Analytical Solutions of Two-dimensional Solute Transport with Spatially and Temporarily dependent Dispersion in Heterogeneous Porous Media

Abstract

The aim of this study is to develop a two-dimensional mathematical model for the conservative solute transport in heterogeneous adsorbing porous media. Solutions for semi-infinite and finite domains are obtained in two separate cases. Groundwater velocity is considered to be a linear function of position as well as a function of time. After a certain time interval, the velocity of the groundwater changes over different time periods, so mathematically it is represented by a different temporarily dependent function. The dispersion coefficient is squarely proportional to groundwater velocity with position in both directions and directly proportional to time. Space and time-dependent groundwater velocity and dispersion coefficients are assumed to be degenerate forms. The assumption of segmented, temporally, and spatially correlated diffusion and groundwater velocities is a unique feature of this paper. The input source applied along the flow is of uniform nature. The concentration gradient along both axes is set to zero at non-source end of both semi-infinite and finite domain cases. The Laplace Integral Transform Technique (LITT) is used to obtain the final solution to the proposed problem. The effect of aquifer heterogeneity and spatiotemporal dependence of dispersion on the solute transport is shown graphically in each case.

Keywords

• Advection
• Dispersion
• Groundwater velocity
• Heterogeneity
• Porous media.

References

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