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To model the two phase system, we accounted for substrate mass balance in both phases, the kinetic equation (reported above) and the substrate transfer (see Figure 2). Table 3 reports the model equations for both SBR and TPPB reactors.

Table 3

Balance equations for single phase and two phase reactors

Substrate mass balanceReactor type
 TPPB (water phase) 
 TPPB (organic phase) 
 SBR 
Biomass mass balanceReactor type
with  TPPB, SBR 
Oxygen mass balanceReactor type
 TPPB, SBR 
Substrate mass balanceReactor type
 TPPB (water phase) 
 TPPB (organic phase) 
 SBR 
Biomass mass balanceReactor type
with  TPPB, SBR 
Oxygen mass balanceReactor type
 TPPB, SBR 

Vw = aqueous phase volume; Vorg = organic phase volume; C = substrate concentration; CO2 = oxygen concentration in the aqueous phase; C*O2 = oxygen concentration in equilibrium with gas bulk phase; Kws = substrate mass transfer coefficient; a = specific surface area referring to the aqueous phase; P = partition coefficient; rS = substrate degradation rate; rO2 = oxygen uptake rate; rX = biomass growth rate; Y = biomass yield coefficient; b = endogenous respiration constant; KO2 = oxygen mass transfer coefficient.

Subscripts: w = aqueous phase; org = organic phase.

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