Modeling particle transport in downward and upward flows

Experimental data obtained for particle transport in downward and upward flows in smooth and rough porous media are analyzed at various flow rates. The data analysis and interpretation are aided through an analytical model with linear kinetics that assumes two sites for particle deposition within a medium, namely, reversible and irreversible, together with a dual mode of irreversible deposition. The bimodal particle transport model is obtained using the Green's function method and is capable of fitting, with reasonable accuracy, the observed transport and deposition behavior of particles. Approximations for advection‐dominated flows are also obtained that could represent a simplified modeling tool. Expressions of the temporal moments are developed and algebraic equations are derived that express the model parameters in terms of the moments of the measured particle concentration distributions. The transport models helped define the relationship of the modeled parameters to flow velocity and media roughness. The fitting results show that the parameters for rough and smooth media vary in a systematic way with the pore fluid velocity. The results also reveal that flow direction has a significant influence on the mode and magnitude of irreversible particle deposition for the conditions investigated. For the same seepage velocity, the rate of particle deposition is greater for upward flows than for downward flows. Moreover, roughness effects increase the irreversible particle deposition in downward flows but have little effect in upward flows.