The bulk dry density of the SR at VR = 0.5 is desired for the calculation. However, this is not available. The calculation will not be greatly affected if we simply estimate the dry density of the SR in its present state. Required is an estimate of the ratio of kerogen weight percent versus TOC weight percent (here called "factor"). The usual rule-of-thumb is to take 1.5 for this ratio. But at higher TOC values, this may lead to kerogen % > 100! Therefore a trick is used to avoid this problem, while at the same time keeping the factor=1.5 for most of the low end of the TOC range. The trick is to use:
Then the dry density can be shown to be:
ρd = Dry density of SR
ρg = Density of mineral grains
ρk = Density of kerogen
Φ = Porosity, fraction
TOC = TOC content, weight %
The organic Carbon lost by expulsion of HC for the same M³ is calculated by using the SR type and the corresponding yield curve. The yield curve gives the fractions of expulsion as a function of vitrinite reflectance for different types of SR and their mixtures, as well as a separate one for gas.
The Potential Ultimate Yield for oil and for gas provide the maximum amount of oil or gas that is expelled from a SR when it is brought to complete maturity, which in this case is equated with VR = 2.50, or larger. The volumes are in liters/M³/1%TOC for oil and in M³ for gas. They are the variables described as Puyo and PUYG . The volumes are transformed into weights by multiplying with the assumed densities of expelled oil and gas (at standard conditions). At a given VR the volumes may be only a fraction of the PUYO or PUYG, according to the yield fraction for maturity that was derived from the yield curve table. Adding the weights of oil and gas expelled for 1% TOC original, the weight lost at 1% is obtained: WHC,1%. The estimates of the proportion of Carbon in the expelled oil and gas are used to find the weight of the Carbon lost in the HC, or Clost,1% This means that the weight of the original M³ is reduced by that amount, times the original TOC % or TOCo. Now we can state:The original organic carbon in a M³ of SR is
and the present weight of organic C as
Then equating the two expressions for TOC and solving for TOC0 we obtain:
The above is only an approximate solution, because we have related it only to the density of the SR as it is today, i.e. on the basis of present TOC and not a TOC0. The uncertainty and/or bias introduced in this way points to a slight overestimation of the original TOC. The above calculation does not take into account the organic C that is expelled in the form of CO2. Results are therefore slightly underestimated. The bias is probably very small, as CO2 is generated in part in the early stages of kerogen diagenesis, i.e. before the onset of HC expulsion. Also the amount compared to HC products are small, on the order of 7% of the total organic C (cf. Killops et al., 1996references). These two simplifications or shortcuts tend to work in opposite directions and are probably not very important as a source of bias.
Note that the correction factor could be as high as 2.3 for a vitrinite reflectance of 1.20! This shows that the amount of charge could be severely underestimated if only data on TOC from mature SR would be taken at face value in a prospect appraisal.
It is difficult to assess the uncertainty of the corrected TOC. The measured TOC may already have a significant standard deviation, depending on how it was derived (Rockeval or wireline log interpretation). Then the uncertainty about the various assumed constants in the calculation compounds the problem. The effect of a 1% change in seven different assumptions is as follows:
|C content oil||1.8|
|C content gas||0.1|
|Density grain||1.0||Density kerogen||0.2|