  Non-monotonic retention profiles (NRP) have been observed in numerous studies
of colloidal-nano flows in porous media. For the first time, we explain the
phenomenon by distributed particle properties (size, shape, surface charge). We
discuss colloidal-nano transport with fines attachment considering
stochastically distributed filtration coefficient (particle attachment
probability) and the influence of area occupation by particles on the rock
surface. The distributed dynamic system allows for exact averaging (up-scaling)
yielding a novel 3x3 system of equations for total concentrations. Besides the
traditional equations of particle mass balance and capture-rate, the novel
system contains a third independent equation for kinetics of site occupation
during particle attachment. Ten laboratory tests exhibiting NRP have been
successfully matched by the upscaled system for binary colloids. Ten laboratory
tests with 7-parametric data arrays have been successfully matched by the
5-parameter model, which validates the model. The tuned parameters belong to
their common intervals. The laboratory data tuning was significantly simplified
by deriving the exact solution of upscaled equations. These results provide
valuable insights for understanding the transport mechanisms and environmental
impact in colloidal-nano flows exhibiting NRP. Besides, the upscaled system and
the analytical model for 1D transport facilitate interpretation of the
laboratory coreflood data and allows for the laboratory-based predictions for
3D colloidal-nano transport at the field scale.
