Hidrológiai Közlöny 1982 (62. évfolyam)

5. szám - Dr. Kovács György: A porózus kőzeg véletlen jellegű szerkezeti változásainak hatása a szennyeződés terjedésére

206 Hidrológiai Közlöny 1982. 5. sz. Dr. Kovács Gy.: A porózus közeg gált mező méretétől, csupán egészen kis tartomány esetében mutatkozott a relatív szórás elhanyagolhatóan kis csökkenése a szennyezési középpont közvetlen környezetében, ami azzal magyarázható, hogy a tengely mentén feltételezett állandó érték-szakadással csatlakozik a középpont zérus paraméteréhez, jóllehet a valóságban itt folytonos átmenetnek kell kialakulnia, és ez az eltérés kis mező és nagy relatív szórás esetében észlelhetővé válik. A felsorolt tézisek alapján határozottan állíthatjuk, hogy az azonos felületű és hosszúságú kapilláris csövekből kialakított fizikai modell alapján számított koncentráció-eloszlás a szerkezeti elemek véletlen kapcsolódása által befolyásolt tényleges koncentrációnak várható értékét megbízhatóan szolgáltatja. A változó valószínűségi jellegének megfelelően azonban ezt a paramétert minden esetben ki kell egészítenünk a valószínt! szórás mértékének meghatározásával is. A relatív szórás a legkisebb a csóva tengelyében. Itt értéke független a szennyezési középponttól mért távolságtól és nagyságát a szerkezeti elemek méretének szórásából elfogadható pontossággal számíthatjuk. A szárnyak felé haladva a relatív szórás ugyan növekszik és meghatározása egyre bizonytalanabbá válik, ennek gyakorlati jelentősége azonban a várható érték rohamos csökkenése miatt elenyésző. IRODALOM [1] Gergely J. (1981): Egy szivárgási föladat megoldása (Sajtó alatt). [2] Kovács Gy. (1980): A mechanikai diszperzió szerepe a felszín alatti szennyeződés terjedésében. Hidrológiai Közlöny, 1980. No. 8. p. 339. [3] Kovács Gy. (1981): Az időben változó szennyezés porózus közegben való terjedésének vizsgálata. Hidrológiai Közlöny, 1981. No. 1. p. 1. Effect of random variations in tlie structure of porous media on the propagation of pollution Dr. Kovács, Gy. Corr. Member, Hung. Acad. Sei. The aim of the research project was to study the effect of internal structural irregularities of the pervious layer on the propagation of pollutants in aquifer rocks. The network composed of capillary tubes —• as a physical model —• has earlier been demonstrated to be suited to simulating the seepage phenomena in granular layers, as well as the mechanical dispersion which influences the propagation of pollution. This model can be modified for studying the present problem by varying in a random manner the diameter of particular tube sections within the network. The problems raised can be answered by calculating the pressures at the network points specified in advance and the flow through the pipes of different diameter. The problem has thus been simplified to the solution of two sets of linear equations,""each of whom contains a large number of members. The investigations performed have lead to the following conclusions

: — When considering particular cases, owing to the random variation of the pore sizes, the concentration at particular points may differ appreciably from the value estimated for the network of identical capillaries having cross-sectional areas corresponding to the average pore diameter. -— The difference between the value obtained in a particular case and the theoretical value was — as could be logically expected — the wider, the greater the variability of the structural elements forming.the layer, i. e., of the sizes of channels formed by the pores. — Considering a large number of fields, but composing the individual networks of indentical sets of tubes and varying in a random manner only the position of the individual t»ibes within the field, for each network point a set of concentration values is obtained, the mean value of which does not differ considerably from the theoretical concentration calculated on the basis of a network composed of identical tubes, and the deviation corresponds to the random character and the statistical method. — The mean value of the data pertaining to the same point of a sufficiently large number of alternatives is — as will be evident from the foregoing thesis — is independent of the size range of the set of tubes simulating the variability of the structural elements. Regardless of what set of numerical values of the tube surface is adopted at the outset, the resultant spatial arrangement of the mean values yields the theoretical concentration distribution. — The concentration ensuing at a particular point considered as a eonsequenceof a continuous point source of pollution is thus regarded a random variable, which depends on the random connections of the structural elements. Consequently, not only the expected value (the mean of the data calculated on the basis of a field varying in different random ways) must be determined, but the standard deviation of the data thus obtained for each point must also be known. — The standard deviation is highest in the centreline of the polluted plume (along the straight line parallel to the main flow direction and passing through the point source of pollution) and diminishes towards the edges. The variation of the relative standard deviation shows, however, an opposite trend, since the expected value decreases in the direction perpendicular to the flow at a higher rate than the standard deviation, so that the relative standard deviation assumes a minimum value in t he centreline. — The magnitude of the standard deviation is no more independent of the probability distribution serving for the statistical description of the pore sizes (thus of the relation, which specifics in the case of the physical model the number of tube elements pertaining, within the set of tubes available for composing the field, to each identical cross-sectional area, in terms of the diameter, or area). — The relative standard deviation of concentration in the centreline of the polluted plume does not vary otherwise with the distance measured from the center, but is in linear correlation with the relative standard deviation characterizing the variability of the set of tubes; In extreme cases it is identical with, or equal o 70 per cent of, the latter. The most probable corlation is given by the proportionality factor 0,85. — The magnitude of the relative standard deviation increases in the direction perpendicular to the centreline as the square of the distance and is practically independent of the variability of the set of tubes used for composing the field. — The magnitude of the expected value and standard deviation of concentration is practically independent of the size of the field considered. A negligibly small decrease of the standard deviation in the immediate surroundings of the polluting source has been experienced in the case of very small domains only. This is attributed to the fact that the constant value assumed along the centreline joins the zero parameter at the centre with a discontinuity, although actually a gradual, continuous transistion must exist here. This difference becomes perceptible in the case of a small field and high relative standard deviation. On the basis of the t heses lised in the foregoing it is claimed on the base of the physical model composed of capillary tubes of identical surface and length yields with a high degree of reliability the expected value of the actual concentration influenced by the random junction of the structural elements. However, in view of the random nature of the variable, this parameter