AbstractThe present study deals with the generalized one-dimensional (1-D) advection fractal dispersion (AFD) equation. The numerical simulation is carried out to simulate the plume’s fate and transport phenomenon in a finite porous medium. The present model is developed for chemical substitute migration in soil with spatial varying advection and its corresponding fractal dispersion. Moreover, it is adequate for deliberating spatial varying sorption and first-order biological degradation due to reaction processes in the soil. As in generalized dispersion theory, the dispersion term is expressed to be directly proportional to seepage velocity by some power α, where α varies from 1 to 2. The present numerical study is capable of dealing with various types of advection and its corresponding fractal dispersion. Initially, we have assumed that the aquifer was pollutant-free. At the inlet of the domain, some pollutant source has been considered, and at the outlet boundary, it is assumed that the pollutant concentration disappears to zero. The pollutant concentration distribution has been observed in different types of porous medium as well as for various hydrological parameters. The current generalized AFD model is based on the implicit finite difference technique, which can illustrate chemical migration in the soil to the groundwater, and further, the MATLAB version R2013a( Pdepe tool technique validates it. A special case study is also discussed regarding the migration of Iron (Fe) and Zinc (Zn) in the soil. Afterwards, the numerical model is used to illustrate the breakthrough curves (BTCs) for the various transport parameters, and the accuracy of the model problem is also discussed using root mean square error (RMSE).

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