ENVIRONMENTAL PROTECTION AGENCY
NORTHWEST REGION, PACIFIC NORTHWEST WATER LABORATORY
THE BARGED
OCEAN DISPOSAL
OF WASTES
A Review of Current Practice and
Methods of Evaluation
July
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THE BARGED OCEAN DISPOSAL OF WASTES
A REVIEW OF CURRENT PRACTICE AND METHODS OF EVALUATION
B. D. Clark, W. F. Rittall, D. J. Baumgartner, and K. V. Byram
Environmental Protection Agency
Pacific Northwest Water Laboratory
200 S. W. Thirty-fifth Street
Con/all is, Oregon 97330
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EPA Review Notice
This report has been reviewed by the Environ-
mental Protection Agency and approved for
publication. Approval does not signify that
the contents necessarily reflect the views
and policies of the Environmental Protection
Agency, nor does mention of trade names or
commercial products constitute endorsement
or recommendation for use.
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ABSTRACT
This report consists of a broad scope examination of barged ocean
disposal of liquid and solid wastes. Basic discussions include: the
physical characteristics of various selected wastes, economics as a
function of haul distance, reported effects of past discharge operations
and the relative importance of environmental factors such as density
and current profiles. The major emphasis of the report centers on
physical fate prediction methods and describes the physical transport
in four separate steps: convective descent, collapse, long term disper-
sion and bottom transport or resuspension.
An existing mathematical model developed by Koh and Fan is used and
demonstrates the complex nature of some of the more obvious parameters,
the potential usefulness of the approach to coastline management efforts
while serving as a vehicle for the discussion of current state of the
art limitations and research needs.
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CONTENTS
Section Page
I SUMMARY "I
II RECOMMENDATIONS 7
III INTRODUCTION 9
Purpose and Scope 10
IV WASTES: CHARACTERISTICS AND EFFECTS 11
Dredge Spoils 11
Sewage Sludge 16
Industrial Wastes 20
Radioactive Wastes 21
Fly Ash and Incinerator Residue 22
Garbage and Refuse 24
V TRANSPORT MECHANISMS 27
Convective Descent 31
Collapse 34
Long Term Dispersion 38
Bottom Transport and Resuspension 43
VI SOLUTION TECHNIQUES 49
Convective Descent 49
Waste Characteristics 55
Physical Modifications 5?
VII BARGE CHARACTERISTICS 75
Barging Economics 81
VIII USERS GUIDE 91
IX BIBLIOGRAPHY 95
X APPENDICES 103
Appendix 1 103
Appendix II ^3
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FIGURES
No. Page
1 Basic Transport Phases 30
2 Convective Descent Terminal Depth
[after Koh & Fan (2)] 35
3 Convective Descent Terminal Size
[after Koh & Fan (2)] 35
4 Coordinate System for Collapse Phase 37
5 Collapse Size and Time for -y = 0
[after Koh & Fan (2)] 39
6 Sediment Concentration Gradient Definition
Sketch 45
7 Drag Coefficient for Spheres as Function of
the Reynolds Number 47
8 Shields Diagram, as Modified by
Vanon£ (1964) 47
9 Penetration Depth and Dilution as Functions
of the Initial Densimetric Froude Number
under Linear Density Gradient 51
10 Penetration Depth and Dilution as Functions
of the Initial Densimetric Froude Number
under a Strong Pycnocline 52
11 Comparison of Reported Methods of Predicting
Penetration Depths 54
12 Schematic Presentation of Fate of Material
when Discharged in Barge Wake 59
13 Predicted Relative Surface Concentrations for
Long Term Dispersion Phase 67
14 Maximum Predicted Concentration for Long Term
Dispersion Stage 68
Vll
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FIGURES
(Continued)
No. Page
15 Predicted X Dimension of Cloud at Level of
Maximum Concentration 69
16 Predicted Relative Concentration Centroid
Location at Level of Maximum Concentration .... 70
17 Concentration Distribution with Depth at
T - 70 hours 73
18 Basic Barge Configurations 78
19 Cost per Trip Mile as a Function of Round
Trip Haul Distance 85
20 Limiting Number of Trips per Year for Preset
Barge Sizes 85
21 Annual Operating Costs for Round Trip Haul
Distance of 20 miles 87
22 Annual Operating Costs for Round Trip Haul
Distance of 50 miles 88
23 Annual Operating Costs for Round Trip Haul
Distance of 100 miles 89
24 Coordinate System and Depth Normalization 116
25 Velocity Profile Normalization 117
26 Vertical Diffusion Coefficient K(y)-
Normalization Method . .118
27 Depth Normalization 119
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TABLES
No. Page
1 Ocean Dumping: Types and Amounts, 1968 12
2 Great Lakes Dredging Spoil Characteristics 15
3 Typical Digested Sludge Characteristics 17
4 Typical Characteristics of Fly Ash 23
5 Long Term Diffusion—Example Results 66
6 Specifications of Corps of Engineer's
Hopper Dredges 76
7 Barge Characteristics 80
8 Reported Costs of Barging Operations in
$/Wet Ton 81
9 Calculated Annual Fixed Costs for Barging
Operations 83
IX
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SECTION I
SUMMARY
The ocean dumping policy recommended by the President's Council on
Environmental Quality provides that only under conclusive proof of no
damage to the marine environment should dumping be authorized, and even
then regulatory control should be exercised based on standards that
consider:
1. The present and future impact on the marine environment,
human health, and amenities.
2. Irreversibility of the impact from dumping.
3. Volume and concentration of the material involved.
4. Location of the disposal site.
The accomplishment of such a policy clearly shows the need for an
areal model with statistical capabilities. Most ocean dumping operations
require discharge within specified areas defined by longitude and latitude
and consist of a number of dumps rather than a single site. Some important
questions regarding the fate of dumped material are:
1. What is the ultimate or equilibrium buildup within the water
column or on the bottom?
2. What percent will be retained in the dump area?
3. What is the distribution of the waste within the dump area?
4. Where will the portion not retained go?
5. What is the effect on the marine resource?
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It is not only desirable but mandatory that the answers to these
similar questions be known within some limit of statistical confidence
if such a policy is to be implemented.
This report shows that the barged ocean disposal of wastes is an
established practice which has been justified primarily through economic
models that exclude consideration of possible damage to the marine re-
source. The deleterious effects of past operations are outlined in the
Introduction, Section III, and serve to reinforce this showing. The
objective of this report is not to condemn but to present a discussion
of the available methods for determining the physical fate of wastes
discharged through barging operations.
The fate models presented here are generally good hydrodynamic models
but are quite deficient in allowing for chemical, physical and biological
interactions that may occur between the waste, the sea water and its con-
stituents. The use of these models assumes a knowledge of a number of
important environmental parameters or characteristics which include:
1. The magnitude of the diffusion coefficients, their variability
with scale and depth and density.
2. Ocean shear, drag and added mass effects.
3. - Ocean current and density structures.
A computerized analytical technique developed by Koh and Fan (2) was
adapted to the barge disposal case and is emphasized as one of the better
models available. The program is available for general use and provides
the greatest degree of input variability of any model considered.
The physical transport of the waste discharged from a barge was
sequentially described by the following four separate transport phases:
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1 . Convective descent
2. Collapse
3. Long term diffusion
4. Bottom transport and resuspension
The effects of the presence of solids in the wastes was investigated
and it was shown that interactions between settling velocity, concentration,
and diffusion rates do exist but that the analytical technique is effective
only when these effects can be ignored and the solids assumed to act like
fluid elements.
The convective descent analysis provides results for the short term
distribution of the waste discharge. The results include the effects of
shear flows, cloud drag and added mass, entrainment and non-linear density
gradients. The results of a series of example cases were presented to
identify the effects and trends caused by varying the environmental and
discharge parameters. The relationship between penetration and dilution
was emphasized and methods of control were discussed.
The collapse phase was the most hypothetical and was recommended only
for determining the relative effects on the long term diffusion of the
waste. The basic assumption made was that at a position of buoyant equi-
librium within the water column, the internal density structure of the
cloud seeking a position of hydrostatic equilibrium was characterized by
a dynamic horizontal collapse. This collaose was assumed to occur without
further dilution and with the effects of particle settling completely
ignored.
The example problems presented show that the effects of the collapse
mechanism appear to cause variances in the long term diffusion values of
several orders of magnitude over those when no collapse is allowed.
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These variations are felt to be too large to be ignored and a clear
need for research of this phenomenon exists. Future studies should attempt
to determine the driving mechanism, the resulting dilution and entrainment
while developing criteria for the description of interfacial instability
and the effects of particle settling on the internal density structure
of the cloud.
In its present form the long term diffusion model is a normalized,
diraensionless model that uses the input from the collapse phase to deter-
mine the initial conditions. The present uncertainty in collapse phase
theory consequently results in low confidence limits for the long term
diffusion analysis. However, if the initial conditions are known then
this model should give reliable and consistent results. The ouptut
tabulates and plots the concentration distribution as a function of both
space and time and locates the X, Z positions of the concentration centroid
and the cloud center. The X, Z size of the cloud can also be determined.
The predictive information is of the form that, within given limits, will
be invaluable in establishing effective monitoring and discharge procedures.
Its present value is, however, limited and only provides a method whereby
the two extremes, either complete collapse or no collapse, can be determined.
A section was included which if complete would require a separate
report. This section deals with resuspension and subsequent transport
of materials which settle to the bottom. Current mathematical models are
not designed to handle this area of concern and circumvent its existence
through proper choice of assumptions.
Methods are presented which for a set of assumed or measured conditions
will allow settling and shear velocities to be determined and compared to
calculated critical shear stresses for particles of prescribed size and
density. This section is at most cursory in nature and completely ignores
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the problems associated with multi-phase wastes which settle at different
rates and are distributed in graded form over a varying topography.
Section VII of this report investigates some existing operations,
attempting to show the variability in barge size, design and use. The
barging costs, excluding loading and shore facilities, were examined
through an analysis technique that provides a guide to the decision maker
as to the size and number of barges required for a combination of haul
distance and annual load.
Practical use methods are discussed in the final section and one
example is given which traces the steps required to meet an arbitrarily
selected criterion. The data presented were cited as not being general
in nature and furthermore not descriptive of any particular operation
or geographic area and used only to explore a use method. It was shown
that this format could be used to determine the dilution, spread, and
drift of the discharged material and was subsequently applied to the
determination of the where, when and how of a discharge to preclude vi-
olating established water quality standards. The sample problem also
evaluated the economics of increasing haul distances to insure such com-
pliance.
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SECTION II
RECOMMENDATIONS
This report has established the fact that current ocean dumping
operations embody many separate risks to the total integrity of the
marine environment. The report attempts to isolate only those problems
associated with physical fate prediction from which the following re-
search needs and recommendations are derived.
Techniques must be developed which will allow the material to be
discharged to be characterized as a multi-phase rather than a single
phase material. The segregation, distribution and deposition of materials
must be handled in such a way that physical fate can be predicted for
three separate areas (a) the floatable portions that rise to the surface
either permanently or for some finite time after which they resettle
(b) the portion which remains in suspension due to temperature, density
or turbulence levels of the receiving fluid and (c) the portions which
settle and are distributed over the bottom.
Phenomena such as the collapse phase have been shown to exist but
remain in the realm of the unknown when it comes to the description of
the driving mechanism and the resulting dilution and entrainment rates.
Therefore, this area is considered one deserving of a great deal of ex-
perimental and theoretical research due to its effect on the results of
a long term analyses of the physcial distribution of suspended and settle-
able materials.
The inclusion of particle settling is a necessity and should be
coupled with an approach that allows for a variable bottom topography
for an adequate description of the subsequent distribution.
One other important area which was not specifically identified in
the text exists and this is the description of the initial conditions
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of the discharge. The question(s) to be answered here is whether
the actual barge discharge dimensions are adequate or whether these
need to be described in terms of an effective size, flow, etc. to
account for possible initial accelerations, decelerations or chemical
changes during the free descent of the materials.
The Environmental Protection Agency's National Coastal Pollution
Research Program is currently sponsoring research designed to answer
several of these needs, however this current effort is in no way
sufficient to provide the total information necessary to satisfactorily
predict the physical distribution of wastes and only touches on possible
chemical and biological effects resulting from discharges to the marine
environment.
8
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SECTION III
INTRODUCTION
The by-product of life on this planet is waste; nearly every
creature produces a waste product in direct proportion to its popula-
tion growth rate. Man, the primary exception to this generality,
produces a variety of waste by-products at rates that now exceed
population growth by several orders of magnitude. Waste disposal
has been primarily terrestrial but present population and urbaniza-
tion trends, fostering competition for available land, have neces-
sitated broad searches for economically feasible, alternative dis-
posal techniques. Seaside communities and industries have found that
a system of barged ocean disposal of hard-to treat solids and liquids
is an economically feasible solution under existing regulations.
The President's Council on Environmental Quality, in a recent
report on ocean dumping (1) shows the current responsiblity for control
of disposal to be dispersed among several governmental agencies. The
jurisdiction of these agencies, generally confined to areas other than
those where the actual disposal occurs, results in what is termed
uncontrolled disposal. Conflicts of interest are also pointed out
for agencies possessing both regulatory and operational responsibilities
in the same area. The Council recommends a national policy that would
ban all unregulated disposal and would place sole responsibility and
control in the hands of a single agency. This agency, through the es-
tablishment of discharge regulations and evaluation orocedures, would
"regulate" all ocean disposal operations. The processes of establishing
regulations, and evaluating permit applications depend on an under-
standing of limitations in existing methods for analyzing the fate of
materials dumped from barges.
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Purpose and Scope
The primary purpose of this report is to document currently available
methods and approaches for evaluating the physical fate and distribution
of wastes discharged to the ocean environment. Emphasis is on the local
as opposed to global distributions. This is only one aspect of a waste's
total effect on the marine environment but one that must be understood
prior to setting standards, as well as evaluating the biological and
chemical effects which, of course, may be different for each type of
waste and each bio-geographical coastal province. Where general mechanisms
are involved or can be approximated, they are included.
This report first classifies the wastes giving typical characteristics
and reported effects of current operations. A discussion of the theoretical
transport mechanisms is then presented. A Methods of Analysis Section
explores solution techniques and presents typical examples, followed by
a section discussing barging costs. The report is concluded with recommend-
ations for operation and for research, supplemented with an extensive
bibliography.
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SECTION IV
WASTES: CHARACTERISTICS AND EFFECTS
Wastes are discharged from barges at over 250 U. S. coastal locations
with the majority of sites in nearshore waters less than 100 feet deep.
Table 1, taken from a Dillingham Corp. report (3) shows the breakdown for
1968 by area and waste type.
Projections for the year 1980 (1) show expected increases in bulk
quantity of most wastes to exceed 100 percent of the 1968 values and,
without a major change in policy, most of this is expected to be barged
and dumped at sea.
For the purposes of this report wastes will be classified as:
1. Dredge spoils
2. Sewage sludge
3. Industrial wastes
4. Radioactive wastes
5. Fly ash and incinerator residue
6. Garbage and refuse
Dredge Spoils
The major disposal of wastes to the oceans is in the form of dredge
spoils, a practice in existence since man first found a need to maintain
and improve harbors.
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ro
TABLE 1
OCEAN DUMPING: TYPES AND AMOUNTS (in tons), 1968*
Dredge spoils
Industrial wastes
Sewage sludge
Construction and demolition debris
Solid waste
Explosives
Total
* Reference (3)
Atlantic
15,808,000
3,013,200
4,477,000
574,000
0
15,200
23,887,400
Gulf
15,300,000
696,000
0
0
0
0
15,996,000
Pacific
7,320,000
981 ,300
0
0
26,000
0
8,327,300
Percent
Total of total
38,428,000
4,690,500
4,477,000
574,000
26,000
15,200
48,210,700**
80
10
9
<1
<1
<1
100
** A recent study by the F.D.A. has shown this total to be closer to 62 million tons. The report will be
published in early 1971.
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Dredging operations are usually carried out in estuaries where the
primary sediment source is the adjacent watershed and its drainage system;
however, additional sediments may be deposited due to:
1. Littoral drift
2. Incoming tides
3. Estuary banks
4. Mud flats
5. Man made waste discharges
Estuarine sediments range in size from finely divided colloidal clays,
a fraction of a micron in size, to larger particles of a few centimeters.
These sediments may include variable amounts of organic and inorganic solids.
The sediments are indigenous to the area and reflect the history of sediment
sources. Development and utilization of lands in the drainage basin have
resulted in additional problems. These problems are in the form of sediment
contamination from fertilizers, chemicals and pesticides as well as a variety
of industrial wastes which create a polluted sediment that when dredged or
otherwise disturbed may adversely affect the marine environment.
To determine the physical fate of the sediment, the following waste
characteristics must be specified:
1. The size distribution of the solids
2. The density distribution
3. Chemical flocculation tendencies
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Table 2 gives some freshwater dredge spoil characteristics as reported
by the University of Wisconsin (4) for the Great Lakes. It should be
emphasized that these characteristics may be entirely different for marine
sediments. Some characteristics of marine sediment are given in an extensive
survey of the literature on ocean sedimentation and deposition near structures
conducted by Einstein and Weigel (5).
Reported Effects of Dredging Operations
A report of a cooperative study between the Corn of Engineers and
FWPCA (6) described a two-year study of harbor dredging operations as they
affect water quality in the Great Lakes. The authors found that the effects
of dredge spoil dumping in open lake areas remain open to question, but
concluded that in-lake disposal of heavily polluted dredgings must be
considered presumptively undesirable pending further study.
The U. S. Fish and Wildlife Service (7) has just published an investi-
gation of the effects of dredging operations in San Francisco Bay on the
fish and wildlife resource. The report indicates that spoiling results
in a temporary reduction in fish abundance. Hopper dredge spoiling was
found to create an oxygen sag of a temporary nature with measured values
as low as 0.1 ppm in bay waters. The effects of increased turbidity were
investigated in a series of laboratory experiments the results of which
indicate that fish exposed to high turbidity levels may exhibit a weight
loss and an increase in the level of pesticide concentration.
The effects of dredging on the waters of Chesapeake Bay were studied
by Briggs (8) who found that the spoils were spread over an area 5 times
that of the defined disposal area and that the total phosphate and nitrogen
in the overlying waters was increased 50 to 100 times normal values.
Material collected from bottom cores was found to be more than 90 percent
silt and clay in the area to be dredged but was reduced to 75 percent in
the spoils area.
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TABLE 2
GREAT LAKES DREDGING SPOIL CHARACTERISTICS*
en
Location
Buffalo
Calumet
Cleveland
Green Bay
Indiana
Rouge River
Sodus Bay
Toledo
-/ Based on
Average
Percent Density
Solids gm/ml
37
40
44
43
35
43
53
39
30 minute
.0
.7
.9
.0
.2
.7
.1
.0
settl ing
1.27
1.33
1.36
1.37
1.23
1.28
1.51
1.30
Settling
Velocity
ft/hr a/
0
0
0
0
0
0
0
0
.068
.144
.201
.103
.150
.290
.506
.023
Average Percentage by Weight
Gravel Sand Silt Clay
d>2 mm 63u
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Servizi, et al., (9) reported on the effects of a proposed dredging
operation in Puget Sound on the salmon fishery. Two types of sediments
were involved: a highly organic, putrifying pulp fiber with a high con-
centration of hydrogen sulfide and a natural silt of low organic concen-
tration. The authors concluded that because of the highly toxic nature
of the sediments to the salmon and because various methods of dispersal
appeared impractical, land disposal of the pulp fiber sediments would be
necessary to protect the fish stock. It was determined that a 1000 to
1 dilution would otherwise be necessary to protect and prevent toxicity
problems to the salmon.
Brehmer (10) outlined some of the detrimental effects of suspended
and sedimenting solids in estuaries and concluded that turbidity and siltation
reduce the quality of estuarine waters and degrade the system as a biological
habitat. O'Connor and Craft (11) in a study of the Mersey Estuary in England
found fine sediments that settled as flocules. An isolated investigation
of individual flocules revealed an inorganic core surrounded by organic
material. The Mersey has a strong salinity gradient over a tidal cycle with
a net landward movement of water near the bed. This action was found to
result in a buildup of organic material in the estuary with the presence of
the large amounts of fine suspended material creating a buoyant system for
larger solids and thus fostering and encouraging siltation of this material.
Brown and Clark (12) found that dredging for navigational purposes in Arthur
Kill near Raritan Bay resuspended bottom sediments having a relatively high
BOD.
Sewage Sludge
The inherent public health hazard and the potential for buildup of
organic solids on the ocean bottom makes the disposal of sewage sludge
one of the most significant wastes considered.
The characteristics of the sludge necessary to predict its physical
fate are essentially the same as those of dredge spoils. The bulk specific
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gravity can be controlled to some degree through watering processes or
through the use of additives such as incinerator residue or fly ash.
Normally a primary sludge will have a solid content of between 2
and 5 percent with 70 to 80 percent volatile matter. A well-digested
sludge will contain 5 percent solids which can be increased upward to
10 percent upon dewatering with a 40-50 percent content of volatile matter.
Typical values of sludge characteristics for both aerobic and anaerobic
processes are given in Table 3.
The settling velocity distribution of digested sludges in the sea
water was investigated by Brooks (13) and Orlob (14) for Santa Monica
and San Diego, California, respectively. Their results indicate a high
proportion of solids have very low settling velocities, with 90 percent
at Santa Monica and 100 percent at San Diego settling at rates less than
one centimeter per second.
TABLE 3
TYPICAL DIGESTED SLUDGE CHARACTERISTICS*
Characteristics Anaerobic Aerobic
Total solids 34,000 68,000
Percent volatile 48 48.6 47 48.9
Specific gravity 1.011
PH 7.7 7.2 6.7 5.6
Max. particle in microns 2,000
*References (15), (16), and (17)
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Reported Effects of Sludge Disposal Operations
Philadelphia's disposal of digested sludge to the ocean via barges
was initiated in 1961 and has been discussed frequently in the literature
(18, 19, 20). The dumping is confined to an area of one square mile, ten
miles off the coast near Cape May, New Jersey. By 1969 (21) the annual
volume had reached 115 million gallons.
The sludge dumping grounds in the New York Bight area, located 11 miles
off the coast in waters no less than 72 feet, have been described as a vast
desert on the ocean bottom (22). Another study of the area stated that,
"the bottom of the area of the mud, rubble-excavation and sewage sludge dump
is so badly fouled that changes in the dump location would be of little help
to the immediate area." (17).
Beulow (23) reported on a bacterial study made in the New York and
Philadephia sludge dumping grounds. While it was noted that the coliform
concentration decreased quite rapidly in the waters receiving the sludge,
high levels of fecal coliform contamination were found in surf clams, forcing
the closure of affected areas to further harvesting. It was also noted that
there was considerable sludge covering the bottom.
Beyer (24) reported on an investigation of sludge dumping in the Oslo
Fjord with primary emphasis on the spreading of sinking particles. It was
reported that heavy sludge particles sank to the bottom rapidly and adhered
to meshes of shrimp trawlers in the area, while a cloud of polluted water was
visible at the surface for long periods of time.
There have also been numerous studies of ocean outfalls for sewage
sludge disposal on the West Coast which are pertinent because of the reported
effects. Orlob (14) reported on the effects of digested sludge discharged
approximately two miles off the San Diego shore in 200 feet of water. The
author's analysis estimates a sludge accumulation rate of one tenth inch per
year near the outfall with 40 percent of the solids settling at such slow
18
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rates that their accumulation within a five mile area could be considered
negligible. Grease and floatables were identified as potential problems
but were not defined quantitatively. Apparently, little consideration
was given the ultimate fate of the solids which are carried away from the
discharge site.
Brooks (13) studying the sedimentation and dilution of digested sludge
in Santa Monica Bay for Hyperion engineers, concluded that sludge accumulation
rates should average 2-3 inches per year within a 500-foot radius decreasing
to 0.25 inches per year at a two-mile radius from the outfall. This analysis
assumed a constant current of 0.2 knot with equal frequencies in all directions.
These rates of accumulation were considered unobjectionable based on 1956
standards. Other studies of this area (25, 26) have reported that the dis-
posal of approximately 4000 tons of solids per day has had no apparent effect
on fish abundance. Another study (27) however, has indicated that California's
giant kelp is being adversely affected by increases in sea urchin population
apparently fostered by waste disposal operations along the coast.
In the Puget Sound area, the disoosal of digested sludge through out-
falls has also prompted studies on effects and fates. Brooks, et al, (28)
studied the outfall design and gave predictions for sludge accumulation.
An earlier study by Sylvester (29) in 1962 also discussed this problem and
pointed out the potential problems that could arise from:
1. The increased nutrient content of the water
2. Sludge accumulation
3. Floatable materials
4. Effects on the marine ecology
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Industrial Wastes
Industrial wastes vary greatly in both physical characteristics
and toxicity. The severe effects that may result from the disposal of
these wastes present the greatest potential hazard to the total marine
environment of any of the wastes discussed.
For industrial wastes, the solid concentration, bulk specific gravity
and solubility in sea water are the minimum characteristics necessary for
the evaluation of the local physical fate of the material. Characteristics
of some industrial waste components may be determined from standard
references.
Reported Effects of Industrial Waste Barging Operations
Hood (3) reporting on the disposal of chlorinated hydrocarbons by
the Shell Oil Company, stated that the organisms endemic to the disposal
area were either killed or seriously imparied immediately upon contact
with the waste. The area was found to return to near normal in three to
eight hours. The author concluded that toxic wastes could be disposed of
beyond the littoral zone of the sea, resulting in only a slight effect on
organism biomass. Dispersal was found to be slow, hence to avoid contam-
ination of fishing grounds and areas of upwelling, disposal within the
Gulf of Mexico was recommended only beyond the 2400-foot depth line.
The toxicity of ferrous sulfate and sulfuric acid was investigated
by the National Lead Company in relation to dumping operations they
carried out in the New York Bight area. Reported conclusions (30) claim
no permanent effect on plant, fish, or animal life. The report mentions
similar studies and conclusions for both containerized and liquid wastes
discharged by U. S. Steel, Champion Paper and Fiber, and National Aniline
Division of Allied Chemical and Dye.
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Radioactive Wastes
Radioactive wastes are a potential hazard to man because of radiation
received from the immediate environment and by substances taken into the
body by ingestion, inhalation, or absorption through the skin. It is
feared wastes may reduce the life span, impair the functioning of parts
of the body, or increase the mutation rate altering the inherited charac-
teristics in future generations (31). The disposal of radioactive wastes
is generally accomplished either by containment--allowing for natural
radioactive decay, or by dispersal--diluting the radioactivity to permissible
levels, or a combination of the two. In the past, ocean disposal has re-
quired containment and placement in waters exceeding 6000 feet in depth.
The increased use of radioactive materials by universities, hospitals, and
research facilities has resulted in a corresponding increase in low-level
radioactive wastes. The AEC licenses commercial firms for the disposal
of these wastes in coastal waters.
The NAS-NCR conducted study (31) considers the disposal of radioactive
wastes into the Atlantic and Gulf coastal waters and reports safe levels
for radioactive wastes, containment requirements and recommends specific
disposal sites. This study also discusses the hazards associated with dis-
posal in relatively shallow water, e.g., recovery by fishermen, buildup of
radioactivity in marine organisms, and washup on beaches of contaminated
materials.
Joseph (32) presented a summary of U. S. disposal operations through
December 1956 stating that the operations were considered to be under controls
adequate to preclude hazards in handling and disposal. He estimated that
8500 drums of 55-gallon capacity had been dumped in the Atlantic and over
13,000 drums in the Pacific, representing a combined total of nearly 16,000
curies.
Waidichuck (33) reported on the containment of radioactive wastes off
the Canadian Pacific coast and Collins (34) discussed container construction
21
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laws, possible discharge limits, liquid effluents, volatile reduction, and
biological concentrations.
Koczy (35) discussed the distribution of radioactive materials in the
sea providing the information on the variation in dispersion rates. Isaacs
(36) discussed the magnitude of disposal of low level radioactive wastes
into Pacific coastal waters as did the Coast and Geodetic Survey (37).
The Pneumo Dynamics Corporation conducted a survey of radioactive waste
disposal sites (38), and an evaluation of sea disposal containers (39).
This problem has been studied in the United Kingdom (40, 41) and, no doubt,.
elsewhere.
Sabo (42) discussed the river and tidal characteristics of the Savannah
Estuary and described the accumulation of nuclides by organisms. Pursuhathaman
and Gloyna (43) reported on the effects of sedimentation on the transport
of certain radionuclides. Sheh and Gloyna (44) also reported on this subject
and presented a mathematical model to predict the influence of sediments on
the transport of solubles in open channel flow.
Fly Ash and Incinerator Residue
Fly ash generated by fossil fuel power stations, represents only a
minor percent of the total volume of wastes discharged to the ocean but
is worthy of discussion for possible desirable properties.
Tenny and Cole (45) reported on the use of fly ash as a sludge conditioner
and examined the subsequent effect on vacuum filtration methods of dewatering.
They found that the addition of fly ash to a sludge reduced the volume of
filtrate due to the absorptive capacity of the fly ash. Table 4 summarizes
the typical characteristics of the fly ash generated from pulverized coal
fired plants. The particle size distribution of the material appears to be
describable as a log normal distribution.
22
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TABLE 4
TYPICAL CHARACTERISTICS OF FLY ASH*
Parameter
Silica (Si02)
Alumina, A1000
2 3
Iron Oxide, Fe^O-
Calcium Oxide, CaO
Sulfur Tri oxide, SO.,
Percent Vol . Matter
Particle Sizes
Bulk Density (computed)
s.g.
Units
mg/1
mg/1
mg/1
mg/1
mg/1
y
PCF
Range
34-48
17-31
2-26.8
1-10
0.2-4
0.37-36.2
0.5-100
70-80
2.1-2.6
* Reference 45
23
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Fly ash possesses an adsorptive capacity which has also been studied
for its potential for removing soluble COD. Deb et al., (46) studied the
effects of adding fly ash to the sludge at a treatment facility and found
it would adsorb soluble COD. The effectiveness of the fly ash reached an
upper limit when the concentrations approached or exceeded 4000 mg/1.
The effects of the treated sludge when diluted with sea water are not
known, therefore it is safe only to consider the physical consequences
resulting from the use of fly ash or incinerator residue as an additive
to sludges.
The immediately obvious consequence of such additives is the increase
in bulk specific gravity that occurs. This control can be put to good use
in barging operations as the penetration depth and the dilution of the dis-
charged waste sludges are both sensitive to changes in specific gravity.
These effects may be positive or negative dependent upon the actual en-
vironmental and discharge conditions.
Garbage and Refuse
The disposal of processed refuse and garbage to the ocean is receiving
considerable attention. This is not a common practice yet, but it is ap-
proaching an economically feasible status relative to land disposal. One
process now being considered involves sinking of properly compressed bales
and depends on the increased pressure with depth to maintain a density
sufficient to keep the material on the bottom.
A five-year study conducted jointly by the Harvard University School
of Public Health and Rhode Island's Graduate School of Oceanography (47,
48, 49, 22) investigated waste incineration at sea and the subsequent dis-
posal of the non-floating residue. The results of this study indicated
little or no toxicity to a series of marine organisms and concluded that
a depth of 200 feet was sufficient to keep the material from reaching the
beaches in the test area. Kinsman (50) however, reports that waves alone
24
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have been responsible for sediment movements in water of this depth. To
date, the burning of garbage and refuse at sea has not proven to be eco-
nomically justifiable and current and future air pollution regulations may
prevent it from becoming technically acceptable.
Gunnerson (3) notes that in 1968, 26,000 tons of garbage and refuse
were dumped into the Pacific Ocean off San Diego and San Francisco. San
Diego, however, discontinued this process in November of that year.
25
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SECTION V
TRANSPORT MECHANISMS
The transport of waste materials dumped into the sea depends, in
general, upon:
1. What is introduced - its physical, biological, and chemical
properties.
2. Where it is introduced - its position with respect to local
ambient-density and velocity distributions.
3. How it is introduced - its residual buoyancy and momentum.
This paper emphasizes both the immediate mixing and dispersion of
wastes over periods of time that are relatively short when compared to
the circulation times of the oceans as a whole and does not consider
the physical oceanographic processes, whereby wastes can be diluted and
dispersed from one part of the ocean to another. These are known to
continually vary with both time and space as well as with changes in
boundary condition. This aspect will be discussed only qualitatively to
aid in visualizing the applicability and limitations of the analyses
subsequently presented.
It is often assumed or theorized (51) that although the ocean is in
continuous motion the rates of motion and exchange cover such wide ranges
that they can be separated into nearshore horizontal and vertical exchange,
intermediate and deep circulation exchange and the exchange associated
with coastal and enclosed basin circulation.
In most coastal and open waters agitation and turbulence generated
by wind stresses on the surface result in a surface or mixed layer
-------
characterized by a near uniform density gradient. This layer varies
between 60 and 1200 feet and is separated from the colder deeper waters
by a stable layer exhibiting a sharp density gradient - the thermocline
or pycnocline. The magnitude of this gradient can vary in both time and
space and characterizes the relative stability or strength of the layer.
Wastes introduced into the mixed layer generally will be rapidly
distributed vertically throughout this layer due to convection, wind-
stirring or mixing, density differences, and internal currents. If
they fail .to penetrate the pycnocline they will be transported from the
area of introduction primarily by wind-driven surface currents which, in
general, extend throughout this layer. The analysis of wastes which do
penetrate the pycnocline will be influenced, if not controlled, by large-
scale global currents such as the Gulf Stream and the Kuroshio. The
average location, magnitude, and direction of these currents has been
documented (52, 53, 54, 55) and in lieu of on-site determinations their
use would produce approximate but reasonable results. Estuarine and
nearshore currents have also been studied, although to a lesser degree,
and typical values are given by Ippen (56), Orlob (14), and Brooks (11).
The presence of eddies resulting from turbulence can act to vertically
disperse waste materials in addition to mean current dispersion. The
rapid increase of density with depth in the thermocline inhibits vertical
transfer, and eddy diffusion is small compared to that of the mixed surface
layer with its near uniform density gradient.
There are other localized phenomenon that can influence the exchange
of material between the surface and sub-surface layers. This occurs in
areas where:
1. The pycnocline is shallow and subject to disturbances, usually
wind generated.
28
-------
2. Offshore transport of surface waters results in an upwelling of
colder sub-surface waters.
3. Downwelling exists caused by an increase in the density of surface
waters due to evaporation or cooling.
The first step in a complete analysis of the effects of a waste
discharged to the ocean is to predict its physical fate. The objective
of the analysis usually dictates a time scale that varies as a function
of the waste material itself. For example, the time required to reduce
a toxic waste through dilution to a non-toxic concentration may be on the
order of hours, if it is susceptible to chemical and biological destruction
but on the orders of weeks if it is refractory. The subsequent analyses
utilize a variety of simplifying assumptions and are limited to environmental
conditions variable only with depth and totally exclude biological and
chemical effects.
The total transport of waste materials can be divided into four
basic transport phases. Using the terminology of Koh (2), these are:
1. Convective descent
2. Collapse
3. Long-term dispersion
4. Bottom transport and resuspension
These phases are graphically presented in Figure 1. It can be noted that
the first two phases, convective transport and collapse are of short duration,
when compared to long-term diffusion and, as will be shown later, are
important in determining the initial conditions for the long term diffusion
stage.
29
-------
u>
o
Long lerm (Months]
Collapse
(Minutes)
jot torn Transport
Convective
Descent
(Minutes)
FIG. 1. Basic Transport Phases
-------
Convective Descent
A waste material dishcarged to the ocean from the surface generally
possesses an initial downward momentum and a density greater than that
of the receiving fluid. These result in forces that cause the waste to
settle in the form of a "cloud." As the cloud settles shear stresses are
developed at the interface between the moving cloud and the receiving
fluid. These stresses result in a dispersion of momentum and in the
creation of turbulent eddies that entrain ambient fluid.
Entrainment of the less dense ambient fluid reduces the density
differential and tends to slow the descent of the cloud. The descent
speed is, at the same time, being reduced as solids with settling velocities
greater than the descent speed of the cloud settle out, further reducing
the cloud's density. The waste cloud may, in a stably stratified fluid,
eventually reach an equilibrium level where the descent velocity is zero
and the density of the cloud is in approximate equilibrium with the ambient
fluid. This zero velocity state is considered the end of the convective
descent stage.
To solve this problem accurately the size and density distribution
of the constituent waste elements would have to be known. If solids are
considered to settle continuously, the end of the convective descent stage
would theoretically never be reached for more than an instant because,
due to continual particle settling, the cloud would become positively
buoyant and begin to rise. Many studies of this phenomenon have shown
that when both the concentration and size of the solids are small the
waste slurry will tend.to act as a pure liquid. For the wastes commonly
dumped into the ocean this assumption is currently made for most classes
excepting dredge spoils and industrial wastes having high solid concen-
trations.
Morton, Taylor and Turner (57) solved the problem for a point source
or slug release in a uniformly stratified fluid assuming:
31
-------
1. Wastes to act as pure liquids.
2. Velocity and buoyancy in the cloud to be of the same form.
3. The mean velocity throughout the cloud to be described by K(Ut)
4. Entrainment proportional to the mean velocity and given by
By writing equations for conservation of volume, momentum and
buoyancy the authors developed the following equations to predict the
final depth of penetration, the final cloud radius and the time of
maximum descent.
Final depth Yf = bQ 1.682 (aK)"3/l*E~^ [1 ]
—^" *~^f f~oT
Final radius bf = bQ 1.632 (aK) H E UJ
Max. time tf = 3.14 10s E"
The solution of these equations requires the constants of proportionality
a, and K to be determined experimentally while relying on a linear density
gradient to determine E defined as follows:
E = e0b0/ps-p0
Where,
e = Density gradient (3p/3Y)
b = Initial cloud radius
o
p = Density of waste
p = Ambient fluid density
g = Acceleration of gravity
32
-------
Morton's experimental value for the product (otK) is 0.285 and upon
substitution allows equations 1 and 2 to be solved. The author gives only
a best fit value for a equal to 0.093 which by using the (aK) relationship
above, allows equation 3 to be solved.
Baumgartner, et al., (58) used Morton's work to determine the
ultimate trap level for a diluted bolus of slurry discharged from a barge
as,
W=3-8b°E"* C5]
Koh and Fan (2) have developed a model designed to predict the
distribution subsequent to a deep underwater nuclear explosion. This
model, however, can be used for analyzing the convective descent stage
of a surface discharged waste and, under the previous assumptions, will
produce results identical to those attributed to Morton, et al. This
model is general in nature and was derived under somewhat different governing
assumptions. The entrainment coefficient a was assumed to be proportional
to the vector difference of the mean cloud and ambient velocities. The
momentum equation was expanded to account for entrained momentum and the
effects of drag and added mass with the resulting set of equations programmed
for numerical computer solution. The program allows for arbitrary, horizontal
velocity distributions and can accommodate any depth-dependent density
structure desired. Koh and Fan (2), when analyzing the deep radioactive
debris cloud, concluded that the inherent errors in the entrainment coefficient
(a) more than overshadowed any effects resulting from the inclusion or drag
or added mass effects. They also concluded that ambient ocean currents were
negligible; however, this was in comparison to relatively high cloud velocities,
initially 600 ft/sec. When applying this deep water model to surface dis-
posals one must assume that a cloud of finite dimensions has been formed and
can be described in terms of known surface dimensions and velocities. It
should also be noted that effects of solid constituents were not present in
the radioactive cloud which requires the further assumption of wastes that
act as liquids.
33
-------
The effects of drag and added mass can be removed by choosing CD = 0
=1, then the maximum
m
quiescent receiving body as:
and C =1, then the maximum depth of penetration can be described for a
m
where, F1 the densimetric Froude number is given by:
F' - V/tg'b)*5 ............................................. [7]
with g', the reduced gravitational potential defined as:
Po(o)
Koh and Fan (2) chose (a) equal to 1/6 assuming a range of 1/3 to
1/8 and ran solutions for various values of e. These solutions were
normalized and plotted as functions of the densimetric Froude number and
are presented here as Figures 2 and 3. Slight differences will result
when comparing these solutions to those using equations 1, 2, and 5
for two basic reasons: (1) the difference in the defined level of
descent and (2) the variance in methods and coefficients used to account
for entrainment.
Collapse
The second phase of transport, the collapse phase, is the transition
between convective descent and long term dispersion. The analysis of this
phenomenon assumes that the cloud has come to rest at some equilibrium
position and that a dynamic vertical collapse characterized by horizontal
spreading occurs. This collapse is driven primarily by a pressure 'force
and resisted by inertia! and frictional forces. Many complex actions may
be occurring simultaneously here and an analogy to a density underflow is
useful in attempting to describe them in qualitative terms. A three-
dimensional form of surge head accompanied by the corresponding reverse
34
-------
10 _
10
10
FIG. 2 - Convective Descent Terminal Depth [after Koh & Fan (2)]
o
= 0
FIG. 3 - Convective Descent Terminal Size [after Koh & Fan (2)]
35
-------
flows should exist, with the circulation increasing the diffusion in the
area of the spread. The internal density structure of the cloud relative
to the ambient density structure will exercise control over the magnitude
of this spreading rate and instability criteria should exist, similar to
that of the two-dimensional case, that will predict breaking interfacial
waves for some velocity level. If this occurs, mixing and entrainment
will further increase. The near zero vertical velocity of the cloud should
allow for an increase in the number of solid elements that can settle
out interjecting another action that may foster not only a decrease in the
driving force but also an upward motion in the cloud itself.
To date, there is no analysis specifically designed to analyze this
problem, however, if one realizes the shortcomings, the analysis presented
by Koh and Fan (2) can be applied—providing a feel, at least, for the
limiting values. It should be pointed out here that the method described
was not intended to describe the collapse phase of a waste slurry and the
shortcomings are to some extent a function of its extrapolation.
To apply this analysis one must assume the following:
1. The cloud has an axi symmetric shape at the end of the convective
descent stage.
2. The ambient density structure is linear.
3. The internal density structure of the cloud is described by an
equation that differs from that for the ambient density through the inclusion
of an internal density distribution term (y). This equation can be written
as:
(y,r) P0
4. No entrainment occurs during the collapse
36
-------
From the equation for the cloud density structure it can be seen that
when y = 0 the driving force would be the greatest and when y = 1 no spreading
would occur because the cloud and the receiving fluid would exhibit equal
densities at all depths. The validity of this approach, as pointed out by
the authors, has not been verified and the results presented here are for
theoretical examples designed to explore the interrelationships between
the defined terms.
A balance of forces in the horizontal directions resulted in the following
equation using the coordinate system shown in Fig. 4.
y
r2/b
2 =
16
FIG. 4.
p Tiab:
~T6
Coordinate System for
Collapse Phase
d2b
de
2a
() da
.[9]
The term on the left is the pressure force term equated to respect-
ively, a local inertia! force, a convective inertial force, and a friction
force. The equation is simplified by defining two new terms Kx and K2 as:
= 4 CI/TT
K =
[10]
[11]
37
-------
In lieu of measured values for C, and C« the authors reasoned that
they should be near unity and, therefore, attention was focused on the
interrelationship of K, and Kp. Figure 5 is typical of the results of
this analysis and shows a series of S-shaped curves for a constant value
of K,. This indicates a pool acceleration at small values of time which
are independent of K? and are interpreted by the authors to indicate the
domination of the inertial and pressure forces which gradually and contin-
ually decrease until the viscous forces described by K« become dominant
and collapse ceases. Figure 5 can be used to predict maximum time and
cloud dimensions for the case where y is equal to zero and K, is taken
equal to 0.1. Examples will be presented in a subsequent section.
It should be pointed out that no ambient horizontal currents are
assumed to be acting during this phase, a condition not likely to be found
in the shallow waters where barge dumping is common.
Long Term Dispersion
Standardized differential equations are available that describe
dispersion and convection in turbulent flows. To date, only simplified
solutions have been used. These are usually applicable for open ocean
conditions only and presuppose a waste that acts solely as a liquid.
To apply these solutions to a waste cloud it is again necessary to
assume a neutrally buoyant cloud acted upon by molecular diffusion, eddy
dispersion and mean convective processes. These simplifying assumptions
result in a series of differential equations for each phase.
The basic diffusion equation may be written as:
If
38
-------
102i-
CO
-Q LQ
t' = t /^
FIG, 5, Collapse Size and Time for y = 0 [After Koh & Fan (2)]
-------
where C denotes the concentration of the waste, D the molecular and K .
Xj
the eddy diffusion coefficients. The last term (m) represents either a
source or a sink. If the waste is subject to decay, flocculation or
chemical and biological reactions, these processes might be appropriately
estimated by incorporation into a first order reaction function, viz.,
dc/dt = -cK. The last term of equation 12 would then include ( -cK)
for each process included. If there is only one source or sink term, it
need not be included in the differential equation, however, the resulting
values'of c(t) the so-called conservative values must be multiplied by
-kt
e to obtain the correct liquid concentrations.
For ocean diffusion problems the molecular diffusion can be shown
to be insignificant when compared to eddy diffusion; therefore, the term
of interest is K . which is a function of the flow field rather than of the
xj
fluid itself.
The general solution, for instantaneous releases of conservative
wastes, can be described by the following equations:
, z t) = M r(x-ut)2+ (y-vt)2 + U
( A \ /2 f (/ (/ t/ \ "^-l- /2 H" Ix t *T ix t T"ixw
1 ^; ^ x yxzj X y
where M is the mass of waste released.
If the source is fixed and continuous and is being discharged into
a uniform flow field the concentration for any time at a point can be described
as follows:
C14]
where q is a measure of the volumetric discharge and has units of [L /T],
and c is the initial waste concentration. For the case given here the
current is assumed to be in the X direction with the eddy diffusion in that
direction assumed negligible.
40
-------
Orlob (11) used the two-dimensional form of equation 13 to predict
sludge accumulation rates adjacent to an ocean outfall. He redefined the
eddy diffusion terms K - to represent the greater effects of current velocity.
Glover (59, 60) also used this relationship to analyze the dispersion of
solid and suspended materials in open channel situations.
Simplified versions of these equations have been used by the Atomic
Energy Commission to analyze the diffusion of radioactivity subsequent to
the sudden rupturing of cubical cannisters residing on the ocean bottom.
The assumed conditions reported (61) provided for an instantaneous rupture
in the absence of currents. Equation 13 under these assumptions reduces to:
c = M/4UK t)3/2 Where M E cQV [15]
The assumptions made should be reviewed to reinforce the limitations
of these solutions. A constant flow was assumed removing shear effects thus
limiting the use of these equations near boundaries. The turbulent diffusion
coefficients were assumed constant, an assumption that will subsequently be
shown not to be valid for many ocean situations. These solutions cannot be
expected to predict the transport of any wastes with high solid concentrations
due to the assumed zero settling velocities. It should also be pointed out
that in the case of surface dumping of waste materials the initial conditions
at the beginning of this phase are described by the waste cloud at the end
of the collapse phase. These conditions, at present, cannot accurately be
predicted which further effect the reliability of derived results.
Solutions recently presented by Carter and Okubo (62), Okubo (63, 64)
and Okubo and Carweit (65) have included shear effects for both continuous
and slug releases. These solutions are applicable only when the settling
velocity can be assumed zero. The eddy diffusivities have also been
considered constant with respect to both time and space based on a division
of the turbulence into large and small scale eddies. The small scale eddies
41
-------
were felt to exhibit small time and length scales relative to those
of observations, thus allowing the use of mixing length theory to describe
this diffusion process. The large scale eddies were assumed to create an
inhomogeneity in the flow that could be described by defining the mean
velocities as:
Vy = Vz = 0 [17]
where, ft , fl denote constant horizontal and vertical shears. This
A £.
assumes a mean velocity along the x axis with the z axis vertical and
leads to a diffusion equation for their model of:
Computer programmed solutions to these equations have been reported
(63) which provide as functions of time:
1. Families of isoconcentration surfaces
2. Dimensions of the contaminated region
3. Volume and quantity of material
Koh and Fan (2) have presented an even more general solution allowing:
1. Turbulent eddy diffusion coefficients variant with both scale
and or depth.
2. Current generated shear in both vertical planes.
3. Non-linear density gradients, when applicable.
42
-------
The environmental conditions are somewhat limited as they are independent
of the horizontal coordinates. This limitation is minor in light of the un-
certainty that exists around the proper choices for coefficients to describe
entrapment, diffusion, drag, and added mass. The analysis does however
provide the gross characteristics of the "cloud" which include:
1. The total material distributed over each horizontal plane.
2. The location of the centroids.
3. The standard deviations of the centroids.
4. Estimated characteristic concentrations.
5. Horizontal cloud dimensions.
Bottom Transport and Resuspension
This final transport phase, contrary to the basic assumption made
earlier, assumes that the solid constituents of the waste slurry do indeed
settle and reach the bottom. This could be accomplished entirely during
the convective descent stage if the water depth were less than the predicted
or theoretical total penetration depth. The resulting distribution- of the
solid constituents for this case would become a function of the residual
momentum of the cloud as well as the existing density disparity. When
the residual momentum is high, a dynamic turbulent rebound effect might
be expected, but for near zero momentum the density disparity would cause
a spread similar in nature to that of the collapse phase. Two questions
are raised regarding the solids once they reach the bottom: [1] will
movement occur? and [2] if movement occurs, what form will occur - bed load
or resuspension?
In general, it is accepted that motion will be initiated in a flow
field when the shear stress on the particle creates a lift force in excess
43
-------
of the submerged weight of the particle. The direction of the initial
particle movement will be nearly perpendicular to the plane of the applied
shear stress and for a horizontal bed will be near vertical. This force
will lift the particle off the boundary and it will resettle, subject to
currents and eddies, either to a position in the flow where the resultant
lift on the particle just equals its settling velocity (suspended transport),
or when the settling velocity exceeds the lift force, to another position
on the boundary (bed load transport). Suspended transport is most common
when the current shear is nearly constant with bed load motion resulting
when an additional shear resulting from turbulent eddies is superimposed.
A method is available whereby one can predict what form of transport
will occur. This method assumes steady uniform flow, a logarithmic velocity
profile and a linear shear stress distribution with depth. An equation
which relates the settling velocity of the particle, the diffusivity of
the system and the sediment concentration c is given by:
H • ^
where K = pUJcz under the above assumption.
This equation can be rearranged and integrated over a region of interest
with the following results:
[201
/•••l \ -t I II !/• ' *»."-*'J
Defining r as (q) we can relate the type transport to the magnitude of
this parameter. By plotting the In (c/ „) against the In (z/,) it can be
ca a
seen that 1/q is the slope of the line and is descriptive of the concentration
gradient.
44
-------
ln(f)
FIG. 6.
1/q
In(f-)
a
Sediment Concentration
Gradient Definition Sketch
When the magnitude of q is less than unity the effects of the shear
stresses are always greater than the gravity effects keeping the material
in suspension with what is termed wash load transport resulting. Studies
have shown that when q is greater than unity but less than three suspended
load transport should be expected with bed load transport predominant when
q exceeds three.
To use this relationship the settling velocity of the particle must
be determined and related to the existing shear velocity U*. The shear
velocity is governed by the following relationship:
u =
[21]
where Z equals the point of interest in the flow--measured from the bottom--,
Zn is the depth where the assumed logarithmic profile goes to zero and k is
Von Karman's constant equal to 0.4. Solving for U* would require an iteration
process if the profile is unknown. If shear stress measurements are available
U* can be determined from the following relationship:
Tb =
,[22]
45
-------
The settling velocity of a particle can also be determined by an
iteration process using the following equations and Figure 7 which relates
the coefficient of drag to Reynolds number defined using the settling
velocity of the particle:
_ 4 PS - p gdA [23]
ws ' T L p CD J
After determining both U* and (w) a direct substitution into the
relationship for (q) will give a prediction of the type transport that
should be expected.
Another approach can be used which compares the critical shear stress
to the calculated or measured stress on the boundary. The critical shear
stress is that stress that will just initiate motion for a particle of
given diameter (d). This stress can be determined using Fig. 8 and the
following equations where the critical shear stress TC is given by:
T. = f(R*,n) = T*(p -l)gd [24]
C *>
with n given by:
n = g[(0.1)(ps-l)gd]
P
For a given U*,n can be determined and T* can be read directly from the
graph and a simple calculation using Eq. 24 will give the critical shear
stress for that combination of shear velocity and particle diameter.
Comparing T to T. given by Eq. 22 will reveal if motion should be expected.
These equations are admittedly simplified, and do not represent a
complete literature review but within the accuracy of any of the other
46
-------
io ;
10
8
lor
FIG. 7.
Reynolds Number R = —
Drag Coefficient for Spheres as
Function of the Reynolds Number
in
O)
s_
1.0
0.6
0.4
S- Q.
ro i
O) to O.2
^Z Q.
oo —
(O
o
O.I
.06
.04
.02
.01
d
v
0.1
4661002 468 1000
O.I 0.2 0.4 0.6 I.O 2 4 6 8 10 2 4 6 8100 2 468 1000
Boundary Reynolds Number
V
FIG. 8. Shields Diagram, as Modified by Vanon£ (1964)
47
-------
transport phases allows the prediction of motion as well as type transport.
These predictions are subject to the several assumptions made, namely:
1. A steady uniform flow
2. A logarithmic velocity profile in lieu of actual bottom shear
stress measurements.
3. A horizontal bed of uniform roughness (i.e., no dunes, growth,
outcroppings, etc.)
Partheniades (66) presents a State-of-the-Art summary of the behavior
of fine sediments in estuaries and documents a number of research needs in
this field. The A.S.C.E. Task Force on Sedimentation (67) also presents
a summary of applicable approaches and presents relationships which account
for non-uniform turbulence.
Other approaches can be found in the work of Schmidt and O'Brien (68, 69),
Souther!in (70), Brooks (13), Shields (71), While (72), Vanoni (73), and
Anderson (74).
48
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SECTION VI
SOLUTION TECHNIQUES
There is no single analytical method currently available that will
completely and accurately predict the dispersion and dilution of a waste
material discharged into the marine environment. The general nature of
the approach used by Koh and Fan (2) does, however, offer a good means of
analyzing these effects for surface discharges under a variety of en-
vironmental conditions. This solution technique has been programed for
general use and the following section will explore hypothetical case
solutions for each of the three separately defined transport phases.
Convective Descent
The convective descent phase allows the initial short term distribu-
tion of the waste to be explored for any combination of density and
velocity profiles. Two separate cases will be investigated; one with
a linear density gradient and the other representative of a strong
pycnocline. For these conditions the penetration depth (Y.r) and the
dilution (DILN) will be investigated under the existence of a two-dimen-
sional shear flow. Discussions will be two-fold in nature; describing
the procedure to be followed to use the program, while pointing out
critical parameters and some of the errors inherent in simplifying assump-
tions commonly made.
The input requirements are listed and discussed in Appendix I
complete with a sample problem. The convective descent solution gives
incremental penetration depths, dilutions, X Y Z positions of the cloud
center all as functions of descent time. The analysis is terminated either
when the cloud has reached the bottom or where the cloud becomes neutrally
buoyant and its descent is stopped. This latter case is characterized by
a reversal in the direction of the cloud velocity with the analysis ter-
minated after one complete cycle.
-------
Discussion of Example Problem Results
A classic example is revealed in Fig. 9 where the dilution is
high for high values of the initial densimetric Froude number with a
characteristic curvilinear decrease with increases in the penetration
depth. For example, an initial densimetric Froude number of 0.09 would
tend to concentrate the material at a depth of 185 feet with a dilution
of 425. Increasing the Froude number one order of magnitude would de-
crease the descent to 95 feet but would increase the dilution approximately
eight times for a total dilution of 3400. The presence of the strong
pycnocline, Fig. 10, at Froude numbers between 0.4 and 2.0 appears to
significantly reduce the penetration and dilution with the waste material
retained in the oycnocline. This figure also indicates two methods by
which the dilution can be increased. An increase in the Froude number
between 0 and 0.2 results in higher dilution and it appears that a decrease
in large Froude numbers to 0.2 will allow the waste cloud to break through
the pycnocline, after which the penetration and dilution rapidly increase.
These results are not descriptive of the general case, but were
designed to represent a typical operational evaluation. A series of computer
runs were made where the discharge radius was varied while maintaining a
flow of 100 cubic feet per second (cfs). This limiting criterion in effect
establishes a unique relationship between the radius of the discharge and
the initial densimetric Froude number. Two sets of environmental parameters
were employed; the first descriptive of the linear density profile, and
second, a strong pycnocline. The penetration depth and the resulting di-
lution were then compared against the initial densimetric Froude number.
Figure 9 for the linear gradient exhibits low penetration and high
dilution for Froude numbers of order 10, which, for this example, correspond
to a small diameter discharge. This result is predictable if one considers
that the entrainment is high and, when applied to a small waste volume,
dilution proceeds rapidly and buoyant equilibrium is attained at a shallow
depth. The same argument applied at the other end of the scale where the
discharge velocity is low, and the radius is large, would predict a biower
rate of dilution and a greater penetration, again as shown by Figure 9.
50
-------
O.
QJ
Q
o
tQ
tu
Q.
-60-
-120
-180-
-240
-300
-360
-420
.480
-500
DILN
Penetration
600
12CO
1800
2400
3000
3600
4200
J I I I I I I I
' I I I I I I 1
I 1 I I I I
Initial Densimetric Froude Number F'
10
4800
5000
FIG. 9.
Penetration Depth and Dilution as Functions of the Initial Densimetric Froude
Number under Linear Density Gradient (E = 1.17xlO"Vft)
-------
cri
r°
-C
-p
O-
-------
When the density profile is complicated through the inclusion of
a pycnocline, the results take on a different form. For Froude numbers
of order 10, the same trend seen for the linear case exists (Fig. 10)
with the cloud's descent terminated above the level of the pycnocline
and its existence is really of no importance. At the low end of the
Froude number scale (F 0.1) entrainment is also reduced and in essence
the descent is governed by the linear gradient that exists below the
pycnocline. The major difference occurs in the intermediate Froude
number range, where entrainment and waste volume are sufficiently
interrelated for the cloud to obtain buoyant equilibrium in the pycno-
cline, but, driven by a high momentum, is carried beyond this position,
with both the velocity and the buoyancy becoming positive. The sub-
sequent dilution and ascent are relatively rapid, with the oscillations
damped almost immediately.
The sudden shift or increase in dilution that occurs in Figure 10
for Froude numbers of approximately 0.2 results when a cloud has in-
sufficient positive buoyancy to reenter the pycnocline and remains
subject to the nearly uniform-gradient below. A long period oscillation
is developed which results in the rapid increase of the time required
for this cloud to reach a stable position (from five minutes to twenty
minutes) with an obvious increase in the dilution.
Comparing the results of the two examples reveals that using a
linear assumption where, in fact, a pycnocline exists would result
in a general overestimage in both the depth of penetration and the di-
lution. This conclusion is valid only under the previously described
conditions; however, generalized plots can be made and presented in a
manner similar to that shown in Figures 2 and 3.
The penetration depths as predicted by the various methods dis-
cussed in the previous chapters are compared in Fig. 11. Curves 1 and 2
53
-------
o.
C/1
-fa.
Q.
OJ
Q
O)
C
-------
utilize the same basic equation, however in case 2 the relative effects
of introducing cloud drag and current generated shear are responsible for
the net differences. The penetration depths for all methods, over the
full range of Froude numbers tested, varied a maximum of only fifty per-
cent compared to a variance in dilution which at times exceeded 800 per-
cent. For this reason alone it would seem that dilution, as well as
penetration should be given consideration in all predictive convective
descent models. The predictive nature of Morton's approach is such that,
on the basis of penetration alone, it could be erroneously interpreted
as a conservative model over the full range of environmental conditions
that might exist.
The penetration depth (Yf) and the dilution (DILN) have been shown
to be conditionally related to the initial densimetric Froude number.
Changes in the magnitude of the Froude number can be effected by altering
the magnitude of the velocity, the diameter, or the method of the dis-
charge or by modifying physical waste and discharge characteristics. With
the exception of the waste specific gravity, physical modification will
directly affect only the initial dispersion that occurs during the con-
vective descent stage. Once a cloud attains buoyant equilibrium within
the water column or reaches bottom, the subsequent dispersion is entirely
dependent on its relationship to the natural environment conditions that
exist. This in essence means that any control over the long term dispersion
must be exercised during the discharge process in such a way as to alter
its convective descent.
Waste Characteristics:
The waste characteristics are infinitely variable; however, in analyzing
the initial distribution, only the physical characteristics need be con-
sidered. The bulk specific gravity of a waste slurry is one characteristic
that, within physical limitations, can be controlled. Changes in the
specific gravity of a waste slurry or sludge, whether through the use of
a thickening process or through the use of additives, can affect both the
55
-------
resulting dilution and penetration. Such changes may result in changes in
either the concentration, density or size of the solid constituents or any
combination of the three. The effects of solids on diffusion in fully de-
veloped turbulent liquid flows has been investigated by Katta and Hanratti
(75), Rouse (76), Vanoni (77), Householder and Goldschmidt (78-79), Singamsetti
(80), McNown and Lin (81), and by Ahmadi and Goldschmidt (82). From these
studies it is generally concluded that suspensions with grain sizes less
than 60 microns can be assumed to act as pure liquids. Inter-relating effects
are shown between such parameters as settling velocity and particle concen-
tration with an increase in particle concentration increasing the diffusion
while causing a decrease in the settling velocities of the particles.
From data presented by Ahmadi and Goldschmidt (82) the turbulent Schmidt
number can be calculated independently of concentration. Such calculations
for typical values for dredge spoils and sewage sludges reveal ratios of mass
to momentum transport that vary between 1.0 and 1.1, indicating that the
motion of the solids is not significantly different from that of the liquid
phase. Such analyses provide the justification needed for a pure liquid
assumption in waste dispersion studies, and, when made, reduce to one the
number of physical characteristics of the waste that must be known; namely
the specific gravity.
The approximate specific gravity of waste sludges or slurries can be
determined from a knowledge of the percentage of solids and volatile matter
or the percent moisture alone when the solid concentration is high. Equations
25 and 26 after Fair and Geyer (83) are commonly used for this purpose.
100SQ S,,
_ b W
_
~ P Ss + (100-P) Sw
= 100 Sf Sv/100 Sv + Pv(Sf-Sv) .............................. [26]
56
-------
where:
S = Specific gravity of waste
$<-= Specific gravity of waste solids
O
Su= Specific gravity of water in waste mixture
Sf= Specific gravity of fixed solids (2.5)
S = Specific gravity of volatile solids (1.0)
P = Percent moisture by wt.
P = Percent volatile matter in sludge
Physical modifications:
Several other controls are available and are of a ohysical nature.
Included among these are the depth, size, and orientation of the discharge
outlet, as well as the barge speed and direction, which can be used to in-
fluence and control the final distribution to some degree. However, the
optimum discharge method must be seoarately determined for each waste and
should include consideration of possible biological and chemical effects.
The general influence of changes in density, discharge radius and velocity
on penetration and dilution can be evaluated in terms of the changes in the
densimetric Froude number. The Froude number can be shown to vary as bQ,
the initial cloud radius, to the minus two-thirds power, and directly with
the discharge velocity. These relationships are not generally independent
and a change in one of the parameters without a compensating change in the
discharge rate will necessitate the use of a continuity relationship.
Pump discharges into the wakes of propeller streams of barges cannot
be analyzed by the Koh technique and must be handled separately, and
in such a manner that the increased turbulence created by the passage
of the barge is accounted for. These discharges are usually employed
57
-------
when the waste is toxic, taking advantage of the increased turbulence
to maximize the rate of dilution.
If this method of discharge is considered for cases where stable
density stratification occurs, the liquid slurry may not settle directly
to the bottom upon discharge. This action can then be described in terms
of three separate flow regimes as shown in Figure 12.
The longitudinal dimensions of Zone 1 can be assumed to coincide
with that distance behind a barge (X1) where a fully turbulent wake is
established. Schlichting (85) states that this is reached, for a cylin-
drical object, when the following relationship is realized:
X ' = 50 CQW .................................................. [27]
where W = barge width and
CD= drag coefficient
Redfield (86), Ketchum and Ford (87) and Hood (30) have analyzed the
discharge of wastes into the wakes of moving barges where mixing was ob-
served to be instantaneous in the vertical direction. Thus, by neglecting
vertical dispersion, and transverse dispersion when the barge travel and
the ambient currents are along the same axis, the problem becomes one di-
mensional. With such a simplification the solution in the established flow
zone becomes one of two variables--the turbulent diffusivity and the dis-
charge rate.
Equation 12, the basic diffusion equation, applied to the dispersion
of a waste in a barge wake has been solved by Ketchum and Ford (87) and
Pearson, Storrs and Selleck (88) with the respective solutions describing
the median and average concentrations per unit cross section along the
centerline of the wake. Both solution equations are identical:
cAq
ci =
o
[28]
58
-------
Zone
III
on
mixed surface
layer
FIG. 12. Schematic Presentation of Fate of Material when Discharged in
Barge Wake
-------
where A. = 0.493 describes the median concentration and A. = 0.282 the
average concentration. The other terms in the equation are:
o
q = volumetric discharge per unit time [L /T]
h = mixing depth [L]
U, = barge speed [L/T]
2
K = "turbulent diffusion coefficient for combined system [L /T]
X
T = the length of time since the barge has passed the point of
interest [T]
c = initial concentration of the discharge
Turbulent eddy diffusion coefficients in wakes have been shown,
2
through field determinations (87, 86), to vary between 1.0 ft /sec and
2
30.0 ft /sec and should be expected to fluctuate.
Schlichting (85) equates the wake diffusion coefficient to the
wake centerline velocity and the defined half width of the barge as
follows:
K = 0.0235 Ur (X'CnW)1'5 [29]
A Li U
The turbulence is known to decrease over the length of the wake. This
relationship is contained in the above equation since the velocity de-
creases as the length of the wake to the minus two-thirds power. The
wake turbulence in a practical sense, has a lower limit equal to the
natural turbulence of the ambient environment. Pearson et^ al_., (88)
used the water depth as the length scale (L) and determined a constant
average diffusion coefficient as defined by the following relationship:
V
3 [30]
60
-------
The mixing depth (h), the last unknown, is a difficult parameter
to determine. Omission of this term from Eq. 28 would result in a de-
scription of the concentration per unit cross section of a water column
of unknown depth. This form of the equation was the one used by Ketchum
and Ford (87) in analyzing the concentration of an iron waste discharged
to the wake of a barge.
Results of full scale experiments where a waste was discharged into
the propeller stream of a ship are given in a recent report by Abraham
and Eysink (84) which discusses the applicability of jet theory to this
method of discharge and concludes that the minimum dilution can be determined
using jet theory calculations.
When the results of the convective descent stage analysis indicate
a situation where the cloud comes to rest at some equilibrium position in
the water column, both collapse and long term dispersion must be considered.
These are sequential analyses with the output of the collapse phase serving
as the initial conditions for long term dispersion. The only method for
the analysis of the collapse phase appears to be the one presented by Koh
and Fan (2) which is at present hypothetical.
The collapsed dimensions of the cloud can be determined for the case
where the constants C-, and C2 are assumed near unity and K-j is assigned a
value of 0.10. The initial shape of the waste cloud must be assumed an
axisymmetrical ellipsoid with the major horizontal radius (bQ) equal to the
predicted cloud radius at the end of the convective descent stage and the
minor radius (a ) defined as (bo/2). The approach is limited by a requirement
that the density gradient be linear over the depth of the cloud which pre-
cludes its use in cases where the cloud collapse transcends a pycnocline.
Conceding this deficiency and choosing a proper set of initial conditions,
the cloud dimensions can be determined for the case of a complete collapse.
61
-------
For the purpose of isolating the effects of a collapse phase on the
long term dispersion of a waste, fixed value results for a convective descent
stage definitive of a set of intial discharge conditions were chosen where:
Bf = radius at end of convective descent state = 66 feet
Yf = 159 feet
E = 1.17 ft x 10~5/ft.
For these values the initial collapse phase dimensions are b - 66 ft,
and a minor radius a = 33 feet. The collapsed dimensions can be determined
directly from Fig. 5 and for this example were taken as:
b 7
bf = 264 feet af - aQ (^-) - 2.06 feet
The time for this collapse to reach completion was determined as 568 sec.
The question, now, is: What is the effect of such a collapse on the
long term dispersion solutions as predicted by this analytical technique?
It was decided to explore these effects for two sets of environmental
conditions: Case I investigates the effects of cloud collapse under en-
vironmental conditions consistent with a linear density profile and Case
II investigates the same cloud effects for parameters descriptive of a
strong pycnocline in which vertical transport is suppressed.
The use of this analytical technique requires that the initial distri-
bution of the waste be assumed axisymmetric about the Y axis and confined
in an ellipsoidal region with a horizontal distribution of material defined
by:
C(y1fO) = (1 -sV) ** [32]
62
-------
where 6 is a dimensionless ratio of the depth of the cloud to its half
thickness. The horizontal diffusion coefficients are assumed to follow a
4/3 law relationship and have been defined in terms of the geometric mean
of the standard deviations along the principal axes as:
Sc - Kz = AK V - °xzl
[33]
The standard deviations of the distributions QX and az in the above
equation are taken as equal to 1/4 the size of the cloud as shown in
Appendix II. The coefficient A will be taken to be constant over the
depth of the cloud but the solution does permit this to be varied if
desired. This coefficient can be determined by considering the 4/3 law
governing horizontal diffusion where:
K .K - A l> [34]
Kx'Kz " \L
A, is a constant dissipation parameter and (L) is a length scale.
For the problem at hand (L) is taken equal to the length of the cloud
which is related to the standard deviation of the distribution by:
, ^ [35]
Lc ' 40x
Substituting we have
Where A = 6.34 A
U)
The choice of a value for A(fi/) was taken for this example as 1.5x10"
ft2/3/sec which makes A equal to 0.001 ft'/Vsec the quantity which will
be used for this example. The vertical diffusion coefficient KyS as used
63
-------
in this analysis, must be determined and related to the existing density
structure. These coefficients are, in general, smaller than those for
horizontal diffusion with the magnitude decreasing with depth to near
molecular values in pycnoclines.
There is no apparent universal law or value for K but a functional
relationship can be shown between vertical transport and the Richardson
number (89) which implies a dependence on one or all of the following
parameters: density gradient, current generated shear and the type of
flow. Reported values for K range from 1.075 x 10" to 3.215 x 10"
ft /sec with exoected variances from flow or density changes. Koh and
Fan (2) have presented estimated coefficient ranges for several areas of
interest:
_2 1 2
K Mixed layer 2.2x10 to 2.2 x 10 ft /sec
3 5 2
K Pycnocline 1.1 x 10" to 1.1 x 10" ft /sec
_2 4 2
K Deep layer 1.1 x 10 to 1.1 x 10" ft /sec
These are suggested values based on limited past information. For the
example problem being considered here a vertical diffusion coefficient
equal to 0.1 ft /sec will be used for the mixed layer, 1.0 x 10 for
a strong pycnocline and 1.0 x 10" for deep layers.
The output from this analysis describes the concentration distribution
in terms of the initial concentration at the beginning of the phase and a
normalized elaosed time. The X, Y size of the contaminated area, the X,
Y, Z position of the concentration centroids and the distribution of con-
centration with depth can also be determined. These allow predictions for
both the concentration and the environmental exoosure time to be made
thus aiding in the development of field sampling and monitoring procedures
and techniques. The results subsequently oresented assume an initial
concentration at time zero equal to unity and the cloud at a real depth of
64
-------
159 feet assigned an X, Y, Z position of (0,0,0). The analyses is ter-
minated when a diffusion time equal to that required for the material
to diffuse to surface under a constant vertical diffusion coefficient is
reached.
The basic problem being considered here is limited to only the collapse
and long-term dispersion phases. For an arbitrarily selected set of initial
conditions four individual sets of solutions are being sought. These solu-
tions compare the results for a cloud that exhibits no collapse to one that
completely collapses under two sets of environmental conditions. These
effects can best be compared through an examination of the magnitude of
various parameters such as the maximum surface concentration, the maximum
concentration or the location of the cloud or concentration centroid. These
same parameters can also be compared on a time base. Such comparisons have
been made for the example considered with the real value results given in
Table 5 and Figures 13 through 16. By using both the figures and the table
trends should be identifiable and observed deviations relatable to either
a cloud collapse or a change in environmental conditions. The effects of
a cloud collapse does represent the two extremes possible and can be con-
sidered a measure of the confidence one can afford any individual prediction.
Discussion of Example Problem Results
Figure 14 relates the maximum concentration to exposure time. Inclu-
sion of either a collapse mechanism or a pycnocline or both acts to de-
crease the rate at which this dilution occurs thus increasing the exposure
time for any given concentration. For example, if the time required for
the maximum concentration to reach 1/1000th of the concentration at t=0
the graph can be used to predict 30 hours for the uncollapsed linear case
and 100 hours for the collapsed cloud in the pycnocline.
The surface concentration-exposure time relation is given in Figure
13 and reveals that a linear uncollapsed cloud reaches its maximum value
in 8.5 hours. If this cloud is collapsed and subjected to the same analysis
65
-------
TABLE 5
Example Problem Results
Parameter
Cs (Max)
T (a Cg max
Lv @ C max
A 5
CEx 9 Cs max
Snax at T=7° hrs
L @ C
x max 70
CCx @ Cmax 70
C$ P T=70
x(s)
Ci- / \ @ T=70
Ex(s)
Linear Gradient Pycnocline
No Collapse Complete Collapse No Collapse Complete Collapse
6.2xlO"4
7
940
3420
l.OxlO'4
31 ,400
5,300
2.5xlO"5
22,200
32,500
3xlO"6
70
27,400
21 ,600
6.5xlO"4
20,600
440
3.0xlO"6
27,400
21,500
1.5xlO"7
25
3200
1900
3.7xlO"4
15,400
6,400
7.8xlO"8
12,700
34,000
0
70
-
-
4.42xlO"3
12,500
386
0
0
-
C = Maximum Surface Concentration
L = X Dimension of Cloud (ft)
X
Cr = X Centroid Location of Concentration Distribution (ft)
T = Time in hours
-------
-iio"
cr>
C = collapsed cloud
U = uncollapsed cloud
L = linear density gradient
P = pycnocline
Cactual CR(Cinitial)
/
I I
L
1st appearance of surface concentration^
4-5
i_
3
(/)
10
-6
10
-7
10
-P
0)
o
o
o
a;
o
3
OO
-a
Q)
+j
u
-a
-------
CTi
CO
u
c
L
P
uncollapsed cloud
collapsed cloud
linear density gradient
pycnocline
I I I I I I i
10
- 1
10
10
10
100
X
03
c
o
•I—
-M
-2 £
- 3
O)
u
(U
to
O)
X
re
Hours
FIG. 14. Maximum Predicted Concentration for Long-term Dispersion Stage
-------
m
U
C
L
P
uncol lapsed cloud
collapsed cloud
linear density gradient
pycnocline
FIG. 15.
1 Hours
Predicted X Dimension of Cloud at Level of Maximum Concentration
00
-------
C = collapsed cloud
U = uncollapsed cloud
L = linear density gradient
P = pycnocline
Hours
- 6000
- 5000
- 4000
- 3000
- 2000
- 1000
X
(O
C
O
o
o
o
•M
C
CD
CD
4->
U
•r—
-o
FIG. 16. Predicted Relative Concentration Centroid Location at Level of Maximum Concentration
-------
the time of maximum surface concentration is increased to 70 hours with
a resulting reduction in the magnitude of this maximum concentration.
The collapsed cloud for the pycnocline case never reaches the surface.
The uncoilapsed pycnocline cloud does, however, reach the surface at
approximately 35 hours but with a much reduced concentration when refer-
enced to the uncoilapsed linear case.
The restrictive nature of the pycnocline essentially appears to trap
the contaminants and prevent the majority from ever reaching the surface.
The maximum concentration for the collapsed cloud in the pycnocline occurred
_1 0
at a depth of approximately 80 feet and reached a maximum of 8.9 x 10~
at 35 hours decreasing approximately 1/3 in the following 35 hours, thus
indicating that for that particular example the surface would have been
essentially free of contamination for all time barring any great changes
in the boundary or environmental conditions.
The maximum concentration centroid locations (Fig. 16) for the collapsed
clouds are found to be relatively stable moving a maximum distance of only
440 feet compared to a 5-6000 foot movement associated with the uncoilapsed
clouds. The surface concentration centroids follow the same general trend
with the centroid locations after 70 hours having moved 6 miles for the
uncollapsed clouds and closer to 4 miles for the collapsed cases. These
values are both for the case of a linear gradient and therefore represent
a different set of extremes, this is necessary because of the failure of
the collapsed thermocline case to penetrate the thermocline and reach the
surface.
Only one representative cloud dimension is examined and that is !_x
the cloud length in the direction of the flow (see Fig. 15). The trend here
follows that seen for the maximum concentration-exposure time curves with
the cloud length at t=70 hours decreased for either the inclusion of a
collapse mechanism or a pycnocline or both. If the conservation of mass
is considered, where:
L = f (M/C) M = Mass C = Concentration L = Length
71
-------
This trend can be explained where as shown in Fig. 13 (t=70 hours),
the concentration increases with both the inclusion of a collapse mechanism
or a pycnocline or both. This relationship applied to the above equation
predicts the same trend as was found for the cloud dimensions.
The cloud dimensions are directly determinate only for X, Z directions
as the analysis, in its present form, gives only the concentration distri-
bution over two non-rigid boundaries and does not include buildups asso-
ciated with the cloud reaching the bottom of the surface.
The distributions of concentration with depth at t=70 hours are shown
in Fig. 17 for all the cases considered. From this figure the wide variance
in surface concentration can readily be realized as well as the variety of
profiles that must be considered when these concentrations are being sampled
for in the field. This figure probably best typifies the problem at hand
and allows a generalization that shows collapse to flatten this vertical
distribution. It can also be concluded that the collapse mechanism represents
a phenomenon as powerful in its effect on some parameters as the inclusion
of the pycnocline over a linear gradient. It is perhaps appropriate here to
point out that while the linear uncollapsed cloud distribution appears to
overestimate the resulting concentrations it underestimates the possible
exposure times by a factor of three. This should not be overlooked as the
effects evidenced in marine plants and organisms are dependent on a combination
of the two.
A need is clear for research on the collapse mechanisms and the forces
which drive it. Emphasis should be placed on the possible entrainment and
dilution that may occur during this phase and on the effect of particle settling
and its influence on the internal density structure of the cloud.
The deviations that may occur from the neglect of cloud collapse have
been shown by this analysis to result in predictions which describe:
72
-------
—i
CO
0
20
40
60
80
100
120
£ 14°
Q.
0)
Q 160
180
200
220
240
260
280
300
UP
collapsed cloud
uncollapsed cloud
linear density gradient
pycnocline
10"
10
-7
10~6 10 10"" 10
Relative Concentration C/R\
-3
10
-2
10
-1
FIG. 17. Concentration Distribution with Depth at T = 70 hours
-------
1. Higher surface concentrations
2. Smaller contaminated surface areas
3. Shorter times to the realization of maximum surface contamination
4. Faster dilution rates for the maximum concentration
5. Larger areas over which the maximum concentration is distributed
For these reasons, the only course of action open at this time is to conduct
analyses that assume both cloud stability and collapse providing the maximum
and minimum conditions expected. These values are, of course, influenced
by the no entrainment collapse mechanism presented herein.
74
-------
SECTION VII
BARGE CHARACTERISTICS
Wastes are discharged from barges either in bulk or containerized
form. Containerized methods have been used for toxic, radioactive,
and a variety of industrial wastes as well as the more notorious surplus
poisonous war gases. Generally the most popular waste container is the
55-gallon steel drum which can be carried to the site and simply dropped
overboard. Reclaimed drums have an expected life of 10 years (90), but
this can be extended by filling with a concrete mixture containing the
contaminants. Scientists have indicated that the voids in the concrete
may result in implosion of the drum and fracture may occur at depths
between 100 and 1000 meters.
Two types of barges, towed or self-propelled, employing either
pumped or gravity discharges are usually used for bulk disposal. Until
recently the self-propelled barge had been limited to the hopper dredge,
however, the "Glen Avon," an automated sewage disposal vessel was recently
purchased by the city of Bristol, England. It has the following features
(91):
1. 900 ton load capacity
2. Maximum speed of 12 knots
3. Discharge time of 15 minutes
4. Low pressure air-gravity discharge system
These characteristics may be compared with those of the Hopper Dredge
(Table 6) which operates in the following manner. During the dredging
process the bottom material is pumped in a diluted state into hoppers
-------
TABLE 6
SPECIFICATIONS OF CORPS OF ENGINEER'S HOPPER DREDGES*
Name
Essayons . . .
Goethals ...
Biddle
Comber
Gerig
Langfit ...
Harding ...
Markham . . .
Mackenzie. . .
Hains
Hoffman . . .
Hyde
Lyman
Davison ...
Pacific ...
* Reference
Length,
beam, and
depth
Feet
525x72x40
476x68x36
352x60x30
352x60x30
352x60x30
352x60x30
308x56x30
339x62x28
268x46x22
216x40x15
216x40x15
216x40x15
216x40x15
216x40x15
180x38x14
(92)
Maximum
hopper
capacity
Cu. yd.
8,270
6,442
3.060
3,422
3,060
3,060
2,682
2,681
1,656
885
920
720
920
720
500
Maximum
draft
loaded
Ft. in.
31-0
29-0
24-33A
24-33/.
24-3'A
24-33/t
20-3
20-0
21-0
13-0
13-0
13-0
13-0
13-0
11-3
Number
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
Dredcje j>um
Size
Inches
32
30
28
28
28
28
20
23
26
20
20
20
20
20
18
ps
Horsepower
1,850
1,300
1,150
1,150
1,150
1,150
650
2650
900
410
410
410
410
410
340
-------
equipped with overflows. The hoppers can be emptied in 3-15 minutes
dependent upon the volume and nature of the material. Generally, rela-
tively fluid materials are dumped quickly whereas sticky clays and certain
granular materials may require the washing of the hoppers with large
volumes of water, a process known as monitoring.
Towed barges are by far the most numerous and are quite variable
in characteristics. They range from the simple bottom release mud scow
used in small dredging operations to specially designed, automated tank
barges for sewage and industrial sludges, toxic liquids and gases, and
pressurized liquids. Creeman, (93) in a discussion of the loading, un-
loading and transport of tank barges illustrates three basic configu-
rations (Fig. 18):
(a) single skin
(b) double skin
(c) double skin with independent containment vessel
Most petroleum products are carried in single skin barges (a) with
poisons, acids and cargos requiring heat or insulation utilizing double
skinned (b) vessels. The cylindrical tank barges (c) are generally used
to carry liquids under pressure, however, it is not uncommon for pressurized
liquids to be transported in double skinned vessels.
Barges can carry large waste loads and discharge the contents quickly.
Servizi, et al. (9), reported on a proposed dredging operation that would
use 300 cubic yard (approximately 350 tons) bottom dump barges with bottom
openings (16 by 65 feet). A self-dumping unmanned 5000 ton barge was
described (94) for dumping chemical insecticide wastes at sea at distances
not less than 125 nautical miles. All valves, pumps, and other machinery
were contained in square tanks that comprised the interior of the 298 foot
x 50 foot barge.
Eberman (95) reported on a deep-sea disposal barge with a rated capacity
of 1150 tons in rough weather, and 1300 tons in fair weather. The barge
77
-------
CARGO
SPACE
CARGO
SPACE
(A) Single Skin
- —
CARGO
SPACE
• .
CARGO
SPACE
VOID
(B) Double Skin
CARGO
SPACE
VOID
(C) Double Skin with Independent Cargo Spaces
FIG. 18. Basic Barge Configurations
78
-------
has six compartments for the cargo, two rows of three each and a loading
manifold for pumping the liquid material into any of the compartments.
A set of spring-closed check valves on the bottom of each compartment are
opened only to permit flow out of the tank when a reduction of pressure
occurs on the discharge side of the valve. A vertical turbine pump with
a capacity of 2200 gpm against a head of 33 feet discharges through an
8-inch pipe, extending 12-feet below the deck level of the barge. In
practice, 4 hours are required to pump out the barge at a pumping rate
of approximately 1000 gpm.
The National Lead Company at Sayreville, N. J., uses a barge for the
disposal of spent acids and ore washing sludge from a titanium processing
plant (96). The system consists of rubber-lined shore storage facilities
including dock and dredged harbor and two barges for the transport to the
disposal area located 38 miles from the plant dock. The two barges have
capacities of 5400 and 3200 tons. The larger barge is used regularly while
the smaller one is on a standby basis. The 5400 ton barge is 289 feet long
with a 22 foot depth and a load draft of 17 feet and 5 feet when empty. All
8 flat-bottomed waste acid tanks and two cone-bottomed mud tanks are rubber-
lined. The disposal operation takes place while the barge is underway at a
speed of 8.5 knots. The waste acid is pumped through two 12-inch discharge
pipes at the keel level past specially designed skegs approximately 50 feet
apart. A load can be discharged in 70 minutes at a rate of 78 tons per minute,
The mud is discharged by gravity from the air-agitated cone-bottomed tanks.
The smaller standby barge has two 12-inch diameter discharge pipes 43 feet
apart at keel depth, which for this barge varies from 15 feet when fully
loaded to 6 feet when empty. The rate of discharge has been reported (86, 87)
to vary from 16 to 39 tons per minute while being towed at a speed of 6 knots.
New York City barges digested sludge with an automated 6300 ton barge
capable of handling cargoes of liquids, acids, or suspended materials. The
226 feet long, 56 feet wide, and 20 feet deep barge is radio-controlled and
has an unloading time of 30 minutes.
79
-------
TABLE 7
BARGE CHARACTERISTICS*
oo
o
(Tons)
Capacity
5,400
3,200
5,000
1,200
1,100
8,000
6,300
350
*Reference
Type of Waste
Iron-acid
Ore washing mud
Iron-acid
Chem-Insecticides
Chlorinated
Hydrocarbons
Chlorinated
Hydrocarbons
Philadelphia
Digested Sludge
NYC Digested Sludge
Dredge Spoil
(34)
Average Discharge Characteristics
Depth of Pipe Number Towing Discharge
Discharge Type Size Spacing Speed Rate
Feet Inches Knots Tons/mi n.
10 Pumped 12 2 @ 50 ft. 8.5 78
10 Gravity - 2 @ 50 ft 8.5
10 Pumped 12 2 @ 43 ft 6.0 16 - 39
10 Gravity - - -
12 below
deck Pumped 81 6.0 5
8 Pumped 41 6.0 4
Gravity 24 8 267'
210
17-20 Gravity Bottom dump - 100 - 200
-------
The City of Philadelphia uses an 8000 ton barge for hauling digested
sludge with a 2700 ton unit for backup (18, 19, 20, 21). The sludge is
hauled approximately 110 miles where it is dumped in 30 minutes through
eight 24-inch bottom valves.
Table 7 summarizes towed barge characteristics from the literature
readily available on this subject.
Barging Economics
Many factors have been shown to influence the dispersion and dilution
of wastes dumped into the ocean. The physical parameters over which some
control can be exercised to minimize the effects of waste disposal on the
ocean environment are the same parameters which influence the associated
costs. These include discharge rate, water, depth, barge capacity and
distance to the disposal area.
The literature contains reports on many individual barging operations,
few of which include enough information for meaningful comparison. A paper
by Gunnerson (3) has summarized the reported costs and presents average
disposal costs on a dollar per wet ton basis. These figures are presented
in Table 8, and are representative of the following geographic areas:
Philadelphia, New York City, Elizabeth, New Jersey, Baltimore, and Washington,
D. C.
TABLE 8
REPORTED COSTS OF BARGING OPERATIONS IN $/WET TON*
Waste Total Pacific Atlantic Gulf
Industrial (a) bulk 1.70 1.00 1.80 2.30
(b) containerized 24.00 53.00 7.73 28.00
Refuse and garbage 15.00 15.00
Sewage sludge 1.00 (.8-1.2)
*Reference (3)
81
-------
To explore and present a method that analyses the towing costs for
various barge sizes, sludge quantities and towing distances the follow-
ing assumptions are made. It is assumed that:
(1) The community owns its own barges and contracts for tug services
thus removing the hidden costs of profit and overhead margins.
(2) A standby barge, similar in design to the primary barge, is
required. The capacity of this barge is set at 1000 tons.
(3) The availability of tug services is limited to 260 days per
year allowing for holidays, strikes, repairs, etc.
(4) Loading costs are included in the operating cost of the facility.
(5) There are three major cost categories, namely:
(a) Capital Costs
(b) Maintenance Costs
(c) Towing Costs
Capital Costs
The capital costs used are based on a figure of $170.00 per ton (14)
and represent the purchase of new, specially constructed barges with radio
controlled rapid discharge systems. The average discharge time will be
taken at 90 minutes.
Service life of ocean going barges varies between ten and twenty years,
For this example a barge life of ten years will be assumed for the primary
barge and 20 years for the standby barge. Annual costs will be calculated
82
-------
using an eight percent interest rate, equal replacement cost and no salvage
value or benefits from depreciation.
Maintenance Costs
Eberman (95) estimated a maintenance cost of $800.00 per trip for a
1500 ton barge making six trios per year or a total yearly cost of $4800.00.
This is approximately 12 percent of the annual capital costs of a barge, as
described for this example, using the capital cost format itemized. This
practice of calculating maintenance costs as a percentage of the annual capital
cost is used in the Portland, Oregon area by several firms (95, 97, 33). This
approach, where maintenance is independent of both frequency and duration of
use, is felt justifiable as salt water corrosion accounts for the major portion
of required maintenance and repairs, usually accomplished during one annual
dry docking. The capital and maintenance are combined to provide one fixed
yearly operating cost. Table 9 shows the distribution of these costs for
this example.
TABLE 9
CALCULATED ANNUAL FIXED COST FOR BARGING OPERATIONS
Capital Costs
Annual Fixed Cost
(Nearest $1000)
48,000
76,000
105,000
161,000
Towing Costs
The greatest amount of variability is expected to occur in the towing
costs. This cost can be influenced by discharge rate, tug speed, distance
Capacity
(tons)
1000
2000
3000
5000
Primary
25,340
50,680
76,020
126,700
Secondary
17,330
17,330
17,330
17,330
Maintenance
5.120
8,161
11,202
17,284
83
-------
traveled and the existing environmental conditions (i.e., wind, sea state,
etc.). Costs in the Oregon, Alaska and Washington areas were found to
range between $75.00/hr and $85.00/hr and on this basis an average cost
of $80.00/hr was selected as representative of the cost of a tug capable
of handling barges up to 5000 ton capacity at an average net speed of
six knots. The towing costs on a per trip basis can be calculated from
a simple relationship of the following form:
Ct = Tc {^+ t} [36]
where:
C. = total towing cost in dollars/trip
Tc = towing charge in dollars/hr
x = round trip distance traveled in miles (point to point)
v = tug speed in miles/hr
t = unloading time in hrs.
From this relationship the total costs per trip can be shown to in-
crease directly with travel time for constant discharge times.
Solving Eq. 36 for various values of (x) reveals a cost/trip mile
relationship as given in Fig. 19.
84
-------
20
18
(D
iie
Q.
±14
o
J L
50 100 150 200 250
Round Trip Distance in Miles
FIG. 19. Cost per Trip Mile as a Function of
Round Trip Haul Distance
300
Assuming a loading time of 3 hrs/ton the limiting number of possible
trips for a single barge operation can be determined for the stated tug
availability of 260 days/year. These limits are shown for this example
in Figure 20.
ton
hrs
•:on
•:on
•;on
ton
50
100
250
FIG. 20,
150 200
Round Trip Distance in Miles
Limiting Number of Trips per Year for Preset Barge Sizes
85
-------
The total annual cost (fixed and towing) can be presented by a
series of graphs where total annual cost is plotted against the number
of trips made in a year for given barge sizes, round trip haul distances,
and the total annual tonnage to be disposed of. This method of display
(Figs. 21, 22, 23) can provide a method that will aid in the evaluation
of alternatives as well as predict the barge size that will accrue the
least cost.
This example was not intended to be a black box model that would
reproduce the reported costs found in the literature but rather an
exercise to expose the controlling variables in barging costs. The
relationships and figures presented can be used to determine many factors,
for example Fig. 21 for x equal to 20 miles shows a 1000-ton barge to be
most economic size for yearly sludge loads that do not exceed 100,000 tons
with the 2000 ton barge economically feasible between 100,000 and 300,000
tons and the 3,000-ton barge becoming the cheapest to operate at 600,000
tons/year. These tonnage figures can be related to peculation of the
community if the percent solids and the percent reduction in solids of
the process are known. Using 250 mg/1 SS, 250 gpd/cap, 10 percent solids
and a 33 percent reduction by digestion it can be shown that a population
of one million will produce 365,000 tons of sludge per year. If the haul
distance were increased to 100 miles round trip, a 5000-ton barge would
be necessary to minimize the costs. The additional operating costs incurred
when the standby barge is needed are also given in Figures 21, 22, and 23.
The average cost shown in Table 8 for sewage sludges ranged between
.8 and 1.2 dollars per wet ton. If an average yearly sludge load of 100,000
tons is assumed with a round trip haul distance of 50 miles, Fig. 23 can be
used to calculate the estimated minimum yearly cost and barge size. This
results in a barge of 1610 ton capacity making 64 trips per year at a total
cost of $117,000 or $1.17/wet ton which is within the average given by
Gunnerson.
86
-------
264
00
Annual Tonnage in Thousands
Operating cost for standby barge
Trips
FIG. 21. Annual Operating Costs for Round Trip Haul Distance of 20 Miles
-------
CO
CO
288
264 '
Annual Tonnage in Thousands
Operating cost for standb^
10
Tri ps
FIG. 22. Annual Operating Costs for Round Trip Haul Distance of 50 Miles
-------
00
vo
fO
rs
c
-p
o
432
396
360
324
288
252
216
180
144
108
72
36
0
Annual Tonnage in Thousands
\ \
50UO ton \
Operating cost for standby.
i •• • i" "t i i i i i i
i i
10
100
1000
Trips
FIG. 23. Annual Operating Costs for Round Trip Haul Distance of 100 Miles
-------
The City of Philadelphia has presented the most complete set of
figures (18, 19) and will serve as a test of the validity of this proposed
analyses. The conditions are:
(1) x = 220 miles
(2) Barge size = 2700 tons
(3) Sludge load equal to 90 million gallons @ 220 gal/ton
Example Costs are as listed below:
Primary Capital Cost $68,418
Standby Capital Cost 17,330
Maintenance Cost 10,289
Total Fixed 96,037
Operating Costs $387,000
TOTAL $483,037
This reduces to $5.36/1000 gallon or $1.20 per wet ton again within
the average cost/wet ton cited by Gunnerson (3). The operating costs
for the Philadelphia operation were given as $3.73/1000 gallons-trip and
can be calculated at $4.14 by this method, however the actual average tug
speed was 6.35 knots and accounts for the majority of the $0.41 differential
shown above.
This approach satisfies the need for a method by which approximate
costs of alternative costs of action can be evaluated. The effects of
factors such as haul distances, barge sizes, sludge loads, barge speeds,
and discharge methods, determined to provide a desired dilution and penetration,
can be economically compared allowing the cheapest equivalent combination
of design factors to be used to accomplish the desired objectives.
90
-------
SECTION VIII
USER'S GUIDE
This report has established the fact that ocean dumping is a
reality and that it embodies certain risks to the integrity of the
marine environment. To this point, little has been said regarding
the practical use of this analytical technique. The information
derived provides a measure of the dilution, spread and travel or drift
of a discharged waste material under various sets of initial conditions
and assumptions. These data, if properly interpreted and applied to a
particular operation and site, may be used to determine how, when and
where a waste should be discharged to preclude violating standards
established to protect areas of high marine productivity.
The California Regional Water Quality Board, San Francisco Bay
Region, has established such standards and they became effective January 1,
1971. This regulation establishes a protected zone extending seaward
approximately thirty three miles. This action was taken to protect the
rich marine nursery which extends to the Farallon Islands, and essentially
bans harmful waste disposal in this area.
The action taken in California was at this writing the most ex-
tensive in the U. S. and may in fact be the forerunner of a more general
trend. Without examining the specific considerations given in the es-
tablishment of such a boundary, it will be assumed that any discharges
made outside this area must be accomplished in such a manner that the
protective regulations are in no way violated. Therefore, the basic
question is again the one of where, when and how such discharges should
be allowed. The approaches and methods outlined in the main text can
be used to determine the answers to such questions provided environmental
conditions descriptive of the area are known. Seasonal environmental
changes may be indicative of the when; dilution, drift and spread, the
where; and initial dilution and penetration, the how. These parameters
-------
are all interrelated and a continuous set of evaluations will have to be
made for each set of conditions used.
The data presented in this report are continuous through the three
transport phases for only one set of initial conditions for which the
following inputs were used. These are in no way descriptive of any par-
ticular operation or geographic area and are used only to explore a use
method. These conditions are:
1. Linear density gradient (Table 10)
2. An initial densimetric Froude number of 0.142 based on an initial
discharge radius (b ) of 8 feet and an initial velocity of 0.494 feet per
second.
All other conditions are identical to those for the example problem in
Appendix I.
From this informational base Fig. 9 can be used to determine the pen-
etration and the dilution that occurs during the convective descent stage.
The computer output, as shown in Appendix I, provides a final cloud radius
and position both of which may be necessary in either determining the input
for the collapse phase or in determining the total extent of the material
transport. For this example these parameters are:
Penetration depth (Yf) = 159 feet
Dilution (DILN) = 580
Final radius (bf) = 66 feet
Travel in X direction =1193 feet
Since the waste cloud reaches a state of buoyant equilibrium both
the collapse and long term diffusion-dispersion processes must be considered.
The two possible limits are exposed by considering both no collapse and
92
-------
a cloud that undergoes a complete collapse. These values are obtained for
a derived value of K~ given by Equation 11 and subsequent use of Figure 5.
_3
For this example K2~3.8xlO~ with the collapsed radius equal to 264
feet and an assumed height of 2.06 feet. The collapse time must also be
determined from Fig. 5 and used to determine the drift. For the cited K~
value the time of collapse was 9.4 minutes and for a net current of 0.2
knots gives a drift of 193 feet.
Figures 13, 14, and 15 were constructed for these particular cloud
dimensions and therefore can be used to predict the concentration and
position as functions of time. The concentrations predicted from this
phase of the analysis are relative and assume an initial concentration of
unity.
Let us assume that to meet the water quality standards it is necessary
to reduce the concentration at the end of the convective descent phase by
a factor of 1000. Figure 14 can be used to determine the time for the max-
imum concentration in the profile to be reduced by this amount. These times
are 30 hours for no collapse and 50 hours for complete collapse. Figure
15 gives the final length or diameter of the cloud at this time and only a
simple calculation is necessary to determine the drift, assuming of course
that the cloud is carried along at the same speed as the current. The total
transport can be determined by simply adding together the various components.
(uL) (cL)
Convective Descent 1193 feet 1193 feet
Collapse Drift - 0 - 193 feet
Long term
Drift (U) (t) 36,000 feet 60,000 feet
Spread 5,250 5,750
42,443 67,036
93
-------
Conversion to nautical miles gives U/L* - 7 miles and
miles. The results of this approach predict that for the input conditions
and assumptions, discharge should not be allowed within 11 miles of the
boundary. The total dilution that has actually occurred during these three
transport phases can be shown, assuming a conservative material with no
decay to be:
3p
1 = (CQ) (1/500) (10~3
_. I-.. —
ufinal =
°final =
If we use the San Francisco Bay Protected Zone as an example and apply
an additional restriction of 11 miles, some feel for the additional costs
involved can be obtained. Assume that before the regulation became effective
discharges were made at a point 19 miles off the coast with a total haul
distance of 25 miles. The annual tonnage was approximately 100,000 tons and
the operation utilized a 2000 ton primary barge with 1000 ton barge held
in standby. Fig. 22 can be used to predict an annual cost, including the
purchase, maintenance, interest and tug fees of $115,000 or $1.15/ton. The
combination of the two additional restrictions increases the haul distance
to 50 miles and by Fig. 23 predicts an increase in annual costs of $20,000
with the cost/ton increased to $1.35 representing an increase of 17.4 oercent
in cost for a 100 percent increase in haul distance.
Hopefully, this exercise demonstrates the potential of analytical ap-
proaches of this form. This is certainly only one use and only the first
step. Future research and development should refine and improve the overall
program limiting the number of assumptions that must be made and making the
results more directly applicable to the real world situations.
94
-------
SECTION IX
BIBLIOGRAPHY
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-------
13. Brooks, N. H. "Predictions of Sedimentation and Dilution of Digested
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27. Carlson, D. E., and C. S. Zichefooze. "Factors Affecting Coliform
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96
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28. Brooks, N. H., D. E. Carlson, and R. C. Y. Koh. "Function of Outfall
and Dilution in Puget Sound." "Disposal of Digested Sludge to Puget
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34. Collins, J. C., (ed.). Radioactive Wastes. Wiley & Sons. 1960.
35. Koczy, F. F. "The Distribution of Elements in the Sea." Disposal of
Radioactive Wastes. Vol 2, p 189-197. IAEA, Vienna, 1960.
36. Issacs, et al. "Disposal of Low Level Radioactive Wastes in Pacific
Coastal Waters." NAS-NRC Report No. 958. 1962.
37. U. S. Coast and Geodetic Survey. "Sea Disposal of Low Level Packaged
Radioactive Waste." C&GS Project No. 10.000-827.
38. Pneumo Dynamics Corporation. "Survey of Radioactive Waste Disposal
Sites." Technical Report ASD 4634-F prepared under Contract AT(04-3)-331
for AEC. p. 131. 1961.
39. Pneumo Dynamics Corporation. "Sea Disposal Container Test and Evalu-
ation." Technical Report under AEC contract AT(04-3)-367, p. 132. 1961.
40. Mauchline, J. "The Biological and Geographical Distribution in the
Irish Sea of Radioactive Effluent from Windscale Works, 1959-60."
United Kingdom Atomic Energy Authority, Harwell, p. 70. 1963.
41. Preston, A., and D. F. Jeffries. "The Assessment of the Principal
Public Radiation Exposure from, the Resulting Control of, Discharges
of Aqueous Radioactive Waste from the United Kingdom Atomic Energy
Authority Factory at Windscale, Cumberland." Health Physics. Vol 13,
No. 5, p. 477-85. 1967.
97
-------
42. Sabo, J. J., and P. H. Beckosian, editors. "Studies of the Fate
of Certain Radionuclides in Estuarine and Other Aquatic Environments."
PHS Publication. No. 999-R-3. 1963.
43. Purushothaman-.f-K. and E.?F. Gloyna. "Radioactivity Transport in Water;
Transport of Sr and Cs under Induced Clay Suspensions." Report
ORO-490-13, Environmental Health Engineering Research Laboratory,
University of Texas, Austin, Texas. 1968.
44. Chia-Shun Shin, and E. F. Gloyna. "Influence of Sediments on Transport
of Solutes." Journal of the Hydraulics Division, ASCE, Vol 95, HY5,
p. 1347-67. July 1969.
45. Tenny, M. W., and T. G. Cole. "The Use of Fly Ash in Conditioning
Biological Sludges for Vacuum Filtration." JVIPCF. Vol 40, No. 8
part 2. August 1968.
46. Deb, P. K., A. J. Rubin, A. W. Launder, and K. H. Manuy. "Removal
of COD from Wastewater by Fly Ash." Proc. 21st Ind. Waste Conference,
Purdue University, Ext. Service 121, 848. 1966.
47. O'Viatt, C. A. "The Effects of Incinerator Residue on Selected Marine
Species." Proceedings of the Annual North Eastern Regional Anti-Pollutior
Conference, July 22-24, University of Rhode Island. 1968.
48. Rogers, B. A. "A Progress Report on Studies to Determine the Effects
of Suspended Solids on Marine Fishes With Special Reference to the Effect
of Finely Divided Incinerator Residue on Selected Species." Department
of Industrial Hygiene, Harvard School of Public Health, p. 24, 1968.
49 Mahoney, J. R. "Feasibility for Ocean Based Solid Waste Disposal."
Harvard University, School of Public Health, Department of Environmental
Health Services, 7 pages, 1968.
50. Kinsman, B. Wind Wave. Prentice Hall, Englewood, N. J. 1965.
51. Wei gel, R. L. Oceanographical Engineering. Prentice Hall. Englewood,
N. J. 1964.
52 U S Navy Hydrographic Office. "Atlas of Surface Currents, North
Atlantic Ocean, 1947a." H. 0. Publication 571, First Edition. 1947.
53 U S Navy Hydrographic Office. "Atlas of Surface Currents, North-
eastern Pacific Ocean, 1947b." H. 0. Publication 570, First Edition.
1947.
54 U S Navy Hydrographic Office. "Atlas of Surface Currents, North-
western Pacific Ocean, 1950." H. 0. Publication 569, First Edition.
1950.
98
-------
55. Montgomery, R. B. "Fluctuations in Monthly Sea Level on Eastern
U. S. Coast as Related to Dynamics of Western North Atlantic Ocean."
J. Marine Research. Vol. 1, p. 165-185. 1938a.
56. Ippen, A. T. (ed.). "Estuary and Coastline Hydrodynamics." McGraw-
Hill Book Company, New York. pp. 558. 1966.
57. Morton, B. R., et al., "Turbulent Gravitational Convection from
Maintained and Instantaneous Sources." Proc. Royal Society Academy.
Vol 234, p. 1-23. 1956.
58. Baumgartner, D. J., R. J. Callaway, G. R. Ditsworth. "Disposal of
Aluminum Process Wastes in the Ocean." Working Paper No. 64, Pacific
Northwest Water Lab, FWQA, Corvallis, Oregon. March 1968. (Reprinted
December 1969)
59. Glover, R. E. "Dispersion of Dissolved or Suspended Materials in
Flowing Streams." Geological Survey Prof. Paper 433-B, USGPO,
Washington, D. C. 1964.
60. Glover, R. E. and C. R. Daum. "Behavior of Dissolved and Suspended
Materials in Flowing Steams." Seventh Hydr. Conf. Proc., lowas
Inst. Hydr. Research, State Univ. of Iowa. June 1958, p. 133-142.
61. Ketchum, B. H., C. S. Yentsch, and N. Corwin. "Some Studies of the
Disposal of Iron Wastes at Sea." Woods Hole Oceanographic Institution
Reference 58-7, 17 pp., unpublished manuscript, 1958.
62. Carter, H. H. and A. Okubo. "A Study of the Physical Processes of
Movement and Dispersion in the Cape Kennedy Area." File Report under
the U. S. Atomic Energy Commission Contract Report No. NYO 2973-1,
Chesapeake Bay Institute, The Johns Hopkins University. 1955.
63. Okubo, A. "A Review of Theoretical Models of Turbulent Diffusion in
the Sea." Journal Oceanpgraphic Society-Japan. 20th Anniversary
Volume, p. 286-320. 1962.
64. Okubo, A. "Some Remarks on the Importance of the Shear Effect on
Horizontal Diffusion." Journal Oceanographic Society-Japan. Vol 24,
p. 2460-69. 1968.
65. Okubo, A. and M. J. Karweit. "Diffusion from a Continuous Source
in a Uniform Shear Flow." Limnology & Oceanography. Vol 14, p. 514-
520. 1969.
66. Partheniades, E. "A Summary of the present knowledge of the Behavior
of Fine Sediments in Estuaries." MIT Hydrodynamics Lab., Tech. Note
No. 8. June 1964.
99
-------
67. Task Committee on Sedimentation, Sediment Transportation Mechanics:
Suspension of Sediment, Progress Report, ASCE Journal of Hyd. Div.
Vol. 89, No. HY5, Part 1. September 1963.
68. Schmidt, Wilhelm. "Der Mussemaustausch in freier Luft und verwandte
Erscheinungen." Probleme der Kosmischen Physick, Band 7, Haul burg,
Germany. 1925.
X
69. O'Brien, M. P. "Review of the Theory of Turbulent Flow and its
Relation to Sediment Transportation." AGU, pages 487-91. April
1933.
70. Sutherland, A. J. "Entrainment of Fine Sediment by Turbulent Flows."
Calfornia Institute of Technology, Report No. KH-R-13. June 1966.
71. Shields, A. "Anwendung der Aehnlichheist-smechauik und der
Turbulenzforschung auf die Geschiebebewegung." Mitt, der Preusss.
Versuchsanstalt fur Wasserbau und Schiffbau, Berlin. 1936.
72. White, C. M. "The Equilibrium of Grains in the Bed of a Stream."
Proc. Roy. Soc. Vol 174A, pp. 322-34. 1940.
73. Vanoni, V. N. "Trans, of Suspended Sediment by Water." Trans. ASCE.
Vol. Ill, pages 670-133. 1946.
74. Anderson, A. G. "Distribution of Suspended Sediment in a Natural
Stream." Trans. AGU. pages 678-683. 1942.
75. Kada, H. and Hanratty, T. J. "Effects of Solids on Turbulence
in a Fluid." AICHE Journal. Vol 6, No. 4. December 1960.
76. Rouse, Hunter. "Elementary Mechanics of Fluids." John Wiley & Sons,
Inc. Hew York. Pages 245 and 348. 1946.
77. Vanoni, Vito. "Some Experiments in Transport of Suspended Load."
Trans. AGU. 1941.
78. Householder, M. K. and V. W. Goldschmidt. "Turbulent Diffusion
and Turbulent Schmidt Number of Small Particles - Part I." ASCE
Nat. Meeting Preprint 692. Chattanooga, Tenn. May 1968.
79. Householder, M. K. and V. W. Goldschmidt. "Turbulent Diffusion
of Small Particles in a Two-Dimensional Free Jet." Purdue University
Technical Report No. FMTR-68-3. September 1968.
80. Singamsetti, S. R. "Diffusion of Sediment in a Submerged Jet."
J. Hydraulics Division, ASCE, Hy 2, pp. 153-168. 1966.
81. McNoun, J. S. and P. N. Lin. "Sediment Concentration and Fall
Velocity." Proc. Second Midwestern Conference on Fluid Mechanics,
Ohio State University, pp. 401-411. 1952.
100
-------
82. Ahmadi, G. and V. W. Goldschmidt. "Dynamic Simulation of the
Turbulent Diffusion of Small Particles." Appendix E, Interim
Annual Report, FWPCA Project No. 16070 DEP. November 1969.
83. Diaschishin, A. N. "Dye Dispersion Studies." Journal Sanitary
Engineering Division, ASCE, Vol 89, No. SA1. January 1963.
84. Abraham, G. and W. D. Eysink, et al. "Full Scale Experiments
on Disposal of Waste Fluids into Propeller Stream of Ships."
Reprint Rome FAO Conference. December 1970.
85. Schlichting, H. "Boundary Layer Theory." McGraw-Hill Book
Company, 6th Edition, pages 692-695. 1968.
86. Redfield, A. C. and L. A. Wai ford. "A Study of the Disposal of
Chemical Waste at Sea." NAS-NRC Pub #201. 1951.
87. Ketchum, B. H. and W. L. Ford. "Rate of Dispersion in the Wake
of a Barge at Sea." Trans. AGU.. Vol 33, No. 5, pp 680-684.
October 1952.
88. Pearson, E. A., P. N. Storrs, and R. E. Selleck. "Some Physical
Parameters and Their Significance in Marine Waste Disposal." In
Pollution and Marine Ecology, T. A. Olson and F. J. Burgess (Editors)
Interscience Publishers. New York. pp. 297-315. 1967.
89. Webster, C. A. G. "An Experimental Study of Turbulence in a
Density-Stratified Shear Flow." J. of Fluid Mechanics, Vol 19,
pp. 221-245. 1964.
90. Fulkerson, Frank B. "Transportation of Mineral Commodities on the
Inland Waterways of the South Central States." U. S. Department of
the Interior, Bureau of Mines, Infor. Circular 8431. 1969.
91. "Sewage Disposal Vessel is Highly Automated." Ocean Industry. Vol 5,
No. 2, pages 55-56. February 1970.
92. Mauriello, L. J. and L. Caccese. "Hopper Dredge Disposal Techniques
and Related Development in Design and Operation." Symposium No. 3 -
Sedimenatation in Estuaries, Harbors and Coastal Areas, Misc. Publ.
970. U.S. Department of Agriculture, Paper No. 65, pp. 598-613.
93. Creelman, W. A. "Pollution Control in the Barge Transportation of
Bulk Liquids." JWPCF. Vol 41, No. 11, Part 1, pp. 1879-1885.
November 1969.
94. Anonymous. "At Sea About Chemical Wastes." Chemical Week., pp. 133.
October 14, 1967.
101
-------
95. Eberman, J. W. Sewerage and Industrial Wastes. Vol 28, No. 11,
pp. 1365-70. November 1956.
96. Peschiera, L. and Freihers. "Disposal of Titanium Pigment Processing
Wastes." JWPCF. Vol 40, No. 1. January 1968.
97. Waller, Robert. "Deep Sea Disposal of Drummed Wastes." E. I. du Pont
de Nemouis & Company, Inc., La Porte, Texas. March 1968.
102
-------
SECTION X
APPENDIX I
This section is intended to be used as a guide for program use,
the input requirements for the convective descent stage analysis are
presented as they are to be entered on the program control card. The
program is currently in conversational mode; however card input re-
quirements will be identical:
PROGRAM CONTROL CARD:
FORMAT: 3F (5.0), 4F (10.0), 2F (5.0, IF (10.0), IF (5.0)
COLUMN DESCRIPTION
1-5 entrainment coefficient (a)
6-10 drag coefficient (CD)
11-15 added mass coefficient (C^)
16-25 initial discharge (V ) (enter
as a negative quantity in Ft/sec)
26-35 initial radius of the cloud (BQ)
36-45 initial density of the receiving
body in gms/cc (p )
d
46-55 initial density of waste sludge
or slurry in gms/cc (pw)
56_60 time increment for internal
integration (use 0.033 for printout
intervals between 5 and 20 feet)
(DT)
61-65 print out interval incremental
depths at which solution printout
is desired (Ym)
66-75 maximum water depth in feet entered
as a negative quantity (Y^)
76_80 number of steps to be entered in the
environmental orofiles (see discussion
in following section) (NC)
-------
10 Pi 20121 30131 40 141 50151 60 I 61 V0|71 80
Y p ' U ' W '
1° 11 20 21 30 31 40 41 50 51 60 61 70J71 80
Y ' p ' U ' W '
1011
2 02 1
3031 4041
W
5051 6061
70 71
DEPTH
Y
1 0|1 1 2 ob 1 3031 40
DENSITY ' VELOCITY ' VELOCITY
(p) (U) (W)
r soi
5051 6061
7071
Format 4(F10.0)
6 1011 15
CD CM
1 6
25E6
3536 4546
F
55
56 60
1 6 5 |6 I
75
W
DT YM -Yr
76 80
NC
Format [3F(5.0), 4F(10.0), 2F(5.0), IF(IO.O), 1F(5.0)]
APPENDIX I: Corrective Descent
-------
DATA CARDS
There should be one card, at least for each depth where a change in
any of the environmental parameters occurs plus one additional card
descriptive of a point one interval above the waters surface which maintains
the same gradient as the first interval below the surface. The program
assumes a linear gradient between entered points; therefore, in areas where
the changes are rapid, closely spaced points should be entered on either
side of the profile change. These cards must be ordered so that the deepest
point is read first proceeding upward to a point one increment above the
water surface. Values must be entered for all terms on each card. The
total number of cards or steps used to describe the profile must be entered
in columns 76-80 on the program control card.
Data Card Format: 4(F 10.0)
COLUMN DESCRIPTION
1-10 Depth of point.. .entered as a
negative quantity when below the
water surface
11-20 Density in gms/cc at the depth
entered in columns 1-10
21 -30 Net hori zontal veloci ty i n X
direction at depth entered in
columns 1-10
31-40 Net horizontal velocity in Z
direction at depth entered in
columns 1-10
The output from this analytical ohase itemizes the control values entered,
prints the environmental profile and presents the convective descent solutions
in tabular form. The output symbols are defined as follows:
106
-------
SYMBOL DESCRIPTION
T Descent time in seconds
Y Penetration depth in feet
X X position of the cloud center in feet
Z Z position of the cloud center in feet
B Cloud radius in feet
V Cloud velocity in ft/sec
BETA Density disparity
DILN Dilution of the cloud
The following example problem is provided as a sample of the input
and output for the Convective Descent Analyses portion.
Initial Conditions:
a = .167
CD = .250
p = 1 .075 gtns/cc
Yf = 500 feet
V = 1975 ft/sec
o
DT = 0.033
b = 4.00 ft
o
p = 1 .025 gms/cc
Y =10.0 feet
m
107
-------
Density profiles are given for the case of linear gradient (Table 10)
and a strong pycnocline (Table 11-13). The output is shown in Tables 12
and 13. A discussion of this example is given in the main portion of the
text.
TABLE 10
Linear Density Gradient [16 steps]
Y
500.0
300.0
250.0
200.0
150.0
100.0
65.0
60.0
50.0
40.0
30.0
20.0
10.0
• 5.0
0
50.0
Pa
1.029850
1.028510
1.027925
1 .027340
1.026755
1.026170
1.025749
1.025691
1.025584
1.025467
1.025350
1.025233
1.025116
1.025058
1.025000
1.024420
U
0
0
0
1 .0000
2.5400
2.8800
3.0620
3.0880
3.1400
3.1920
3.2440
3.2960
3.3480
3.3740
3.4000
3.6600
W
0
0
0
0
0
0
0
.0370
.1075
.1950
.3750
.7050
1.3150
1 .7000
1 .7000
1.7000
108
-------
TABLE 11
Strong Pycnocline [23 steps]
Y
-500.0
-300.0
-250.0
-200.0
-150.0
-100.0
- 65.0
- 60.0
- 56.0
- 55.0
- 54.0
- 53.0
- 52.0
- 51.0
- 50.0
- 49.0
- 40.0
- 30.0
- 20.0
- 10.0
- 5.0
0
50.0
pa
1.028900
1.028500
1.028400
1 .028300
1.028200
1.028100
1 .028030
1.028020
1 .028001
1.028000
1.027400
1 .026800
1 .026200
1.025600
1.025000
1 .025000
1.025000
1.025000
1 .025000
1 .025000
1.025000
1.025000
1 .025000
U
0
0
0
1 .6000
2.5400
2.8800
3.0620
3.0880
3.1088
3 . 11 40
3.1192
3.1244
3.1296
3.1348
3.1400
3.1452
3.1920
3.2440
3.2960
3.3480
3.3740
3.4000
3.6600
W
0
0
0
0
0
0
0
.0370
.0655
.0725
.0795
.0865
.0935
.1005
.1075
.1077
.1950
.3750
.7050
1.3150
1.7000
1.7000
1.7000
109
-------
TABLE 12
Linear Profile Convective Descent Output
X Z B V BETA DILN
3.3
5.2
11.1
18.3
27.1
37.4
50.1
65.2
84.0
109.1
155.4
189.7
372.0
554.4
-6.61
-10.04
-20.10
-30.07
-40.13
-50.02
-60.11
-70.13
-80.11
-90.07
-100.02
-101.84
-92.51
-95.40
4.43
8.28
22.78
41.37
64.42
91.64
124.65
163.89
212.01
275.66
390.83
474.87
915.34
1354.46
2.22
4.08
10.06
15.66
20.57
24.63
28.11
30.94
33.28
35.38
37.85
39.07
41.97
42.78
5.705
6.403
8.312
10.192
12.121
14.059
16.089
18.188
20.398
22.868
26.516
28.942
43.740
59.066
-1.931
-1.838
-1.531
-1.263
-1.047
-0.877
-0.731
-0.598
-0.469
-0.326
-0.114
.000
-0.000
.000
-0.0171812
-0.0121227
-0.0054572
-0.0028725
-0.0016150
-0.009434
-0.0005364
-0.0002732
-0.0000936
.0000332
.0001145
.0001061
-0.0000280
.0000106
2.90
4.10
8.97
16.54
27.83
43.42
65.08
94.01
132.61
186.86
291.32
378.79
1307.58
3219.89
-------
TABLE 13
Strong Pycnocline Convective Descent Output
X Z B V BETA DILN
3.3
5.2
n.i
18.2
26.7
36.7
57.5
91.9
118.1
-6.62
-10.05
-20.14
-30.04
-40.00
-50.02
-59.35
-50.19
-54.94
4.43
8.28
22.78
41.05
63.34
89.67
144.01
233.16
300.97
2.22
4.08
10.06
15.57
20.33
24.28
29.62
35,35
38.70
5.705
6.403
8.317
10.180
12.081
14.021
16.557
20.053
22.573
-1.932
-1.841
-1.539
-1.282
-1.083
-0.929
.003
-0.003
.001
-0.0172300
-0.0121896
-0.0055622
-0.0030334
-0.0018147
-0.0010084
.0013284
-0.0016155
.00105910
2.90
4.10
8.99
16.48
27.55
43.07
70.93
126.00
179.70
-------
•" 10 11 1516 20J21 30 31 35 3
DTi NTCi NPTr ' DT2 NTC2 IN
V
INPUT FORMAT 4(E
1 Oil 1 15162021 3031 35364
DYi 'NDYI — DYZ NDYJ —
INPUT FORMAT 4(ElO.
6 "» d if 1 5051
PT2 DT3 NT
5556 60 61
C3 NPT3 DT,,
7071 75J7680
NTCH WT,,
10.5, 215) 4 Points/Card
0 "f 1 50J51 55
DY3 NDY3
5, 15, 5X) 4
56 60E 1 703
— DY4
Points/Card
NDY^ —
1011 2021
Yk2 Yk3
30
3 1
5051
6061 7071
80
ToTll 20|21 30J31t(J41
4(]41 5051 6061 70
Yr GAMW Yw
71 80
FORMAT 8(E 10.5)
•^ 56
NEND I NDY
1 Oil 1 1 5J1 6 20J2 1
Y I NOT SPRINT'
FORMAT (10I5)1
APPENDIX II: Long Term Dispersion
-------
APPENDIX II
Both the input and output for the long term dispersion stage analyses
are normalized, dimension!ess, values. There are two basic input control
cards and three or more output and program control cards as shown on the
face sheet of this Appendix section.
The input controls are entered in accordance with the following format
and normalization scheme:
Format 8(E 10.5)
Column Symbol Normalization Reference Fig.
1-10 A hA/Ky(l)bo
11-20 6 h/aQ
21-30 UQ Ush2/Ky(l)bo2/3
31-40 YE Y/h 25
41-50 YE1 Y/h 25
51-60 GAMW W(max)h2/Ky(l)bo2/3YW 25
61-70 YW Y/h 25
71-80 YK Y/h 26
i
Card #2 26
1-10 YK Y/h 26
2
11-20 YK Y/h 26
21-30 YK3 Y/h 26
31-40 BETA 1 Ky(y)/KyO) 26
41-50 BETA 2 Ky(y)/Ky(D
-------
The initial conditions which must be known, all of which are defined
and described in the text, are:
a = Y dimension of cloud at end of collapse period [ft]
b = X dimension of cloud at end of collapse period [ft]
h = depth of cloud center at end of convective descent stage [ft]
U/ \= max x velocity component [ft/sec]
W = max z velocity component [ft/sec]
2
K /,» = vertical diffusion coefficient used to describe mixed layer [ft /sec]
YUy 2/3
A = dissipation parameter usually assumed as a constant [ft /sec]
The program will accept velocity and vertical diffusion coefficient
profiles only when they are normalized as shown in the following diagrams:
+1.0
0.0 -
-1.0 -
, .0
0.0
-1.0
VI
DEPTH NORMALIZATION
VELOCITV CHORD. SYSTFM
FIG. 24. Coordinate System and Depth Normalization
116
-------
1.0;
0.0
-i.a
i.o
0.0
-l.O1-
U Profile
NOTE: Both profiles must
go to zero at same
point (Y£)
W Profile
FIG. 25. Velocity Profile Normalization
117
-------
1.0
0.0
-1.0-
1.0,
Ykl52)
p(y)
K(y)
LINEAR
0.0
-1.0
P(y)
K(y)
PYCNOCLINE
FIG. 26. Vertical Diffusion Coefficient K(y) - Normalization Method
The vertical diffusion coefficient profile relates the decrease in
vertical diffusion with increasing density to the magnitude of the K^
value with depth.
A normalized depth and time grid system must be established for
program output control. The depth grid should include one interval above
and below the normalized depths of (+1.0). The grid is defined as follows
DY/.^v = size of the individual step
NYC,.% = number of steps of that size
NDY = total number of step size changes
NPRINT = number of Y grid points established between but including
(+1.0) N print = [(E
118
-------
+1 0
0
-i.o -
\7
DY3
DY2
For tht
MI DY1=
DY2 =
DY,=
DY2
DY3 N Pr
NDY
j= 8
NYC2= 6
NYC3= 6
FIG. 27. Depth Normalization
The time grid is normalized as follows:
t1 = K
y(i)t
solving this equation for t'=1.0 will allow real time choices to be selected
for output. The output will then, using the plotting subroutine, plot the
distribution of concentration with depth at the requested times.
The time grid utilizes symbols similar to those of the Y grid namely:
DT/.-j = size of individual normalized time stop
NTC/.-v = the number of steps of that size
NOT
= the number of step sizes used
NPT/-1 = the number of steps required to reach the requested output time
The summation of [(DT,. J(NTC,. J should equal 1.0.
119
-------
If output is desired at normalized times .01, .1, 15 and 1.0 the
steps could be arranged as follows:
Example 2
Step change (i)
1
2
3
NOT 4
.001
.002
.005
.010
NIC
10
45
80
50
(i)
T. Nor. time
NPT,
.01
.10
.50
1.00
10
45
80
50
The output from this program is also in normalized form and uses the
following symbols:
T = time
oo
= total concentration of material in XZ plane
I(C ) = integral of C over the depth
oo
max
a a a
xx xa
oo
= X centroid location
= Z centroid location
= Max concentration in XZ plane
= normalized Y (as given by grid)
= standard deviations of the concentration distribution
These values can be denormalized as follows-:
(1) The horizontal dimensions of the cloud L/.
where L,^ = 4bQai where i = x,z
(2) The cloud centroid locations in X,Z where:
CE
(x)
CE(z) • bZc
120
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