Homogenization for Fe²+ deposition near drink water tube wells during arsenic remediation

Abstract

Homogenization is a well established methodology that can be used for upscaling. The advantage of homogenization over other upscaling methods is that it only requires the choice of a periodic unit cell to overcome the closure problem. The choice of the unit cell is completely flexible and only limited by computer capacity. Our interest is in the upscaling of reactive diffusion convection flows in connection with arsenic contaminated water remediation. We will re-derive the homogenized equations with emphasis on the physical aspects. By considering a simple two-dimensional example we cover all computational aspects linked to the actual application of the method. However, the method can be easily extended to more complicated configurations in 3-D. The computed dispersion coefficient shows a similar (qualitative) dependency on the Peclet number as literature data, albeit that the values for this 2-D example are considerably smaller. Moreover in the case of non-linear adsorption the dispersion coefficient depends on the concentration.