Review http://repositorio.utp.edu.co/dspace/bitstream/11059/3659/1/5430858R621.pdf

I am not sure you can find a suitable function to represent the reaction rate coefficient for predicting the concentration distribution of dissolved heavy metals within a river. This is highly site and process specific. If you are interested in predicting metal release through mineral dissolution, the 1st posted answer may be a good approach, but it assumes mineral dissolution is at chemical equilibrium (and dissolution of some mineral is causing the release). You would need to consider both the mineral dissolution solubility and the river flow rate, because additional water flow in the river can dilute and reduce the concentrations. 

I would recommend measuring the mass release as a mass flux along with the flow rate. You can empirically determine the rate coefficient from the observed mass release. Please find the attached, and hope this is helpful.