1.725 Chemical Fate and Transport
Quiz #1
Friday, 10 October, 2003
Q20
pntS ecI')
1) At an experimental watershed, you have received permission to carry out experiments
in which small amounts of several radionuclides are introduced into a small river as
tracers. In one experiment you introduce an 85 mCi pulse of arsenic-76 (t 1/ 2 =26.4h) in
the chemical form of sodium arsenate into the river. Flow at the time is 2.7 m 3 /s, and
the relatively uniform but winding natural channel has a cross-section of 19 m2 and
average depth of 1.2 meters. u* is 0.3 m/sec.
a)
Estimate a longitudinal dispersion coefficient for this river.
b)
Determine the distance from injection point to point of maximum concentration of
arsenic-76, as well as spatial standard deviation of the radionuclide, 8 hours after the
spill.
c)
What is the activity of the radionuclide at this time and location (expressed as
mCi/L), assuming no sorption occurs?
-'Ad-1\ -f
\I
-
S
's.
bo
di6;act=
'e\ovt
*tine
I M-t
O
= Gklrn , %Nlr i&
b)6%&-%nt ; Xt 0
e~
=
d
OA*2rfI\S
\.1m.
O'\\
(o.\S~m~s
rr\~,~'sm~LC\.2'5O
rs
a-w
EE
vm
EtS
E
'o9
Z
r
om
2~.ts
6- JlTO;S~r~s^
I b}s.
ZaS
C)
CXZ)
6 P_('*It
-s
qr-Y''to
tt _\L
e
ty~~%
soec(L~t
S.
' = \4t
M
\=
areo-
cc,t')
S.oI -mo6%
,
\
e
36.mt
\L. kn2- :
I\m
0 nu
cwr
a
e- O.OLu
JW'
b
OU
-%
I
-
-'\;
t'\J
1. o-2AJ
=L\IA~
4.q
\OL
qAIM(:%JMI
Y
0~M
V~n
(t, L \'
-.
_n
QhI)
,ant
\ 'oo L
mC'L
rL.\
%oAsc - jou bd t
WNs
on6 tht
cues
'nQa
n'tt
tre
tue
o
C
cX' tteitQd YV Coentio),
Q* o
0f%
th
*eo
nt jar 6stvc" \
to qred out,
-Ve
'c
s Wt\ko
mo4mumn
acti'r
SnXt 't;S'on
Cc-tVt decol,
decrees
Wt tmn
Xr rs:odecwj.
W
't eCo
Cxi
t tclat
Cm--
2 (o66f\0noA)
or nVco8nW\ing
ng
'%ytlirutc\u)
.
.
4bAtmt
ast; ctreaies,
mtnWt
6tcrtes,.
'at
OUWt-treaked lkr
_'t\L, a-
SOyntiDW
.
.
.
I
.~~~~~~~~~~~~~~~~-
etV
2) Several large tanks of water are to be adjusted to different pH values in order to test
fish survival under conditions of acidification. Well water with an initial Alk of 6 x 10-4
eq/L and pH of 6.5 is pumped into open storage tanks and amended with H2 SO4 to make
waters having pH values of 6.0, 5.0, and 4.0, respectively.
a) How much H 2CO 3* is initially present in the well water?
b) How much sulfuric acid (in equivalents/L) must be added to the well water to
adjust it to pH 6.0?
c) A day after the storage tanks are filled and adjusted to their correct pH, it is found
that the pH 6 tank has risen to pH 6.5! How could this happen, if nobody has
made any further additions of chemicals to the tanks?
SupshfOn
~
(A
a-)
'4
ejtCS6r-anwW
%tt
WY
C%,
4,
5
V
_
w)
i'CtC-
ttz. r
' c-r
. t
ttYW
5 W.
,s
tCo's t
Ctun nyt\-etCt
C'tr ,t-
~-F -
or c
b) S e C-7 N\L- 3\o- el
A.Vh\naS64crea0td b
5 th.
-
c)
kt
n\Ait\x'naue'o\u\bn
wter
et\\o
ours~tuate\
*t C-L \-AQ\A\nd t es\tNaeq
Iq
tb
Vnct
\
dotsyn cnat
csw
SYct O\ ngI R\VsU\`4
no
tws
rnt0N,
YC)q\
fro Y9
e
0C%6
s r
&
ktCte
tt 6\8
dsgwn
vcreawmu\m.
so sornre
WOA\t \%qr C ,
h
DCLs
L
Ot
'%n,\4\ct6
we
3) A pond has depth d (cm) and area A. Propane gas is added as tracer; propane is
inexpensive, non-toxic, has large Henry's constant, and is easily measured at low
concentrations.
a) What is the expected concentation of propane in the pond as a function of time,
expressed in terms of initial concentration ([C3 H81o)and depth d? (Use kw(cm/sec) =
4 x 104 + 4 x 0l5 ulo2 to estimate gas exchange velocity). Wind is 0.5 m/s. Assume
bulk [C3 H8] is uniform throughout the pond. As always, be clear about units.
b) An experiment is carried out in which methane (CH4 ) is added along with propane.
Methane is more likely than propane to experience significant oxidation (by
methanotrophic bacteria), as well as tend to escape to the atmosphere. If there is no
bacterial oxidation, and methane and propane are initially added in equal
concentrations, what is the expected ratio methane to propane concentration in the
pond as a function of time?
-C
-
d
~.
t2
Nex
6:sOhf0
Cads:
0\ tl
_.\"\ -. I 0"1\d
'L
S~~~~a-r~~~~~~~d;
r
,\chet-\~o
-\;
3*°t\
.\ o- t\d
4) Sediment oxygen demand (or benthic oxygen demand as it may be called) is the rate at
which oxygen is consumed by the bottom sediments of a river or lake. It is often
expressed as a flux density having no dependency on the exact oxygen concentration
of the overlying water (this is obviously an approximation that can not be true for very
low overlying oxygen concentration). One way to estimate benthic oxygen demand is
to put sediment in the bottom of a tank and observe the rate of oxygen consumption
from the water.
In such a test, you put a layer of sediment in the bottom of a cylindrical tank (crosssectional area = 0.5 m2 ) and cover the sediment with a layer of water. The tank is
open to the atmosphere (T = 250 C, Po 2 = 0.2 atm), and you observe that at steady state
the bulk water overlying the sediment in the tank arrives at a constant [02] of 6 mg/L.
The only source of 02 to the water is atmospheric gas exchange. The Henry's constant
for
2
is
L-') at 250C, and you may use a gas exchange velocity (note:
774 'a(mci
m-
it is water side controlled) of 4x10 -4 (Cm/s)under the test conditions.
).
a) Calculate the oxygen demand of the sediment (
\iCcw-W\A):0
\Lt C
--
t- 4'W-'IymS
at
tto'j
1
e
}
&Jtare con&tao't
.
C- 4·\o-*
.AW,
cc .1~t
Ioe')
so i\us
0n
Ad
deml'n
dtm Wayetd\Mnt
Otta
\0L
4\-3K
-1
,%
MS
t\u O'*
3(s a
Yed VA-
.
\ti\oSI
Mn.
5) Estimate the rate of sediment accumulation
(in cm/year) in the following lake (the
result will be essential for purposes such as calculating the associated fluxes of
contaminants to the bottom). Measurements of Lead-210 (t 1/2= 22.3 y) activity yield the
following table and graph. (ignore the excessive sig figs in In (activity)!)
Depth range (cm)
0 to 2
2 to 4
Activity (DPM/g)
Mean depth
3
4
2.7
4 to 6
5
2.1
6 to 8
8 to 10
10 to 12
12 to 14
7
9
0.9
1
14 to 16
16 to 18
18 to 20
1.4
11
0.7
13
0.51
15
17
19
0.33
0.25
0.17
In (Activity)
1.38629436
0.99325177
0.74193734
0.33647224
-0.10536052
-0.35667494
-0.67334455
-1.10866262
-1.38629436
-1.77195684
In activity vs depth
2
1.5
1
X
0.5
0 Series2
-0.5
-1
-1.5
-2
depth (cm)
,
tolvng
Wttn6dronts
\vi \irOe\PII
CorA
C
o\so
Ha
m'winmt
\irn6
a' b-tt
e
eci EsBt-) \Tfer
LAdt
_t at)
'OAVOV~=0.?Jy,
%
1\:
-
'A
-
ntatL
2, -:
t2 13-011
-tklj,
Ulk
- -0 '~l
(
i)
- 0
14
IV
Arot;=
\cr'4r- / \g
/I
i 0%Ir
t-t \0- Ir
1.725 Chemical Fate and Transport
Quiz #2
December 3, 2003
1. (24 pts.) The owner of a small factory has installed a new well to supply process
water. The well is 0.3 m in diameter, and it is fully screened for the entire 12-m
depth of the aquifer, which is composed of coarse sand having an estimated bulk
density of 2 g/cm3 , K of 0.1 cm/s, porosity of 0.25, and organic content of 0.5%. The
radius of influence of this well can be taken as approximately 3,000 meters.
a)
What is steady state drawdown, in the well, if the average water use of the
factory is 360 L/min?
b)
A plume of TCE - contaminated groundwater lies at a distance of 800 m from
the well. What is the average seepage velocity of this groundwater due to well
pumping?
c)
How fast is the TCE plume moving toward the well? Neglect any movement
that may result from regional aquifer flow, plume density, etc. and consider only
dissolved TCE under the influence of well pumping at hydraulic steady state. Note
that log Kowof TCE is 2.42, suggesting that log Ko is about 2.26 according to
regression equations compiled by Lyman et al.
2). (16 pts.) A vulture is circling in a "thermal" above a plowed, open field in which he
has spotted some attractive carrion. While waiting for a party of hunters to depart,
the vulture wants to circle as high as possible (to avoid possibly becoming additional
carrion) while keeping lunch in sight (i.e. remaining below the clouds). Temperature
of air above the plowed field is 18°C and RH is 70%.
a)
What is the dew point at ground level?
Estimate how high the bird can go before reaching the altitude of the lowest
clouds.
3). (20 pts.) The "inventor extraordinaire" has a new idea, namely to mitigate solvent
vapor in the air of automotive spray-painting booths using OH radicals. Your job as her
technical assistant (the inventor is mostly into marketing) is to determine the performance
of the proposed system. The OH generator would need to generate a high enough OH
concentration to maintain solvent vapor concentrations at the same level or lower than
produced by the commonly-used ventilator fans. A suggested "model" for a spray booth
is a box measuring 3 m x 4 m x 8 m, whose volume is 96 m3 , or 96 x 106 cm3 . Assume
ventilator fans provide 5 air changes/hour, and solvent input is about 80 moles/hr (= 4.8 x
1025molecules/hr = 1.3 x 1022molecules/sec) while painting is in progress.
What is steady-state vapor concentration during car painting with the ventilators
a)
running (and no OH generator)?
b)
What is the necessary OH concentration needed to maintain the above solvent
vapor concentration with ventilators off (assume the air in the room is nonetheless wellmixed). Assume the average rate constant for reaction of OH with various paint solvents
is approximately 4 x 10- 13 cm 3 /(molecule/sec).
c)
Are there any problems with this invention (assuming that it is economically
viable and appears to be marketable to potential users)?
4). (20pts). A plane is flying at an altitude of 2,500 meters, in clouds. Outside air
temperature is -3 degrees C, and the pilot has noticed the beginning of icing on the
wings. She calls air traffic control to ask for a different altitude, to avoid the ice.
How low would she have to fly to get out of the ice, if the atmosphere in the cloud
a)
were of neutral stability?
b)
Due to terrain clearance issues, the altitude of part a) is not good, so she instead
asks for clearance to climb out of the cloud to avoid further icing. Although the cloud
tops are at 3000 meters, she is instructed to climb to 3700 meters to avoid other air
traffic. What is the temperature at this altitude? Again assume neutral stability.
5. (20 pts) You have invented a very accurate, lightweight instrument to measure carbon
dioxide in the atmosphere; it can detect as small as a 1 mg per cubic meter change in
concentration over a period of a few seconds. One of your customers wants to use this
instrument to locate moonshine stills hidden in the backwoods, by detecting their carbon
dioxide plumes. For this purpose your detector will be mounted on a robotic blimp, which
will traverse an area of interest.
Grandpa Smith has a distillery that burns 25 kg of dry hickory wood (CH2 0) each hour,
and combustion products are vented via a 10 meter high chimney; however the effective
height is 40 m due to plume rise. The blimp is 50 m above ground and passes 100 m
downwind of Smith's still. What maximum carbon dioxide concentration (in mg/m3 )
does it detect? Assume it is nighttime (of course), with cloudy sky and a 2.5 meter per
second wind.
6) (6 pts) Give brief answers:
a) What is-the principal mode of formation ofstratospheric ozone? How does this
pathway contrast with that for the formation of urban ozone?
b) In what two processes is nitrous oxide naturally formed in ecosystems?
c) Describe why the deposition velocities for ozone and for sulfur dioxide often
follow diurnal cycles in a vegetated region.
7) (2 points Thanksgiving bonus) As discussed in class, when roasting a turkey, roasting
time should be enough to bring the coldest partof the meat up to 180 degrees F.
Recalling that heat and mass both obey the diffusion equation, what scaling rule would
you use to estimate cooking time for a large turkey, if the correct time is known for a
small turkey? (specifically we posed the question: if a 3 lb turkey cooks in an hour, how
long do you cook 20 poundturkey?)
TABLE 4-2 Vapor Pressure of Water
Temperature ( C)
V.P. (mm Hg)
Temperature ( C)
V.P. (mm Hg
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
3.16
3.41
3.67
3.96
4.26
4.58
4.93
5.29
5.68
6.10
6.54
7.01
7.51
8.04
8.61
9.21
9.84
10.52
11.23
11.99
12.79
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
13.63
14.53
15.48
16.48
17.54
18.65
19.83
21.07
22.38
23.76
25.21
26.74
28.35
3004
31.82
33.70
35.66
37.73
39.90
42.18
44.56
'Source: Weast(1990).
TABLE 4-5
Pasquill Stability Categories
Insolation'
Surface
wind speed
(m/sec)'
Strong
Moderate
Nightb
Slight
Thinly
overcast or
-2 low
cloud
S< cloud
<2
A
A-B
B
-
2-3
3-5
A-B
B
B
B-C
C
C
- E
D
5-6
F
E
C
C-D
D
D
D
>6
C
D
D
D
D
'Strong insolationcorrespondsto sunny midday in midsummerin Englandu
slight insolation to similar conditionsin midwinter.
bNight refers to the period from I hr beforesunset to hr after sunrise.
'The neutral categoryD should also be used,regardless of wind speed. for
overcastconditionsduring day or night and for anysky conditionsduring
the hour precedingor following night as defined above.Source:Stern dt aI.
(1984).
. .-.
0
'T
,
I
IO)
i
]
Ic)
0
ssJala&
ljospuDsnoql
a)
N
(D c) d
I 1 '
1
i
1 [
v
.A
b
1,Jt"p
p
1
n
I
I
I
.-1
-
I
I
O
&
0
)LL
)
q
nL
;D
0
10
100
10
,.DISTANCEDOWNWIND
(km)
2
10
x. DISTANCE DOWNWIND Ikm)
--
1.125 Fatet Tn s
2oo
F\
1.
ar
quA 2
b
a\er:
C Ao?)
1, 14Mn
ZeZ·,OOOM
.Pt' 2rcrjm\
1
C~d~~- A
n 0 2j
bvet Vyl
LLI)
~nd 6"wdo wn
uv)
V tk l
ow 'In ( \Z
9:
W
4molm)
\*%ife r= rj\f5m
Cra,
114 V-10
mOOL
S-
mtn
ur° S
, oo-v3f
S
\n100u,
2n
¶.oo m\s\xrw
b) s-eeoie
r30uw-ls
\000t
-
(0.1r:11-ft
FO 1-1
-9%El
e6(ch 'oorn Xom Ne4\
Q :- a, A
.C=.
o9PM3\
25=rbO
mkater
1-C\-3 Gom)0lrr-
OsS
Ufasr.Ptvils
oaert
1 4.0
.O
&00--
Can GO 0
Yn
-e d
'e1C\0C oI
1)
,
4f ict
or; 6 thtn
Qw
C:dh
-Y_d,\
C\o
pW
u net
&
t - Cencts ou-)
, · 'r
I2
.vo5Ciot
) - 0.-ms
'tO
-.r
.
R.mC\C
\ be =\
^ a
0,25
Nnsl~i=li-lar
tat
2~Yxb
dr
c
mi
o.n2
i
B~~EA
jti'ris \0
E
NT,\&
2. at round
e\,
\kC or,d Vt; lol
-
a) dt' pont:t T t W.ch wot tr 'oior covdenkes
prA0 3essAre i Nattera Or
t
\bStnur
o1.24tnrng
o-1
( t t iS trM. erAture,
mis mc~rrticnd tt \T9-W Se
NT 5'5C
b)
uAs%9dr% o.d
3,
C)bO, SS"'c,
\ooo
Pkcv~
~3
· ~~qze
~cl
Yev~t~~\af\On
3.Ar - g 0
oM
-up~o
od
c;
-C 81 tC + sources
C- S'3JUReS
o)
\t \O p6
sOurCeS-
St\iS
so
o
Y.6 Y\°^>bm\t
°
fb~.is
c¢- sOUiC es
"U6O-\tt Ord, cr V.-o
-lb, \tt ee
By tomp~in pagts KtS
pur oreonteratorn,
Lt\-\
re
Xrdc £o\t
7 514"Penjrr\,
vw':° mtcly
= O
- C.-\-V,[;
SourCes
C) we
no;\hr
ourctS:
-o
SO
o to M6rfyvyt A\-t ^Cir;&mjo
VC'oAneeds
o
uo
gh
(erM
AcCVt.
foshenc3)
mo0rethw
\Mtd "hnuCLYM\ \
it C'MY
kte \'4tcWq
oana ouo\a
t
C
t¢5j\b\tC
F
s 4 t\ooo0s
-1
N. ~c£.O'A%
v6uQrmu\ tao humarh
Utxk&in tt
heth.
nce t't
spmaboj,
L), condtions;
2oorm, in\lo udS, 7-3"C
fo\\ow wet Go,^sbautV\
T o
dnd-T
at iJoyn
3o
-
)_OTtn
&j
-7
)
\\fhlOUl 9o to
n
\QU tps
t "Ko(oVo
- ft\kow Vat CrLd'bat to 000fm, Alnt drj dcbat
toQ
\eft3 - 34on
(wskct
upw rC
Sit
- i X-3°t'
5.
\ \if
o d tnodockt
\t- Ik m
\00,
.-
'`\gtZ%(Jud
,
-2 \ n
I ;
-:3)s\R~di
Zaltwy II Z
- vm:)
t- lOOm (lCo
2'
=-
U
IV bj13
61
7
Urn, 6z=
3t
I
-
_
!6ato
,
16 5(
,e
i J*1\C,;co , hr
IojMo\ CtL
qm11' t. m
_______%a-
"'
\PB4S
%~m/ I
-latu rsz
-1y)c t
u)
int dtsf
Ali
rAmv
k
0
"COC3
3Uces
)te
t~
r E-'u's
j2ac
vag
v~~~~~*O.
"
:s tk.\ t \-4
Mlb
(3, k\ -n7\
rrA
rlmkt '
a e~vany
Crcd~r~~h
~it: cfj oh j\
aIrh
Ia) sMUtospntO& v- ; O.
~t
0iC
& \
IM
YIm)
c
(t\rrm
Cg9t
TOL, 1)dlnd
0, Ioyh
r\ ctus
Iw
- AUftr 0\o?
Ur'OPxy
. V.Wt'tyi't
CoWso
NO 2
b) ;\kt6S't
w0on ttl -3etrivf4\iCat,%Q
n
Ctu
-
Tw Otre
ly-t
mutn-ye
an nktr"Mdatt r sdt
\\t,
nduces
a to
vtcv V
f
027,)
proS~uOt
02)
RI)
mt\c
roduct,
oerv\ ion
7, CK
\A t
\&
trit~r\tc Srce
sto~tts
u\x\~
Crad
o
Gnoe
a\\owY~v\X
\et \
tye d cv
V)n8g
oa
~de~d
enr
-t
C,
QS · el
E-~trA Cred'\d.
Sc\kn
OV-r\m,
coin
vO\\t for tvr\LeJ COO'Y-% 6CdO0
tur\ix wtegr\,
C o
rokt
on S}are
tCr
BcL-o@-t-~r\opt
trsvgt h
13
or
vSait'%
t
,.j
-en
s9\mpc estvcae:
tior zuar,\e
\
s~ tre tuuk
-
I
- rcrt rnees to 90 tyokughv t ,\ctt
-
,QcX . e\trtut
\p~ct
dnCr, \n\\O
\s cZS~3\ee
-r
3ort
ed 0 &
rec&(;Et
g \ritn n 6 ,c\~S
S
.),twfimf 6- ot
wreLbing
^P. \
=s
Cbn-,tn\rngie
\E 6C
z
tUrte~Y
7'r,
~ r~~ ~ ~~~~~f7r
tiwo, Wte hcrit
tL53
-?\
\\^r
( 3b X
|-tt35
ho0U(tE
tl
2-l
dtl
On