MODELING REACTIVE TRANSPORT IN SEDIMENTS SUBJECT TO BIOTURBATION AND COMPACTION

Abstract

Current bioturbation models are marked by confusion in their treatment of porosity. Different equations appear to be needed for different biodiffusion mechanisms, i.e., interphase mixing, where biological activity causes bulk mixing of sediment affecting both tracer and porosity profiles, versus intraphase mixing, where the solid components are intermixed, but the porosity is left unchanged. Another issue is whether the model depends upon the particle type with which tracers are associated, e.g., 137Cs on small clay particles versus 210Pb on larger grains. This uncertainty has lead to conflicting conservation equations for radiotracers, and in particular, to the question whether the porosity should be placed inside or outside of the differential term that governs the biodiffusive flux. We have reexamined this situation in the context of multiphase, multicomponent continuum theory. Most importantly, we prove that under the assumption of steady-state porosity, there exists only one correct form of the steady-state conservation equation for a radiotracer, regardless of biodiffusion mechanism and particle type, i.e., where x is depth, Cs is the concentration/activity of the tracer, Fseds is the constant flux of solid sediment to the sediment, ρs is the density of the solid phase, φs is the solid volume fraction, DB is the biodiffusion coefficient, and λ is the decay constant. This pertinent finding results from a substantial revision and extension of diagenetic theory. By considering the conservation of momentum, as well as mass, we have identified the correct reference velocities to define biodiffusional fluxes. From that, we have formulated a consistent set of model equations that govern (1) transient porosity and transient tracer concentrations, (2) steady-state porosity and transient tracer concentrations, and (3) steady-state porosity and steady-state tracer concentrations, in sediments that are subject to both compaction and bioturbation.