Non-Probabilistic Uncertainty Analysis for Radon Transport Mechanisms

Abstract

Radon is a well-known radioactive inert gas that usually emanates from rock, soil, concrete and enclosed places like house, building, and underground mine, etc. It is usually undetectable to the human senses. Radon may enter into various enclosures such as buildings and it can be able to accumulate due to improper ventilation. A worldwide average of 60.4 percent of total indoor radon originates from under-ground and surrounding enclosures (Cothern et al., (2013)). High concentrations of it may cause lung cancer. Radon is the second leading reason for the cause of lung cancer after alcohol and tobacco. It causes more deaths per year than drunken driving, earthquakes, flood, and drought (Clavensjo and Akerblom, (1992)). In general, the radon problem is a major concern in cold climate regions compared to other regions. Further, it has also been used as a trace gas in terrestrial, hydrogeological and atmospheric studies because of its ability to travel long distances from host rocks as well as its efficient detection at very low levels. Radon transport in soil pore is mainly governed by two physical processes namely, diffusion and advection. Different transport models are developed by various researchers to study the anomalous behavior of soil gas radon in geothermal fields. These models have been employed to estimate process-driven parameters (such as diffusion coefficient, carrier gas velocity, etc.) from the measured data of soil gas radon. Estimation of these parameters may deviate significantly from the true values if the uncertainty associated with the various input parameters of the models are not taken into consideration. The primary aim of this investigation has been to solve uncertain (interval/fuzzy) radon transport equations. As such, new methods have been proposed to handle steady and unsteady-state uncertain radon transport equations in various mediums. In this regard, Galerkin and collocation methods are extended to solve the steady-state uncertain radon transport equations. On the other hand, the uncertain unsteady-state radon transport problem has been solved by introducing interval midpoint and parametric concepts in the explicit finite difference method. vii Further, Geo Station Continuous Monitoring System Lab has been set up for a soil chamber experiment. Corresponding experiments are conducted for estimating the uncertain (fuzzy) band of radon concentration in order to predict the anomaly behavior of the radon transport in the earth's crust. The experimental results are also used to validate few of the proposed methods. In this research, another challenge has been to study the related forward and inverse problems with respect to fractional order in an uncertain environment. Accordingly, the fractional uncertain diffusion problem has been studied. To the best of our knowledge, the inverse problems with respect to the diffusion problem of an integer as well as fractional order in the uncertain environment have been investigated for the first time. Finally, the experimental results are used to validate few of the proposed methods