Modeling the Integration of Adsorption with Biological Processes in Wastewater Treatment - Activated Carbon for Water and Wastewater Treatment - page 167

Table 6.1 Main dimensionless groups characterizing GAC adsorbers with biological activity
(BAC reactors).

Dimensionless group Physical meaning Relevant point

Rate of liquid film transport
Rate of biofilmdiffusive transport

Sherwood number, Sh Node 2: Basic analysis at

liquid film-biofilm
boundary

Contaminant at the adsorbent surface
Contaminant in the liquid phase

Solute distribution
parameter, D g

Node 3: Basic analysis
around a carbon particle in
the absence of biofilm

Rate of biofilmdifusive transport
Rate of surface diffusion in the particle

Modified Biot number,
Bi s '

Node 3: Basic analysis at the
biofilm-carbon boundary

Rate of advective transport
Rate of transport by axial dispersion

Peclet Number, Pe Reactor analysis

Rate of liquid film transport
Rate of advective transport

Stanton number (St)
or modified Stanton
number (St*)

Reactor analysis

Rate of surface biological reaction
Rate of advective transport

Damk¨hler number
Type I, Da I

Reactor analysis

Rate of surface biological reaction
Rate of liquid film transport

Damk¨hler number
Type II, Da II

Node 2: Basic analysis at
liquid film-biofilm
boundary

or

Rate of surface biological reaction
Rate of biofilmdiffusive transport

Biofilm analysis

this table, Table 6.2 presents typical values of key parameters that can be used for
estimating dimensionless numbers for experimenting andmodeling of BAC reactors.
The Peclet number (Pe) given by Eq. (6.61) shows the relative importance of
advective transport with respect to axial dispersion. In reality, in all environmental
systems such as the one shown in Figure 6.3 there is some degree of dispersion. In
the limiting cases when Pe - 0(D - N , very high dispersion) the reactor has a

completely-mixed regime and when Pe - N

(D - 0, no dispersion) it behaves as
a plug flow reactor. If the L B v i term is much larger than the dispersion coefficient
D, as in the case of high filter velocities, the dispersion term can be neglected.
Knowing the maximum adsorption capacity q 0 which is in equilibrium with the
influent concentration S 0 , and the parameters related to carbon bed, one can
estimate the solute parameter D g in Eq. (6.64). A higher D g shifts the adsorption
equilibrium toward the solid phase and thus retards breakthrough.