MASS BALANCE CIVL270-Maraqa Objective Develop a mass balance expression under different case scenarios and design a simple system to meet desired needs Conservation of Mass Mass cannot be created nor destroyed Implication Atoms are conserved but molecules may change to other forms CIVL270-Maraqa Types of Reactors • Batch Reactors V • Completely Stirred Tank Reactors (CSTR) Q, Cin Q, Cout V • Plug-Flow Reactors Q Q Q CIVL270-Maraqa Q to t1 t2 Q Q • Dispersed Plug-Flow Reactors Q Q to Q Q t1 Q Q t2 • Packed bed Reactors • Fluidized Packed bed Reactors Q, Cin Q, Cout Q, Cout CIVL270-Maraqa Q, Cin Completely-Mixed Tank Reactor (CSTR) Accumulation Input, Cin System boundary Output, Cout Decay Mass Balance- General Equation Input rate CIVL270-Maraqa = Ouput rate + Decay + rate Accumulation rate Steady-State Conservative System Steady state Conservative Accumulation = Decay = Input = Q C +Q C s s w w rate Ouput = QmCm rate Cs Qs + C w Q w Cm = Qm CIVL270-Maraqa } Input = rate Stream Ouput rate Mixture Qs, Cs CSTR Waste Qw, Cw Qm, Cm Steady-State with Nononservative Pollutants Steady state Accumulation = Nonconservative Input = rate Ouput + Decay rate rate Input QsCs+QwCw rate = Ouput = QmCm rate Decay = kCmV rate Cs Qs + C w Q w Cm = Q m + kV CIVL270-Maraqa Decay rate (1st-order) = kCV = kCmV CSTR Stream V Mixture Qs, Cs k Qm, Cm Waste Qw, Cw Reaction Term Sedimentation Radioactive decay Volatilization Biodegradation Bio uptake Hydrolysis Photodegradation CIVL270-Maraqa Example Stream Qs=5 m3/s Well-mixed lake Cs =10 mg/L V=10x106 m3 Waste k=0.2/day Qw 0.5 m3/s Solution Cw =100mg/L Qm= Qs+ Qw = 5.5 m3/s Cm = Cs Qs + C w Q w Q m + kV mg m mg m3 (10 )(5 ) + (100 )(0.5 ) mg L s L s Cm = = m3 day L (5.5 ) + (0.2 × )(10 × 10 m ) s day 24 × 60 × 60s If there was no reaction in the reactor, Cm will be 18.2 mg/L CIVL270-Maraqa Outgoing Qm=? Cm=? Example Stream Qs=5 m3/s V=5x106 m3 V=5x106 m3 Cs =10 mg/L k=0.2/day Waste Cm1 k=0.2/day Cm2=? Qw 0.5 m3/s Solution Cw =100mg/L Qm= Qs+ Qw = 5.5 m3/s Cm = Cs Qs + C w Q w Q m + kV Cm1=5.86 mg/L Cm1Qm=Cm2Qm+kCmV Cm2 C m1Q m = Q m + kV Cm2=1.9 mg/L CIVL270-Maraqa