Regulating the environmental discharge of Rn-220 (historically known as thoron) and its decay products from thorium processing facilities is important for protection of environment and general public living in the vicinities. Activated charcoal provides an effective solution to this problem because of its high adsorption capacity to gaseous element like radon. In order to design and develop a charcoal based Thoron Mitigation System, a mathematical model has been developed in the present work for studying the Rn-220 transport and adsorption in a flow through charcoal bed and estimating the Rn-220 mitigation factor (MF) as a function of system and operating parameters. The model accounts for inter- and intragrain diffusion, advection, radioactive decay and adsorption processes. Also, the effects of large void fluctuation and wall channeling on the mitigation factor have been included through a statistical model. Closed form solution has been provided for the MF in terms of adsorption coefficient, system dimensions, grain size, flow rate and void fluctuation exponent. It is shown that the delay effects due to intra grain diffusion plays a significant role thereby rendering external equilibrium assumptions unsuitable. Also, the application of the statistical model clearly demonstrates the transition from the exponential MF to a power-law form and shows how the occurrence of channels with low probability can lower mitigation factor by several orders of magnitude. As a part of aiding design, the model is further extended to optimise the bed dimensions in respect of pressure drop and MF. The application of the results for the design and development of a practically useful charcoal bed is discussed. (C) 2017 Elsevier Ltd. All rights reserved.