An analytical solution to multi-component NAPL dissolution equations

Scott K. Hansen, Bernard H. Kueper

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


This note presents a novel method for determining the changing composition of a multi-component NAPL body dissolving into moving groundwater, and the consequent changes in the aqueous phase solute concentrations in the surrounding pore water. A canonical system of coupled non-linear governing equations is derived which is suitable for representation of both pooled and residual configurations, and this is solved. Whereas previous authors have handled such problems numerically, it is shown that these governing equations succumb to analytical solution. By a suitable substitution, the equations become decoupled, and the problem collapses to a single first-order equation. The final result is expressed implicitly, with time as a function of the number of moles of the least soluble component, m1. The number of moles of each other component is expressed explicitly in terms of m1. It is shown that the time-m1 relationship has a well behaved inverse. An example is given in which the analytic solution is verified against traditional finite difference analysis, and its computational efficiency is shown.

Original languageEnglish
Pages (from-to)382-388
Number of pages7
JournalAdvances in Water Resources
Issue number3
StatePublished - 1 Mar 2007
Externally publishedYes


  • Analytical solution
  • Dissolution
  • Multi-component
  • NAPL
  • Raoult's Law
  • Solubility

ASJC Scopus subject areas

  • Water Science and Technology


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