Natural attenuation in heterogeneous aquifers: combined effect of biodegradation and rate-limited mass transfer

Natural attenuation processes are modelled within a stochastic Lagrangian framework. We consider advection, rate-limited mass transfer, and biodegradation in the mobile and immobile domains. These processes may all depend on spatially variable parameters. Temporal moment equations are derived; the results provide means for quantifying the combined effect of the transport processes for a single streamtube and at the field scale. A qualitative analysis of the interaction of mass transfer and biodegradation along a streamtube is provided, which shows that degradation in the immobile domain and rate-limited mass transfer may interact to form kinetic terms in moment equations of any order. Results are illustrated for the special case of a homogeneous streamtube. Field-scale measures of natural attenuation are defined, and their quantification within a stochastic framework is discussed.