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Journal of Porous Media
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ISSN Imprimir: 1091-028X
ISSN En Línea: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v8.i2.60
pages 175-191

Radon-222 Exhalation Rates from Phosphogypsum-Bearing Embankment Subjected to Constant Temperature and Fixed Activity Concentration

J. A. Rabi
Faculty of Zootechny and Food Engineering, University of Sao Paulo, Av. Duque de Caxias Norte, 225, Pirassununga, SP, 13635-900, Brazil


Stack or embankment disposal of phosphogypsum — a by-product from phosphate fertilizer industries-has given rise to environmental issues concerning 222Rn exhalation rates into the local atmosphere. Early models for radon transport in porous media have considered both diffusion and convection, although basically taking into account air flow driven by predefined pressure differences and Darcy's law. The present paper introduces buoyant effects and outlines a steady-state two-dimensional model for 222Rn transport through a phosphogypsum-bearing embankment, inside of which there are sources and sinks for this gaseous radionuclide. The embankment is treated as an open cavity filled with porous material and surrounded by isothermal and impermeable ground. Its top surface is subjected to fixed activity concentration and fixed lower temperature. Buoyancy-driven interstitial air flow is supposedly laminar and modeled according to Darcy-Brinkman-Boussinesq formulation. Governing equations are written in dimensionless form in order to account for concurrent effects of the various physical parameters involved, and three unconventional dimensionless groups are put forward apart from usual controlling parameters, such as Darcy, Grashof, Prandtl, and Schmidt numbers. An analytical solution regarding a strictly diffusive approach is inferred, whereas full model equations are solved numerically by adapting an existing finite-volume simulator. As a preliminary investigation, results are reported for Pr = 0.71 and Sc = 15, while Da and Gr are allowed to vary from 10−7 to 10−13 and from 107 to 109 , respectively. Results are also presented as a function of the modified Grashof number Grm = Gr·Da. For porous media with relatively low permeability (Da ≤ 10−9), 222Rn transport is diffusion dominated (i.e., natural convective effects play a minor role) and both Nusselt and Sherwood numbers prove to be insensitive to Grashof number. At approximately Grm ≈ 10, circulation cell splitting occurs within each embankment half, as the natural convective fluid flow increases its strength, which results in very low 222Rn concentration levels inside the porous matrix.