Prediction of travel times of phosphate in soils at a disposal site for wastewater

Adsorption of phosphate in soils is both concentration and time dependent. An expression for the mobility of phosphate in a soil should follow from substitution of an equation for the adsorption of phosphate into a mass balance equation for movement of phosphate. Substitution is only allowed if the time frames of the (static) adsorption equation and the (dynamic) mass balance equation are compatible. This is not the case, however. Incompatibility of time frames is avoided in this paper by basing adsorption and mass flow processes in a soil on the minimum time for dispersive mixing. This time is determined by the dispersion length, which is the change in longitudinal dispersive spread (variance) of a solute per unit depth of soil. The average adsorption, as seen by the moving front of a step increase in the concentration of phosphate in a soil, is found by substituting the time for longitudinal dispersive mixing into the adsorption equation for phosphate. Mobilities and travel times in soils are then calculated from this average adsorption. Applying this method to soils at a disposal site for wastewater from a sewage treatment plant in Albany, Western Australia, travel times of phosphate to deep groundwater are calculated to be at least 500 years and very likely to be of the order of 1000 years or more. Disposal of wastewater in soil makes conditions favourable for precipitation of phosphate in calcium phosphates. Theoretically >95% of phosphate from wastewater can be stored in the soil as hydroxyapatite and fluoroapatite.