RADON MIGRATION MODEL FOR COVERING U MINE AND ORE PROCESSING TAILINGS *

Transcription

1 RADON MIGRATION MODEL FOR COVERING U MINE AND ORE PROCESSING TAILINGS * A. VÁRHEGYI, J. SOMLAI 2, Z. SAS 2 MECSEK-ÖKO Environment Protection Co. H-7633 Pécs, Estergár L. str. 9. Hungary, varhegyiandras@mecsekoko.hu 2 University o Pannonia, Institute o Radiochemistry and Radioecology, H-82 Vesprém, Egyetem str.. Hungary, somlai@almos.vein.hu 2 University o Pannonia, Institute o Radiochemistry and Radioecology, H-82 Vesprém, Egyetem str.. Hungary, iloas@almos.vein.hu Received November 5, 22 Several radioactive and radiation dose limit values should be kept or the remediation o waste rock piles and tailings ponds o ormer uranium mining. Using some m order o magnitude thick inactive cover on the tailings, the requirements or ambient gamma dose rate and or radioactive aerosol generation are ulilled automatically. Keeping the limits or radon concentration in air and or radon exhalation rate rom soil surace is more diicult task due to the high mobility o radon. Construction o suitable radon barrier on the emission sources (irst o all: tailings ponds) is one o the basic points o remediation planning. A radon transport model has been developed to study the cover options and the acceptable versions o the available cover layer materials were experimentally surveyed in practice. In the present state the model deals onedimensional, stationary and single cover layer situations only. The basic soil-physical parameters are involved into the model and their role in radon exhalation rate is particularly analysed. Both the model calculations and the ield experiments supported that the oicial requirements or radon exhalation rate are ulilled well in the case o applied versions o cover. Key words: Radon migration, radon transport in homogeneous media, one-layer cover o tailings, remediation o U tailings.. INTRODUCTION The radon (radioactive noble gas with relatively long hal-lie (3.82 d)) can get out o the matrix into the pore space and into the air as well. Due to the diusion and convection the radon can be exhaled rom the pore space into the air [-2]. The radon exhalation greatly depends on the eatures o the investigated material, such as the thickness, the internal structure and the moisture content o the solid phase as well [3-4]. * Paper presented at the First East European Radon Symposium FERAS 22, September 2 5, 22, Cluj-Napoca, Romania. Rom. Journ. Phys., Vol. 58, Supplement, P. S298 S3, Bucharest, 23

2 2 Radon migration model or covering U mine and ore processing tailings S299 A theoretical model has been constructed or the analyses o diusion transport mechanism o radon, taking into account the basic soil physical, radiological and geometrical eatures determining the process. The role and eect o all parameters are analysed or the depth dependence o radon concentration in pore space, and or the radon exhalation rate o the surace [5]. 2. RADON MIGRATION MODEL FOR ONE LAYER COVER ON TAILINGS 2.. DIFFUSION TRANSPORT PROCESS OF RADON Movement o radon ( 222 Rn) in any porous material is determined by the ollowing physical processes: Diusion o radon drited by concentration gradient, Movement o pore-illing luid or gaseous material (iltration), Radioactive decay o radon, Continuous generation o radon rom the radioactive decay o its parent element 226 Ra. Dierential equation describing the radon transport can be derived rom the Fick s law, the radioactive decay law and the material balance law; the onedimensional orm o that equation is presented in several papers []: 2 d C dv ( C) D C Q 2 λ + = () d d where: D diusion constant o Radon (m 2 s - ), C concentration o radon (atom m -3 ), vertical distance (m, a positive downwards), v speed o pore-illing material transporting Radon (m s - ), λ radioactive decay constant o radon (2. -6 s - ), Q intensity o local generation o radon (atom m -3 s - ). That equation is valid not only or the material but or the activity concentration (Bq m -3 ) o radon as well (that is equivalent o multiplication o each part o equation by λ). For the urther considerations concerning the cover o tailings, the iltration component is neglected (v = ), because o the physical reality. In that case, solution o () di. equation can be written in the general orm: e d 2 C = K + K e d + C b (2) where K and K 2 are boundary condition dependent constants, while d and C b are introduced new parameters:

3 S3 A. Várhegyi, J. Somlai, Z. Sas 3 D d = λ is the so called diusion length (by that length the radon concentration decreases by the actor o e, basic number o natural logarithm); and Q C = (4) λ b is the so called background or saturation radon concentration; that concentration would prevail in the medium i no any transport mechanism changed that value (in hermetically sealed sample or in ininity depth o homogenous layer). It represents the radon source strength o any radium containing material as well. 2 (3) 2.2. DIFFUSION CONSTANT OF RADON IN POROUS MEDIUM The equations ( 4) are strictly valid in homogeneous medium only, where radon can ill continuously the whole amount o space available. In porous media like soil as well, the situation is dierent: radon transport can be actually perormed in the pore space only; the rock matrix itsel is excluded rom that process. However, the parent element 226 Ra o radon is situated within the rock matrix and generates radon by its radioactive decay. Only a certain part o the whole amount o generated radon can be escape into the pore volume and take part in the long distance transport process. The ratio o that mobile part o radon to the whole generated amount is called emanation coeicient (E). The ratio o pore space related to the whole rock volume can be described by the porosity (n). In the case o whole pore volume is illed with air (soil gas), the diusion constant describing the radon transport process can be the product o diusion constant in air (concerning the whole space) and the porosity as a maximum value: D D air n. Generally, the actual value o diusion constant is somewhat less than the D air n product because the diusion process takes place not in linear way but in curved pathways determined by the shape o pore space (tortuosity). That eect cannot be taken into account precisely thereore the above given product can be regarded as a theoretical maximum value o diusion constant or porous media. In the case o complete water saturation o rock pores, in analogue way like above, the diusion constant is given by the product the diusion constant in water and the pore space: D Dw n. In real natural conditions, however, the pore space is illed both with water and with air and the diusion processes in water and in air are parallel perormed. The radon transport process taking place in the three phase (rock matrix + water + air) medium can be described by the eective diusion constant and the most important rock physical parameters: D v D + ( n v) D, (5) e w air

4 4 Radon migration model or covering U mine and ore processing tailings S3 where v is the volume ratio o rock space illed with water. Because o the 4 orders o magnitude dierence between the diusion constants in air and in water (Dair = -5 m 2 /s, Dw = -9 m 2 /s), the latter can be neglected in most o the practical cases. Really, the diusion length o radon in pure water alls into the cm order o magnitude what means that radon practically cannot escape rom completely water saturated media by diusion way. In the ollowing only the diusion via air-illed space is taken into consideration; using the w water content o rock (m/m, instead o the v volume ratio o water), ρ (wet) bulk density o rock or soil and ρ w water density, the diusion constant o partly water saturated porous media can be expressed by the ormula: ( ρ/ ρ w ) w D e = n Dair w + (6) (For simplicity the e index is not used in the ollowing.) 2.3. RADON SOURCE STRENGTH The physical meaning o the c b background radon concentration deined by (4) equation is the radon source strength which expresses the radon activity generated in unit volume and in unit time. That evidently equivalent with the radium concentration (q Ra ) o the medium i the radioactive equilibrium between Ra and Rn exists (is stationer state). Studying radon diusion in porous medium the source strength means the radon activity which can enter the pore space. That is the product o radium content and emanation coeicient, divided by the porosity (the space volume available or the urther movement o radon): Cb = ( q Ra E ρ )/ n (7) In the three phase space, however as it considered above only that part o emanated radon can take part in the urther transport which enter the gaseous phase o the pore space (n-v). The distribution o radon between the air and water phase is a unction o solubility o Radon. That temperature dependent parameter expresses the radon concentration ratio between the air and water phases [2]: k = C w / C air (8) This ratio is k =.25 at room temperature while at the C yearly average temperature (in Hungary) k =.35 is taken (in the urther model calculations that latter value is used but one have to take into consideration the eect o temperature variation, primarily the yearly changes and its depth dependence on that parameter). Based on the above considerations, the radon source strength parameter characteriing the diusion process in 3 phase porous space is given: q Ra E ρ C b = (9) nw ( + ) ( ρ/ ρ ) w ( k) w

5 S32 A. Várhegyi, J. Somlai, Z. Sas 5 It s concluded rom the written that the ormula (9) is valid in not completely water saturated conditions (n < v) only because C b means the radon concentration o pore illing air SOLUTION OF DIFFUSION EQUATION FOR HOMOGENEOUS MEDIUM In the irst step the diusion equation is solved or ininity depth homogeneous medium bordered by horiontal surace. Any type homogeneous soil (even uncovered tailings ponds etc.) can be modelled by this way. The sketch o that simple model is given below: = /////////////////////////////////////// surace: C = homogeneous medium at : C = C b Taking into account the boundary conditions, the depth dependence o radon concentration is given by the ormula: C = Cb e d () Radon concentration diagrams assuming typical soil with average U nat (natural Uranium) concentration ( Clark ~ 3 ppm) and radioactive equilibrium state within the U radioactive decay series is given in Figure. It that cases the 226 Ra activity concentration o soil is 37 Bq/kg. The soil physical parameters (assumed as typical): radium concentration: q Ra = 34 Bq/kg ( Clark U-ekv.), emanation coeicient: E =., bulk density: ρ = 2 kg/dm 3, porosity: n =.4, moisture content: w =.24 (varied parameter). Radon lux perpendicular to the bordering surace is expressed by the product o diusion constant and concentration gradient: J = D (d C/d ) () The value o that at the = bordering surace is called radon exhalation rate. For our model it is given: 2 J = = Cb ( D λ ) (2)

6 6 Radon migration model or covering U mine and ore processing tailings S33 In Figure the values o radon exhalation rates are also given (written onto the respecting curve) alling into the range o 5 mbq/m 2 s, typical or normal soils. 45 Soil gas Rn-222 concentration, kbq/m D=.3-7 m 2 s c b=4. kbq/m 3 Exh= 2 mbq/m 2 s D=3.9-7 m 2 s c b =36.5 kbq/m 3 Exh= 33 mbq/m 2 s D=6.7-7 m 2 s c b =33.5 kbq/m 3 Exh= 4 mbq/m 2 s D=.2-6 m 2 s c b=28.8 kbq/m 3 Exh= 47 mbq/m 2 s D=2. -6 m 2 s c b=23.8 kbq/m 3 Exh= 5 mbq/m 2 s D=4. -6 m 2 s c b=8.5 kbq/m 3 Exh= 53 mbq/m 2 s w = Depth below surace, m parameter o curves: moisture content (w, m/m) Fig. Pore gas radon concentration vs. depth in homogeneous soil; parameters assumed: 226 Ra = 3 ppm Ueq E =. ρ = 2 kg/dm3 n =.4. Rn-222 exhalation rate rom surace, Bq/m 2 s.. Normal soil C b = kbq/m 3..E-8.E-7.E-6.E-5 Diusion constant o soil, m 2 /s parameter o curves: C b Radon source strength (kbq/m 3 ) Fig Rn exhalation rate rom porous, homogeneous soil as a unction o diusion constant.

7 S34 A. Várhegyi, J. Somlai, Z. Sas 7 Formulas () and (2) or diagrams in Figure serve the possibility to derive the value o diusion constant determining basically the radon transport without the knowledge o soil physical parameters barely by the way o measurement o radiological eatures. I the radon exhalation rate on the soil surace and/or the depth distribution o radon concentration in pore gas has been measured in situ, the value o diusion constant can be determined based on the mentioned relations. That possibility can be used in the model calculation or covering the tailings, in respect either or the cover or or the tailings material. Radon exhalation rate o the surace can be analysed as a unction o radon diusion constant through ormulae (2). Calculation results or dierent radon source strength (or or 226 Ra concentrations) are shown in Figure 2. Connection between diusion constant, radon source strength and the decisive soil parameters are shown in the diagrams o Figure 3 and 4., deined by (6) and (9) equations..e-5 Diusion constant o medium, m 2 /s.e-6 n = E Moisture content (w, m/m) parameter o curves: porosity (n, v/v) Fig. 3 Diusion constant vs. moisture content o soil; ixed: bulk density ρ = 2 kg/dm 3. Among the soil eatures, the moisture content o soil is the most critical parameter or the radon exhalation o soil surace, because it can signiicantly change in time (or example variation o rainy and dry meteorological periods, ater heavy rainalls or thawing o snow etc.). In that sense the basic assumption o the model (homogeneous medium) can be regarded as a rough approximation only.

8 8 Radon migration model or covering U mine and ore processing tailings S Rn source strength, kbq/m Ra ppm Moisture content (w, m/m) parameter o curves: 226 Ra content (ppm U eq ) Fig. 4 Radon source strength (C b ) as a unction o moisture o soil; ixed parameters: E =., n =.4, ρ = 2 kg/dm3, k = Surace 222 Rn exhalation, mbq/m 2 s Ra ppm U eq Moisture content (w, m/m); complete saturation at.25 parameter o curves: 226 Ra content (ppm U eq ) Fig. 5 Radon exhalation rom homogeneous soil as a unction o moisture; ixed parameters: E =., n =.4, ρ = 2 kg/dm 3, k =.35. Radon exhalation o soils characteried by dierent 226 Ra concentration is shown in Fig. 5 as a unction o moisture o soil. Diagrams indicate well that the Radon exhalation is practically ceased by the complete water saturation o soil

9 S36 A. Várhegyi, J. Somlai, Z. Sas 9 pores, independently rom the even high Radium content. That is also valid or the bare surace o U tailings ponds. One can conclude rom that result that the water looding o tailings ponds is a very eective way to reduce the radon escape rom those types o mining objects. The moisture (in that case: water) content belonging to the completely saturated condition is deinitely depend on the porosity and the bulk density o the given soil as well; that is the case at 25% water content in the Figure 5. The w max saturation water content o soil can be expressed by the ormula (n: porosity, ρ: bulk density, ρ w : water density): n w max = (3) ρ ρ n / w 2.5. DIFFUSION RADON TRANSPORT MODEL FOR ONE COVER LAYER ON TAILINGS Let s cover the above discussed homogeneous medium by an also homogeneous layer o constant h thickness as a realistic approximation o one layer cover o tailings ponds. The model structure and the respective boundary conditions are illustrated below: = / / / / / / / / / / / / / / / / / / / / / / / surace: C = = h homogeneous cover homogeneous tailings boundary: C = C ; J = J at : C = C Taking into account the boundary conditions, the authors derive the depth unction o radon concentration in the cover layer, expressed by the ormula: h sh sh d d C = ( C C ) + C h h sh sh d d and the radon concentration in tailings material: h (4) d C = ( C C ) e + C (5)

10 Radon migration model or covering U mine and ore processing tailings S37 Indexes and represent the cover and tailings material, respectively. The unknown value o c boundary radon concentration can be determined by introducing an additional boundary condition: the lux o radon at the boundary must be the same approximating either in the cover layer or in the tailings material. The mathematical orm o that: ( ) ( ) dc dc D = D (6) d d = h = h Ater substitution o boundary conditions, the C radon concentration at the tailings-cover boundary can be expressed by: C h D 2 h C C d D d = h D 2 h sh + ch sh + ch d D d One can conclude rom eq. (7) that the boundary radon concentration is a rather diicult unction o the soil physical parameters (D and D diusion constants and d diusion length) o both materials. In Figure 6 radon concentration proiles are demonstrated or dierent moisture content o.5 m thick cover layer assuming average cover soil and tailings material parameters (in details see in the igure). In Figure 7 concentration diagrams are shown or dierent (.5 3 m) cover layer thicknesses, at ixed soil parameters. 2 (7) Soil gas 222 Rn concentration, kbq/m Cover parameters: 226 Ra = 3 ppm U eq E =. r = 2 g/cm 3 n =.4 w - varied Tailings parameters: 226 Ra = ppm U eq E =. r = 2 g/cm 3 n =.4 w =.2 w = Depth, m parameter o curves: moisture content o cover layer (w, m/m) Fig. 6 Soil gas radon concentration vs. depth or.5 m thick one layer cover.

11 S38 A. Várhegyi, J. Somlai, Z. Sas 2 Cover parameters: Soil gas 222 Rn concentration, kbq/m Ra = 3 ppm U eq E =. ρ = 2 g/cm 3 n =.4 w =.2 Tailings parameters: 226 Ra = ppm U eq E =. ρ = 2 g/cm 3 n =.4 w =.2 H = m Depth, m parameter o curves: thickness o cover layer (m) Fig. 7 Soil gas radon concentration vs. depth or one layer cover; dierent thicknesses. For radon exhalation rate rom the surace the next ormula the authors derived: ( d 2 λ) h J = = C + C ch h d sh d (8) That ormula is the inal result o our eort to indicate the relation o radon exhalation rate rom a covered (remedied) tailings pond with the most important soil physical and radiological parameters o tailings and cover layer, as a unction o the thickness o cover. The model calculation results are to be compared to the limit value o radon exhalation (in the Hungarian case:.74 Bq/m 2 s). Calculated radon exhalation rates as a unction o one homogeneous cover layer on tailings pond are indicated in Figure 8 (varied parameter o diagrams: moisture content in cover soil). The pore gas radon concentration diagrams at the cover-tailings boundary (or the same soil physical conditions as in Figure 8) are shown in Figure 9.

12 2 Radon migration model or covering U mine and ore processing tailings S39 6 Cover parameters: 222 Rn exhalation rom surace (Bq/m 2 s) Limit:.74 Bq/m 2 s 226 Ra = 3 ppm U eq E =. ρ = 2 g/cm 3 n =.4 w - varied Tailings parameters: 226 Ra = ppm U eq E =. ρ = 2 g/cm 3 n =.4 w =.2 w = Thickness o cover layer, m parameter o curves: moisture o cover soil (w, m/m) Fig. 8 Surace radon exhalation rate vs. thickness o cover; (case: one homogeneous cover layer on tailings). 9 c boundary 222 Rn concentration kbq/m w = Thickness o cover layer, m parameter o curves: moisture content o cover soil (w, m/m) Fig. 9 Cover tailings boundary radon concentration (C ) vs. cover thickness; (case: one homogeneous cover layer on tailings). Acknowledgements. We acknowledge the inancial support o the Hungarian State and the European Union under the TÁMOP A-//KONV-22-7).

13 S3 A. Várhegyi, J. Somlai, Z. Sas 3 REFERENCES. UNSCEAR 28 Report Vol I. Sources o Ioniing Radiation, Report to the General Assembly, with Scientiic Annexes, United Nations, New York, (2). 2. C. Cosma, F. Dancea, T. Jurcut, D. Ristoiu, Determination o 222 Rn emanation raction and diusion coeicient in concrete using accumulation chambers and the inluence o humidity and radium distribution, Appl. Radiat. Isot. 54, (2). 3. B. Papp, C. Cosma, M. Moldovan, D.N. Constantin, Radon potential rom soil and radon risk evaluation, Ecoterra 6, (29). 4. B. Zmaeka, M. Živčićb, J. Vaupotiča, M. Bidovecc, M. Poljakc, I. Kobal, Soil radon monitoring in the Krško Basin, Slovenia: Appl. Radiat. Isot., 56, (22). 5. A. Várhegyi, I. Baranyi, G. Somogyi, A model or the vertical subsurace radon transport in "geogas" microbubbles, Geophys. Trans., 32, (986).