XYLENE POWER LTD.

PETM DATA ANALYSIS

By Charles Rhodes, P. Eng., Ph.D.

INTRODUCTION:
The geological record shows that about 55.5 million years ago at the commencement of the PETM the [C-13 / C-12] ratio in ocean sediments suddenly dropped by 0.44% from its prior normal value. This drop appears to have been sustained for about 20,000 years and then gradually rose by about 0.2% over the following 200,000 years.

The source of the carbon with a low [C-13 / C-12] ratio is believed to to biomass and fossil fuels. Due to C-13 rejection by both the sea water evaporation and the photosynthesis processes, the [C-13 / C-12] ratio in forest biomatter is about 2.85% lower than in normal sea water. The [C-13 / C-12] ratio in fossil fuels is also lower than in sea water because fossil fuels are the result of anaerobic decay of biomass.

The normal C-13 / C-12 ratio is about 0.01108

Let Xa = number of C-12 atoms initially in the sea water;
Let Ya = number of C-13 atoms initially in the sea water;
Let Xb = number of organic C-12 atoms injected into the atmosphere that then quickly dissolved in sea water;
Let Yb = number of organic C-13 atoms injected into the atmosphere that then quickly dissolved in sea water

The the mass spectrometer isotope data indicates that:
Ca = (Ya / Xa)
and
Ct = (Yt / Xt)
= (Ya + Yb) / (Xa + Xb) = (Ya / Xa)(1 - 0.0044)
= Ca((1 - 0.0044)
and
Cb = (Yb / Xb)
= [Ya / Xa](1 - .0285)
= Ca (1 - .0285)

Hence:
(Ya + Yb) = Ct(Xa + Xb)
or
Ca Xa + Cb Xb = Ct(Xa + Xb)
or
(Ca - Ct) Xa = (Ct - Cb) Xb
or
Xb / Xa = (Ca - Ct) / (Ct - Cb)
= (Ca - Ca(1 - 0.0044)) / ((Ca (1 - 0.0044) - Ca (1 - 0.0285))
= (.0044) / (0.0285 - 0.0044)
= .0044 / .0241
= 0.1825726141

We need to find the ratio:
(Xb + Yb) / (Xa + Ya)
for use on the web page titled WARM STATE TRAPPING.

(Xb + Yb) / (Xa + Ya) = [((1 + (Yb / Xb)) Xb] / [((1 + (Ya / Xa)) Xa]
= [(1 + Cb) / (1 + Ca)] [Xb / Xa]
= [(1 + Ca (1 - .0285)) / (1 + Ca)] [0.1825726141]

Recall that the nominal value of Ca is:
Ca = (Ya / Xa) = 0.01108

Thus:
(Xb + Yb) / (Xa + Ya) = [(1 + Ca (1 - .0285)) / (1 + Ca)] [0.1825726141]
= [(1 + 0.01108 (1 - .0285)) / (1 + 0.01108)] [0.1825726141]
= [1.01076422 / 1.01108][0.1825726141]
= 0.1825155931
~ 0.1825

Note that this result is relatively insensitive to the actual value of Ca.

Hence 0.1825 is the fractional increase in the number of CO2 molecules in the ocean-atmosphere pool that occurred at the beginning of the PETM.

Assume that during the organic carbon injection at the commencement of the PETM all the excess CO2 went into the atmosphere in a relatively rapid surge and that during the subsequent century most of this excess carbon dissolved into the ocean.

From the web page titled CARBON DIOXIDE at an atmospheric CO2 concentration of 280 ppmv the steady state ratio of:
(CO2 in ocean) / (CO2 in atmosphere at 280 ppmv) = 32.76

Thus if the conditions immediately prior to the PETM were similar to immediately prior to the industrial revolution he amount of organic CO2 injected into the atmosphere at the commencement of the PETM that then dissolved in the ocean water is given by:
0.1825 X (initial CO2 in ocean) = 0.1825 X 32.76 X (initial CO2 in atmosphere)
= 5.9792 X (initial CO2 in atmosphere)
= 5.9792 X (280 ppmv)

Hence immediately after the initial organic carbon injection into the atmosphere the atmospheric CO2 concentration would have been:
(1 + 5.9792) 280 ppmv
= 1954 ppmv

During the PETM the [O-18 / O-16] ratio in the ocean sediments decreased to its smallest ever value indicating total melting of the polar ice caps.
 

This web page last updated October 17, 2015.