Contaminant Dispersion and Breakthrough in Groundwater Flow: Case Study in Maui, Hawaii

Previously published field data, from groundwater tracer studies in Hawaii, are used to develop a theory for dispersion based on the probability density function for tracer particle velocities in the aquifer. The density function is derived from tracer breakthrough curves associated with wastewater injection wells at the Lahaina Waste Water Reclamation Facility in Maui, HI. The aquifer dispersion coefficient is found to be proportional to the product of the time since tracer release and the pore velocity variance, developed empirically from the breakthrough data. Although particle velocity data are well described by Fickian diffusion with this dispersion coefficient, an empirical Weibull distribution provides an even better fit to the data, thereby enabling determination of tracer residence time in the aquifer. Based on the data, two independent methods of determining the cross-sectional area of the aquifer occupied by the $\mathrm{12,000}{\mathrm{m}}^3/\mathrm{day}$ of injectate plume are found to be in close agreement at approximately $\mathrm{26,500}{\mathrm{m}}^2$. It is also estimated that treated wastewater arriving at the two tracer measurement sites is less than 2% of the injectate.