where ISOinf. is isotopic ratio of the influent sludge; ISObio.B. is isotopic ratio of the biofilm in the BF; ISOeff.B.is isotopic ratio of the effluent sludge in the BF; Pinf./eff.B. is contribution ratio of the influent sludge to the effluent sludge of the BF; Pbio.B./eff.B. is contribution ratio of the biofilm to the effluent sludge of the BF.