A semi-analytical solution for the transport of solutes with complex sequences of first-order reactions

Abstract

A semi-analytical solution for one-dimensional transport of multiple species along a reaction chain is introduced. The DECAY solution considers advection, dispersion, equilibrium sorption, and arbitrarily complex sequences of first-order reactions. The treatment of branching accommodates transport that potentially involves multiple parents and daughter products. The solution is general in that the individual species may have different dispersion and sorption coefficients and different decay rates specified in the dissolved and sorbed phases for each species. Yield coefficients can be specified so that the calculations can be conducted in terms of concentrations expressed in units of either mass or moles per unit volume of water. The DECAY solution accommodates Dirichlet and Cauchy inflow boundary conditions with general influent concentration histories. The concentrations of each species are evaluated by accurate and efficient numerical inversion of the Laplace-transform solutions. The semi-analytical solution has been tested extensively and verified against existing analytical solutions and numerical simulations.