An approximate solution for one‐dimensional absorption in unsaturated porous media

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Abstract
The “boundary layer” or “integral” method is used to derive a closed‐form approximate solution for one‐dimensional absorption of water in an unsaturated porous medium whose characteristic curves are of the van Genuchten type. In this approach, an assumed saturation profile is substituted into the governing equation, and integrated from the boundary out to the wetting front. This yields closed‐form solutions for the front location and the instantaneous liquid flux at the boundary. The accuracy of this solution in predicting the flux, as determined by comparison with numerical solutions utilizing a Boltzmann‐type transformation, is always within 15%, for any value of the initial saturation. As an example of the use of this approximate solution, saturation profiles are calculated for absorption into the Topopah Spring volcanic tuff at Yucca Mountain, Nevada, the site of the proposed nuclear waste repository.