A Source-Environment-Response (SER) approach for solving Spatio-Temporal Radon Transport in Different Media

A human receives more than half of the annual individual radiation dose from the radon and its progeny contained in indoor air. Therefore, in order to limit domestic exposure of the population in the Russian Federation the national radon control levels have been established. The excess of these levels is not allowed in buildings with a long people’s residence. Radon entry into the building through horizontal underground walling from the soil base and therefore, the restricting of the soil radon flux in the ground floor rooms indoor air is possible only with construction technologies and means. The effectiveness of radon-protective technologies directly depends on the understanding of the laws of radon transport in porous media, since this transport may occur through diffusion and/or convection (filtration). Each of these mechanisms may be dominant under the certain conditions and requires its own radon-protective measures. This article compares the density of diffusive and convective radon fluxes in the entire range of soils permeabilities. The range of underground walling and soils permeability was determined, in which the prediction of radon conditions in a building can be built exclusively on the patterns of diffusive radon transport in porous media. The approach to the underground walling design on the basis of the one-dimensional model of stationary diffusive radon transport in porous media is proposed.

A unified model of radon emanation, adsorption, absorption, and transport has been developed and incorporated into the RAETRAN code that uses new mathematical models of advective transport, moisture effects, and radon emanation. The model accounts for advective depletion in radon source regions, and for the effects of varying moistures on radon emanation, diffusion, absorption, adsorption, and advective transport rates. Radon transport in gas- and water-filled pore space is characterized, and exchange between the phases is considered. Correlations are also given for diffusion and permeability coefficients. The model provides a comprehensive assessment of source potentials for indoor radon accumulation based on soil moistures, radium, emanation, and advection of soil gas. 10 refs., 10 figs., 1 tab.

A two-dimensional numerical model for radon transport based on the finite difference time domain (FDTD) method have been developed. The model is governed by the radon transport equation taking into account the mechanisms of diffusion, advection, and decay. The purpose of this model is to simulate the evolution of radon concentration which can be influenced by various parameters including depth and diffusion coefficient of the soil layer plus the velocity and initial concentration of radon. The obtained results were compared to an analytical solution to demonstrate the ability of this model for predicting the spatio-temporal evolution of radon transport in the porous media of soil layers.

Characteristics of radon transport in porous media were studied through both in situ and lab-scale measurements. In situ measurements of radon activity concentration, together with soil thoron and carbon dioxide efflux, were carried out on Mt. Etna volcano. More detailed information on radon transport mechanisms has been obtained from laboratory measurements. In particular, we report the first results of a systematic study carried out at the University of Catania (Italy) by means of a facility consisting of a large cylindrical stainless steel vessel, homogeneously filled with different materials. Radon concentration vertical profiles were extracted in low-moisture samples for different advective fluxes, temperatures and porosities.

This report documents the activities by Rogers and Associates Engineering Corporation during the extension period of the second year of grant DE-FG02-88ER60664. The overall research objectives have been to develop a general, unified theory of radon emanation and transport and to implement it in a computer code for application in routine and specialized field studies and research programs. A theoretical correlation of soil textural properties with radon transport characteristics was predicted by analyses with the unified theory model. This correlation was dominated by soil water contents, but exhibited also some particle-size dependence. Feasibility measurements were completed for partitioning moisture effects on radon emanation into two categories: pore water contents and hydrated (crystalline) water contents. Preliminary radon emanation measurements that control these water categories provide new insight into radon emanation mechanisms and parent radium distributions in the selected mineral samples. The 2-dimensional RAETRAD model for indoor radon entry was further refined to include the complete multiphase aspects of the unified theory as incorporated in the RAETRAN model. The RAETRAD model was applied to various generic and site-specific problems, and was specifically compared with indoor and soil-gas radon measurements for 12 houses in Florida. During these analyses, and as part of other sensitivity analyses with the RAETRAD model, the importance of diffusive radon entry through the concrete floor was observed. Further analyses and measurements of the diffusion and permeability coefficients of residential floor concretes were conducted.

A tri-dimensional model for radon transport in a porous medium

This report documents the activities by Rogers and Associates Engineering Corporation personnel in the second year of a grant from the Office of Health and Environmental Research at the US Department of Energy. The project objective is to integrate theories of all significant radon generation and transport mechanisms into a unified, self-consistent theory. During the second year of the project, the following activities were performed. Several field permeabilities were measured to develop a soils data base for a simple permeability correlation. Simple soil gas permeability and radon diffusion coefficient correlations were developed from the RAE data base. A methodology was developed to characterize the air permeabilities and radon diffusion coefficients of soils in general, and the Soil Conservation Service soil classifications in particular. The RAETRAN code was benchmarked against two different sets of measurements. Using RAETRAD, a multidimensional code that was developed with internal funds, the radon source/receptor coupling characteristics were investigated. Several important trends are identified. 76 refs., 19 figs., 5 tabs.

Radon transport equation in Earth's crust

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 Jse and Jfi, respectively). Analysis of the equivalency of Jse and Jfi 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.

The effective diffusion coefficient of radon was determined in polymer/silicate gels and clay suspension used as sealing materials in environmental protection. On the basis of the experimental findings, it was concluded that both materials drastically decrease the convective mass transport in porous media. Simultaneously, the effective diffusion coefficient was reduced significantly. Thus, the radon flux might be decreased by 5 to 6 orders of magnitude in porous systems originally having gas or low water saturation by injection of gel-forming materials or placement of clay suspensions. At high water saturation, however, the diffusion transport of radon can be slightly restricted in consolidated and unconsolidated porous media. The laboratory studies may firmly allow us to conclude that hydrogels and clay suspensions are prospective candidates in an integrated environmental technology to be used for restriction of radon migration in subsurface regions.

In this work, an efficient algorithm, using a finite-difference time-domain (FDTD) technique, is proposed for modeling the variation of radon concentration as a function of soil structure parameters and vice versa. The development of the FDTD model is based on the simultaneous resolution of the radon transport equation in a porous, homogeneous medium, namely the soil. This equation describes the concentration of radon per pore volume unit. The numerical results are compared with those of the literature or with the theoretical ones.

Stack or embankment disposal of phosphogypsum — a by-product from phosphate fertilizer industries-has given rise to environmental issues concerning 222Rn exhalation rates into the local atmosphere. Early models for radon transport in porous media have considered both diffusion and convection, although basically taking into account air flow driven by predefined pressure differences and Darcy's law. The present paper introduces buoyant effects and outlines a steady-state two-dimensional model for 222Rn transport through a phosphogypsum-bearing embankment, inside of which there are sources and sinks for this gaseous radionuclide. The embankment is treated as an open cavity filled with porous material and surrounded by isothermal and impermeable ground. Its top surface is subjected to fixed activity concentration and fixed lower temperature. Buoyancy-driven interstitial air flow is supposedly laminar and modeled according to Darcy-Brinkman-Boussinesq formulation. Governing equations are written in dimensionless form in order to account for concurrent effects of the various physical parameters involved, and three unconventional dimensionless groups are put forward apart from usual controlling parameters, such as Darcy, Grashof, Prandtl, and Schmidt numbers. An analytical solution regarding a strictly diffusive approach is inferred, whereas full model equations are solved numerically by adapting an existing finite-volume simulator. As a preliminary investigation, results are reported for Pr = 0.71 and Sc = 15, while Da and Gr are allowed to vary from 10−7 to 10−13 and from 107 to 109 , respectively. Results are also presented as a function of the modified Grashof number Grm = Gr·Da. For porous media with relatively low permeability (Da ≤ 10−9), 222Rn transport is diffusion dominated (i.e., natural convective effects play a minor role) and both Nusselt and Sherwood numbers prove to be insensitive to Grashof number. At approximately Grm ≈ 10, circulation cell splitting occurs within each embankment half, as the natural convective fluid flow increases its strength, which results in very low 222Rn concentration levels inside the porous matrix.

A 40-year retrospective European radon flux inventory including climatological variability

Usage of the radon flux density at the Earth’s surface as an indicator of seismic activity is proposed in addition to unit-volume radon activity in the soil air that has previously been used for this purpose. Numerical calculations based on the diffusion-convection equation for radon transport in porous media are presented, which confirm that the radon flux density is more sensitive to changes in convection rate than unit-volume radon activity. It has been indicated that the advantage in using radon flux density could be greatest for homogeneous geological media.