**3. Conclusions**

382 Mass Transfer - Advanced Aspects

solids mass (first row, second column), and the COD mass (third row, first column) in the effluent are set to match the plant operating characteristics (and also effluent regulatory requirements, 5 mg/L solids and 3 mg/L COD). The volume, solids mass, and the COD mass for the sludge recycle are calculated by subtracting the effluent values from the

(1 ,1 )

= − (3 ,1 ) *Effluent rdRow stColumn*

(1 ,2 )

0

,Re , . , 2 , sin , , 2

*Solids cycle Solids Leaving Clarifier Solids Effluent COD StartASba COD Leaving Clarifier COD*

= −

*Q Q Q stRow stColumn*

*Mass Mass Mass*

0

*Mass Mass Mass stRow ndColumn*

As with separation after the primary clarifier, the transport of drug compound is modeled to mirror the transport of the phase containing the drug compound (i.e. inter-phase flux, or *j*, is assumed to not be significant owing to equilibrium conditions). If 66% of the aqueous phase goes into the effluent stream (first row, first column, Effluent), then 66% of the drug mass present in the aqueous phase leaving the secondary clarifier will go into the effluent stream (second row, second column, Effluent). The drug masses in the sludge recycle stream are the calculated by subtracting the effluent masses from the masses leaving the secondary

After separation following the secondary clarifier, the next modeled process is the sludge recycle stream. As mentioned above, the values for the aqueous volume (first row, first column), the solids mass (first row, second column), the mass of COD (third row, first column), the aqueous drug mass (second row, second column), and the sorbed drug mass (third row, second column) for the recycle stream are calculated by subtracting the effluent values from the values leaving the secondary clarifier. The recycle stream is then split into two separate streams, the return activated sludge (RAS), which is pumped back to the beginning of the activated sludge basins, and the waste activated sludge (WAS), which is merged with the primary sludge stream and pumped to the anaerobic digesters (not modeled here). In this case, the treatment plant's operating characteristics define the separation between these two streams, specifically, the RAS is 95% of the recycle stream, whereas the WAS is 5% of the stream. Both the aqueous phase (first row, first column) and the solids phase (first row, second column) are split proportionately with 95% moving to the RAS and 5% moving to the WAS. Additionally, the COD mass dissolved in the aqueous phase (third row, first column) and the drug mass in the aqueous phase (second row, second column) are split proportionately to the phase (95% to RAS, 5% to WAS), as is the mass of

The final component of the model is the iterative step that is part of the RAS stream. This two-step process was necessary to eliminate circular calculation errors that arise due to the recycle stream which otherwise would have produced an indeterminate system. This error can be highlighted by looking at just the aqueous phase drug mass. The mass at Start A.S. Basin is calculated from the mass leaving the primary clarifier and the mass in the RAS stream. The mass at Start A.S. EQM is calculated from the mass at Start A.S. Basin. The mass at Leaving A.S. Basin is calculated from the mass at Start A.S. Basin. The mass Leaving 2° Clarifier is calculated from the mass at Leaving A.S. Basin. The mass at Recycle is calculated from the Effluent and the mass at Leaving 2° Clarifier. Finally, the mass in the RAS stream is

secondary clarifier values:

clarifier.

**2.2.6 Sludge recycle** 

0

= −

Re 2 .

*cycle Leaving Clarifier Effluent*

drug in the sorbed phase (third row, second column).

Modeling the simultaneous sorption and biodegradation in wastewater systems has proven to be a challenging problem for researchers. Because the two processes are intrinsically linked, a novel approach was needed to develop a comprehensive mathematical expression to be used in modelling analyses. To that end, the volume averaging methodology commonly employed in groundwater systems was used with one key difference: rather than the having the solid phase be stationary, it was mobile. This paradigm shift allowed for fate and transport modelling throughout a wastewater treatment plant. This new model is sufficiently robust that it can have applications with many different types of compounds in different treatment plants with varying operational characteristics.
