|
|
| Bildiri Özetleri | |
| Ana Sayfaya Dönüş |
| ISD Ana Sayfası |
|
Mikayilov Fariz University of Selcuk, Agricultural Faculty,Department of Soil Science, Konya, TURKEY Fatih Er University of Selcuk, Çumra Meslek Yüksekokulu, 42500, Çumra, Konya, TURKEY ABSTRACT To prevent of the system of soil ecology from pollution is the main part of the general problems on protection of environment. Because of watertable or antropogenic reasons, water transpiration mechanism of the chemical materials in the system of water, soil, plant fertilizer atmosphere must permanently be examined and known, because pollution is a bio-physical and geo-chemical process and the pollution of soils effect the productivity in a negative way. For this reason the source of pollution and its degree and reasons must be known well and the estimation of pollution must be taken in to consideration, which is very important to increase the productivity of soil. The aim of this work is to examine the transportation mechanism of the chemical materials in watertable and estimate its quantity by using mathematical modeling. INTRODUCTION Soil salinity is one of the oldest challenges encountered by irrigated agriculture. Managing soil salinity remains an important problem in many regions (Ghassemi, et al., 1995). Salts are transported as solutes with water in soils, and therefore hydrological regimes of irrigated soils and landscapes govern direction and intensity of salinization. As the knowledge about solute transport has accumulated, the solute transport models have been developed that accounted for a number of processes in salt affected soils (Van Genuchten and Dalton 1986). Hydrodynamic dispersion, molecular diffusion, and heterogeneity of the flow regime are the primary mechanisms of the solute movement in soil pore space. Chemical, biological, and microbiological processes account for local changes in solute concentrations. Both analytical and numerical solutions of the equations in solute transport models are studied and used. Numerical solutions allow for the flexibility in boundary and initial conditions to encompass real field situations. Analytical solutions usually assume a steady-state water flow and constant in time and space dispersivity coefficient, and therefore the applicability of these solutions is limited (Leij and Toride, 1998).However, analytical solutions can be useful to provide initial estimates of alternative salinization and desalinization scenarios when implemented over large temporal and spatial scales (Toride et al.,1993). A large number of analytical solutions have been reported for one-dimensional non-equilibrium solute transport (Lassey, 1988; Leij and Toride, 1998 & Sardin, et al.,1991). A semi-infinite porous medium was considered most often. Solute transport in the finite column or layer was received relatively less attention (Mikayilov,1989; Van Genuchten and Alves 1982).The problems mentioned above and their investigations and solutions are presented properly in following literatures (Jury et al., 1991). Analytical solutions for solute transport in a finite layer are of interest when the concentration of a soluble salt or an ion is monitored on both top and bottom of the layer. When the salt transport in soil occurs in presence of shallow ground water, observations of salt concentrations in ground and irrigation water coupled with water balance estimation can provide necessary data to apply the analytical solution for the finite soil layer to assess salt transport in soil at field scale. The purpose of this work was to develop an analytical solution for the two-region solute transport model in finite layer that would take in account the effect of groundwater salinity on the soil salinity. SOLUTE TRANSPORT EQUATION The two-site non equilibrium solute transport model is given by (Karakaplan et al.,1999; Bayrakli, et al.,1996; Lapidus and Amundson 1952; Mironenko and Pachepsky 1984 ; Van Genuchten and Wagenet 1989):  Here  and  are the volumetric contents of mobile and immobile water, respectively;  is the volumetric water content; C (x, t) and N (x, t) are solute concentrations in mobile and immobile pore water, mol m-3; W (t) is the evapotranspiration rate, m s-1. The hydrodynamic dispersion D is assumed to be proportional to the pore velocity D(t)=y |v(t)|, the effect of molecular diffusion is ignored; y is the hydrodynamic dispersion coefficient, m; k1 & k-1 are first-order rate constants, s-1 ; the inequality between k1 and k-1 accounts for effects of the anion exclusion. The initial conditions are: Where L is the water table depth, m. The boundary conditions are:  Here C2(t) are solute concentrations in the ground water. ANALYTICAL SOLUTION The Laplace transform will be used to obtain the analytical solution. The following dimensionless variables and parameters will be employed:  The auxiliary variables w and u will replace concentrations C (x, t), N(x, t) and C2 according to the following equations:  Using the dimensionless parameters and new variables, Eq. (1)-(4) can be re-written as:  Here;  The Laplace transforms of the introduced variables are:  Transforming of Eq. (7) and (8) with initial condition (9), we obtain:  Excluding U (y, p) from these two equations results in:  Here, for the sake of brevity,  Applying Laplace transform to the boundary conditions (10) and (11), we obtain:  Respectively. Eq. (14) has a general solution ( Karakaplan et al.,1999):  The expression for U (y, p) is:  Here the Green's functions  ,
 and
 are defined as; Inverting the Laplace transforms (20) and (21), we find the auxiliary variable w (y, t), u (y, t) and using (5) , (6), we arrive to the expression for C(x ,t) and N(x ,t):  Where  are roots of transcendental equation:
 and DISCUSSIONS We have described the solute transport as the transport in a system with physical non equilibrium with two regions of water with different mobility. Pointed out that models of systems with chemical non equilibrium, i. e. systems that consider sorption on some sites to be governed by first-order kinetics, can be put in the same dimensionless form as models of system with physical non equilibrium (Nkedi-Kizza, et al.,1984 and Van Genuchten and Wagenet, 1989).Therefore, solutions developed in this paper can be applied when the adsorption of the solute occurs in the soil that does not have distinct separated mobile and immobile water. This can be true for some pollutants rather than salts. REFERENCES Bayrakli, F., Mikayilov, F.D. and Mamedov, A.I. (1996). Mathematical modeling of soil salinity. 1st Inter. Conf. on ''Land Degradation '' Proceedings: pp. 1 - 8, 10 - 14 June, ADANA. Ghassemi, F., Jakeman, A. J. and Nix, H. A.(1995). Salinisation of land and water resources: human causes, extent, management and case studies. CAB International, Wallingford, and Oxon Jury W., Gardner W.R., Gardner W.H.(1991). Soil Physics. 5th ed. John Wiley and Sons, NEW YORK Karakaplan, S., Mikayilov, F.D. and Sariyev,A.(1999). Tuzlu Toprakların Islahının Bazı Problemleri. "GAP I. Tarım Kongresi", ŞANLIURFA Cilt: II, s. 1019 - 1026. Lapidus, L. and Amundson, N.R.(1952). A descriptive theory of leaching. Mathematics of adsorption beds. J. Phys. Chem., 56: 984 - 988. Leij, F.J, and N. Toride.(1998). Analytical solutions for non equilibrium transport models. P.117 - 155. In: Physical non equilibrium in soils : modeling and application / edited by H. Magdi Selim, Liwang Ma. Ann Arbor Press, Chelsea, Mich. Mikayilov, F. D. (1989). Modeling of salt transport in soils and grounds in leaching and irrigation conditions. Ph.D. Thesis. Institute of Agrochemistry and Soil Science. BAKU(In Rus.) Mikayilov, F.D. (1997). Studies of the salt transfer processes in the heterogeneous media on the basis of mathematical modeling, Eurasian Soil Science, MOSCOW 11: 1390 - 1395. . Mironenko E.V., and Y. A. Pachepsky.(1984). Analytical solution for chemical transport with non equilibrium mass transfer, adsorption and biological transformation. J.of Hyd., 70:167-175. Nkedi-Kizza, P. J., J. W. Biggar, H. M. Selim, M. T. van Genuchten, P. J. Wierenga, J. M. Davidson, and D. R. Nielsen. (1984). On the equivalence of two conceptual models for describing ion exchange during transport through an aggregated oxisol. Water Resour. Res., 20: 1123-1130. Sardin, M., D. Schweich, F. Leij, and M. Th. van Genuchten. (1991). Modeling the non equilibrium transport of linearly interacting solutes in porous media: a review. Water Resour. Res., 27:2287-2307. Toride, N., F.J. Leij and M.Th. van Genuchten. (1993). A comprehensive set of analytical solutions for non equilibrium solute transport with first-order decay and zero-order production. Water Resour. Res. 29:2167-2182. Van Genuchten, M. Th., and Wagenet, R. J. (1989). Two-site/two-region models for pesticide transport and degradation: Theoretical development and analytical solutions. Soil Sci. Soc. Am. J., 53(5): 1303-1310. Van Genuchten, M. Th., and Alves, W. J. (1982). Analytical solutions of the one dimensional convective dispersive solute transport equation. USDA Tech. Bull. 1661, U.S.Govt. Printing Office, WASHINGTON, DC. Van Genuchten, M. Th., and Dalton, F. N. (1986). Models for simulating solute movement in aggregated field soils. Geoderma, 38:165 183 |