A random walk model to simulate the atmospheric dispersion of radionuclide

Transcription

1 IOP onference Series: Earth and Environmental Science PAPER OPEN AESS A random alk model to simlate the atmospheric dispersion of radionclide o cite this article: Jn Zho et al 208 IOP onf. Ser.: Earth Environ. Sci Vie the article online for pdates and enhancements. his content as donloaded from IP address on 03//208 at :33

2 ESMA 207 IOP onf. Series: Earth and Environmental Science (208) doi :.88/755-35/8/4/04207 A random alk model to simlate the atmospheric dispersion of radionclide Jn Zho, Lixing Hang, Shengli Ni, Honggang Xie, Feihong Kang Northest Institte of Nclear echnology, Xi an 7024, hina orresponding athor zhojn82@63.com Abstract. o investigate the atmospheric dispersion of radionclide in large-medim scale, a nmerical simlation method based on random alk model for radionclide atmospheric dispersion as established in the paper. he rote of radionclide migration and concentration distribtion of radionclide can be calclated ot by sing the method ith the real-time or historical meteorological fields. In the simlation, a plme of radionclide is treated as a lot of particles independent of each other. he particles move randomly by the flctations of trblence, and disperse, so as to enlarge the volme of the plme and dilte the concentration of radionclide. he dispersion of the plme over time is described by the variance of the particles. hrogh statistical analysis, the relationships beteen variance of the particles and radionclide dispersion characteristics can be derived. he main mechanisms considered in the physical model are: () advection of radionclide by mean air motion, (2) mixing of radionclide by atmospheric trblence, (3) dry and et deposition, (4) disintegration. A code named as developed according the method. And then, the Eropean racer Experiment () in 994 is simlated by the and codes, the simlation reslts of the concentration distribtion of tracer are in good agreement ith the experimental data.. Introdction Radionclide can be released into the atmosphere in the form of gases or particles after nclear accident. he spatial distribtion of radionclide radiation doses and the change of time have important significance to formlate and implement protective measres to redce pblic radiation hazards. he diffsion behavior of radionclide, as a special air polltant, mainly depends on the average ind speed and trblence of atmosphere. Wind field leads to space displacement of radionclide in the atmosphere, and radionclide is mixed ith the ambient air by trblent motion. Most existing atmospheric diffsion models are established based on gradient transport theory, trblence statistics theory and similarity theory, sch as analytical soltion derived from trblence statistic - Gassian model. he model has clear physical concept, hich is more sitable for calclation of medim and small scale scope in steady state flo field. It has high comptation efficiency and spatial resoltion, hich is still one of the most poplar models at present. For example, Gassian plme model is adopted for AERMOD model [], ADMS model [2] and HotSpot program [3], etc. to simlate the radionclide transport diffsion. Hoever, becase Gassian model is based on stable and niform conditions, it is determined that it only applies to radionclide diffsion simlation of local scope generally [4, 5]. ontent from this ork may be sed nder the terms of the reative ommons Attribtion 3.0 licence. Any frther distribtion of this ork mst maintain attribtion to the athor(s) and the title of the ork, jornal citation and DOI. Pblished nder licence by Ltd

3 ESMA 207 IOP onf. Series: Earth and Environmental Science (208) doi :.88/755-35/8/4/04207 Atmospheric trblence has high degree of randomness. herefore, the diffsion behavior of air polltants in the atmosphere can be simlated by a random alk method. Namely, random motion of a large nmber of particles is tracked to simlate the diffsion process of polltants in the air [6-8]. he random alk method for simlating atmospheric diffsion process of air polltants reflects the random natre of trblent diffsion, hich not only can simlate the atmospheric diffsion of polltant in homogeneos trblence field [9-], bt also can be applied to simlate polltant diffsion problem nder non-niform, nsteady and strong shear complex flo field condition [2, 3]. rrently, some scholars have tried to apply the random alk method to radionclide atmospheric diffsion simlation [4, 5]. In hina, Zheng, Yan Zheng, etc. se the random alk method to simlate the radiation of nclear accident radioactive plme in small scale [6]. Establishment of medim and large scale radionclide atmospheric diffsion calclation model and verification research on the reliability of the model calclation reslts has not been reported at home. In the paper, a calclation model sitable for radionclide diffsion in large and medim scope is established based on the random alk method. Radionclide atmospheric diffsion simlation program is developed. he program is sed for simlating and calclating () process. he calclation reslts are compared ith measred reslts, and the correctness and reliability of the program are verified and analyzed. 2. alclation model In the random alk method, each radionclide particle is regarded as an independent identifying particle. he trajectory of the particle is calclated by releasing a large nmber of particles. he particles are applied for describing the migration and diffsion of radionclide in the atmosphere. Particles are transported in the flo field according to average ind. Meanhile, a series of random displacements are sed for simlating trblent diffsion. o fnctions of advection and trblent diffsion are described. Finally, the distribtion of radionclide is estimated throgh overall distribtion of the particles in space and time. he particle motion trajectory can be ritten into the folloing form by integral particle motion eqation: X( tt) X( t) V X( t), t tv X ( t), t t () Wherein X refers to the three-dimensional coordinate component (x, y, z) of the particle; V is the average ind velocity component ( v,, ) ; V velocity component (, v, ) of the trblent plsation; t is the time series; t is step for time. he plsation speed of each time step is assmed by assming that the motion obeys Markov (n + moment is only associated ith the n time), namely [8]: 2 /2 ( tt) ( t) R ( R) 2 /2 v ( t t) v ( t) Rv ( Rv) v 2 /2 ( t t) ( t) R ( R) (2) In the to formlas of trblent velocity components, the second item on the right represents the random part in the velocity flctation. is the random nmber in line ith the normal distribtion (the 2 /2 2 /2 2 /2 mean vale is 0 and the standard deviation is ). ( ), v ( v ) and ( ) are standard deviations of the plsation qantity V ; Ri( t) exp( t Li) Lagrange atocorrelation fnction; Li is the Lagrangian time scale, here i represents three direction components of, v, and. It is obvios that the implementation of the random alk diffsion simlation has the key of determining the bondary layer trblence diffsion parameters i and Li. hese parameters can be obtained by analyzing the real-time meteorological observation reslts. he calclation method is 2

4 ESMA 207 IOP onf. Series: Earth and Environmental Science (208) doi :.88/755-35/8/4/04207 closely related to the stability of the atmosphere [9, 20]. oncrete calclation method is shon as follos: ) he atmospheric stability is nstable. he standard deviation of trblence velocity is shon as follos: H 2 2 L v /3 (3) /3 z L z H H H / z L z z min , H H H H z z H H z H (4) Lagrange time scale: L H Lv 0.5 (5) L z z z-z , - z z0 H L L z z z-z H 5z z 0.5 exp H 0. H , - H L (6) 2) he atmospheric stability is stable. he standard deviation of trblence velocity is shon as follos:.3 v 2 z H z H (7) (8) Lagrange time scale: 3

5 ESMA 207 IOP onf. Series: Earth and Environmental Science (208) doi :.88/755-35/8/4/04207 L H z 0.5 H 0.5 (9) Lv H z 0.07 H v 0.5 () L H z 0. H 0.5 () 3) he atmospheric stability is netral. he standard deviation of trblence velocity is shon as follos: 2.3 (2) v 2.0 (3) 2z.3exp H (4) Lagrange time scale: 0.5z L Lv L (5) 5z H In the above formla, H is the bondary layer height, L is the length of Moring, ω is the convective velocity, z 0 is the srface roghness, and is the friction velocity. he motion trajectory of the particles can be completely determined by the nmber of trblent diffsion parameters i and Li nder the above atmospheric stability conditions. In addition, radionclide particles sffer from the inflence of decay, precipitation and other removal effects in the migration process of radionclide particles, and the particle eight ω ill be changed as follos: exp( t)exp( t) (6) Wherein, Ʌ refers to precipitation scavenging coefficient, and β refers to a decay constant. If total radionclide release is Q, and total simlated particles are N, then the total eight the particles in each recording grid is calclated at the time of t, and the concentration distribtion of radionclide at t moment is obtained: n j j of 4

6 ESMA 207 IOP onf. Series: Earth and Environmental Science (208) doi :.88/755-35/8/4/04207 i Q n j j (7) NV Wherein, i represents the record grid nmber, n is the nmber of particles in a corresponding grid, j is the eight of the jth particle in the grid, and Δ V represents the grid volme. In practical application, the time integral concentration is generally sed instead of the instantaneos concentration in order to redce the flctation of the calclation reslts: i Q N ji, j j (8) NV Wherein, i,j the residence time of the jth particle in ith recording grid. Figre. he flo chart of code he above method is sed for developing radionclide atmospheric diffsion simlation program. he procedre flo is shon in figre. 3. alclation reslts and analysis INSAG nder IAEA cooperated ith WMO for to large-scale particle tracer experiments [2, 22] in order to establish a set of calibration database hich can be sed as a planetary bondary layer atmospheric diffsion model. hey are called (). In the paper, to experiments are simlated and calclated in order to evalate the reliability of program. he tracer particles concentration at integral point time in each monitoring station beteen 0 to 90 hors after particle release is recorded. he nearest distance of the monitoring site and the release point is abot 200km (Alencon site). he farthest distance is abot 2000 km (ervena site). able shos the release conditions of the to tracer experiments. 5

7 ESMA 207 IOP onf. Series: Earth and Environmental Science (208) doi :.88/755-35/8/4/04207 able. Smmary of operating conditions of Release featres he first tracer experiment he second tracer experiment Particle release position Monterfil( "N, "W) Monterfil( "N, "W) racer particle PMH PMP Release starting time /U : :00 Release ending time /U : :45 otal release /kg PMH velocity/g s Meteorological condition No ind Rain, heavy ind Wind direction West ind West ind he concentration and measred reslts of the tracer particles in several typical sites are compared ith the measred reslts as shon in fig. and 2. he reslts obtained by sing the program are also presented in the figre. he is a model of atmospheric diffsion developed by Noregian Atmospheric Research Institte, hich has been idely recognized and applied in the field of atmospheric diffsion calclation [23]. It can be seen from the figre that the calclated reslts given by and are consistent ith the measred reslts in the aspect of radionclide concentration and concentration change trend 站点名称 :Alencon 站点名称 :ervena 站点名称 :Nebrandenbrg 站点名称 :Praha Lids 站点名称 :Jaegersborg 站点名称 :Zielona Gora Figre 2. he tracer concentration at stations for tracer sampling dring the first 6

8 ESMA 207 IOP onf. Series: Earth and Environmental Science (208) doi :.88/755-35/8/4/ 站点名称 :Offenbach 站点名称 :aen 站点名称 :Strasborg 站点名称 :Beek/Z.Limbrg 站点名称 :Nancy Essey 站点名称 :olmar Figre 3. he tracer concentration at stations for tracer sampling dring the second In the radionclide diffsion event, radionclide maximal concentration vale M and transit time P are to important monitoring parameters in varios monitoring sites. he maximm concentration and transit time are are compared ith the measred reslts for analysis in order to frther analyze the reliability of the calclated reslts as shon in fig.4 and 5, herein, D (9) M M M M D (20) M P P P M Wherein, M and tracer particles respectively. and M are measred vales and calclated vales of the peak concentration of the M P P are respectively the measred vale and calclated vale of the transit time. he y coordinate in the figre represents monitoring site nmber, figre (a) shos the comparison of the calclated reslt ith the measred vale of 49 monitoring sites in the first experiment. Figre (b) shos the comparison of the calclated reslts ith measred vales of 25 monitoring sites in the second experiments. 7

9 ESMA 207 IOP onf. Series: Earth and Environmental Science (208) doi :.88/755-35/8/4/ (a) 20 (b) D M /ng m -3 0 D P /ng m Site No Site No. Figre 4. A comparison of maximm trace concentration in stations for tracer sampling. (a) for the first and (b) for the second D P /h (a) Site No. D P /h Site No. Figre 5. A comparison of trace pass-time in stations for tracer sampling. (a) for the first and (b) for the second. he average distance normal beteen the calclated vale and the measred vale is defined as follos in order to measre the consistency beteen the program calclated reslts and the measred reslt more intitively: 2 2 n n M M M x x x x x x k (2) Wherein, x i ( i,2,, k) the monitoring vale of the tracer particle peak concentration on the is M ith measrement site. x i ( i,2,, k) is the calclated vale of the peak concentration on the i measrement site. k is the total nmber of monitoring sites. he average distance norm can be sed to represent the overall fitness of the calclated reslts and the measred reslts. he average distance normal is smaller, the calclated reslts are more consistent ith the measred reslts. able 2 shos the average distance norm of the peak vale concentration and transit time calclated time corresponding to the measred reslts. he average distance norms of and given in the table are compared. It is obvios that the average distance normal of the calclated reslt is smaller in both the first and the second experiments. It is obvios that the calclated reslt given by is more consistent ith the experiment reslt, thereby verifying that the calclation model established in the paper based on random alk method is correct and effective in radionclide atmospheric diffsion. In addition, the calclated reslt of the second experiment given by to programs are greatly (b) 8

10 ESMA 207 IOP onf. Series: Earth and Environmental Science (208) doi :.88/755-35/8/4/04207 different from the experiment data compared ith the calclated reslt in the first experiment. It is obvios that the error of to calclation program calclated reslt and measred vale is alays larger than the calclated error nder calm eather conditions in case of heavy ind and rain as ell as other extreme eather conditions. able 2. he mean radial distance norm given by and codes Peak vale concentration ransit time onclsion () In the radionclide atmospheric diffsion nmerical simlation method established based on the random alk method, real-time or historical meteorological data can be tilized for calclating the radionclide diffsion problem in medim and large scale scope. (2) he self-developed radionclide atmospheric diffsion simlation program is tilized for simlating the process. he change condition of monitoring site concentration ith time, site peak vale concentration, tracer particle transit time and other parameters are given throgh calclation. he reslts sho that the calclated reslts of given at simlation of snny and ind-free eather conditions have small deviation from the measred reslts. he calclated reslts given at simlation of extreme eather conditions-heavy ind and rain have great deviation from the measred reslts. (3) Radionclide atmospheric diffsion process is very complex, hich is not only affected by the atmospheric ind field, bt also is related to the sorce natre, diffsion area characteristics of landform and physiognomy and climate hmidity in different areas. Next, these inflence factors ill be added in existing calclation model in order to improve the reliability of the calclated reslts. References [] imorelli A J, Perry S G, Venkatram A, et al. AERMOD: A dispersion model for indstrial sorce applications. Part I: General model formlation and bondary layer characterization. Jornal of Applied Meteorology, 2005, 44(5): [2] ER. ADMS-EIA User Manal. ambridge, 2002:. [3] Bradley M M. NARA: An emergency response resorce for predicting the atmospheric dispersion and assessing the conseqences of air-borne radionclides. Jornal of Environmental Radioactivity, 2007, 96(): 6-2. [4] Raza S S, Iqbal M. Atmospheric dispersion modeling for an accidental release from the Pakistan Research Reactor-(PARR-). Annals of Nclear Energy, 2005, 32(): [5] Venkatesan R, Mathiyaras R, Somayaji K M. A stdy of atmospheric dispersion of radionclides at a coastal site sing a modified Gassian model and amesoscale sea breeze model. Atmospheric Environment, 2002, 36(8): [6] Wilson J D, Saford B L. Revie of Lagrangian stochastic models for trajectories in the trblent atmosphere. Bondary-Layer Meteorol., 996, 78: 9-2 [7] Ley A J. A random alk simlation of to-dimensional trblent diffsion in the netral srface layer [J]. Atmospheric Environment, 982, 6(2): [8] Davis P A. Markov chain simlations of vertical dispersion from elevated sorces into the netral planetary bondary layer. Bondary-Layer Met, 983, 26: [9] Oettl D, Kkkonen J, Almbaer R A, et al. Evalation of a Gassian and a Lagrangian model against a roadside data set, ith emphasis on lo ind speed conditions. Atmospheric environment, 200, 35(2): [] Manomaiphiboon K, Rssell A G. Effects of ncertainties in parameters of a Lagrangian Paritcle model on mean grond-level concentrations nder stable conditions. Atmospheric 9

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