9 Sediment-Water Exchange
IntroductionSediment-water partitioningParticle settling and depositionSediment erosion and resuspensionTransport equation with sedimentsContaminant transport within sediment bedModel of sediment-water exchangeContaminated sediment remediation
Interest in Sediments
“Geo-morphology”Sediment as pollutantSediment as carrier of pollutants
ClassificationClass name Diameter
(mm)φ Class name Diameter
(mm)φ
Very coarse gravel 64-32 -5.5 Very fine sand 1/8-1/16 3.5
Coarse gravel 32-16 -4.5 Coarse silt 1/16-1/32 4.5
Medium gravel 16-8 -3.5 Medium silt 1/32-1/64 5.5
Fine gravel 8-4 -2.5 Fine silt 1/64-1/128 6.5
Very fine gravel 4-2 -1.5 Very fine silt 1/128-1/256 7.7
Very coarse sand 2-1 -0.5 Coarse clay 1/256-1/512 8.5
Coarse sand 1-1/2 0.5 Medium clay 1/512-1/1024 9.5
Medium sand 1/2-1/4 1.5 Fine clay 1/1024-1/2048 10.5
Fine sand 1/4-1/8 2.5 Very fine clay 1/2048-1/4096 11.5
Non-cohesive
cohesive
ASCE, 1975; φ= -ln(dmm)/ln(2) Most environmental interest in finer fractions
Table 9-1 Sediment grade scale (adapted from ASCE, 1975)
1.010
10
30
50
70
90
SAND
Coarse Coarse CoarseMedium Medium MediumFine Fine Fine
SILT CLAY
0.1
Diameter (mm)
0.01 0.001 0.0001
Grain Size Distribution
MITClassification
d50
Figure by MIT OCW.
Equilibrium PartitioningPartition (or distribution) coefficient:
Sorbed phase conc cs (mass contaminant per mass solid) divided by dissolved phase conc cd (mass contaminant per volume solvent) in equilibrium
Units of Kp: volume/mass, e.g., cm3/g
More complicated partitioning models
d
sp c
cK =
Simplest model: two phases
Kp depends on contaminant, its concentration, concentration of organic matter, redox potential, etc. Typical values: 101 to 102 cm3/g (hydrophilic) to 104 to 105 cm3/g (hydrophobic)
In sediment bedMass of dissolved contaminant/volume
1)1()1(
+=
+−
−=
ρρ
φφρφρ
p
p
ps
ps
KK
KK
f
dcφ=Mass of sorbed contaminant/volume
)1()1( φρφρ −=−= dpsss cKc
Ratio of sorbed to total massif equilibrium
Unit volume with porosity φ
Solid-water phase ratio (solid mass/water mass)
φρφφρρ //)1( ,dbs =−=
)1(, φρρ −= sdb Bulk (dry) sediment density
φφρρ +−= )1(, swb Bulk (wet) sediment density
Surficial sediments
ρs ~ 1.5 - 2.5 g/cm3; φ ~ 0.6 – 0.8 =>
ρb,d ~ 0.3-1 g/cm3, ρb,w ~ 1.1-1.6 g/cm3, ρ ~ 0.4-1.7 g/cm3
1+=
ρρ
p
p
KK
f ρ~ 1 => for Kp >> 1 most contamination is sorbed to particles
While most of the contaminant is associated with solids, the dissolved phase is very important because it is more bio-available and amenable to sediment-water exchange
Sediment quality criteria often derived from target dissolved phase concentrations assuming equilibrium partitioning
In water column
[ ]TSSs ≡−= φφρρ /)1(“porosity” ~ 1 so
[TSS] ~ 1 to 100 mg/L (10-4 to 10-6 g/cm3)
1)1010()1010(
1][][
1 64
64
+=
+=
+= −−
−−
p
p
p
p
p
p
KtoKto
TSSKTSSK
KK
fρ
ρ
For hydrophobic contaminants (Kp ~ 104 to 105) concentrations in sorbed and dissolved phases can be comparable. Hydrophylic contaminants are mostly in dissolved phase
Non-equilibrium conditionsRate of increase of dissolved phase mass⎟
⎟⎠
⎞⎜⎜⎝
⎛−= d
p
sd cKc
dtdc
κ
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
p
sd
s
Kc
cdt
cdκ
ρ )( Rate of increase of sorbed phase mass
κ Rate constant (t-1); e.g. (Wu and Gschwend, 1986)
2
)1(2.0R
KD pm
φρφ
κ−
= R = aggregate radius, Dm = molecular diffusivity
( ) 0=+ sd ccdtd ρ Total mass is conserved
Non-equilibrium, cont’dκ/Kp Time scale for desorption from particle
= days to months => equilibrium assumption not very good for suspended sediments (may be OK for stationary sediments)
( ) 0=+ sd ccdtd ρ Total mass is conserved
Additional Comments
Fine particles usually most importantMost easily resuspendedSettle most slowlyProbably have highest foc => Kp
Highest κ ~ (diameter)-2
Models often have multiple particle sizes with individual settling velocity, tendency to resuspend, and κ
Sediment movement
EPA, 2004
Modes of transport
Settling & deposition (non-cohesive and cohesive)Erosion & resuspension (non-cohesive and cohesive)Bed-load (non-cohesive)
Particle settling (WWT jargon)
Discrete (Type 1) (non-cohesive)Flocculant (Type 2) (cohesive)Hindered or zone (Type 3)Compression (Type 4)
Focus on Types 1 and 2
Terminal velocity
6)(
3dgF fsgπρρ −=
Fd
421 2
2 dwCF sdfdπρ=
Fg
23)1(4
sd w
sdgC −=
s = ρs/ρf
Equating,
Cd = f(R); R = Reynolds number = wsd/ν
Applicable to cohesive and non-cohesive sediments, but aggregate shapes and densities are ill-defined for cohesive sediments
Spherical particles
R < 1; d < 100 µm (Stokes settling)
sd dwF πρυ3=
RCd
24=
υ18)1( 2dsgws
−=
R < 104 (Metcalf & Eddy, 1991)
34.0324++=
RRCd
More generally (0.01 mm < d < 100 mm; Dietrich, 1982)
)*(log00056.0)*(log00557.0)*(log09815.0*)(log92944.176715.3*log
43
2
DDDDw
+−
−+−=
υgsw
w s
)1(*
3
−=
2
3)1(*υ
gdsD −=
Spherical & non-spherical particles
s
p
AD 2π
=Ψ Surface area of equivalent sphere/surface area of particleBrown et al. (1950)
10,000
10,000
1000
1000
600400
200
1006040
20
1064
2
10.60.4
0.2
0.10.001 0.01 0.1 1 2 4 6 10 100 105 106
Stokes
Sphere
ψ = 0.125
ψ = 0.220
ψ = 0.600
ψ = 0.806
ψ = 1.000
Dra
g C
oeff
icie
nt, C
D
Reynolds number, based on DP
Figure by MIT OCW.
Settling of Cohesive SedimentsSettling velocity depends on concentration. Empirical formula from EPA (2004):
COH
WLCOHWLs C
CCdmCdmdmw
)(/30/1.0)/(
−+=
CWL = wash load concentration (5 mg/L); CCOH = cohesive sediment concentration (mg/L). Within range of empirical observations, e.g., Hawley (1982)
1.00.80.60.40.20.0
0 2 4 6 8 10
30
25
20
15
10
5
00 50 100 150 200
Concentration (mg/L)
Settl
ing
Velo
city
(m/d
)
Figure by MIT OCW.
Sewage particles
Often a wide range of settling velocities
Settling Basins: discrete settling
Inlet Outlet
ws
u
Time to settle Ts = h/ws
Hydraulic residence time Tres = V/Q = Ah/Q
Tres > Ts => Ahwsc/Qh > 1
wsc > Q/A or Q < Awsc or A > Q/wsc
Comments
Q/A = overflow rate (really a velocity); particles settling faster will depositFlow capacity depends on area (not depth) => make tanks as shallow as practicalIncrease area using stacked clarifiers, inclined plates/tubes, etc.Similar concepts apply to field: deposition at river deltas, in ponds & reservoirs, downstream from outfallsExample of particulate phosphorus loading in reservoir (Vollenweider plots)
Retention in lakes & reservoirs: critical phosphorus loading
Qm,&
wsp
p
Qp
ApwQpmdtdpV s−−= &
V = impoundment volume
A = impoundment area
Q/A = impoundment “overflow rate”
p = average P concentration
In steady state
s
s
wAQAmp
pwpAQ
Am
+=
+=
//&
&
Phosphorous loading diagram
ws = 10m/yr
eutrophic
oligotrophic
Q/A <<ws Q/A >> ws
Q/A = ws
After Vollenweider (1975); Chapra (1997)
Particle scavengingRemoval of marine contaminants (e.g., metals) by natural particle settling
234Th: particle-reactive tracer; t1/2 = 24.1 d
w/o deposition ce = equil conc of 234Th:
Rad decay = -λce, λ = decay rate (ln2/t1/2)
Production = λce (must be same in equil)
238U
234U
234Thα
β(ce)h
Particle scavenging, cont’d
238U
234U
234Thα
β
With deposition, 234Th conc c < ce
f = fraction of 234Th sorbed to particles
(c)
1][][+
=TSSK
TSSKf
p
p
chw
f s ⎟⎠⎞
⎜⎝⎛
fws/h is effective 234Th removal rate (t-1)
cfhccw
ccc
hfw
hfwcc
es
es
se
λ
λ
λλ
)(
)(
−=
−=
⎟⎠⎞
⎜⎝⎛ +=h
ce measured offshore;
c measured locally => ws
Particle scavenging, cont’dUse 234Th deposition to trace deposition of another metal (call it x), with different partitioning
hccfccfwcfJ
hccfcwJcf
hccw
exx
sxxx
esTh
es
λ
λ
λ
)(
)(
)(
234
−==
−==
−=
−
1][][+
=TSSK
TSSKf
px
pxx238U
234U
234Thα
β(c)h
chw
f s ⎟⎠⎞
⎜⎝⎛JTh-234
DepositionFlux of settling particles
Cws C = sediment concentration (TSS)
Deposition rate, D
p = probability of depositing (sticking)CpwD s=
For non-cohesive sediments, p = 1
For cohesive sedimentsτc,d = critical depositional shear stress
dc,ττ <)/1( ,dcp ττ−=
0.06 < τc,d < 1.1 N/m2 (Mehta & Partheniades, 1975; Ziegler et al, 1995)
Particle accumulation on bottom
ws z
h
)1( φρ −==
so
Ddtdhw
Rate of mass approaching interface/unit area = D
Rate of accumulation in surface sediments
[ ])1( φρ −shdtd
Equating
If φ = 0.8, ρs = 2.5 g/cm3, ρs(1-φ) = 0.5
How to determine wo = dh/dt?
Depth of natural, accidental or intentional marker
e.g., paint pigments in Fort Point Channel
Decay of radioactive tracere.g., 210Pb,
Fort Point ChannelRecall discussion in Chapter 4
Northern Ave.
Congress St.
Summer St.
Gillette
Dorchester Ave.Broadway
BOS 070
Inner Harbor
Boston
18 ft
18 ft
18 ft
N
100 0 500
Meters
Cores 2,3
Core 1
Fluorescent dye and pigment particles released May ’90 and July ‘91
Figure by MIT OCW.
Paint chips as markers
6m
8 cm
6 cm
Stolzenbach and Adams (1998)
Pigment surveyed with freeze corer
July 1991
May 1990
Dec 1993
May ’90 to Dec ’9314 cm/3.6 yr = 3.9 cm/yr
Jul ’91 to Dec ’938 cm/2.4 yr = 3.3 cm/yr
Stolzenbach and Adams (1998)
Comments
Deposition rates of 1-4 cm/yr in FPC (three cores)Loading rates for all FPC sediment sources ~ 0.14 cm/yrSubstantial import of (contaminated) sediment
Cs-237Fallout from bomb testing
USGS Gravity cores, Lake Worth, TX, 2000-01
Measuring deposition with Excess 210Pb
Pb-210 particle reactive tracer; t1/2 ~ 23 yr
c = excess concentration
Relative to (moving) interface, steady state, no sediment mixing
co c
owz
o
o
ecc
cdzdcw
λ
λ
−
=
−=−
Alternatively -z
∫∞−
=0
)(1 dzzcc
wo
o λ
Erosion and Resuspension
Associated with bottom shear stress
zuEwu z ∂
∂=−= ρρτ ''
2uc fρτ = cf is bottom friction factor
Erosion of non-cohesive seds
Critical shear stress τc required to initiate particle motionws > (τ/ρ)0.5 > (τc/ρ)0.5 => bedload(τ/ρ)0.5 > ws, τc => suspended loadRe-suspension flux depends on near-bed concentration; many formulations
EPA, 2004
Cohesive sedimentsMany formulations; most apply for shear stress above a critical erosional shear stress, τc,e
Erosion rate E (g/m2-s)
n
ec
ME )1(,
−=ττ
τc,e = 0.05 to 0.3 N/m2;
M = 0.1 to 3 g/m2-s; n = 1-3
Cohesive sediments, cont’d
n
ecm
d
o
Ta
)1(,
−=ττε
Erosion potential ε (g/m2)
Td = time (days) after deposition
τc,e = 0.1 N/m2 ; ao = 50; m = 2; n = 2.7
Erosion over specified time interval ~ 1 hr
Above parameters from Ziegler, et al., 1995 for Watts Bar Reservoir, TN
Measurement of erosion
Linear laboratory flumeLinear flume in fieldLaboratory annular flumePortable resuspension device (Shaker; Tsai and Lick, 1986)
Sedflume(after McNeil et al., 1996)
Measures erosion rates in the labFigure by MIT OCW.
Ravens & Gschwend (1999)
Measures erosion rates in the field
Top, Front View
Bottom, Front View
Grid Boundary layer trap
To boat
Lateral angle iron
Lateral angle iron
2.4 m12 cm
6 cm
81 cm i.d. hose
1 m
Angle iron Sediment bedtest section
Boundary Layer Development Region
Figure by MIT OCW.
Commentsτc,e increases & E decreases with time after deposition and depth below sediment bed reflecting increased strength due to compaction, armoring from larger particlesRegions with τ > τc,e on regular or intermittent basis exhibit erosionaltendenciesNet erosion (erosion – deposition)
⎥⎥⎦
⎤
⎢⎢⎣
⎡−−
⎥⎥⎦
⎤
⎢⎢⎣
⎡−=−=
dcs
n
ec
cwMDE,,
11ττ
ττφ
Transport Equation with Sediments
)()()()()()(zcE
zycE
yxcE
xcww
zvc
yuc
xtc
zyxs ∂∂
∂∂
+∂∂
∂∂
+∂∂
∂∂
=−∂∂
+∂∂
+∂∂
+∂∂
z positive upward, origin at sediment interface; c = sediment concentration; ws = settling velocity
Neglecting horizontal transport & vertical water velocity
)(zcE
zcw
ztc
zs ∂∂
∂∂
=∂∂
−∂∂
Boundary conditions
0=∂∂
−−zcEcw zs
cwzcEcw szs )1( −=
∂∂
−− α
at surface (z = h)
at bottom (z = 0)
Surface and bottom BCs
α=0 α=1 α>1
dzdcEz−cws
z
ch
0
α denotes relative amount of erosion
Vertical sediment distributionUnder steady state
dzdcEcw zs =−
Logarithmic velocity profile in channel; turbulent diffusivity = viscosity
*)(uw
a
s
aha
zzh
czc
κ
⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
−⎟⎠⎞
⎜⎝⎛ −
=
*/ uws κ Rouse number
Depth-average Ez (= 0.07u*h)
z
s
EhwPe = Peclet number ~ 6 ws/κu*
c(z/h,T,Pe)
No erosion (α=0)
Constant Ez
z
s
EhwPe =
Pe < 0.2 => well-mixed)
Pe > 100 => stratified
Dhamothran et al (1981)
Pe = Vh/D = 200
Vh/D = 0.02
Vh/D = 2.0 x 10-8Pe = Vh/D = 2.0
T = tV/h
Vh/D = 20
0 20 40 60 80 100
0
.2
.4
.6
.8
1.0
1.81.71.6
C/Co (%)
1.51.4 1.3 1.2 1.1 1.0 .9.8
.7.6
.5.4
.3
.2
T = .1
.025
Z/h
0
0
20 40 60 80 100
.2
.4
.6
.8T = 1.6T = 1.5
1.0
C/Co (%)
1.4 1.3 1.2 1.1 1.0.9
.8.7
.6.5
.4.3
.2
T = .1
.025
Z/h
Vh/D = 0.2T = tV/h
0 20 40 60 80 100
0
.2
.4
.6
.8
1.0
C/Co (%)
2.0
.3
.2
T = .4
T = 3.0.1
.025
Z/h
0 20 40 60 80 100
0
.2
.4
.6
.8
1.0
C/Co (%)
1.21.1
1.0 .9 .8 .7 .6 .5 .4 .3 .2 T = .1.025
Z/h
0 20 40 60 80 100
2.03.0
2.5
2.1
0
.2
.4
.6
.8
1.0
C/Co (%)
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
.9
.8
.7.6
.5 .3T = .4
Z/h
0 20 40 60 80 100
T = 3.02.2
2.0
0
.2
.4
.6
.8
1.0
C/Co (%)
1.9
1.8
1.7
1.6
1.51.4
1.3
1.2
1.1
1.0.9 .8 .7
.6.5
.4
.3
.2
T = 1
.025
Z/h
Pe=200
20
2
0.2
0.02
0.002
T=tws/h
hz
Figure by MIT OCW.
Application: Settling basin & river
L = 50m, W = 6m, h = 4m, Q = 0.2m3/s
100 mg/L40 mg/L
h = 1 m, u = 0.3 m/s
Pe = wsh/Ez
Ez = 0.07u*h; assume u* ~ 0.05u => Ez = 0.0035uhPe = ~ 300ws/uws = 10-2 to 10-6 m/s (Table 9.2)
Often a wide range of settling velocities
Focus on Basin
L = 50 m, W = 6 m, h = 4 m, Q = 0.2 m3/s
100 mg/L40 mg/L
h = 1 m, u = 0.3 m/s
u = Q/hW = 0.0083 m/sPe = ~ 300ws/u (second column of Table 9.3)
wsc = Q/A = Q/LW = 7.7x10-4 m/s(faster settling particles theoretically removed)
Basin
Pe for settling basin and river
Ws
(m/s)Pe = wsh/Ez
(Basin)Pe = wsh/Ez
(River)10-2 340
10-3 34
10-4 3.4 0.1
10-5 0.34 0.01
10-6 0.034 0.001
Focus on River
L = 50 m, W = 6 m, h = 4 m, Q = 0.2 m3/s
40 mg/L100 mg/L
h = 1 m, u = 0.3 m/sRiver
Pe = ~ 300ws/u (third column of Table 9.3)
Comments
In basin, turbulence insufficient to mix particles that settle (Pe > 30)In river, turbulence sufficient to mix particles that don’t settle in basin (Pe < 0.1) (river can be treated as well mixed)In basin, τb = ρu*
2 = 0.07 N/m2 < τc,e
In river, τb = ρu*2 = 0.22 N/m2 <~ τc,e
(possible resuspension)
Vertically well-mixed conditionsPe < 0.2
3-D equation
)(zcE
zcw
ztc
zs ∂∂
∂∂
=∂∂
−∂∂
Vertical integration
bot
s
surf
zs zcEcw
zcEcw
tch ⎥
⎦
⎤⎢⎣
⎡∂∂
+−⎥⎦
⎤⎢⎣
⎡∂∂
+=∂∂
=0
Vertically well-mixed conditions, cont’d
No resuspension (α = 0)
hcw
dtcd s−=
)exp( htwcc so −=
co = initial depth-averaged concentration
ws/h = first order removal rate, κs
Partially-mixed conditions sometimes analyzed using κs > ws/h (because near bottom concentrations are greater than co)
Multiple size fractions
∑−=i
is
hcw
dtcd
ws/h = 0.3x10-5s-1
1.0x10-5s-1
0.3x10-5s-1
Ave 2nd O settling (Bco = 3x10-4s-1)
First order settling of different size fractions can resemble second order settling:
o
o
Btcc
c+
=1
Contaminant transport within & across the sediment bed
da ucJ φ=
Porewater advection (GW movement; sediment compaction; wave or bedforminduced pressures; biomixing
Contaminant transport within & across the sediment bed
Porewater advection (GW movement; sediment compaction; wave or bedforminduced pressures; biomixing
da ucJ φ=
Porewater diffusion
mDD φ='
dzdcDJ dd 'φ−=
Contaminant transport within & across the sediment bed
Porewater advection (GW movement; sediment compaction; wave or bedforminduced pressures; biomixing
da ucJ φ=
dzccdDJ ssdbb /)( ρ+−=
Bulk sediment motion (“turbulence”)
Porewater diffusion
dzdcDJ dd 'φ−=
mDD φ='
Sediment Profile Imaging
Benthic fauna mix dissolved oxygen and other sediment characteristics (oxygen rich areas are light colored)Note feeding tubes near surface
EPA, 2006
Measuring bioturbation with 234Th
Th-234 particle reactive tracer (c); t1/2 ~ 24.1 day
Relative to (moving) interface, steady state, including sediment mixing
co c
cdz
cdD
dzdcw s
bo λ−=− 2
2
For Dbλ >> wo
cdz
cdD sb λ−= 2
2
0
)exp( zDcc
bo
λ−=-z
Comments
Db correlates with wo (reflecting flux of organic matter)Coastal sediments: Db = 10-7 to 10-6
cm2/sDeep sea sediments: 10-9 to 10-8 cm2/s
DDT on Palos Verdes Shelf (WE 9-4)
DDT commonly used pesticide until 1970s (Silent Spring).~ 1700T discharged by LACSD’s White Point outfall (60m depth) (also agricultural run-off)~100T (p-p’-DDE) still buried in sedimentIssues of environmental racismEPA Superfund Site (Montrose Chemical Co.)
Vertical ProfilesCore 8C 1981 (solid) to 1989 (open)
0100200300400500600700
0 20 40 60 80
Depth in cm
ppm 1981
1989
Concentration vs depth (USGS; Lee, 1994)
Vertical distribution of porosity (open squares) and bioturbation coefficient
(closed squares)
00.20.40.60.8
1
1 5 9 13 17 21 25 29 33 37 41 45 49
Depth in cm
φ
Db/Dbo
Exponential distribution of porosity and bioturbation (latter based on worm density)
IssuesContamination slowly decreasing. But is it bio-degradation or surface loss?Will natural sedimentation cap contaminants? Decreasing since WWTP upgrade; introduce clean sediments from flood control reservoirs?Current strategy of institutional controls (public outreach, fish monitoring, etc.) Is this enough?Possible future capping. Will this work? (2000 pilot capping failed.)
Sediment Fate ProcessesDeposition of clean sediment (deposition velocity w in cm/yr)Biological mixing (Dbin cm2/yr)Biodegradation (1st O rate λ in yr-1)Release to surface (kin cm/yr)
Core 8C 1981 (solid) to 1989 (open)
0100200300400500600700
0 20 40 60 80
Depth in cm
ppm
Lee, 1994 (USGS)
19811989
sos ckJ )1( φρ −=
Mass Transport in Sediments
sssbssss
s ccDcwtc
ρφλφςς
ρρφς
ρφ )1(])1[(])1([)1( −−⎭⎬⎫
⎩⎨⎧
−∂∂
∂∂
=−∂∂
+∂
∂−
Boundary conditions
sos
b cwkc
D )( +=∂∂
ς 0=ςat ζ = depth below (moving) sediment bed
∞=ς0=sc at
Use observations to calibrate unknown parameters w, Db, λ and k
Simplification
'']''[)''('' /
ssL
bosos cceDcwt
cλ
ςςςς −
∂∂
∂∂
=∂∂
+∂
∂ −
)1/()1('' oss cc φφ −−=where
)1()1( oo ww φφ −−=
Lbob eDD /ς−=
Spatial Momentsςς dcM i
si ∫∞
=0
ςςς decM iLsi ∫
∞−=
0
/' ςς dcM isi ∫
∞
=0
'''' ςςς decM iLsi ∫
∞−=
0
/'''''
''''
osoo Mkc
dtdM
λ−−= 4 moment equations in 4 unknowns
''''''1
1 MML
DcDMw
dtdM
obo
sobooo λ−−=−
'''''2
'''22''211
2 MMLD
MDMwdt
dM booboo λ−−=−
Surface loss and degradation loss comparable; times scale of each ~ 30 yrs
''''''3
'''63''
32123 MM
LD
MDMwdt
dM boboo λ−−=−
wo = 1.7 cm/yr, Dbo = 44 cm2/yr, λ = 0.03 yr-1, k = 9.6 cm/yr.
sock''oMλ
Sediment water exchange model
Steady stateIncludes bioturbation, pore-water diffusion and sorption kinetics, but no resuspension, deposition or bio-degradationColloidal transport included but not described hereApplied to PAH’s in Boston Harbor
Chen, 1993
-H
-ZW
ZS
Z
L
Cd0
Cd1
1 Flushing
cd2 = cs2/Kp
cdL = csL/Kp
2 Water-side diffusion
3 Sorption kinetics
4 Bio-mixing
Figure by MIT OCW.
Sediment water exchange model
)()'(0 2
2
dpsp
db cKc
Kdzcd
DD −++=κ
)(0 2
2
sdpp
sb ccK
Kdzcd
D −+=κρ
dissolved
sorbed
Boundary Conditions
1dd cc = at z = 00=dzdcs
at z = L sLspd ccKc ==
Approximate Solution
z
-H
-zwzs
L
cd0
cdL=csL/Kp
cd1 cd2=cs2/Kp
1 flushing
2 water-side diffusion
3 sorption kinetics
4 bio-mixing
rLrze
cKccc rz
dpsL
dd
εε
++−
=−
− −
11
1
1
)1)(1
1
1
rLerz
cKccKc rz
dpsL
dps
εε
+++
=−
− −
rDDzDrLcDrLKcDD
cbwm
dwmpsbd )'()/)(1(
)/)(1(/)'( 01 +++
+++= ∞
φεδεφ
)'/( DDr b += κ
bp
b
DKDD
ρε
)'( +=
Flux to surface
pbspsmbm
w
psL
KDL
KDDDR
Dz
H
KcJ
ρφρφτ
)1(])')[(1(2.2
/
2/1 −+
+−++
=
Dissolved phase concentration in equilibrium with csL
1 2 3 4
Denominator: 4 “resisters” in series: 1) flushing, 2) water-side diffusion, 3) sorption kinetics, 4) bio-mixing
Variable
Definition Value(s)
Dm Aqueous solution diffusivity 0.8x10-5
cm2/sD’ Aqueous solution diffusivity
corrected for porosity0.5x10-5
Db Bioturbation coefficient 10-7, 10-6, 10-5
cm2/s
Kp Solid-water partition coefficient 101 to 106cm3/g
L Biologically active depth 5 cm
φ Porosity 0.8
ρs Sediment density 2.5 g/cm3
Sorbed concentration at z = L 10-6 g/g
R Characteristic aggregate radius 0.01 cm
Water-side boundary layer thickness
0.06 cm
Hydrodynamic residence time of overlying water
5 day
H Depth of overlying waterbody 6 m
Desorption rate constant Eq (9.5)
Parameters
Db = 10-5 cm2/s
D4/D
D3/D
D2/D
D1/D
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 2 3 4 5 6
log (Kp in cm3/g)
Frac
tiona
l Res
ista
nce
Db = 10-6 cm2/s
D4/D
D3/D
D2/D
D1/D
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 2 3 4 5 6
log (Kp in cm3/g)
Frac
tiona
l Res
ista
nce
Db = 10-7 cm2/s
D4/D
D3/D
D2/D
D1/D
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 2 3 4 5 6
log (Kp in cm3/g)
Frac
tiona
l Res
ista
nce
Comments
Water side bl (2) controls for large Kp & Db
Bioturbation (4) controls for small Kp & Db
(Resistance on side with smallest equilibrium concentration)Desorption not limiting factorLongest clean-up times for high Kp (nearly a century for benzo(a) pyrene (Kp ~ 105) in Boston Harbor)
Dealing with Contaminated Sediment
Natural attenuation (Let it sit)If evidence of natural recovery (deposition, bio-degradation)Or if other options problematicCombined w/ active monitoring & inst controls
Capping (Cover it up)With clean sedimentIn situ or in confined aquatic disposal (CAD) cells
Dredging (Remove it)Environmental (remove contamination)Maintenance (keep harbors/channels open)Improvement (make harbors/channels deeper)
Boston Harbor Navigation Improvement Project
Deepen to 38-40’(versus maintenance or environmental)1.7x106 yd3 clay (MBDS)1.1x106 yd3 silt (CAD cells)
Confined Aquatic Disposal Cells
Figure by MIT OCW.
Dredge buckets
Environmental Clam shell
CAD ChallengesE W
Subbottom line 6-003 from cell M4 (OSI 1999), annotated at bottom showing location of cores,fluidized mud layer (above red dashed line), sand zone (between red and blue dashed lines),and approximate bottom of cell (green dashed line). Note reversal of East and West.
Core M4-5 Core M4-4 Core M4-2
Cell M4 - Post-Cap Sub-Bottom Profile
7 17 3 5 0 7 17 45 0 7 17 55 0 71 7 6 5 0 71 7 7 5 0 71 7 8 5 0E a s tin g
505750
505850
505950
506050
Northing
Hitting target
Verifying CAP integrity
Waiting for sufficient consolidation
Additional Issues
Containing dredged and capping material (during descent & upon impact)Time of disposal (environmental windows to allow migrating fish passage)Residual silt (should you “rake all the leaves?”)Open cells (exposure to uncapped material)
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