|
|||||
|
|
Exact analytical solutions for two-dimensional advection-dispersion equation in cylindrical coordinates subject to third-type inlet boundary condition |
|
| Authors: | Jui-Sheng Chen Yiu-Hsuan LiuChing-Ping Liang Chen-Wuing LiuChien-Wen Lin |
| Institution: | a Graduate Institute of Applied Geology, National Central University, Jhongli City, Taoyuan County 32001, Taiwan b Department of Environmental Engineering and Science, Fooyin University, Ta-Liao Dist., Kaohsiung City 83102, Taiwan c Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei 10617, Taiwan |
| Abstract: | Exact analytical solutions for two-dimensional advection-dispersion equation (ADE) in cylindrical coordinates subject to the third-type inlet boundary condition are presented in this study. The finite Hankel transform technique in combination with the Laplace transform method is adopted to solve the two-dimensional ADE in cylindrical coordinates. Solutions are derived for both continuous input and instantaneous slug input. The developed analytical solutions are compared with the solutions for first-type inlet boundary condition to illustrate the influence of the inlet condition on the two-dimensional solute transport in a porous medium system with a radial geometry. Results show significant discrepancies between the breakthrough curves obtained from analytical solutions for the first-type and third-type inlet boundary conditions for large longitudinal dispersion coefficients. The developed solutions conserve the solute mass and are efficient tools for simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment or an in situ infiltration test with a tracer. |
| Keywords: | Advection-dispersion equation Analytical solution Finite Hankel transform Laplace transform Dispersion coefficient Third-type inlet boundary condition |
| 本文献已被 ScienceDirect 等数据库收录！ | |