Trickling Filter Theories
A. W.  BUSCH,  Professor
Rice University
Houston, Texas
G. A. HUGHMARK, Senior Chemical Engineering Associate
Ethyl Corporation
Baton Rouge, Louisiana
INTRODUCTION
Several models have been proposed to represent the trickling filter used
for the biological treatment of organic-bearing waste. These models represent
two general categories.
The first is a "curve-fitting" type of model that fits the typical overall response of a filter to variables such as BOD loading and filter depth. The Velz (1)
model is an example:
L
■D
10"KD (1)
L      =s removable BOD
Lp   = remaining removable BOD at filter depth D
K     = logarithmic constant of BOD removal for filter
Stack (2) revised this model and proposed that the fraction of BOD that is
consumed in one pass throughone unit depth be used in place of the Velz logarithmic constant. Empirical models of this type are useful in the interpolation of experimental data but must be used with caution for extrapolation.
The second is mechanistic models in which mass transfer and reaction kinetics
are considered as distinct processes. Atkinson, Busch, and Dawkins (3) proposed a
model for film flow on a vertical wall in which the reaction rate controlled and
the concentration gradients of the substrate and oxygen were negligible. Swilley,
Atkinson, Busch, and Williams (4) extended the model to consider dillusional resistance for continuous liquid application and laminar flow of the film on an inclined surface. Experimental data obtained on an inclined plate showed that the
magnitude of the reaction rate for a glucose solution is such that the liquid phase
resistance is significant and can be controlling. The complexity of the model is
greatly increased when mass transfer is included and becomes impractical for
analytic solution of anything other than a laminar film.
The purpose of this paper is to present a model that is applicable to solution
by a digital computer and can be used to represent eddy mixing in the liquid film.
CELL MODEL
The mathematical model selected is the "cell" model. This assumes that
the substrate and oxygen are consumed at the surface of the inclined plate and
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