The role of a porous wall on the solute dispersion in a concentric annulus

Abstract

We studied the role of a porous wall on the dispersion of a solute in an annular space in the presence of a pressure-driven flow. The continuity of concentration and mass flux at the annulus–porous medium interface is used to handle the interaction between the two media. The Reynolds decomposition technique and the cross-sectional averaging method are used to derive a reduced-order advective–dispersive transport model with the associated equivalent diffusion and advection terms. The resultant dispersion and advection coefficients for an annulus with a porous wall are fully characterized as a function of the inner solid core radius of the annulus. The findings reveal that dispersion is retarded in the presence of the inner core in an annulus for both porous and non-porous outer walls. The results also indicate that the transition to a fully advective regime occurs at higher Peclet numbers for an annulus with a porous outer wall. The results suggest that dispersion and advection in an annulus can be controlled by proper selection of the inner core diameter. We also identified the inner core size where the solute dispersion in an annulus with a porous wall is minimum compared to a non-porous boundary. The developed model and insights find applications in many engineering processes where a fluid containing a solute in an annulus interacts with a surrounding porous medium.