Laminated Sand/Shale Analysis

Purpose

Laminated sand analysis finds the properties and the water saturation of a sand that is interbedded with shale in layers too thin for the logs to resolve. The logs average the layers. A shale volume that looks modest hides a clean sand with full porosity, and a resistivity that looks low hides a high-resistivity sand layer. Conventional shaly-sand equations that correct the porosity and resistivity with the clay volume give a water saturation that is too high and a net pay that is too low. The step separates the shale into laminated, structural and dispersed parts, finds the sand-only porosity and resistivity, and computes the water saturation of the sand layers.

Position in the workflow

Upstream. The step needs the clean, normalized logs of Stage 1 and a shale volume from the Clay Volume step (the ratio option), plus density and neutron porosity (Porosity) and a horizontal resistivity. A vertical resistivity is used where a triaxial or anisotropic tool was run.

Downstream. The results replace the conventional porosity and water saturation in laminated zones:

the sand porosity and sand Sw feed the Water Saturation outputs and the volumetrics,
the net-to-gross factor scales the hydrocarbon pore volume of the interval, and
the shale distribution (laminated, structural, dispersed) tells the permeability and cutoff steps which sand is reservoir.

Error propagation. The laminated shale volume enters every sand property. An error of 0.1 in it changes the sand porosity of a typical example by about 0.02 to 0.025 and the sand resistivity by a larger factor, especially where the horizontal resistivity is high.

Key concepts

Why conventional analysis fails. The logs read a volume-weighted mean of sand and shale. For porosity this is a small error. For resistivity the shale conducts in parallel with the sand, so the horizontal resistivity is pulled toward the shale value, and the sand is hidden. A clay-volume equation applied to the whole interval treats the shale as clay in the sand pores, which is another geometry. See Thomas-Stieber.

Three shale distributions. Laminated shale, Structural shale and Dispersed shale give different lines on a diagram of total porosity against shale volume. Laminated shale takes volume from the sand but leaves the sand unchanged. Dispersed shale fills the pores of the sand and destroys quality.

Triangulation. The position of a sample on the diagram gives its mix of clean sand, pure shale and structural or dispersed rock, and so the laminated shale volume (triangulation).

Sand-only properties. With the laminated volume known, the shale is removed from the porosity logs and, with the Parallel conductor model, from the horizontal resistivity (sand properties).

Anisotropy. Laminations make the vertical resistivity higher than the horizontal one, Resistivity anisotropy. A tool that measures both gives the sand resistivity without a porosity-based volume (resistivity Sw).

Method selection guide

Method	Inputs	Use when	Strengths	Weaknesses
Thomas-Stieber	Total porosity, shale volume, two end-member porosities	You need to know how shale is distributed, or to pick the end members	Shows how shale changes sand quality; simple diagram	Needs clean end members; qualitative on its own
Triangulation	Total porosity, shale volume, end members	You need volumes of laminated, structural and dispersed shale on every sample	Gives the laminated volume used downstream; fast	Depends on the end members and on shale volume; samples outside the triangle are limited
Shale Volume Options	Clay volume, gamma ray, density, neutron	Always; the shale volume is the input of the triangulation	Five options for different data quality	No option is right everywhere; radioactive sand and gas bias them in opposite ways
Sand-Only Porosity and Resistivity	Laminated volume, density, neutron, horizontal resistivity, shale values	The reservoir is the sand and laminae are below log resolution	Removes the shale term from porosity and resistivity	Has a limit (pole) where no sand resistivity exists; sensitive to the shale resistivity
Horizontal and Vertical Resistivity Sw	Sand porosity, sand resistivity, Rw, m, n; optionally Rv	You need the Sw and net-to-gross of the sand layers	Recovers pay hidden by laminations; uses Rv where it exists	Needs Rsh and the laminated volume; triaxial data are less common and have lower resolution

Decision guidance

Use the analysis only in zones where laminations are expected from core, image logs or the geological setting. In thick clean sand or thick shale it adds nothing.
If you cannot tell the type of shale, start with the diagram and the triangulation. Samples that fall near the laminated line need the full treatment, and samples far above or below it need a different model, with structural or dispersed clay.
Take the ratio shale volume (from the Clay Volume step) when it is already calibrated, the neutron-density estimate when the gamma ray is radioactive and there is no gas, and compare the three before choosing.
If a triaxial tool was run, solve for the laminated volume from Rh and Rv as a check on the porosity-based one.
If the logs resolve the beds (beds thicker than the tool resolution), do bed-by-bed analysis and skip this step.

Shared parameter picking

End-member porosities. The clean-sand porosity (Clean-sand porosity) and the shale total porosity (Shale total porosity) are picked once per zone from the cross-plot and are used by the diagram, the triangulation and the sand Sw.

Shale values on the logs. The pure-shale density (Pure-shale bulk density) and neutron (Pure-shale neutron porosity) are used by the neutron-density shale volume and by the sand-only porosity. Use the same values in both.

Gamma ray end points. Clean gamma ray and Clay gamma ray are the same as in the Clay Volume step.

Shale resistivity. Horizontal shale resistivity and, where a vertical measurement is used, Vertical shale resistivity are read in thick shale.

Matrix density. Matrix density is the grain density of the sand, 2.65 g/cm³ for quartz.

Dip. The relative dip (Relative dip) is the well inclination minus the bed dip, along the same azimuth.

Zones. All parameters are chosen by zone. Switch the analysis on only in the zones that are laminated.

Recommended default approach

Absent other information, a careful generalist would:

Mark the laminated zones from core, image logs or the response of the shale volume and porosity, and run the analysis there only.
Compute the three shale volumes (ratio, gamma ray, neutron-density) and compare them. Use the ratio volume if it agrees with the others, and the average where they scatter.
Cross-plot total porosity against shale volume. Pick the clean-sand porosity at the top of the cloud and the shale porosity in thick shale.
Triangulate to get laminated, structural and dispersed volumes. Check that most samples are inside the triangles.
Compute the sand-only porosity and resistivity from the laminated volume, and check the density and neutron porosities agree.
Compute the sand Sw with the same Archie parameters as the rest of the well, and carry the net-to-gross factor into the volumetrics. If a vertical resistivity exists, use it to check the laminated volume.

Combining methods

There are two places to combine. The first is the shale volume: the minimum is the optimistic choice (least shale, most sand), the average is a compromise, and a single estimate chosen by zone is usually better than either. The second is the saturation. In laminated zones the sand Sw replaces the conventional Sw, and outside them the conventional Sw stays. Switch between them by zone with a flag and do not blend them across a boundary, since they answer different questions. Where a triaxial tool exists, the laminated volume from Rh and Rv is a check on the porosity-based one and the two can be averaged if they agree. See Shale Volume Options.

QC of results

A good result:

has most points of the porosity against shale volume cross-plot inside the end-member triangles,
has laminated, structural and dispersed volumes that are not negative and add up to the shale volume,
has sand density porosity and sand neutron porosity that agree in water-bearing sand,
has a sand resistivity above the horizontal resistivity in high-resistivity zones and no NaN values, and
has a sand Sw below the conventional Sw in hydrocarbon sand and equal to it where there is no laminated shale.

Signs of a bad result: a large dispersed volume in clean thick sand (wrong end members or gas), sand resistivity that does not exist over long intervals (shale resistivity too low or laminated volume too high), a sand Sw above the conventional value, and sand porosity above the clean-sand porosity.

Common pitfalls

Running the analysis in thick sands or thick shales, where there are no laminations.
Picking the clean-sand porosity from a thick shaly sand and not from the top of the cloud.
Using a gamma ray shale volume in radioactive sand, or a neutron-density volume in gas.
Using total porosity of a shale as if it were effective.
Using a vertical shale resistivity where the horizontal one is needed, or the reverse.
Ignoring the pole of the sand resistivity: it is not a number to be clamped.
Mixing neutron porosity on different lithology scales.
Applying the net-to-gross factor and also a net reservoir cutoff to the same sand, which counts the shale twice.
Using an uncorrected horizontal resistivity in a high-angle well.

Going Deeper

The treatment of shale in sand has two older traditions. One treats the shale as clay in the sand pores and corrects the saturation with a clay volume. The other treats the shale as layers and models the rock as sand and shale in parallel. The first goes back to the shaly-sand equations of the 1960s and later, and the second to the laminated-sand models of the 1950s. Thomas and Stieber placed both on one diagram, and later work added the resistivity anisotropy of laminated rock and the induction and triaxial tools that measure it. A modern analysis also uses thin-bed resolution enhancement, image logs and, in some wells, NMR to check the laminations. None of these removes the difficulty that the answer rests on a shale volume and two end members that have to be picked, so the main uncertainty is in the inputs and not in the equations.