Approximate analytical model for high-order power function of solute transport in soil
Wei Feng1,2, Wang Quanjiu1, Zhou Beibei1
1. Institute of Water Resource, Xi′an University of Technology, Xi′an, Shaanxi 710048, China; 2. School of Science, Xi′an University of Technology, Xi′an, Shaanxi 710048, China
Abstract：To simulate the soil solute transport and estimate the transport parameters with a simple analytical model, an approximate six-power function model for describing the distribution of solute concentration was developed based on six-power function concentration profile assumed and the extended boundary layer theory describing the soil solute transport. The solute concentration profiles predicted by using the model proposed with different power indexes were compared and analyzed at two time instances(t=360, 720 min)and a long distance(120-450 cm). The simulated results showed that the solution of six-power function method is more close to the exact solution compared with other power models when the pore water velocity is 0.01 cm/min at a short time experienced(t=360 min)in a long traveling distance(x>50 cm). More computations indicated that the small pore water velocity(v≤0.01 cm/min)has little effect on the boundary layer distance. In that case, a series of error analysis on the transport parameters estimated with different boundary layer distance formulas were also carried out. The results indicated that the transport parameters such as diffusion coefficient and delay factor in the solute convection-dispersion equation can be decided precisely by using the boundary layer distance predicted with six-power function model based on measured results by means of instrument with higher sensitivity.
魏峰,, 王全九, 周蓓蓓. 土壤溶质迁移的高次幂函数近似解析模型[J]. 排灌机械工程学报, 2013, 31(7): 617-622.
Wei Feng,, Wang Quanjiu, Zhou Beibei. Approximate analytical model for high-order power function of solute transport in soil. Journal of Drainage and Irrigation Machinery Engin, 2013, 31(7): 617-622.
[1]Walter M T, Gao B, Parlange J Y. Modeling soil solute release into runoff with infiltration[J]. Journal of Hydrology, 2007, 347(3/4): 430-437.[2]Florido A, Valderrama C, Arévalo J A, et al. Application of two sites non-equilibrium sorption model for the removal of Cu(II)onto grape stalk wastes in a fixed-bed column[J]. Chemical Engineering Journal, 2010, 156(2): 298-304.[3]Coppola A, Comegna A, Dragonetti G, et al. Solute transport scales in an unsaturated stony soil [J]. Advances in Water Resources, 2011, 34(6): 747-759.[4]Wang Quanjiu, Horton R, Lee J. A simple model relating soil water characteristic curve and solution breakthrough curve[J]. Soil Science, 2002, 167(7): 436-443.[5]Shao M, Horton R, Miller R K. An approximate solution to the convection-dispersion equation of solute transport in soil [J]. Soil Science, 1998, 163(5): 339-345.[6]Wang Quanjiu, Horton R. Boundary layer theory description of solute transport in soil [J].Soil Science, 2007, 172(11): 835-841.[7]Ziskind G, Shmueli H, Gitis V. An analytical solution of the convection-dispersion-reaction equation for a finite region with a pulse boundary condition [J]. Chemical Engineering Journal, 2011, 167(1): 403-408.[8]Sharma P K, Srivastav R. Numerical analysis of virus transport through heterogeneous porous media[J]. Journal of Hydro-Environment Research, 2011, 5(2): 93-99. [9]Kool J B, Parker J C, Van Genuchten M T. Parameter estimation for unsaturated flow and transport model—A review [J]. Journal of Hydrology, 1987, 91(3/4): 255-293.[10]刘春平, 夏卫生, 邵明安,等. 多孔介质中溶质运移参数拟线性化估计方法[J]. 水利学报, 2005, 36(12): 1445-1449. Liu Chunping, Xia Weisheng, Shao Ming′an. Quasi-linear method of parameter estimation for solute transport in porous [J]. Journal of Hydraulic Engineering, 2005, 36(12): 1445-1449.(in Chinese)[11]郑纪勇, 邵明安. 应用边界层方法确定溶质迁移参数的实验研究[J]. 水利学报, 2002, 33(1): 92-96. Zheng Jiyong, Shao Ming′an. Experimental study on the application of boundary layer theory method to the estimation of soil solute transport parameters[J]. Journal of Hydraulic Engineering, 2002, 33(1): 92-96.(in Chinese)[12]Lindstrom F T, Haque R, Freed V H, et al. Theory on the movement of some herbicides in soil: Linear diffusion and convection of chemicals in soil [J]. Environmental Science and Technology, 1967, 1(7): 561-565.[13]Lee J, Horton R, Jaynes D B. A time domain reflecto-metry method to measure immobile water content and mass exchange coefficient[J]. Soil Science Society of America Journal, 2000, 64(6): 1911-1917.[14]Staub M J, Laurenta J P, Gourc J P, et al. Applicability of time domain reflectometry water content measurements in municipal solid waste soil[J]. Vadose Zone Journal,2010, 9(1): 160-171.
