Hemispheres-in-cell geometry to predict colloid deposition in porous media

A "hemispheres-in-cell" geometry is provided for prediction of colloid retention during transport in porous media. This new geometry preserves the utilities provided in the Happel sphere-in-cell geometry; namely, the ability to predict deposition for a range of porosities, and representation of the influence of neighboring collectors on the fluid flow field. The new geometry, which includes grain to grain contact, is justified by the eventual goal of predicting colloid deposition in the presence of energy barriers, which has been shown in previous literature to involve deposition within grain to grain contacts for colloid:collector ratios greater than approximately 0.005. In order to serve as a platform for predicting deposition in the presence of energy barriers, the model must be shown capable of quantitatively predicting deposition in the absence of energy barriers, which is a requirement that was not met by previous grain to grain contact geometries. This paper describes development of the fluid flow field and particle trajectory simulations for the hemispheres-in-cell geometry in the absence of energy barriers, and demonstrates that the resulting simulations compare favorably to existing models and experiments. A correlation equation for predicting collector efficiencies in the hemispheres-in-cell model in the absence of energy barriers was developed via regression of numerical results to dimensionless parameters.