TOC from Schmoker
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Summary
Schmoker's method estimates Total organic carbon from the bulk density alone, with a relation that is linear in the inverse of the density. It needs only a density log and two fitted coefficients. Use it when there is no usable resistivity curve, or as an independent check on a resistivity-based estimate.
Inputs and outputs
| Item | Units | |
|---|---|---|
| Input | Bulk density | g/cm³ |
| Input | Schmoker coefficient A | wt%·g/cm³ |
| Input | Schmoker coefficient B | wt% |
| Output | Total organic carbon | wt% |
Equations
TOC is a linear function of the inverse bulk density:
The result is limited to the interval 0 to 100 wt%. The two coefficients are fitted to core TOC for the formation.
| Symbol | Variable | Units | Typical range |
|---|---|---|---|
| \(\rho_b\) | Bulk density | g/cm³ | 1.8 to 3.0 |
| \(A\) | Schmoker coefficient A | wt%·g/cm³ | 100 to 200 |
| \(B\) | Schmoker coefficient B | wt% | 40 to 80 |
| \(\mathrm{TOC}\) | Total organic carbon | wt% | 0 to 15 |
Single-value calculator
Behavior
TOC falls as density rises, because organic matter is much less dense than the minerals. Near a density of 2.45 g/cm³ the slope is about 0.26 wt% for each 0.01 g/cm³. The two curves show how a change in coefficient B shifts the whole curve up or down: a 2.7 unit change in B moves TOC by 2.7 wt% at every density.
Parameter guidance
Schmoker coefficient A and Schmoker coefficient B are best fitted to core: cross-plot core TOC against the inverse of the bulk density at the same depths and fit a straight line. If no core is available, published values for a similar formation are a starting point only. The pair 154.5 and 57.3 is used here as an example. Use a separate pair for each formation with a different mineralogy. Calibration is covered on the TOC Analysis page.
Worked example
A bulk density of 2.45 g/cm³ with A = 154.5 and B = 57.3:
rhob, A, B = 2.45, 154.5, 57.3
toc = A / rhob - B
print(f"TOC = {A:g} / {rhob:g} - {B:g} = {toc:.2f} wt%")
# the density at which TOC reaches zero
print(f"TOC is zero at a density of {A / B:.3f} g/cm3")
Output
TOC = 154.5 / 2.45 - 57.3 = 5.76 wt%
TOC is zero at a density of 2.696 g/cm3
Assumptions and limitations
- Density changes are caused by organic matter alone. Porosity, pyrite, heavy minerals and changes in mineralogy also change the density, and are read as TOC.
- The mineral matrix is constant over the interval being evaluated.
- The density log is good. Washouts lower the density and are read as extra TOC.
- The coefficients were fitted to a formation like the one being evaluated.
QC checks
- TOC is zero or close to zero in non-source rock and in tight limestone and sandstone.
- TOC tracks core TOC with no bias. A bias that varies with depth indicates a mineralogy change.
- TOC does not spike in washouts. Check against the caliper.
- TOC is lower than a resistivity-based estimate in pyrite-rich rock only if pyrite is being read as matrix.
Going Deeper
The relation is a direct consequence of a two-component mixture. If the rock is organic matter of density ρk mixed with a matrix of density ρma, then the inverse of the bulk density is a weighted mean of the inverse densities, and the kerogen weight fraction is linear in the inverse bulk density:
Multiplying by the carbon fraction \(\fC\) and by 100 gives TOC in weight percent, so \(A\) and \(B\) are not free: \(B/A\) equals the inverse of the matrix density, and \(A\) depends on the kerogen density and carbon fraction. With A = 154.5 and B = 57.3 the implied matrix density is about 2.70 g/cm³. This is a useful check: if the fitted coefficients imply a matrix density that is far from the real mineralogy, the fit is absorbing something else.
References
- Schmoker, J.W., 1979. Determination of organic content of Appalachian Devonian shales from formation-density logs. AAPG Bulletin, 63(9), 1504–1509.
- Schmoker, J.W. and Hester, T.C., 1983. Organic carbon in Bakken Formation, United States portion of Williston Basin. AAPG Bulletin, 67(12), 2165–2174.
Python reference implementation
Python reference implementation
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