A general unified expression for solute and heat dispersion in homogeneous porous media

Abstract

Key Points An expression for the transverse and longitudinal dispersion coefficient The relation between the solute and heat dispersion coefficient is clarified A new material property is introduced, the critical Peclet number Perturbations of temperature or solute concentration in a porous medium spread out by heat or molecular diffusion, respectively. If the pore-filling medium (e.g., water in soil) flows, this causes additional spreading of the perturbation due to the variation of local flow velocities and the tortuous flow lines through pore space. Together, this is termed dispersion, which plays an important role in geothermal energy production, contaminant transport, and reactor beds. Numerous models have been proposed to describe the dispersion coefficient as a function of flow rates, diffusion rates and other parameters, such as pore geometry. These models are either for heat (thermal) or solute dispersion, and often only valid for a limited range of flow rates, typically expressed in terms of the Péclet number. Here we present a single, universal expression for both the heat and solute dispersion coefficient in homogeneous porous media, valid over a wide range of Péclet numbers. Only three parameters have to be determined, which depend mainly on the pore geometry of the material. The expression facilitates the physical understanding of dispersion and may be helpful for the interpretation of numerical microscopic modeling results. It has the practical advantage that the heat dispersion coefficient can easily be calculated from the solute dispersion coefficient (or vice versa) and that dispersion coefficients over a wide range of Péclet numbers can be estimated from measurements over only a limited range. ©2013. American Geophysical Union. All Rights Reserved.