AN APPLICATION OF LEAST-SQUARES INVERSE ANALYSIS IN KINETIC INTERPRETATIONS OF HYDROUS PYROLYSIS EXPERIMENTS

A least-squares inverse method is applied to the estimation of optimum kinetic parameters with statistical error bounds from concentration data obtained in isothermal hydrous pyrolysis experiments. The inverse method requires the specification of a data-parameter relationship (e.g., classical kinetic theory), the prior covariance matrices of data and parameter errors, as well as the prior central estimates of data and parameters. The reaction scheme considered is the common case of kerogen breakdown by Gaussian-weighted independent parallel first-order reactions and bitumen cracking by a single first-order reaction. The nonlinearity of the problem is reduced by a logarithmic transformation, which suggests a parameterization in terms of logarithmic concentrations, activation energies, and logarithmic Arrhenius factors. The linearized variance analysis is valid for the case studied, and the posterior covariance matrix reveals which parameters are constrained by the data. We find that the statistical errors in the average activation energy and the associated Arrhenius factor are strongly correlated. Hence, the parameters which determine the temperature dependence of the reaction rate have not been resolved independently. Furthermore, the kinetic results are very sensitive to the presence of a distribution of activation energies in kerogen breakdown. This distribution is not constrained by the data. As a consequence, neglecting the consideration of distributions of activation energies results in activation parameter values which are much too low. This is the major reason for the commonly encountered discrepancy between kinetic parameter values obtained from hydrous pyrolysis and micropyrolysis experiments, respectively.