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In a recent paper by Lasseux, Vald\'{e}s-Parada and Porter (J.~Fluid~Mech.\textbf{805} (2016) 118-146), it is found that the apparent gas permeability ofthe porous media is a nonlinear function of the Knudsen number. However, thisresult is highly questionable, because the adopted Navier-Stokes equations andthe first-order velocity-slip boundary condition are first-order (in terms ofthe Knudsen number) approximations of the Boltzmann equation and the kineticboundary condition for rarefied gas flows. Our numerical simulations based onthe Bhatnagar-Gross-Krook kinetic equation and regularized 20-moment equationsprove that the Navier-Stokes equations with the first-order velocity-slipboundary condition are only accurate at a very small Knudsen number limit,where the apparent gas permeability is a linear function of the Knudsen number.

A comment on `An improved macroscale model for gas slip flow in porous media'