Three-dimensional solute transport in finite and curved porous media with surface input sources

In this paper, an analytical solution for three-dimensional solute transport in porous media between two curved surfaces is investigated. It is assumed that the groundwater velocity and dispersion coefficient vary with time and position. Groundwater velocity is not considered to be horizontal. The components of dispersion coefficient along the axes are considered to be proportional to the square of corresponding the position variable. The dispersion coefficient components along axes are proportional to the corresponding component of groundwater velocity in temporal aspects while former is squarely proportional to letter one in position components. It is assumed that the sources originate from two curved surfaces. The nature of the source on the two surfaces is the same, but there may be a variation in potential. Initially, the aquifer's domain is supposed to be uniformly polluted. The Laplace Integral Transformation Technique (LITT) is used to obtain analytical solutions. Numerical examples are given to demonstrate the effects of various factors on the solute concentration profile in a system where advection and dispersion play important roles.

In addition, the sub-case of horizontal flow is also discussed. The model is extremely useful in analyzing and dealing with widespread surface sources of groundwater pollution in simulated agricultural fields or urban dumping areas.