Temporally dependent solute transport in one-dimensional porous medium: Analytical and fuzzy form solutions

Abstract

Advection-dispersion equation-based one-dimensional water quality model is created in the current work. Laplace integral transform approach is used to get an analytical solution for time dependent dispersion along a uniform flow velocity in a semi-infinite domain. The domain or medium is not initially free of solutes i.e., concentration of pollutants already exit there. The pollutant concentrations corresponding to the selected confidence level of can be derived from the fuzzy model using the ?-cut technique and mathematical operations on triangular fuzzy numbers. Triangular fuzzy numbers, which are a version of the solution in fuzzy theory, are also obtained. Graphs are used as examples, and the results are discussed in the discussion and numerical examples sections. The definition of triangular fuzzy parameter is that the mean of each parameter is roughly equal to the maximum potential concentration of contaminants. The analytical solution of the advection-dispersion equation further supports the validity of the fuzzy model.