Parameter correlation study on two new analytical solutions for radially divergent tracer tests in two-zone confined aquifers with vertical dispersion effect

This study develops two new analytical models for radially divergent tracer tests at a fully-penetrating well in two-zone confined aquifers of skin and formation zones. Mixing length in the well is below the well length for inducing vertical dispersion. One model treats skins as an adsorptive Robin boundary condition for reflecting the adsorption effect. The other model applies skin's governing equation. The analytical solutions of the models are derived. The deep neural network is applied to obtain second model's solution. Results suggest the boundary condition is applicable when a Peclet number is below 0.2 for dominant dispersion in skins. The analytical solution considering the boundary condition predicts reliable parameters by using absorbed and non-absorbed tracers to avoid parameter correlation. The other solutions demonstrate skin's width correlated to its retardation factor and skin's transverse dispersivity to formation's one. The parameter correlation results from the model formulation rather than model-solving methods.