A chloride transport model for identifying sequential bioreactive systems of chlorinated solvents

Chlorinated solvents, such as tetrachloroethylene (PCE) and trichloroethylene (TCE), are often biodegraded to produce daughter species under aerobic and anaerobic conditions. During the biodegradation, chloride is produced in groundwater as a byproduct. For this reason, chloride concentrations in contaminant plumes are elevated relative to background concentrations. Because of the neutral chemical behavior of chloride, it can be treated as an indicator to identify the sources of contaminants and to estimate biodegradation rates of chlorinated solvents. However, chloride is produced from multiple reactions in the PCE/TCE reaction chain. The partial differential equation of chloride transport, which is coupled with four reactants, can only be solved numerically. In this paper, we use singular value decomposition (SVD) to decouple the coupled partial differential equations into independent subsystems. Then, we derive the analytical solution of chloride transport and use it, in turn, as a handy tool to quantify biodegradation of chlorinated solvents.