Application of the Kissinger equation to the problem of evaluating reaction kinetics using T[sub]max[/sub] and formation temperature data from the Tyler Formation (Pennsylvanian) of North Dakota.
The North Dakota Geological Survey has recently completed analysis of samples of the Pennsylvanian Tyler Formation in an effort to evaluate the kinetics of oil generation in this formation within the Williston Basin of North Dakota. The data include the results from Rock Eval 6 analyses of cuttings and cores as well as a single set of analyses aimed at determining the activation energy (Ea) and frequency factor (A) of a potential source interval. The determination of activation energy and frequency factor is done by plotting the ln (β/Tp[sup]2[/sup]) versus 1/ Tp[sup]2[/sup] where Tp is the temperature ([sup]o[/sup]K) that causes the maximum rate of hydrocarbon generation during pyrolysis that involves a constant increase in temperature ( β). According to the Kissinger equation (Eq. 1), if the data form a linear trend then the slope equals the activation energy divided by the gas constant (R) and the intercept equals ln (AR/Ea). Using five heating rates the Tyler Formation sample yields an activation energy of 216 kJ/mole and a frequency factor of 1.31 X 10[sup]15 [/sup]min[sup]-[/sup]. Eq. 1 [c] [i] ln( β/Tp[sup]2[/sup]) = -Ea/RTp + ln (AR/Ea)[/i][/c] These values when included with published activation energies and frequency factors show a significant linear relationship between the natural logarithm of the frequency factor and activation energy. This relationship allows for a numerical solution to the Kissinger equation for a given heating rate and results in a relationship between activation energies, frequency factors and peak reaction temperature. Recalibration of Rock Eval Tmax data to actual peak hydrocarbon evolution temperatures allows for the determination of the corresponding activation energy and frequency factor. This is significant because it allows Tmax to be combined with formation temperature to calculate an instantaneous reaction rate using the well known Arrhenius equation. The map of the instantaneous reaction rate derived for the average per well Tmax measured in the Tyler Formation compares well with the level of maturation predicted by a simple basin model. The advantage of the Tmax based map is that it allows for the determination of the temperature-Tmax combinations that define the "maturation" threshold that signals the onset of exponentially accelerated reaction rates.
AAPG Search and Discovery Article #90156©2012 AAPG Rocky Mountain Section Meeting, Grand Junction, Colorado, 9-12 September 2012