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A Simplified Dimensionless Model of the Passive Diffusion of Gases and Solutes in Groundwater Through Polymer Tubing
Author(s) -
Dubé JeanSébastien,
Boudreault JeanPhilippe
Publication year - 2011
Publication title -
groundwater monitoring and remediation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.677
H-Index - 47
eISSN - 1745-6592
pISSN - 1069-3629
DOI - 10.1111/j.1745-6592.2011.01351.x
Subject(s) - dimensionless quantity , groundwater , laplace transform , diffusion , aquifer , sparging , dissolution , ordinary differential equation , mechanics , environmental science , thermodynamics , chemistry , differential equation , mathematics , geology , geotechnical engineering , physics , mathematical analysis
The dissolution of gases, such as oxygen, in groundwater is a means to provide electron acceptors required for the biological degradation of organic contaminants in aquifers. The use of polymeric emitters for passive gas diffusion in groundwater significantly increases the efficiency of oxygen transfer to the groundwater compared to conventional sparging. A critical parameter for the design of polymeric emitters is the diffusion coefficient ( D ) of the polymer tubing used to construct the emitters. Wilson and Mackay (1995) proposed a mathematical model (WM model) for the analysis of laboratory passive diffusion experiments aimed at characterizing D . Their analytical solution is obtained in Laplace space and its inversion requires the use of a numerical approximation technique. This article proposes an alternative to the WM model by simplifying it as a dimensionless ordinary differential equation (ODE) which is solved using simple integration. The validity of the dimensionless solution is discussed and the latter plotted into charts to provide easy‐to‐use analytical tools applicable to gas or solute diffusion in groundwater.