Radon Transport Model Research Articles

Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber

Mathematical modeling is used to study the hereditary mechanism of the accumulation of radioactive radon gas in a chamber with gas-discharge counters at several observation points in Kamchatka. Continuous monitoring of variations in radon volumetric activity in order to identify anomalies in its values is one of the effective methods for studying the stress–strain state of the geo-environment with the possibility of building strong earthquake forecasts. The model equation of radon transfer, taking into account its accumulation in the chamber and the presence of the hereditary effect (heredity or memory), is a nonlinear differential Riccati equation with non-constant coefficients with a fractional derivative in the sense of Gerasimov–Caputo, for which local initial conditions are set (Cauchy problem). The proposed hereditary model of radon accumulation in the chamber is a generalization of the previously known model with an integer derivative (classical model). This fact indicates the preservation of the properties of the previously obtained solution according to the classical model, as well as the presence of new properties that are applied to the study of radon volumetric activity at observation points. The paper shows that due to the order of the fractional derivative, as well as the quadratic nonlinearity in the model equation, the results of numerical simulation give a better approximation of the experimental data of radon monitoring than by classical models. This indicates that the hereditary model of radon transport is more flexible, which allows using it to describe various anomalous effects in the values of radon volume activity.

Radon signature of CO2 flux constrains the depth of degassing: Furnas volcano (Azores, Portugal) versus Syabru-Bensi (Nepal Himalayas)

Substantial terrestrial gas emissions, such as carbon dioxide (CO2), are associated with active volcanoes and hydrothermal systems. However, while fundamental for the prediction of future activity, it remains difficult so far to determine the depth of the gas sources. Here we show how the combined measurement of CO2 and radon-222 fluxes at the surface constrains the depth of degassing at two hydrothermal systems in geodynamically active contexts: Furnas Lake Fumarolic Field (FLFF, Azores, Portugal) with mantellic and volcano-magmatic CO2, and Syabru-Bensi Hydrothermal System (SBHS, Central Nepal) with metamorphic CO2. At both sites, radon fluxes reach exceptionally high values (> 10 Bq m−2 s−1) systematically associated with large CO2 fluxes (> 10 kg m−2 day−1). The significant radon‒CO2 fluxes correlation is well reproduced by an advective–diffusive model of radon transport, constrained by a thorough characterisation of radon sources. Estimates of degassing depth, 2580 ± 180 m at FLFF and 380 ± 20 m at SBHS, are compatible with known structures of both systems. Our approach demonstrates that radon‒CO2 coupling is a powerful tool to ascertain gas sources and monitor active sites. The exceptionally high radon discharge from FLFF during quiescence (≈ 9 GBq day−1) suggests significant radon output from volcanoes worldwide, potentially affecting atmosphere ionisation and climate.

Understanding radon (222Rn) transport in one and multi-layer soils using analytical and finite element modeling

This study investigates the transport of Radon (222Rn) which is the second leading cause of lung cancer after smoking. A new and optimized finite element numerical model (FERM-1D, Finite Element Radon Modeling in one dimension) of Radon transport is developed and tested with analytical models’ solutions under different conditions in addition to verification against field data for soils with multi-layer behavior. The interaction between the Radon 222Rn different mechanisms such as diffusion, advection, decay and generation is explained in details. Transport numbers are proposed that determine conditions under which each mechanism of diffusion, advection, decay and generation dominates. A transport similarity concept is presented in which different combination of mechanisms and model parameters can produce the same Radon activity concentration profile. Moreover, new prospective is presented to modeling soils with multi-layer Radon transport characteristics and behavior.

МОДИФИКАЦИЯ РЕАЛИЗАЦИИ МЕТОДА ЯКОБИ ПРИ МОДЕЛИРОВАНИИ СУПЕРДИФФУЗИИ РАДОНА НА РЕКОНФИГУРИРУЕМЫХ ВЫЧИСЛИТЕЛЬНЫХ СИСТЕМАХ

When studying natural objects, the problem of modeling complex systems with a structurethat cannot be described by means of Euclidean geometry tools often arises, therefore, fractalgeometry and the corresponding mathematical apparatus are used to represent them. So the modelof radon transport in an inhomogeneous medium, using superdiffusion, displays real data moreaccurately than the classical one. An increase in the concentration of radon in the air is one of thesigns of an approaching earthquake, which makes it necessary to simulate the propagation of thisradioactive inert gas in real time. Reconfigurable computing systems have great potential for solvingproblems in real time, but the currently existing means for solving systems of linear equationshave low efficiency due to the irregular structure of matrices obtained by discretizing the radonsuperdiffusion model using adaptive grids. The basic subgraph of the Jacobi method is transformedas follows: the input data is vectorized, the structure of the frame in which the value of oneunknown is calculated is divided into several microframes, parallelizing the calculations in thefirst microframe, where the sum of the products of the matrix coefficients and the values of theunknowns from the previous iteration is performed. The results obtained are buffered for subsequentdelivery to the second microframe, where the final processing and output of the iterationresult takes place. The described approach allows to reduce equipment downtime when solving asystem of linear equations with sparse irregular matrices, and gives a speed gain by 5–15 times incomparison with existing methods for solving linear system on reconfigurable computing systems.

Development of radon transport model in different types of dwellings to assess indoor activity concentration

The influence of different building types on the activity concentration of Radon indoor is studied through transport models in soil and building materials. The numerical solutions of the relevant transport equations are solved by the finite differences method (FDM) and used to evaluate the indoor Radon activity concentration. Several boundary conditions are introduced to simulate the Radon entry into the buildings from soils and to assess the Radon activity concentration at the different floors. The types of dwelling investigated differ in the position of the lower floor respect to the ground. Comparisons are made to modeling assessments obtained considering different soil characteristics underneath the building and building materials to simulate indoor Radon activity concentration. These investigations lead to the conclusion that, in addition to the nature of the soil and building materials, the position of lower floor of dwellings plays a significant role in determining the amount of radon entry into residential buildings. This work is effective to assess the health hazards coming from the Radon accumulation in living environments.

The Evaluation of Radon-Protective Characteristics in Engineered and Existing Buildings with the Radon Diffusive Entry from the Soil

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 simple model to simulate the diffusion pattern of radon in different soil media

Radon is transported through soil matrix and is exhaled at soil-atmosphere interface. The exhalation rate from soil is largely governed by the concentration gradient and the pressure differences. Study of the transport phenomenon aids in evaluating the radon exhalation rate of the source matrix. The present study deals with numerically solving the well established one-dimensional radon transport model and simulates the radon propagation till the attainment of steady state. The modeling was done by adopting the finite difference method. The effect of advection phenomenon coupled along with diffusion was studied. The limitation of the explicit scheme was overcome by employing the implicit scheme. The model developed was fed with experimentally derived input parameters. The radon depth profile thus obtained was compared with the experimental values. The model was used to investigate how the radon concentration profile evolves with time, for two different diffusion coefficients.

Algebra of Fuzzy Random Variable and its Application to Science and Engineering Problem- Radon Transport from Soil into Building

The theme of this paper is to bring out the mathematical details of fuzzy random variable and its application to model radon transport from soil into buildings. The physical processes that influence radon transport are advection and diffusion. Parameters associated with the governing partial differential equation describing radon transport from soil into buildings are radon diffusion coefficient and advective velocity of radon in air. Both the parameters are imprecise. Imprecision of these parameters is addressed as fuzzy random variable due to presence of inherent randomness within their fuzziness. Handling fuzziness within randomness is an innovative concept of computation to quantify the uncertainty of any physical system. Paper presents the mathematical structure (algebra) of fuzzy random variables. The concept of fuzzy randomness is implemented in developing radon transport model. Numerical solution of radon transport model with fuzzy random parameters is obtained by explicit forward time central space finite difference method. Support, uncertainty index, possibility, necessity and credibility of the spatial and temporal behaviour of the random behaviour of radon concentration are also computed to explore the concept and role of the fuzzy randomness in decision making issue

Resistance of building foundation to radon penetration

Two-dimensional model of the steady-state diffusion radon transport from the soil to the ground floor of the building is developed. Radon concentration distributions in the soil and the living space are calculated at different foundation geometries. The model considers radon entry from enclosing structures, outside air, and diffusion from the soil. The radon field under the building is described. The quantitative criteria for the resistance of the building foundation to radon penetration from the soil are defined. It is found that the resistance of the ground slab to radon penetration and radon concentration in the plane of the soil structure contact have a decisive influence on indoor radon, and that the initial distribution of radon concentration in the soil changes significantly after the building erection. These changes depend on the radon potential in the soil, its radon permeability, resistance of the floor structure to radon penetration, and building geometry.

Investigation the building walling influence on the radon concentration distribution in the soil

Radon and its progeny in the indoor air form more than 70 % of the annual individual radiation dose for a modern human; they are the second leading cause of lung cancer after smoking. Under such conditions ensuring of the buildings radon safety is an extremely important scientific and practical problem, which is especially relevant for projected constructions. In this case mathematical simulation is the only way to predict radon levels in the future. Soil under the building is the main source of radon entry in indoor air, therefore radon safety of building project is determined by the construction and condition of its underground walling. The article deals with the influence of the building structural features on the amount of radon load on underground walling as one of the main factors of the formation of the radon conditions in the building. Two-dimensional stationary model of diffusion radon transport in the system «soil-atmosphere-building» is used for the calculation of radon concentration fields in the soil air of the base of the building. The obtained fields of radon concentration in the soil air give an opportunity to estimate the changes in the radon field in the neighbourhood of the building.

Transient radon signals driven by fluid pressure pulse, micro-crack closure, and failure during granite deformation experiments

In seismically active fault zones, various crustal fluids including gases are released at the surface. Radon-222, a radioactive gas naturally produced in rocks, is used in volcanic and tectonic contexts to illuminate crustal deformation or earthquake mechanisms. At some locations, intriguing radon signals have been recorded before, during, or after tectonic events, but such observations remain controversial, mainly because physical characterization of potential radon anomalies from the upper crust is lacking.Here we conducted several month-long deformation experiments under controlled dry upper crustal conditions with a triaxial cell to continuously monitor radon emission from crustal rocks affected by three main effects: a fluid pressure pulse, micro-crack closure, and differential stress increase to macroscopic failure. We found that these effects are systematically associated with a variety of radon signals that can be explained using a first-order advective model of radon transport. First, connection to a source of deep fluid pressure (a fluid pressure pulse) is associated with a large transient radon emission increase (factor of 3–7) compared with the background level. We reason that peak amplitude is governed by the accumulation time and the radon source term, and that peak duration is controlled by radioactive decay, permeability, and advective losses of radon. Second, increasing isostatic compression is first accompanied by an increase in radon emission followed by a decrease beyond a critical pressure representing the depth below which crack closure hampers radon emission (150–250 MPa, ca. 5.5–9.5 km depth in our experiments). Third, the increase of differential stress, and associated shear and volumetric deformation, systematically triggers significant radon peaks (ca. 25–350% above background level) before macroscopic failure, by connecting isolated cracks, which dramatically enhances permeability.The detection of transient radon signals before rupture indicates that connection of initially isolated cracks in crustal rocks may occur before rupture and potentially lead to radon transients measurable at the surface in tectonically active regions. This study offers thus an experimental and physical basis for understanding predicted or reported radon anomalies.

Radon transport model into a porous ground layer of finite capacity

The model of radon transfer is considered in a porous ground layer of finite power. With the help of the Laplace integral transformation, a numerical solution of this model is obtained which is based on the construction of a generalized quadrature formula of the highest degree of accuracy for the transition to the original - the function of solving this problem. The calculated curves are constructed and investigated depending on the diffusion and advection coefficients.The work was a mathematical model that describes the effect of the sliding attachment (stick-slip), taking into account hereditarity. This model can be regarded as a mechanical model of earthquake preparation. For such a model was proposed explicit finite- difference scheme, on which were built the waveform and phase trajectories hereditarity effect of stick-slip.

Modeling and experimental examination of water level effects on radon exhalation from fragmented uranium ore

In this study, a one-dimensional steady-state mathematical model of radon transport in fragmented uranium ore was established according to Fick's law and radon transfer theory in an air-water interface. The model was utilized to obtain an analytical solution for radon concentration in the air-water, two-phase system under steady state conditions, as well as a corresponding radon exhalation rate calculation formula. We also designed a one-dimensional experimental apparatus for simulating radon diffusion migration in the uranium ore with various water levels to verify the mathematical model. The predicted results were in close agreement with the measured results, suggesting that the proposed model can be readily used to determine radon concentrations and exhalation rates in fragmented uranium ore with varying water levels.

Comparison of two numerical modelling approaches to a field experiment of unsaturated radon transport in a covered uranium mill tailings soil (Lavaugrasse, France)

Uncertainties on the mathematical modelling of radon (222Rn) transport in an unsaturated covered uranium mill tailings (UMT) soil at field scale can have a great impact on the estimation of the average measured radon exhalation rate to the atmosphere at the landfill cover. These uncertainties are usually attributed to the numerical errors from numerical schemes dealing with soil layering, and to inadequate modelling of physical processes at the soil/plant/atmosphere interface and of the soil hydraulic and transport properties, as well as their parameterization. In this work, we demonstrate how to quantify these uncertainties by comparing simulation results from two different numerical models to experimental data of radon exhalation rate and activity concentration in the soil-gas measured in a covered UMT-soil near the landfill site Lavaugrasse (France). The first approach is based on the finite volume compositional (i.e., water, radon, air) transport model TOUGH2/EOS7Rn (Transport Of Unsaturated Groundwater and Heat version 2/Equation Of State 7 for Radon; Saâdi et al., 2014), while the second one is based on the finite difference one-component (i.e., radon) transport model TRACI (Transport de RAdon dans la Couche Insaturée; Ferry et al., 2001). Transient simulations during six months of variable rainfall and atmospheric air pressure showed that the model TRACI usually overestimates both measured radon exhalation rate and concentration. However, setting effective unsaturated pore diffusivities of water, radon and air components in soil-liquid and gas to their physical values in the model EOS7Rn, allowed us to enhance significantly the modelling of these experimental data. Since soil evaporation has been neglected, none of these two models was able to simulate the high radon peaks observed during the dry periods of summer. However, on average, the radon exhalation rate calculated by EOS7Rn was 34% less than that was calculated by TRACI, and much closer to the measured one for physically-based soil radon diffusion models. Unlike TRACI, EOS7Rn was able to simulate qualitatively seasonal variations of both radon exhalation and concentration. These results show that EOS7Rn produces less numerical errors than TRACI, and can be considered as a promising model for predicting radon transport in the landfill, if soil evaporation is modelled and its numerical inversion for parameter estimation is realized.

Radon transport to the near-surface soil and air layers

Observational data on the content and distribution of radon to a depth of 2 m are given. A model of radon transport from the interior of the earth to the near-surface soil and air layers due to bubble hydrogen and methane formations is proposed. This model has been verified for soil methane contents of 10−6–10−5 and 10−3–10−2% by volume.

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

In this work, a 40-year retrospective European radon flux inventory has been calculated. Average values of the radon exhalation rate, probability distributions and seasonal fluctuations have been obtained. To achieve this, a numerical model of radon transport through finite, heterogeneous and porous media has been implemented, enabling us to calculate the radon exhalation rate of European soils with a horizontal resolution of 0.5′ (∼1 km). Geological, geochemical and climatological parameters derived from European and international databases (FOREGS, HWSD, ERA-40) have been coupled to the model.The theoretical model is based on the fundamental equation of radon transport in porous media, taking into account the dependency of the transport coefficient on temperature and humidity. It also includes a simple model that evaluates the effect of snow cover. In general, the results show wide variations depending on location and season of the year, with a spatial standard deviation close to the annual average value (30 Bq m−2 h−1) In turn, the seasonal deviation is about 25% of the annual average value.The inventory can be easily integrated into atmospheric transport models acting as baseline that could be used for policy decisions regarding the identification of areas with a high risk of exposure to radon. The gridded data are available for the scientific community upon request. The limitations and sources of errors and uncertainties of the model are also discussed in detail.

Preliminary Study on a Regional Radon Concentration in Surface Soil Prediction Method

A reformulated mathematical equation for predicting radon concentration in surface soil has been established based on the diffusive and convection theory. The parameters in the equation, such as radon emanation coefficient, convection velocity, diffusion coefficient, porosity of soil and so on, are closely related to the soil types. In order to determine these parameters, field measurement were carried out in totally 31 sites covering four types of soil in Chengdu Area, China. And least squares fitting algorithm and inversion fitting computation were also used. The prediction equation is ultimately applied to map the radon concentration in surface soil of Chengdu Area along with the geochemical databases of uranium content distribution in soil and soil texture distribution. According to the field measurement results on 17 sites in Chengdu, the prediction was verified to work property. About 50% of the natural radiation dose which people accepted is contributed from radon and its short-life progenies. And more and more attentions are paid on the issue of the health risks from them. In fact, radon in the ambient air is mainly released from the radioactive elements uranium and radium in the soil and rocks underground. Therefore, it is of significance for radon control to delineate the potential high radon zone combining the local geological background. Especially in China, the environmental radon survey started relatively late. A large-scale indoor radon measurement has not been conducted yet. However, the database based on regional geological survey has been built in many localities. A great number of geochemical data such as the uranium content and the distribution of soil texture are available. It is a feasible way to predict the regional radon distribution quickly and efficiently by combining these data with radon migration theory. Based on a steady-state radon transport model in porous materials 1) , combined with the local geological and pedological parameters, several methodologies were also developed for predicting a regional radon concentration 2-4) . In this paper, a methodology for predicting the radon distribution in surface soil of Chengdu Area was introduced. First, a reformulated simplified mathematical equation for the prediction was established by using a new boundary condition, i.e., the flux density of radon on ground-air interface is continuous and equal. Second, the parameters in the radon concentration equation, such as radium content, soil porosity and so on, were measured by field samples. The theoretical radon value was calculated and compared with the measured value. The ultimate prediction equation was derived by corrected and verified by field measured results.

地中ラドン輸送モデルを用いた気象要素のラドン散逸への影響

The radon exhalation from soil surface varies with various meteorological and soil parameters. As the observed radon exhalation rates are simultaneously affected by various parameters, it is difficult to estimate an effect of each parameter on radon exhalation. The effect of each parameter is studied based on the time-dependent one-dimensional radon transport model we developed. The model simulates the radon exhalation rate by using various meteorological and soil parameters under the realistic environmental conditions. The effect of the precipitation on the radon exhalation is explained by change of water porosity in the soil. Under the loamy soil condition in Kanto area, the radon exhalation was found to stop during the precipitation more than 5 mm. It is well known that the radon exhalation closely depend on the change rate of atmospheric pressure. From our simulation results, we can know the mechanism of pressure effect on radon exhalation. The change of atmospheric pressure is propagated to the deep soil layer from the surface. The time lag causes the pressure difference between the surface and the deep soil layer and produces the change of radon exhalation. In addition, it is found that atmospheric pressure dependence of radon exhalation is not affected by the variation of permeability in the range of three orders. The reason of remarkable calculation results is explained in this paper. The radon exhalation increases with increasing wind speed and may rise double by the wind speed exceeding 10 m s-1. The wind effect has a threshold value, about 5 m s-1 in this study and is ignored in the wind speed below the value. Therefore, we can conclude that contribution of the wind speed to the radon exhalation is relatively small.

Analytical risk-based model of gaseous and liquid-phase radon transport in landfills with radium sources

An analytical model of gaseous and liquid-phase radon transport through soils is derived for environmental modeling of landfills containing uranium mill tailings or Ra-226 sources. Processes include radon diffusion in both the gas and liquid phases, advection of soluble radon in percolating water, radioactive decay, equilibrium partitioning between gas and liquid phases, and emanation from different source terms. A probabilistic framework for the radon-transport model is introduced that provides uncertainty and sensitivity analyses for risk-based assessments. Uncertainty analyses are used to compare simulated performance metrics (e.g., radon surface flux) against regulatory standards. Sensitivity analyses are used to identify key parameters and processes that impact the variability of the simulated results. The models and analyses are illustrated with a probabilistic performance assessment of the Mixed Waste Landfill at Sandia National Laboratories in Albuquerque, NM.

Suppression of Radon Exhalation from Soil by Covering with Clay-mixed Soil

The effectiveness of bentonite-mixed soil as a barrier to radon exhalation from soil is investigated experimentally at a closed uranium mine in Japan. Continuous observations of radon flux from a clay-covered soil surface and a bare soil surface were conducted for a period of 80 days. The mean radon flux from the clay-covered plot was one fifth of that from the bare plot, demonstrating that the clay-mixed soil is effective as a boundary suppressing radon exhalation from the contaminated soil. Numerical analyses using a one-dimensional radon transport model for an unsaturated soil for the dry weather conditions confirmed the effectiveness of the clay-mixed soil cover under a range of weather conditions.