Analytical solutions of the one-dimensional advection-dispersion solute transport equation subject to time-dependent boundary conditions

作者：Perez Guerrero J S; Pontedeiro E M; van Genuchten M Th; Skaggs T H^*

来源：Chemical Engineering Journal, 2013, 221: 487-491.

DOI：10.1016/j.cej.2013.01.095

• Duhamel theorem
• Analytical solution
• Advection-dispersion equation
• Solute transport

Analytical solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subject to transient (time-dependent) boundary conditions. Generalized analytical formulas are established which relate the exact solutions to corresponding time-independent auxiliary solutions. Explicit analytical expressions were developed for the instantaneous pulse problem formulated from the generalized Dirac delta function for situations with first-type or third-type inlet boundary conditions of both finite and semi-infinite domains. The developed generalized equations were evaluated computationally against other specific solutions available from the literature. Results showed the consistency of our expressions.

• 出版日期2013-4-1