NAME GROUP CEE 330 Spring 2015 Exam 1 Write legibly if you want to receive all deserving points Closed book closed notes no cheat sheets nothing from class or book stored on calculators List of relevant formulas and equations is given Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 20 16 20 30 10 4 Question 1 20 points Poorly treated municipal wastewater is discharged into a lake The incoming river flow rate is Qin 10 m3 hr The discharge from the wastewater plant into the lake occurs at a flow of Qd 1 m3 hr The concentration of a pollutant i e BOD in the discharge flow that is decaying with first order kinetics is 100 mg L The lake has a volume of 100 m3 BOD is removed with a first order decay rate constant equal to 0 20 day The concentration of the pollutant BOD in the incoming river is 10 mg L a What would the BOD concentration be in the lake at steady state b The wastewater treatment plant is just upgraded and the pollutant concentration in the discharge is now just 5 mg L Find the BOD concentration in the lake at the new steady state Solution a VdC dt C1Qd C2Qin QoutC kCV When steady state VdC dt 0 Qout Qd Qin C C1Qd C2Qin kV Qd Q2 C1 100 mg L 105 mg m3 Qd 1 m3 hr 24 m3 day C2 10 mg L 104 mg m3 Qin 10 m3 hr 240 m3 day k 0 20 day V 100 m3 C at steady state 16 9 mg L b C C1Qd C2Qin kV Qd Q2 C1 5 mg L 5 103 mg m3 Qd 1 m3 hr 24 m3 day C2 10 mg L 104 mg m3 Qin 10 m3 hr 240 m3 hr k 0 20 day V 100 m3 C at steady state 8 87 mg L 1 Question 2 16 points A non reacting solvent is released at a room at a constant rate of 0 1 kg h The maximum permissible concentration of this solvent in air under occupational safety and health regulation is 0 1 mg m3 The air in the room is well mixed a Find the ventilation flow rate m3 hr of uncontaminated air into the room required to meet the regulation at steady state Make all necessary assumptions 6 points b The solvent source was found and eliminated How long does it take for the solvent concentration in the room to be reduced by half at the same ventilation flow rate found in part a The volume of the room is 100m3 10 points Solution a Assume well mixed Mass accumulation rate rate in rate out rate of generation destroy dC V CinQin CsolvQsolv Cout Qout dt dC Assume steady state mass accumulation rate V 0 dt Also assume that Qin Qout Qventilation and this is a lot lager than Qsol Correct mass balance equation 3 points b Well mixed room C Cout 0 CinQin CsolvQsolv Cout Qout CsolvQsolv Cout Qout C Cout Csolv Qsolv mg 0 1 3 Qout m mg Csolv Qsolv 0 1 3 Qout m C Q 0 1kg hr Qout solv solv 106 m3 hr mg mg kg 0 1 3 0 1 3 6 m m 10 mg b When the source is eliminated the mass balance is simplified to VdC dt QoutC The initial condition is C C0 0 1 mg L at t 0 Ln C C0 Q V t When C 0 5C0 t ln 0 5 100 m3 106 m3 hr 3600 sec hr 0 2484 sec 2 Question 3 20 points 20 of the energy produced from a nuclear power plant is converted to 1000 MW of electrical energy The remaining 80 of the energy from this plant is converted to heat waste 10 of the heat waste is released out of the smoke stack 80 of the heat waste is taken away by cooling water that is drawn from a nearby river Specific heat of water 4 184 kJ kg C a How much of the heat waste is taken away by the cooling water MW b How fast does the cooling water need to be pumped to remove this heat from part a so that the temperature of the cooling water only increases by 10 C The density of water is 1000kg m3 Solution a the total energy produced by the plant 1000 MW 0 2 5000 MW of nuclear energy Energy loss 5000 1000 4000 MW 5 points Energy goes to cooling water 4000 0 8 3200 MW 5 points b The rate of change in internal energy for the cooling water m C T m is the mass flow rate of cooling water E in E out 3200MW E in m c T E in 3200MW m 76 48 103 kg s 6 c T 4184 J kg C 10 C 1MW 10 J s Mass flow rate m can be converted to flow rate 5 points for correct m 2 points if correct equation is used m kg s 76 48 103 kg s Q 76 48m3 s 3 3 kg m 1000kg m 5 points for correct Q 2 points if correct equation is used 3 Question 4 30 points Carbon sequestration is a technology that buries CO2 released from power plants deep down underground This technology has been proposed as a way to reduce greenhouse emission A limestone CaCO3 groundwater aquifer is receiving CO2 at a partial pressure of p CO2 Set up an analysis to determine the pH of the groundwater given the necessary equilibrium constants and partial pressure of CO2 Note that this problem does not ask you to give numerical answers a Write the list of species 5 points b Write the equilibrium relationship between these species and express the concentration of each species in terms of the equilibrium constants and concentration of CO2aq 10 points c Write the electroneutrality equation 5 points d Write the equation to relate partial pressure of CO2 gas to aqueous concentration of CO2 5 points e Use the results from part a b c and d to find 2 equations with 2 unknowns that could be used to solve for the concentration of each species and pH You do not have to solve these equations for species concentrations or pH 5 points Solution a List species present in the aqueous phase Ca2 H HCO3 CO32 OH CO2aq 5points b 2 points for each equilibrium Because water is on contact with limestone then we need to consider the solubility for CaCO3 solid CaCO3 Ca 2 CO32 Ca 2 CO32 K sp 4 57 10 9 K sp Ca 2 CO32 Speciation of CO3 2 containing compounds HCO3 H CO32 H CO32 H CO32 K 2 HCO3 K2 HCO3 CO2 aq H 2O H HCO3 H HCO3 K1 CO2 aq HCO3 CO32 K1 CO2 aq H CO2 aq K1K 2 H 4 2 H CO32 K2 K sp CO2 aq K1K 2 Ca 2 Ca CO3 CO32 Water dissociation H OH Kw 10 14 You can express OH Kw H 2 2 H …