Simulation of phosphate transport in soil columns. I. model development

Abstract

A phosphate (P) transport model is developed assuming one-dimensional steady-state flow. It is assumed that P-adsorption follows the Langmuir isotherm and is reversible. Besides adsorption also non-equilibrium and irreversible precipitation may occur, which is modeled using a semi-empirical description from the unreacted shrinking core concept. The used P-sorption model is in agreement with short- and long-term batch experiments and has been validated with laboratory-scale transport experiments in previous work. The equations for transport in combination with adsorption and precipitation are solved numerically using the modular approach, in which the chemical and transport equations are decoupled. The additional dispersion due to this decoupling is quantified and methods to decrease computation times resulting from a fine discretization in time and space are discussed. The numerical program is verified with analytical solutions for the transport equations in case of linear and nonlinear (Langmuir) sorption with excellent results. Neglecting precipitation a very sharp front of P is found. The dependence of front thickness on parameter values is illustrated. When taking precipitation into account a relatively sharp front may also develop, which has travelling wave characteristics (a front shape and velocity independent of time for a uniform soil column).