Adaptive Multirate Mass Transfer (aMMT) model: A new approach to upscale regional-scale transport under transient flow conditions

The long-term evaluation of regional-scale groundwater quality needs efficient upscaling methods for transient flow. Upscaling techniques, such as the Multirate Mass Transfer (MRMT) method with constant upscaling parameters, have been used for transport with steady-state flow, yet the upscaling parameters (i.e., rate coefficients) may be time dependent. This study proposed and validated an adaptive MRMT (aMMT) method by allowing the mass transfer coefficients in MRMT to change with the flow field. Advective-dispersive contaminant transport simulated in a 3-D heterogeneous medium was used as a reference solution. Equivalent transport under homogeneous flow conditions was evaluated by applying the MRMT and aMMT models for upscaling. The relationship between mass transfer coefficients and flow rates was fitted under steady-state flow driven by various hydraulic gradients. A power law relationship was obtained, which was then used to update the mass transfer coefficients in each stress period under transient flow conditions in the aMMT method. Results indicated that for advection-dominated transport, both the MRMT and aMMT methods can upscale the anomalous transport dynamics affected by subgrid heterogeneity under transient flow conditions. Whereas for diffusion-dominated systems, the MRMT model failed to capture the tails of tracer breakthrough curves after the boundary condition changed, but the results from the aMMT model were significantly improved. However, if the overall flow direction changed, both MRMT and aMMT failed to represent the breakthrough curve tail generated by the heterogeneous system. The results point toward a promising path for upscaling transport in complex aquifers with transient flow.