Fate and Transport of Solute with Temporally Varying Pulse Type Input Source under Sorption in Heterogeneous Porous Formation

A mathematical model is developed to describe the conservative solute migration under sorption in a groundwater reservoir. For the complexity of the aquifer, it is assumed as heterogeneous and semi-infinite. Dispersion is considered as a varying power of seepage velocity. For the sake of real scenario of the aquifer, the seepage velocity, first-order decay (FOD), zero-order production (ZOP), and retardation factor are taken as spatio-temporal dependent parameters. Initially, the aquifer is assumed as polluted by a background source throughout the domain. Also, a temporally dependent pulse type sinusoidal input source is taken at origin of the aquifer. The other end of the aquifer is assumed as flux free. The retardation factor considered with a special form due to regional and complication of the porous medium. The transient velocity is considered as sinusoidal, exponential, algebraic sigmoid and asymptotic forms to study the solute transport behavior under different velocity patterns. The analytical solution of the proposed model is obtained by Laplace and inverse Laplace transform techniques. All the graphical plots are obtained by MATLAB software. The present study may be helpful for scientists, geologists to determine the time and position of harmless concentration level and can be treated as preliminary tool for solute migration for the future researchers.