Optimization of kinetic parameters for thermal degradation of kerogen: A Pascal program

Abstract

Kinetic parameters for the thermal degradation of kerogens are derived both from isothermal and nonisothermal heating experiments and from field observations, and the data used in computer-aided basin modeling to simulate the maturation of source rocks and the timing of hydrocarbon generation and expulsion. A Pascal program for determination of kinetic parameters is presented, together with a simplified application. Thermal degradation of kerogen is modeled as a set of parallel, independent, irreversible first-order chemical reactions. The parameters for optimization are the fractional contributions of the parallel reactions, each characterized by a discrete activation energy level, and a single, global preexponential frequency (Arrhenius) factor. For a given frequency factor, determination of the reaction proportions reduces to least-squares regression analysis of an overdetermined set of linear equations, subject to nonnegativity and closure (sum to unity) constraints, solved using an active set method. The error function (mean-squared residual) then is a nonlinear function of the frequency factor and is minimized by one-dimensional interval reduction and line-searching techniques (minimum bracketing, golden section search, and inverse quadratic interpolation). The modular program operates in a UCSD Pascal P-system environment on a 640K IBM-compatible PC. Several sets of data may be combined, including simultaneous optimization of reaction rate and cumulative evolution (or transformation ratio) data. The number of parallel reactions, distribution of activation energies, and initial estimate for the frequency factor may all be changed. The program includes a procedure for fitting data to a single, first-order reaction, requiring optimization of one activation energy and the frequency factor. A mean-squared residual objective function is minimized using a multidimensional direction set method.