Determination of Hydro-chemical Parameters of Salt Transportation in Soil by Using the Solution of Convective Diffusion Equation
According to the solution of convective diffusion equation, which defines salt transportation in soils, effectiveness and practical value of calculations depend on hydro-chemical parameters. In this study, mathematical expressions, which enable to find hydro-chemical parameters of salt transportation in soil, were determined based on the solution of convective diffusion equation. In 100 cm depth of saline-sodic soils, hydrochemical dispersion parameter (λ), Peklet parameter (Pe) and soil`s salt loss coefficient (α) have been found to be 1.667, 0.6 and 1.024, consecutively. The values of θ(ξ,η) function, which depends on salt concentration of soil before (C0) and after (Sor) washing (C0) and in washing water (Cy), is calculated. And it is possible to determine λ parameter, Ny- the amount of washing water and the amount of soil in layer, which is washed, by using the calculated values that are mentioned above.
Different mathematical models are used for expression of transportation processes in soil. The empiric (static, observation) models, which are used very often among these models, are derived based on statistical evaluation of results obtained from many observations. Such models consider fundamental factors effecting soil processes in general, not in detail. Generally, the models of such kind make applications that are outside of the experimental conditions very hard by not taking mechanisms of soil processes and cause-result relationship into account (Aydarov, 1985).
Theoretically, it is possible to express the mathematical expression of all factors in researches and processes with ideal or complete models (Pollyak, 1976; Yemelyanov et al., 1978; Pachepsky, 1990). These models enable the research of different factors, processes and relationships between them. The determination of parameters included in ideal (or complete) models necessitates implementation of many experimental studies. Rapid variance of some soil properties and consequently, rapid variance of experimental conditions of model parameters based on time and place makes the control and implementation of ideal (or complete) models practically impossible. Therefore, simplification of these models based on scientific facts enables their application in solution of theoretical and practical subjects (van Genuchten et al., 1977; Shukla et al., 2002; Nobuo et al., 2003).
The calculation of water-salt variance in soil, amount of washing water to be used for soil improvement and timing of its implementation, heat transportation, etc. can be conducted by usage of theoretical (half-empiric) models. These models are derived based on universal laws (mass conservation, thermodynamic equations, similarity and criterion theory, etc.) (van Genuchten and Wagenet, 1989; Mikaiylov and Pachepsky, 2003; Gülser and Ekberli, 2004).
Taking homogeneous structure of soil into account, the mathematical expression
of processes in soil is achievable by application of theoretical (semi-empiric)
models, which necessitate determination of hydro-chemical parameters for different
soils depending on soil properties. The factors, such as climate-soil conditions,
filtration in soil, evaporation, humidity, etc. effect hydro-chemical parameters
significantly. The practical value of application of convective diffusion equations
solution in water-salt variance of soil and its estimation depends on accuracy
of hydro-chemical parameters (Mikaylov and Azizov, 1985; Ekberli and Gülser,
2001). The hydro-chemical parameters comprises many physico-chemical and hydrological
factors, which effect water and salt variance in soil, but arent widely
subject to research. The determination of hydro-chemical parameters in porous
media also depends on limit conditions of convective diffusion equation (Aydarov,
1985; Ellsworth et al., 1996). The analytical expressions of diffusion
and dispersion processes in soil are also related with hydro-chemical parameters
depending on solution of convective diffusion equation (Ellsworth et al.,
1996; Shulka et al., 2003). The hydro-chemical parameters have an obvious
effect on occurrence of salt transportation in soil as a result of water injection
to soil. Depending soil properties, hydro-chemical parameters are determined
in laboratory and arable field experiments with different approaches (Lee et
The objective of this research is determination of analytical expressions used in calculation of some hydro-chemical parameters of soils that are comparatively hard to determine in arable field experiments by using the solution of theoretical (semi-empiric) model and calculation of some hydro-chemical parameters values.
MATERIALS AND METHODS
The application of scientific-technical methods in harmony is essential for the most optimum exploitation of soil fertility. Nowadays, the application of different mathematical models in agriculture is increasing, like in all other areas. The soil improvement depends on realization of soil improvement methods as a result of determination of salt transportation in soil. The quantitative evaluation of salt transportation in soil and its estimation is possible by usage of theoretical (semi-empiric) convective diffusion equations solution, which is based on the equations valid beginning and limit conditions, as well.
The adequacy of derived mathematical model to the values obtained from arable field experiments is highly related with determination of hydro-chemical parameters and their accuracy. The mathematical models for calculation of hydro-chemical parameters based on solution of convective diffusion equation were determined by taking the results of arable field experiment, which are determined easily, into account. In calculation of hydrochemical parameters, the data obtained as a result of research conducted in the saline-sodic soils of the Lower Kızılırmak Plain in Turkey by Sönmez (1990) are used.
RESULTS AND DISCUSSION
In the process of determination of salt regime in soil and usage of mathematical
models, approximately 20 numeric parameters in soil-underground water system
are needed to be determined. Although, parameters, such as filtration coefficient,
porosity level, etc. can be easily determined, the determination of parameters,
such as convective diffusion coefficient, soil transportation in soil, soil
dissolvement coefficient, is very hard and necessitates conduction of special
studies (Anonymous, 1976).
The below equation represents transmission of water, which is poured on soil surface for washing purposes, to lower layers or to drainage and salt dissolvement by that water (Verigin et al., 1979; Mikaiylov, 1997; Mikayilov and Ekberov, 1999; Mikaiylov and Pachepsky, 2003)
In this equation D = Dm + λυ,-convective diffusion coefficient;
Dm-molecular diffusion coefficient; λ-hydrodynamic dispersion
coefficient that expresses internal structure of filtration environment; υ
(t)-filtration speed; γ-dissolvement speed coefficient; Cd-
concentration of solution; C(x,t)-soil concentration on x point of soil during
t time. As the washing time is considered as, ,
Dm≈0 is considered (Verigin et al., 1979).
The numerical and analytical solution of Eq. 1 obtained in different limit and beginning conditions (Brenner, 1962; Polubarinova-Kocina, 1977; Averyanov, 1978; Mikayılov, 1979; Akperov, 1989; Mikaiylov and Pachepsky, 2003), are used for determination of water-salt regime estimation and hydro-chemical parameters.
In case average integral value of salt amount is
and initial salt dispersion is constant (C0(x) = C0 =
constant in R layer of soil, total soil concentration in R layer of soil after
washing is expressed as following (Mikaylov and Azizov,1985; Mikayilov and Ekberov,
1999; Ekberli and Gülser, 2001):
In this equation, Cy-soil concentration of water used for washing;
l= τ/m (τ-amount of water used for washing; m-the level of porosity);
erfc-known Gauss error (integral) function (Likov, 1967). The expression (2)
is obtained as a result of considering equal dispersion of initial saltiness
along soil profile during washing period (Aydarov et al., 1982).
|| Values of θ(ξ,η) function
|| The values justifying η ctg h = h equation for special
values of η
Eq. 2 can be expressed in more simplified way:
The variance of salt concentration in R layer of soil is calculated based on expression (4) by giving values to ξ and η parameters. The obtained results are shown in Table 1. The calculation of hydro-chemical dispersion coefficient is possible, if amount of salt and washing water after washing in soil layer is determined based on Table 1 and values of m, R, Cy, C0, Sor and τ are known.
In the research conducted for improvement of salty-sodium soils of area called as Lower Kızılırmak Plain in Turkey (Sönmez, 1990), for R = 100 cm soil layer, m = 0.49; Cy = 1.5 mmhos/cm; C0 = 19.26 mmhos/cm; Sor = 3.43 mmhos/cm; τ = 270 cm data are obtained.
According to these data and expression (3), the values of θ and ξ are calculated (θ≈0.109, ξ≈5.5). Based on θ and ξ values, η = 0.015 is found by referring to Table 1. The hydro-chemical dispersion parameter will be λ = lm/4x0.150 = 1.667 m by referring to the expression of λ = R/4η .
The Peklet coefficient (Pe), which is considered to have no criterion and is included in solution of water-salt transportation models (Likov,1967; Averyanov, 1978; Mikaylov and Azizov, 1985) , will be calculated as
Pe = 0.6 from the expression of
After determination of λ, m, R, τ, Cy, C0 parameters,
are calculated, θ(ξ*, η*) = θ*
is found by referring to Table 1 and salt concentration in
soil layer is determined based on the expression of Sor = Cy+(C0-Cy)θ*.
In order to reach salt concentration amount (Sivor) that
is acceptable to remain in R layer of soil, parameters of λ, m, R, Cy,
C0 Sivor have to be known for the calculation
of needed water amount -Ny. Taking these values into account θ*
Cy/C0 - Cy and η* = R/4λ
are calculated and ξ* = τ/mR is found by referring to Table
1. Based on obtained values, the amount of washing water is determined as
Ny = mRξ*.
Volobuyev Equation obtained from many number of field experiments is as following:
(α-the level of salt amount that is possible to wash away parameter, which is related to soil structure and soil composition) (FAO/UNESCO, 1973). Theoretically, this expression is obtained from convective diffusion equation as following (Verigin et al.,1986):
In this equation h, ηctg h = h are values justifying transandent equations, whose some special values are shown in Table 2. If the values of m, λ, Cy, C0, RveSt are known, the amount of washing water can be calculated from expression (5), also the α parameter can be found by determining h value complying to η from Table 2.
Based on the calculated η = 0.15 value, h = 0.3779 is found from Table
2. By taking the above values into account; α = [2.303 x 0.49 x 0.15
x 1]/[(0.15)2 + (0.3779)2] ≈ 1.024 is obtained.
The expression (4) enables determination of soil amount in certain layer of soil, calculation of the amount of washing water and λ-hydro-chemical, Pe-Peklet parameters, which are important in modeling of salt regime, based on amount of salt in layer of soil before and after washing process.
The Table 1, which consists of values obtained from the function θ(ξ,η) by using computer, makes the calculation of λ parameter, Ny-amount of water to be used for washing and the soil concentration amount in soil layer that will be washed easier.
The calculation of α-the level of salt amount that is possible to wash away, which is generally related to soil structure and salt composition parameters, can be realized by using the Eq. 5.
1: Akperov, I.A., 1989. Optimization of water-salt regime of arable fields of siyazan-sumgati massive. Ph.D. Thesis, Baku, Azerbaijan.
2: Anonymous, 1976. Modeling and management of water-salt regime of soils. Alma-Ata, Kazakhstan, pp: 188.
3: Averyanov, S.F., 1978. Struggle Against Salinization of Arable Fields. Kolos Publishing House, Moskow, Russia, Pages: 288.
4: Aydarov, I.P., A. Golovanov and M.G. Mamayev, 1982. Soil Improvement Via Washing Method. Kolos Publishing House, Moskow, Russia, pp: 176.
5: Aydarov, I.P., 1985. Management of Water-salt and Nourishment Regimes of Arable Fields. Agropromizdat, Moscow, pp: 304.
6: Brenner, H., 1962. The diffution model longitudinal mixing in beds of finitelength. Chem. Eng. Sci., 17: 229-243.
7: Ekberli, I. and C. Gulser, 2001. Determination of hidrochemical dispersion parameter in irrigated soil. J. Fac. Agric. OMU, 16: 21-26.
8: Ellsworth, T.R., P.J. Shouse, T.H. Skaggs, J.A. Jacobs and J. Fargerlund, 1996. Solute transport in unsaturated soil: Experimental design, parameter estimation and model discrimination. Soil Sci. Soc. Am. J., 60: 397-407.
Direct Link |
9: FAO/UNESCO, 1973. Irrigation, Drainage and Salinity. Hutchinson and Co. Ltd., London.
10: Gulser, C. and I. Ekberli, 2004. A comparison of estimated and measured diurnal soil temperature through a clay soil depth. J. Applied Sci., 4: 418-423.
CrossRef | Direct Link |
11: Lee, J., D.B. Jaynes and R. Horton, 2000. Evaluation of a simple method for estimating solute transport parameters: Laboratory studies. Soil Sci. Soc. Am. J., 64: 492-498.
Direct Link |
12: Likov, A.V., 1967. Theory of Heat Transition. Visshaya Skola, Moskow, Russia, pp: 599.
13: Mikaylov, F.D., 1979. Implementation of analytical methods for the solution of issues regarding water-salt regime of underground waters in arable fields. Rep. Sci. Acad. Azerbaijan SSR, 35: 76-81.
14: Mikaylov, F.D. and K.Z. Azizov, 1985. Determination of the hydrochemical parameter of dispersion by salts transfer in the course of washing of saline water-saturated soils. Eurasian Soil Sci., 5: 84-90.
15: Mikaiylov, F.D., 1997. Studies of the salt transfer processes in the heterogeneous media on the basis of mathematical modeling. Eurasian Soil Sci., 11: 1390-1395.
16: Mikayilov, F.D. and A. Ekberov, 1999. Analytical analysis of mass transporation in heteregenous media. Proceedings of 1st Turkish World Mathematics Semposium, June 29-July 29, 1999, Turkey, pp: 163-163.
17: Mikaiylov, F.D. and A.Y. Pachepsky, 2003. Analytical solution of the equation of the nonequilibrium solute transport in soil with dual porosity. Eurasian Soil Sci., 4: 441-450.
18: Nobuo, T., I. Mitsuhiro and J.L. Feike, 2003. Hydrodynamic dispersion in an unsaturated dune sand. Soil Sci. Soc. Am. J., 67: 703-712.
Direct Link |
19: Pachepsky, Y.A., 1990. Mathematical Models of Physico-chemical Processes in Soils. Nauka, Moskow, Russia, pp: 188.
20: Pollyak, Y.G., 1976. The issues of computer modelling theories during research of system reliability. Izvestiya of the USSR academy of sciences. Power Manage. Transport, 2: 81-97.
21: Polubarinova-Kocina, P.Y.A., 1977. Theory of Movement of Underground Waters. Nauka, Moskow, Russia, pp: 664.
22: Shukla, M.K., F.J. Kastanek and D.R. Nielsen, 2002. Inspectional analysis of convective-dispersion equation and application on measured breakthrough curves. Soil Sci. Soc. Am. J., 66: 1087-1094.
Direct Link |
23: Shukla, M.K., T.R. Ellsworth, R.J. Hudson and D.R. Nielsen, 2003. Effect of water flux on solute velocity and dispersion. Soil Sci. Soc. Am. J., 67: 449-457.
Direct Link |
24: Sonmez, B., 1990. Determination of the Amount of Gypsum, Leaching Water and Leaching Duration for Reclamation of the Saline-Sodic Soils of the Lower Plain. The Institute of Soil and Fertilizer, General Publication, Ankara, pp: 33.
25: Van Genuchten, M.T.H., P.J. Wierenga and G.A. O`Conner, 1977. Mass transfer studies in sorbing porous media: III. Experimental evaluation with 2,4,5-T. Soil Sci. Soc. Am. J., 41: 278-285.
Direct Link |
26: Van Genuchten, M.T.H. and R.J. Wagenet, 1989. Two-site /two-region models for pesticide transport and degradation: Theoretical development and analytical solutions. Soil Sci. Soc. Am. J., 53: 1303-1310.
Direct Link |
27: Verigin, N.N., S.V. Vasilyev and N.P. Kuranov, 1979. Methods of Forecasting Salt Regime of Undergrounds and Underground Waters. Kolos Publishing House, Moskow, Russia, pp: 336.
28: Verigin, N.N., K.Z. Azizov and F.D. Mikaylov, 1986. On the impact of boundary conditions in simulation experiments on salts transfer in soils during washing. Eurasian Soil Sci., 6: 67-73.
29: Yemelyanov, S.V., V.V. Kalashnikov, V.I. Lutkov and B.V. Nemcinov, 1978. Methodological Issues of Construction of Imitative Systems. The Soviet Research Institute of Construction, Moscow, Russia, pp: 83.