A Novel Eulerian Reaction-Transport Model to Simulate Age and Reactivity Continua Interacting with Mixing Processes

Abstract. In geoscientific models, it can be useful to attribute properties to particles in a continuum. Lagrangian frameworks aim to simulate sufficiently large numbers of individual particles to describe the evolution of the properties and their statistical distributions. Here we present an Eulerian approach: Diffusion-advection-reaction type of partial differential equations are derived for centralized moments, which can describe the distribution of properties associated with chemicals in reaction-transport models. When the property is age, the equations for centralized moments (unlike non-central moments) do not require terms to account for aging, making this method suitable for modeling age tracers. The properties described by the distributions may also affect reaction rates. In practical applications, continuous distributions of ages or reactivities are resolved to simulate organic matter mineralization in surficial sediments, where transport is typically dominated by macrofaunal and physical mixing processes. These applications show the potential of the method to simulate reactivity continua in disturbed environments and reveal practical limitations.