MODELS FOR OXYGEN TRANSFER: THEIR THEORETICAL BASIS
AND IMPLICATIONS FOR INDUSTRIAL WASTEWATER TREATMENT
Michael K. Stenstrom, Assistant Professor
School of Engineering and Applied Science
University of California
Los Angeles, California 90024
INTRODUCTION
Most models for oxygen transfer are based upon early work by Lewis and Whitman
[ 1 ] who showed that absorption of gases could be expressed as a diffusion process
across two stagnant films. For the special case of sparingly soluble gases and liquids,
such as oxygen in water, the model reduces to a single film transport process. For a
complete mixing oxygen absorption reactor, the Lewis and Whitman model can be
written as follows:
JT = KLa  <CS " C> «
r
where:      K. a    ■   apparent mass transfer coefficient (T )
Co      =   apparent saturation dissolved oxygen concentration (mg/l)
C        =   dissolved oxygen concentration (mg/l)
In developing Equation 1 and its common integrated form, several assumptions are
generally made, including constant transfer coefficient and saturation coefficient with
respect to time. It has been shown by later investigators that neither assumption is valid
for all cases, including applications commonly found in wastewater treatment.
The true mass transfer coefficient, Kj^ varies with the "age" of the liquid-gas interface [2,3]. Also the saturation oxygen concentration is not constant and varies with
hydrostatic head and gas-phase oxygen pressure. This phenomena was noted experimentally as early as 1935 by Ressner and Ribbius [4], The combined effects of the
partially valid assumptions, which were used to develop Equation 1, produce discrepancies between predicted oxygen transfer capability and actual process performance.
Nevertheless, Equation 1 is widely used for measuring and predicting oxygen transfer
and will be used until a more fundamental model can be universally accepted.
The problem of determining and predicting oxygen transfer capability for a wastewater treatment process becomes one of estimating meaningful parameters for Equation
1. Often the parameters for Equation 1 are estimated from clean water non-steady state
testing, and are then applied to field applications through appropriate conversion factors.
The objective of this paper is to show the shortcomings of the commonly used
model, and how these shortcomings affect process performance. The theoretical problems
stem from the steady state assumptions which were used to develop Equation 1. The
inability to precisely and accurately estimate parameters is one practical result of model
imperfections; scale-up problems from test facilities to commercial installations is
another.
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