CE 384
Introduction to Environmental Engineering
Problems
Dr. Crist Khachikian Department of Civil Engineering
© 2006
1. Units, Unit Conversions Conversions and Concentrations Concentrations 1.1.
The air quality standard for ozone (O3) is 0.08 ppm. Express the standard in g/m3 at 1 atm pressure and T = 20oC. [160 g/m3]
1.2.
A volume of 1 L (liter) of water (H 2O) contains 10 g of dissolved salt (NaCl). Express the concentration of salt in the following units: a. mg/L [104 mg/L] b. ppm (mass of salt per mass of total solution [104 ppm] c. moles/L (M or molarity) [0.17 moles/L]
1.3.
A 100 mL sample of water is found to contain 1 mg of dissolved arsenic. Express the concentration of arsenic as: a. mg/L [10 mg/L] b. ppm (mass of arsenic per mass of solution). Actually do the unit conversion and do not use the fact that 1 mg/L ~ 1 ppm in water. [10 ppm] c. gram-moles/L [1.3 x 10-4 g-mole/L]
1.4.
Suppose the average concentration of SO2 in an air sample is measured to be 400 3 o g/m at 25 C and 1 atm pressure. Does this exceed the (24 hour) air quality standard of 0.14 ppm? [0.153 ppm; exceeds the standard]
1.5.
A nitrogen analysis of a wastewater sample gives the following results: Ammonia 30.0 mg/L of NH 3 Nitrite 0.10 mg/L of NO −2 Nitrate 1.50 mg/L of NO −3 Organic nitrogen 15.0 mg/L of nitrogen Find the concentration in mg/L of total nitrogen in the sample. [40.08 mg/L]
1.6.
The following is from a laboratory test to determine the suspended solids concentration of a sample of untreated wastewater. A 100 mL sample is filtered through a filter pad that removes all the suspended solids. The dry and cool weight of the pad and crucible before filtration is 48.610 g. After filtration, drying, and cooling, the weight of the crucible, filter pad, and dried solids is 48.903 g. What is the concentration of suspended solids in the wastewater sample, expressed in mg/L? [2,930 mg/L]
1.7.
In Contra Costa County, CA, the median indoor airborne concentration of chloroform (CHCl3) was found to be 0.4 µg/m3. a. Convert this concentration to a mole fraction in parts per billion. b. A typical adult inhales about 20 m3 of air each day. Calculate the amount of chloroform (in µg) swallowed by an adult each day.
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2. Chemical Mass Balances Balances 2.1.
A total mass of 500 lbs of ethanol (C2H5OH) is accidentally spilled into a river, where it is degraded by microbes. The degradation reaction involves the ethanol reacting with oxygen (O2) to form carbon dioxide (CO 2) and water (H2O). a. How many kilograms of oxygen are consumed? [474 kg O2 consumed] b. How many kilograms of CO2 are produced? [434 kg CO2 produced]
2.2.
The use of petroleum as a fossil fuel accounts for about 1.4 x 1020 Joules/year of world-wide energy generation. Petroleum has an approximate chemical formula of C2H3 and an energy content of about 43 x 106 Joules/kg. The combustion process consists of petroleum combining with oxygen (O2) to form carbon dioxide (CO 2) and water vapor (H2O). Estimate the total mass of carbon dioxide emitted to the atmosphere each year by the burning of petroleum. [1.1 x 1013 kg CO2 /yr]
2.3.
Pond water contains 15 mg/L of algae which can be represented by the chemical formula C6H15O6N. The decomposition of algal biomass uses oxygen according to the following reaction: C6H15O6N+8O2 6CO2+NO−3 + H+ + 7H2O
Calculate the “biological oxygen demand” (BOD) expressed as mg of O2 consumed by each liter of pond water assuming that all of the algae are decomposed. [19.5 mg/L O2 consumed; this is the total BOD]
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3. Mass Balances Balances (no reactions) 3.1.
Each year, a total of 600,000 acre-feet (one acre-foot is the volume equivalent to one foot of water covering one acre of land) of water from the Colorado River is diverted for use by Southern California. The concentration of dissolved salts in the Colorado River is 800 ppm. How many tons (English ton = 2000 lbs; metric ton = 1000 kg) of salt are imported each year as a result of this water diversion? [592,000 metric tons salt]
3.2.
A city situated on a large river disposes of its treated wastes to the river on a continuous basis. The minimum flow in the river is 210 m3 /s, and the discharge rate from the treatment plant is 12.5 m3 /s. If the maximum acceptable limit for a certain pollutant is 1.0 mg/L in the downstream river, and the ”background” concentration of this pollutant upstream is 0.4 mg/L, what is the concentration of the pollutant, in mg/L, that can be safely released from the water pollution control plant? [11.1 mg/L]
3.3.
A domestic wastewater flow contains 350 mg/L of suspended solids. Primary sedimentation in a wastewater treatment plant removes 65% of these solids, forming sludge that contains 5% solids and 95% water (by weight). If the total wastewater flow is 450 MGD (million gallons per pe r day), what is the total volume of 3 sludge produced each day (expressed in m )? (Assume that the solids have a density of 1500 kg/m3) [5,200 m3 /day]
3.4.
The L.A. Hyperion wastewater treatment plant has a total inflow of Q = 20 m3 /s. Ferric chloride (FeCl 3) is added to the influent to create additional suspended solids by reacting with water (H 2O) to form solid ferric hydroxide (Fe(OH)3) and hydrochloric acid (HCl). The desirable concentration of the solid Fe(OH)3 after the reaction and complete mixing with the flow is 20 mg/L. If FeCl3 costs $0.27/kg, what is the total annual cost of the FeCl3 addition? [$5 x 106 /yr]
3.5.
Dust removal from an airstream of a municipal mun icipal incinerator is accomplished by b y four dust collectors operating in parallel, each holding one fourth of the total airflow ai rflow of 3 3 200 m /min. The airstream contains 10 g/m of suspended solids. Each dust collector removes 98% of the suspended solids passing through it. a. What is the total mass of dust per day collected by all four collectors? [2822.4 kg/day] b. One of the dust collectors has to be taken out of service for one month. During that time, one fourth of the air will still s till pass through the collector that is out of service, but no dust will be removed by that collector. The maximum permissible suspended solids concentration in the combined stack discharge is 1.0 g/m3. Will the plant be able to meet the standard during the shutdown period? [2.65 g/m3; does not meet the standard]
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3.6.
Two manufacturing facilities discharge effluent containing a toxic organic pollutant through a common conduit into a pollution free (Ca = 0) river with a steady flow Qa = 10 m3 /s and a cross-sectional area A = 100 m2. Facility A discharges a flow QA = 0.1 m3 /s with a pollutant concentration CA = 10 mg/L, and facility B discharges a
A
B
QA
QB CA
CB
e m Qa Ca
Ce Cm
flow QB = 0.2 m3 /s with a pollutant concentration CB = 2mg/L.
e discharged into the river? [1.4 x 10-3 a. What is the total mass flow of pollutant m kg/s] b. What is the concentration Ce of the combined effluent flow into the river? [4.67 mg/L] c. Assuming that the pollutant discharge mixes mix es completely with the river flow, what is the pollutant concentration Cm in the river immediately downstream from the region of mixing? [0.14 mg/L] 3.7.
A sewage treatment plant discharges effluent at a rate of Qe = 450 MGD (million e = 20 gallons per day). The mass flow of mercury dissolved in the effluent is m mg/s. The effluent discharges into a large water body with an ambient mercury concentration Ca = 20 ng/L. Determine the initial dilution d ilution necessary to meet the following water quality constraints on the concentration co ncentration of mercury after mixing: a. Toxicity: Cm < 25 ng/L [196; [196 ; difficult] b. Chronic exposure (long-term exposure): Cm < 146 ng/L [7.8; easy] c. Acute exposure (short-term but intense exposure): Cm < 2100 ng/L [No dilution necessary since Cm > Ce already]
3.8.
An effluent discharge Qe = 10−2 m3 /s carries a total mass flow of a dissolved metal e = 10−4 kg/s. The effluent discharges into a water body with an initial equal to m dilution Sm = 50. The ambient dissolved metal concentration is zero (Ca = 0). Determine whether the following environmental regulations are met by this discharge:
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Water body Effluent Flow Qe e Ce, m
Mixing zone (S m = 50)
Ca
a. An effluent concentration limit: C e 10 mg/L. [10mg/L; just meets standard] b. An “in stream” water quality limit (after initial mixing): C m 0.1 mg/L [0.2 mg/L; Does not meet standard] 3.9.
A river carries a flow Q R = 10 x 109 m3 /yr with a concentration if dissolved salts CR = 0. An irrigation flow Q I = 8 x 109 m3 /yr is diverted to crop land with a total land area AI = 6 x 109 m2. The annual rainfall is P = 0.25 m/yr and the total loss by evaporation from the irrigated area is E = 0.75 m/yr. The irrigation flow leaches minerals from the soil and leaves the irrigated area with a concentration Cs = 2000 ppm. The drainage from the irrigated area discharges back into and mixes completely with the river upstream from the point of withdrawal. QR,CR
E
P
QI AI
Cs
Cd
Assuming steady state conditions, determine:
a. The salt concentration Cd in the river downstream. [667 ppm]
s at which the salt is leached from the soil. [10 x 109 kg/yr] b. The rate m 3.10.
The automobile emission standard for carbon monoxide (CO) is 3.4 g/mile. Each day, about 10 million cars make a single trip across a region in West Los Angeles that is about L = 10 km on a side (see figure below). Each car may be assumed to be emitting CO at the maximum permissible rate (given above). Because of the inversion layer, the atmosphere above this region may be considered to be a wellmixed volume with a height H = 1000 m. The wind from the ocean enters from the west (across one side of the volume) and leaves the region to the east (across the opposite side) with a velocity U = 2 m/s. The concentration of CO in the “clean” ocean air entering the volume is Ca = 200 ppb. Assuming steady-state conditions
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L
L
Top View
Side View
and neglecting possible reactions involving CO (i.e., assume CO is a conservative substance), compute the well-mixed concentration of CO in the atmosphere above West L.A. Does it meet the air quality standard of 10 mg/m3 (assume the air temperature is 25oC)? [0.37 mg/m3; meets state standard]
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4. Mass Balances (with reactions) 4.1.
A steady wastewater flow passes through a well-mixed tank with a volume V = 20 3 m . While it is in the tank, the mass of the waste decreases by reaction with a firstorder rate k r = 0.15/day. Determine the magnitude of the wastewater flow that can be handled if the desired level of treatment is 98% removal of the waste 3 constituents by reaction. [0.061 m /day]
4.2.
A railroad tank car spills a mass M o = 104 kg of chemical pesticide into a river. The river has a rectangular cross-section with width W = 100 m and a depth H = 3 m. 3 The steady river flow is Q r = 30 m /s. The “cloud” or plume of spilled pesticide moves downstream with the river flow. As it moves, the pesticide degrades according to a first order reaction rate k r = 1/day. What fraction of the original mass of pesticide will be undegraded by the time the plume reaches a reservoir a distance L = 20 km downstream? [0.1 or 10%]
4.3.
A town draws its water from a river with an average flow Q a = 10 m /s and a cross2 sectional area A = 100 m . The town is located 10 km downstream from a discharge e = 10−3 kg/s which may be assumed to mix completely of pollutant at a rate of m
3
with the river flow. As it flows downstream, the pollutant concentration decreases by reaction with a first-order reaction rate k r = 1/day. If a drought occurs and the 3 river flow decreases to Qa = 1 m /s, will the pollutant concentration in the water withdrawn by the town be greater or less than the pollutant concentration during -6 average flow conditions? Assume steady conditions and Qe << Qa. [C = 9.4 x 10 mg/L; concentration is much lower with the lower flow smaller velocity and longer time to react] 7
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4.4.
A lake with a constant volume V = 10 m is fed by a pollution free stream with a 3 3 flow rate Qa = 50.0 m /s. A factory dumps Q e = 5.0 m /s of a non-conservative waste with initial concentration C e = 100 mg/L into the lake. The pollutant reacts at −1 a rate k r = 0.25 day . Assuming the lake is well-mixed and steady, find the concentration of the pollutant in the lake. [5.95 mg/L]
4.5.
Leachate (water with dissolved constituents leaching from somewhere) seeps from 3 a landfill into a river at a rate of Q e = 0.01 m /sec (see figure below). The river has a 3 2 stead flow Qa = 10 m /s and a cross-sectional area A = 100 m . The concentration of an organic pollutant dioxolane downstream from the region of initial mixing between the leachate and the river flow is C m = 1.0 mg/L. The ambient concentration of dioxolane is Ca = 0.
e of dioxolane from the landfill into the river? [0.01 a. What is the mass flow m kg/s] b. What is the concentration C e of dioxolane in the leachate? [1000 mg/L] c. As the dioxolane is carried downstream by the river, the concentration of it decreases as a result of reaction with a first-order rate k r = 0.1/day. If the
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drinking water standard specifies that water have a dioxolane concentration less than 0.001 mg/L, how far downstream will the water by safe to drink (without additional treatment to remove dioxolane)? [597 km] Landfill
4.6.
A drainage channel discharges storm water runoff into Santa Monica Bay at a rate 3 of Qe m /s (which may be assumed to be constant during a very rainy week). The 4 bacterial level in the runoff is C e = 10 counts/100mL (one count is one E. coli bacterium, the indicator species; you can treat these units just like concentration units). The coastal current flowing from the south has an average velocity of about U = 5 cm/s and a bacterial concentration C a = 50 counts/100mL (because of other storm water discharges located to the south). The cross-sectional area of Santa 5 2 Monica Bay at the location of the inflow is about A = 2 x 10 m (about 50 meters deep and 4000 meters wide). The current leaves Santa Monica Bay by flowing to the north past Malibu. The portion of the Bay between the discharge and where the 9 3 current leaves the Bay has a volume V = 10 m , and may be considered to be wellmixed. Calculate the concentration of bacteria (C m) in the flow leaving the Bay taking into the account that the bacteria die off at a rate given by a first order coefficient k r = 1/day. Assume steady state conditions. [23.6 counts/100 mL]
4.7.
The sewage treatment plant in Boston, Massachusetts discharges a pesticide (nonvolatile organic compound) into Boston Harbor. Boston Harbor is nearly an enclosed embayment that may be assumed to be well-mixed. The harbor has an area 2 A = 100 km and a depth H = 5 m. The harbor is flushed by a pollution free (C a = 0) 8 3 tidal flow equivalent to an ambient flow rate Q a = 10 m /day. Assume Qe<< Qa.
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The pesticide in the effluent has a first-order reaction k r = 0.01/day. Does the reaction have a significant effect on the concentration of the pesticide (C m) in the mixed flow leaving the harbor? [Qm >> k rV; so the reaction has little effect]
4.8.
A sewage treatment plant discharges tertiary effluent into the Los Angeles River. 3 N = 8 x 104 The effluent flow is Qe = 4 m /s and the effluent nitrogen mass flow m mg/sec (as N not a compound). The ambient river flow upstream from the plant is 3 Qa = 1 m /s, and the ambient N concentration is C a = 0. The cross-sectional area of 2 the river is A = 5 m and the discharge is located at a distance L = 70 km from the ocean.
a. What is the nitrogen concentration C m in the river just downstream from the treatment plant? [16 mg/L] +
b. Nitrogen (in the form of NH 4 is converted to phytoplankton (C 106H263O110N16P) according to the following chemical reaction: 106CO2 + 16NH+4 + H2PO−4 + 106H2O C106H263O110N16P +106O2 +15H+ Assuming that all of the N is converted to phytoplankton, either in the river or in the p (in kg/s)? [1.3 kg/s] ocean, what is the total rate of phytoplankton mass production m
c. The rate at which the N is converted to phytoplankton is k r = 1/day. What percent of the total phytoplankton mass production occurs in the river? [56%]
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4.9.
A cooling tower (used to cool water for air conditioning purposes) has a steady evaporative loss of water equal to QE = 1 m3 /s. To make up for the loss, water is withdrawn from a nearby river which has a steady ambient flow Qa = 10 m3 /s. The steady flow withdrawn from the river is Q in and the steady discharge back into the river is Qout. The ambient concentration of total dissolved solids in the river is Ca = 10 mg/L. The concentration of dissolved solids in the evaporative flow QE is CE = 0 mg/L.
a. Determine the values of the flows Qin and Qout required to limit the concentration of dissolved solids in the cooling tower to Cmax = 20 mg/L. Assume that the cooling tower is like a well-mixed volume and that there are no reactions occurring in the tower. [2 m3 /sec] b. Assuming that the concentration of dissolved solids in the discharge from the tower is Cout = Cmax = 20 mg/L, what is the mixed concentration of dissolved solids Cm in the river just downstream from the discharge point? [11.1 mg/L] c. As the river flows downstream, the concentration of dissolved solids decreases as a result of a first-order reaction with constant reac tion coefficient k r. Measurements of the dissolved solids concentration CL at a distance L downstream have been made for a range of values of the ambient river flow Qa. A qualitative plot of these measurements looks like this:
Explain briefly why the plot looks as it does, i.e., why does the dissolved concentration CL increase with river flow Q a and then decrease. Assume that all other parameter values given in the problem remain constant. [For low values of Q a, velocity is small and the travel time is large; thus, the reaction makes C L small. For high velocities, C m is small and so is C L]
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4.10.
Rainfall flows steadily from a storm drain into Santa Monica Bay at the shoreline at a rate of Qr = 0.01 m3 /s and with a bacterial concentration Cb = 105 counts/100mL. The beach slopes downward in the offshore direction at a rate of 1:50 (vertical drop per horizontal distance). A steady current runs parallel to the shore with a uniform velocity U = 1 cm/s. Assuming that the rainfall flow mixes completely with the alongshore flow over an offshore distance Lm = 10 m, and that the bacteria die at a rate given by a first-order rate k d = 1/day, use plug flow analysis to determine if the concentration of bacteria at a point x = 200 m along the shoreline downcurrent from the point of discharge meets the swimming standard of 1000 counts/100mL. [C = 4 x 104 counts/100mL; does not meet the standard]
4.11.
A river has a steady ambient flow Qa = 10 m3 /s and a constant cross-sectional area A = 100 m2. A factory withdraws a flow Qe = 5 m3 /s from the river through a pipe and discharges it at a point a distance L = 10 km upstream from the point of f of a toxic chemical withdrawal (see figure). The factory discharges a mass flow m into the flow Q e. The volume flow of the factory in put is negligible (QF << Qe). Once it reaches the river, sunlight degrades the toxic chemical by a first-order reaction with a reaction coefficient k r = 1.0/day. No degradation of the chemical occurs in the flow Qe (no sunlight in the pipe). The concentration of the toxic chemical in the river just downstream from the point where Q e is discharged back into the river is C m = 10 mg/L. The ambient concentration of the toxic chemical is Ca = 0 mg/L.
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L River Cm
Qa, Ca
Cd
k r
Qe, Ce
Qe
Pipe
f m Factory
a. Calculate the concentration of the toxic chemical Ce in the flow Qe just before it is discharged back into the river. [30 mg/L] b. Calculate the concentration of the toxic chemical Cd in the river downstream from the point where the flow Q e is withdrawn from the river. [4.7 mg/L]
f discharged from the factory. [0.08 c. Calculate the mass flow of toxic chemical m kg/s] 4.12.
Consider a lake with 108 m2 of surface area for which the only source of phosphorus is the effluent from the wastewater treatment plant. The effluent flow rate is 0.4 m3 /s and its phosphorus concentration is 10 mg/L. The lake is fed by a stream having a flow of 20 m3 /s with no phosphorus. a. If the effective settling rate of phosphorus is estimated to be vs = 10 m/yr, estimate the average phosphorus concentration in the lake. [0.077 mg/L] b. What percent of phosphorus removal at the treatment plant would be required to keep the average lake concentration below 0.01 mg/L? [87%]
4.13.
A river with a steady flow Q a = 1 m3 /sec flows into a small harbor with a volume V = 107 m3 and a bottom area A = 106 m2. The flow then passes out of the harbor to the ocean. The harbor may be considered to be well-mixed.
River Ca Qa
Flow to Ocean Harbor V = Volume A = Area
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a. Seepage from old septic tanks causes the bacterial concentration in the river (just before it enters the harbor) to be C a = 104 /100mL (i.e. 104 bacteria per 100 mL sample). The bacteria die off according to a first-order reaction rate k r = 0.5/day. Does the water in the harbor meet the swimming standard which is that the wellmixed concentration of bacteria in the harbor be less than 200/100 mL? [170/100mL meets the standard]
dredge = b. A dredging operation in the river removes a total mass flow of solids m 106 kg/day from the river bottom. About 1% of the mass of dredged material is lost by leakage into the river and enters the harbor as suspended solids. If the settling velocity of the solid material is w s = 0.1 m/day, what is the mass of dredged solids that settles to the bottom of the harbor each day? [5400 kg/day] 4.14.
Santa Monica Bay has a surface area A = 5x107 m2 and an average depth H = 50 m. The bay may be considered as well-mixed and as being flushed by an ambient ocean current with a total flow into the bay equal to Qa = 104 m3 /sec. The City of Los Angeles discharges treated sewage in to Santa Monica Bay at a steady rate Qe = 10 m3 /sec. It is estimated that 35% of the solids in the effluent settle to the bottom of Santa Monica Bay. The following quantities have been measured in the effluent: Csse = total suspended solids concentration = 50 mg/L CDDTe = total concentration of DDT = 1 µg/L CLe = total concentration of lindane = 1 µg/L
Qe Santa Monica Bay
Qm CDDTm CLm Cssm
CDDTe CLe Csse
Qa CDDTa CLa Cssa
a. Estimate the settling velocity of the waste particles in the bay. Assume that the ambient suspended solids concentration is negligible. [9.3 m/day] b. DDT has a sediment-water partition coefficient K s = 106 L/kg and does not react. Estimate the total concentration of DDT in the water leaving the bay CDDTm, assuming that the ambient concentration of DDT is CDDTa = 0. [0.00066 µg/L]
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c. Lindane has a sediment-water partition coefficient Ks = 103 L/kg and a reaction coefficient k r = 1/day. Estimate the total concentration of lindane in the water leaving the bay CLm, assuming that the ambient concentration of lindene is 0. [0.00026 µg/L] 4.15.
A steady flow QN = 30 x 106 m3 /day of water from Northern California reaches the Sacramento Delta Region where a steady irrigation flow QI = 20x 106 m3 /day is withdrawn. The flow Q I is used to irrigate crops in a region with a (hypothetically) steady rainfall P = 0.5 m/yr and evapotranspiration ET = 1 m/year. A steady return flow QR = l0 x 106 m3 /day from the irrigation region returns to the main channel at a point upstream from where QI is withdrawn, resulting in a steady flow QLA = 20 x 106 m3 /day that provides Los Angeles with drinking water. A mass flow of organic oc enters the irrigation flow as it passes through the agricultural region. carbon m The resulting concentration of dissolved organic carbon is Cm = 100 mg/L in the flow downstream from the point where the return flow mixes with the main channel (including in the irrigation flow Q I). The dissolved organic concentration in the flow from the north (Q N) is CN = 0 mg/L.
a. What is the total area A I of the agricultural region experiencing the rainfall P and evaportanspiration ET? b. Use a mass balance at the point where the flows QN and QR mix to determine the value of the organic carbon concentration in the return flow CR. c. What is the value of the mass flow of organic carbon? [hint: use a mass balance for the overall system] d. The channel bringing water from the Delta to Los Angeles has a cross-sectional area Ac = 200 m2 and a length L = 500 km. Assuming that the disso1ved organic
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carbon degrades (into harmless products) at a rate k r = 1/day, does the flow reaching LA exceed a proposed standard for dissolved organic carbon in drinking water Cmax = 2 mg/L? 4.16.
A well-mixed reservoir has a constant volume V = 10 m3 and a horizontal crosssectional area A = 106 m2. The steady flows of water into and out of the reservoir are the river inflow Qin, the outflow Qout, the rainfall P, and the evaporation E. p = 106 kg/year by the Suspended solids in the reservoir are generated at a rate m growth of phytoplankton (C106H263O110N16P) according to the following chemical equation: 106CO2 + 16NH4+ + H2PO4- + 106H2O C106H263O110N16P + 106O2 + 15H+ The concentration of suspended solids (phytoplankton) in the reservoir is C ss = 50 mg/L. The fraction of the solids generated that settle to the bottom is F s = 0.5. The remainder of the solids leave the reservoir in the outflow. There are no suspended solids in the inflow to the reservoir or in the precipitation or evaporation.
a. Assuming that the rainfall is P = 1.5 m/year and the evaporation is E = 0.5 m/year, use the information on the suspended solids balance to determine the values of the inflow Qin and the outflow Qout.[0.9 x 107 m3 /yr; 1.0 x 107 m3 /yr] b. What is the settling velocity w s of the settling solids? [10 m/yr]
N into the reservoir is required to maintain the c. What mass flow of nitrogen m
P ? [6.3 x 104 kg/yr] generation of phytoplankton at the rate m d. If the phytoplankton decompose, the reaction given above is reversed and oxygen is consumed rather than generated. What is the BOD of a sample of water from the reservoir with the phytoplankton mass concentration Css given above? [47.8 mg/L] e. A pesticide with a sediment-water partition coefficient K s = 2 x 104 L/kg enters the reservoir in dissolved form and comes to sorption equilibrium with the suspended solids (phytoplankton) in the reservoir. What percentage of the mass flow of the pesticide settles to the bottom with the phytoplankton solids? [25%] 4.17.
A steady flow Q = 107 m3 /year passes through a well-mixed lake that has a volume V = 106 m3. The concentration of suspended solids in the flow entering the lake is Css,in = 100 mg/L and the concentration of suspended solids in the flow leaving the
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lake is Css,out = 10 mg/L, which is lower than Css,in because of particle settling in the lake. a. The flow entering the lake carries a mass flow of dissolved ammonia nitrogen N = 2 x l04 kg/year. In the reservoir the ammonia nitrogen is degraded to other m compounds by a reaction with a reaction rate k r = 10/year. What is the concentration of ammonia nitrogen CNout in the outflow from the lake?
DDT = 100 kg/year b. The flow entering the lake carries a total mass flow of DDT m which is partially in dissolved form and partially sorbed to the suspended solids in the inflow. The solid water partition coefficient for DDT is Ks = 5 L/mg. What is the total (dissolved plus sorbed) DDT concentration CDDToutt in the outflow from the lake?
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5. Water Supply 5.1.
A country with a population of 500,000 people has a total land area of 104 km2. The annual freshwater runoff available for use is 109 m3, which is 20% of the total annual rainfall: a. Is the annual rainfall in this country more or less than the global average? [50% of global average] b. Is this country short of water? [no, not water stressed]
5.2.
A country has a total area A = 105 km2 and a total annual rainfall I = 0.8 m/yr of which 75% evaporates and the rest is available as water runoff. a. What is the maximum population this country can support without become water stressed? [107 people] b. The largest city in the country discharges its treated sewage effluent into a e = 104 kg/day. What is the nearby river. The rate of BOD input into the river is m minimum river flow (Qa) necessary to keep the BOD level in the river less than the BODm = 5 mg/L at a point just downstream from the effluent mixing zone? Assume that the effluent mixes completely with the river flow and that the upstream BOD is zero. [2 x 106 m3 /day]
5.3.
Rain falls steadily on a watershed with an area Aw = 104 km2. The total annual precipitation P = 75 cm. All the water that is not evaporated or transpired flows into a reservoir as surface water runoff at a constant rate Q = 107 m3 /day. The reservoir may be considered as well-mixed. The outflow from the reservoir is also steady and equal to Q = 107 m3 /day.
a. Is the annual rainfall per unit area on this watershed greater or less than the global average annual precipitation per unit area onto land? [less than 1m/yr] b. What is the annual evapotranspiration rate ET (in cm/yr)? [38.5 cm] c. Assuming that the flow into the reservoir Q is the only source of fresh water, what population can this watershed support without experiencing water stress? [1,825,000 people]
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d. Human activities and other sources in the watershed create a mass flow of p = 1000 kg/day. What is the phosphorus into the surface runoff equal to m concentration of phosphorus Cp in the runoff entering the reservoir? [0.1 mg/L] e. Once in the reservoir, all of the phosphorus is converted from H2PO−4 to algal biomass (C106H263O110N16P) according to the following reaction: 106CO2 + 16NH+4 + H2PO−4 + 106H2O C106H263O110N16P +106O2 +15H+
a in kg/day in the reservoir? [114,500 What is the rate of algal biomass production m kg/day algae]
5.4.
Water usage during peak days in small towns follows the following pattern: Time interval Midnight - 3 AM 3AM-6AM 6AM-9AM 9AM-Noon Noon-3PM 3PM-6PM 6PM-9PM 9 PM-Midnight
Gal per capita used 5 5 15 25 85 40 15 10
Assuming that the total daily demand is met by a pumping plant pumping continuously and steadily at the same rate, determine the storage required to provide the peak hourly demand and the required fire flow for a town with a population of 40,000 people. [6.6 x 10 6 gallons]
5.5.
A storage reservoir is to be built to store a river flow Q R and to supply a steady flow QD = 108 m3 /year to a town with a population of 100,000 people and an irrigation project with a total land area A = 108 m2. P QR
E A
reservoir V
irrigation QD town
s m Cs
The town has a per capita water demand of 200 m 3 /person/year. The annual precipitation and evaporation from the irrigation area are estimated to be P = 0.5 m and E = 1.0m, s= respectively. In addition, the irrigation project leaches a mass flow of dissolved salts m 107 kg/year from the soil. Assuming that the salt concentration in the water leaving the reservoir is negligible, will the flow from the reservoir Q D = 108 m3 /year be sufficient to provide the town the needed water, to water the crops, and to insure that the concentration of dissolved salts in the downstream river C s will be less than the maximum drinking water standard which is 500 mg/L? [yes – total required is 2 x 10 7 m3 /yr for town; 5 x 107 m3 /yr for irrigation and 2 x 10 7 m3 /yr for dilution = 9 x 107 m3 /yr]
19
6. Waste Water Treatment 6.1.
The concentration of suspended solids in the outflow from a well-mixed sedimentation tank Cout was measured during steady-state operation for different values of the tank overflow rate U (defined as flow through the tank per unit horizontal surface area) and for a constant suspended solids inflow concentration Cin:
a. Estimate the concentration of suspended solids in the inflow Cin and the settling velocity of the particles ws (hint: try plotting C out vs. U). [ws = 100 m/day] b. What overflow rate must be maintained to achieve 80% removal of solids in the tank? [25 m/day] 6.2.
A water treatment plant is to be designed to treat a flow Q = 0.1 m3 /s. a. Particles entering the sedimentation unit have a diameter D = 500 m, a porosity 3 = 0.9, and a solids density s = 1100 kg/m . Determine the required area of the sedimentation unit such that 80% of these particles will be removed. [286 m2] b. The raw water entering the treatment plant has a total concentration (dissolved plus sorbed) of the pesticide endrin equal to Ctot = 0.001 mg/L and a total suspended solids concentration Css = 100 mg/L. If the sediment-water partition coefficient for endrin is K s = 100 L/kg, determine if 80% solid removal is sufficient for the treatment plant outflow to meet the primary drinking water standard for the total concentration of endrin, Ctot = 0.0002 mg/L. [Ctot ~ 0.001 mg/L; No]
6.3.
A rectangular tank of length L, width B, and depth H is to be designed to serve both as a well-mixed reaction tank for a dissolved constituent in the inflow as well as a well-mixed settling basin for suspended solids in the inflow. The flow through the tank is 0.1 m3 /s, the particles in the inflow have a settling velocity = 10-3 m/s, and the reaction rate is 1/hr. For good mixing, the tank dimensions should be such that L=2B. a. Determine the dimensions required if the concentration of the dissolved constituent in the outflow is to be 20% of the inflow concentration and if 90% of 20
the suspended particles are to be removed by settling.[B = 21.2m; L = 42.4m; H = 1.6m] b. The outflow concentration of the dissolved constituent is 1000 mg/L. The standard for discharge for this compound is 0.1 mg/L. A consultant offers to design a discharge into a nearby large water body to obtain the necessary dilution to meet the standard (ambient concentration = 0). Do you think this is a feasible solution? Give your reasons. [Sm = 10,000; Very, very difficult to achieve in any water body, therefore, the solution is not feasible] 6.4.
An activated sludge secondary treatment unit is to treat an inflow Q = 0.5 m3 /s with an inflow BOD concentration So = 150 mg/L so that the outflow from the unit has a BOD concentration S = 30 mg/L. The MLVSS of the plant is to be maintained at X = 2000 mg/L, and the concentration of the solids in the flow leaving the secondary clarifier is X s = 10,000 mg/L. Determine the bacterial growth rate , the sludge age , the aeration tank volume V, the sludge return flow Qr, the sludge volume outflow Qs, and the F/M ration. Assume that Y = 0.5 mg VSS/mg BOD, m = 2.5/day, and Ks = 100 mg/L. [µ = 0.58/day; θc = 1.72 days; V = 2234 m2; QR = 0.12 m3 /s; Qs = 260 m3 /day; F/M = 1.45 day-1]
6.5.
A sewage effluent has a total suspended solids concentration TSS = 100 mg/L. Chemical analysis of the effluent indicates the following sediment-water partition coefficients for three organic pollutants: For each of these constituents, calculate the fraction sorbed to the suspended solids at the following locations: a. In the effluent flow. [0.99 for DDT; 0.91 for PCB; 0.091 for Lindane] b. In the mixed flow resulting from mixing of the effluent with a pollution-free and particle-free ambient water body. The dilution factor is S m = 10. [0.91 for DDT; 0.5 for PCB; 0.0099 for Lindane] c. In the mixed flow (S m = 10) after 90% of the solids have settled to the bottom. [0.5 for DDT; 0.09 for PCB; and 0.001 for Lindane]
6.6.
A water treatment plant with a flow Q = 1 m3 /sec adds FeCl3 to increase the concentration of suspended solids. The reaction of FeCl3 with water that produces the solids (in the form of Fe(OH)3 is: FeCl3+3H2O Fe(OH)3 +3HCl This reaction may be assumed to happen very rapidly and to result in the formation of small particles. After FeCl3 addition and reaction, the flow passes through a flocculation chamber, where the size of the suspended particles increases, to a sedimentation basin where a fraction of the particles are removed by settling, and finally to a filter where essentially all of the remaining suspended solids are removed.
21
a. In the flocculation chamber, which may be considered well-mixed, the small particles are converted to large particles with a first-order rate k r = 20/hr. What is the required flocculation basin detention time = V/Q, where V is the basin volume, in order that 90% of the small particles are converted to large particles by this “reaction”? [0.45/hr] b. If the large particles have a settling velocity v s = 500 m/day, what is the required overflow rate vo = Q/A, where A is the area of the settling basin, in order that 90% of the large particles are removed by the settling process? [55.6 m/day]
FeCl3 necessary for the treatment plant to c. Calculate the FeCl3 mass inflow m remove 90% of a toxic compound that is dissolved in the inflow and that has a sediment-water partition coefficient Ks = 1 L/mg. Assume that the suspended solids concentration in the inflow to the plant is negligible compared to the suspended solids generated by the addition of FeCl3 and that the toxic compound reaches sorption equilibrium with the suspended solids in the flocculation basin. [1,170 kg/day]
6.7.
Water “hardness” is defined as the concentration of calcium and magnesium (Ca++ and Mg++). One way to “soften” water is to add a chemical that will combine with these ions to form solid precipitate that can be settled out. For calcium hardness, soda ash (Na2CO3) may be added to produce the following reaction: Ca++ + Na2CO3 CaCO3(s) + 2Na+ where the calcium carbonate (CaCO 3) is in solid form.
a. A water treatment plant must soften a total flow of Q = 1m3 /s that has a calcium ion concentration of 100 mg/L. What mass of soda ash must be added each day to completely remove the calcium hardness? [22,848 kg] b. The softened water passes into a settling basin. If the solid CaCO3 particles have a settling velocity vs = 100m/day, what should the area A of the settling basin be if the objective is to remove 80% of the CaCO3 solids? [3,456 m2] 6.8.
The table and diagram below give the flows of water, solids, and BOD for the Hyperion Treatment Plant in Los Angeles. Use this information to answer the following questions:
22
a. Does the secondary effluent (#7) meet the water quality requirements that the total suspended solids concentration and the BOD concentration must both be less than 30 mg/L? [14 mg/L] b. What percent of the solids in the primary influent (#4) are removed b y primary settling? [14 mg/L] c. How many kg per day of solids are generated by the secondary treatment plant? [3.9 x 105 lb/day] d. How many kg per day of solids are degraded back to soluble material in the anaerobic digesters? [5.7 x 105 lb/day] e. Is the net effect of the total treatment process, including sludge processing, to create or diminish the mass of solids in the waste? [-1.7 x 105 lb/day; solids lost!] 6.9.
In a wastewater treatment plant, sludge from the primary clarifier and wasteactivated sludge from the secondary system are mixed and thickened in a gravity thickener. The primary sludge contains 1250 kg of dry solids per day with a 4% solids content by volume (relative to the total volume including liquid) and the
23
waste-activated sludge contains 525 kg dry solids per day with a solids content by volume of 1.2%. After thickening, the mixture has a solids content by volume of 3%. Assume that all dry solids have a density of 1000 kg/m3. a. Calculate the volume of thickened sludge produced each day. [59 m3 /day] b. Calculate the percent volume reduction in the thickener. [79% = volume after thickening/volume before thickening] 6.10.
An activated sludge secondary treatment unit has the following configuration:
Q = inflow to the secondary unit = 1000 m 3 /day Qr = sludge return flow = 200 m 3 /day X = bacterial biomass concentration = 2000 mg/L Xs = sludge return biomass concentration = 10,000 mg/L V = aeration tank volume = 500 m 3
a. In the aeration tank, the organic matter in the inflow (C5H12) reacts with oxygen to form bacterial biomass (C 5H7NO2) according to the following reaction: C5H12 + 3O2 + NH3 C5H7NO2 + 4H2O If the molecular weights are C = 12g, H = 1g, O = 16g, and N = 14g, determine the theoretical maximum yield of the reaction Y = bacterial biomass produced per mass of BOD (organic matter) consumed. [1.2] b. Assuming the entire system is at steady-state, what is the growth rate of the bacteria in the aeration tank? [0.4/day] c. Assuming the system is at steady-state, find the sludge outflow rate Qs. Neglect the bacterial biomass flow in the outflow from the settling tank, i.e., assume all of the solids entering the settling tank end up in the sludge outflow or sludge return flows. [40 m3 /day]
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6.11.
A water treatment plant consists of a flocculation tank, a settling basin, and a filtration unit. The plant is to be designed to treat a total flow of Q =1 m3 /s.
Css = 0
Css = 25 mg/L
Css = 5 mg/L
Css = 0
Q
Q
Flocculation
FeCl3 m
Settling
Filtration Qs
a. To increase the suspended solids concentration, a mass flow of dissolved FeCl3, FeCl3 , is added to the flocculation tank. In this tank, the dissolved FeCl3 is m converted to solid Fe(OH)3 in a reaction with a first order rate coefficient k r = 12/hr. Determine the necessary volume of the flocculation tank, V, such that 90% of the FeCl3 is converted to Fe(OH)3. You may assume that QFeCl3 << Q. [2,700 m3] b. The purpose of the settling basin is to reduce the suspended solids concentration before filtration. Assume that the suspended solids concentration in the inflow to the settling basin is 25 mg/L and the settling velocity of the solids, vs = 200 m/day. Determine the necessary area, A, of the settling basin so that the suspended solids concentration leaving the settling basin is 5 mg/L. (Assume that no more formation of Fe(OH) 3 occurs in the settling basin and neglect the volume of settled material compared to Q.) [1,728 m2] c. The filtration unit reduces the suspended solids concentration to essentially zero in the outflow from the treatment plant. Determine the volume discharge Qs of sludge generated by the filtration and settling processes combined. Assume that the sludge is 5% solids by volume and that the density of the solid material is 2500 kg/m3. [20 x 10-5 m3 /s = 17.3 m3 /day] 6.12.
A wastewater treatment plant has the following configuration and the indicated TSS (in MTD = flows of volume Q (in MLD = 106 L/day), total suspended solids m metric tons/day = 103 kg/day), and total BOD (in MTD):
25
a. The regulatory limit on the BOD concentration in the effluent is C BOD < 30 mg/L. Does the effluent meet this regulatory limit? [13.9 mg/L; meets standard] b. What are the advantages to an environmental regulator of placing a limit on the effluent concentration rather than the concentration in the receiving water body after mixing has occurred? c. What is the yield Y (bacterial biomass produced per mass of BOD consumed) in the secondary treatment process of this plant? [0.42] d. In the sludge digester, which has a volume V = 10 L and may be considered well-mixed, a fraction of the suspended solids are converted back to a dissolved form by a first order reaction. What is the reaction coefficient k r for the digestion process in the sludge digester? [0.0096/day] e. Is the treatment plant a net sink or source of suspended solids, i.e. is the total mass flow of suspended solids coming out of the plant greater or less than the total flow of suspended solids entering the plant? [Total inflow of solids is greater than total outflow; solids get consumed in digestion; Plant is a net sink of solids] 6.13.
A sewage treatment plant that uses activated sludge as the secondary treatment process treats a flow Q = 1 m3 /sec. The suspended solids and BOD concentrations in the inflow to the plant are Css,in = 250 mg/L and So = 250 mg/L, respectively, and the suspended solids and BOD concentrations in the outflow are Css,out = 50 mg/L and S = 50 mg/L, respectively. The yield of the secondary process is Y = 0.5 kg bacterial mass/kg BOD consumed. The effluent from the plant (Qe ~ Q) is discharged into a river with a steady discharge Qa = 10 m3 /sec, a constant crosssectional area A = 100 m2, and a suspended solids concentration Css,a = 1 mg/L.
26
a. Assuming that all the BOD reduction occurs in the secondary treatment unit, s produced in both the primary and what is the total mass flow of sludge m secondary units (before any sludge digestion)? [25,920 kg/day] b. If the overflow rate of the settling tank in the secondary unit is U = 50 m/day and the tank removes 90% of the bacterial solids, what must be the effective settling speed ws of the bacterial solids? [450 m/day] c. The effluent contains DDT which has a sediment-water partition coefficient Ks = 5 L/mg. Could the concentration of DDT in the river be significantly affected by the settling of solid particles in the river? [yes, because fraction sorbed = 0.96] 6.14.
The Hyperion wastewater treatment plant has a total inflow Q = 20 m3 /s with a total suspended solids concentration TSS = 300 mg/L. a. Ferric chloride (FeCl3) is to be added to the influent to create additional suspended solids by reacting with water (H2O) to form solid ferric hydroxide (Fe(OH)3) and hydrochloric acid (HC1). The desirable concentration of the solid Fe(OH)3 after the reaction and complete mixing with the flow is 20 mg/L. If FeCl3 costs $0.27/kg, what is the total annual cost of the chemical addition? [$5x106 /yr] b. The inflow with the original TSS and the added ferric hydroxide solids enters a primary settling basin The total solids concentration of the inflow to the basin is Cin = 320 mg/L. The concentration of suspended solids (influent solids and Fe(OH)3) in the outflow from the settling basin is Cout = 80 mg/L. What is the s that must be removed from the settling basin (expressed mass flow of sludge m in kg/day)? [4.1 x 105 kg/day] c. If the settling basin has a total bottom area A = 105 m2, estimate the settling velocity of the solids ws. Assume the settling basin is well-mixed. [51 m/day]
6.15.
A sewage treatment plant uses primary treatment and activated sludge secondary treatment to treat a flow Q = 10 5 m3 /day. The concentration of suspended solids is TSSin, = 350 mg/L in the inflow and TSSe = 50 mg/L in the effluent. The BOD of the flow entering the secondary treatment is So = 350 mg/L and the BOD of the effluent is BODe = 50 mg/L. The dissolved oxygen concentration of the effluent is DOe = 0. The effluent flow Qe ~ Q discharges into a river with a constant velocity U = 104 rn/day, a cross-sectional area A = 100 m2, an ambient BODa =0, and an ambient DOa = DOsat = 12 mg/L.
27
a. If the total sludge mass flow generated by the plant is 5 x 104 kg/day, what is the yield Y = bacterial biomass produced per mass of BOD consumed of the activated sludge secondary treatment process? [0.67] b. Calculate the minimum dissolved oxygen concentration DOmin. Assume that the reaeration coefficient is k r = 0.5/day and the deoxygenation coefficient is k d = 0.2/day. [10.7 mg/L] 6.16.
A population of 5xl06 people live in a region with an area AL = 104 km2. The freshwater runoff available to this population is 40% of the rainfall falling on this area. The sewage flow generated by the population is Q = 10 m3 /sec, which is 50 % of the available freshwater runoff. The sewage flow is treated in a treatment plant with an activated sludge secondary treatment system. The effluent from the plant discharges into a large waterbody.
` The characteristics of the treatment plant are: Inflow to the plant: BODin = ultimate BOD in the inflow = 300 mg/L TSSin = total suspended solids concentration in the inflow = 300 mg/L Primary settling tank: Percent of TSS entering tank that is removed = 60% Percent of BOD entering tank that is removed = 30% Q/A = Overflow ratio 50 m/day
o
Secondary unit: Percent of TSS entering unit that is removed = 90% Percent of BOD entering unit that is removed = 90%
28
Yield of activated sludge process = 1.0 F/M = food to mass ratio = S oQ/XV = 0.5/day So = BOD concentration entering the unit X = bacterial mass concentration in the aeration tank V = aeration tank volume Sludge flow: Percent solids by volume = 5% ρs = solids density = 1500 kg/m 3 Effluent discharge: BODm,max = maximum permissible value of BOD after dilution =3 mg/L BODa = ambient BOD = 0 mg/L.
a. Is this region water stressed? [126 m3 /person/yr; very water stressed] b. Is the annual rainfall (expressed as depth = volume/area) greater or less than the global average? [0.16 m/yr; much less than the global average] c. What is the settling velocity w s of the particles in the primarly settling tank? [75 m/day] d. What is the growth rate µ of the bacteria in the secondary unit? [0.45/day] e. What is the total volume flow Q s of sludge generated (including water) from both the primary and secondary units including the suspended solids and bacterial solids removed? [5495 m3 /day] f. What fraction of a toxic chemical present in the inflow to the plant is removed from the effluent (to the sludge) by the treatment plant if the solid-water partition coefficient of the chemical is Ks = 1000 L/kg? [22%] g. What value of dilution Sm is required to meet the regulatory limit on BODm? Is this value of dilution easy or difficult to achieve? [7; easy]
29
7. BOD in surface waters 7.1.
Wastewater saturated with dissolved oxygen (DOsat = 12 mg/L) is discharged into a river that has zero BOD and is saturated with oxygen (also DOsat = 12 mg/L) upstream of the discharge point. The minimum DO in the river downstream from the discharge is DOmin =2 mg/L. Calculate the five-day biological oxygen demand (BOD5) of the wastewater being discharged, assuming that k d = 0.2/day, k r = 0.42/day, and the ratio of the river flow to the wastewater flow is Qa /Qe = 10. [286 mg/L]
7.2.
After receiving the discharge from a waste treatment plant, a river has a dissolved oxygen concentration of 8 mg/L and an ultimate BOD of 20 mg/L. The saturation dissolved oxygen concentration is DOsat = 10 mg/L, k d = 0.2 day−1, and k r = 0.6 day−1. The river travels at a velocity of 10 km/day. Calculate the location of the critical point (time and distance) and the oxygen deficit and concentration at the critical point.
7.3.
The ultimate BOD of a river just below a sewage outfall is 50.0 mg/L and the DO is at the saturation value of 10.0 mg/L. The deoxygenation rate coefficient is 0.3/d (k d) and the reaeration rate coefficient is 0.90/day (k r). The river is flowing at a speed of 48.0 miles/day. The only source of BOD on this river is this single outfall. a. Find the critical distance downstream at which the DO in the river is a minimum. [87.9 miles] b. Find the minimum DO value. [0.38 mg/L] c. If a wastewater treatment plant is to be built, what fraction of the BOD would have to be removed from the sewage to assure a minimum of 5.0 mg/L of DO everywhere downstream. [48% removed]
30
7.4.
A municipality discharges sewage with an ultimate BODe = 300 mg/L and a DOe = 0 mg/L. The discharge is into a large coastal water body with an ambient BODa = 0 BODa DOa
U
coastline BODe DOe
BODm DOm Mixing zone
BODx DOx
and a saturated dissolved oxygen level Doa = DOsat = 10 mg/L. a. If the BOD and the DO concentrations immediately after initial mixing is measured to be BODm = 6 mg/L and DOm = 9.8 mg/L, what is the initial dilution Sm? [50] b. The mixed flow is carried along the coastline with a velocity U = 1km/day. If the deoxygenation and reaeration rates are k d = 0.25/day and k r = 0.5/day, respectively, what will the dissolved oxygen concentration DOx be in the mixed flow at a distance x = 1 km down the coast? Use the values of BODm and DOm given in part (a). [8.85 mg/L] c. For the same conditions as part (b), what will be the ultimate BODx measured in a water sample from the mixed flow taken a distance x = 1 km down the coast. [4.7 mg/L] 7.5.
A well-mixed oxidation pond with a total volume V = 100 m3 treats a steady water flow Q = 100 m 3 /day. Measurements indicate that the dissolved oxygen concentration is reduced from DOin = 10 mg/L in the inflow to DOout = 5 mg/L in the outflow as a result of the BOD in the inflow consuming oxygen within the pond. The pond is covered, so there is no reaeration occurring within the pond
COVER
Q
Q DOin Cin BODin
Pond
k d
V
DOout Cout
31
a. The oxygen-consuming organic material in the flow is C5H12 and the reaction is: C5H12 + 3O2 + NH3 C5H7NO2 + 4H2O where C5H7NO2 is bacterial biomass and the molecular weights are H = 1, C = 12, N = 14, and O = 16. If C in and Cout are the concentrations of C 5H12 in the inflow and outflow respectively, calculate the concentration change ∆C = Cin – Cout. [3.75 mg/L]
b. Assuming that BOD in the pond reacts with a first-order coefficient k d = 0.25/day, calculate the ultimate biological demand of the inflow BODin. [25 mg/L] c. If the cover is removed and reaeration occurs, will ∆C increase or decrease or stay the same? Why? [stays the same] d. If the cover is removed and reaeration occurs, will DOout increase or decrease or stay the same? Why? [increase] 7.6.
A sewage treatment plant discharges a steady flow of effluent into a river upstream from the point where the river discharges into the ocean. The river has a constant cross-sectional area AR = 100 m2, and upstream from the sewage treatment plant the average river velocity is steady and equal to UR = 104 m/day, the dissolved oxygen concentration is DOR =10 mg/L, and the biological oxidation demand is BODR =0 mg/L. The effluent flow from the treatment plant is QP = 105 m3 /day, the effluent dissolved oxygen concentration is DOP = 0 mgIL, and the ultimate BOD of the effluent is BODP = 100 mg/L. The discharge from the plant mixes completely with the river flow and passes into a section of the river that extends a distance LR = 11,000 m to the ocean and that is covered so that no oxygen exchange with the atmosphere can take place. The coefficient of deoxygenation in the river is k d = 1.2/day.
a. The ambient dissolved oxygen concentration in the ocean is DOo = 8 mg/L. With the present river channel configuration, the dilution of the river flow by ocean water is Sm =2. For these conditions, what is the dissolved oxygen concentration DOm in the ocean after initial dilution? [5.4 mg/L]
32
b. The EPA requires that the dilution be increased. Your consultant offers to redesign the discharge of the river into the ocean to obtain additional dilution such that the dissolved oxygen concentration in the ocean after mixing becomes DOm = 7.99 mg/L for DO o = 8 mg/L and for the worst case condition when the dissolved oxygen level of the river discharge into the ocean is zero. Do you think this is a feasible proposal? Why? [800; no; Sm too large; not practical] 7.7.
A combined sewer (sewage mixed with stormwater) carries a steady flow Qs = 0.5 m3 /sec in a culvert with a cross-sectional area As = 50 m2 and a length ls = 1500 m. At the upstream end of the culvert the BOD in the sewer is LSO = 20 mg/L and the dissolved oxygen is at the saturated value DOSO = 10 mg/L. The culvert enters a river with a steady flow QR = 5 m3 /sec and a cross-sectional area AR = 250 m2 at a distance lp. = 4 km downstream from a dam. The river flow leaving the dam has zero BOD and a dissolved oxygen concentration DORO = 5 mg/L. The rate of deoxygenation of BOD in the culvert is k = 0.25/day, and the rate of reaeration in the river is k r = 0.5/day.
a. Assuming that no reaeration occurs in the culvert, what is the BOD (LS) and dissolved oxygen concentration DOs in the culvert flow at the point where it meets the river (before mixing with the river water)? [Ls = 12.9 mg/L and DOs = 2.9 mg/L] b. What is the dissolved oxygen concentration DOR in the river right before it mixes with the culvert flow? (Assume that DOsat = 10 mg/L everywhere.) [8.4 mg/L] c. What is the BOD and the dissolved oxygen concentration in the river after mixing with the culvert flow (L M and DOM)? [L = 1.2 mg/L and DO = 7.9 mg/L] 7.8.
A sewage treatment plant discharges treated effluent into a large water body. The total flow through the plant is Q = 104 m3 /day. The BOD of the effluent entering the secondary treatment unit is So = 350 mg/L and the BOD of the effluent is S = 50 mg/L. The BOD and dissolved oxygen in the water body at the end of the mixing
33
zone are BODm = 1.0 mg/L and DOm = 10 mg/L, respectively. The ambient BOD is BODa =0. The saturated value of dissolved oxygen is DOsat = 12 mg/L everywhere.
a. What is the dilution Sm (do not confuse with a BOD value!) achieved in the mixing zone of the effluent and the water body? [50] b. If the yield of the secondary treatment unit is Y = mass biosolids produced/mass BOD consumed = 0.5, what is the total mass flow of sludge biosolids produced in the secondary unit? Assume that BOD is removed only in the secondary unit. [1500 kg/day] c. What is the minimum dissolved oxygen concentration DOmin that could possibly occur at any point in the water body as a result of the effluent discharge? [9 mg/L] d. What is the maximum value of dissolved oxygen DOmax that can occur at any point in the water body? [12 mg/L]
34
8. Groundwater 8.1.
In a laboratory test, a one cubic meter sample of an aquifer saturated with water was found to weight 1400 kg. After being allowed to drain thoroughly, the sample weighed 1100 kg. After being crushed and thoroughly dried, the sample weighed 900 kg. Calculate the specific yield, the porosity, the specific retention, and the specific gravity of the solids (ratio of solid density to that of water). [η = 0.5; Sy = 0.3; Sr = 0.2; Specific gravity = 1.8]
8.2.
Radioactive material is spilled accidentally into an aquifer. The groundwater elevation of the aquifer at the site of the spill is 10 m above the water surface of a river 1.5 km away. Neglecting any effects of retardation, estimate the length of time required for the material to reach the river if the aquifer material is: a. b. c. d.
8.3.
Gravel Clay Sandstone Granite
[12.5 days] [2.3 x 108 days] [7500 days] [5 x 106 days]
An accidental spill of pollutant creates a ``blob'' of contaminated groundwater moving horizontally in an unconfined aquifer. Two wells are drilled a distance L = 100 m apart directly in the path of the blob. At each well, a continuous 1.3 mg/L h1
h2
L BLOB
c1
250 days c1
c2 c2
0.7 mg/L
500 days
measurement is made of the water level in the well and the concentration of the pollutant in the aquifer at the site of the well. a. If the water levels in the wells are observed to be steady at h1 = 100 m and h2 = 90 m, and the pollutant concentrations are as shown in the plots, estimate the hydraulic conductivity of the aquifer, K. Assume that the pollutant is not retarded by sorption and that the porosity of the soil is η = 0.5. [2 m/day] b. Assuming that the pollutant undergoes a first-order reaction that decreases the concentration as it moves, use the information on pollutant concentration to estimate the first order reaction coefficient, k r. Assume that dispersion is negligible. [2.5 x 10-3 /day]
35
c. Discuss briefly and qualitatively how retardation and dispersion will affect the time history of and concentrations measured at the wells. [retardation will increase all the travel times; dispersion will spread out the concentration over more groundwater, reducing the peak concentrations] 8.4.
A confined aquifer with a thickness B = 10 m and width W = 100 m is contaminated with a toxic pollutant over a region with a length L = 500 m. The soil in the aquifer has a hydraulic conductivity K = 1 cm/s and a porosity η = 0.2. The retardation factor for the pollutant R = 10. To clean up the contamination a uniform flow of water is created in the aquifer by pumping out contaminated water on one side and pumping in clean water on the other. The total rate of pumping is Q = 0.02 m3 /sec. Q
Q
∆h
L
Flow
Contaminated Soil
B W
a. What is the difference in the piezometric head ∆h between the injection and removal wells? [1 m] b. How long will the pumping have to last to remove the pollutant completely? [578 days] c. If the initial total concentration of pollutant (sorbed and dissolved) is C tot = 100 mg/L, what is the initial concentration of dissolved pollutant in the water pumped out of the aquifer? [50 mg/L] 8.5.
An accidental spill results in 100 gallons of a toxic liquid chemical entering an unconfined aquifer. The aquifer has a porosity of 0.25 and a hydraulic conductivity of 10-3 m/s. The density of the liquid is 1200 kg/m3 and the sorption to solids is negligible. Groundwater samples show that the chemical quickly dissolved in water, forming a “blob” with a total volume of 105 m3. a. What is the minimum volume of porewater that must be pumped out to remove the contaminant? [2.5 x 104 m3]
36
b. What is the concentration of the chemical in the porewater within the blob immediately after dissolution in the groundwater? [18 mg/L] c. The aquifer water table has a constant slope given by ∆h/L = 0.001. The blob is moving with the groundwater. As it moves, the chemical is degraded by reaction at a rate of 1/yr. How far will the blob move before the concentration is reduced to 1% of its initial value? [580 meters] 8.6.
An unlined landfill is located on a hill above a populated area. The landfill area is 100 m2 and the bottom of the landfill is 100 m above the water table. The groundwater flows at a Darcy velocity of 1 m/d toward a drinking water well (1 km away). The hydraulic conductivity of the soil is 10 m/d and the porosity is 0.4. Estimate how long it will take a contaminant plume with a retardation factor of 5 to reach the well by leaching from the landfill and traveling horizontally with the groundwater flow.
8.7.
A landfill is lined with a 10cm thick layer of clay (porosity = 0.45, K=5 x 10-8 cm/s) overlying sandy soil (porosity = 0.35, K=10-2 cm/s). Estimate how long it will take for the leachate to penetrate the clay liner. Also, If the liner was not there, how long would it take a toxic compound with a retardation factor of 5 to reach the water table 10 m below the landfill?
8.8.
Municipal solid wastes are placed and compacted in a landfill (layers of 2m deep). Before placement, the material has a density of 300 kg/m3 of which 25% (by weight) is water. After compaction the waste has a density of 600 kg/m3 and a maximum moisture content of 0.3. The annual rainfall is 900 mm, of which 67% is lost to evaporation and 17% to runoff. Estimate the time for one layer of waste to become saturated (achieve maximum water content) with rain.
8.9.
An agricultural area (of 10 4 m2) is fertilized with sludge containing high lev els of arsenic that pose a health threat. The area gets an annual rainfall P = 1 m and an annual evaporation E = 0.5 m. Water enters the area as irrigation flow QI and leaves as seepage downward to the soil. The aquifer has a ∆h/L = 0.1, K = 0.01 m/d, and η = 0.4. a. Estimate the magnitude of the irrigation flow Q I (in m3 /day) necessary to keep the agricultural area saturated (for growing rice).[290 m 3 /day] b. Once the arsenic reaches the aquifer, how much time will it take to read a drinking water well located 50 m from the area in the direction of flow? Assume that arsenic has an R = 2.
8.10.
The annual precipitation and evaporation for a watershed of area Aw = 109 m2 are P = 1 m/year and E = 0.5 m/year. Infiltration is negligible because of a relatively impermeable clay layer close to the ground surface. To allow rainfall to be astored as groundwater, rainfall is routed to a spreading basin constructed with a bottom surface in contact with soil with a coefficient of permeability K = 1m/day and a porosity n = 0.4 at all depths. Water flowing from the watershed and then through the bottom of the spreading basin eventually reaches the water table of a regional
37
unconfined aquifer located a distance La = 10 m below the spreading basin. The water table of the regional aquifer has a slope ∆h/L = 0.001. The runoff from the watershed contains bacteria that sorb to the solids in the soil with a retardation coefficient R = 2.
P
watershed (Aw)
Impermeable layer
La
As
well
Lw
E
Spreading basin water table
∆h/L Aquifer (K, n)
a. What should the area As of the spreading basin be to allow all of the excess rainfall (precipitation less evaporation) to reach the groundwater? Assume that all processes are stead and that the water depth in the spreading basin is very small relative to La. b. A nearby town has a water supply well located a distance Lw = 1.0 km from the spreading basin. What is the total time it takes for a bacterial cell to travel from the spreading basin to the well? 8.11.
A total volume Vo = 104 m3 of oil stored in an unlined reservoir leaks into the soil below. After some time all of the oil reaches the water table, where it floats on top of the water without mixing with the water. The density of the oil is ρo = 900 kg/m3 and the viscosity of the oil is µo = 10-1 kg/m-sec.
38
Reaction Tank Oil reservoir Leak L
Q
Q
Floating oil
a. If the hydraulic conductivity of the soil is K = 10 m/day and the porosity of the soil is 0.4, how long will it be before the oil first reaches the water table, which is a distance L = 10 m below the surface of the oil reservoir (assume that the oil level in the reservoir remains nearly constant during this interval)? Assume that the effects of sorption are negligible (R = 1). [note: the viscosity of water is µo = 10-3 kg/m-sec] [44.4 days] b. If the porosity of the soil is 0.4, and the oil completely saturates the soil, what is the total volume of solid material (soil) that is contaminated after all of the oil reaches the water table? (do not include the soil between the reservoir and the water table.) [1.5 x 104 m3 solids only] c. A pump and treat system is to be used to clean up the floating oil. Oil is pumped from the ground at a rate Q = 1 m3 /day into a well-mixed reaction tank where the oil is degraded by bacteria at a first-order rate k r =0.1/day. The undegraded oil and water generated by the reaction is pumped back into the ground. What should the volume V of the tank be so that 50% of the oil entering the tank is degraded? [10 m3] d. The oil degradation is accomplished by a culture of bacteria (C5H7NO2) that consume the oil (C2H3) according to the following reaction: 20C2H3 + 15O2 + 8NH3 8C5H7NO2 + 14H20 After all of the oil is degraded, what will be the total mass of bacteria generated by the pump and treat system?
8.12.
A superfund site contains a large number of buried barrels of hazardous waste containing PCBs. The barrels begin leaking slowly, which results in a concentration of 5 µg/L in the groundwater directly beneath the barrels. A private drinking well is located one kilometer from the site in the direction of groundwater flow.
39
a. The Darcy velocity in the aquifer is V = 0.2 m/day, the porosity of the aquifer is 0.4, and the retardation factor for PCB is R = 5. How long will it take for the PCBs to reach the drinking water well? [10,000 days] b. If the first-order rate constant for degradation of PCB in the aquifer is 4 x 10-4 /day, what will be the concentration of PCB in the groundwater when the PCBs reach the drinking water well? [0.092 µg/L] 8.13.
Use the Kozeny-Karman equation to determine: a. The hydraulic conductivity of sand with a uniform grain size of 0.1 mm and a porosity of 0.35. [5.5 x 10-3 cm/s] b. The conductivity of the same sand with respect to a flow of oil with a specific gravity of 0.9 and a viscosity µoil = 0.1 kg/m-sec. [~5 x 10-5 cm/s; oil moves 100 times slower]
8.14.
A 750-meter long section of river runs parallel to a channel 1000 m away. A confined aquifer connecting the two has a hydraulic conductivity equal to 7.0 m/day and a thickness of 10 m. The surface of the river is 5.0 m higher than the surface of the channel. Estimate the rate of seepage from the river to the channel. What material is the aquifer made of? [262.5 m3 /d; based on the K, sandstone]
8.15.
A confined aquifer with a porosity η = 0.5, height B = 10 m, and constant width W = 100 m connects directly to a lake with a surface area AL = 105 m2. The groundwater flow in the aquifer is toward the lake with a steady Darcy velocity V = 0.1 m/day. There is no outflow from the lake and the flow from the aquifer is balanced by evaporation from the lake surface.
40
a. What is the rate of evaporation from the lake surface E, expressed as meters per year? [0.365 m/yr] b. The piezometric head at a distance L = 100 m from the lake is h1 = 16 m, and the piezometric head at the lake is h2 = 15 m (all relative to the datum at the bottom of the aquifer). What is the hydraulic conductivity of the aquifer K? [10 m/day] An old underground tank is leaking PCB steadily into the aquifer at a distance L 100 m from the lake. The flow of PCB from the tank mixes uniformly with the groundwater flow in the aquifer as it passes by the tank, creating a uniform dissolved PCB concentration C 1 = 2 x 10-2 mg/L in the aquifer at that point. The dissolved PCB concentration in the aquifer just before it flows into the lake is C 2 = 1 x 10-2 mg/L.
c. What is the mass flow of PCB leaking from the tank? Assume that there are no other sources of PCB and that the volume flow of the leak is negligible compared to the flow in the aquifer. [2 g/day] d. The PCB degrades with a first-order reaction coefficient k r = 10-4 /day in the aquifer. What is the retardation coefficient R of the PCB in the aquifer? [13.9] The dissolved PCB concentration in the lake water is C L = 9 x 10-5 mg/L. The lake has a steady suspended solids concentration C ss = 1 mg/L and a steady particle settling velocity of ws = 1m/day. The sediment partition coefficient between the PCB and these particles is Ks = 105 L/kg. The PCB is concentration in the lake fish with a bioconcentration factor BCF = 10 5 L/kg. The fish are caught and completely consumed by the residents of a nearby town with a population of 1,000 at a rate of 1 fish weighing 10 g per day per person.
e. Assuming that the PCB also degrades in the lake with a first-order coefficient k r = 10-4 /day, determine the rate (mass/time) at which the PCB in the lake: i) ii) iii)
degrades in the lake [9 mg/day] sorbs to suspended solids in the lake and settles to the bottom [900 mg/day] is removed with the fish [90 mg/day]
f. The carcinogenic potency of the PCB for oral ingestion is 7.7 [mg/kg/day]-1. How many of the occupants of the town will die of cancer from eating the fish
41
from the lake? Assume that all the people are adults weighing 70 kg and that they eat fish all their adult life. [9.9 or 10 people will die]
42
9. Solid and Hazardous Waste 9.1.
An incinerator burning chlorobenzene has an inflow rate of chlorobenzene of 153 kg/hr and an outflow rate of 0.01 kg/hr. The outflow rate of HCl (measured after pollution control) is 1.2 kg/hr and the outflow rate of particulates is 3.615 kg/hr (measured at 7% O2). The stack gas flow is 375.24 dscm (dry standard cubic meters) per minute. a. Does the incinerator meet a target DRE of 99.99% for chlorobenzene? b. Assuming that all of the chlorine in the chlorobenzene is converted to HCl, does the incinerator meet the standards on HCl specifying that the outflow will be less than the larger of 1.8 kg/hr or 1% of the HCl in the stack gas before pollution control? (compute both limits, assume 1 mole of chlorobenzene gives 1 mole of HCl) c. Does the incinerator meet the target of 180 mg/dscm of particulates (measured at 7% O2)?
9.2.
Solid waste is generated by a small municipality with a population of 100,000. The total waste generated is 2.5 kg/person-day. Characteristics of the waste are shown below. The compaction ratio is the ratio of the compacted to uncompacted density: Type
Paper Food Rubbish Ash/Metal
% of total (by weight) 45 15 15 25
Density (kg/m3)
Compaction ratio
80 300 160 480
5.0 2.5 4.0 3.0
Estimate the area of land required for a landfill with an average depth of 7.5 meters that will serve the municipality for 20 years assuming that the volume of waste is 85% of the total landfill volume (the rest being fill). [5 x 105 m2] 9.3.
Municipal solid wastes are placed and compacted in a landfill (layers of 2m deep). Before placement, the material has a density of 300 kg/m3 of which 25% (by weight) is water. After compaction the waste has a density of 600 kg/m3 and a moisture content of 0.3. The annual rainfall is 900 mm, of which 67% is lost to evaporation and 17% to runoff. Estimate the time for one layer of waste to become saturated (achieve maximum water content) with rain. [2.14 years]
9.4.
Domestic municipal solid waste is a small fraction of the total solid waste. Why should we care about recycling our papers and plastics if we contribute a small fraction of the total waste? Shouldn’t the focus be on industries rather than individuals?
9.5.
An incinerator burns toxic waste, producing a plume that extends downwind. Before pollution control equipment is installed, the rate of sulfur dioxide (SO2) gas
43
emission is measured to be 100 kg/day. For the most common wind and atmospheric stability conditions the maximum concentration of SO2 is measured at a point one kilometer downwind to be 100 µg/m3. 9.6.
Vinyl chloride is used by a manufacturing facility which discharges to a nearby river a steady effluent flow Q eF = 0.01 m3 /sec with a vinyl chloride concentration CeF = 1 mg/L. The river has a steady flow Qa = 1 m3 /sec, a constant cross-sectional area A = 100 m2, and an ambient vinyl chloride concentration Ca = 0. The facility also pumps a quantity of the vinyl chloride to a treatment plant which also discharges to the river, at a distance Lp = 1000 m downstream from the facility discharge, a steady effluent flow QeP = 0.5 m3 /sec with a vinyl chloride in , from the treatment plant is concentration CeP = 0.01 mg/L. A sludge flow m burned in an incinerator with a destructive removal efficieny DSR = 99.99% and a out =10-4 kg/day of vinyl chloride in the stack gas (leaving the mass flow m incinerator).
a. Assuming that the vinyl chloride has a first-order decay rate k r = 1/day in the river, calculate the concentration of vinyl chloride CmP immediately downstream from the discharge from the treatment plant. (neglect any decay in the channels leading to the river.) b. Calculate the mass flow of vinyl chloride in kg/day used by the facility. (do not consider any decay of the vinyl chloride in the facility, treatment plant, or sludge flow.)
44
10. Air Quality 10.1.
A single story home with infiltration rate of 0.5 ach has 200 m2 of floor space and a total volume of 500 m3. If 0.6 pCi/m2-s of radon is emitted from the soil and enters the house, estimate the steady-state indoor radon concentration.
10.2.
A manufacturing company has gathered the following information on annual mass flows of methylene chloride (CH2Cl2) in and out of the manufacturing plant: Purchases of CH2Cl2: Concentration of CH 2Cl2 in the flow to the treatment plant: Discharge to the treatment plant:
228 barrels 4.04 mg/L
0.076 m 3 /s 228 barrels (25% CH 2Cl2 CH2Cl2 shipped out as hazardous: by volume) Unused barrels of pure CH 2Cl2: 8 Estimate the annual mass emissions of CH 2Cl2 from the plant to the atmosphere. (Note: 1 barrel = 0.12 m3 and the density of CH 2Cl2 is 1326 kg/m 3)
10.3.
in ) A manufacturing plant receives shipments of pure chlorine (Cl2) at a rate of ( m 750 kg/day. The plant manufactures trichloroethylene (TCE) (C2HCl3) which it out ) at a rate of 700 kg/day. Liquid and solid waste from the plant ships out ( m passes through a settling basin at a rate of Q = 1000 m3 /day. TCE in the sludge s = 100 kg/day. The concentration from the settling basin is removed at a rate of m of TCE vapor in the air inside the plant is Cp = 10 mg/m3. The air flow through the plant volume achieves a ventilation rate I = 1/hr, and the inside volume of the plant is V = 105 m3. The ambient concentration of TCE in the outside air is zero. I
in m
Plant
out m V
Cp
Cout Settling basin Q
s m a. Assuming that the above quantities are the only mass flows in and out of the plant, and that there is no storage of Cl2 or TCE inside the plant, what is the concentration Cout of TCE in the flow out of the settling basin?
45
b. A total of 100 workers in the plant (each assumed to weigh 70 kg) are exposed to cancer risk by breathing the air at a rate of 20 m3 /day for 50 years out of their 70 year lifetimes. The potency factor for TCE by inhalation is 1.3 x 10-2 [mg/kg/day]-1. The benefit of reducing the risk is estimated to be $2 x 106 per life saved. If the cost of ventilation is $100,000 x I, where I is measured in hr-1, should the ventilation rate be increased (or decreased) so that the benefits equal the costs? c. The sludge from the settling basin is continuously removed and burned in a hazardous waste incinerator. The mass flow of TCE in the airflow from the incinerator is 10-3 kg/day. Does the incinerator meet a performance standard of DRE 99.99%? 10.4.
Determine the PSI and the air quality description for a day in which the following maximums occurred: [PSI = 150] 1-hr O3 concentration 230 µg/m3 8-hr CO concentration 12 mg/m3 24-hr TSP concentration 200 µg/m3 24-hr SO2 concentration 325 µg/m3 1=hr NO2 concentration 100 µg/m3
10.5.
A freeway has 10,000 vehicles per hour passing a house 200 m away. Each car emits an average of 1.5 g/mile of NOx, and the wind is blowing at 2 m/s across the freeway toward the house. Estimate the NOx concentration at the house on a clear summer day at noon (neglect any reactions involving NOx). [0.038 mg/m3]
10.6.
A stack emitting 80 g/s of NO has an effective stack height of 100m. The wind speed is 4 m/s at 10m, and it is a clear summer day with the sun nearly overhead. Estimate the ground level concentration at the following locations: a. Directly downwind at a distance of 2 km [38 µg/m3] b. At a point located 2 km downwind and 0.1 km off the downwind axis. [36 µg/m3]
10.7.
Sidestream smoke from a cigarette contains roughly 100 µg of benzo-a-pyrene. How many cigarettes per day would yield enough sidestream smoke to increase the cancer risk for a non-smoker by 1 x 10-6 if that individual spends all of his time indoors in a 150-m3 home having 0.5 air exchanges per hour? Assume that benzoa-pyrene has a half-life of 3 days, an inhalation potency factor of 6.11 [mg/kg/day]1 , and that its ambient concentration is negligible. [0.01 cigarettes/day]
10.8.
An office building with a volume V = 2000 m3 and an infiltration rate I = 1/hr is exposed to the 100 µg/m3 SO2 concentration so that the ambient concentration around the office building is Ca = 100 µg/m3. Assuming that there are no other sources of SO2 in the office, and that the reaction rate for SO2 is K = 0.23/hr, determine if the concentration of SO 2 in the office air exceeds the recommended limit of 80 µg/m3.
46
a. If the SO2 emission rate is reduced to 20 kg/day, what will be the maximum SO2 concentration one kilometer downwind form the most common wind and atmospheric conditions? b. To reduce the SO2 emission rate from 100 to 20 kg/day, a wet scrubber is installed that injects lime (CaO) and water (H 2O) into the air flow leaving the incinerator. The lime and water react with the SO2, creating solid calcium sulfite dihydrate (CaSO3·2H2O) according to the following reaction: CaO + SO2 + 2H2O CaSO3·2H2O c. Determine the mass flow of solid calcium sulfite dihydrate generated in the scrubber, assuming that the required reduction in SO2 output is achieved and that all of the injected lime reacts. 10.9.
A tank full of liquid chlorine ruptures and chlorine vapor (Cl2) is emitted at a mass rate of 30 kg/min at ground level. The wind speed is 3 m/s. You are asked by the fire marshal whether she should evacuate an apartment building that is located at a distance L = 300 m downwind from the tank car. The threshold concentration of Cl2 vapor for health effects is 1.0 ppm. What is your recommendation?
10.10. A plume of particulate material from a point source has a centerline concentration C1 = 100 µg/m3 at a distance x1 = 100 m from the source. The atmospheric stability condition is B. plume
u C1
C2
e m H
X1 X2
a. What is the centerline concentration of particulates C2 in the plume at a distance x2 = 1000m from the source? b. Health data from adult workers exposed to the particulates at a concentration Cw = 1000 µg/m3 for a total duration T d = 0.1 years indicate that the risk of dying from this exposure is 10-6. What is the risk to the same adults if they were to
47
breath the air in the plume at concentration C1 = 100 µg/m3 for a lifetime T 1 = 70 years. c. A building with a volume V = 100 m3 is exposed to the plume so that the ambient concentration of the particulates for the building is Ca = C1 = 100µg/m3. There are no sources of particulates in the building. The concentration of the particulates inside the building C has been measured for different values of the air exchange rate I, as shown on the following plot: 100 90 80 70 ) 60 3 m / g 50 µ µ ( C 40
30 20 10 0 0
1
2
3
4
5
6
7
8
9
10
I (1/hr)
What is the decay coefficient K (same as k r and λ) for the particulates inside the building? 10.11. The centerline (y = 0) ground level (z = 0) concentration of benzo(a)pyrene at a distance x = 1000 m downwind from a smokestack with an effective height H = 50 m is Cg = 10 µg/m3 at a time when the wind velocity at the effective height is u = 10 m/sec and the atmospheric stability class is C. plume
u
e m
Cg
H
x
a. What is the mass flow the of benzo(a)pyrene out of the stack (kg/day)? [294] b. If the carcinogenic potency of benzo(a)pyrene is 6.1 [mg/kg/day]-1, what is the lifetime risk to a person exposed to Cg = 10 µg/m3, assuming that the person breaths 20 m3 /day of air and weighs 70 kg? [Risk = 0.017; high]
48
c. What is the lifetime risk from exposure to benzo(a)pyrene of a person (with the same weight and rate of breathing as in part (b)) who spends all the time in a building exposed to the concentration cg = 10 µg/m3 (i.e. Cg = Ca for the building), assuming that the building has a volume V = 1000 m3 and an air exchange rate I = 0.5/hr, that the benzo(a)pyrene has a half-life T1/2 = 3 hours, and that there is no source of benzo(a)pyrene in the building? [Risk = 0.012] 10.12. A factory located on property with dimensions 200 m by 200 m emits a total mass = 100 kg/day of a conservative (no decay) toxic compound from a vent flow m located a height H = 10 m off the ground (assume this is the effective height of release). The wind speed magnitude, measured at 10 m above the ground, is constant at u = 5 m/s. but the direction of the wind can vary. The ambient concentration of the compound is zero. Compute the time averaged concentration of the toxic compound experienced by an individual living at ground level (z = 0) on the boundary of the factory property which is a distance L = 100 m from the source. Do this computation in two ways: a. Use the worst-case atmospheric stability condition and assume that the individual experiences the laterally centered plume concentration (y = 0) at ground level (z = 0) a total of 10% of the time. The other 90% of the time the individual experiences no effect from the source. Use Table 7.8 and Figure 7.48 in the text. [3.2 x 10-8 kg/m3] b. Assume that the air volume over the property is well-mixed to an inversion height of 50 m and that the individual experiences the mixed concentration 100% of the time. Assume the airflow into and out of the volume is through one of the 200 m long sides at the velocity given above. [2.3 x 10-8 kg/m3]
10.13. A tank truck carrying liquid chlorine overturns and the chlorine vapor (Cl2) is e = 0.5 kg/sec, generating a potentially toxic plume. The wind is emitted at a rate m estimated to have a speed of u = 3 m/sec directly toward an office building filled with people that is located a distance L = 300 m downwind.
49
a. The fire marshal asks you to help estimate if the people in the building could possibly, in the worst case conditions, be exposed to a plume concentration greater than 10 ppm of Cl2. What advice do you give her? [238 ppm; evacuate] b. Experiments with chlorine vapor indicate that in a room with a volume V = 100 m3 and an infiltration rate I = 1/hr, the concentration inside the room (C) is related to the ambient concentration (C a) by the following plot:
Use this information to estimate the reaction coefficient k r (also K) of the chlorine in the room. Assume that there is no other source of the chlorine other than the ambient air. [4/hr]
10.14. An unlined hazardous waste landfill is located on a hill above a populated area. The landfill area is A L = 100 m2 and the bottom of the landfill is a height LL = 100 m above the water table. The groundwater flows with a Darcy velocity V = 1 m/day toward a well located a distance Lw = 1 km from the edge of the landfill. The hydraulic conductivity of the soil is K = 10 m/day everywhere and the porosity is η = 0.4 everywhere. A wind with velocity u = 10 m/s carries a plume of hazardous waste vapor toward the well site at a height H = 50 m above the ground. The atmospheric stability category is C.
50
a. Estimate how long will it take a contaminant plume with a retardation factor R = 5 to reach the well by leaching from the landfill and traveling horizontally with the groundwater flow. [5.5 years] b. After the contaminant reaches the well, the concentration in the well water is Cw = 10 mg/L. If the porewater concentration of the contaminant in the landfill is CL = 100 mg/L, what is the area of the aquifer AA though which the groundwater flows? Assume that the contaminant leaching is a continuous process that has reached steady state and that the leaching flow mixes uniformly over the aquifer area. [104 m2] c. The measured concentration of contaminant vapor in the air is CA = 10 mg/m3 at ground level at the well site. Use the dispersion diagrams in your text to estimate the rate of contaminant vapor emission Qv (mass/time) from the landfill. [3.5 kg/sec] d. If a person living near the well breathes 20 m3 of air a day and drinks 2 L a day of water from the well, what is the ratio of the risk of cancer from breathing to cancer from drinking? Use the values for CA and Cw given above. [Risk of cancer from breathing is 10 times the risk of cancer from drinking] 10.15. A recent article in the New York Times said that airline passengers are complaining of headaches they claim are caused by reduced rates of ventilation of the passenger cabin. The airlines admit that to conserve energy (the air from outside has to be heated) they have increased the time for a complete change of cabin air from 3 minutes to 9 minutes. a. Does this change in the rate of air exchange pose any additional non-cancer health risk due to inhaling acetone vapor for a 70-kg person who flies once a week for 10 hours (coast to coast and back) for 40 years out of a 70-year lifetime? You may assume that the person inhales air at a rate of 5 m3 /day. The RfD for acetone is 0.1 [mg/kg/day] -1 and the rate of decay is zero. The airplane has a volume of 500 m3 and carries 250 passengers each of whom emits acetone at a rate of 50 mg/day. You may assume the cabin is well-mixed and that the
51
outside air contains no acetone vapor. [CDI = 3.9 x 10-4 mg/kg/day << RfD; no non-cancer risk] b. In response to these complaints, investigators conducted controlled measurements of the cabin concentrations of three different compounds (A, B, and C) for different rates of air exchange I. The results of these measurements are shown schematically on the following plot of cabin concentration CC vs. the rate of air exchange I:
Briefly explain why each of these curves might look the way they do, i.e. why the concentration of the different compounds vary in different ways to changes in the cabin air exchange rate. (note: these tests are independent of the conditions given in part ( a)) [A: Ca = K = 0 and S 0; B: S = 0, K >> I, and Ca 0; C: Ca = 0, K >> I, and S 0 or K = S = 0 and C = Ca]
52
11. Radiation/Radioactivity 11.1.
A 55 gallon drum of tritiated water (water containing some 3H) is found on November 11, 1993 in a warehouse. The label specifies an activity of 30 Ci/mL and is dated November 11, 1960. a. If the half-life of tritium is 12.3 years, what is the activity of tritium in the drum now? b. The drinking water standard for tritium is 3 x 10 -6 Ci/mL. Would it be safe to empty the drum into a reservoir with a volume of 5 x 109L? (assume instantaneous mixing) c. How long would you have to store the drum for the activity to decay to the drinking water standard (without dilution)?
11.2.
Liquid radioactive material with a half life of 3 d ays is accidentally discharged into a river that has a constant velocity U = 0.1 m/s and an area A = 104 m2. As it discharges, the radioactive material mixes completely with the river flow. The flow rate Qe and concentration Ce of the accidental discharge are given be the following plots: Qe
Ce 105 µCi/mL
1 L/sec
1000s
time
1000s
time
a. You are responsible for setting the time and distance downstream over which drinking water withdrawals from the river will be restricted until the concentration of the radioactive material in the river falls below the water quality standard of Cmax = 10-3 µCi/mL. What is your recommendation? Give a single time interval and a single distance. Neglect any sorption of radioactive material to suspended solids and assume that the ambient radioactivity level is zero. [173 km] b. At one point in the river after the spill, the total concentration of radioactive material (dissolved and sorbed) is measured to be Ctot = 0.01 µCi/mL. If the sediment-water partition coefficient for the radioactive material is K s = 105 L/kg and the suspended solids concentration in the river is Css = 10 mg/L, what is the dissolved concentration of the radioactive material in the river at that point? [0.005 µCi/mL]
53
11.3.
The radon concentration in a house is measured to be C = 1.5 pCi/L (the Ci is a unit of radiation that is analogous to mass and 1 pCi = 10-12 Ci). The infiltration rate is I = 1/hr and the house volume is V = 500 m3. The decay rate for radon is K = 7.6 x 10-3 /hr. a. One route for radon to enter the house is to be carried in with outside air that enters the house. Assuming that this is the only way radon enters this house, calculate the ambient concentration of radon Ca in the outside air. With this mode of radon entry, will the concentration increase or decrease if the infiltration rate I were to increase? [does not change much as I increases] b. Another route for radon to enter the house is for it to be emitted by the materials from which the house is constructed, essentially forming a source within the house. Assuming that this is the way radon enters this house, calculate the effective radon source strength S in pCi/hr. With this mode of radon entry, will the concentration increase or decrease if the infiltration rate I were to increase? [decreases as I increases; S = 750,000 pCi/hr] c. Data from uranium miners indicate that breathing air with a radon concentration of 100 pCi/L for one month of working hours (173 hours) is estimated to cause a risk of 3 x 10-4 of dying of lung cancer. What is the risk associated with a lifetime (70 years) of breathing air with a radon concentration of 1.5 pCi/L (the average in US households)? Assume that the rate of breathing, body weight, lifetime, and potency are the same as for uranium miners. [Risk = 0.016; too high]
54
12. Risk 12.1.
One way to estimate maximum acceptable concentrations of toxic compounds in drinking water or air is to pick an acceptable lifetime risk and calculate the concentration that would give that risk assuming standard daily intakes given in the handouts. Find the acceptable concentrations of the following substances: a. Benzene in drinking water at a lifetime risk of 10 -5 (in mg/L). b. TCE in air at a lifetime risk of 10-6 (in mg/m3)
12.2.
Suppose a factory releases a continuous flow of wastewater into a local stream resulting in a carcinogen concentration c = 100 µg/L just downstream of the outfall mixing zone. Suppose this carcinogen has an oral potency factor of 0.30 (mg/kg/day)-1 and that it is degradable at a rate k r = 0.1/day. The stream velocity is 1 mi/hr. What is the lifetime cancer risk to individuals in a town 100 miles downstream who use this stream as the only source of drinking water?
12.3.
The RfD for methylene chloride is 0.06 mg/kg/day. Which would be more stringent, a methylene chloride oral concentration standard based on a carcinogenic risk of 10-6 or a standard based on the lifetime oral risk at this RfD (treat this as the potency factor)?
12.4.
In New Bedford Harbor, the well-mixed concentration of PCB is 10-4 mg/L. The FDA limit on acceptable PCB concentration in shellfish to be eaten is 2ppm. How many people are “saved” from dying of PCB-induced cancer by enforcing this regulation among a population of 10,000 people (each weighing 70 kg and consuming 6.5 g of shellfish daily over a lifetime)?
12.5.
The EPA lists Cr(VI) (chromium 6) as a carcinogen with an inhalation route potency factor of 41 (mg/kg-day)-1. A sludge incinerator with no air pollution control equipment is expected to emit Cr(VI) at a rate such that the airborne concentration at the plant boundary immediately downwind of the incinerator is 0.001 ug/m3 (micrograms/m3). Will it be necessary to treat the emissions so as to reduce the Cr(VI) to stay within the risk level of 1 additional cancer per 106 people?
12.6.
Compute the total dose of lead due to inhalation by a child over a period of 2 years for two situations: a. The airborne concentration of lead has a constant value of Co = 1ug/m3 over the 2-year period. b. The airborne concentration of lead is Co = 1ug/m3 at t=0, but then decreases linearly to 0.8 ug/m3 over the 2-year period according to Cair(t) = C o (1 - 0.1t), where t is measured in years. Data: Intake rate for child: 10m 3 /d and f air = 0.3
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12.7.
The child in problem #2 is also exposed to lead in water, food, and dust over the 2year period (f dust=f air, f food = f water = 0.5). The airborne lead concentration is characterized as in part b of problem #2. The lead concentrations in water and food are equal to 10ug/L and 0.1 ug/gram, respectively. The concentration of lead in dust is assumed to be proportional to that in air (see 2b) because lead in dust is a result of settling airborne particles. a. Determine the exposure of the child to lead from all four exposure routes (total dose) over the 2-year period. b. Determine the carcinogenic risk posed by lead if the inhaled potency factor is 42 (mg/kg-day)-1 and the potency factors for water and food are zero. c. Determine the non-carcinogenic risk if the Oral RfD for Cr(VI) is 0.1 (mg/kg-d) 1 and the Inhaled RfD is 5.7 x 10-5 (mg/kd-d)-1. Note that non-carcinogenic risk is defined as (CDI – RfD) x Potency Factor.
12.8.
Suppose 1.0 g/day of heptachlor leaks into a 30,000 m3 pond with no inflow or outflow (neglect the volume of heptachlor). If heptachlor has a half-life of 2 days, and the pond can be assumed to be well-mixed: a. What would be the concentration of heptachlor in the pond (after steady-state had been reached)? b. Estimate the maximum risk of cancer to a 70-kg person who drank 2L/day of that water for 5 years.
12.9.
A simplified view of the PCB contamination problem in New Bedford Harbor is as e = 1 kg/day of PCB into follows: The sediments in the harbor release a total of m the estuary. The estuary is flushed by an effective flow of about Qa = Qm = 100 m3 /s of water with zero PCB concentration (Ca = 0). The released PCBs mix completely with the flushing flow and shellfish located just outside the harbor are exposed to the mixed concentration Cm. For PCB the potency (taken orally) is 7.7 [mg/kg/day]-1, the bioconcentration factor is BCF = 105 L/kg, and the rate of
degradation is zero. a. The FDA (Food and Drug Administration) limit on the acceptable PCB concentration in shellfish to be eaten is 2ppm. How many people are being “saved” from dying of PCB-induced cancer by enforcing this regulation at New
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