The identification of transport parameters by inverse modeling often suffers from equifinality or parameter correlation when models are fitted to observations of the solute breakthrough in column outflow experiments. This parameters uncertainty can be approached by the application of multiple experimental designs such as column experiments in open-flow mode and the recently proposed closed-flow mode. Latter are characterized by the recirculation of the column effluent into the solution supply vessel that feeds the inflow. Depending on the experimental conditions, the solute concentration in the solution supply vessel and the effluent follows a damped sinusoidal oscillation. As a result, the closed-flow experiment provides additional observables in the breakthrough curve. The evaluation of these emergent features allows intrinsic control over boundary conditions and impacts the uncertainty of parameters in inverse modeling.
We present a comprehensive sensitivity analysis to illustrate the potential application of closed-flow experiments. We show that the sensitivity with respect to the apparent dispersion can be controlled by the experimenter leading to a decrease in parameter uncertainty as compared to classical experiments by an order of magnitude for optimal settings. With these finding we are also able to reduce the equifinality found for situations, where rate-limited interactions impede a proper determination of the apparent dispersion and rate coefficients. Furthermore, we show the expected breakthrough curve for equilibrium and kinetic sorption, the latter showing strong similarities to the behavior found for completely mixed batch reactor experiments. This renders the closed-flow mode a useful complementary approach to classical column experiments.
