The process of transport and trapping of arsenic ions in porous water filters is treated as a classic mass transport problem which, at the pore scale, is modeled using the traditional convection-diffusion equation, representing the migration of species present in very small (tracer) amounts in water. The upscaling, conducted using the volume averaging method, reveals the presence of two possible forms of the macroscopic equations for predicting arsenic concentrations in the filters. One is the classic convection-dispersion equation with the total dispersion tensor as its main transport coefficient, and which is obtained from a closure formulation similar to that of the passive diffusion problem. The other equation form includes an additional transport coefficient, hitherto ignored in the literature and identified here as the adsorption-induced vector. These two coefficients in the latter form are determined from a system of two closure problems that include the effects of both the passive diffusion as well as the adsorption of arsenic by the solid phase of the filter. This theoretical effort represents the first serious effort to introduce a detailed micro–macro coupling while modeling the transport of arsenic species in water filters representing homogeneous porous media.

Weitzenböck et al. have proposed a theoretical framework for permeability estimation in two-and three-dimensions using a set of channel (1-D) flow experiments. [1] For determining the 2-D permeability tensor, three channel flow experiments must be conducted, whereas for estimating the 3-D permeability tensor, six unidirectional channel flow experiments along six unique orientations need to be performed.The authors have noted important errors in the above-mentioned widely-cited research article. [1] Here we highlight the errors involved in the theoretical derivation of the 3-D permeability tensor and report the corrected forms of the expressions for the tensor components.In Section 4.2 of Weitzenböck et al., [1] based on the Direction of Permeability Measurement, there are two errors. These errors are related to the incorrect rotation angles of the measurement direction as follows: first, the rotation of the measurement direction by 90 ∘ about the y-axis for finding out the effective permeability K V , and second, the rotation of the measurement direction by 45 ∘ about the y-axis for finding out the effective permeability K VI .The recommended corrections for these errors are as follows. First, the effective permeability, K V , should be computed by rotating the measurement direction about the y-axis by À90 ∘ such that it becomes parallel to the z-axis in the laboratory frame of reference, as shown in Figure 1. This leads to the following expression for the effective permeability K V :

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