Modelling of radon concentration peaks in thermal spas: application to Polichnitos and Eftalou spas (Lesvos Island--Greece).

A mathematical model was developed for the description of radon concentration peaks observed in thermal spas. Modelling was based on a pragmatic mix of estimation and measurement of involved physical parameters. The model utilised non-linear first order derivative mass balance differential equations. The equations were described and solved numerically by the use of specially developed computer codes. To apply and check the model, measurements were performed in two thermal spas in Greece (Polichnitos and Eftalou-Lesvos Island). Forty different measurement sets were collected to estimate the concentration variations of indoor-outdoor radon, radon in the entering thermal water, the ventilation rate, the bathtub surface and the bath volume. Turbulence and diffusive phenomena involved in radon concentration variations were attributed to a time varying contact interfacial area (equivalent area). This area was approximated with the use of a mathematical function. Other model parameters were estimated from the literature. Through numerical solving and use of non-linear statistics, the time variations of the equivalent area were estimated for every measurement set. Computationally applied non-linear uncertainty analysis showed less sensitive variations of the coefficients of the equivalent area compared to parameters of the model. Modelled and measured radon concentration peaks were compared by the use of three statistical criteria for the goodness-of-fit. All the investigated peaks exhibited low error probability (***p<0.001) for all criteria. It was concluded that the present modelling achieved to predict the measured radon concentration peaks. Through adequate selection of model parameters the model may be applied to other thermal spas.