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Effects of Column Conditions on the First‐Order Rate Modeling of Nonequilibrium Solute Breakthrough
Author(s) -
Young Dirk F.,
Ball William P.
Publication year - 1995
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/95wr01612
Subject(s) - dimensionless quantity , diffusion , mass transfer , thermodynamics , mechanics , non equilibrium thermodynamics , sorption , range (aeronautics) , constant (computer programming) , fick's laws of diffusion , pulse (music) , column (typography) , magnitude (astronomy) , statistical physics , mathematics , chemistry , materials science , physics , geometry , computer science , adsorption , connection (principal bundle) , astronomy , detector , optics , composite material , programming language
First‐order mass transfer models are commonly used as a means of interpreting sorption‐related mass transfer in laboratory columns, often with the intent of approximating diffusion‐based processes. We have fitted first‐order model parameters to computer‐simulated breakthrough curves from hypothetical column experiments in which Fickian diffusion into spherical particles limited the rate of sorption and desorption. Using both step and pulse inputs, we show that the fitted first‐order coefficient is a function not only of the intrinsic diffusion rate, but also of the column length, the step experiment's duration, the input pulse width, the fluid velocity, and the solute retardation factor. For a range of typical column run conditions and a given diffusion rate, we show that the fitted first‐order coefficient varies over three orders of magnitude in a manner roughly predictable through proper definition of a dimensionless timescale. In general, step inputs (as opposed to pulse inputs) provide a more consistent and predictable relationship between fitted coefficients and underlying diffusion rates. For either type of input, we recommend cautious use of the first‐order model, since many observed variations in fitted rate constants are not the result of mechanistic phenomena.