Simplified calibration of continuous-time random walk solute transport models

Continuous-time random walk (CTRW) models of non-Fickian solute transport are defined by a temporal pdf and three parameters: a velocity-like constant, a dispersion-like constant and a “time constant”. Presently, to identify a model, all are jointly calibrated against solute breakthrough data. We show that without loss of generality the time constant can be set to unity and velocity-like and dispersion-like CTRW parameters can be set equal to well-defined classical counterparts, and thus physically pre-constrained. Thus only one entity, the pdf, requires empirical fitting during model calibration, rather than four. Our assertions are backed by numerical analysis.