Shale Volume Options

Summary

Laminated sand analysis needs a shale volume that stays reliable in thin laminations. Five options are common: the clay volume from the Clay Volume step (the ratio method), a linear gamma ray index, a neutron-density separation, the minimum of the three and their average. The choice matters because every sand-only property that follows depends on the shale volume. Use the option that matches the data quality and the risk you want to take.

Inputs and outputs

Equations

Ratio method. The clay volume \(\Vcl\) already computed in the Clay Volume step is used as the shale volume, limited to 0 to 1.

Gamma ray. A linear index between a clean-sand and a shale gamma ray:

Neutron-density separation. The density porosity, from the matrix density and a fluid density of 1.0 g/cm³, is compared with the neutron porosity. In shale the neutron reads higher than the density porosity, and in clean sand the two agree. The separation is scaled by its value in pure shale:

limited to 0 to 1. The neutron porosity must be on the same lithology scale as the density porosity, normally sandstone.

Minimum and average. Of the three estimates, the smallest and the mean:

The shale volume used in the analysis is capped at 0.99, which keeps the divisor \(1 - \Vlam\) of the sand-only porosity away from zero.

Single-value calculator

Behavior

The plot sweeps the gamma ray from 0 to 130 gAPI with a clean-sand reading of 10 and a shale reading of 100, and holds the density and neutron at 2.30 g/cm³ and 0.27, the ratio estimate at 0.30. The neutron-density estimate stays at 0.324 because it does not depend on the gamma ray, and the gamma ray estimate rises linearly from 0 at 10 gAPI to 1 at 100 gAPI (0.333 at 40, 0.667 at 70). The minimum follows the gamma ray up to the point where it passes the lowest of the other two (0.30), then stays at 0.30, and it is 0 at 10 gAPI. The average is 0.208 at 10 gAPI, 0.319 at 40 and 0.541 at 100. The gamma ray alone swings Vsh by 0.67 between 10 and 70 gAPI, while the neutron-density estimate does not move: this is why a single estimate should not be trusted where the gamma ray is affected by something other than shale.

Parameter guidance

Gamma ray end points. Take the clean-sand and shale readings from histograms of the zone, as in the Clay Volume step. Use the same end points as the clay volume where the gamma ray is the clay indicator. Pure-shale density and neutron. Read both in a thick shale next to the sand, from the cleanest shale point. Use sandstone-scale neutron porosity if the matrix density is a sandstone value. Matrix density. 2.65 g/cm³ for a quartz sand, adjusted for the mineralogy. Choosing the option. The ratio method keeps results consistent with the rest of the workflow. Use the gamma ray alone only when density and neutron are poor. Use neutron-density where the gamma ray is radioactive (feldspar, mica, glauconite) and the density and neutron are good and not affected by gas. The minimum is the optimistic choice (least shale, most sand), and the average is a compromise. See the step page for the decision guide.

Worked example

A sample with a gamma ray of 40 gAPI, a bulk density of 2.30 g/cm³ and a neutron porosity of 0.27, with a clay volume of 0.30 from the Clay Volume step. The last lines show how much a shale volume error changes the sand porosity of a purely laminated sample with a total porosity of 0.205 (clean-sand porosity 0.25, shale porosity 0.10):

def c(x): return min(1.0, max(0.0, x))
gr, grc, grs = 40.0, 10.0, 100.0
rhob, nphi, rma, rsh, nsh, vcl = 2.30, 0.27, 2.65, 2.45, 0.30, 0.30
v_gr = c((gr - grc) / (grs - grc))
phid = (rma - rhob) / (rma - 1)
phid_sh = (rma - rsh) / (rma - 1)
v_nd = c((phid - nphi) / (phid_sh - nsh))
print(f"density porosity {phid:.4f}, pure-shale density porosity {phid_sh:.4f}")
print(f"ratio {vcl:.3f}  GR {v_gr:.3f}  ND {v_nd:.3f}")
print(f"minimum {min(vcl, v_gr, v_nd):.3f}  average {(vcl + v_gr + v_nd) / 3:.3f}")
print()
phit, ph = 0.205, 0.10
for v in (0.2, 0.3, 0.4):
    print(f"Vsh used {v:.1f}: sand porosity = {(phit - v * ph) / (1 - v):.4f}")

Output

density porosity 0.2121, pure-shale density porosity 0.1212
ratio 0.300  GR 0.333  ND 0.324
minimum 0.300  average 0.319

Vsh used 0.2: sand porosity = 0.2312
Vsh used 0.3: sand porosity = 0.2500
Vsh used 0.4: sand porosity = 0.2750

Assumptions and limitations

• The ratio method is only as good as the clay volume it takes. If the clay volume was set for a dispersed-clay sand, it may not be the laminated shale volume.
• The gamma ray is a clay indicator. Feldspar, mica, glauconite and uranium-rich sand raise the reading and overstate the shale volume.
• In the neutron-density separation, the sand is clean and water-filled, or the neutron and density are corrected for fluid. Gas reduces the neutron porosity and raises the density porosity, so the separation is read as less shale, and the estimate is too low.
• The neutron and density are on the same lithology scale and the matrix density is right. A wrong matrix density shifts the separation in clean sand away from zero.
• The thin laminations are not resolved by any of the logs, so each of them gives an average shale volume over the log window.

QC checks

• The shale volume is 0 in clean sand and close to 1 in thick shale, for all five options.
• The options agree in trend. A large difference in one interval has a cause: radioactive sand for the gamma ray, gas for the neutron-density, or a clay volume tuned for a different shale type.
• The minimum is never above the average, and the average is between the minimum and the largest estimate.
• Shale volume is limited to 0.99 and not negative anywhere.
• Compare the chosen volume with core description or image logs where thin laminations are visible.

Going Deeper

The ratio, gamma ray and neutron-density estimates are three independent tools with different failure modes. The gamma ray fails in radioactive sand, the neutron-density separation fails in gas and in rocks with heavy minerals, and the clay volume depends on whichever log it was made from. Combining them reduces the chance that one error is passed on to the sand properties. The minimum is the optimistic choice and the average is a compromise. Neither is a weighted estimate, and a better answer is to choose a single one by zone after looking at them together. For laminated sands the shale volume has one more property: it should reflect the volume of the laminae. Shale seen by the logs includes dispersed or structural clay that stays in the sand and affects its properties, so the shale volume can overstate the laminated shale volume.

References

References will be added once verified.

Python reference implementation

Related methods

• Thomas-Stieber
• Triangulation
• Sand-Only Porosity and Resistivity
• Horizontal and Vertical Resistivity Sw