On the equivalence of the power and reactive continuum models of organic matter diagenesis

Abstract

The decomposition of organic matter in marine sediments is usually described by models in which it is assumed that organic matter is composed of a small number of reactive types (a discrete finite distribution), and that each type follows first-order kinetics. Two diagenetic models adopting a more physically realistic assumption that organic matter is composed of an infinite number of reactive types (a continuous distribution) have recently been developed: the reactive continuum model and the power model. The reactive continuum model, as it has been applied, is based on a gamma distribution of organic matter reactive types and can generate an apparent reaction order greater than one. The power model is based on the premise that the reactivity of organic matter gradually decreases with time; thus, the apparent rate constant becomes a continuously varying parameter. It is shown in this note that the reactive continuum model, based on a gamma distribution, is mathematically equivalent to the power model for simple closed-system decay.