Dilution of Reactive Plumes: Evolution of Concentration Statistics Under Diffusion and Nonlinear Reaction

Abstract

Concentration fields of solutes in porous media often exhibit large fluctuations, driven by physical and chemical heterogeneity from the pore to the Darcy scale. For many applications, ranging from reactive transport modeling to toxicology, the knowledge of mean concentrations is not sufficient, and quantifying concentration variability is necessary. The probability density function (PDF) of concentration quantifies the frequency of occurrence of concentration values throughout a spatial domain. While evolution equations and analytical solutions for the concentration PDF Highlights• We introduce a general framework quantifying the link between concentration PDFs and spatial concentration profiles.• We derive a dynamical equation for the evolution of the concentration PDF under diffusion and nonlinear reaction in 1D.• We derive analytical predictions for the concentration PDF and its moments using a weakcoupling approximation.