How well do mean breakthrough curves predict mixing-controlled reactive transport?

Macroscopic transport models calibrated by flux-averaged breakthrough curves of conservative compounds do not necessarily characterize mixing well because such breakthrough curves do not provide information on fluctuations of concentration within the solute flux, which may influence mean reaction rates. We numerically examine the validity of macroscopic transport models, which are capable of describing all details of flux-averaged breakthrough curves, for predicting a mixing-controlled bimolecular precipitation reaction in heterogeneous media. We consider a homogeneous, isotropic medium with an elliptical, low-permeability inclusion and random heterogeneous fields. For the single-inclusion case, slow advection through the inclusion results in a multimodal breakthrough curve with enhanced tailing. We vary the hydraulic conductivity contrast and Peclet number to investigate the performance of a perfect macroscopic transport model for predicting the total precipitated mass within the domain and the peak concentration difference between the conservative and reactive cases at the outflow boundary. The results indicate that such a model may perform well in media with either very small or very high permeability contrast or at low Peclet number. In the high-contrast case, most flow takes place in preferential flow paths, resulting in a small variance of the flux-weighted concentration, even though the offset in the breakthrough between the slow and fast travel paths is substantial. Maximum relative errors in terms of total precipitated mass and the peak concentration difference between the conservative and reactive cases occur at intermediate permeability contrasts and large Peclet numbers. Numerical simulations on random heterogeneous fields confirm the finding of the single-inclusion case. Thus, in cases with intermediate hydraulic conductivity contrast, making macroscopic models fit flux-averaged concentration breakthrough curves better may not improve the prediction of mixing-controlled reactive transport, and it becomes necessary to quantify and account for the variability of conservative concentrations in the flux in order to formulate an appropriate macroscopic transport model that predicts mixing-controlled reactive transport.