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PART A C E:
Cemplete 4 of the 5 following problems each worth 20 points Problem A1. [19 points] Plug flow reactors can be approximated by a series of completely mixed reactors. A waste
stream contains a degradabie substance with ﬂow rate Q = 10 m [min and concentration Co = 40
mg/L The substance decays at a ﬁrst order rate (R = 2 per hr.). If a plug ﬂow reactor has volume
V equal to 500 m3, determine the substance efﬂuent concentration for this reactor. if the plug
volume reactor is approximated by 2 completely mixed reactors in series each with volumes 250
or“ determine the efﬂuent substance efﬂuent concentration from the second reactor. Assume
steaggzstate. CEE 3S 0 Environmental Quality Engineering 0 Second Preliminary Exam 0 a Spring 20l0
Page 2 I . PART A Complete 4 of the 5 following problems each worth 20 points Problem A1. [19 points] As noted in class, our model. for the rate of consumption of BOD by bacteria is a simpliﬁcation
as — kxs . in the BOD model, (IL  _ I r
— E; = le , we have assumed cell concentration, X, [S constant, and that S<<Ks so that k] as E (remember that L is Just 8 expressed in units of oxygen demand). Both of these kinetic
5 models assume that the food concentration is the only environmental parameter that inﬂuences the biodegradation. rate. However, at oxygen concentrations below 2 rag/L lack of 02 might slow the rate at which bacteria consume their food. A possible model for the rate of BOD use when the effect of low 02 concentration is considered is:  111 2 [(11.1 02 . Here: 02
(Kslo2 + 02 dt
= dissolved oxygen concentration in mg/L, and (1(5),;3o is the “half velocity” constant for oxygen
. . 02 I
(1.e., the 02 concentratlon when —«———— = w ).
(Ksloz +02 2 a) 0n the diagram on the following page show the STELLA model you would create to
describe the disappearance of L in a BOD test bottle when the effect of O; is included as
described above. [Hint, in addition to L, you will need a stock for 02. Remember that use
of BOD uses 02, and that there is no reaeration in a stoppered 1301) test bottle] b) Write the equation used to model L g?” l ' $391.} c) Write the equation that would be used to model 02 Ace a CEE 35] I Environmental Quality Engineering  Second Preliminary Exam  0 Spring 2010
Page 2 g} SIELLAG AI: .11" W
CEE 35! 0 Environmental Quaiity Engineering  Second Preliminary Exam I 0 Spring 2010
Page 3 ‘ Problem A3. [19 points]  .
An industry dumped ten “SO—gallon drums of TCE, which is equivalent to 3000 kg of TCE, into a river 1km upstream from the intake to a drinkingwater treatment plant. The river has a cross
seotional area of 100 mg; a velocity of 1000 mfhr and a dispersion coefﬁcient of 10 mzlsec.
SinCe the atmosphere has virtually zero TCE, and it’s saturation concentration C* = zero, the mass transfer rate of TCE : 2,9sz (C‘ — C): — sz (he. the loss of to the atmosphere obeys ﬁrstorder kinetics). dt 10053 ‘3 i like 7’ '
Assume k2= 35 h‘1 . X Determine if the concentration. of TCE at the intake ever reaches concentrations above the MCL
of TCE, .which according to EPA regulations, is 0.5ppb. 7015/19/11, 1 57 l0 “3/ L (a em “'4 C? Qﬁgelc WM 43% Per/v; ..  AW
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' naeroe Mummmid—W t ‘
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Time“) Problem A4. [ 19 points} An industry wishes to discharge 1000 m3/day of a wastewater containing dissolved organic
matter to a river. The raw industry waste (before possible treatment) has a BODL concentration,
Lw, of 200 mg/L and dissolved oxygen concentration, Cw, of 2 mg/L. The river characteristics
before introduction of the waste are as follow: ﬂow, QR == 10,000 m3/day; crosssectional area, A = 10 1112; BODL concentration, Ln = lmg/L; and dissolved oxygen concentration, CR _= 9 mglL.
The rate of BODL removal by biodegradation in the river is 0.] Slday, and the removal of
BODL by sedimentation is negligible. The mass transfer rate for reaeration in the river is
0.2fday. The saturation concentration of dissolved oxygen at the stream temperature is 10 mg/L.
The water intake for a town is located 4.4 km downstream from the industry. It is desired to
haVe a dissolved oxygen concentration of at least 5 mg/L at this point. Show through a
calculation whether or not the industry wilt need to treat its wastewater. QR = 10,000 m3/day
LR = kl = 0.] Slday
kg : 0.2/day A=10mz
(3* =10mg/L Lw = 200 mg/L Qw = 1000 m3/day
CW = 2 mg/L Desired minimum
02=SmglL
" “’9 ,x=4.4 km.
LO r ’lxlodooo {19430}! 1 (9'0? MJ/L @
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C O _ yesTgwrw CEE 35i 0 Environmental Quality Engineering 0 Second Preliminary Exam 0 0 Spring 2010
Page 6 1. torts“4 “’3b'j/tr < y'j/V wt, Problem A5. [ 19 points] An aquifer is being continuously recharged with treated domestic sewage to prevent depletion of
the aquifer. A recharge well is located 1000 meters upstream from the withdrawal well in the
aquifer. At steadystate operation (continuous input and withdrawal) the wells have a water
elevation difference of 3 meters. Aquifer characteristics are: Porosity = 0.4, aquifer bulk density
= 2.5 g/cm3, hydraulic conductivity = 100 m/day, crosssectional area of aquifer (perpendicular
to ﬂow) = 100 m2. For some unknown reason cadmium concentration in the sewage discharge
suddenly increased from zero to I rug/L and stayed at this level. Cadmimn is toxic but adsorbed
in the aquifer (K: = 15 cm3/g) . Estimate the time (from when cadmium ﬁrst appears in the
recharge) it will take for cadmium to reach the withdrawal well. Neglect dispersion in the aquifer. . #
CEE 351 0 Environmental Quality Engineering 0 Second Preliminary Exam 0 0. Spring 2010
Page 7 PART B 
Choose one of the following problems Problem B1 [24 points] An industry in a city sited on a tidal estuary 5 km from the ocean has a spill of 50 kg of organic
waste. If the waste decay rate is 0.2/day, the ﬂow velocity past the city is 5 kin/day, the
volumetric ﬂow rate is 500,000 m3/day, and the salt concentration in the estuarine water next to
the city is 1/50 of the ocean concentration; what will the waste concentration be (in mg/L) at the
mouth of the estuary Ge, 5 km downstream from the city) one day after the spill occurs? You
can assume that the dispersion caused by tidal action is signiﬁcant, and that a PFR would be a
bad choice of a model for the estuary. Note: 1 m3 = 1,000 L. WATCH UNITS! Salt Conc. = 1/50 ocean salt concentreation City I
’ “#51311 M: Ocean Q=500,000 m3/d $ U= 5 km/d Estuary I
r Spill I
= 50 kg 5 APR ad! Cami. "inpui‘ a? in tact E
C 7' CD ‘6; 3—K /® modﬁﬁj
r g ~ _ _
5‘" 28 l' Cl— tame—a 5"— my Mg?) , ~ " 55a Lg: waness “Ml/a CEE 351 0 Environmental Quality Engineering 0 Second Preliminary Exam 0 0 Spring 2010
Page 8 Problem B1. Additional Work Space (1‘ ' “’0 we imm my ZAWE} “15+
W153 123
14:05; M _
Wﬁmlﬂwo “M JV 7”“
{QT—573mm “433
x“? § km
_ a , 2
A"; G/LA "5333: ='00m
SD 105 _ [A \
2 Y—fz ex ﬁmw‘im 5mm" —~ MAM r?
C Zuli ’1\‘x(b3°ws€5‘%*\o\ (115+ : Wmmdg Ka/m‘s
7" Di (M4517 W CEE 351 0 Environmental Quality Engineering 0 Second Preliminary Exam 0 0 Spring 2010
Page 9 Problem BZ. [24 points] Assume 10 kg of a pesticide is accidentally spilled into an incremental volume of 5 tn3 in the
tributary to the town’s water supply, giving an initial concentration of 2 g/L. The spill occurs 10
km from the town’s reservoir, the tributary’s ﬂow velocity is l km/day, and it’s cross sectional
area is 5 m2. The pesticide obeys first order kinetics with a decay rate of 0.2/day. The maximum
acceptable drinking water concentration of the pesticide is 10 mm. Assume the tributary can be
modeled as a PFR and the reservoir can be modeled as a CSTR, with a volume of 1.5 x 104 In“.
How long will the town have to use an alternative water source because the pesticide level
exceeds the acceptable level? [You may assume the tributary is the only ﬂow into the reservoir
and the water level in the reservoir is constant. When the pesticide reaches the reservoir you
may assume that it is added all at once (i.e, the time it takes a volume of 5 m3 to ﬂow from the
tributary into the reservoir is negligible).] 1 m3 = 1000 L. WATCH UNITS!
L: 09‘ 'Xda o
.. 00 L
Co ' 5‘ 3/4: ’71:? ' 9.0393“; Reservoir ;u=lkmlda ,ﬁt=5m2 Tributar PF R
Qonl Pesticide 5pm Water for town Extra work space is provided on the following page. CEE 35] I Environmental Quality Engineering 0 Second Preliminary Exam 0 0 Spring 20!!)
Page 10 TOW Mm 61‘ farm/APE: Wm+9f (ﬁr 0&7A_ AWFLL, I ...
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