Prediction of collector contact efficiency for colloid transport in porous media using Pore-Network and Neural-Network models

Conventional colloid filtration theory (CFT) uses the single collector contact efficiency (eta) to describe the mass transfer of colloids to a collector surface. However, this approach neglects the full complexity of the pore structure and flow field of real porous media. In this study, the porous medium geometry, flow field, and colloid mass transfer are quantified using a pore-network model (PNM). A database of pore scale eta is established by finite-element method to train a Neural-network model (NNM). The reasonable prediction of eta indicates the potential of using the developed NNMs as an alternative to correlation equations, which can free the users from repeated numerical simulation. In contrast to the prediction by conventional CFT, the value of eta in the PNM occurs as a distribution, which is dependent upon the geometry parameters of the PNM. The mean value of eta increases with the standard deviation of pore radius and decreases with the curvature number, but the dependency on coordination number is more complex. Upscaled values of the deposition rate coefficient (kd) corresponding to the distribution of eta are calculated by the breakthrough curves by PNMs. The prediction of kd by PNM is then compared with that by CFT. Results show that kd predicted by PNM shows more significant response to velocity change, and less remarkable response to colloid density change than kd predicted by CFT. The comparison between the flow velocity distribution between PNM and CFT shows that the high-velocity region of the flow field in the porous media has been neglected in CFT, which can lead to insufficient consideration of convection. The results of this work imply that it is necessary to consider the influence of the complex pore structure of porous media on the collection of colloids.