Vízügyi Közlemények, 1985 (67. évfolyam)
3. füzet - Kovács György: A hosszirányú diszperzió jellemzésére szolgáló modell
A hosszirányú diszperzió jellemzésére szolgáló modell 403 — on the basis of the network-model a generally valid relationship was derived which provides an analitical description of both the break-through curve and the longitudinal-section of concentrations-distribution; — the good fit of the curves calculated by the network-model has proved the reliability of earlier formulated theoretical statements, primarily the applicability of the recommended setup of the network-model. Due to the variability of the pore-structure a channel with large diameter may exist within short sections. Here the tracer will speed ahead and the time of its first appearance in the investigated section will become substantially short. Medium concentrations usually advance with average pore-velocities. Only in the starting section — where the effect of chemical dispersion related to mechanical dispersion cannot yet be neglected — will have a velocity larger than the value of v ef r by some percents (the ratio t s 0/t p is less than unity). The almost constant value of t s o and the shortness of t 0 decreases the slope of the breakthrough-curve over the initial strech. Along longer flow space the random effects are equalized and both the time of arrival t 0 and the product Ar 0 affecting the shape of the curve are approximating the theoretical value. When the uniformity coefficient U of a grain-size distribution is large, the above mentioned equalizing process is slow. Consequently the development of a general break-through curve is expected only after a longer seepage than in layers with equal grain-size. In a mixture of extreme grain-sizes (with very large U) no continuous system of the voids will be available. In such cases the break-through curves are uncertain, sometimes incomprehensive. Similar uncertainties arise when the hydraulic gradient is low. In such cases, the discharge is not evenly distributed in the profile of the sample. Point measurements of concentrations cannot be characteristic for the whole profile. Diverging results of earlier measurements may be explained by the fact that the lengths of the samples were different and the random effects were equalized also in different ways. Especially the values gained through samples with extremely mixed grain-distribution were contradictory. This is a logical consequence of the fact that the length of seepage needed for equalization is substantially longer than in columns with equal grain-size. The gradual development of the break-through curve over the section of equalization has a profound influence on laboratory measurements. In practice-however — this change occuring in the vicinity of the source of pollution (within a distance of 500... 1500 D 6 0) can be neglected. It is sufficient therefore if the general break-through curve is characterized with adequate accuracy. The relationship used in general is given in Eq.ll. It can be plotted as a function of the dimensionless variable t/t p or t/t 0 (Fig. 10). The parameters of Eq. 11 except t p can be fixed as constants on the basis of the assumed geometry of the network-model. The structure of the network is independent of the soil-physical characteristics of the layer, therefore, size, shape and distribution of the grains will not influence the break-through curve assuming that the general curve is constructed in such a way that the time belonging to different concentrations is related either to t 0 or to t p. The time period t p ~ t 5 0 may be calculated as the ratio of length .x and pore-velocity v ef r. This latter is a function of the gradient, of the seepage coefficient and the porosity which all will contribute to Eq. 11 indirectly. The effect of the uniformity coefficient is apparent only if the U value is large. In this case a long seepage distance is needed to equalize the consequences of the random structure. For practical purposes, however, this relationship can be neglected. Consequences of variability of the structure are not compensated entirely over the section of equalization. Hence the general curve of penetration is only the expected value of this relationship. Therefore, it is unavoidable to consider some standard deviation along the time axis and in the slope of the break-through curve (estimated as 10 percent) as this is demonstrated in Eq. 11 and from Fig. 10. Measured break-through curve have a good fit with the theoretically calculated results if the
