Vclay from Neutron-Density

Summary

The neutron-density method estimates Clay volume from the position of the measured Bulk density and Neutron porosity relative to a clean-rock line and a clay point on the crossplot. Because the density log constrains the porosity, it separates clay from porosity better than the neutron alone, and it does not use the gamma ray. Use it where both logs are good and gas is not dominant, and as the main independent check on gamma-ray clay volume.

Inputs and outputs

	Item	Units
Input	Bulk density	g/cm³
Input	Neutron porosity	v/v
Input	Density at first clean point	g/cm³
Input	Neutron porosity at first clean point	v/v
Input	Density at second clean point	g/cm³
Input	Neutron porosity at second clean point	v/v
Input	Clay bulk density	g/cm³
Input	Clay neutron porosity	v/v
Output	Clay volume	v/v

Equations

The two clean points \(A\) and \(B\) define the clean-rock line on the bulk density-neutron porosity crossplot, and the clay point is the 100% clay end. The clay volume is the offset of the measured point from the clean line, as a fraction of the offset of the clay point:

\[ \Vcl = \frac{(\rhoCleanB - \rhoCleanA)(\phiN - \phiNCleanA) - (\rhob - \rhoCleanA)(\phiNCleanB - \phiNCleanA)}{(\rhoCleanB - \rhoCleanA)(\phiNClay - \phiNCleanA) - (\rhoClay - \rhoCleanA)(\phiNCleanB - \phiNCleanA)} \]

and the result is clamped to the interval 0 to 1. The numerator and denominator are both proportional to a perpendicular distance from the clean line, so their ratio does not depend on the units or the scaling of either axis.

Symbol	Variable	Units	Typical range
\(\rho_b\)	Bulk density	g/cm³	1.8 to 3.0
\(\phi_N\)	Neutron porosity	v/v	-0.02 to 0.60
\(\rho_{b,A}\)	Density at first clean point	g/cm³	2.55 to 2.75
\(\phi_{N,A}\)	Neutron porosity at first clean point	v/v	-0.05 to 0.05
\(\rho_{b,B}\)	Density at second clean point	g/cm³	2.0 to 2.4
\(\phi_{N,B}\)	Neutron porosity at second clean point	v/v	0.15 to 0.40
\(\rho_{b,clay}\)	Clay bulk density	g/cm³	2.2 to 2.7
\(\phi_{N,clay}\)	Clay neutron porosity	v/v	0.25 to 0.50
\(V_{cl}\)	Clay volume	v/v	0 to 1

Single-value calculator

Behavior

Clay volume is a straight-line function of each measurement, so the plot lines are straight and are clipped to 0 and 1. The lines shift to the left as the bulk density increases: at a given neutron porosity, a denser rock lies farther from the clean line toward the clay point, which is denser than clean rock of the same neutron porosity because its neutron response comes from bound water rather than pore space. The slope is set by how far the clay point is from the clean line.

Parameter guidance

Six picks define the method: two points on the clean-rock line and one clay point. A common choice for the clean line is the matrix point (for example 2.65 g/cm³ and 0 v/v on a sandstone scale) and a second, porous clean point read from the cleanest water-bearing sand in the zone. The clay point is read from a thick shale. The neutron clay value is shared with the neutron-only method. The general principles are in the Clay Volume page.

Worked example

A measured point of 2.50 g/cm³ and 0.20 v/v. The clean line runs through (2.65, 0.0) and (2.20, 0.27), and the clay point is (2.45, 0.40):

A, B, clay = (2.65, 0.0), (2.20, 0.27), (2.45, 0.40)   # (density, neutron)
rhob, nphi = 2.50, 0.20
num = (B[0] - A[0]) * (nphi - A[1]) - (rhob - A[0]) * (B[1] - A[1])
den = (B[0] - A[0]) * (clay[1] - A[1]) - (clay[0] - A[0]) * (B[1] - A[1])
vcl = min(1.0, max(0.0, num / den))
print(f"numerator = {num:.4f}, denominator = {den:.4f}")
print(f"Vcl = {vcl:.3f}")

Output

numerator = -0.0495, denominator = -0.1260
Vcl = 0.393

Assumptions and limitations

The clean points lie on a single straight line, so lithology and fluid are constant along it. A change in lithology moves the clean line and biases the result.
The neutron and density are on the same lithology scale, and the clean points are read on that scale.
There is no gas. Gas lowers the neutron and the density, moves the point toward the clean-rock side or beyond it, and biases the clay volume low.
The logs are not affected by washouts or heavy minerals. Barite mud and heavy minerals move the point without a change in clay.
The clay point is representative and lies off the clean line. If it lies on the clean line the denominator is zero and the method is undefined.

QC checks

The result is between 0 and 1 without relying on the clamp. Many values hitting 0 or 1 means the picks are wrong.
Clean, water-bearing sands read near zero.
Clay volume is high in washouts only if the bad-hole flag has failed. Check the repaired logs.
Compare with the gamma-ray clay volume. A gamma ray that is much higher points to radioactive minerals, and a neutron-density value that is much lower in a gas zone points to gas.

Going Deeper

This is the dual-clay formulation of the neutron-density clay indicator, which writes the clay volume as a ratio of two signed distances from the clean-rock line. Because it is an affine function of each measurement, it is easy to evaluate and to invert, and the same form works for any pair of porosity-sensitive logs, which is why the sonic-density and neutron-sonic methods use it too. It was introduced as a way to estimate clay from porosity logs in rocks where the gamma ray is unreliable.

References

Bhuyan, K. and Passey, Q.R., 1994. Clay estimation from GR and neutron-density porosity logs. Transactions of the SPWLA 35th Annual Logging Symposium, Paper DDD.

Python reference implementation

Python reference implementation

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