Simulation Study On Tailing And Multi-Peaking Phenomena Of Breakthrough Curves In 1D Channel

Accurate prediction of pollutant transport in water systems is an important topic in hydrological research.The classical Advection Dispersion Equation(ADE)based on Fick's law of diffusion could not well agree with the observations.Up to now,at least three kinds of non-Fickian models have been proposed and widely used: The Continuous Time Random Walks(CTRW),the Multi-Rate Mass Transfer(MRMT)model,and the Fractional order Advection-Dispersion Equation(FADE).The complex mathematical connections and significant differences in physical assumptions of these models could confuse the researchers attempting to select the best model for a given situation.Therefore,it is necessary to make comprehensive comparations for these models.On the other hand,the multi-peaking phenomenon in a breakthrough curve(BTC)is beyond the simulation ability of the above models.The simulation power of the Fractional-in-Space Advection-Dispersion Equation(s FADE),the Fractional-in-Space Transient Storage model(FSTS),the Fractional Mobile-Immobile model(FMIM),the Truncated Time Fractional model(TTFM),the Continuous Time Random Walks with Truncated Power Law waiting times(CTRWTPL),the Single Rate Mass Transfer model,and the Power-law Multi-Rate Mass Transfer model were compared and analyzed with the consideration of the number of parameters in each model.On this basis,a Fractional-in-Time Transient Storage model(FTTS)was proposed and further improved to simulate the multi-peaked BTCs.Additionally,the global sensitivity analyses of the above models were conducted in this study.The main results of this study are as follows:Through comparative study it was found that the FSTS(? =-1)is a more effective model when simulating the tailing behavior of a BTC.In addition,the FSTS model has the potential to be an effective tool for detecting different types of immobile zones(i.e.,surface immobile zones and deep hyporheic zones)in a real-world flow field.In this study,a Fractional-in-Time Transient Storage model(FTTS)was proposed based on the FMIM.Compared with the FMIM,the FTTS performs more accurately.Especially for the MSR-1,the FTTS performs better than the FSTS.The reason could be that in the FTTS the description of the immobile zones is more accurate and reasonable.Further improvement for the FTTS showed that,the FTTS could well simulate the multipeaking phenomenon in a BTC and show strong simulation ability and flexibility.By performing global sensitivity analyses for the above non-Fickian models,the ranking of influences of parameters and their interactions in each model was obtained.In conclusion,the results of this study could provide theoretical support for simulation of pollutant transport in rivers.