Analysis of equivalent thickness of geological media for lab-scale study of radon exhalation

Geological media are omnipresent in nature. Lab-scale tests are frequently employed in radon exhalation measurements for these media. Thus, it is critical to find the thickness of the medium at an experimental scale that is equivalent to the medium thickness in a real geological system. Based on the diffusion-advection transport of radon, theoretical models of the surface radon exhalation rate for homogeneous semi-infinite and finite-thickness systems were derived (denoted as J_se and J_fi, respectively). Analysis of the equivalency of J_se and J_fi was subsequently carried out by introducing several dimensionless parameters, including the ratio of the exhalation rates for the semi-infinite and finite-thickness models, ε, and the number of diffusion lengths required to achieve a desired ε value, n. The results showed that when radon transport in geological media is dominantly driven by diffusion effect, if n > 3.6626, then ε > 95%; if n > 5.9790, then ε > 99.5%. When radon migration is dominantly driven by advection effect, if n > 2.5002, then ε > 95%; if n > 4.0152, then ε > 99.5%. Therefore, if the thickness of the geological media (x₀) is greater than a certain n times the radon diffusion length of the media (L), the media can be modeled as semi-infinite. To validate the model, a pure radon diffusion experiment (no advection) was developed using uranium mill tailings, laterite, and radium-bearing rocklike material with different thicknesses (x₀). The theoretical model was demonstrated to be reliable and valid. This study provides a basis for determining the appropriate thickness of geological media in lab-scale radon exhalation measurement experiments with open bottom.