Parametric modelling and numerical simulation of natural-convective transport of radon-222 from a phosphogypsum stack into open air

An existing finite-volume computational simulator for heat and mass transfer in media fully or partially filled with porous material has been adapted to predict radon-222 exhalation rates. For validation purposes, this paper numerically examines the extent of natural-convective effects on radon-222 steady-state transfer from a phosphogypsum stack into the surrounding atmosphere. The stack is approximated by a dry rectangular porous matrix having uniform porosity and isotropic permeability whereas the supposedly laminar buoyancy-driven air flow is modelled following Darcy–Brinkman–Boussinesq approach. Differential governing equations are cast in dimensionless form in order to encompass simultaneous effects from physical factors involved. Dimensionless groups related to decay and emanation processes are put forward apart from usual controlling parameters such as Prandtl, Schmidt, Darcy and Grashof numbers. Results are reported for 106 ⩽ Gr ⩽ 108 and 10−13 ⩽ Da ⩽ 10−7. Natural-convective effects on typical low-permeability phosphogypsum stacks proved to be of minor importance, as radon-222 transfer becomes diffusive dominant as expected.