Adjoint models with non-Fickian reactive transport to identify pollutant sources in water

Abstract

Pollutant source identification (PSI) has remained a research topic in environmental sciences for decades for hazardous chemicals, with the assumption that the transport of pollutants is Fickian. Pollutant transport in natural media, however, is usually non-Fickian, characterized by slow retention or preferential movement, and PSI models remained unknown for non-Fickian, reactive transport. To fill this knowledge gap, an adjoint fractional advection-dispersion-reaction equation (fADRE) was derived in this study to identify the source location of reactive pollutants undergoing non-Fickian diffusion with multiple phases in subsurface water with any dimension and boundary conditions. Six fundamental chemical reactions varying from radioactive decay to bimolecular reactions were considered, whose backward-in-time rate equations were simulated by particle tracking combined with backward non-Fickian diffusion. Applications showed that the adjoint fADRE identified the source location of reactive tracer transport in “homogeneous” sand columns repacked in our laboratory and a heterogeneous alluvial aquifer in an actual field site, while the Fickian-based, classical PSI model overestimated by four times the source location of reactive pollutants undergoing strong non-Fickian transport. To expand the applicability of the adjoint fADRE for PSI, we also discussed the impacts of the immobile pollutant phase and reactive kinetics on PSI, pollutant release history recovery, and usage of PSI for complex chemical reactions. The results showed that the fundamental chemical reactions considered in this study can affect PSI by adjusting the location and value of the peak of the probability density functions under conditions such as a relatively large decay constant or a space-dependent reaction rate, and the immobile pollutants can also affect PSI by shortening the source location and elongating the release time for pollutants usually detected only in the mobile phase. Therefore, non-Fickian dynamics and pollutant phases (which were missed by the adjoint ADRE), as well as reaction kinetics, must be captured by the adjoint model, such as the adjoint fADRE derived in this study, for PSI in real-world geological media.