TOC from Vernik

Summary

Vernik's method computes the Kerogen weight fraction from the bulk density with a two-component mixing relation, then converts it to Total organic carbon with the carbon fraction of kerogen. Unlike the Schmoker relation it has no fitted coefficients: it uses the density of the inorganic shale and of the kerogen. Use it when a representative inorganic shale density can be picked.

Inputs and outputs

Equations

The kerogen weight fraction follows from a mixture of kerogen and inorganic shale:

TOC is the carbon share of that kerogen:

The kerogen weight fraction is limited to the interval 0 to 1.

Single-value calculator

Behavior

TOC falls as density rises and is zero where the bulk density reaches the inorganic shale density. The three curves show that the shale density sets the zero point: at a bulk density of 2.45 g/cm³, shale densities of 2.55, 2.65 and 2.75 give about 2.7, 5.0 and 6.9 wt% TOC, so each 0.1 g/cm³ of shale density is worth about 2 wt%. This is the main sensitivity of the method.

Parameter guidance

Inorganic shale density is the density of the rock with no kerogen, read from the cleanest low-TOC shale in the same formation, or computed from the mineral volumes. Kerogen density is typically 1.1 to 1.4 g/cm³ and rises with maturity. Kerogen carbon fraction is the weight fraction of carbon in kerogen. The value here is 0.67, while the kerogen volume calculation on the Kerogen Volume and Maturity page uses 0.8. Use one value consistently across a project. Calibration against core is covered on the TOC Analysis page.

Worked example

A bulk density of 2.45 g/cm³, an inorganic shale density of 2.65 g/cm³ and a kerogen density of 1.26 g/cm³:

rhob, rho_s, rho_k, f_c = 2.45, 2.65, 1.26, 0.67
w_k = rho_k * (rho_s - rhob) / (rhob * (rho_s - rho_k))
toc = 100 * f_c * w_k
print(f"Wk = {rho_k:g} x ({rho_s:g} - {rhob:g}) / ({rhob:g} x ({rho_s:g} - {rho_k:g})) = {w_k:.4f}")
print(f"TOC = 100 x {f_c:g} x {w_k:.4f} = {toc:.2f} wt%")

Output

Wk = 1.26 x (2.65 - 2.45) / (2.45 x (2.65 - 1.26)) = 0.0740
TOC = 100 x 0.67 x 0.0740 = 4.96 wt%

Assumptions and limitations

• The rock is a mixture of kerogen and one inorganic component of constant density. Variations in mineralogy or porosity move the inorganic density and are read as TOC.
• The inorganic shale density is known. An error of 0.1 g/cm³ changes TOC by about 2 wt% at a bulk density of 2.45 g/cm³.
• The kerogen density and carbon fraction are representative of the organic matter being evaluated.
• The density log is good. Washouts, heavy minerals such as pyrite, and gas change the density without a change in kerogen.

QC checks

• TOC is zero in the inorganic reference interval by construction. Check that other known low-TOC intervals also read near zero.
• TOC compares with core TOC. A constant offset points to the shale density, and a slope to the kerogen density or carbon fraction.
• Compare with the Schmoker estimate. They share the same physical basis, so a large disagreement is a calibration problem.
• TOC does not spike in washouts.

Going Deeper

The expression is the mixing relation for kerogen and matrix expressed as a weight fraction. It is the same physical model as the Schmoker relation, and with constant densities the two are algebraically equivalent to a linear function of the inverse bulk density. The difference is where the constants come from: Schmoker's coefficients are fitted to core, while this form is computed from physical densities. The cost is that the inorganic density has to be known, and that error is the main source of uncertainty. It appears in studies of source-rock elastic properties, where kerogen volume and weight fraction are needed together.

References

1. Vernik, L. and Landis, C., 1996. Elastic anisotropy of source rocks: implications for hydrocarbon generation and primary migration. AAPG Bulletin, 80(4), 531–544.

Python reference implementation

Related methods

• TOC from Passey ΔlogR
• TOC from Schmoker
• TOC from Faust
• Combining TOC Estimates
• Kerogen Volume and Maturity