An analytical solution of tetrachloroethylene transport and biodegradation

In this manuscript, we consider a transport system with a dechlorination reaction network, in which tetrachloroethylene (PCE) reacts to produce trichloroethylene (TCE), TCE reacts to form three daughter products, cis-1,2-dichloroethylene (cis-1,2-DCE), trans-1,2-dichloroethylene (trans-1,2-DCE), and 1,1-dichloroethylene (1,1-DCE), three DCEs further react to produce vinyl chloride (VC), finally VC reacts to produce ethylene (ETH). Because the partial differential equation describing the reactive transport of VC, is coupled by three reactant concentrations, currently the problem must be solved numerically. Following Lu et al. (2003), we extend the analytical solution from five species to the entire PCE reaction network. Using the singular value decomposition (SVD) the system of transport equations with convergent reactions is decoupled into seven orthogonal subsystems. Previously published analytical solutions of single species transport become the basic solutions in the transformed domain for each independent subsystem. The solutions in real concentration domain are obtained using the inverse transform. The solution derived in this study can then be used instead of Sun et al. (1999) in BIOCHLOR for simulating more realistic systems of biodegradation and reactive transport.