This study presents a generalized analytical solution for one-dimensional solute transport in finite spatial domain subject to arbitrary time-dependent inlet boundary condition. The governing equation includes terms accounting for advection, hydrodynamic dispersion, linear equilibrium sorption, and first order decay processes. The generalized analytical solution is derived by using the Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate. Some special cases are presented and compared to illustrate the robustness of the derived generalized analytical solution. Result shows an excellent agreement between the analytical and numerical solutions. The analytical solutions of the special cases derived in this study have practical applications. Moreover, the derived generalized solution which consists an integral representation is evaluated by the numerical integration to extend its usage. The developed generalized solution offers a convenient tool for further development of analytical solution of specified time-dependent inlet boundary conditions or numerical evaluation of the concentration field for arbitrary time-dependent inlet boundary problem.

Chronic arsenic (As) exposure continues to be a public health problem of major concern worldwide, affecting hundreds of millions of people. A long-term groundwater quality survey has revealed that 20% of the groundwater in southern Taiwan’s Pingtung Plain is clearly contaminated with a measured As concentration in excess of the maximum level of 10 µg/L recommended by the World Health Organization. The situation is further complicated by the fact that more than half of the inhabitants in this area continue to use groundwater for drinking. Efforts to assess the health risk associated with the ingestion of As from the contaminated drinking water are required in order to determine the priorities for health risk management. The conventional approach to conducting a human health risk assessment may be insufficient for this purpose, so this study adopts a geostatistical Kriging method to perform a spatial analysis of the health risk associated with ingesting As through drinking groundwater in the Pingtung Plain. The health risk is assessed based on the hazard quotient (HQ) and target cancer risk (TR) established by the U.S. Environmental Protection Agency. The results show that most areas where the HQ exceeds 1 are in the southwestern part of the study area. In addition, the high-population density townships of Daliao, Linyuan, Donggang, Linbian, Jiadong, and Fangliao presently have exceedingly high TR values that are two orders of magnitude higher than the acceptable standard. Thus, the use of groundwater for drinking in these townships should be strictly avoided. A map that delineates areas with high TR values and high population densities is provided. The findings broaden the scope of the spatial analysis of human health risk and provide a basis for improving the decision-making process.

The two-dimensional advection-dispersion equations coupled with sequential first-order decay reactions involving arbitrary number of species in groundwater system is considered to predict the two-dimensional plume behavior of decaying contaminant such as radionuclide and dissolved chlorinated solvent. Generalized analytical solutions in compact format are derived through the sequential application of the Laplace, finite Fourier cosine, and generalized integral transform to reduce the coupled partial differential equation system to a set of linear algebraic equations. The system of algebraic equations is next solved for each species in the transformed domain, and the solutions in the original domain are then obtained through consecutive integral transform inversions. Explicit form solutions for a special case are derived using the generalized analytical solutions and are compared with the numerical solutions. The analytical results indicate that the analytical solutions are robust, accurate and useful for simulation or screening tools to assess plume behaviors of decaying contaminants.