Beijing Air Pollution Forces 20 Million People Indoors Mass Balance 4 1 textbook 1 2 Consider NOx and air mass accumulation rate mass input rate mass output rate mass accumulation rate dm VdC dt dt dm d VC dC V dt dt dt dC dm 0 or 0 dt dt mass accumulation rate steady state input rate Qin Cin output rate Qout Cout input rate Qin Cin output rate Qout Cout 3 4 reactor types to be considered 4 4 reactor types to be considered 1 Batch non flow reactor with reacting pollutants 2 Steady state completely mixed flow reactor CMFR with conservative or non reacting pollutant 3 Steady state completely mixed flow reactor CMFR with non conservative or reacting pollutant 1 Batch non flow reactor with reacting pollutants 5 6 http www dcwater com drinking water about cfm 1 4 reactor types to be considered 1 Batch non flow reactor with reacting pollutants 2 Steady state completely mixed flow reactor CMFR with conservative or non reacting pollutant 3 Steady state completely mixed flow reactor CMFR with non conservative or reacting pollutant 4 Plug flow systems A contaminant is released to a room at a constant rate What is the unit of the released rate A kg m3 B kg C kg day D None of the above 7 8 http www dcwater com drinking water about cfm Type 1 Batch system with nonconservative pollutants Steps in mass balance problems 1 Draw a schematic diagram of the situation 2 Identify the control volume and all influent and effluent flows 3 Mass accumulation rate rate in rate out rate of generation 4 Determine if the problem is steady state 5 Determine if the compound is conservative or reacting 6 Replace the rates with known values 7 Solve the problem 9 V Batch system means no flow i e IN OUT 0 The mass balance equation becomes Mass accumulation rate rate of generation rate of decay dC VkC dt dC If decay follows zero order kinetics V Vk dt If decay follows first order kinetics V 10 Bacterial growth in a closed water storage dC VkC dt dC kC dt dC kCdt t dC C 0 C 0 kdt C ln C C0 kt C Co e kt 11 Given Closed container of volume V Bacterial growth follows first order reaction rate kC The initial concentration is C0 Question Bacterial concentration after time t A C C0exp kt B C C0exp kt C C C0 kt D C C0 kt E None of the above 12 2 A Solution Mass accumulation rate rate in rate out rate of generation Not steady state so Mass accumulation rate 0 Non conservative pollutants rate of generation kC Batch reactor means rate in rate out 0 What we have is Mass accumulation rate rate of generation V dC VkC dt Which graph A or B represents the concentration of a substance reacting in a batch system with zero order kinetics B ln C C0 kt C Co e kt 13 14 One Box Model without Flow for Atmosphere The chlorofluorocarbon CFC 12 CF2Cl2 is removed from the atmosphere solely by first order chemical reaction with reaction rate constant of 0 01 year 1 In the early 1980s before the Montreal protocol began controlling production of CFCs because of their effects on the ozone layer the mean atmospheric concentration of CFC 12 was 400 pptv and increased at the rate of 4 yr 1 What was the CFC 12 emission rate during that period number of molecules of air in the atmosphere 1 8 x 1020 molecular weight of CFC17 12 118 g mole Which of the following is the mass balance dm E dt dm 2 E km dt dm 3 E km dt dm 4 km dt 5 None of the above m mass of CFC in the atmosphere E emission rate k decay rate 1 18 Atmosphere Known parameters k decay rate 0 01 yr 1 1 dm 1 accumulation rate in unit time 1 0 04 yr m dt m concentration of CFC 400 pptv Mass accumulation rate rate in rate out rate of generation rate of decay dm dt dm dt dm E km dt dmemission dmdecay dt dt E total number of moles of air 1 8 1020 number of moles of CFC 400 10 12 1 8 1020 720 108 moles VCk m 720 108 moles 118 g moles 8 5 1012 g 19 dm E km dt E dm km dt 20 3 E Type 1 Batch system with nonconservative pollutants dm km dt dm 1 E m k 8 5 1012 g 0 04 yr 1 0 01yr 1 dt m Batch system means no flow i e IN OUT 0 The mass balance equation becomes Mass accumulation rate rate of generation rate of decay 0 04 0 04 0 01 12 g E 8 5 1012 g 0 425 10 yr yr yr dC VCk dt dC If decay follows zero order kinetics V Vk dt If decay follows first order kinetics V 21 Type 2 Steady state CompletelyMixed Flow Reactor CMFR with conservative pollutants 22 Mississippi River 23 24 Two streams contaminated with Cryptosporidium oocysts from sewage and animal runoff Two polluted streams Cs 20 oocysts L Qs 10 m3 s Cs 20 oocyst L Cw 40 oocysts L Qw 5 m3 s Cm oocysts L Qm m3 s Cw 40 oocyst L 25 Question Flow rate and oocyst concentration downstream 26 4 Steps in mass balance problems 1 Draw a schematic diagram of the situation 2 Identify the control volume and all influent and effluent flows 3 Mass accumulation rate rate in rate out rate of generation 4 Determine if the problem is steady state 5 Determine if the compound is conservative 6 Replace the rates with known values 7 Solve the problem 27 What is the oocyst concentration downstream A B C D Cm 26 7 oocysts L Cm 400 oocyst L Cm 4 oocyst L None of the above 29 Poorly treated municipal wastewater is discharged to a stream The river flow rate upstream of the discharge point is Qu 8 7 m3 s The discharge occurs at a flow of Qd 0 9 m3 s Concentration of a conservative pollutant is 50 0 mg L Assuming that the upstream concentration of that pollutant is negligible a What is the pollutant concentration just downstream of the discharge point Let s summarize the problem and define a system Mass accumulation rate rate in rate out rate of generation Because this is a steady state problem mass accumulation rate 0 Because the pollutant is conservative rate of generation 0 Input rate output rate What is the flow rate A Flow rate 5 m3 s B Flow rate 50 m3 s C Flow rate 15 m3 s D None of the above Let s summarize the problem and define a system Mass accumulation rate rate in rate out rate of generation Because this is a steady state problem mass accumulation rate 0 Because the pollutant is conservative rate of generation 0 Input rate output rate Input rate CsQs CwQw 20 oocyst L x 10 m3 s …