Hidrológiai Közlöny 1980 (60. évfolyam)

8. szám - Dr. Kovács György: A mechanikai diszperzió szerepe a felszín alatti szennyeződés terjedésében

Dr. Kovács Gy.: A mechanikai diszperzió szerepe Hidrológiai Közlöny 1980. 8. sz. 347 ueu rpanHH B y3JiOBbix Towax pacmiTbiBatoTcsi npu noMOIHH ypaBHCHHH 5. XLBYMCPHYIO MO«ejib MO>KHO ofíoűmHTb H /yiji HccJieaoBanHH TpexMepHoro «BH>KeHH«. OnncaHHyio BI.IUIC ztByMepHyio cHCTeMy cjie«yeT npeacTaBiiTb MHoroKpaTHo paccTaBJieHHoii napajiejuibno /iByjvi nji0CK0CT>IM, KOTOPMC nepneHAHKyjrapHbi apyr apyry. TaKHM 0öpa30M no;iy<iiiM NPOCTPAHCTBEHHYIO pemeTKy, B KOTOpoií ysjioBbie TOWKH íiyayT pacnojio>KeHbi Ha napanejiJibHbix IIJIOCKOCTJIX, KOTopbie neprieHflHKyjiapHbi HanpaBJiemiio noTOKa H cjieayioT flpyr sa jipyroM lepes OflHHaKOBbie HHTepBaJiH «a». B y3iiax BCTpeMaeTCfl no BOceMb TpyöoieK H3 K0T0pwx no MeTbipeM Boaa nocTynaer B y3en a no apyrHM icrbipeM OTBOFLHTCÍI orryaa. Pacnpeflejicnne KOHQEHTPAUHH B TaKOÍÍ pcuieTKe nos fleiiCTBHeM MEXAHHMECKOH ;;HcnepcnH onnci>iBaeTca ypaBHeHiieM 7. 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Cjie«yeT TaKwe pacKpbiTb cB3Hb M«K«y e;THNCTBeHHHM napaMeTpoM MoaejiH «a» — xapaKrepnoií ajihHOÍi — H IieTpO(J)H3HHCCKHMH XapaKTCpilCTHKaMH. HccjieaoBaHHji nnn BbiyiBjieiiHH ycTaHOBHBuierocji coCTOMHUH juicnepcHOHHoro npouecca B nopwcTbix cpeaax HaiaTbi. O pe3yjibTaTax no Mepe npofl BH>KCHHH 6y,neM AOKna;;BIBATB. flo OKOHMAHHH aToro 3Tana MOJKHO (iy^er nepeiÍTH K anajiii3y HeycTaHoBiiBimixcíi BO BpeiweHH npoi;eccoB. The role of iiiochanical dispersion in the subsurface spreading of pollution by Kovács, Gy. C.M. Acad. Sci. Hung. One of the objeetives of the investigations started reeently into the spreading of pollutants in ground water reservoirs is to find a method for deseribing the process of dispersion, which is simple, readily handled in practice and, moreover, capable of expressing properly the effects resulting from the structural properties of the porous médium. The first analvses have indicated that the dimension perpendicular to the direction of flow of the space element affected by pollution in the waterbearing layer is but slightly affected by molecular diffusion and turbulent mixing, although the lattor predominate in similar phenornena taking place in surface waters. The factor controlling the transverse spreading of the tracer, or polluting substance in the porous médium may be assumed to be mechanieal dispersion, i.é., the process by which the water particles are transported in the random network of cormnunicating channels enclosed l)y the solid skeleton, even in directions other than the generál path of müvement. Starting from this recognition, the aim of the present investigations has been limited to the exploration of the possibility of using a simplified physical model to reproduce the cornplex channel network in deseribing in a simple manner the probable position of the boundaries of the labelled plume, further in determining within these boundaries the probable distribution of concentration ratios. Striving at the simples possible model, several important simplifying assumptions have been adopted in the initial stage, thus — steady conditions have only been considered, eliminating thus the need of analysing the progress of the tracer over time; — the representative network has been composed of capillary tubes, assuming as a first approximation each tűbe section to have the same conveying capacity (identical length and diameter of the tűbe sections); -— in the system composed of tűbe sections and nodal points the fluid of specific concentration is transported in the tubes without any change in concentration, while at the nodal points the discharges arriving from the different connecting tubes are completely inixed without delay in time; •— although geometrically the chances of channel orientation are equal in all directions, somé directions must be weighted according to their role in conveyance. For this reason the projection of the model tubes in the direction of flow is twice as large as that of the projection on a pláne perpendicular to the direction of flow. Investigations have first been limited to the analysis of two-dimensional flow. In this case four tubes connect in each nodal point of the representative capillary tűbe network, tvvo arriving from the direction of flow, two removing the fluid from the node. In this network the mechanieal dispersion of the fluid having the concentration C

n fed continuously at the entrance point, i.e., the distribution of concentration in the pláne of flow (at the nodal points of the network) is found from Eq. (5). The two-dimensional model can be extended to the analysis of three-dimensional flow as well. The pláne network deseribed in the foregoing is fitted to two mutually perpendicular series of planes, resulting in a three-dimensional grid, the nodal points of which are situated on planes parallel to each other, perpendicular to the direction of flow and spaced at the fixed distance a. Eight tubes connect to each of the nodal points, four conveying water towards the node, whilst four remove it therefrom. In the network of such geometry the concentration distribution produced by meehanical dispersion is deseribed by Eq. (7). The practical applicability of the highly simplified model depends on the extent to which it is capable of reproducing the actual phenornena. The exploration thereof is the primary objective of the present study. In the interest thereof the pattern of the network is maintained constant, but the tűbe diameters are varied in a random manner, checking whether the resulting concentration-distribution differs again by a random scatter from the concentration values estimated by assuming tűbe sections of uniform diameter, or whether any change in the conveying capacity of the tubes affects fundamentally the patterns of tracer distribution. Once a positive answer is obtained to the first question (if we succed in demonstrating that the concentration computed for a particular nodal point in the network composed of tubes having uniform diamefers is actually the probable value of the data set of which each term is determined by distributing in a random manner the different ffube section diameters over the network and computing thus the concentration in the same nodal point), the verification of the model can be attempted. By an experimentál approach it is necessary to check whether the data obtained analytically on the hasis of the model agree with accept.able accuracy with the concentration distribution observed in the natural layers. The other aim of the series of ex. periments is to explore the relationship between the only pararneter involved in the model—namely the characteristic length a—and the rock-physical parameters of the various layers. The research project outlined above for deseribing the steady state of the dispersion process in porous média is under way. The results obtained will be reported successively as progress is made. After the termination of these investigations an at.tempt will be made at analysing unsteady phenornena as well.