Application of Fractional Differential Equations in Analysis of Seepage Line in Coarse Porous Media

Document Type : Research Paper


1 Department of Irrigation and Reclamation Engineering, Faculty of Agricultural Engineering and Technology, University College of Agriculture and Natural Resources, University of Tehran, P. O. Box 4111, Karaj, 31587-77871, Iran.

2 Associate Professor, Department of Irrigation and Reclamation Engineering, University College of Agriculture and Natural Resources, University of Tehran, P. O. Box 4111, Karaj, 31587-77871, Iran

3 Associate Professor, Soil Science Department, College of Agriculture, Yasouj University, P.O.BOX: 353, Yasouj, 75918-74831, Iran.


In this study, the fractional-order differential equations in range of (0,1) were used to model the water surface profile under Darcy's law condition in porous medium for a fully developed turbulent flow. The developed equation is solved analytically. The laboratory model used in this study consists of a coarse-grained porous medium with 6.4 m length, 0.8 m width and 1 m height, including rounded corner materials, which are tested for different flow rates and three longitudinal slopes of 0, 4, 20.3%. Then, parameters of model and porous media were calibrated based on laboratory data. In order to evaluate the proposed analytical solution, the obtained results from fractional-order differential model were compared with the laboratory data. The results showed a satisfactory agreement with experimental data of water surface profile (seepage line) in all three slopes. The maximum error of the proposed model is 3.5% compared to the experimental data. It can be concluded that the proposed method can provide better description of water surface profile analysis under non-Darcy flow conditions as compared to Darcy model in porous media.


Main Subjects

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