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)