Colloidal detachment in porous media: Stochastic model and upscaling

[Display omitted] •Microscale model of detachment: torque balance of forces exerting attached particles.•Macro (core) scale model: maximum attached concentration of particles versus velocity.•Upscaling by probabilistic distribution of model coefficients in torque balance.•Upscaled maximum attached concentration versus salinity, pH, and temperature.•Downscaling determines distribution of torque-balance coefficients from corefloods. We discuss colloidal-suspension-nano transport in porous media with particle detachment and further capture by the matrix. Previous works formulate particle-scale detachment conditions and porous-media-scale transport equations with empirical coefficients, which are determined from flow tests and cannot be predicted from the particle scale. The present work derives the upscaling technique by stochastic distribution of torque and force balances on the attached particle, yielding a macro-scale equation for detachment. The upscaled detachment equation has the form of the maximum retained concentration of attached particles as a function of velocity, pH, salinity, and temperature of the carrier fluid. The upscaling procedure allows for direct calculations of the maximum retention function (MRF) from micro-scale parameters. The sensitivity analysis shows that MRF is most sensitive to the particle aspect ratio and pore size, while it is less sensitive to the standard deviations of the lever-arm ratio and particle size distributions. The exact solution for 1D flow problem is used to determine the MRF from laboratory tests and matches it with the stochastic microscale model for detachment. The high match obtained for four colloidal coreflood experiments validates the stochastic model and upscaling procedure.