United States
Environmental Protection
Agency
Environmental Research
Laboratory
Athens GA 30613
Research and Development
EPA/600/S3-86/044 May 1987
Project Summary
Modeling the Benthos-Water
Column Exchange of
Hydrophobic Chemicals
P. M. Gschwend, S-C. Wu, 0. S. Madsen, J. L Wilkin, R. B. Ambrose, Jr.,
and S. C. McCutcheon
An analysis and modeling framework
was developed to simulate and predict
the transfer of hydrophobic organic
chemicals between bed sediments and
overlying waters. This approach entails
coupling a description of the micro-
scopic scale process of sorption kinetics
with models of the exposure of bed
particles to adjacent waters of varying
composition (i.e.. due to diffusion of
solutes in interstitial fluids or pore water
advection, due to biological mixing of
surficial sediments, due to suspension
of bed solids for a period into the over-
lying water column.) Numerical simula-
tion routines are developed both for
sorption kinetics and to demonstrate
coupling of this particle-water exchange
to particle movements in the case of a
biologically mixed bed. These routines
were used to assess the sensitivity of
sorption kinetics and the overall trans-
port to chemical and sediment pro-
perties. Similar computer programs can
be used as subroutines in global chemical
fate models. Also a formulation of bed-
load transport and of sediment resus-
pension was developed which yields
the contact time of bed particles with
the overlying water column. This model
result is then combined with the sorption
kinetics subroutine to estimate bed-
water exchange in instances where
these processes greatly facilitate bed
particle-water column contact.
This Protect Summary was developed
by EPA's Environmental Research
Laboratory, Athens, 6A, to announce
key findings of the research prelect that
Is fully documented In a separate report
of the same title (see Project Report
ordering Information at back).
Introduction
Several models have been recently
devised to describe the fate and transport
of pollutants in bodies of water. However,
these models are based on incomplete
descriptions of the processes that control
the exchange of chemicals between the
bed and water column. In the current
project, the authors describe the im-
portant processes and develop mathe-
matical descriptions that should be useful
in updating existing models and devising
new models. In addition, the final project
report will be a useful reference in
describing the conceptual framework and
relationships between direct sorption or
desorption, diffusion, advection; biotur-
bation and sediment transport.
Figure 1 gives the conceptual frame-
work for describing the benthic exchange
processes. For the purpose of this study,
the aquatic environment was envisioned
as consisting of a water column^ an
active, moving bed load transport layer
and an immobile bed where sediment is
stored. The definition of the active bed
layer is taken to be two grain diameters
in thickness for sediment transport, and
about 5 to 20 cm thick for bioturbation;
however these definitions are arbitrary
because thickness is difficult to forecast.
The depth of the immobile layer is to be
governed by burial, compaction, and
erosion processes. The water column may
be described with more than one layer if
significant chemical gradients exist and
are necessary to describe benthic
exchange.
Figure 1 also ranks the processes in
terms of process energy requirements
and expected contact time between bed
particles and the dissolved phase of a
-------
Geo-
Morphological
State
Hydraulic
State
Ci.w
Deposition, Burial, Compaction
Scour
Water
Column
Coastal Areas, Estuaries, Streams
Lakes, Coastal Areas, Reservoirs. Estuaries
Laminar or
Quiescent Flow
Smooth
Turbulent
Flows
Rough
Turbulent
Flows
\
1
/ Ejection
I /"t. Ploughing
-ajwr-
-STsr
o
o
ojo
Q
o
Conveyor
Bed
Ca.vt
C3,S
op
olo
oo
o
IV
o
o
o
p
"o
oo
oo
oo
Exchange of
Sediment and
Surrounding
Fluid
Immobile
Bed
Direct
Sorption
Exchange
(I)
Pore Water
Diffusion of
Dissolved
Species
(ID
Advective-
Dispersive
Flow
(III)
Biotur-
bation
(IV)
Bed Load
Transport
(V)
Suspended
Transport
(VI)
Increasing Energy, Velocity, and Sediment Movement
Figure 1.
Generally Increasing Contact Time
Processes involved in bed-water column exchange.
chemical in the water column. Direct
sorption is expected to be the least
energetic and slowest exchange process,
whereas sediment transport is expected
to be the most energetic and, to involve
some of the largest fluxes of material.
However, the limiting process may involve
the slowest, least energetic process.
Although this work significantly im-
proves our understanding and modeling
capability for bed-water pollutant ex-
change, several other important issues
remain incompletely developed. For
example, the inclusion of colloids and
their impact on transport. We do not
understand the sources and sinks of these
nonsettltng sorbents, particularly in sedi-
ment beds, and our knowledge of their
mobility in porous media and ability to
bind pollutants is limited. Additionally,
the importance of bioturbation and other
sediment modifying activities of benthic
organisms to bed load transport and
resuspension is uncertain. Finally, sus-
pension of sediment particles from cohe-
sive beds remains poorly understood, and
therefore modeling of bed-water column
exchange for pollutants where cohesive
sediment is involved is limited to diffusion
and bioturbation-controlled situations.
Sorption Kinetics
The formulation for sorption kinetics is
a physically based description of the
microscale processes encompassing dif-
fusion of nonpolar hydrophobic chemicals
into the pore space of natural aggregate
particles coupled with local partition
equilibrium as illustrated in Figure 2. The
research conducted during this study
indicates that many natural particles of
importance to the sorption process can
be described as porous spheres having
an intraparticle porosity of about 0.13.
Based on this conceptual model the
sorption kinetics can be described as
9CJ(r)
dt
-=D,
'eff
32Csw(r) 2 3Cgw(r)
[_ 3r2 r dr J
(D
where c^fr) = total concentration of
sorbate (chemical) at a radial distance r
from the center of a particle and
(1-n)psKp+n
(2)
in which Dm = molecular diffusivity that
can be determined by the method of
Hayduk and Laudie, n = intraparticle
porosity of about 0.13, ps = specific gravity
of the particles, and Kp = partition coef-
ficient that can be predicted from the
normalized octanol-water partition coef-
ficient, KOV,, and the fraction of organic
carbon contained in the natural particles.
Thus equation 2 provides a physically
based method for predicting sorption and
desorption.
The flux of material from a layer of
particles on the surface of the bed can be
determined from the description of the
fraction that is sorbed or desorbed at the
end of the residence time, tr. The fraction
-------
Turbulent
Flowing Exterior
Partitioning
Molecular Diffision
'"Pore Fluid
Impenetrable
Mineral Grain
Stagnant, Nonllowing
Interior forewater
Figure 2. Physical picture of processes controlling sorption kinetics.
Bioturbation
In the case of bioturbation, mixing by
benthic organisms is described using an
eddy viscosity scheme. This results in a
flux expression of the form
dC z
Flux = - Eb = wbC = / f(z) C dz (5)
dz 0
where Eb = mixing coefficient, C = total
concentration of chemical in the dis-
solved, colloidal-bound, and sediment-
sorbed phases, wb = vertical sediment
velocity induced by biological mixing, and
f(z) = feeding activity due to ingestion of
particles.
For plow-like bioturbation involving
mixing at the surface. Equation 5 can be
applied by noting that wb andf(z) are zero.
Table 1 gives the known values of ED and
the depth of the mixed layer for several
species of benthic animals. The wide-
spread application of the method will
require determination of Eb and mixing
depth for all species of interest. Alter-
natively, the rate of benthic mixing is
related to individual reworking rates, r'
depth of mixed layer, L, population density,
and bulk density of the sediments, p,, via
Eb = L r'lpopulationj/pb
(6)
sorbed or desorbed from or to an infinite
volume of water is given by:
Mt/M00 =
m=1
(3)
where M, = mass sorbed to the layer of
surficial bed particles over time tr, M«, =
mass attached to surficial bed particles
after infinite time, m = the number of
particle sizes the sediment is arbitrarily
divided into, Deff = effective intraparticle
diffusivity that is essentially molecular
diffusivity retarded by sorption, and R =
particle radius. The residence time, tr, for
sediment particles can be determined
from descriptions of bioturbation and
sediment transport. Equation 3 for infinite
water bodies is expected to be accurate
for many streams, lakes, and estuaries
where water volumes are large compared
to the volume of surficial sediments. In
cases where this may not be true, a
numerical solution is derived to compute
M,/M«, and this solution is incorporated
in a basic program included in the final
report.
Diffusion and Advection
The diffusive and advective flux of dis-
solved and colloidal material is described
by
Flux =
5CW
dz
(4)
Dc
asccc
dz
= W2SCCC
where n2 = porosity of the bed, i = an
empirical factor dependent upon n2 and
determined by the formation factor that
describes the effect of tortuosity on
molecular diffusion, Dm = molecular dif-
fusivity, Dc = diffusivity of colloidal
material, Sc = concentration of colloidal
and nonsettling material, and w2 = pore
water velocity in the bed. Here it is
assumed that the size of the pores is
large compared to the colloidal material.
Table 2 gives estimates of individual re-
working rates and mixing depths for
benthic ploughers and conveyor-type
species. Figures 3, 4, and 5 show the
sensitivity of the computed flux to particle
diameter, particle porosity, and phase
partitioning. The values on which these
calculations are based are given in Section
3.3.2.3 of the final report.
Conveyor-belt bioturbation involves
worms that ingest sediment at some depth
z into the bed and egest the reworked
sediment at the bed surface. The worms
ingest the sediment for the organic carbon
contained in the sediments and in the
process rework the sediment into pellets
or trails of inorganic sediment bound by
mucous. The reworking rate is
w'b = (r'/ph) population
(7)
Figure 6 shows the sensitivity of the flux
to pellet diameter and the partitioning
coefficient. See Section 3.3.2.4 for more
details.
Sediment Transport
The description of sediment transport
is based on a physical framework for
cohensionless particles where the resis-
tance to movement derives from the
-------
Table 1. Biogenic Mixing Coefficients. (Source: review by Lee and Swartz)
Location
Species
Ucm)
Erfcnf/sec)
* Calculated from data.
b Calculated by Guinasso andSchink (1975).
c Calculated by Alter (1978).
Vertical diffusion coefficient.
* Horizontal diffusion coefficient.
Method
Deep Sea, various sites
Mid-Atlantic Ridge
Long Island Sound
Chesapeake Bay
New York Bight
Rhode Island
0-1 cm
2-1 Ocm
La Jo/la, California
Barnstable Harbor,
Long Island Sound
Long Island Sound
Laboratory
Laboratory
Laboratory
Laboratory
?
?
Yoldia, Nucula
?
?
Leptosynapta, Scoloplos
Euzonous mucronata
f=Thoracophelia)
Pectinaria gouldii
Yoldia limatula
Yoldia limatula
Yoldia limatula
Clymenella torquata
Clymenella torquata
Molpadia oolitica
70-45
8
4
10-15
?
1
8
30
6
2
3
3
11
11
7-9
3.6 x Iff" -3.16 x Iff*
6x10'9
1. 2-3.5 x Iff6
1 x 1O6
5x10'7
2.9 xW6 -1.6x10'5
8.3 x Iff7 -4.3 x Iff6
1.5x10's
7.6 x Iff8
3.2 x107
2 x Iff6
1 x 10s
2-3 x 1O4
4.5 x Iff5
5.7-9.4 x Iff5
Dimensional analysis
210 Pb pattern
234 Th pattern
Dimensional analysis?
23*Thpattern
Dimensional analysis*
Dimensional analysis*
Dimensional analysis*
Dimensional analysis1'
Dimensional analysis'
Dimensional analysis'
Pore water prof lies
Pore water profiler
Pore water prof lies'
Depth of oxidized layer*
Table 2. Individual Particle Reworking Rates. Annual Reworking Rates, and Depth of Reworking. (Source: review by Lee and Swartsj
Species
Guild
Individual
Reworking
Rate
(mg/ind/dayl
Total
Reworking
(g/m'/yr)
Depth of
Reworking
Comments
Source
Annelids
Abarenicola claparedi
Abarenicola pacifies
Abarenicola pacifies
Amphitrite ornata
Amphitrite ornata
Arenicola marina
Clymenella torquata
Clymenella torquata
Euzonous l=Thoracophelia)
mucronata
Melinna palmata
Pectinaria californiensis
Pectinaria gouldii
Pectinaria gouldii
Polycirrus eximius
Tharyx acutus
Scoloplos robustus
Freshwater oligochaetes, CB,
3 species
Bivalves
Macoma balthica
Macoma balthica
Macoma nasuta
Scrobicularia plena
Scrobicularia plane
Yoldia limulata
Gastropods
Hydrobia minute
Hydrobia ventrosa
LUtorina irroteta
Crustaceans
Callianassa californiensis
FUN
FUN
FUN
SISDF
SISDF
FUN
CB
CB
MISSDF-V
SISDF
CB
CB
CB
SISDF
MISDF-V
MISSDF-V
MISSDF-V
MISDF-V
MISDF-V
MISDF-V
MISDF-V
MISDF-V
MISSDF-V
MESDF
MESDF
MESDF
3.600
10,900
0-4,500
0-1S.OOO
5,100
2.600-5.200
4.700
900
1.650
23O
290
0.5-330
6.000
2.000
7
7
99
510
1-250
1.7
370
520
15-550
7.300
14.400
3.9-90
280
1
1
0.4
— — Average high and low tide, 1-3.5 g/ind.
— — Average high and low tide. 1-3.5 g/ind.
— — 0.7g/ind.. 9°C
— — 2g/ind..9°C
310 kg <15 cm Site 3, mean 3 samplings
— Surface <*>17°C
— Surface 22°C
— — Average of field measurements
54.000 20cm 11°C
73.000 20 cm Beaufort. North Carolina
Annual rate adjusted for T
— Surface Cephalic plate width 2-8 mm, all sediment
8.600 5 cm Cephalic plate width 2-8 mm, all sediment
6.OOO 6cm All sediment, annual rate adjusted for r
— Just feces
0-173 Surface Just feces. April-October
0-1,300 Surface Just feces. April-October
1.200-11.000 2-13 cm Ingestion. April-October
6.200-56.OOO Burrowing, April-October
18-230 kg 4-6 cm Just feces. annual rate adjusted for T'
420 Surface
90.500
— Surface
— 1 mm
— Surface
— Surface
2,300 2 cm
26-8.900 2 mm
0-12.000 2mm
100 Surface
Just feces, 10°C, annual rate not adjusted for T'
Feces and pseudofeces. 10°C
Feces and pseudofeces. 15°C
Just feces. 10-50 mm/ind.
Feces and pseudofeces. 48 mm/ind.
Feces and pseudofeces
Just feces
Feces and pseudofeces
Annual rate not adjusted for T
Annual rate not adjusted for TC
Just feces. recalculated from data
0*
0
0
0
0
0
0
0
Pe
0
0
0
c
c
c
0
0
0
0
Hd
0
0
0
c
MISSDF-E 33.000-82.500 —
<76cm Amount deposited per entrance.
Excavation and feeding?
-------
ruble 2. (continued)
Species
Catlianassa mayor
6 species
Paraphoxus spinosus
Uca pugillator
Uca pugnax
Echinoderms
Caudina chilenses
Echinocadrium cordatum
Holothuria spp.
7 species
Leptosynapta tenuis
Leptosynapta tenuis
Scotoplanes sp.
Stichopus moebil
Stichopus variegatus
Enteropneust
Balanoglossus gigas
Guild
MISSDF-E
MISDF-V
MISDF-E
MISDF-E
CB
MSSDF-V
MESDF
FUN
FUN
MESDF
MESOF
MESDF
FUN
Individual
Reworking
Rate
fmg/ind/day)
3.500
8.910
9$
75
160,000
3.000
Total
Reworking
Rate
(g/mz/yr>
12.6-630 kg
64-2.200 kg
230
820
—
—
Depth of
Reworking
to<10cm
0-1 cm
—
—
—
—
Comments
Amount deposited per entrance, just feces
Burrowing
Just feces, recalculated from data
Just feces, recalculated from data
2S.OOO-220.000 — —
W.4OO-18.400
34.000
100.000
38,000
49.000
—
530-3.000 kg
—
—
—
0.5-10 cm
1.15cm
1 mm
—
—
Feces and below surface reworking
Feces and below surface reworking
Feces
200,000-250.000 — —
Source
0
C
C
C
P
P
P
0
C
0
P
P
P
"O-original data C = calculated from data eP = calculated by Power (1977) H = calculated by Hargraved 9721
NOTE: Guilds CB, FUN. SISDF, MISDF-V. MISSDF-E are primarily tube, funnel, or deep burrow forming species whereas MISSDF-V. MESDF and MIFF are primarily
surface ploughing or mixing species.
weight of the individual particles rather
than through interparticle bonds. Thus
this component of the description is
limited to silty sediment and coarser sizes.
Furthermore the formulation is limited to
particles of a uniform size, and following
the work of Einstein, assumes that several
discrete size classes can be separately
described. This ignores the effect of large
sizes on the critical shear stress of the
small particles and vice versa. Finally, the
conceptualization assumes that the
transport system is instantaneously in
equilibrium between the suspended, bed,
and immobile-bed loads illustrated in
Figure 7.
Based on this conceptual model, the
distribution of sediment mass at equili-
brium between the suspended, bed, and
immobile compartments is given by
P23
m, =
a ;
" P23 + P32 + P21 P32/P12
M (8)
P32
m, =
P23 + P32 + P21 P32/P12
P21 P32/P12
P23 + P32 + P21 P32/P12
M (9)
M(10)
where M is the total mass in the three
compartments and pnm are exchange
coefficients for sediment between layers
n and m.
The mean downstream velocity for the
sediment mass is given as
MU = m1ooU, + m^Uz (11)
where U, is the velocity of the suspended
sediment mass and U2 is the velocity of
the sediment mass in the bed-load layer.
From the average velocity of the sediment
mass, it is possible to compute the ex-
posure time of the sediment particles to
the water column over reaches of given
length as tr = length/U.
The time of exposure or residence time
is coupled with the sorption kinetics
model given in Equation 3 to describe the
transfer of a contaminant to or from the
sediment moving in the stream. The
solution of Equations 8 through 10 in the
downstream direction describes distribu-
tion of contaminated sediment. The final
report illustrates the solution of these
equations in examples for a river and
deep river or reservoir.
Summary and Recommendations
for Future Research
To estimate bed-water exchange of
hydrophobic organic pollutants, a two-
step modeling approach or description is
recommended. First, particle-water ex-
change on the microscopic scale must be
quantified; this can be done using the
retarded radial diffusion model, which
treats each case as a function of com-
pound solution diffusivity and hydrop-
hobicity and sediment particle size and
organic content. Section 2 of the final
report describes a numerical simulation
routine to handle such solid-water ex-
change of chemicals even in cases where
there is a spectrum of particle sizes in-
volved and the solution concentrations
vary in time. Second, this particle-water
exchange kinetics description must be
coupled with descriptions of the relative
translations of sediment particles and the
adjacent fluids (i.e., due to porewater
advection, bioturbation, bed-load trans-
port, or particle resuspension). This pro-
duces a prediction of the overall exchange
of chemicals between the bed and the
water column. Section 3 of the final
report demonstrates the coupling of
particle-water pollutant exchange in
biologically mixed beds. Section 4 devel-
ops a quantitative description of the expo-
sure of a moving bed particle to the
overlying water column and then couples
this transport to sorption kinetics. In any
case of interest, decisions concerning the
intensity of various processes facilitating
bed particle-water column contact are
necessary before good predictions of pol-
lutant transfer can be expected.
Several areas of future research are
suggested to improve and extend these
analytical methods:
(1) The sources and fates of colloidal
materials in sediments needs to be
examined. Additionally, the sorbent pro-
perties of these macromolecules or
microparticles should be assessed. These
sorbents may be particularly important in
transporting very hydrophobic pollutants
from beds that are not biologically mixed.
(2) The nature of bed particle and pore
water movements under the influence of
benthic infauna should be explored fur-
ther. Pore water pumping (or irrigation)
was neglected here for want of a general
-------
I
s
0.12-1
0.08
0.06
0.04
0.02\
0.00
Diameter (cm)
0.005
Diameter (cm)
100
200
300
Time (days)
0.00
rcr1
diffusion length scales and intra-aggre-
gate porosity for solids as they exist in a
bed should be researched further. Also,
to extend this approach to other con-
taminants such as trace metals and polar
organic compounds, the mechanisms
controlling their sorption kinetics inter-
actions with sediment particles should
be examined.
(6) Finally, efforts should be made to
test the accuracy of model predictions
against real world situations. Currently,
there is a dearth of field data for com-
parison with model predictions. Thus,
bed-water fluxes must be measured at
times and places where the prevailing
bed mixing processes are known and
ancillary data are obtained to estimate
their intensity.
Figure 3. Sensitivity of the plow-like bioturbation mediated pollutant flux to 5 different
sediment particle sizes. The values of other parameters are same as those in
the example problem in Section 3.3.2.3 of final report.
quantitative description of this process as
a function of organisms involved. Also,
approaches for estimating parameters and
better quantifying the mixing activities of
benthic infauna from field measurements
are needed.
(3) The development of a basic under-
standing for the factors and processes
governing cohesive sediment resuspen-
sion and transport is also necessary.
These cohesive organic-rich muds are
the predominant sites for collection of
many pollutants discharged to natural
waters, yet our ability to quantitatively
describe the movements of particles in
these beds remains poor.
(4) In the sediment transport models
formulated here, steady flow conditions
were assumed. The impact of unsteady
(e.g., tides in estuaries), and even
catastrophic (e.g., storms) phenomena to
the modeling of sediment transport still
remains an important area to be
examined.
(5) Further assessment of the con-
ceptualization of the microscopic scale
particle-water exchange of chemicals
from particles in beds to the surrounding
pore waters should be done. The retarded
radial diffusion model has been tested
primarily for aggregate particles in sus-
pension. Issues such as the appropriate
-------
0.30-t
I
s
3
0.20
o.ro
o.oo
"Si
(Q
•§
\
ft
-------
0.70
^ 0.08
"5 0.06 -I
\
0.04
0.02
0.00
/O8
700 200
Time (days)
300
0.80-t
0.00
10
Figure 5.
Sensitivity of the plow-like bioturbation mediated pollutant to chemical partitioning.
The values of other parameters are same as those in the example problem in
Section 3.3.2.3 of final report.
-------
Initial Concentration - 1
Reworking Rate = 0.052 cm/day
0.03 -\ Bulk Density of Sediments = 0.5 g/cm3
Microporosity = 0.13
0.02-
------- |