TY - JOUR
T1 - An analytical solution for one-dimensional advective–dispersive solute equation in multilayered finite porous media
AU - Shen, Xiaolong
AU - Reible, Danny
N1 - Publisher Copyright:
© 2015, Springer Science+Business Media Dordrecht.
PY - 2015/4
Y1 - 2015/4
N2 - A general analytical solution for the one-dimensional advective–dispersive–reactive solute transport equation in multilayered porous media is presented. The model allows an arbitrary number of layers, parameter values, and initial concentration distributions. The separation of variables technique was employed to derive the analytical solution. Hyperbolic eigenfunctions, as well as traditional trigonometric eigenfunctions, were found to contribute an important part to the series solution and were not included in some existing solutions. The closed-form analytical solution was verified against a numerical solution from a finite difference-based approach and an existing solution derived from general integral transform technique (GITT). The solution has several important advantages over the GITT technique and other existing solutions. The limitations of existing solutions and the ability of the current solution to address those limitations are identified. Among other applications, the current analytical solution will be useful for modeling the transport of contaminants in sediments and, particularly for the design of layered caps as a remedial approach. The analytical solution also has significant advantages over numerical solutions for sensitivity analyses and the solution of inverse problems.
AB - A general analytical solution for the one-dimensional advective–dispersive–reactive solute transport equation in multilayered porous media is presented. The model allows an arbitrary number of layers, parameter values, and initial concentration distributions. The separation of variables technique was employed to derive the analytical solution. Hyperbolic eigenfunctions, as well as traditional trigonometric eigenfunctions, were found to contribute an important part to the series solution and were not included in some existing solutions. The closed-form analytical solution was verified against a numerical solution from a finite difference-based approach and an existing solution derived from general integral transform technique (GITT). The solution has several important advantages over the GITT technique and other existing solutions. The limitations of existing solutions and the ability of the current solution to address those limitations are identified. Among other applications, the current analytical solution will be useful for modeling the transport of contaminants in sediments and, particularly for the design of layered caps as a remedial approach. The analytical solution also has significant advantages over numerical solutions for sensitivity analyses and the solution of inverse problems.
KW - Analytical solution
KW - Hyperbolic eigenfunction
KW - Multilayer porous media
KW - Solute transport
UR - http://www.scopus.com/inward/record.url?scp=84925485318&partnerID=8YFLogxK
U2 - 10.1007/s11242-015-0460-6
DO - 10.1007/s11242-015-0460-6
M3 - Article
AN - SCOPUS:84925485318
SN - 0169-3913
VL - 107
SP - 657
EP - 666
JO - Transport in Porous Media
JF - Transport in Porous Media
IS - 3
ER -