Analytical Solution for Unidirectional Advection-diffusion Equation with Variable Viscosities

More attention has been paid to understanding and evaluating the pollutants and solute transport in porous media. In this paper, an analytical solution for unidirectional A-D equation is obtained to study the effects of the solute to solvent viscosity ratio on solute dispersal and temporal velocities. From these studies we draw following conclusions: 1)At δ>1, the temporal velocities decline exponentially with the transport time and the influences of the viscosity to hinder the solute dispersion are more and more obvious with the increasing viscosity ratio and the transport time. 2)At δ<1, velocities tend to ascent linearly with the transport time and the solute spreading are strengthened. 3)Concentration profile differences at δ < 1 are not as significant as that at δ > 1. And it could be ignored in the calculations to reduce the computation complexity in practice when the viscosity ratio is smaller than one. It helps predict the position and time to reach the harmless concentration in monitoring the groundwater quality and pollution level, such as oil tank and pipeline leak. It is also possible to design and interpret the laboratory experiments and study the miscible flow in homogeneous and stable reservoirs.