mud filtrate
$\begin{array}{l}\{ s_w, \, s_o, \, s_g \}\end{array}$	original water, oil, gas reservoir saturations $\begin{array}{l}s_w + s_o + s_g = 1\end{array}$

The values of $\begin{array}{l}N_m\end{array}$ and $\begin{array}{l}N_{sh}\end{array}$ are calibrated for each lithofacies individually and can be assessed as vertical axis cut-off on $\begin{array}{l}N_{log}\end{array}$ cross-plot against the lab core porosity $\begin{array}{l}\phi_{\rm air}\end{array}$ and shaliness $\begin{array}{l}V_{sh}\end{array}$ .

The model also accounts for saturating rock fluids with fluid CNL $\begin{array}{l}N_f\end{array}$ .

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 neutron porosity $\begin{array}{l}\phi_n\end{array}$ equation is:

(5)	$\begin{array}{l}\displaystyle \phi_n = \frac{N_n - N_m}{N_{fl}-N_m}\end{array}$

The effective neutron porosity $\begin{array}{l}\phi_{en}\end{array}$ equation is:

(6)	$\begin{array}{l}\displaystyle \phi_{en} = \phi_n - \frac{N_{sh}-N_m}{N_f - N_m} \cdot V_{sh}\end{array}$

The fluid density $\begin{array}{l}N_f\end{array}$ is calculated in-situ using the following equation:

(7)	$\begin{array}{l}\displaystyle N_f = s_{xo} \rho_{mf} + (1-s_{xo}) ( s_w N_w + s_o N_o + s_g N_g )\end{array}$

The matrix CNL is calculated from the following equation:

(8)	$\begin{array}{l}\displaystyle N_m = \sum_i V_{m,i} N_{m,i}\end{array}$

where

$\begin{array}{l}V_{m,i}\end{array}$ – volume share of the i-th matrix component,

$\begin{array}{l}N_{m,i}\end{array}$ – density of the i-th matrix component,

$\begin{array}{l}\sum_i V_{mi} =1\end{array}$ .

Sonic Porosity

The sonic porosity is usually abbreviated SPHI and denoted as $\begin{array}{l}\phi_s\end{array}$ in equations.

The key measurement is the p-wave velocity sonic log $\begin{array}{l}V_{p \ log}\end{array}$ .

The key model parameter is rock matrix sonic velocity $\begin{array}{l}V_{p \ m}\end{array}$ which is calibrated for each facies individually and can be can be assessed as vertical axis cut-off on $\begin{array}{l}V_{p \ log}\end{array}$ cross-plot against the core-data porosity $\begin{array}{l}\phi_{\rm air}\end{array}$ .

The model also accounts for saturating rock fluids with p-wave velocity $\begin{array}{l}V_{p \ f}\end{array}$ 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 $\begin{array}{l}\phi_s\end{array}$ equation is :

(9)	$\begin{array}{l}\displaystyle \frac{1}{V_{p \ log}} = \frac{1-\phi_s \ C_p}{V_{p \ m}} + \frac{\phi_s \ C_p}{V_{p \ f}}\end{array}$

where $\begin{array}{l}C_p\end{array}$ is compaction factor, accounting for the shaliness specifics and calculated as:

(10)	$\begin{array}{l}\displaystyle C_p = \frac{V_{shс}}{V_{sh}}\end{array}$

where

$\begin{array}{l}V_{sh}\end{array}$ – p-wave velocity for adjacent shales,

$\begin{array}{l}V_{shc}\end{array}$ – p-wave velocity reference value for tight shales (usually 0.003 ft/μs).

GGG Equation (Gardner, Gardner, Gregory)

The GGG sonic porosity $\begin{array}{l}\phi_s\end{array}$ equation is :

(11)	$\begin{array}{l}\displaystyle \frac{1}{V^{1/4}_{p \ log}} = \frac{(1-\phi_s)}{V^{1/4}_{p \ m}} + \frac{\phi_s}{V^{1/4}_{p \ f}}\end{array}$

The above equation is based on the Gardner correlation for sonic density:

(12)	$\begin{array}{l}\displaystyle \rho_s = 171 \cdot V_{p \ m}^{1/4}\end{array}$

where $\begin{array}{l}\rho_s\end{array}$ is measured in $\begin{array}{l}\rm \big[ \frac{m^3}{kg} \big]\end{array}$ and $\begin{array}{l}V_{p \ m}\end{array}$ is measured in $\begin{array}{l}\rm \big[ \frac{m}{\mu s} \big]\end{array}$

and mass balance equation:

(13)	$\begin{array}{l}\displaystyle \rho_s = (1-\phi_s)\rho_m + \phi_s \rho_f\end{array}$

RHG Equation (Raymer, Hunt, Gardner)

The RHG sonic porosity $\begin{array}{l}\phi_s\end{array}$ equation is :

(14)	$\begin{array}{l}\displaystyle V_{p \ log} = (1-\phi_s)^2 V_{p \ m} + \phi_s V_{p \ f}\end{array}$

and only valid for $\begin{array}{l}\phi_s < 0.37\end{array}$ .

Cross-Porosity Analysis

Neutron vs Density

(15)	$\begin{array}{l}\displaystyle \phi_e = \frac{ \phi_{ed} + \phi_{en}}{2}\end{array}$

for oil/water saturated formations

(16)	$\begin{array}{l}\displaystyle \phi_e = \sqrt{\frac{ \phi_{ed}^2 + \phi_{en}^2}{2} \ }\end{array}$

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.

Page tree

GGG Equation (Gardner, Gardner, Gregory)

RHG Equation (Raymer, Hunt, Gardner)

Cross-Porosity Analysis

Neutron vs Density

Sonic vs Density

Reference

Page tree

Porosity Log Interpretation

Objectives

Definition

Density Porosity

Neutron Porosity

Sonic Porosity

WGG Equation (Wyllie)

GGG Equation (Gardner, Gardner, Gregory)

RHG Equation (Raymer, Hunt, Gardner)

Cross-Porosity Analysis

Neutron vs Density

Sonic vs Density

Reference