Reliable modelling of the source rock transformation ratio

Abstract

Basic modelling results are reliable only if they are accompanied by error bars which reflect modelling uncertainties. Estimation of error bars by repeated forward calculations (Monte Carlo simulation) can be time consuming due to the calculation time of basin models. Applications in exploration hence call for new techniques in error analysis. A fast analytical method has been developed for the calculation of error bars on the source rock transformation ratio. The method is a stochastic generalization of the traditional deterministic approach, which is reproduced in the deterministic limit of vanishing parameter uncertainties. Assuming normally distributed errors in the kinetic parameters and in the source rock temperature history, the marginal cumulative distribution function of the source rock transformation ratio can be determined at arbitrary times during source rock evolution. From this distribution different statistical moments, such as the mean, standard deviation, median and mode, of the transformation ratio can be obtained. The parameters of the stochastic model comprise the distribution parameters in the joint normal distribution of uncertainty in the average kinetic parameters, and standard deviations and correlation scales of uncertainty in the surface temperature history, heat flow history, thermal resistivity history and burial history. The temperature history uncertainty can be reduced by the addition of temperature constraints at specified times, e.g. at the present. The marginal cumulative distribution function of the source rock transformation ratio is fast to compute. Monte Carlo simulating the transformation ratio at a particular time during basin evolution hence reduces to drawing random outcomes from the distribution function, which is many orders of magnitude faster than recalculating the basin model. The method is useful whenever a reliable value or a stochastic simulation of the source rock transformation ratio is needed and can be applied with one-, two- and three-dimensional basin modelling systems.