A two-dimensional analytical model for contaminant transport in a finite domain subjected to multiple arbitrary time-dependent point injection sources

Predicting the fate and transport of contaminants in a subsurface environment is essential to the evaluation and remediation of soil and groundwater pollution. Point source models have been widely used to describe the accidental leakage of contaminants and the intended injection of chemicals, but previous researches are limited to a single source in an infinite/semi-finite domain with oversimplified injection types. Thus, this study establishes a two-dimensional analytical model for contaminant transport involving advection, dispersion, sorption and degradation in a finite domain with multiple arbitrary time-dependent point sources. Four representative time-dependent sources are applied to study the transport behavior of contaminants in a more realistic environment. Results reveal that assuming multiple sources as an equivalent-intensity single point source would significantly undervalue the polluted range by 17.7% in the early stage but overvalue the maximum downstream concentration, when the sources are spaced at an interval larger than 1 m. An infinite effluent boundary assumption would cause a noticeable deviation in the concentration near a real finite border, especially in a dispersion-dominated migration system. Moreover, a larger decay coefficient for decay injection will linearly reduce the area of contaminated region, while a larger injection rate for finite pulse injection will logarithmically expand the contaminated region. Thus, close attention should be paid to the time-dependent characteristics of point sources in practice to facilitate soil and groundwater remediation, and the present model is a promising tool to address this issue.