Transport and concentration controls for chloride, strontium, potassium and lead in Uvas Creek, a small cobble-bed stream in Santa Clara County, California, U.S.A.: 2. Mathematical modeling

Abstract Three models describing solute transport of conservative ion species and another describing transport of species which adsorb linearly and reversibly on bed sediments are developed and tested. The conservative models are based on three different conceptual models of the transient storage of solute in the bed. One model assumes the bed to be a well-mixed zone with flux of solute into the bed proportional to the difference between stream concentration and bed concentration. The second model assumes solute in the bed is transported by a vertical diffusion process described by Fick's law. The third model assumes that convection occurs in a selected portion of the bed while the mechanism of the first model functions everywhere. The model for adsorbing species assumes that the bed consists of particles of uniform size with the rate of uptake controlled by an intraparticle diffusion process. All models are tested using data collected before, during and after a 24-hr. pulse injection of chloride, strontium, potassium and lead ions into Uvas Creek near Morgan Hill, California, U.S.A. All three conservative models accurately predict chloride ion concentrations in the stream. The model employing the diffusion mechanism for bed transport predicts better than the others. The adsorption model predicts both strontium and potassium ion concentrations well during the injection of the pulse but somewhat overestimates the observed concentrations after the injection ceases. The overestimation may be due to the convection of solute deep into the bed where it is retained longer than the 3-week post-injection observation period. The model, when calibrated for strontium, predicts potassium equally well when the adsorption equilibrium constant for strontium is replaced by that for potassium.