PRESCREENING FOR ENVIRONMENTAL
HAZARDS-A SYSTEM FOR SELECTING
AND PRIORITIZING CHEMICALS
Final Phase II Report to
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF PESTICIDES AND TOXIC
SUBSTANCES
ASSESSMENT DIVISION
WASHINGTON, D.C. 20460
EPA CONTRACT NO. 68-01-3208
ADL NO. 78486
SEPTEMBER 1980
Arthur D Little, Inc.
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PRESCREENING FOR ENVIRONMENTAL HAZARDS—
A SYSTEM FOR SELECTING AND PRIORITIZING CHEMICALS
by
George H. Harris
Arthur D. Little, Inc.
Cambridge, Massachusetts 02140
Contract No. 68-01-3208
Project Officer
Andrew L. Colb
Assessment Division
Office of Pesticides and Toxic Substances
Washington, D.C. 20460
OFFICE OF TOXIC SUBSTANCES
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
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DISCLAIMER
This document has been reviewed and approved for publication by the Office of
Toxic Substances, Office of Pesticides and Toxic Substances, U.S. Environmental
Protection Agency. Approval does not signify that the contents necessarily
reflect the views and policies of the Environmental Protection Agency, nor does
the mention of trade names or commercial products constitute endorsement or
recommendation for use.
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CONTENTS
Page
List of Figures v
List of Tables v
Acknowledgment vi
I. SUMMARY i
II. INTRODUCTION 3
A. Purpose and Scope 3
B. Background 3
C. The Data Problem 7
D. Project Design 9
1. Phase I 9
2. Phase II 10
E. Status of System n
F. Organization of This Report 12
III. OVERVIEW OF THE PRESCREENING SYSTEM 14
A. System Design Criteria 14
B. Practicability 17
C. Basic Parallel System Structure 18
D. Environmental Levels 18
E. Levels of Concern and Ranking 22
IV. ESTIMATION OF ENVIRONMENTAL LEVELS 24
A. Environmental Compartment Model 24
B. Compartments 30
C. Limitations of the Model 32
D. Extensions of the Model 36
1. Spatial Limitation 36
2. First Case 37
3. Second Case 37
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Page
V. USING THE MODEL 39
A. Computer Program 39
B. Basic Steps To Use the System 39
C. Review The Model 40
D. Data Requirements For Using Model 41
1. Physico-chemical Properties of Chemical 41
2. Initial Concentrations of Chemical 42
3. Chemical Emission Rates 42
4. Compartment Data 42
E. Completing the Data Sheets 43
1. Types of Data Sheets 43
2. First Data Sheet 43
3. Second Data Sheet 48
4. Third Data Sheet 50
F. Accessing the System 50
G. Executing the Model 52
1. Input Process 52
2. Input in the APL Environment 54
H. Sample Session Involving All Three Types of Emission Rates 55
Run 1 - Example of Type 1 Emission Rate Including
Printing of Compartment Data and Intermediate 61
Results
Run 2 - Example of Type 2 Emission Rate 70
Run 3 - Example of Type 3 Emission Rate 75
Comments 79
REFERENCES 81
APPENDIX 1 - MATHEMATICAL ANALYSIS 82
APPENDIX 2 - CONVECTIVE MASS TRANSFER 103
APPENDIX 3 - ESTIMATION OF DIFFUSION COEFFICIENTS 111
APPENDIX 4 - ESTIMATION OF EMISSION RATES 115
APPENDIX 5 - PROGRAM DESCRIPTION 117
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LIST OF FIGURES
Number Page
III-l SCHEMATIC DIAGRAM OF THE SYSTEM 19
III-2 SCHEMATIC DIAGRAM OF THE FIRST BRANCH
20
OF THE SYSTEM
III-3 SCHEMATIC DIAGRAM OF THE SECOND BRANCH
OF THE SYSTEM 23
IV-1 SCHEMATIC DIAGRAM OF INTERCOMPARTMENT 25
FLOWS OF EMITTED CHEMICAL
V-l DATA SHEETS: PHYSICO-CHEMICAL DATA 44
CHEMICAL INITIAL CONCENTRATIONS 45
COMPARTMENT DATA 46
LIST OF TABLES
Number Page
IV-1 U.S. COMPARTMENT DATA 31
IV-2 BULK WATER FLOWS BETWEEN COMPARTMENTS 33
IV-3 CHEMICAL REACTIONS AND FLOWS BETWEEN COMPARTMENTS 34
V-l CONCENTRATION CONVERSION FACTORS TO YIELD UNITS OF
49
KG OF CHEMICAL/KG OF MEDIUM
V-2 COMPARTMENT DATA (DEFAULT VALUES) 51
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ACKNOWLEDGMENT
The basic steady-state environmental model development work (Phase I)
summarized here was performed by E. Venezian, with assistance from J.
Berkowitz, R. Home, and E. Payne.
The extension of the basic model to the time-de pendent case and its
computer implementation in Phase II was directed by G. Harris, with
significant contributions from L. Lapide and C. Richmond. Substantial
assistance in report preparation was provided by P. Smith and J. Mayer.
The valuable assistance of Office of Pesticides and Toxic Substances
project staff — Frank Kover, Anne Barton, Amy Rispin, and Andrew Colb—
over the course of this work is gratefully acknowledged.
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I. SUMMARY
The overall objective of this program is the development for the
Environmental Protection Agency of a system for ranking chemicals emitted
into the environment in order of their hazard potential. Although the
major focus is on preliminary screening of chemicals prior to full commer-
cial production, the recommended scheme could also be used for evaluating
the potential hazard of chemicals already in production.
The work reported here was conducted in two closely coordinated
but distinct phases. The Phase I program summarized here has been
previously documented in a final report to USEPA. Phase II
extends the conceptual system design conducted in Phase I to produce
an operational interactive computer system for estimating the distribu-
tion of a chemical in the environment.
Phase I
A number of alternatives have been explored for ranking chemicals
so that subsequent experimental research efforts may be properly focused.
The recommended method has the potential of fulfilling identified needs.
Basically, the method consists of selecting chemicals for further atten-
tion by comparing the concentration of each chemical that may be expected
in the environment to the concentration levels of that chemical which are
of concern.
The method for estimating future environmental levels is based
on a multi-compartment model of the environment. In order to provide
estimates with moderate effort, the model is substantially simplified.
The emphasis has been on ensuring that the model does not underestimate
future levels, and that overestimation is kept within reasonable bounds.
A test using available information on tolerable air concentrations indi-
cates that the estimated levels would be adequate for preliminary
screening.
The method also provides the capability of ranking the selected
chemicals into more refined priorities by estimating the time horizon
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r
during which regulatory action would prevent significant deleterious
effects.
Phase II
The basic steady-state model formulation accomplished in Phase I
has been extended so that concentrations at any future time can be
estimated, given current levels and knowledge of future chemical emis-
sions. The model has been implemented as an interactive program on a
commercial time-sharing service and complete user documentation, includ-
ing sample cases, has been prepared.
It is recommended that the system, though operational, should
first be used by the Office of Pesticides and Toxic Substances on a
trial basis before actually trying to rank chemicals on a routine basis.
Additional research is needed on the development of improved
methods of predicting levels of concern from available information on
chemical composition. The performance of the system with a number of
test chemicals also needs further investigation.
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II. INTRODUCTION
A . Purpose and Scope
The overall goal of this project is to provide the Environmental
Protection Agency (EPA) with an objective system(s) for selecting and
ranking chemicals, chemical classes and use classes for prescreening
as to their environmental hazard. The study is to include an analysis
and evaluation of existing systems, an evaluation and testing of the
proposed system(s), and the implementation of the proposed system within
the Office of Toxic Substances. The system may consist of a procedure,
scheme, or mathematical model.
The Environmental Protection Agency is concerned with chemicals •
in the environment which have adverse effects upon man and his living
and non-living surroundings. It is the goal of the EPA to be able to
predict and identify potential chemical hazards before these chemicals
become widely dispersed and uncontrollable (typical examples of such
chemicals are mercury and polychlorinated biphenyls). However, before
attempting to initiate a testing procedure for the evaluation of hazard,
it is first necessary to identify and select on the basis of minimal
information those chemicals, chemical classes and use classes that are
most likely to pose a hazard. It is the goal of this project to develop,
implement and install an efficient system(s) to accomplish the afore-
mentioned identification and ranking process.
B . Background
The hazards posed to the total environment by certain substances
is now widely appreciated. These substances affect the environment,
threaten the integrity of ecological niches, or endanger man by a variety
of modes of action ranging from direct effects, through effects of their
decomposition products, bioaccumulation in prey-predator chains, syner-
gism, and interaction products.
It is generally recognized that the potential for damage could
often be anticipated if there were adequate data on the toxicity of the
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substances involved in a variety of relevant species. Yet, the collec-
tion of an adequate data base on chronic toxicity would entail substan-
tial expenditures and extended periods of time.
In an economy that relies heavily on new materials to improve the
quality of life, decrease the cost of goods and thereby improve their
distribution to people of all income levels, the potential delays and
costs associated with thorough testing prior to production is viewed
with substantial concern. This concern is quite justified when we ack-
nowledge that the eventual distribution of substances in the environment
is not easy to predict; indeed, decades may pass before we are able to
estimate such distributions with sufficient accuracy so as to relate
these levels to the toxicological information. A further cause for
concern is that in some compartments of the environment the concentra-
tions may continue to increase well beyond the time at which release of
the substance has been discontinued.
In spite of and because of these difficulties, it is essential
that some methodology be developed that will allow an orderly review
of environmental contaminants and lead to the selection of some subset
of these as being of sufficient concern as to warrant the development of
an adequate toxicological data base or, in extreme cases, a reduction in
the level of emissions into the environment.
The Toxic Substances Control Act requires the testing of chemical
substances and mixtures which "may present an unreasonable risk of
injury to health or the environment." Test data might be required, for
example, to establish potential risks of acute toxicity, subacute
toxicity, chronic toxicity, persistence, carcinogenicity, mutagenicity,
teratogenicity, behavioral disorders, etc. The Act recognizes the need
for prioritizing chemicals for testing, and provides for the establish-
ment of a list of chemicals, not to exceed 50 at any time, for which
test data are most urgently required.
Prioritization is of key importance to protecting health and the
environment, without imposing both major economic burden on the chemical
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industry and a major administrative review burden on the EPA. The National
Institute for Occupational Safety and Health "Registry of Toxic Effects
of Chemical Substances" (formerly called "The Toxic Substances List")
1978 Edition, for example, includes nearly 34,000 different chemicals,
and the numbers expected to be included in subsequent editions is cur-
rently estimated at about 100,000 unique toxic substances. Development
of a full battery of health and environmental effects test data for all
of them is clearly impractical within a realistic time frame. The al-
ternative described in this report is aimed at the development of an
objective prioritization methodology capable of (1) classifying chemical
substances with respect to the probable risk they present to human health
and/or the environment; and (2) identifying the kinds of test data that
would assist in determining whether or not the probable risks are
"unreasonable."
To be effective in reducing the amount of data which must be
developed, while at the same time directing data development efforts to
the most crucial problem areas, such a methodology should have the
following characteristics:
(1) The screen should "pass" a significant fraction of
chemical substances, on the grounds that they have
such a low probability of presenting unreasonable
risks under current and projected conditions of use,
that additional data development does not appear to
be worthwhile. (This assumes of course that a large
number of chemical substances can defensibly be cate-
gorized in this way.)
(2) Ideally the screen should also provide some indication
of the nature of the probable risk for substances that
do not "pass" (i.e., indicate whether the risk is to
air, water, and/or ground pollution, and whether it
is carcinogenic, teratogenic, mutagenic, chronically
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toxic, etc., to humans; phytotoxic; persistent; bioac-
cumulative; synergistic, etc.).
(3) The data and resource (e.g., personnel) requirements
must be consistent with the level of confidence desired
for the screen. A highly accurate screen may be expected
to generate very significant input demands.
The list of substances which "pass" the screen would include
substances such as those on the FDA's GRAS list and substances which,
though potentially damaging at some concentrations, are not likely to
reach concentrations which pose unreasonable risks to health or environ-
ment. They would be substances, which on the basis of current knowledge
and perceptions, appear to be sufficiently safe to require no further
testing at the moment. As new knowledge develops and perceptions change,
the list would have to be reexamined and reevaluated.
To say that a chemical substance is not hazardous to human health
and/or the environment is to imply that the substance does not induce
a whole variety of potentially adverse effects traditionally associated
with chemicals. To say that a chemical substance hazardous is to
imply that the substance exhibits at least one adverse human health or
environmental effect. If only one such effect is suspected, then that
is the effect for which data development should be prescribed. Even if
there is a high probability that a chemical substance may produce several
adverse effects, it may not be necessary to document all of them. If,
for example, a substance is a suspected human carcinogen and also may
lead to fires in landfills, data development could probably most use-
fully be focused on the question of carcinogenicity.
A reasonable and defensible chemical screening system is not a
substitute for experimental and environmental monitoring data. A
screening system is nothing more than a systematic mechanism for review-
ing available data, and for prioritizing future data needs, so that
resources (which are always limited) may be directed as early as possible
into the most crucial problem areas. This report is concerned with the
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development of an objective screen based on the amounts of chemical
substances released into the environment and the kinds of problems
associated with the projected levels of such substances in the environ-
ment. Prioritization of the problems identified with respect to their
need for attention and with respect to the kinds of data that should
be sought is a subjective matter which is well beyond the scope of the
present effort.
C. The Data Problem
The primary rationale for an early warning or prescreening
system for environmental hazard identification and prioritization stems
from the desirability of reducing the requirements for extensive experi-
mental data development. A complete experimental evaluation of the
potential environmental impact of a chemical substance would involve
toxicological, pharmacological, and metabolic studies in a number of
species (e.g., mice, rats, dogs, rabbits, domestic animals, fish,
wildlife, lower aquatic organisms, plants); transport mechanism and
persistence studies in air, water, and various soil types; potentiation
studies; bioaccumulation studies; degradation studies and evaluation of
the hazardous effects of degradation products. Not only would such an
experimental program be time consuming and expensive, but so much data
would be developed that it would be difficult to sort out what the real
problems are. Technical resources would be more effectively utilized
in developing data in particular areas for specific chemical substances
where there is good reason to believe that serious health or environ-
mental effects may be found. Choosing productive areas to work on is
not an easy task for anyone. Nonetheless, it is not possible to do
everything, and the choice is made, with greater or lesser degrees of
success, by individuals, corporations, and agencies. An early warning
system should be an effective tool for helping to guide data develop-
ment efforts towards major problems.
The more data that must be developed experimentally as input to an
early warning system, the less useful it can be as a planning tool for
focusing future technical effort, i.e., the more effort required to
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develop routine input data, the less effort available to investigate
specifically identified potential problem areas.
For chemicals that are either produced commercially or under
consideration for commercial production, the manufacturer can usually
supply a data sheet which includes:
• Common and/or trade name;
• Chemical class and/or structural formula;
• Physical properties (e.g., melting point, boiling point,
vapor pressure, solubility, etc.);
« Chemical properties (e.g., reactions with air and moisture,
if any, and other relevant reactions); and
• Suggested applications.
A large chemical company has reported that they would normally
make some additional measurements during the course of development of
a new product specifically to provide some preliminary indications of
potential environmental impacts. One parameter that might be experi-
mentally determined is the octanol/water partition coefficient, which
appears to be correlated with bioconcentration in the environment.
Another is five-day biological oxygen demand (BOD^), which provides some
indication of the possibility of microbial decay in aquatic or soil en-
vironments. In addition, some initial toxicological tests would be
carried out. These might include, for example, a determination of
acute oral, inhalation, dermal, and/or ocular toxicity to rats or mice.
Most chemically-induced health and environmental effects (with the
possible exception of cancer) are concentration dependent. Even a rough
assessment of possible environmental hazard, therefore, requires some
knowledge of the concentration levels to which potentially affected popu-
lations might be exposed. The primary data likely to be available that
Papers of a Seminar on Early Warning Systems for Toxic Substances
(EPA-560/1-75-003), Environmental Protection Agency, Office of Toxic
Substances, Washington, D.C., July 1975, p. 167.
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might be related to environmental concentrations are planned production
and major uses. Manufacturers usually have such data, but would
generally be reluctant to release it unless required by law to do so.
On the basis of a structural formula, a few easily obtainable
physical and chemical properties, a five-day BOD, an indication of acute
toxicity, and some estimate of production and use, it is not possible to
predict with certainty the human or environmental hazards of a chemical
or chemical class. If only the minimal data base is available, then,
the real question is whether a system can be developed which will iden-
tify potentially hazardous chemicals, chemical classes or use classes
with sufficient accuracy to justify its implementation.
D. Project Design
1. Phase I
The project has been conducted in two distinct phases:
\
• Phase I — System conceptualization, analysis, and
design
• Phase II — System development, testing, and
implementation
Phase I was completed in April 1977 and documented in the report "Pre-
screening for Environmental Hazards—A System for Selecting and
Prioritizing Chemicals." EPA Office of Toxic Substances, EPA-560/1-77-
*
002. That report documents the conceptual development of the proposed
prescreening system. Phase I encompassed the following seven tasks:
• Task 1 - System Design Criteria - Criteria were developed
to guide the design and development of an environmental
hazard identification system that would meet the needs of
the Office of Toxic Substances.
• Task 2 - Analysis of Information Needs - Minimum input
parameters were defined that should enable a system to
select and rank chemicals potentially hazardous to the
environment.
•k
as^B^f o£?m National Technical Information Service, Springfield, VA 22161
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• Task 3 - Formulation of System Concepts - A number of
potential system concepts were formulated to serve as
informal models against which to evaluate selected
systems.
• Task 4 - Evaluation of Existing Identification Systems -
Prior work had shown that none of the many existing systems
were readily adaptable to meeting the specific needs of the
ft
Office of Toxic Substances. Several of the more promising
approaches, however, were evaluated against the design
criteria, information requirements, and system concepts
developed in Tasks 1-3 in order to define their shortcomings
more precisely.
• Task 5 - Resolution of Information Gaps - The problem of data
availability, not just for specific chemicals, but in whole
areas of health and environmental concern, was consciously
and seriously considered, but not entirely resolved.
• Task 6 - Proposed System - A basic system with a number of
variations of increasing complexity, has been developed for
selecting and prioritizing environmental hazards.
• Task 7 - System Test Methodology - A methodology was presented
for testing the applicability and reliability of the basic
system, and for evaluating the potential benefits of the more
complex variations.
2. Phase II
Phase II encompassed the following five tasks:
• Task 8 - Model Refinement and Extension - The principal effort
undertaken was to extend the multiple compartment environmental
model so that levels of pollution could be estimated at any
Literature Search and State-of-the-Art Study of Identification Systems
for Selecting Chemicals or Chemical Classes as Candidates for Evaluation
(EPA-560/1-74-001), Environmental Protection Agency, Office of Toxic
Substances, Washington, D.C., November 1974.
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future time (given current levels), whereas the Phase 1 model
was limited to eventual (steady-state) concentrations under the
assumption that "eventual" pollutant emission rates would be
known.
• Task 9 - System Specification - An interactive (conversational) com-
puter program specification was developed which defined the system's
operational features, capabilities, inputs, and outputs.
• Task 10 - System Development - The multiple compartment environ-
mental model was completely reprogrammed in the APL computer
language.
• Task 11 - System Implementation - The model was implemented as
an interactive program on a time-shared computer system. How-
ever, very considerable difficulty was experienced in locating
adequately supported computer facilities. The program was
transferred from National Institutes of Health facilities in
Bethesda, Maryland, to EPA's National Computer Center at Research
Triangle Park, North Carolina, and finally to a commercial time-
sharing service (Scientific Time Sharing Corporation of Bethesda,
Maryland) which has in the past provided similar services directly
to EPA offices.
• Task 12 - System User Documentation - Documentation was prepared
to enable EPA personnel to properly use the system.
E. Status of System
The multiple-compartment environmental model described in this re-
port is currently accessible via a commercial time-sharing service. The
model yields temporal estimates of chemical concentrations by compartment,
given the necessary physical/chemical properties of the chemical and ini-
tial concentration values. Knowledge of computer programming is not
necessary to use the model. Access to the model may be gained by contact-
ing the U.S. Environmental Protection Agency, Office of Pesticides and
Toxic Substances, Assessment Division (TS-792), Washington, D.C.
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The current implementation of the model is structured to process
one chemical at a time—essentially it is intended to operate as a
research tool. The system is not now designed to process multiple
chemicals in a production mode as might be necessary in ranking a set
of chemicals, although this feature may be easily added later if
desirable. The computer system interacts with the user by requesting
requisite input data (in specified physical units) and providing the
user with various input, analytical, and reporting options.
F. Organization of this Report
Chapter III reviews the system design criteria developed in Phase
I and acknowledges that paramount importance was placed upon devising a
practicable system that would not generate onerous demands for input
data. The twin concepts concerning
• Levels of concern versus
• Environmental levels
also developed in Phase I, are briefly summarized.
Chapter IV extends the steady-state compartmental model to the
more realistic time-dependent case. The exact solution to the governing
vector differential equation is presented. The chemical transport re-
lationships among the 19 defined environmental compartments (media)
are described. Next the inherent limitations of the model are summarized
and suggestions given for extending the model to overcome its principal
limitation, that of spatial invariance.
Chapter V describes how to use the interactive computer system
that has been programmed for evaluating the environmental model. First
the basic structure and data requirements of the model are summarized,
including the principal assumptions and limitations inherent in its
derivation. Next the prospective user is guided through all operational
steps, from completing input data sheets, to executing the model, to
interpreting output. Three sample problems are provided, along with
actual system output, to help orient the user to the interactive nature
of the system.
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Appendix 1 contains the mathematical details for solving the general
multiple compartment model of the environment. Two distinct analytical ap-
proaches are taken and then these are resolved. The mathematical basis
for calculating via computer the matrix solution to the underlying differen-
tial equations is also presented.
Appendix 2 develops expressions for determining the rate of convec-
tive mass transfer of the chemical between phases. The presentation here
is much more thorough than in the Phase I report. Several of the mass
transfer expressions in the Phase I report are revised.
Appendix 3 presents methods for estimating the diffusivities of
the pollutant in air and of the chemical in water. These properties
are required in the model. The estimation methods in Appendix 3 are
improved over those given in Appendix III of the Phase I report and some-
what easier to use.
Appendix h provides a brief discussion on estimation of emission
rates.
Appendix 5 describes the computer program and provides a listing
of the APL code.
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III. OVERVIEW OF THE PRESCREENING SYSTEM
A. System Design Criteria
In Phase I the following criteria were developed to guide the
design of a workable environmental hazard identification and prioritiza-
tion system; the criteria are presented roughly in descending order of
importance.
(1) Practicability. Recognizing that the intent of the system is
to select and rank chemicals, chemical classes and use classes for pre-
screening as to their environmental hazard, an unreasonably difficult
and resource-demanding process is not warranted. Prescreening, by im-
plication, has quite limited goals in terms of expected accuracy and
precision. As stated earlier, a reasonable and defensible chemical
prescreening system is not a substitute for experimental and environ-
mental monitoring data. The system, then, should recognize practical
limitations in terms of EPA personnel skill levels and numbers, opera-
tional cost, and response time. This issue is further discussed in the
next section.
(2) Data Requirements. The system should be capable of selecting
and prioritizing potential chemical environmental hazards on the basis
of data normally provided by the manufacturer. More to the point, the
system should make minimal demands for data. In general, this criterion
is antithetical to the achievement of scientific credibility. For example,
if the viscosity of a material is a necessary property but is not likely
to be furnished by a manufacturer, then we may decide to circumvent the
need for an experimental measurement of viscosity by using some empirical
correlation.
(3) Objectivity. Policy decisions with respect to potentially
toxic substances in the environment must of necessity be subjective.
The subjective decisions, however, are generally required to be reason-
able and defensible in the legal sense. This usually means that they
must stem from an even-handed interpretation of objective facts. The
desired identification system should be objective, in terms of input
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requirements and procedures or rules to be followed in selecting and
ranking chemicals. Use of the output results in decision making is
subjective and need not, in fact cannot, be addressed by the objective
system sought. The necessity of objectivity implies that the system
should accept only a modicum of external judgment or personal interpre-
tation. To the extent that it may be desirable or necessary to distin-
guish hazards to target populations, OTS has established the following
order of importance (descending): (a) man, (b) economically signifi-
cant animals and plants, (c) ecologically important species, and (d)
presumably, then, the inanimate environment.
(4) Credibility. The system should possess demonstrable
credibility in selecting and prioritizing chemical environmental hazards.
The results should be statistically credible, i.e., at most a relatively
small percentage of the substances ranked as non-hazardous should turn
out to give rise to major health or environmental problems; and at most
a relatively small percentage of the chemicals ranked as highly hazard-
ous should in fact prove to be benign.
(5) Consistency. The identification system(s) should be capable
of producing identical results (at any given point in time) when operated
by different people. This is not a trivial problem due to the plethora
of information sources and the likelihood that some judgment may be re-
quired even in the most objective system.
(6) Tested Concepts. The system should utilize only proven tech-
niques, methodologies, information sources, etc., and not attempt to
incorporate hertofore untested or incompletely developed approaches.
For example, a new and unknown theory relating chemical structure to
biological activity should be incorporated into the system only as a last
resort because its merit would not be known beforehand. The same
consideration would hold, for example, in deciding whether to include
a new information center under development and not yet operational.
(7) Specificity. The system should classify chemicals, chemical
classes, or use classes into their probable major hazard categories, e.g.,
carcinogenicity, mutagenicity, teratogenicity, oral toxicity, dermal
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toxicity, inhalation toxicity, aquatic toxicity, bioaccumulation, etc.
It may also be desirable to rank chemicals according to the perceived
risk presented to different target populations, i.e., man, animals,
plants, and the inanimate environment.
(8) Discrimination. The system must possess the ability to
roughly scale chemicals according to their associated risks of environ-
mental hazard. A process of discrimination is needed to distinguish
among different potential hazard levels and thereby achieve a prioriti-
zation. In general, it may be expected that the simpler systems will
yield coarser gradations.
(9) Knowledge Gaps. The system should identify the existence
of information gaps which, if filled, would permit improved predictions.
(10) Statistical Confidence. If possible, hazard predictions
should be accompanied by statements of statistical confidence, however
approximate these might be. The measure of statistical confidence can
be viewed as an indicator of the need for additional information. A
hazard evaluation accompanied by a low confidence level indicates that
more data may be required to yield a stronger statement.
(11) Built-in Hierarchy. In recognition of the many potential
information sources and voluminous data (not all of which are necessarily
pertinent), it would be desirable to develop a hierarchical system which
would produce results of increasing specificity and credibility the
further the process was followed. That is, an early indication of
probable chemical toxicity (but one with limited credibility) might be
achieved by following the recommended process to a predetermined point.
Succeeding stages of evaluation requiring more information and analysis
would lead to improved predictions of hazard classes and levels.
(12) Expansion/Extension. The system should be devised so that it
may evolve without undue hardship as new information sources and techniques
become available in the future.
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(13) Degradation Products. Chemically induced health and
environmental effects may be due not only to manufactured chemical
substances, but also, and sometimes entirely, to degradation products.
Where such products and their properties are known, the system should
be capable of handling them in a normal way. When the routes of de-
gradation of a chemical substance are unknown or very complicated, it
is unlikely that any simple identification and prioritization system
will be able to flag the potential hazards accurately.
(14) Synergism. The goal of the project is to design an objec-
tive system for selecting and ranking chemicals, chemical classes or
use classes, based on their environmental hazards. It is implied that
any selection or ranking algorithms that may be developed will be
applied to individual chemical substances or chemically related groups
of substances. Environmental hazards, however, may result from or be
amplified by synergistic interactions between or among unrelated chemi-
cal substances. There is very little data on the importance of syner-
gism in the environment, and even if there were more, it would not be
easy to incorporate synergistic effects into an objective system design.
From the subjective regulatory viewpoint, the problem of synergism would
be even more difficult to deal with.
It has not been possible to satisfy all these criteria equally.
Greater success has been realized with respect to the first five
criteria than for the remainder.
B. Practicability
As noted above, paramount importance was assigned to designing
a practical and readily-operable system. For several reasons, this basic
requirement was restated as a need for inherent simplicity. One is that
the current state of knowledge about factors that produce environmental
hazards is so primitive as to preclude any but the simplest of identifi-
cation systems. Another is that to a simple or even simplistic system,
refinement and embellishments may be added as needed. Every additional
17
-------
refinement, however, will usually entail greater efforts at data collec-
tion, information processing, and finally interpretation of results. It
is clear that any contemplated system must not entail greater effort at
selection and ranking than would be involved in the experimental pre-
screening tests themselves. For example, it might be of interest to de-
velop for each selected chemical to be prioritized a comprehensive
statement of the conditions of exposure pertaining to the principal plant,
animal, and inanimate populations at risk. The enormity of this under-
taking alone would seem to overwhelm the basic objective of developing
a tool for selecting and prescreening candidates.
C . Basic Parallel System Structure
The system consists of two parallel branches, the results of which
are eventually merged and used for ranking, as shown in Figure III-.l. The
general concept is to estimate, on the one hand, the levels of a chemical
that will be encountered in the environment, and on the other, the
levels which can be tolerated in the environment. A comparison of these
two sets of numbers then leads to a preliminary ranking of the potential
pollutants in priority order.
D. Environmental Levels
The first branch of the system is shown in Figure III-2. It has as
its purpose the computation of the levels of a chemical that will be
attained in the environment at any time in the future, given current
levels. We do not expect that the computed levels will correspond
closely to what would be found in the environment after decades or
centuries, but we feel that estimation to within one or two orders of
magnitude will go a long way toward meeting the objectives of prescreen-
ing. Closer estimation would require detailed information on the modes
of emission of each product and on the distribution (geographical and
temporal) of these emissions, and it is unlikely that these would be
known within orders of magnitude when a product is in the early stages
of commercialization.
18
-------
FIGURE 111-1
SCHEMATIC DIAGRAM OF THE SYSTEM
Branch 1
ESTIMATION OF
FUTURE
Environmental
Levels by
Compartment
based on data on:
RELEASE
PERSISTENCE
PHYSICAL PROPERTIES
AND COMPARTMENT DATA
Branch 2
ESTIMATION OF
Levels of
Concern by
Compartment
BASED ON DATA ON:
CHEMICAL COMPOSITION
STRUCTURE
PHYSICAL PROPERTIES
RANKINGS
19
-------
FIGURE 111-2
SCHEMATIC DIAGRAM OF THE FIRST BRANCH OF THE SYSTEM
PERSISTENCE
DATA
COMPARTMENT
DATA
ESTIMATED
RELEASES
SECONDARY
EMISSION
DATA
PHYSICO-
CHEMICAL
PROPERTIES
PRODUCTION AND
USE DATA
COMPOSITION
AND
STRUCTURE
DATA
FUTURE
ENVIRONMENTAL
LEVELS BY
COMPARTMENT
20
-------
This branch of the system will include several types of data
inputs:
• quantification over the time period of interest of the
total industrial rate of production and allocation of
this production to modes of use for various ranges of
emission;
• quantification of the emission of the product from
non-industrial sources (e.g., natural production by
plants, production as a result of chemical reactions
of other materials in the environment, unintended or
by-product emissions);
• quantification of the gross geographic distribution
of the emissions;
• estimation of the half-life for degradation of the
product into final products in water and air; and
• quantification of basic physico-chemical constants,
such as solubility in water, partition coefficient
between fat and water, vapor pressure, etc.
Based on these data and fixed data on regional water flows,
the system will compute the chemical levels in various environmental
compartments (e.g., air, surface water, soil, etc.) over time.
Further details regarding the multiple compartment model of the
environment will be found in the next chapter.
21
-------
E. Levels of Concern and Ranking
The second branch of the system is shown in Figure III-3. It has the
aim of estimating the levels of the chemical which are of concern.
Again, we do not expect that the computed levels will correspond closely
with toxicity data on any specific compound. We feel that, given the
current state of the art, estimation of levels of concern which are
within two or three orders of magnitude of those dictated by toxicolo-
gical data would be adequate. Moreover, we believe that this kind of
accuracy can be achieved with relatively simple methods.
At the simple level which we propose, the input into this part of
the system consists of information on the presence or absence of a number
of functional groups in the compound in question. Further details concerning
the second branch of the prescreening system wili be found in Chapter IV
of the Phase I report.
Ranking of chemicals would then proceed according to the methodology
described in Chapter V of the Phase I report. Five example test cases
appear in Chapter VI of that report.
22
-------
FIGURE 111-3
SCHEMATIC DIAGRAM OF THE SECOND BRANCH OF THE SYSTEM
LEVELS OF CONCERN
BY COMPARTMENT
COMPOSITION
OF
CHEMICAL
DATA ON
COMPOSITION-TOXICITY
RELATIONSHIPS
PHYSI COCHEMICAL
PROPERTIES
OF
CHEMICAL
23
-------
IV. ESTIMATION OF ENVIRONMENTAL LEVELS
A. Environmental Compartment Model
The Phase I report (Chapter III) documented the theoretical under-
pinnings of the proposed multiple compartment model of the environment.
Only the highlights of that work will be presented here, along with
clarification of certain aspects that were not entirely apparent in the
original model description. However, the interested reader is strongly
encouraged to also consult the Phase I report for further background
information.
Estimation of the levels of a chemical that will be encountered
in the environment can be conducted in a number of ways. Ideally, the
whole chain from release of the substance through dissolution, evapora-
tion, sorption, transport, and degradation would be considered in detail,
but this would require voluminous data on physicochemical characteristics
of each compound to be considered and extensive computations. At the
other extreme, very simple projections or guesses could be provided, but
these would fail to meet a basic requirement of objectivity.
A simple multiple compartment model of the environment is proposed,
as shown schematically in Figure IV-1. The distribution of a chemical
among the compartments of the environment is determined by the inter-
compartmental flows and compartment concentrations of the chemical.
The ocean is considered a residual compartment in which the chemical
is absorbed or decomposed so that flows back from the ocean can be
neglected. For present purposes we do not provide a compartment for
the upper atmosphere; this is neither by oversight nor because of the
difficulty in dealing with this compartment. It reflects the recogni-
tion that most of the damage in this compartment is due to compounds
of low molecular weight; reasonable chains of degradation products would
have to be predicted and their interactions with the higher atmosphere
would have to be estimated before a reasonable assessment of potential
damage could be made. Furthermore, the air compartment over the entire
United States is assumed to be finite and closed.
24
-------
FIGURE IV-1
SCHEMATIC DIAGRAM OF INTERCOMPARTMENT FLOWS
OF EMITTED CHEMICAL
(man and biosphere omitted)
[AIR MOISTURE
OCEAN
AIR
SOIL
MOISTURE
SURFACE
WATER
GROUND
WATER
SOIL
^'7"HOSPHfc^
EMITTED CHEMICAL
BULK FLOW
DIFFUSIONAL
OR
CONVECTIVE
FLOW
25
-------
Compartments for animals and vegetable matter (biomass) are not
shown in Figure IV-1. We propose to compute the concentration in
*
these by applying the octanol/water partition coefficient to the average
fat content as a reasonable approximation.
The quantitative model assumes that each of the compartments
behaves as a completely mixed, flow reactor, with flows between compart-
ments. In most cases, the flows are bulk flows determined by water flows
and concentration in the compartment in which the flow originates. The
concentration of the chemical is assumed to be uniform everywhere within
the compartment. The model does not recognize geographical variations
in chemical concentration. In the case of transport between air
and surface water or soil moisture, convective mass transfer processes
are involved as well as bulk flows (through rainfall).
The total amount of chemical in a compartment at time t + At must
be equal to the amount in that compartment at time t plus the amount
created in or flowing into the compartment in time At minus the amount
degraded in or flowing out of the compartment in time At. The mass
balance for compartment x recognizes:
(1) Bulk water flows
(2) Diffusion
(3) Convection
(4) Emissions (by industry, etc.)
(5) Reactions
Hence,
See Neely, W. B., D. R. Branson and G. E. Blau, "Partition Coefficient
to Measure Bioconcentration Potential of Organic Chemicals in Fish,"
Environmental Science and Technology 8, 1974, pp. 1113-1115.
W C (t + At) = W C (t) + At P (t)
XX XX X
(1)
26
-------
where
= weight of compartment x, in kg,
C = concentration of chemical in compartment x, in kg/kg
X
•
F = bulk flow rate of chemical solution from compartment
x+y
x to compartment y, in kg/yr,
r = convective flow rate of chemical from compartment x to
x^y
compartment y, in kg/yr/unit concentration,
- chemical emission rate into compartment x, in kg/yr,
= first order reaction constant for compartment x,in yr 1
This difference equation can be converted to an ordinary differen-
tial equation by subtracting W C (t) from both sides of the equation,
X X
dividing by At, and taking the limit as At approaches zero.
" 57 C (O = P„(t> + Z
(F + r ) C (t) - K W C (t)
x dt x x y+x y-»-x y x x x
- C,<0 I
yfx
(2)
with initial conditions
C (t): = C (0) at t = 0 (3)
x x
where for several compartments F and r may be zero or negligible. In
equation (2), the first term on the right-hand side gives the emission
rate into the compartment, the second term gives the flow rate into
compartment x from all other compartments, the third term gives the rate
of degradation of the chemical in compartment x, and the final term
gives all flow rates out of compartment x into all other compartments.
27
-------
As shown in Appendix 1, equations (2) and (3) may be conveniently
rewritten in vector-matrix notation:
^ = M C(t) + p(t) (4)
with initial conditions
C(t) = C(0) at t = 0 (5)
where
C(t) is a column vector with elements [C (t)]
p(t) is a column vector with elements [p^(t)]
M is a constant square matrix with elements [m ] and
xy
m = -a ; m = b x/y
xx x xy yx
and
b =p/W,p = F +r. /(l\
yx yx x yx y-»x y-^x, \o)
a = K + W-1 2, p , (7)
x x x j Kxy
y fx
p (t) = P (t)/W (8)
X XX
In the notation used in writing equation (4), the new coefficients
and terms have the following interpretations:
a = total concentration loss rate per unit concentration
x
from compartment x, produced by chemical reactions (rate
K ), bulk flows to other compartments (rates F /W ), and
x x-»-y x
convective flows to other compartments (rates rx^.y/wx)»
b,,„ = concentration gain rate per unit concentration from
yx
compartment y to compartment x;
p (t) = concentration gain rate from direct emissions into
compartment x.
28
-------
For the case of constant emission rates p over a time interval
T [0'< t <_ T], tne solution to the linear, first-order vector differen-
tial equation (4) is
C(t) = eMtC(0)+ / eM(t " X)dA
0 < t < T (9)
Suppose that the time interval t of interest can be decomposed
into equal subintervals T so that all emission rates p(t) are constant
in each subinterval. If onl" the sequence of chemical concentrations
at times T, 2T, 3T, ... are of interest, then equation (9) can be
written as a recurrence formula
— , mtp— —
C [(k + 1)T] = e C(kT) + A p(kT) k=0, 1, 2, ... (10)
where ^
I- dJ (XI)
Jo
Finally, if p(t) is constant over all time periods t _> 0 and
T = 1 year, equation (10) becomes
C(k + 1) = eMC(k) + A p k = 0, 1, 2, ... (12)
M
Equation (12) is particularly easy to evaluate because the matrix e
and the vector A p are constant independent of time. The computer
M
methods for evaluating e and A p are presented in Appendix 1.
Equation (9) for incremental constant annual emission rates
(i.e., p(0), p(T), p(2T), ...) and equation (12) for constant p over
time have been programmed for computer evaluation. Finally, a third
option that has been programmed provides for a constant fractional
increase or decrease per year f in the chemical emission rate,
separately for each compartment. That is,
p(k) = E(k)p(0) (13)
where E(k) is a diagonal matrix (e ) with
xy
29
-------
e (k) = (1 + f )k; e (k) = 0 x # y (14)
xx x xy
Hence, equation (10) with T = 1 year becomes
C(k + 1) = eMC(k) + A E(k) p(0) k = 0, 1, 2, ... (15)
In order to calculate the chemical concentrations in the various
compartments at any time according to the preceding equations, the
emission rate vector p, coefficient matrix M, and initial concentration
vector C(0) must be evaluated or estimated. For compounds not previously
manufactured and not existing in nature, C(0) = 0. Mechanisms for
estimating these data are discussed at length in Chapter III of the
Phase I report. Certain of these estimation methods are explicated
further in Appendix 2 of this report.
B. Compartments
Thus far in the development of the multiple compartment environ-
mental model, we have not defined the nature of and interrelationships
among the compartments of interest. In principle, there is no restric-
tion on the number of compartments that may be defined; however, the
data requirements become quite substantial as the number of compartments
increases.
In order to demonstrate the utility of the model, we have defined
19 environmental compartments, as shown in Table IV-1. That is, we
assume that these 19 compartments represent an ideal abstraction of the
environment of the entire contiguous United States. As noted above,
each compartment is viewed as a completely mixed, flow reactor, with
bulk and convective flows between compartments. Therefore, the con-
centration of the chemical is assumed to be uniform everywhere
within the compartment. No geographical variations are permitted in
any physical or chemical properties (including concentration) of the
chemical or the environment within a compartment. Thus, for example,
the model presumes that all lakes throughout the United States may be
arithmetically combined (in terms of surface area, volume of water,
flow, etc.) into a single lake compartment.
30
-------
TABLE IV -1 U.S. COMPARTMENT DATA
Compartment
Mass
go13 kS)
Effective Area
<1010 „2,
Annual Flow
, 15
(10 kg)
Air (1 Mile High)
Atmospheric Moisture
Surface Water (Lakes)
(Streams)
Soil Moisture (0-lm)
(l-5m)
(5-10m)
(10-15m)
(15-30m)
(30-50m)
Ground Water (Shallow)
(Deep)
Ocean
Soil (0-lm)
(l-5ra)
(5-10ra)
(10-15m)
(15-30m)
(30-50m)
16.2
0.18
18.8
0.05
0.6
0.4
0.2
0.2
0.2
0.2
63.7
63.7
50
15.2
60.9
76.1
76.1
228.5
304.4
14
2.5
769
4. 8*
0.19
1.86
3.1
0.31
0.006
Note: Dash (-) denotes value not required.
* 15
Net of short-term reevaporation of approximately 1.2 x 10 kg/year.
Source: Phase I Report, page 36.
31
-------
Table IV-2 gives the estimated annual bulk water flows between
compartments containing water. These flows are based on Case 4 presented
in Table III d and Figure 8d of the Phase I Report.
Table IV-3 identifies the basic type of first-order degradation
reaction appropriate for each compartment and the nature of chemical
flows between compartments. For example, in the stream-stream cell
indicates that the reaction rate or half-life of the chemical in water
is a necessary model parameter (if no degradation in water occurs, then
R =0). The notation B in the soil moisture 10-15 meters - ground
w
water (shallow) cell indicates that a bulk flow of chemical containing
water occurs from the former to the latter compartment. The notation
C-9 in the soil moisture 0-1 meter - air cell indicates that chemical
mass transfer occurs from the former to the latter compartment and that
transport equation (9) in Chapter III of the Phase I report governs.
The notation E in the air - air moisture cell indicates that chemical
transport between these two compartments is nearly instantaneous so
that equilibrium conditions obtain at all times. Finally, a blank cell
indicates zero flow.
C. Limitations of the Model
The principal limitation of the model is
(1) Failure to recognize spatial (geographic) variations in
model parameters (e.g., chemical mass transfer rates)
and chemical concentrations. This, of course, is a conse-
quence of devising a lumped-parameter system. Again, this
was an intentional limitation in order to balance data
requirements and computational demands with the basic
intent of prescreening. As discussed in the next section,
this limitation may be readily relaxed.
Other limitations or key assumptions are:
32
-------
TABLE IV-2
bulk water flows between compartments
(in 1015kg/yr)
r LUW X
FROM: \T0:
1
2
3
c
R
7
R
9
1 0
11
12
l.AIR MOISTURE
000
1.
ROO
.100
2.000
.
000
. ooo
.000
.ooo
. ono
. 000
.
000
. 000
2.LAKES
170
#
000
1 . C: 9 0
.080
.
050
. 025
.015
.010
.010
.100
.
000
. 000
3.STREAMS
0 30
160
.000
. 120
.
050
. 015
.005
. 000
.000
.100
.
000
1.500
H.SOIL MOISTURE
0-1,V
2 .
800
100
. 100
.000
.
110
. 000
. 000
. 0 0 0
. 000
. ooo
.
ooo
. ooo
5.SOIL MOISTURE
1-5 M
•
000
«
05 0
.05 0
.010
.
000
. 000
.000
.coo
.000
.020
.
ooo
. coo
f>. SOIL MOISTURE
5-10 M
•
000
•
020
.020
.00 0
.
010
. 000
. 0U5
.000
.0 00
.020
.
020
.000
1.SOIL MOISTURE
10-15M
•
oon
•
010
.010
.000
.
00 0
.005
.000
.012
0 r' 0
. ni o
.
020
.000
n.SOIL MOISTURE
15-3 Of
•
000
»
005
.005
. 00 0
.
000
.000
. 002
.000
.005
. nco
.
00 5
.000
H.SOIL MOISTURE
30-50M
•
000
•
005
.005
. 000
.
000
. 000
. 000
.000
.000
. ooo
.
005
. 000
10.GROUND WATER (S
HALLOW)
000
•
000
. 000
. 000
.
000
.000
. ooo
.ooo
.000
. 000
.
250
. 000
11 . GROUIW WATER {DEEP)
000
000
. 000
.000
.
000
. 000
.000
. ooo
.000
.000
.
000
.3 00
12.OCEAn
1 .
800
000
.000
. 000
.
000
.000
. 000
.00 0
.000
. 000
•
000
. 000
Source: Phase I Report, Page 41.
-------
TABLE 1V-3. CHEMICAL REACTIONS AND FLOWS BETWEEN COMPARTMENTS
Bulk Flow
ConvectLve flow (Number indicates governing transport
equation in Phase I Report)
E ° Equilibrium condition (instantaneous flow)
R = Reaction in air
a
Ry ¦ R-'flCtion in water
Rg ° Reaction in soil
31ank indicates zero
TO
FROM X.
1
AIR
2
AIR
MOISTURE
3
LAKES
4
STREAMS
5
SOIL
MOISTURE
0-1M
6
SOIL
MOISTURE
L-sn
7
SOIL
MOISTURE
5-10M
6
SOIL
MOISTURE
10-15M
9
SOIL
MOISTURE
15-30M
10
SOIL
MOISTURE
30-50M
11
GROUND
WATER
(SHALLOW)
12
CROUND
WATER
(DEEP)
13
OCEAN
14
SQIL
0-1M
15
SOIL
1-5M
16
SOIL
5-10M
17
SOIL
10-15>'
18
SOIL
15-30M
19
SOIL
30-50M
1 AIR
R
a
E
C-7
C-8
C-10
2 AIR MOISTURE
E
R
w
3
B
B
3 LAKES
C-5
B
R
w
B
B
B
B
B
B
B
C
4 STREAMS
C-6
B
B
R
w
B
B
B
B
B
B
B
B
5 SOIL MOISTURE
0-1M
C-9
B
B
B
R
w
B
C-13
6 SOIL MOISTURE
1-5M
B
B
B
R
V
B
B
C-13
7 SOIL MOISTURE
5-10M
B
B
B
R
w
B
B
B
C-13
8 SOIL MOISTURE
10-15M
B
B
B
R
w
B
B
D
C-13
9 SOIL MOISTURE
15-30M
B
B
B
R
w
B
B
C-13
10 SOIL MOISTURE
30-50M
B
B
K
B
C-13
11 CROUND WATER
(SHALLOW)
Li
12 CROUND WATER
(DEEP)
B
13 OCEAN
B
R
V
14 SOIL
0-1M
C-14
K
s
15 SOIL
1-SM
C-14
R
s
16 SOIL
5-10M
C-14
R
s
17 SOIL
10-15M
C-14
F
s
18 SOIL
15-30M
C-14
R
a
19 SOIL
30-50M
C-14
R
S
34
-------
(2) The first limitation above arises from two assumptions:
(a) Each environmental compartment behaves as a completely
mixed, flow reactor, and
(b) The concentration of the chemical is uniform everywhere
within a given compartment.
(3) The upper atmosphere (above one mile) is ignored.
(4) The air compartment over the United States is finite and
closed.
(5) There is no compartment for biomass.
(6) Prediction of chemical adsorption by soil is not well
developed in the literature yet.
(7) Knowledge of bulk water flows between compartments is
imperfect.
(8) No provision has been made to account for loss of water
due to transpiration from plants.
(9) The solute concentrations in the water and air phases at the
interface are in equilibrium, such that Henry's law pertains.
Generally, this implies that the solute concentrations in
the bulk water and air phases are low, say, less than 0.02
mole fraction in water.
Finally, we note that at present it would be quite difficult to
test the veracity of the model due to the paucity of environmental
monitoring data across all compartments of interest.
35
-------
D. Extensions of the Model
1. Spatial Limitation
The present mathematical formulation of the environment is commonly
referred to as a lumped-parameter model, as distinct from a distributed-
parameter model. The model now recognizes the spatial distribution of a
chemical only to the extent that it occurs in the 19 defined environ-
mental compartments. The model assumes that perfect mixing occurs in
each compartment, so that the concentration of the chemical within that
compartment is everywhere uniform. Clearly, it is not realistic to
assume, as the model does, that the concentration of a chemical in, say,
the air compartment is everywhere the same in the United States. This
assumption of uniformity is reasonable if we seek only to estimate the
relative distribution of the chemical among the various media.
There are two possible approaches to extending the model to deal
with geographic variation. First, we could convert the lumped-parameter
ordinary differential equations to distributed-parameter partial differen-
tial equations. However, the resulting set of partial differential
equations would be most difficult and expensive to solve via computer.
Second, and more practical, we can add a new geographic region dimension
to the set of environmental compartments.
There are two practical cases to be faced:
Case 1. The objective may be to estimate the concentration of
a chemical within a single geographic region (say,
a given river basin) or
Case 2. The objective may be to estimate the concentration
of the chemical throughout the United States.
These two problems are very closely related but
different.
36
-------
2. First Case
For the selected region of interest, we will make the reasonable
assumption that the concentration of the chemical is uniform within
each of the 19 environmental compartments. (If this assumption were
not valid, then it would be necessary to subdivide the given geographic
region into a number of sub-regions for which the assumption would be
true. This would be Case 2.) In the case of the single geographic
region, the current model is immediately applicable with only modest
programming changes. One technical hurdle, however, is finding some
way to express chemical flows between the exogenous world and the 19
regional compartments. It would be necessary to estimate the size of
each of the 19 compartments in the region as well as the annual water
flows between compartments as we have already done when the region is
defined to be the entire United States. No particular difficulty is
foreseen in estimating these necessary environmental compartment data
for a specified region using such sources as the U.S. Geological Survey.
3 . Second Case
Here we are concerned with estimating the concentration of a
chemical throughout the United States while recognizing the effect of
geography (which is ignored in the present model). This can be accom-
plished in a fairly straightforward manner by subdividing the United
States into a number of distinct geographical regions chosen so that
the concentration of a chemical in a given environmental compartment
in a specified region may be assumed uniform.
To make this idea clearer, suppose we decide to subdivide the
United States into 10 distinct regions. For each of these regions,
then, we will define 19 environmental compartments; in any given en-
vironmental compartment in any region the concentration of the chemical
may be assumed uniform. In total there are now 190 environmental com-
partments whose linkages must be specified. For example, transport of
the chemical can in principle occur between any two compartments in
contiguous regions. For each of the regions we would have to estimate
the sizes of its 19 environmental compartments and the water flows
37
-------
between them, as well as the water flows across the geographic region
boundary into an adjoining environmental compartment.
In principle, there is no great difficulty in modifying the exist-
ing mathematical model to recognize interconnected regions. The compart-
mental data requirements, of course, will be increased by a factor roughly
equal to the number of regions.
We believe that the present mathematical environmental compartment
model can be extended rather easily to handle multiple geographic regions.
The closed-form matrix exponential solution to the coupled set of ordinary
differential equations remains the same but the size of the matrix of
coefficients will be greatly enlarged; no doubt the cost of computer time
would be fairly high compared to present costs. Because the basic
structure of the mathematical model of the environment is not changed
by extending it to geographic regions, we do not foresee any conceptual
difficulties. As always, the difficult problem will be to collect all
the descriptive geographical region compartment data, but that task is
definitely feasible using published U.S. Geological Survey data and need be
done but once.
A good regional subdivision of the entire conterminous United
States is that currently used by the Water Resources Council, which is
•k
well-documented in the First National Assessment of Water Resources.
The 17 water resource regions are (1) North Atlantic, (2) South Atlantic-
Gulf, (3) Great Lakes, (A) Ohio, (5) Tennessee, (6) Upper Mississippi,
(7) Lower Mississippi, (8) Souris-Red-Rainy, (9) Missouri, (10) Arkansas-
White-Red, (11) Texas-Gulf, (12) Rio Grande, (13) Upper Colorado, (14)
Lower Colorado, (15) Great Basin, (16) Columbia-North Pacific, (17)
California.
The Nation's Water Resources, Water Resources Council, Washington,
D.C.,•1968.
38
-------
V. USING THE MODEL
A . Computer Program
The basic multiple compartment environmental model described in the
preceding chapter has been implemented in a time-shared computer environment
in order to facilitate user interaction in directing the course of the com-
putations. The program has been coded in machine-independent APL because
this language is particularly adept at handling matrix manipulations; the
APL code appears in Appendix 5. However, in order to operate the system
no knowledge whatsoever of APL by the user is necessary. The interested
potential user should contact the U.S. Environmental Protection Agency,
Office of Pesticides and Toxic Substances, Assessment Division (TS-792),
Washington, D.C., to determine the operational status of the system.
The system has been intentionally designed to be easy to learn and
use and to make minimal demands for data.
B . Basic Steps to Use the System
1. The user should first familiarize himself/herself with the
overall purpose and structure of the model as described in both
this and the Phase I reports. The importance cannot be over-
stressed of having a thorough understanding of the limitations
and basic assumptions inherent in the model.
2. The user should next formulate a clear statement of the
environmental issue to be certain that the multimedia model offered
here is truly appropriate.
3. The user should next refer to the data sheets in Figure V-l
to determine the basic data requirements imposed by the model.
The user must decide whether the default values provided auto-
matically by the system, Table V-l, are adequate for the problem
at hand or whether they should be replaced.
4. The user should next complete the data sheets, as described
in Section V.E.
39
-------
5. The user should next access the system via his/her terminal,
following the directions provided in Section V.P. The system
will then automatically prompt the user to enter data and out-
put instructions, as described in Section V.G.
6. The user should then review the results obtained for
reasonability to guard against the possibility of inadvertently
inputing incorrect data.
C. Review of the Model
The proposed model represents the air-land-water environments of
the United States as a closed system of interconnected compartments,
each containing a specified chemical at some compartment-average concen-
tration which varies with time. The distribution of the chemical among
the various compartments, which behave individually as completely-mixed,
flow reactors, is determined by the level of direct emissions and inter-
compartmental convective mass transfer and bulk water flows containing
the chemical as solute. The 19 environmental compartments are described
in Table IV-1.
Some of the more important assumptions and limitations inherent
in the model to be borne in mind are the following:
• The concentration of chemical is uniform everywhere within
a compartment and does not vary geographically.
• There is no spatial (geographic) variation in model parameters.
• Note that the use of compartment-average concentrations
may lead to substantial underestimates in some locales and
overestimates in others.
• The upper atmosphere (above 1 mile) is ignored.
• The air compartment over the United States is finite and
closed.
40
-------
• There is no compartment for biomass.
• Chemical concentrations are presumed low in all compartments
(e.g., less than 0.02 mole fraction in water).
The model computes the exact solution to Equation (2) — that is,
the time-varying and steady-state chemical concentrations and percentage
of the total mass of chemical (distribution) in each compartment —
given the input data specified below. The model also reports, as a
user option, the magnitude of the intercompartmental chemical flows
and the matrix of coefficients M [see equations (6-8)].
As presently programmed, the user cannot change (1) the bulk water
flows between compartments specified in Table IV-2, and (2) the basic
compartmental linkages described in Table IV-3.
D. Data Requirements for Using Model
1. Physico-chemical Properties of Chemical
The following data must be available in order to use the model:
a. Molecular weight
A
b. Vapor pressure , atm
*
c. Solubility in water , kg of chemical/kg of aqueous solution
d. Soil/water partition coefficient for organic fraction of soil*
2
te. Diffusion coefficient in air at 1 atm"", meters /sec.
& 2
+f. Diffusion coefficient in water , meters /sec.
* *
g. Reaction rate or half-life in
- Air
- Water
- Adsorbed to soil
*
Temperature-dependent property.
^These properties will be estimated by the system on request; see
Appendix 3.
41
-------
2. Initial Concentrations of Chemical
The concentration of the chemical in kg/kg at time t = 0 must be
provided for each of the 19 compartments. If the material does not
presently exist in the environment, the initial concentration in each
compartment is zero.
3. Chemical Emission Rates
The annual emission rate (kg/yr) of the chemical from all sources
(e.g., production, use, nature, etc.) into the following four compartments
must be provided over the future time period of interest:
- Air
Lakes
Streams
Soil moisture 0-1 meter
4 . Compartment Data
The following data are automatically incorporated in the model but
may be overridden with user-supplied data if desired.
a. Mass of Compartment
Table IV-1 gives the estimated mass (in 10^ kg) for each of the
19 compartments.
b. Surface Area
10 2
The total surface area (in 10 meter ) for convective mass transfer
is also given in Table IV-1 for the three compartments lakes, streams,
and soil moisture 0-1 meter.
c. Fraction of Organic Material In Soil
The estimated fraction of organic material in the six soil
compartments, f , are given below:
42
-------
Soil Layer, Meters
f
o
0-1
0.10
1-5
0.05
5-10
0.03
10-15
0.03
15-30
0.03
30-50
0.03
E_; Completing the Data Sheets
1. Types of Data Sheets
There are three data sheets (Figure V-l) , one each for
(1) Physico-chemical data
(2) Initial concentrations and emission rates
(3) Compartment data
The physico-chemical data, initial chemical concentrations, and
emission-related data may change from computer run to computer run,
but the basic compartment data are general to the model and will change
infrequently if at all.
2. First Data Sheet
The chemical name and run descriptor may not exceed forty charac-
ters each (including spaces). The run descriptor is included to differen-
tiate between runs of the same chemical, or to provide the user with a
place to make comments. The descriptor appears in terminal display and
report output. The physico-chemical data are entered as indicated. For
temperature-dependent properties, values at 20°C are recommended. All
properties must be entered only in the units indicated on the data sheets.
Enter the soil/water partition coefficient pertaining to the organic
fraction of the soil. If this is not avaiable, the octanol/water parti-
tion coefficient may be substituted.
A3
-------
FIGURE V-l
PHYSICO-CHEMICAL DATA
CHEMICAL NAME:
RUN DESCRIPTOR:
¦p-
PHYSICO-CHEMICAL PROPERTIES
MOLECULAR WEIGHT
VAPOR PRESSURE
SOLUBILITY IN WATER
SOIL/WATER PARTITION COEFFICIENT FOR ORGANIC FRACTION
OF SOIL
DIFFUSION COEFFICIENT IN AIR
NORMAL BOILING POINT
MOLAL VOLUME (AT NORMAL BOILING POINT)
DIFFUSION COEFFICIENT IN WATER
MOLAL VOLUME (AT NORMAL BOILING POINT)
ATM
KG/KG OF SOLUTION
meters2/sec
KELVIN
3
CM /GRAM MOLE
2 ,
METERS /SEC
3
CM /GRAM MOLE
COMPARTMENT TYPE EXTREME HIGH MODERATE PERSISTENT INERT B. HALF-LIFE C. REACTION CONSTANT
AIR
WATER
YRS /YR
ADSORBED TO SOIL
YRS
YRS /YR
J YR
/YR
-------
FIGURE V-l (Cont.)
CHEMICAL INITIAL CONCENTRATIONS (KG/KG)
AIR AM LAKES STREAMS SM 0-1 SM 1-5 SM 5-10 SM 10-15 SM 15-30 SM 30-50
GRND WATER GRND WATER
SHALLOW DEEP OCEAN SOIL 0-1 SOIL 1-5 SOIL 5-10 SOIL 10-15 SOIL 15-30 SOIL 30-50
EMISSION DATA
Ul
EMISSION RATE TYPE
(1) CONSTANT EMISSION RATES:
(2) CONSTANT PERCENT CHANGE:
(3) INCREMENTAL EMISSION RATES:
YEARS OF INTEREST
YEARS OF INTEREST
DURATION IN YEARS
PER EMISSION RATE
EMISSION RATE TIME PERIODS
it 1
it 2
it 3
//A
it 5
it 6
PERCENT CHANGE EMISSION RATES (KG/YEAR)
COMPARTMENT (FOR TYPE 2) RATE 1 RATE 2 RATE 3 RATE 4 RATE 5
AIR
LAKES _
STREAMS
SOIL MOISTURE 0-1 M
-------
FIGURE V-l (Cont.)
COMPARTMENT DATA
FRACTION
COMPARTMENT ORGANIC WEIGHT (KG) SURFACE AREA (SQ. METERS)
AIR
AIR MOISTURE
LAKES
STREAMS
SOIL MOISTURE 0-1M
SOIL MOISTURE 1-5M
SOIL MOISTURE 5-10M
SOIL MOISTURE 10-15M
SOIL MOISTURE 15-30M
SOIL MOISTURE 30-50M
GROUND WATER (SHALLOW)
GROUND WATER (DEEP)
OCEAN
SOIL O-IM
SOIL 1-5M
SOIL 5-10M
SOIL 10-15M
SOIL 15-30M
SOIL 30-50M
-------
The diffusion coefficients should be entered if known; otherwise
they can be calculated by the model based on the estimation methods
in Appendix 3. In this case, to compute the diffusion coefficient per-
taining to air mixtures or to aqueous solutions, the user must supply
the chemical's molal volume at its normal boiling point. Alternatively,
the user may choose to utilize methods described in Appendix III of
the Phase I Report. As a last resort, when no other method is available,
order-of-magnitude values may be used: set the diffusion coefficient
-5 2
for air at 1 x 10 meters /sec and the diffusion coefficient for water
-9 2
at 1 x 10 meters /sec.
The user must provide either the effective first-order reaction
rate constant pertaining to air, water, and soil media or sufficient
information from which the reaction rate constant may be determined.
If the half-life is specified, then the computer will evaluate the reaction
rate constant as ln2 divided by the half-life. If the reactivity is
known only in a qualitative sense, then the following approximate clas-
sification is used:
Reactivity
Extreme
High
Moderate
Persistant
Inert
Half-Life, Reaction Rate Constant,
Years per Year
0.01 (~ week) 69.3
0.1 (~ month) 6.93
1 0.693
10 0.0693
100 0.00693
If in doubt concerning the reactivity, a conservative (long-half
life) guess would be best.
If the reaction rate constants in all media are exactly zero, there
will be no steady-state solution (this situation is not recommended).
Finally, if all the reaction rate constants are near zero, the steady-
state solution may not be computable. These conditions will not impede
the time-varying solutions.
47
-------
3. Second Data Sheet
a. Chemical Initial Concentrations
Enter the initial concentration (at time zero) of the chemical in
each compartment in kg/kg. Some useful concentration conversion factors
are given in Table V-l. The default concentration value is zero for all
compartments, so that it is necessary to enter only the nonzero initial
concentrations.
b_. Emission Rate Data
The chemical emission rate* (kg/year) may be expressed in three
ways: (1) constant emission rate for all years, (2) base emission rate
with constant percent annual change, and (3) emission rates which change
incrementally for specified years. The same method must be used for
all compartments (but not necessarily the same emission rate). Accord-
ing to the model, the chemical may be emitted only to four compartments:
air, lakes, streams, and the first (shallowest) soil moisture layer.
First, check the emission rate type desired. Then on the same
row as the rate type, specify the time period information (maximum of
six entries). For the first two types, constant emission rate and con-
>'c
stant percent change, the time information consists of the years of
interest (the years for which the user wishes to examine the model out-
*
put). For incremental emission rates, enter the duration in years that
the specified emission rate persists.
'k
See Appendix 4 for a brief discussion on estimation of emission rates.
Only integral values are permitted.
48
-------
TABLE V-l
CONCENTRATION CONVERSION FACTORS TO YIELD
UNITS OF KG OF CHEMICAL/KG OF MEDIUM
Original
Medium Concentration Unit Multiply by
Air tig/1000m3 0.833 x 10 *2
-9
Water Hg/1 10
ng/1 10 12
-9
Soil ^g/kg 10
, ^ -12
ng/kg 10
Density of dry air at 20°C and 1 atra taken as 1.20 g/1.
49
-------
Finally, enter the emission rates themselves. For emission rate
types (1) and (2), only a single rate should be entered in the^column
"RATE 1." For emission rate type (2), also enter the percent change
(positive or negative) that is to be applied to each of the four com-
partments each year. For emission rate type (3), enter up to five
emission rates corresponding to the time periods specified previously.
Only one reaction rate method may be used for each medium, but the same
method need not be used for all three media. Examples of completed data
sheets are provided in Section V. H.
4. Third Data Sheet
The compartment data sheet need be completed only if the user
wishes to deviate from the default values built into the system. The
default values are shown in Table V-2. For any individual data items,
the default values may still be used even though other data items are
changed. To use specific default values, make no entry on the data
sheet, i.e., it is necessary to enter data only for those items that
change. The organic fraction is required only for the six soil compart-
ments. Transport surface areas are required only for the lakes, streams,
and shallowest soil moisture compartments.
F_. Accessing the System
After signing on, the computer model is activated by typing:
)LOAD MODEL
After the computer prints the time and date that data were last saved,
the user is prompted for a variety of options concerning input, running
the model, and display. The eight options are:
50
-------
TABLE V-2
COMPARTMENT DATA
(DEFAULT VALUES)
COMPARTMENT
F-ORCANIC
WEIGHT (KG)
SURFACE AREA (SO. METERS)
AIR
AIR MOISTURE
LAKES
STREAMS
SOIL MOISTURE 0-1M
SOIL MOISTURE 1-5M
SOIL MOISTURE 5-10M
SOIL MOISTURE 10-15M
SOIL MOISTURE 15-30M
SOIL MOISTURE 30-50M
GROUND l-.'ATER (SHALLOW)
GROUND l-.'ATER (DEEP)
OCEAN
SOIL 0-1M
SOIL 1-5M
SOIL 5-10M
SOIL 10-15M
SOIL 15-30M
SOIL 30-50M
.10
.05
,03
.03
.03
16.2E15
¦18E15
18.8E15
.05E15
.60E15
.A0E15
. 20E15
.20E15
.20E15
.20E15
63.7E15
63.7E15
50E15
15.2E15
.03
60.9E15
76.1E15
76.1E15
228.5E15
304.4E15
14E10
2.5E10
769E10
-------
0
Exit from model
1
=
Input all data
2
=
Input only physico-chemical data
3
=
Input only emission-related data
4
=
Print current data
5
=
Print intermediate data
6
=
Run model based on current data
7
=
Examine last outputs
The usual sequence of operations involves entering new data and
performing a computer run. The input is divided into three sections:
chemical data, compartment data, and emission-related data. All input
in specified units is prompted. Compartment data need not be entered
or displayed if default values are acceptable. Following input of data,
the user has various options for displaying the data entered, and if
necessary all or part of the data may be re-entered. If the data are
acceptable, the model is executed and the resulting chemical concentra-
tions are printed. After completing a run, any or all subsections of
the model may be executed selectively. Upon exiting the model, the
input data may be saved by typing:
) SAVE
which overwrites the old data. Then, to end a session, type:
) OFF
G_. Executing the Model
1. Input Process
After completing the data sheets, the user enters the data into
the model. The input routine takes the user through the data sheets
in much the same manner as they were filled out.
The user is specifically prompted for each item of data by the
system. The physical units of the data are also specified. Internal
program checks are made to verify that the input is in the correct form
with regard to number of characters and numeric range. A message is
52
-------
printed if an error is encountered, and the user is requested to re-enter
the input. Most of the data for the model are numeric and such input is
indicated in APL by a Q:. There is no strict convention for literal
(also known as alphanumeric) data, but a colon at the end of a prompt
has been adopted here. The chemical name and run descriptor are examples
of literal data. Procedural input which requires a yes/no response is
indicated by a question mark. Procedural input to select among options
asks the user to type an option number (e.g., the form of the emission
rates).
An effort has been made to simplify the data entry process. Data
items that require more than one number, such as compartment-based infor-
mation and the time periods, are entered all at once in vector form—as
numbers separated by spaces. The prompts will indicate how many values
are needed. Zeros are entered when there are no data for a given
compartment.
The entire compartment data section may be skipped by answering
"YES" to the question: "DO YOU WISH TO USE DEFAULT VALUES FOR ALL
COMPARTMENT DATA?" For the compartment data (when entered individually)
and for the initial concentrations, the user may enter "DEFAULT" which
causes the default values to be used for those data items.
After the input process is completed, the user has the option of
printing out the data as entered: "WOULD YOU LIKE TO PRINT THE INPUTS?"
This input summary may include, at the user's option, the compartment
data: "INCLUDING COMPARTMENT DATA?" The input summary is one computer
page in size or less, even with the compartment data included.
The intermediate calculated results may be displayed after the
input display section: "WOULD YOU LIKE TO PRINT THE INTERMEDIATE
RESULTS?" The intermediate results are the intercompartmental chemical
flows, both due to convection (r ) and bulk transport (F ), and the
_ xy xy
matrix M [in equations (6-7)J.
53
-------
At this point the user is queried: "ARE ALL INPUTS OK?" If so,
the model proceeds to the run output section. If the data are in error,
the user can transfer to the beginning of the data input process or only
to the emission-related data. To get to the latter point, answer "YES"
to the question: "ARE THE CHEMICAL AND COMPARTMENT DATA OK?" If the
answer is "NO", then the entire input process (and the model) begins
again.
The final section executes the model based on the data resident
and prints the output. The output consists of the final calculated
results from the model, i.e., the chemical concentrations in the various
compartments at the time periods indicated by the emission-related data.
For the special case of constant emission rates, the output also includes
the steady-state concentrations.
After printing the outputs, the seven model options are listed
again and the user proceeds as desired. At this point, the user may
wish to view the emission rates, especially if the percent change type
emission rates were used. To do so, enter option 3, display current
data; the emission rates at all time periods will be shown. This fact
highlights a difference between display and output—output involves
calculation while display does not.
2. Input in the APL Environment
Numbers are entered much the same as on a calculator. Only the
minimum form is necessary to enter a number. In other words, decimal
points are not needed for integers and neither are trailing zeros after
the decimal point. Negative numbers are indicated by a high minus sign
(~), not by the middle minus (-) which is used for the operational symbols
of subtraction and negation.
Given the scale and mathematical nature of this model, the use of
scientific notation is desirable. What would be written in mathematics
as
2.6 x 1015 and -320 x 10"5
54
-------
are written in APL as
2.6E15 and ~320E~5
or as
26E14 and 3.2E 3, etc.
The E means "times ten to the power of ..." or exponent. It is recom-
mended that the user utilize the APL style of scientific notation to
facilitate the computer input process. This form also requires less
space.
In APL input, strings of numbers (such as the compartment data
and initial concentrations) are separated by spaces. More than one
space is permitted between the numbers, but no spaces may be imbedded
within the number itself. Incorrect input of this sort results in an
APL syntax error, which must be corrected. Press carriage return to
end a line of input. If an error is discovered, backspace to that
point in the line and press linefeed or attention (depending on the
type of terminal being used). This causes everything to the right of the
attention to be deleted. Then continue the line from that point on
and end as usual with a carriage return.
H. Sample Session Involving All Three Types of Emission Rates
The sample session on the computer is described via:
1. The set of five data sheets that describe the runs. The
estimates of initial environmental compattmental loadings
and emission rates for benzene are taken from a 1980 draft
document "Exposure Assessments of Priority Pollutants: Benzene"
prepared by Arthur D. Little, Inc. for USEPA. The reaction
rate data for benzene are not valid, having been chosen for
demonstration purposes only. Literature reaction rate data
indicate that benzene undergoes fairly rapid degradation
in the air and water environments, so that the true steady-state
in these phases is achieved quickly.
2. Annotations that help interpret the interactive session that
follows. (Page 79)
3. The terminal-printed record of the session, with comment codes
provided.
55
-------
PHYSICO-CHEMICAL DATA
CHEMICAL NAME: BENZENE
RUN DESCRIPTOR: BASE CASE
PHYSICO-CHEMICAL PROPERTIES
MOLECULAR WEIGHT
VAPOR PRESSURE
SOLUBILITY IN WATER
SOIL/WATER PARTITION COEFFICIENT FOR ORGANIC FRACTION
OF SOIL
DIFFUSION COEFFICIENT IN AIR
NORMAL BOILING POINT
MOLAL VOLUME (AT NORMAL BOILING POINT)
DIFFUSION COEFFICIENT IN WATER
MOLAL VOLUME (AT NORMAL BOILING POINT)
COMPARTMENT TYPE EXTREME
AIR
WATER
ADSORBED TO SOIL
HIGH MODERATE PERSISTENT
X_
X
78
_J. ATM
.0018 KG/KG OF SOLUTION
135
METERS2/SEC
353 KELVIN
3
96 . 0 CM /GRAM MOLE
2
METERS /SEC
3
96.0 CM /GRAM MOLE
INERT B. HALF-LIFE
50 YRS
YRS
YRS
C. REACTION CONSTANT
/YR
39 /YR
/YR
-------
CHEMICAL INITIAL CONCENTRATIONS (KG/KG)
AIR AM LAKES STREAMS SM 0-1 SM 1-5 SM 5-10 SM 10-15 SM 15-30 SM 30-50
3E-9 0 1E-8 1E-8 0 0 0 0 0 0
GRND WATER CRND WATER
SHALLOW DEEP OCEAN SOIL 0-1 SOIL 1-5 SOIL 5-10 SOIL 10-15 SOIL 15-30 SOIL 30-50
0 0 0 00 0 0 0 0
EMISSION DATA
m
".MISSION RATE TYPE
(1) CONSTANT EMISSION RATES:
(2) CONSTANT PERCENT CHANGE:
(3) INCREMENTAL EMISSION RATES:
YEARS OF INTEREST
YEARS OF INTEREST
DURATION IN YEARS
PER EMISSION RATE
EMISSION RATE TIME PERIODS
H
1
it 2
5
a 3
10
n
// 6
COMPARTMENT
AIR
LAKES
STREAMS
SOIL MOISTURE 0-1 M
PERCENT CHANGE
(FOR TYPE 2)
RATE 1
230E6
EMISSION RATES (KG/YEAk)
2 . 1E6
0.53E6
230E6
RATE 2
RATE 3
RATE 4
RATE 5
pa
-------
COMPARTMENT DATA
COMPARTMENT
F-ORCANIC
WEIGHT (KG)
AIR
AIR MOISTURE
LAKES
STREAMS
SOIL MOISTURE 0-1M
SOIL MOISTURE 1-5M
SOIL MOISTURE 5-1OM
SOIL MOISTURE 10-15M
SOIL MOISTURE 15-30M
SOIL MOISTURE 30-50M
GROUND WATER (SHALLOW)
GROUND WATER (DLEP)
OCEAN
SOTL 0-1M
SOIL 1-5M
SOIL 5-10M
SOIL 10-.1 5M
SOIL 15-30M
SOIL 30-50M
Default
Default
SURFACE AREA (SO. METERS)
Default
-------
CHEMICAL INITIAL CONCENTRATIONS (KG/KG)
AIR AN LAKES STREAMS SM 0-1 SM 1-5 SM 5-10 SM 10-15 SM 15-30 SM 30-50
3E-9 0 1E-8 1E-8 0 0 0 0 0 0
CRND WATER CRND WATER
SHALLOW DEEP OCEAN SOIL 0-1 SOIL 1-5 SOIL 5-10 SOIL 10-15 SOIL 15-30 SOIL 30-50
0 0 000 0 0 0 0
EMISSION DATA
Ul
vo
F.MISSION RATE TYPE
(1) CONSTANT EMISSION RATES:
(2) CONSTANT PERCENT CHANCE:
(3) INCREMENTAL EMISSION RATES:
YEARS OF INTEREST
YEARS OF INTEREST
DURATION IN YEARS
PER EMISSION RATE
EMISSION RATE TIME PERIODS
Jl 1 .'l '
//6
JiL_ 25
COMPARTMENT
AIR
LAKES
STREAMS
SOIL MOISTURE 0-1 M
PERCENT CHANGE
(FOR TYPE 2)
RATE 1
230E6
2.1E6
0.53E6
230E6
EMISSION RATES (ICC/YEAR)
RATE 2
RATE 3
RATE 4
RATE 5
?a
-------
CHEMICAL INITIAL CONCENTRATIONS (KG/KG)
AIR AM LAKES STREAMS SM 0-1 SM 1-5 SM 5-10 SM 10-15 SM 15-30 SM 30-50
3E-9 0 1E-8 1E-8 0 0 0 0 0 0
GRND WATER GRND WATER
SHALLOW DEEP OCEAN SOIL 0-1 SOIL 1-5 SOIL 5-10 SOIL 10-15 SOIL 15-30 SOIL 30—f
0 000000 O 0
EMISSION DATA
o
EMISSION RATE TYPE
(1) CONSTANT EMISSION RATES:
(2) CONSTANT PERCENT CHANCE:
X (3) INCREMENTAL EMISSION RATES:
YEARS OF INTEREST
YEARS OF INTEREST
DURATION IN YEARS
PER EMISSION RATE
EMISSION RATE TIME PERIODS
ir 1
n
//3
if 4
10
a 6
COMPARTMENT
AIR
LAKES
STREAMS
SOIL MOISTURE 0-] M
PERCENT CHANGE
(FOR TYPE 2)
RATE 1
230E6
2.1E6
0.53E6
230E6
EMISSION RATES (KC/YEAR)
RATE
250E6
4E6
1E6
250E6
RATE 3
300E6
6E6
1.5E6
300E6
RATE b
270E6
5E6
1.3E6
270E6
RATE 5
P3
c
55
-------
RUN 1
EXAMPLE OF TYPE 1 EMISSION RATE INCLUDING PRINTING OF
COMPARTMENT DATA AND INTERMEDIATE RESULTS
)LUAD AODEL
SAVED 15:3b:59 10/01/60
wSSi'^E IS C91o90
OPTIONS Atib:
0 " La 1 'i FRO'A .'iGULL
1 - luPUT ALL DATA
2 - INPUT ONLY PHYSICG-CiimiCAL DATA
3 - In PUT ONLY MISSION-hELAIEU DATA
4 - PRINT CURRENT DATA
5 - PRINT INTERMEDIAIL RESULTS
6 - RUN MODLL BASED Oii CuRREnT DATA
7 - EXAMINE LAST OUTPUTS
ENTER UPTlUii nUAEER
L:
1
PHYSICO-CHEMICAL DATA
ENT'Eu CHEMICAL nAME: BEU'6EltE
ENTER tiUii DESCnIPTOR: EASE CASE
En'l'ER MOLECULAR WEIGHT-.
U:
7a
EiiTEh VAPOR PRESSURE (ATM.)-.
U:
.1
ENTER SOLUtiiLlTl In WATER (KG/KG):
D:
.0018
enter soil/water paixTITion coefficient for organic fraction of soil
Li:
135
DO YOU HAVE THE DIFFUSIVITY In AIR? NO
ENTER nORl-iAL BOILInG POINT t°K):
LI:
353
ENTER MOLAL VOLUME AT NORMAL nOILING FT. {CR*3/G-MDL):
G:
9b
DO YOU HAVE THE DIFFUSIVITY IN WATER? NO
DIFFUSIVITY In WATER HAS BEEN CALCULATED
DO YOU HAVE THE REACTION RATE CONSTANT IN AIR? NO
DO YOU HAVE THE HALF-LIFE IN AIR? Y
ENTER HALF-LIFE {YEARS):
Li:
50
61
-------
r
RUN 1
DO YOU HAVE rut REACTIOU tiATE CONSTANT IN kATER? HO
DO YOU HAVE THE HALF-LIFE lit' kATER? u
ENTEh I-lNERl, P=FERSISI/h. ON, 'DEFAULT1 IS NO LONGER A VALID lutuT
ENTER 1 FOR CONSTANT Ei-ilSSIUii RA'iES
ENTER 2 FOn COnSTAnT PERCENT InCiiEASE
ENTEti 3 FOR INCREMENTAL EMISSION RATES
ENTER UPTION NUMBER:
LI:
i
ENTER EMISSION RATES FOtx AIR, LAKES, STREAMS, SOIL MOISTURE {'KG./YEAR):
Li:
23UEli 2.1E6 .53£6 230&6
ENTER YEAtiS OF INTEREST:
U:
1 b 10
rtOULD YOU LIKE TO Phi NT THE INPUTS? Y
INCLUDING COi'lPAaTMEN'l DATA? Y
62
-------
BEu'LEiiE
(BASt, CASE)
tiGLECULAis HEIGHT:
VAljOR PRESSURE:
SGLUblLL'Ti In HATER:
S01L/»A±ER COEf:
itGnXAL BOILING RJluT:
MOLAL VULUME:
DIFL-USIVin IN AIR:
kATEri:
7 d
0.1 (ATol.)
0.U01U (KG/KG)
13b
3b3 i°K)
96 (CM*3/G-i-iUL)
9. 3607£~06 (,V*2/SEC)
6.9lJ49£,"lO ih*2/SEC)
REACT 10 ii HAW CGitSU'AiiT iPtii MAR)
Alii: .013a 6
WATER: ,bb31b
SOIL: .b931b
COMPARH-iEiiT
f-OhGAUlU
EIGHT
(KG.)
AIR
1.620216
Alii MOISTURE
1.8C0£li*
LAKES
l.b80£16
STREAMS
5. 000213
SOIL MOISTURE 0-1 .'¦/
6.000214
SOIL I'iOi SiUnL 1-5 W
4.000214
SOIL MOISTURE 5-1 Uv
2.000214
SOIL i-iOlSTORE 10-lb/';
2.000214
SOIL MOISTURE lb-30/>'
2.000214
SOIL MOISTURE 30-50W
2.000214
Gi\OUitO WATER (SiiALLUW)
6.37021o
GROUiiij kAIER (DEEP)
6.37Oil6
OCEAli
5.000216
SOIL u-i/.;
0.1
1.b2U2lb
SOIL 1-b/.;
0.05
6. 0lJu216
SulE 5 —10/'i
0.03
7. 61 Oi'l6
SOIL lJ-lb/B
0.03
7. ii 102lb
SulL 15-3U-;
O.Uo
2. 265217
SOIL 30-bOr-'t
0.03
3.044217
AREA
[N* 2)
0.000£0
0.000AO
1.H0QL11
2.500£1U
7.690£11
O.OOOEO
O.OOOcO
0.000£0
O.OOOA'O
O.OOOAO
O.OOOc'O
O.uOOi'O
0.000£0
0. D00/L0
0. 000£0
O.OOOi'O
U.i.i, U
0.uOOiG
O.OOOEO
63
-------
RUN 1
CGMi-'Aii'isiEili' C"0 Li>iISS10u RATES
{KGJ In)
XL Mi 1 It, An b lb'Aii 10 (j)
All,
3.UE b
2. 3£B
Alu MOISi'UiiE
0. OhU
U.UAli
LAMS
1.0 b a
2. lib
S'i'txLAMS
1.0 £fo
5.3/j
SOIL MOlSi'UuE
0-1 M
U.Oi/O
2.3 LU
801L MOl S'i'dt (b
1-5 .'•/
O.CiO
0.0//U
SOIL MOISTURE
b-iu,.;
0. OEO
u . U£ 0
SOIL MOISTURE
10-15.-/
U.UbV
0. 0£'0
SOIL MOISTURE
1 £> — 3 Lij V
o.oeo
O.OEO
SOIL MOISTURE
3U-50.-V
O.OEO
u. ozi'o
GliOUuD nATbh
(SilAL LOw)
0. OEO
U.OiJ
GiiUUiiD k'ATEn
\di;ep)
O.DEO
: O.Ui'O
OCt,/hi
0. DEO
O.OEO
SOIL 0-lAi
0. GEO
O.OEO
SOIL 1-bi".
U. U£0
O.OEO
SOI L 5-10; -j
0. OEO
o. obo
SOIL 10-1 Sift1
O.OEO
O.OEO
SOIL lS-3u/'.:
0. OEO
O.OEO
SOIL 3 0 - b 0.V
0. U&'O
0. OEO
WULl) IOU LI Kb TU tblilT THE ItiTEritiEUIATK HkSULTS? 1
64
-------
CONV ECTIV E t'LO»S PER UiiIT COl.CEnTRXilON Ut./fo.)
COMPARTMENT fnOM\TO
AIR
AIR MOISTURE
LAKES
STREAMS
SOIL MOISTURE 0-1 M
SUIL MOISTURE 1-5 M
SOIL MOISTURE 5-1 OA/
SOIL MOISTURE 10-1SM
SOIL MOISTURE 15-30/.,'
SOIL MOISTURE 30-50/-;
GROUND WATER {SHALLOW)
ground water [deep)
ocean
SOIL 0-1M
soil i-5a;
SOIL 6-1 OA'
SOIL 10-1 b.'-j
SOIL 15-30/-;
SUIL 30-50A/
Ln
compartment eromkto
air
AIR MOISTURE
LAKES
STREAMS
SOIL MOISTURE 0-1 M
SOIL MOISTURE 1-5 A
SOIL MOISTURE 5-1 OA/
SOIL MOISTURE 10-15A/
SOIL MOISTURE 15-30M
SOIL MOISTURE 3U-SOW
GROUND WATER {SHALLOh )
GROUND WATER {DEEP)
OCEAN
SOIL 0-1/-;'
SOIL 1-5M
SOIL 5-10M
. SOIL 10-15M
SOIL 15-30/-;
SOIL 30-5OA/
0.0EOO
6.1E27
3.4E18
6. OE'17
1. 9E19
O.OEOO
O.OEOO
O.OEOO
O.UEOO
O.OEOO
0.OEOO
0.0E00
O.OEOO
0. OEO 0
0.OEOO
O.OEOO
0.0600
O.OEOO
O.OEOO
Alt
7.0E25
O.OEOO
U.OEOO
O.OEOO
0.UE00
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0.0E00
O.OEOO
0. OEO 0
O.OEOO
O.OEOO
0.0L00
LAKES
2.3E'16
O.OEOO
0. OEOO
O.OEOO
0.0too
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
STREAMS
4.0E15
O.OEOO
0. OEO 0
0. OEOO
0.OEOO
0.OEOU
0. OEOO
0.0E00
O.OEOO
0. OEOO
O.OEOO
0. OEOO
O.OEOO
O.OEOO
O.OEOO
0.OEOO
0. OEOO
O.OEOO
O.OtOO
C» 1
0. OEO 0
O.OEOO
0.OEOO
O.OEOO
O.OE'OO
O.OEOO
O.OEOO
O.OEOO
0.OEOO
O.OEOO
O.OEOO
O.OEOO
0.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOu
O.OEOO
GW 2
0.OEOO
O.OEOO
0. OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0. OEO 0
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0.0£00
O.OEOO
O.OEOO
OCEAN
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0.OEO 0
O.OEOO
0.OEO 0
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0.OEOO
O.OEOO
O.OEOO
SOIL 1
O.OEOO
O.OEOO
O.OEOO
0. OEOO
9.9E08
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0.OEOO
O.OEOU
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
.<>; l
S/'J 2
SM 3
SM 4
SM 5
ss i
1.2E17
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0. OE'U 0
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOu
0.OEO 0
0.OEO 0
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OECO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0.OEO 0
O.OEOO
O.OEOO
0.OEO 0
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0. OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0. OEOO
O.OEOO
O.OE'OO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOC
O.OEOO
7.3EU7
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
2.9E0 a
O.OE'OO
0.OEO0
O.OEOO
O.OEOO
0.OEOO
O.OEOO
3.7E08
O.OEOO
O.OEOO
O.OEOO
0.OEOO
O.OEOO
O.OEOO
3.7E08
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0.OEOO
0.OEOO
1.1E09
O.OEOU
O.OEOO
0.OEOO
O.OEOO
0.OEO 0
O.OEOO
1.5E09
SOIL 2
SOIL 3
SOIL t
SOIL 5
SOIL 6
O.OEOO
0. OEO0
0.GEO 0
0.OEO 0
O.OEOO
O.OEOO
O.OEOC
0.OEOO
O.OEOO
0. OEOO
O.OEOO
O.UEUO
O.OEOO
G. u/,00
0.OEO 0
O.OEOO
0. OEOO
O.OEOO
0.OEO 0
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0.OEO 0
O.OEOO
2.OEO9
0 . Oi-O U
O.OEOO
O.OEOO
O.OEOO
O.OEOO
1.5E0'J
O.OEOO
0.OEO 0
O.OEOO
O.OEOO
O.OEOO
1.5EOlJ
O.OEOO
0.OEO 0
O.OEOO
0.OEOO
O.OEOO
4.5E09
O.OEOO
O.OEOO
O.OEOO
0.OEO 0
O.OEOO
5.9E0 9
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
93
G
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEVO
O.OEOO
Z
O.OEOO
0. OEOO
O.OEOO
0. OEOO
O.OEOO
1—•
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0. OEOO
O.OEOO
O.OEOO
O.OEOO
©
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
0,OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
O.OEOO
-------
BULK »ATEh FLGhS (KG./ YR
.)
-------
(m)
M, MATRIX OF COEFFICIENTS (PER IE All)
COMPARTMENT TO\FROM
A!4
LAKES
STREAMS
Aid MOISTURE
~9.4t00
2.It02
3.7t01
LARES
1.2£00
1.8t02
8.5t"03
STREAMS
8.ltOl
3.4t01
~1. 2t'04
SOIL MOISTURE 0-1 M
2.It02
1.3t 01
H
0
1
o
CM
SOIL MOISTUtiE 1-5 M
o.otoo
1.3t~01
1.3t~01
SOIL 'ACISi'UhE 5-10/-;
o.otoo
1. 3t~01
7.5t~02
SOIL MOISTURE 10-15;-;
o.otoo
7.5t 02
2.6t~02
SOIL MOISTURE 15-30/-;
o.otoo
S.0t~02
o.otoo
SOIL MOISTURE 30-50/4
0.otoo
5.01 02
o.otoo
GROUND WATER {SHALLOW)
o.otoo
l.bt~03
1.bt~03
GROUND WATER (DEEP)
o.otoo
o.otoo
0.OtO 0
OCEMi
o.otoo
o. otoo
3.0t~G2
SOIL 0-1/-;
o.otoo
o. otoo
o.otoo
SOIL 1-5/.;
o.otoo
0.otou
o.otoo
SOIL 5-10;*
0.0£0 0
o.otoo
o.otoo
SOIL 10-15AT
o.otoo
o. otoo
o.otoo
SOIL 15-3 OM
o.otoo
o.otoo
o.otoo
SOIL 30-50.V
o.otoo
o.otoo
o.otoo
COMPARTMENT 'TO J FROM
GW 1
Li t* 2
OCEAM
AIR MOISTURE
o.otoo
o.otoo
-------
RUN 1
AliE ALL InPUTS OK? 1
ALlGiJ 1'Atbri AhD PiibSS CAhrtlAOb hb'l'UiUi
BtuiiZEliu (6/uJE CASH)
COuCbiiTUA 'i I On UlbYnlBU'i'iOli
(Kit. / tiU.)
©
CU:-lfAhlVA.i'i'i
YE An 0
XL Ah 1
YEAh
b
YE An 10
STEADY ST
AlU
3.0£~j
H.0£"8
1. 2b
1
o>
H
3. 3£'~7
Alii i'iUlSTUivL
u. u£o
2.7 ti~ 10
8. 3E
10
1. 3 b 9
2.2b 9
LA MS
1.Ob~H
2. 7&'~10
8.3 b~
10
1.3/'," 9
2.2£~9
S'lnbAhS
1.0b'a
2.7i~l0
8.3 i~
10
i. 3£' y
2.2&~9
SUiL MOl STUuE
0-1 a;
0. OA'O
2.AE 10
8. Hb~
10
1.3£~9
2.'2b~'j
SOI L Ml SI 'Ui\ £
1-b ,V
u. ObO
d.S£~11
3.1 E~
10
5.3b~10
9.3b~10
SOIL MOIST'UHE
5-10 M
O.OflO
3.4£'~11
2. ob~
10
3.5£ 10
6.3/TlO
SOIL tiOlSi'Uiil.
10-15M
u. oz.o
1. 7£T~11
1.0E~
10
1.9£~10
3.5t~10
SOIL kOISTUnb
15-3 OAi
0.0L0
8.4£~12
k.7L~
11
8.7b 11
l.&£'~10
SOlL i-iOlS'TUhb
30-5u/'j
0.0£,0
8.1E~12
4.4£~
11
8. 0£ 11
l.b/TlO
CiiOUliD *'ATbi\
^SHALLOW)
O.OZi'O
5.0£~13
3.1b'
12
5.7£~12
1.1£~11
ChOUhi) yA TEh
(.DEEP)
0.0£0
8.3fc~lb
1.2b'
13
2.bifl3
b.U£~13
OCbkt
O.OEO
H.2L~12
2.7E"
11
4.9£~11
9.0£/~ll
SOIL o-l;'-;
O.OMj
'J.It lo
6.1if
17
1.I/Tie
2.1E~16
SOIL 1-bN
O.Ob'O
8.8if 19
1. lb'
17
2.2E~11
k.HE~17
SOIL 5-10M
0.0 eo
2.j>£~iy
4. Of"
lti
8.7E 18
1.6b'~ 17
SOIL 10-15;-;
O.ObO
l.bZTl'J
2.1b'
18
4.7£~18
9.9Zi'~18
SOIL 15-30/4'
0. 0£.'0
7.7E 20
9 .HE'
iy
2.2fi 18
4.5E~1U
SOIL 30-50/
0.0 to
7.5/f 20
-------
RUN 1
MASS UlSinlBlTlIOh
(°/°)
COMtAuTMEliT
1'EAR 0
Yi:.Ai( 1
YEAR 5
YEAh 10
STEADY ST
ALk
13.0
97.0
96.8
96.8
96.7
Alii MO I Si'U hi
0.6
0. b
0.6
0.6
LAKES
43. 5
0.6
0.6
0.6
0.6
STREAMS
43.5
0.7
0.6
0.6
O.b
SOIL MOISTURE
0-1 :¦>
0.7
0.7
0.7
0.7
SOIL MOISTUtit'
1-5 M
0.2
0.2
0. 3
0.3
SOIL MOISTURE
5-10;-;
0.1
0.2
0.2
0.2
SOIL MOISTURE
10-15/-;
0.1
0.1
0.1
SOIL WISTUhE 15-31W
SOIL MOISTURE 30-5OA."
GiiQUUD wATEii iSHALLOn)
GtiUUii0 WATLU iUEEf)
OCEAli
SOIL 0-1W
SOIL 1-5.7
SOIL 5-10M
SOIL 10-15.'*'
SOIL 15-30.*;
SOIL 3 0-5 OA:
100.0
100.0
100.0
100.0
100.0
69
-------
RUN 2
EXAMPLE OF TYPE 2 EMISSION RATE
OPi'IOuS AtiE:
0 - EXIT FhUM i-lOULL
1 - It;iJUT ALL DATA
2 - INPUT ONLY PHYSICO-CHEMICAL DATA
3 - INPUT ONLY EMI&SIUii-RELATED DATA (p)
4 - PaltiT CURuENT DATA
5 - PhMT IMTEiiHEDIATE hESULTS
b - RUN iiODEL bASED CtJ CUhRENT DATA
7 - EjiAMIub LAST OUTPUTS
bN'lEh Ut'i'l Uii NUMBER
Li: ©
3
EMISSION RELATED DATA
t.NTEiI iy INITIAL Cu.jCENIixAUONSi
Lis
3i,'~9 U IE~ 6 liTi* OOOUOUGUUtluUUOU
ciiUi-i t/Uh O.i, 'DLt'AULT1 IS liU LOliiCEn A VALIU 1;
b NT Eh TilE ANNUAL PERCENT GROWTH b'Ou A1H, LAkbS, STREAMS, SOIL NOISTUhEi
LjS
b b 5 U .
ENTER THE YEAtiS Of iNTbHEST ^
li:
1 S 10 25
»UULD YOU LIKE 10 rid NT THE INPUTS'/ Y
L'ACLUDhiU COMPAix'iMEu'T DATA? N
70
-------
tiL'iiZb 'liE
(BASE CASt)
i-\ULLCULAh n'E IGlJ'i'
VAtUix PliESSUnL:
SOLUalLiTI lit » ATE hi
SOlL/tiATEii COEh'i
uUiCAAL tiUlLlNG PUiu'i:
MOLAL VULUi'ib
Dlt't uS'IViTY lit Alii-.
*iA TEH:
7o
U.l \IYmA.)
0.U016 (KG/KG)
135
3 53 ( °/l )
bb {CM*'3/G-rtUL)
U'i
Gi(OuiiL) * ATE ft {SHALLOW)
GaUUtiD wATEii (DEEP)
UCEAli
SOIL 0-Uu
SOIL 1-5..;
SOIL 5-10M
SOIL 10-16/4
SOIL 15-3 0.V
SOIL 30-5ao
CD PEhCEUT Efc iiA'l
(KG/xL)
lE All
3.Ui, a 5.0 2. 3iii
O.Oii'O u.0Z,0
1.0t"a 5.0 2.1Eb
1.0E~H b.O b.3£b
O.OtO 2.3f,a
G.Ot'O O.OtO
0. Gill O.OEO
O.OEO O.OEO
O.uEO O.OEO
O.OEO O.OEO
O.OEO O.OEO
O.OEO O.OtLi
0. OE'O O.OEO
0.0L0 O.OEO
O.OEO O.OEO
O.OEO O.OEO
O.OEO O.QEO
0.OEO 0.OfO
O.O£"0 O.O/iO
nOULD YOU LIKE TO PRlaT THE INTERMEDIATE hESULTS? N
AHE ALL INPUTS OK? Y
ALIGli PAPEn AiW PhESS C/UihIAGE iiLTUkii
71
-------
BEN ZE lib
(BAbE, CASE)
RUN 2
COiJCEii'TRAi'10iJ UlSThioUTlOU
(KG . / idi.)
C Ok FA til ', 'i EiJT
YEAR 0
YEAR 1
YEAR b YEA:\ iG YEAR 25
Alri
3.0/;" j
4.0£~8
1.4ZV 7
2.5i~7
6.7 7
Alii MOISTURE
0.0£G
2.1E 1G
9.2£~1G
1.7£~9
4. bE (J
LAKES
l.U£~8
2.7iflG
y.it'io
1.7£"y
4.4£" 9
STREAMS
1.0£~8
2.7£,~iu
y.2t"io
1, 7E~CJ
4.5£~y
SOIL MOISTURE 0-1 ,¦!
0. 0E0
2.U/;"lO
u.yiTio
1.6 b~\)
4.1£~9
SOIL MOIST Ui\E 1-5 M
O.OtO
6.bE 11
3.3£~10
6.4£~10
1.7£~9
SOIL MOISTURE 5-1G.,
0. 0£'0
3.4£~11
2.1l~ 10
4.2£'~10
1.2£~9
SOIL MOISTURE 10-15k
U. O&O
1. 7i,'~ll
1.1E~10
2. 3&'~10
6.3E~10
SOIL MOISTURE 15-30M
0.0£0
8.4i-"l2
5.0/Tll
1.0£~10
2.9£~10
SOIL MOISTURE 30-5GAJ
O.Oi'O
8.1£~12
4.6£~11
y.6£~n
2.6£~10
GRUURL) WATER (SHALLOW)
O.Oi'O
5.0£~13
3.2E~12
6.8£~12
i.y£~n
GROUiJO * ATE a (DLELJ)
O.OEO
8.3£~1S
1.2E~13
3.0E~13
9.1£ 13
OCEAR
O.OEO
4.2£~12
2.HE'11
5.9£~11
1.6£"lO
SOIL 0-1M
O.OEO
9.''i,"lci
G.5/,~17
1.3£~16
3.7£~16
SOIL 1-5 m
0.0 EO
8.8£~19
1.1E 17
2.6£ 17
7.GA~17
SOIL 5 — 1 OA/
0. UE 0
2.8£~19
U.2£"l8
1.0E~17
3.Ob~ 17
SOIL 10-15.V
O.OEO
1.5£'~19
2.1E~lli
5.5£"lU
1. 7 17
SOIL 15 - 3 OW
0. OEO
7.7E~2u
y.8i"l'J
2.5£~16
7.6£ lb
SOIL 3U -50/-;
G. OL'O
1.6E~20
y.2ZTld
2.3£~18
7.0/;" lb
k.ASS DlS'i'hldWIUu
(»/°)
COMFARTMERT
YEAR 0
YEAR 1
/£717r 5
/£71;i 10
YEAR 25
AIR
13.0
y7.o
96.9
96.8
96.9
AIR MOISTURE
0.6
0.6
0.6
0.6
LAKES
13.5
0.6
0.6
0.6
O.o
STREAMS
43.5
0.7
0.6
0.6
0.6
SOIL MOISTURE
0-1 m
0.7
0.6
G. 6
0.6
SOIL MOISTURE
1-5 M
0.2
0.2
0.2
0.3
SOIL MOlSTUub
5-10 M
0.1
0.1
0.2
0.2
SOIL nOISTURE
10-lbM
0.1
0.1
0.1
SOIL MOISTURE 15-30/tf
SOIL MOISTURE 30-5(1'';
GtiUUl'iU WATER (SHALLOW)
GRUUUU »ATER (DEEP)
OCEAli
SOIL 0-1M
SOIL 1-bM
SOIL b-lOM
SOIL 10-15/'-;
SOIL 15-30.'-/
SOIL 30-50<<1
100.0
100.0
100.0
100.0
100.0
72
-------
OFi'lOliS A tiki
U - La 1T FHOi-i IWDEL
1 - lliL'UT ALL uATA
2 - iiiPuT Oi
-------
BEriZEtiE
(BASE CASE)
MOLbCULAii WEIGHT'.
VAROft PRESSURE'.
SOLUBILITY 1H WATER:
SOIL/WATER CUE v.
li 001-1AL EOlLInG PUliiT:
MOLAL VOLUME-.
DIt'FUSIVITY lit AIR'.
WATER:
7b
0.1 i,Am.)
0.0018 (KG/KG)
135
353 (°K)
96 (CM*3/G'-M0L)
9.3607£~06 (r4*2/SEC)
8.D9U9E 10 CM*2/SEC)
REACT 10 ti RATE CUiiSTAUT (PER YE Aii)
AIRi .013d6
WATEhi .69315
SOIL: .69315
C OMR A RTMEtSl'
CO
RERCEi'iT
YEAR 0
EMISSION MTES
{KG/YR)
YEAR 1 YEAR 5
YEAR 10 YEAR 2 5
AIti
3.0E 3
5.0 2.3 £ii
2.3 Ed
2.HE&
3. 6£'H
7 .tE8
AIR MOISTURE
0. 0£'0
0. 0£'0
0.0E0-
0.0E3
0. 0£'0
0. 0£'0
LARES
1.0£~8
5.0 2.1£6
2. li'G
2.6 £0
3. 3 £'6
6.8£'6
STREAMS
1. 0£"
-------
RUN 3
EXAMPLE OF TYPE 3 EMISSION KATE
OPTIONS AJiE:
0 - EXIT FROM MODEL
1 - Hi PUT ALL DATA
2 " INPUT ONLY PHYSIC0-CHEMICAL DATA
3 - INPUT ONLY EMiSSIOu-txbLATED DATA
4 - PiihiI CUniiENT DATA
5 - PRINT INTERMEDIATE RESULTS
6 - RUN MODEL BASED Oh CURRENT DATA
7 - LA AMINE LAST OUTPUTS
ENTER OPTION NUMtEn
Li:
3
EMISSION RELATED DATA
ENTEh ly INITIAL COuCENTtiATlUuS:
Li:
3£~9 0 l£/~8 1E~6 OOUOOOOOOOOUOUUll
ENTER 19 NUMBERS Q
enter 19 initial concentrations:
LJ:
3 E b 0 1£'~8 lE~d OOOOOOOOOUUOOOG
EhUM NOW On, 'DEFAULT' IS i<0 LONGER A VALID INPUT
EuTER 1 FOh CONSTANT E.4ISS1 UN iiATES
ENTER 2 FOR CONSTANT PLRCENT INCREASE
EN'i'En 3 for incremental Eihssiun rates
ENTER OFl'ION NUMbER:
C:
3
HO* MANY INCREMENTS?
Li:
U
ENTER THE 4 INCREMENTAL TIME PERIODS:
Li: ©
5 b 5 10
EhTER MISSION NATES FOh Alh, LAKES, STREAMS, SOIL MOISTURE FOR TIME PERIOD 1 (KG./YR.):
LI:
230£'b 2.1E6 . 53£'6 230£'6
ENTER EMISSION RATES FOR TME PERIOD 2 {KG./YR.):
Ll:
250£/6 U£6 lEb 2bOEb
ENTER EMISSION RATES FOh TIME PErdOD 3 (KG./YR.):
Li:
300£>'tj 6£'b 1.5£'6 30QEL
ENTER EMISSION RATES FOR TIME PEVIOD 1 (KG./YR.):
U:
270£6 5£'b 1. 3£6 270EL
WOULD YOU LIKE TO PRINT THE INPUTS? Y
INCLUDING COMPARTMENT DATA? N
(w)
75
-------
RUN 3
Dtili /jblVE
(EASE CASK)
1-iOLECULAh WEIGH 1".
VAtUh iruESSUk E:
SOLUBILITY Iii nATER:
SOlL/WATEii COEFi
tiORi
-------
liEu 6ENE
{BASE CASE)
RUN 3
COtiCEl^TkATxOn
DISTiilbUiIOli
(KG.
/ At. )
CUVPAhlAEUT
IE Ah 0
HEAii 5
IEAn 10
it Ai\ 15
HEAR 2 5
Alii
3.0& y
1. 2t~_l
2. 1£~7
2.Bt"7
3.HE~7
AIt\ riOIS'TUiiL
o.oto
8.3 E 10
i.4t~y
l.yt 9
2.3t~y
LAKES
1.0L~8
a.3t~io
1.4t~9
l.yt'y
2.3£~
0.6
0.6
SOIL MOISTURE
0-1 {¦<
0.7
0.7
0.7
0.7
SOIL MlSTUkE
1-5 /¦!
0.2
0. 3
0.3
0.3
SOIL HOlSTuEE
b-lOM
0.2
0.2
0.2
0.2
SOIL ''lOIS'iUiiE
10-15W
0.1
0.1
0.1
0.1
SOIL MISTUiiE 15-30M
SOIL MOISTURE 3U-50w
GhOUtW wATBli (SilALLU» )
GiiUUlW kATEH (DEEP)
OCEAli
SOIL 0-1M
SOIL 1-5/-7
SOIL i>-10;V
SOIL 10-15/*
SOIL 15-30;*
SOIL 30-5 OA?
100.0
100.0
100.0
100.0
100.0
77
-------
OPi'lOuS AnL:
0 - LJi.iT tEOM MULL
1 - In PUT ALL DATA
2 - luPUT On LI P'tiiSiCQ- CHEMICAL DATA
3 - IMPUT ObL'i EMISSIUU-hLLATEU DATA
4 - FiilitT CUiiiibiJT DATA
b - PiilUT hiTEiitiEDlATE RESULTS
6 - nUli MODEL BASED Of» CUlxntuT DATA
7 - EiAUiiE LAST OUTPUTS
EitTEh OPTiOlt li UMBEL
Li:
0
)SAVt.
3b: 59 O'J/ou/dO MODEL
)OPt'
78
-------
Comments
a The load command prints the last time the workspace (the model
and data) was saved.
b Q: is an APL notation for indicating numeric input.
3 ,
c cm /g - mol in APL symbols.
d Only the first letter is necessary for a YES/NO response.
e No compartment data explicitly entered,since default values
are used.
f Example of vector input and scientific notation in APL.
g The boiling point and molal volume are printed when applicable,
h Undistributed reaction rate constants,
i The default compartment data
j For display purposes, the emission rates are not repeated for
each year.
k Convective flows (calculated).
1 Bulk flows (constant)
m Matrix of coefficients (calculated).
n A carriage return was entered here to start the printing process,
o The steady-state is included on Type 1 when it can be calculated,
p At the end of run the options are listed again.
q Option 3 is chosen to begin another run using different emission
rates.
r The soil moisture emission rate is constant.
s Year 0 is the base or initial rate. This base rate also applies
to year one.
t Option 4 is chosen so that the emission rates for each year
after applying the growth rate can be viewed, since they are
calculated along with the concentrations.
Note that when a printing option (i.e., four or five) is chosen,
the options are presented again, which allows the user to view
the current data without necessarily running the model.
79
-------
An example of incorrect input: too many numbers were entered.
This means that the duration for the first emission rate is
5 years; the second 5 years; the third 5 years; and the fourth
10 years.
The compartment data does not change during the three runs shown
here and so are displayed only during the first run.
Run the model again after an exit, enter the word MODEL.
Since only one run may be stored at a time, data is not saved
automatically and the user has the option of filing data through
the use of the )SAVE command. This can be done at any point
outside the model (i.e., after the exit option).
The sign-off message has not been included here.
80
-------
REFERENCES
Arthur D. Little, Inc. 1977. Prescreening for environmental hazards—
A system for selecting and prioritizing chemicals. Washington,
DC: U.S. Environmental Protection Agency. EPA-560/1-77-002.
NTIS PB 267 093.
Battelle Columbus Laboratories. 1974. Literature search and state-of-the-
art study of identification systems for selecting chemicals or
chemical classes as candidates for evaluation. Washington, DC:
U.S. Environmental Protection Agency. EPA-560/1-74-001.
Bellman, R. 1960. Introduction to matrix analysis. New York:
McGraw-Hill Book Company, Inc.
Bennett C 0, Myers J E. 1962. Momentum, heat, and mass transfer.
New York: McGraw-Hill Book Company, Inc.
Mackay D, Wolkoff A W. 1973. Rate of evaporation of low-solubility
contaminants from water bodies to atmosphere. Environ. Sci. Technol.
7: 611-614.
Neely W B, Branson D R, Blau G E. 1974. Partition coefficient to
measure bioconcentration potential of organic chemicals in fish.
Environ. Sci. Technol. 8: 1113-1115.
Ogata K. 1967. State space analysis of control systems. Englewood
Cliffs, NJ: Prentice-Hall, Inc.
Reid R C, Prausnitz J M, Sherwood TK. 1977. The properties of gases
and liquids. New York: McGraw-Hill Book Company, Inc.
USEPA. 1975. U.S. Environmental Protection Agency. Office of Toxic
Substances. Papers of a seminar on early warning systems for
toxic substances. Washington, DC: U.S. Environmental Protection
Agency, p. 167. EPA-560/1-75-003.
Ward R C. 1977. Numerical computation of the matrix exponential with
accuracy estimate. SIAM J. Numer. Anal. 14: 600-610.
WRC. 1968. The nation's water resources. Washington, DC: Water
Resources Council.
81
-------
APPENDIX 1
MATHEMATICAL ANALYSIS
A. General Time-Dependent Solution of Multiple Compartment Model
of the Environment
1. Laplace Transform Approach
The distribution of a chemical among the compartments of the
environment is given by the solution to the set of simultaneous, first-
order, linear, ordinary differential equations defined in Section IV. A,
Equation (2 ) can be written in the form:
cx(t) + VV" ¦ rx(C) +S Vy(t)- (1)
y^x
"h"e V ¦ V/K*' V - + w «>
'.¦K>+ii/vr,:xv •<»
y^x
and p (t) - I' (t)/V: (U)
x x x '
In the notation used in writing equation (1) the new c.nefticients and terns
have the following interpretations:
ax = total concentration less rate per unit concent r;. ¦. Ion fron.
compartment x, produced by chemical reactions (rate *',)>
bulk flows to other compartments (rates F /W ),
x—> y x
and diffusional flows to other compartments (rates r /W );
x—> y x
b = concentration gain rate per unit concentration from compartment
y x
y to compartment x;
Px(t) = concentration gain rate from direct emissions into compartment x,
82
-------
For a given index x, the index y runs over the residual set of
indices. Writing equation (1) for x= 1, 2, nwe have a set of n
linear differential equations in n unknown functions. This set of
equations can be solved by taking Laplace transforms, solving the set
of linear equations in the transforms, and taking inverse transforms.
Let
'V n
Cx00 = I Cx (t)exp (-st )dt. (5)
Multiplying equation (1) by exp(-st) and integrating, we have
%
(c? ^ V. r / _ \ a / \
(6)
(s + ax)Cx(s) -^V,W -Qx(s).
where
Qx(s> = pw(s) + c (0+)
(7)
We now solve the set of linear equations (6) with x = 1, 2, ..., n to
obtain Cx(s), x = 1, 2, ..., n and then invert these functions to obtain
C (t), x = 1, 2, ..., n.
2. Constant Emission Rates
The solution is relatively easy to obtain when the emission rates
are constant. Then
px(0 = px(0) = constant (designated by p^), (8)
and
Qx(s) = (px/s) + cx, cx = Cx(0+). (9)
When Q (s) is substituted in (6), the solution for £(s) is a quotient
X X
of polynomials, and the inverse transforms are sums of exponential func-
tions.
To illustrate the procedure we use n = 3. The set of equations (6)
becomes
83
-------
(s + a1)C1(s) - b21C2(s) - b31C3(s) = (p^s) + ^
- b12C1(s) + (s + a2)C2(s) - b32C3(s) = (p2/s) + c2
^ "\f "X,
- b^c^ts) - b23C2(s) + (s + a3>C3 (s) = (p3/s) + c3 -
The determinant of the coefficients of the variables is
D (s) = (s - s^) (s - s2) (s - s3),
where s , s_, s. are the roots of the characteristic equation, D(s)
1 I J ^
Then the solution for C^(s) is
P1 + cls _b21 -b31
p~ + c~s s + a„ -b.
= 0.
Cj_(s) =
P3 + c„s
21.
s + a.
s (s - s ^) (s - s 2) (s - s 3)
A10 + ^11 + ^12 + A13
s-s, s-s.
s-s.
Taking the inverse transform of C^(s) the solution C^(t) is
Cl(t) " A10 + A11 6
St S-t s.t
+ A12 c + A13 e '
In general, the solution will have the form
n
Cx(t) "Ax0+1]A»J "''V1,
j = l
where s,, s», ...s are the roots of D(s) = 0, and
1 L n
D(s) =
9 + a^ - b
- b
12
21
s + a.
- b
nl
n2
b].3 ~b
23
- b. - b
In 2n
s + a
(10)
(11)
84
-------
It can be shown that D(s) > 0 for s >. 0, and therefore there are no
real roots that are non-negative, except for the unlikely case that the
reaction rates = 0, i = 1, 2 n. The proof is based on the fact
that
'i = Kt
a. = K, + / , B1Jt Btj = b1JWJ/W1I
from which D(s) can be expanded into a sum of products of the factors
(s + K^), with positive coefficients. For n = 2,
For n = 3,
D(s) = (s + K^Cs + K2) + B21(s + K ) + B 2(s + K2).
D(s) = n (s + K )
i=l
+ (B^ + B^2)(s + KjHs + Kj) + ...
+ (B23B31 + B32B21 + B21B31)(S + V + ' <12)
If the reaction rates are not all zero, the roots s. , s„, s are
1 L n
real negative roots or complex roots (occurring in conjugate pairs) having
negative real parts. The sum of the terms for a pair of conjugate complex
roots Is a sum of exponentially-damped sine and cosine terms. Hence, is
the steady-state solution.
To find the solution (10) we find the roots s^, s2, •••, s of
D(s) = 0 with D(s) from (11). The solution for C^(s) is
^ n
C (s) = N (s)/s il (s - s.) (13)
J=1 J
where N^(s) is the determinant obtained by replacing the xC^ column of
D(s) by the column consisting of the elements p^ + c^s, P2 + CjS,
p + c s. The A . coefficients are
n n xj
85
-------
Axi = Nx^Si^Si n ^Si ~ Sj^' 1 = 1' 2' n*
It is easy to show that N (0) > 0, and it is obvious that n (- s, ) > 0
X k=l
since the roots are negative or complex-conjugate pairs. Hence, the
concentration approaches a steady-state solution Athat is positive,
in agreement with our intuition.
The solution is obtained by substituting the values of the roots and
A from (14) and (15) into equation (10). The operations involved are
XJ
elementary but tedious. The difficult step is to find the solutions of
D(s) = 0, particularly when some of the roots are complex. The remainder
of the operations can be programmed easily for machine computation.
3. Increasing Emission Rates
Now assume that the emission rates increase with time t. We will treat
the case for which
k
P (t) = a t x, k > 0, (16)
X XX
which should be general enough for most purposes, since it is unlikely that
the emission rate for any pollutant will increase at a faster rate than a
power function of t.
We start with the case k = k, independent of x. The variation from
x
compartment to compartment is described solely by the coefficient a^. From
(A) and (7) we obtain
k+1
Q (s) = g /sK + c , g = a I"(k+1)/W . (17)
X X X X X
The solution of the set of equations (6) for x = 1, 2, ..., n is
% k+1
C (s) = N (s)/s* 1 D(s), (18)
X x
86
-------
where D(s) is given by (11) and Nx(s) is the determinant obtained from D(s)
by replacing the column by a column in which the j^1 element is
k+1
gj + Cj s . We now must find the inverse Laplace transform of (18) to
obtain C (t).
x -v
If k is a positive integer, we can expand ^x(s) into partial fractions,
% n ^ k ^
:x(s) = ^jAxi/(s " Si) + ^ "xj
C (s) = 7. h ,/(s - s4) + 7, B„4/sJ+1. (19)
Inverting (19) the solution is
n k
CxCt) " £Axi e*>> i = 2 (2D
j=l
J*i
Also,
n
Bxk ¦ si>- <22>
The other B coefficients can be obtained by expanding N (s).
Xj X
k,
The dominant term in the solution C (t) for large t is B , t /k!,
X X K
which has a positive coefficient by the argument used in the previous
section. Hence, C (O increases indefinitely as a power function t ,
the same type function as the emission-rate function, as t increases
indefinitely.
It is not likely that the emission rates will increase as fast as
k
t with k a positive integer. Values of k in the range 0 < k < 1 are
more likely. Assume that k is a rational number, k = h/m, where h and m
1 /m ^
are positive integers. Put r = s . Then C (s) in (18) becomes
87
-------
/ m. , h+m _ . m.
Nx(r )/r D(r ),
which is a quotient of two polynomials in r. We expand into partial
fractions and then replace r by s m. When this has been done and the
%
terras involving roots of D(r ) = 0 are collected, C^(s) can t»e written
in the form
ni+h
Vs*= S A*i/(s - si>+
where the A . and B , coefficients are deterniined from the expansion,
xi xj
Inverting (23) the solution is
n_ m+h
C
r ' ' ,, 1 ¦ * 1
j =
% rn+h
:v(t) = 2-^ A , exp (s t) + t(J"m)/ni/r(j/m). (24)
* i=l xl 1 i^O XJ
The dominant term in C^(t) for large t is the term involving t^^m(=t^)
with a positive coefficient. Again, we conclude that C (t) increases
k x
indefinitely (in the form t ) as t increases indefinitely.
The problem is more complicated, but not essentially more difficult,
when is not the same for all compartments. The solution can be obtained
by the method described above for rational values of k . The dominant
"Sc X
term in ^x(t) for large t is a term involving t , if the flow rates into
compartment x from compartments having higher k-values are negligible; and
y
it is a term involving t , where k is k or the largest k-value with a
y x °
non-negligible flow rate into compartment x, whichever is larger.
4. Decreasing Emission Rates
First, assume that
x x
Then
P (t) = a t"k, 0 < k <1. (25)
Qx(®) = 8X/s1 k + cx, gx =
-------
Put k = h/m. By the method used above, Cx(t) has the form (24) except that
the upper limit in the second sum is m-h, instead of m+h. The dominant
—
term in (t) for large t is a terra involving t . Hence, the steady-
state solution is zero.
The solution for the case in which k in (25) is replaced by k^ can be
obtained in a similar way. Again, the steady-state solution is zero.
Second, assume that
px(t) = cx exp(- h^t), h^ > 0. (27)
Then
V> " ex/ + v - VV (28)
and
n n
C~(s> = ^ Axl/
-------
5. Step-wise Increasing or Decreasing Emission Rates
For step-wise increasing or decreasing emission rates, the time
interval t, [0 £ t < 00] can be decomposed into subintervals for which
all emission rates p (t) are constant in each subinterval. The solution
x
for this case, given in Section A.2 above, can be applied to each sub-
interval, starting with the initial values C^CO) f°r the first subinterval
and using the values C (t.) at the end t, of the first subinterval as
x 1 1
the initial values for the second subinterval, etc.
In each subinterval the solution will have the form of equation (10),
but the coefficients A . (j = 0, 1, ...n) will change from subinterval to
subinterval as some of the p^ values change. However, if there are no
changes in the reaction rates or in the transition rates b with time,
the values of the roots s. will be the same for all the subintervals.
J
6. Steady-state Solution
From equations (10) and (14) the steady-state solution for compart-
ment x is
n
C (<*>) = A = N (0)/ n (-s.) = N (0)/D(0). (31)
X xu x j=l ^ ^
This follows since D(s) = (s - sn)(s - s„) ... (s - s ). The last member
12 n
of (31) displays the fact that the steady-state solution can be obtained
without finding the roots of the characteristic equation.
7. Multiple Roots
Thus far in the analysis we have assumed implicitly that each root
s. of D(s) = 0 occurs but once. In the general case multiple roots may
occur, making the computations more difficult. For simplicity we omit
the compartment index x. It is understood that a separate set of compu-
tations must be made for each compartment.
Assume that there is one multiple root s^ of multiplicity k. The
concentration C(t) is the inverse Laplace transform of C(s), where
90
-------
r/ ^ - N(s) - N(s)
s D(s) , .k n , ,
s(s - s.) n (s - s.)
j=k+l 3
The partial-fraction expansion of C(s) is
«s> =ir + —^-k+ "2 k-i+ - +rb t £ J^rr) (33)
3 (S - S]r (S - S]r 1 si j=k+i u sj;
The functions in (32) and (33) must be identical. Multiplying by the least
common denominator we obtain the identity
N (s) = [aq(s - + s £ Ah(s - 1
h=l
n(s)
.k n
+ s(s - s ) Yj Ai n i » W)
j=k+l J J
where
n
ji(s) = n (s - s ), n!(s) = n(s)/(s - s.) (35)
,,, m ' J
m=k+l J
Putting s - 0, s - s^, s = sk+^i ••• , s = in (3) we obtain
k n
A0 = N(0)/(-s,) n (-s ) (36)
¦l=k+l 1
al " . !' ¦¦ y »7>
j=k+l J
Aj = N^sj^sj^sj ~ Si^k nj^sj^' i = k+1> •••> n
These equations are modifications of equation (15) for unequal roots.
91
-------
To obtain the values of k^, A^, ... we can substitute other
particular (and arbitrary) values of s into the identity (34) to obtain
simultaneous linear equations to solve. A second method is to equate
coefficients of like powers of s from both sides of identity (34). A
third method is to differentiate (34) successively k-1 times and put
s = s^ in the derivatives. Although the third method yields the missing
coefficients by explicit equations in terms of the derivatives of N(s)
evaluated at s = s^, it is not a practical solution. Hence, we use the
first two methods.
We can obtain an explicit equation for A^ by the second method when
we equate coefficients of sn. In this way we obtain
n
\ " 'x " A<) " ^ A|' (39)
| kl I 1
where c^ is the concentration in compartment x at t = 0. A possible
objection to (39) is that it accumulates errors in A^, •••> An*
But this objection can be raised to the first method also.
Perhaps the best compromise is to use (39) to obtain A^ — which
completes the computations for a double root — and then use k - 2
arbitrary values of s to obtain k - 2 simultaneous equations in A^, A^,
Multiple roots are not likely to occur in practical applications.
And roots of multiplicity 3 or more are much less likely to occur than
roots of multiplicity 2. Hence, equations (36), (37), (38), and (39)
will suffice for almost all cases.
The case of two double roots can be treated in a similar way. Let s1
'V, 1
and S£ be the double roots. Then C(s) can be expanded in the form
^ An A A. A- A, n A,
c(s> = r + 7 77+ (s - + T2" + 4 £ x^rr-) (40)
(s - sp 1 (s - s2) 2' j=5 j'
Putting s = 0, s = s^,'s = 2p, s = s^, ..., s = s in the identity
corresponding to (34) we obtain
92
-------
2 2 n
A„ = N(0)/(-s ) (-S.T n (-s.) (41)
j=5 J
2 n
Ax = N(s1)/s1(s1 - s2) n (s1 - Sj) (42)
2 n
A2 = N(s2)/s2(s2 - S;L)Z n (s2 - s.) (43)
j=5 J
A = N(s )/s (s - s )2(s - S2)2 n'(s ), j = 5, n. (44)
J J «J J J J
The equation corresponding to (39) is
n
cx = A0 + A2 + A4 + Aj "
Use an arbitrary value, not equal to a root, to obtain a second equation
to solve simultaneously with (45) to obtain A. and A,.
2 4
This completes the solution for the coefficients for two double
roots. However, it is very unlikely that cases of this type will occur
in practice.
%
The inverse Laplace transforms of C(s) in (33)and (40)can be obtained
easily from the simple transform
°? st
I ,• 1 ,| i : I /(:; - N,). (46)
/>
Di f fp.rcntinL-inp, (k-1) t:1nirs w:l.t:li respect to s1 wo obt.nin
00
I(t" ° ' "l!) ^ - v'"'- '' = i k-i (47)
The inverse transform of (33) becomes
s..t k k-h n s.t
C(t) = Aq + e £ A ^ + Z A e J (40)
u h=1 n IK nj. j=k+1 j
93
-------
The inverse transform of (40) becomes
si t s t n s. t
C(t) = AQ + e ^ (Axt + A2) + e Z (A t + A^) + ]T A. e J <49)
j=5 J
8. Complex Roots
Thus far in Appendix 1, the analysis applies to real or complex
roots. The only differences between the case in which all roots are
real and the case in which some (or all) of the roots are complex are
(1) the computation of the A^ coefficients, whether or not there are
multiple roots, will require arithmetical operations with complex num-
bers, and (2) the exponential functions of complex exponents in C(t)
must be expanded into real and imaginary components to obtain a form
for C(t) that involves only real-valued functions of real numbers. The
fact that this expansion yields real-valued functions depends on well-
known properties of rational functions.
First, the Fundamental Theorem of Algebra states that the poly-
nomial equation, D(s) = 0, of degree n has exactly n roots (when multi-
plicities are counted) that are in the complex field, of which the real
field is a part. Then it is easy to show that complex roots (if any)
occur in conjugate pairs, if the coefficients of D(s) are real. Hence,
if = r + iq, i = ^ - 1, is a root, then = r - iq also is a root.
The proof follows directly from the fact that s^ and s^ are conjugates
for integral values of j.
First, assume that is a single root. Hence, s2 is a single
root. Let A^ and A2 be the corresponding coefficients of 1/(s - s^)
and l/(s - S2) in the expansion of £(s). Then
N(s1) N(s2)
A1 = (sx - s2)M(Sl) ,A2 = (s2 - s1)M(s2) ' (50)
where
n
M(s) = s H (s - s.) (51)
J J
Since N(s) and M(s) are polynomials having real coefficients,
N(s^) and N(s2) are conjugates, and M(s^) and M(s2) are conjugates. Then
94
-------
it is easy to show that arid in (50) are conjugate, using the fact that
s1 - s2 = 2 iq. The details are elementary and are left as an exercise.
Now write A^ and in complex form,
A2 = R + iQ, A2 = R - iQ (52)
Slt V
and expand e and e as follows:
Slt r S2t rt
e = e (cos qt + i sin qt), e = e (cos qt - i sin qt) (53)
Then
V S2 rt
A^ e + A^ e = 2e (R cos qt - Q sin qt), (54)
which is a real-valued function of real variables.
Similarly, if = r + iq is a double root, then = r - iq is a
double root. In C(t) shown in (49) A^ and A^ are conjugates, while A^
and A^ are conjugates. Then again the sum of the involved terms is a
real-valued function including terms of the form (54) and these terms
multipled by t.
The real-valued functions could have been used in the inverse
transform C(t) and their coefficients determined directly. However,
it is much easier to use the exponential form to obtain the coefficients
and then expand by (53) to obtain the real-valued functions. The ex-
ponential function of a complex variable is easier to use and manipulate
than are the damped exponential functions of real variables.
•k
B. Matrix Representation
1. General Solution
It will be convenient to express the governing set of ordinary
differential equations (1) in matrix notation:
A
A working knowledge of matrix analysis is assumed. Of many suitable
references on the subject, two are Bellman, R., Introduction to Matrix
Analysis, McGraw-Hill Book Company, Inc., New York, 1960, and Ogata, K.,
State Space Analysis of Control Systems, Prentice-Hall, Inc., Englewood
Cliffs, NJ, 1967.
95
-------
^ = MC + p(t) (55)
with initial conditions C = C(0) = C (56)
o
where C = C(t), C^, and p(t) are column vectors and M is a square
matrix (m ) with
xy
m=-a;m=b x ^ y (57)*
xx x xy yx
The complete solution to the linear dynamic equations (55) and (56) is
C(t) = eMtCo+f eM
° J0
2. Constant Emission Rates
The matrix integration above may be readily carried out if M is
assumed to be nonsingular and the emission rates are assumed constant.
In Section A.2, M has been shown to be nonsingular unless all the reac-
tion rate constants are exactly zero, that is, the chemical under-
goes no reactions in any of the environmental compartments. Under this
assumption and for the case that p is held constant over time, equation
(58) becomes
— Mr— Mt — —
C(t) = e lCq - M (I - el ) p det M f 0 (59)
_-l _
where M denotes the inverse of M and I is the identity matrix.
3. Step-wise Increasing or Decreasing Emission Rates
Now consider that the integration in equation (58) is to be per-
formed only over a time interval T and that over this interval the
emission rates p(t) are to be maintained constant at their values p(0);
that is, the time interval t [0 <_ t < 00] can be decomposed into subin-
tervals for which all emission rates p (t) are constant in each subinterval.
_ _ x
Thus, p(t) = p(0) for 0 <_ t <_ T. On this basis, equation (58) can be
written as
C(t) = e^^C - M (I - e^C) p(0) det M M 0 < t £ T (60)
A —
Note that from equation (11) D(0) = -det M. Also, no relationship is
implied between M and M(s) in equation (51).
96
-------
If only the sequence of constant time periods T, 2T, 3T, ... is
involved, equation (60) may also be written in the recurrence form
_ MT— —MT —
C[(k + 1)T] = e C(kT) - M (I - e ) p(kT) k = 0, 1, 2,... (61)
For example, if T = 1 year, then
C(k + 1) = eMC(k) - M (I - e^) p(k) k = 0, 1, 2,... (62)
M
This is particularly easy to evaluate because the matrices e and
—_1 M
M (I - e ) are constant independent of k.
4. Steady-state Solution
The steady-state solution in the case of constant emission rates
p and for nonsingular M is obtained from equation (55) by setting ^ = 0.
- _~i_ _
C(°°) = -M p det M 4 0 (63)
As expected, the steady-state compartment concentrations do not depend
upon the initial conditions C(0). We next demonstrate that equations
(31) and (63) are equivalent.
Let the inverse of M be the matrix U = (u ). From the equation
xy
MU = T, (64)
where I is the identity matrix, the elements of the inverse matrix
are
u = -y /D(0), (65)
xy yx
11 [ t ll
where y is the cofactor of the element in the y row and x column
'yx
of the determinant D(s) in equation (11). The solution (65) is obtained
by solving n sets of n equations each, obtained by equating elements in
(64).
From equations (63) and (65), C(°°) is the column vector having the
til
element in the x row equal to
97
-------
-------
(2) Computer programs to calculate the complex eigenvalues
(characteristic roots) of a matrix are not widely available.
Whether they can cope with multiple complex roots is moot.
(3) Exponential functions of complex variables must be
manipulated by computer to yield exponential functions
of real variables (i.e., sines and cosines).
In view of these problems, the matrix formulation offers very
significant computational advantages, as will be seen below. We will
assume in the following development that the emission rates p are
constant over a time interval T (i.e., the emission rates are step-wise
increasing or decreasing). For constant p over the interval [0 £ t <_ T],
equation (58) can be rewritten
C(t) = eMtC
o+|>-
•'O
x)- , ,
p d A
0 < t < T
(67)
where C(t), Cq, and p are (n x 1) column vectors and M is an (n x n)
square matrix defined in equation (57).
Mt
Next we will show how e and the definite integral in equation
(67) may be computed simultaneously. We define
1
L-
M
p
=1
II
lo
1
1
o
L
(68)
where N is a constant (n + 1) x (n + 1) matrix. Then it folllows that
.Mt
Nt
t - X)-
Jo
e '" "'p d x
1
(69)
where 0 is a (1 x n) row vector, each of whose elements is zero.
99
-------
We can prove equation (69) as follows. By definition
Nt
k ^
k=0 k=l
k
k!
M*
tf-V
1
0
0
Continuing to simplify equation (70), we obtain
(70)
Nt
t.k ^
tk kl
tk+1 f^p
k (k+1)!
0
(71)
Now consider the following integral
0
where s = t - X,
X
t Ms -
e p ds =
-P{±®4- f] -.-e/1
0 L k=0 J ifn ^0
(Ms)k - .
k=0~u ~TT p ds
(72)
-2 t^lp =V tk+1 Mk -
6& k! M p h ~mrrp
Comparing the final result of equation (.73) with equation (71) , we see
that equation (69) is proven.
100
-------
2. Computation of e
We see from equation (69) that the computation of the matrix expon-
ential defined by
eSt - 5 ^
r=0
will permit the calculation of C(t) from equation (67). Note that the
solution (67) also holds when M is singular.
The algorithm we used for computing the exponential of a matrix
[equation (74) is not efficient for this purpose] is based upon diagonal
a ^ Li
Pade table rational approximations. The basic steps for computing e ,
where L is an (n x n) matrix, are as follows:
1. Scale down by
(a) forming L' = L - [tr(L)/n]I where tr(L), the trace
of L, is the sum of the elements on the main diagonal
of L and I is the identity matrix;
(b) determining || L' | | , the norm of L', which is the largest
of the absolute sum of the elements of each column;
(c) calculating b equal to the larger of 1 and the logarithm
to the base 2 of | | L' | | , rounded up to the nearest
integer; and
(d) computing L" = L' 2
2. Calculate the exponential of the scaled down matrix, L", by
(a) computing Q(L") and Q(-L") where Q(L") = P + N and
P = I + c„L"2 + c.L"4 + c,L"6
I 4 o
•k
R. C. Ward, Numerical Computation of the Matrix Exponential with Accuracy
Estimate, SIAM J. Numer. Anal, 14 (Sept. 1977), pp. 600-610.
101
-------
N = cL L" + c3L" + c3L"3 + C5L"5
and the (c^) are those shown in Table 1.
(b) computing eL = Q ^(-L") Q (L")
3. Scale the matrix up by
T' L" 2^ ~L"
(a) calculating e = (e ) , i.e., square e b times;
> 11^.! L tr(L)/n L'
(b; calculating e = e e
Table 1
Coefficients for the P and H Polynomial Forms
1 1/2
2 5/44
3 1/66
4 1/792
5 1/15840
6 1/665280
102
-------
APPENDIX 2
CONVECTIVE MASS TRANSFER
A. Transport Between Liquid and Vapor Phases
In order to obtain the solution to equation (2) in Section IV.A,
we must first evaluate the convective transport of the chemical between
the liquid and vapor phases. In particular, we need to estimate the
following transport rates:
^sw+a = convective transport rate from surface water to air, kg/yr
Ta+sw = convective transport rate from air to surface water, kg/yr
T la = convective transport rate from ground (soil) moisture to air, kg/yr
Ta->"gm = convective transport rate from air to ground (soil) moisture, kg/yr
The rate of mass transfer across a phase boundary can be expressed
in terms of an overall mass-transfer coefficient multiplied by a
concentration difference:
N = k (y* - y) (i)
net y
In this equation N is the net molal flux of chemical from surface
net 2
water to air expressed as kg moles/yr/meter . The quantity y* represents
the mole fraction of chemical in air at the interface which would be in
equilibrium with the actual composition of the surface water containing
the chemical. The quantity y is the mole fraction of chemical at some
point within the uniformly-mixed air compartment. Thus, (y* - y)
represents the overall driving force for mass transfer between the
water-air phases. The mass-transfer coefficient k is expressed in the
2 ^
units kg moles/yr/meter . The subscript y signifies that it applies to
the gas phase and must be used in conjunction with a driving force
expressed in terms of mole fraction in the gas phase.
103
-------
Equilibrium between the gas and liquid phases at the interface is
assumed to follow Henry's law,* such that
where
y* P = (C /S) V for C s S
sw p sw
= v for C * S
p sw
(2)
P = atmospheric pressure = 1 atm
C - concentration of chemical in surface water
sw as weight fraction, kg of chemical/kg of solution
S = solubility of chemical in water as weight fraction,
kg of chemical/kg of solution
V = vapor pressure of chemical at ambient temperature, atm
P
Equation (2) may now be used to eliminate y* from equation (1):
N = k (V C /SP - y) (3)
net y p sw
For dilute mixtures of chemical in air
y = (M /M) C (4)
J a a
where
M = molecular weight of air (28.97)
cl
M = molecular weight of chemical
*Valid for low-solubility compounds. See Mackay, D., Wolkoff, A.W.,
Environ. Sci. Techno 1. _7 , 1973, pp. 611 - 614.
104
-------
Equation (3) can be rewritten in terms of a net convective transport
rate T between water and air:
net
/ MV \
T = k A 2- C - M C (5)
net y V SP sw a a J
where T has units of kg/yr and A is the interfacial area across which
net ° 2
transport occurs, expressed in meter .
We now define
T = k MA V /SP C (6)
sw-*a V y P / sw
and
T = k M A C (7)
a-»sw y a a
then
T = T - T (8)
net sw—^a a-^sw
which is consistent with equation (2) in Section IV.A.
In equation (5) only k is presumed to be unknown at this point.
105
-------
On both theoretical and experimental grounds for mass transfer
*
with laminar or turbulent flow, it has been shown that
Sh = a(Re)B(Sc)Y W
where
Sh = dimensionless Sherwood number = kM L/p D
a a ca
Re = dimensionless Reynolds number = Lv p j\i
a a a
Sc = dimensionless Schmidt number = u /P D
a a ca
M = molecular weight of air
a
L = characteristic path length of convective transport, meters
3
p = density of air, kg/meter
3
2
D = diffusivity of chemical through air, meter /sec.
ca
v = velocity of air, meter/sec.
a
p = viscosity of air, kg/meter/sec.
ci
a,3,y = constants
We next determine the convective transport (evaporation) of water
across the same boundary layer that the chemical traverses. Equation
(9) also holds in this case with the substitution of k for k and D
w wa
for D , where
ca'
k = mass-transfer coefficient of water,
W 2
kg moles of water/yr-meter
D = diffusivity of weter vapor through air,
Wa 2 -5 2
meter /sec. (2.60 x 10 meter /sec at 25°C)
Hence,
k/D
" "
-------
For many situations of practical interest (e.g., laminar flow)
Y = 1/3 (11)
so that
k = k (D /D )2/3 (12)
w ca wa v
Under the reasonable assumption that D is a known physical property
*
or can be estimated, we must still find a means to estimate k . We
W
will estimate k^ based upon measured rates of evaporation of water
throughout the United States. According to equation (6) the rate of evapora-
tion of water from lakes and streams may be expressed as
T =/k M A V IS P]C (13)
w I w w pw/ W J W
where
M = molecular weight of water (18.0)
w
V = vapor pressure of water at ambient temperature, atm
S = solubility of water, kg/kg (1.0)
w
P = atmospheric pressure (1.0 atm)
= weight fraction of water, kg/kg (1.0)
Thus,
k = T /M A V
w ww pw (14)
•k
See Appendix 3
107
-------
Tw may be calculated from the average U.S. annual evaporation rate
measured in meters, d
T = dAp (15)
w w
Combining equations (9) and (10), we obtain
k = dp /M V (16)
w w w pw
The rate of evaporation from lakes throughout the United States
A
ranges from 20-90 inches per year. We will use an average value of
70 inches at 6°C. Then with
d = 70 inches/vr = 1.78 meter/yr
3
Pw = 1000 kg/meter
M = 18.0
w
and
V = 0.0092atm. at 6°C,
pw
3 2
k 11 x 10 kg moles/yr/meter
w
Hence equation (6) becomes
T
sw+a
11 x 103 M A (D /D )2/3V /SpI C (17)
ca wa p J sw
which is identical to equation (3) in the Phase I report.
Similarly, equation (7) becomes
¦D )2/3l L
a (18)
= [n X 1C)3 MaA
-------
Equation (18) differs somewhat from equation (4) in the Phase I report.
The expression for the rate of transport from ground (soil) moisture
to air, T , is identical to equation (17) and the expression for the
gm+a
reverse rate from air to ground moisture, T is identical to equation
a-* gm
(18).
B. Transport Between Air and Air Moisture
Because of the very large surface area available, the mass transfer
of chemical between air (a) and atmospheric moisture (am) is very rapid;
in effect the chemical is in equilibrium between the two compartments,
Thus,
• •
T = T (19)
anr+a a+ara
or
r C = r C (20)
anr»-a am a-»-am a
Again applying Henry's law, we obtain
r C
an""a = = MVn/M SP = 1/j (21)
r C Pa
a-+ara am
where J is a constant.
Equation (21) indicates that the chemical concentrations in the
air and air moisture compartments are not independent. Therefore, one
of these two compartments should be eliminated from the set of equations
(1) - (4) in Appendix 1. Suppose we eliminate the redundant air moisture
compartment. Then it is easy to show that for the remaining set of 18
differential equations, the new coefficients are given by
a' = [(a - b ) + J(a - b )] (1 + J) 1 (22)
a a a,am am am,a
b' = (b + b Ml + J)"1 y#a, am (23)
y,a y,a y,amy
109
-------
p'(t) = [p (t) + p (t)](l + J)"1 (24)
a a am
and b1 = b + J b y^a,am (25)
a,y a,n am,y
All other terms a , b , b , and p (t) for x,y^a or am are unchanged
x y,x x,y x
from equations (2) - (A) in Appendix 1.
Furthermore, by expanding the expression for a' in equation (22),
it can be shown that ar is independent of both r and r . Hence,
a am->a a->am
there is no need to evaluate either of these in order to use the model.
Once the differential equations are solved for the air and other
17 compartments, we can calculate
C = JC . (26)
am a
110
-------
APPENDIX 3
ESTIMATION OF DIFFUSION COEFFICIENTS
A. Diffusion Coefficient for Chemical in Air
There are several empirical correlations reported in the literature
for estimating the diffusion coefficient (diffusivity) for a binary gas
system at low pressure. This physical property is required in order to
evaluate the rate of convective mass transfer of the chemical between
aqueous and air phases. It is also required to estimate the rate of
transport between soil moisture and air. It should be noted, however,
that an experimentally measured value of the diffusivitv will always be
preferred to an estimate based on empirical methods.
The method of Wilke-Lee* has been found to be slightly more reliable
than other equations for predicting the diffusion coefficient in air
at ambient conditions. This method is accurate to perhaps 5-10 percent
of observed values.
The empirical correlation (suggested from the solution of the
Boltzmann equation) is
B T
3/2
M
1/2
r
Meters /Sec
D
2
ca
Pa
a
ca
&
Reid, R. C., Prausnitz, J. M. , and Sherwood, T. K., The Properties of
Gases and Liquids, Third Edition, McGraw-Hill Book Company, Inc., New
York, 1977, pp. 553-560.
Ill
-------
where
10~7 (2.17 - 0.50 Mr 1/2J
M
1 1
+
28.97
M
M
Molecular Weight of Chemical
Absolute Temperature (293 K)
ca
Atmospheric Pressure (1.0 atm)
( 3.711 + 1.18 Vc1/3V2 %
Molal volume at normal boiling point of chemical,
3
cm /mole, estimated by the additive-volume increment
method of Le Bas, using Table A3-1.
n
,-B
A(T*) + C exp(-DT*) + E exp (-FT*) + G exp (-HT*)
with
and
A
1.06036
E
1.03587
B
0.15610
F
1.52996
C
0.19300
G
1.76474
D
0.47635
H
3.89411
yj (78.6) (1.15 Tb)
112
-------
TABLE A3- 1
ADDITIVE-VOLUME INCREMENTS FOR THE CALCULATION OF MOLAL
VOLUMES v. AT THE NORMAL BOILING POINT
b
¦k
BY METHOD OF LE BAS
Increment, cm"Vg-mol*'v
Carbon 14.8
Hydrogen 3.7
Oxygen (except as noted below) 7.4
In methyl esters and ethers 9.1
In ethyl esters and ethers 9.9
In higher esters and ethers 11.0
In acids 12.0
Joined to S, P, N 8.3
Nitrogen
Doubly bonded 15.6
In primary amines 10.5
In secondary amines 12.0
Bromine 27
Chlorine 24.6
Fluorine 8.7
Iodine 37
Sulfur 25.6
Ring, three-membered -6.0
Four-membered -8.5
Five-membered -11.5
Six-membered -15.0
Naphthalene -30.0
Anthracene -47.5
Ibid, pp. 57-60.
A*
The additive-volume procedure should not be used for simple molecules. The
following approximate values are employed in estimating diffusion coeffi-
cients: H , 14.3; 0 , 25.6; N , 31.2; air, 29.9; CO, 30.7; CO , 34.0; S02, &4.8;
NO, 23.6; N20, 36.4; NH3, 25.8; h o, 18.9; H^, 32.9; COS, 51.5; Clj, 48.4;
Br2, 53.2; I2> 71.5.
113
-------
. . o
T = Normal boiling point, K
b
The variables above to be provided on input are , v , and T ,
B. Diffusion Coefficient for Chemical in Water
The diffusivity of the chemical in a dilute aqueous solution is
required in order to estimate the chemical transport rate between ground
(soil) moisture and soil, equations (13) and (14) in the Phase I report.
One of the best methods for estimating infinite dilution diffusion coef-
ficients of nonelectrolytes in water is the correlation of Hayduk and
A
Laudie:
no - n m"9 "J--1* "0.589
D = 13.26 x 10 n v
cw
where
w
2
D° = binary diffusion coefficient at infinite dilution, meters /sec
cw
nw = viscosity of water, cP (1.002 cP at 20°C)
v = solute (chemical) molal volume at normal boiling point,
c 3
cm /g-mol
v may be estimated by the additive-volume increment method of Le Bas
c
using Table A3-1. The average estimation error for this method is
about 4 percent.
Ibid, pp. 567-578. N.B. Exponent of n in reference is incorrect and
should be -1.14. w
114
-------
APPENDIX 4
ESTIMATION OF EMISSION RATES
At a naive level, the rate at which a substance is produced could
be used as an estimator of the rate of emission of that substance into
the environment, either directly or by applying a proportionality con-
stant to it. Such a simple procedure would fail to recognize the fact
that some chemicals are produced primarily for conversion to other chem-
icals, in which case only a small fraction will be emitted in the original
form; whereas others are used in ways that are, directly or indirectly,
dispersive. For example, phosgene is produced primarily as an inter-
mediate in chemical synthesis, whereas freon is (or was) produced mainly
for use in aerosols (which are directly dispersive) and for refrigeration
equipment (from which it is dispersed by leaks or eventual destruction
of the equipment).
A variety of ways for estimating emission rates were considered. We
believe that for present purposes it is sufficient to allocate total
production into three ranges of usage:
(a) Low emission uses, comprising use as chemical intermediates
in the same or proximal plants. We estimate that in this
type of use emissions would not exceed 5% of production.
The use of a factor of 3% for purposes of estimation would
lead, at most, to a 50% underestimate of emissions in extreme
cases and would be highly conservative for most chemicals
in this use class.
(b) Intermediate emission uses, comprising uses involving sub-
stantial handling and transportation prior to transformation
of the compound. We estimate that in this type of use
115
-------
emissions would range from 5% to at most 50% of production.
For estimation, a factor of 30% will be used; it would
be about as conservative as that for low emission uses.
(c) High emission uses, comprising uses in which the compound
is not modified chemically. For these, long-term production
rate will make up for losses in use, so the uses may be
considered to be completely dispersive. A factor of 100%
will be applied to production to estimate emissions.
In addition to these three categories of use, total "emissions" from
sources other than intended production will have to estimated. This
category includes "emissions" from unintended production, such as pro-
duction as a by-product, and from production occurring in the environment
through natural processes or as the result of reactions between other
emitted chemicals. These also have to be estimated and provided to
the model.
The emissions in each category, computed as outlined above, must
next be allocated to the following compartments:
• Air
• Surface Water (Lakes and Streams)
• Soil Moisture (0-1 Meter)
116
-------
APPENDIX 5
PROGRAM DESCRIPTION
117
-------
COMPUTER MODEL OVERVIEW
The computer model is divided into five major sections:
Model Options Section Description
1,2,3 I Data input
6 II Intermediate calculation
4,5 III Display of section I and II (optional)
6 IV Final calculations
7 V Final output from section
The programs are called in a sequential fashion upon executing option
one. Options two and three also start this process,but skip one half
of the data input.
MODEL
INPUT
*CALCdDCA
*CALCdDCW
INPUTE
FORMER
FORMA*
CTYPE
*P4INP
*P4lNT
PRINTR
PRINTF
PRINTM
RUN
RUN1
RUN2
RUN3
All of these call MEXP IDEN
V. [ OUTPUT
* Will be called at user option.
118
-------
DESCRIPTION OF PROGRAMS
MODEL
INPUT
CALC4DCA
CALCdDCW
INPUTE
FORM4R
FORM^M
CTYPE
PdlNP
PdINT
PRINTR
PRINTF
PRINTM
RUN
OUTPUT
The main program is automatically called upon
entering the workspace, but it can be explicitly
executed as well.
Input program for physico-chemical data and com-
partment data
These programs calculate the diffusivity of the
chemical in air and water respectively. They
are called only if the diffusivities are not
available.
Input program for all emission-related data.
Forms the convective flow matrix by applying
the physico-chemical and compartment data.
Forms the matrix of coefficients using reaction
rates and the bulk and convective flows.
The compartment type 1 = air, 2 = water, 3 = soil;
used for assigning reaction rates to compartments.
Prints the physical chemical data and emission .
data with the option to display compartment data.
Prints intermediate results by sequentially calling
the following three subprograms:
For the convective flows
For the bulk flows
For the matrix of coefficients
Calls appropriate module for the specified emission
type either 1, 2, or 3.
Displays the final results: concentration in
kg/kg and as a percent by compartment for each
year.
119
-------
Note all other programs are general APL utilities to aid in formatting,
etc. Three programs are independent of the model:
DET A stand-alone program for calculating matrix
determinant.
WSDOC For printing out an entire workspace of functions.
This calls ALP, which alphabetizes a character
matrix.
TABS For invoking tabular output on an AJ832 terminal.
120
-------
YwSID
IS MODEL
L>:A
644840
ULX
MODEL
ALP
IDEn
HUu
AX
LF
VAHS
)FNS
CALCLDCA
INPUT
hum
) VAHS
BASEYn
toA
VAiiSI
Hi PUTS
HUN 2
COMP
MbAR
VARS 2
LIP
HUN 3
COM FA
AlV
vc
LIP2
SQ
Ca
I'J Af'lE
VP
CALClDCw
kEXP MODEL
TAbS
CX
NO
*'PC
VTM
CX 0
HUM
k'X
CEhTER
NIP
h'SDOC
DCA
FOOT
YhS
COLNAI-IES CTYPE D
OUTPUT PH1NTF PklNTM PHINTR
Yn hh'MT
DC*
PEk
t£
FOOT
k
hL'li
FOiiG
kliO
LDEPTH
HID
S
bMAX
VET
PtJNP
K
SOL
FOM&M
PUNT
KX
TB
FORMhR
RJUST
LEN
TYPE
V Z+-ALP XiA
LIj A*-* ABCUEFGUIJKL\tiOPuliiSTUVMA.XZLA6CDBFGaiJtiLMMP(ihi?iVV»,/iXZbQ,l2WttT&Al3j
L3] !<+-293 O P*-1
L4] O*- 1.06036 0.193 1.03567 1.76474 , 0.1561 0.47635 1. 52996 3.89411
L 5 J i'lb?*-+ /H4A ,MC
Lb] b<-lE~7x(2.17-(MH*i2)i2)
l7] S«-(3. 711 + 1.16*VC*i3)i2
L8] 'T+Ti ( 78.6x1.15*i1^)*i-2 C 0*-+/£>Li4]*(r*6'i5]) ,*rxOL5 + i3]
L9] l*-{B* ('1*3i2 )x (MR* *2 ) ) (.S*2 )*0
V
V Z*-CALCbDCW VC\NW
[1] nC/XLCULATES DIFFUSION COEFFICIENT GF THE SUBSTANCE IN »ATEk
L2] Nw-1.002 flVISCOSITY OF n'ATEk AT 20 DEC. CENT.
L3] Z«"13.26x( 10*~9)x( ftV*~1.14) xl/(7*~0. 589
V
V Z+-* CENTER X
Ll] '£¦*¦** (. -L 0. bx^+p ,X) tA
V
-------
V WwS C0LUA!4bi> LVioViLOCibbiiiiWi
LI] Z-"-f ' 0 -(0=pFkS4-,FWS)i>0
12] bV-LV=liLV+-,LV 0 ;iAX*-<{/F»S)[l/LEt,Hl*LOC,,l+pLV)-l+LOC4-BV/\QL\/
[3] Z+(,LLM°.>$\MAX)\(~BV)/LV 0 -*(l=»h»i>)»bviV2
[4] O -K)
L 5 ] EIW2: Z«-. ((»Lbl-i), -F»S) t ((pLEU) .MAX ) pZ
V
v whpe
Ll] fiCOAPARTMENl TYPE (1=AIR, 2=^ATER, 3=S0IL)
L2] >12 , (llp2),6p3
V
v z<-a z; r
Ll] «DIVISION BY ZERO
12 j zMo*y)xATY+'o=y
v
V Z«-M7 A\B\P\I
Ll] ,1 DE'i'EtMHiAii'i
L2] rBASED On PGM FROt-i IBM APL LAu'G REF MANUAL P. 87
L3] l+lUO 0 Z«-l
[4] Ll:P<-( ML;i])ir/ML;i]
L5] -*-{P-I)/ L2
Llij AlI,P-,~\^AlP,Ii'l
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L8] L2-.B*-A^I\I] 0
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L10] 1 1 +/l-(/lL ;/]*£) o .*/iLI; ]
[11] -+L1
V
V F0MM',A\B\H0
Cl] Ht'OixKS 'M* MATRIX
L2] RAC=1 - COMBINE AIR At'iD AIR MOISTURE FOh CALCULATION'S
L3] hiiU*-R*{'2pl£lJ)H0 1 ,llpl)\tO 1 .llpDW
L4] t&C/'RUOLl 2;1 2]-0'
L5] B+AhHU D( pRtiU)qh'X
Lg] Ka^ShOICTYPEI
L7] A*-KX+(+/JMO)iwX
L8] nDIAGONAL INSEiiL.- OF AX Hi M
[y] /to/lirK-0,ri+AC,iV)4>(-'4). 0 1 +(0,i~l+AC/<)4>£
110] -»'(~A6,)pO
111] Cit-(MAxS)*t>M*VF A CGliCEUTRATIONS RATIO OR 'a'
L12 ] i'lhAnl;2 ]*-:'•!bAtiL ;2 \ *CR
L13] MBARl; 2 ]+-* /MBARL ; 1 2]
L14 ] Aj£/1A [ 2; }+{+-/i'lBARl 1 2 ; ]) * 1+CA1
L15 D 1 1 U-1BAR
V
122
-------
V F0iMtiiiA-,DtiiWA-,E^13iEV.lH
LI] nEQUATIONS U05. REFER TO PHASE 1 nEPOtii'
12] nINDICILo AkE COMPARTMENT NOS. (X-Y)
13] nSET UP FOR ORIGINAL SYSTEM OF 20 CQMPAKTMh'WfiS
[4j R- 20 20 pO
Lb] nA IS THE 20 COMPARTMENT VERSION OF AREA, 'AX'
L6] A-0,AX
[7] nDIbb'USIVrn OF wATER In AIR
L8] DWA- 2.6*10*"5
[y] hdiffusivities ratio
Q10 j UR*-(DCAibWA)*2*'6
[11J ^FORMERLY CONVERTED G-l./GM. TO MOLES/MOLE.
L12 ] &-SOL
[13] fll2fi 12A
LIU] tf[l;2>7£2b 0 *[2;1 >1 l*l£/2S*yPiS
[15] n7 A*-L
Lib] /?L 1; 1+.5 b>11000*/lLi+ 5 6~jxMA*DR
L17] «3 Sk'-»-/1 GENEnAL FORi4 OF b b 9
[18] >V[4 5 6 ;l>ll*1000x/l[U 5 6~}*Mk*DRxVP*S
Liy] n 13 Gf'l-SUIL
L 20 ] EQV3*-MJEPrTH* 1.1 x ( 10* 19 ) x ZZh xFOMJ
[21] /r[6;15>£yl3[l] 0 RH ;lb ]-££felU[lj 0 A;[l6 ;7 >£'(*m[ 2] O A[ 17 ;8 >££14[3 ]
[2b] ^ELIMINATE OLD 3RD COMPARTMENT
[26] i20)c3)/(~(i20)e3)/ii
V
O tf[9;18]-«-EG13l>] O /iL'lO;19>£-$13Lb] O /.'[ 11 ;20]-££l 3[6 ]
O A[18;9]^£,'il4[4] O iV[ 19 ; 10 >£*14[ b ] O A[20;ll>£flU[6]
V i,—IDEN N
[1] PtlULNl'ITY MATRIX OF RANK N
[2] Z«-(2p/;)pl.rtp0
V
-------
fO
¦O
V INPUT;DEFAULT;I;SAME;Tn-,'j.iil
L111 Lb\ 'PHYSICO-CHEMICAL DATA1 ,LF
L2] . NAi-\E+-hti\LIP 'ENTER CHEMICAL HAVE: '
L 3 3 NO*-W*LIP ' ENTER RUN DESCRIPTOR: '
L
-------
ho
Kjy
[34j LiiCbi !•*¦!* 1 0 ¦*( 32-1) pLRC 0 LP
L 3b j hSECTION 2: 2 EMPER A'1 URE
[3bj nASSuMED W 6E 20 DEGnEES CENT.
[37] i'iA+-2ii. 97 WIRE MOLECULAh WEIGHT OF AIR
[38] FORG*- 0.1 0.05 ,4p0.03
[39] Wa.*-( 10*15) x 16.2 0.18 lb.b 0.05 0.6 0.4 .I4p0.2). 63.7 63.7 50 15.2 60.9 76. 1 76. 1 228. 5 304.4
[40] /Ja«-A£7."K10*11)x (j 0 1.4 0.25 7.69 0 0 0 0
[41] -HM 'DO YOU WISH W USE DEFAULT VALUES FOR ALL COM PARTMENT DATA? • )p0
[42] LF,'COMPARTMENT DATA' O 'TO USE THE DEFAULT VALUES FOR ANY INPUT TYPE "DEFAULT"'
l4 3] PlSECTIGN 3: FORG Hi PUT
[44 j DEFAULT*-F0ixG
[45] FORG*- 6 0 1 U1P 'EuTEti Fh ACTION OF ORGANIC MATERIAL IN EACH Ot THE 6 SOIL COMPARTMENTS:'
[46] ASECTION 6: MASS OF COMPARTMENTS
[4 7] DEFAULT** A
L4d] «/-*-(. Ai'N ,0) NIP 'ENTEh THE MASS FOR EACH COMPAhIMRnI (KG.)i '
L49] ^SECTION 7: EFFECTIVL SURiACE AREA OF COMPARTMENTS
[50] rONLY WATER COMPARTMENTS RAVE AREAS
[bl] DEFAULT*-AA.
L52] AX*-( AON ,0) NlP 'ENTER SbltFACE AliEA OF EACH COMPARTMENT (METEii*2)'
Lb3] ^SECTION 8: BULK FLUnS
L54 ] A NO LONGEti /JjV INPUT
[55] FD0T*-II1D
V
-------
V 1 NPUTE\W\C\C7 ;DE'FAULT;I;SAME;TR
Ll] LP,'GMISSIOn RELATED DATA' ,LF
[2] nSECTIUli k: lulTIAL CONCENTRATION CONDITIONS OR LOADINGS
L 3] DEFAUL1-LCNpO
Lt] cxo^(hCu,o) nip 'EiiTbr ',{ihCn) ,' initial concentrations-. '
LS] 2-HJiA 'DEFAULT' O LF.'FRQV NOW Oil. "DEFAULT" IS /VO LONGER A VALID INPUT'
Lb] ^SECTION 5: EMISSION RATES
L7] 0 OO * /AIR/LAKES/STREAMS/SOIL MOISTURE' 0 C2^~l+^(' ' .RJUST C) ,', • O bV-AC7/t 1 0 1 1 1 0 ACft.O )p0
[#] LP-' EiJYEli 1 /•WA' CONSTANT EMISSION MATES'
LlJ] 'ENTER 2 i-'Uii C OUST ANT PERCENT INCREASE'
LlOj '&7.MA 3 FOif INCREMENTAL EMISSION RATES'
[11] fl£fAAV6'/7 i'Mi' IiVPi;r SUBSECTION FOR THE SPECIFIED EMISSION RATE TYPE
[12] TYPE*- 113 NIP 'ENTER OPTION NUMbER:' 0 -+{L1 ,L2 ,Lj)LTYPE]
[13] Ll:PD01^{l,hCti)pBV\{ UppC) ,0) NIP 'ENTER EtUSSIOi, RATES FOR '.C2.' {KG./YEAR): '
LlU] YRS+-,i{-M>iAX) ,G) NIP 'ENTER YEARS OF INTERESTO LEI*-YRS-0 ~l±Yi
L15 J L2 :PUGT*-(. 1, A6"A)pbV\((lppC),0) /,IF 1 ENTER EMISSION tiATES FOR \C2,' {KG./YEAR) : '
L lb j LEl\h- 0 0 PEit*-bV\(lvpC) NIP 'ENTER THE AIM UAL PERCENT GROWTH FOR ' ,C2 ,' :»
L17] YRS-{{-£MAX) ,0) NIP 'EnTER THE YEAtiS OF INTEREST' O YhS*-YRSi\YRSl 0 -0
[18] LI'.LEIMI 1 .MAX) NIP 'HO* MANY INCREMENTS? '
[19] YRS--+ \LElr*-(LLN,0 ) AtfP 'MSA' ZW& ',{*LEN),' INCREMENTAL TINE PERIGDS: '
I
L 2 0 ] MC C (pL&7/). AC/*) p 0
L 21J kThSAtoE*-k'UOTiIi1+-BV\( (lppC) .0) NIP 'ENTER EMISSION tiATES', ((1=1)/• FOR ',C2),' FUR TIME PERIOD '.(* I),' {KG./YR.):
f
[22] I+-I+1 C -*-{I^vLEN) vti.Il
V
V A/56'
[1] ft LITERAL INPUT WITH PROMPT
L2] ,Aj'5'6' O Z-»-( p/^6'6')
V
V Z-S&T LIF2 /-;6'6'
[1] ftLITERAL INPUT WITH PROMPT, Eli'TdYLl] MUST tiB ELEMENT Of 'SET'
l2 ] Ll :tt*-MSG*-.MSG 0 -{\/SET=Z+-ltSQ{pXSG)iZ+V])pO O 'TRY AGAIN' 0 -Ll
V
-------
V EC-*-MEXP C\B\CP\CP2 ;CPU ;G'P6; EC; i; N;ft £G\POS\<*\T
LI] n £"*C WHERE C IS A MATHIX
[2 j /^ippc o £^-irr2®r /+y i£7
L3] aCP *12 4 6
L4 3 CP6+CP2 +. *CPH+CP2 +. *CP2+CP+. *CP+Ci2*B
[5] y*-0.5.(7*60).* 60 624 9360 205920 7207200 518918400
[6] POS+UDE7V //) + (CZ32x^L2])+(CP4*t1)L4j) + (tL6]xCP6)+yL8]xC^b+.xCF2
L 7 ] /if£'0(CP*ki.1 ])+(QL 3 ]*CP2+. "CP) + (L b >CPH+. *CP)+<* L7 ]*CP& +. xCP
l3] T+-({HFOS-NEG) + .*POS+i;EG
19] Ec*-r+.*r o i+2
L10] LI :-»¦(£lICAL DATA'
Lb] '3 - 2AWA' CWLY EMISSION-RELATED DATA1
l7j '4 - PRINT CURRENT DATA'
Lb] 'b - PRINT INTERMEDIATE RESULTS'
L'J] '6 - ji£//V ,V0tfEL fl/ISfctf ON CURRENT DATA'
L10] '7 - EaAMINE LAST OUTPUTS'
Lll] 1 0 6 A//P 'ENTER OPTION NUMBER' 0 ¦+( 0,£l,£l ,£3,L4 .LS.FIN.L? )L 1+/1]
Li2] Li:input o -*-(a=2) / fin
L13] Z/3 ilNPUTE
l14] FIN: FORMER O FORM Mi 0 -(A=6)/Lu 0 L* 0 -*(~Y/V 'WOULD YOU LIKE TO PRINT THE INPUTS? ') p/V'Pl
[15] IA:PCJNP 0 -*(/J=4)/Z,0 0 £/-'
L16 ] NP1:H~YN 'WOULD YOU LIKE TO PuINT THE INTERMEDIATE RESULTS? ' )^NP2
L17 ] LS-.PMNT O -»-(/l=S)/Z£ O LF
L18] NP2 :-*-{YN 'ARE ALL INPUTS OK? *)p£6 O -(YN 'ARE THE CHEMICAL AND COMPARTMENT DATA OK? • )+Ll
L19] Lb:RUN
120] -»-(0*pLIP 'ALIGN PAPER AND PRESS CARRIAGE RETURN') p0
L21] LI-.OUTPUT
L 22] -L0
V
-------
V Z+LI'A NIP MSG; LI Ml
LI] PiNUi-lERIC INPUT WI'IH PROMPT
L2 "j LlMl—lpLlfi+- ,Ll!-l
L3j LI-.MSG
L^] ¦*¦( lLIMi. 3]
L8] ERRO-.'RAnK ERROR' 0-Ll
L'j] AAA!: 'ENTER ', (? | LI* 1 ) ,' NUMBER' ,(1<\ LIM)/'S' t(0>LIM\ )/' OR LESS' O "Ll
L10 J ERR2:'ALL NUMBERS MUST BE 2. ' ,wLMl2l O -Ll
Lll] ERR 3 -.'ALL LUMBERS MUST BE <, ',vLIMl 3] 0 -Ll
V
V OUTPUT; FC; *• V; Pw; ASV; ri
Ll] nPRlNT THE RESULTS OF THE MODEL
L2J nA:2V = AGW TITLE WIDTH; /¦'* = f'I£Z,2J WIDTH-, FC- &FMT CODE\ FW= PRINT WIDTH
L3] RTw+-UvCUi-iP 0 Fk'-»-10 O FC+'E', (VF#),' .2l 0 iV-yi2W+iF*'xl+pYjY5
L4 J LF.NAVE,' (' . (Sfe «0) . ') ' ,LF
Lb] LF.PW CENTER 'CONCENTRATION DISTRIBUTION* 0 P* CENTER '(KG./KG.)'
L6] ) .i-V COLHAMESi .'/*.< *PUYEAR UI',lFW) &FMT 6ASEYR+Q 'tXRS) ,H pYtiS) * 1 + pCA') / 1 /STEADY ST'
L7] LF,T1,LF O COMP.FC &FNT CXO ,CX
Lei] MASS DISTRIBUTION IS THE CONCENTRATION DIST. UN A PEuCENT BASIS
L9] LF 0 iV CENTER 'MASS DISTRIBUTION' 0 P» CENTER ' (»/«)• 0 LP,T1,LF
LlO] COtiF.CBF' .1' ) ti'iAT 100x(6a0,CA) £(U 1 +pOf)p+/L 1 ] CXQ.Ck
Lll] (A-aVp' TOTAL'). OV , 1) ? (1+ ( pCA ) L 2 ]) p 10 0
V
V PR IN IF \bV \F* \t\'lW
Ll] fiPiilNTS OUT F-DOT
L2] AiWl+pCGVP O *W«-B 0 LF,'BULK WATER FLOWS (KG./ Yti.)» ,LF
L3] BV^LCN10,12p 1
LU] (RTWi'COMPARTMENT FRCM\TO')tFW COLN&4ES Sv '/' .BV/COMPA
Lb]
16] ,(fV, 2 ) Vr'DO'I
V
-------
V I'tii ulw; fa ; /YiW
LI] nPFUJTS OU'l' •/<;'
i_2] nlV^lfpCa-/^ 0 10
L3] LF.'M, HATklA OF COEFFICIENTS (PEn' YEAii)1 ,LF
L*+] ((/i!2V)t 'COMPARTl'iEitT WXFKOM' ) ,Fw COtiiAVES '/' .CO/P/ll AC+1 10 ;]
Lb] * •
16] ( (1£ . 0) +C,C?M^) , (Fw ~2 ) 1MBARI i ( ~LC) + 110 ]
L7] LF
Lb] (if2W+'COMPAti'mEitiX TO\FitQM* ) ,Fw COLuAMES SQ ' /' . C10,0+CCWP/?
L9] "
LlU] ( UC.OHCWr/r') ,(*V. 2)?(0,10-A6'MAto/lii
V
V Fult'j'fh ; r W ; /u V
L1J fiPhllilS OUT Vi"
[.2] /i^V-^l + pCCWP 0 £V/",-10
L3] 'COiiVECTIVE FLOw'S PER UiJIT COUCEllTKA'UON (KG Jla.)' ,LF
L1* ] ((i('l'#)t 'COMPAhimnT FiiOMVlV') ,fV COLHAMES £W ' /' L110; ]
Lb] • •
16] C0J4P, (FW ,~2)irt\_; i10]
L7] LF
La j (RTUt'COMtAR'L'AEU'i FtiOt-WIO ') ,Z-V COLHAMES SQ 10 0 tCOMPA
L9] lf
£10] COMP, (FW ,'~ 2) ¥ A L ; 1 o + IACi'i ]
V
-------
V Pb.lNP\A\CDF\U\; tC; b'w ; Pb'\ PF2 ;^V;/Jv'2
Li] sprint inputs
L if J *V«-1U C n?*h-UpC(Jt<[> 0 Pc^TYPE=2 0 PF2-Pf*0=l*(jCX 0 Ul+(PF2/pYtiS). \~PF2 O RW2+22
L 3 j CDF-YiV ' I rJL'LUUItJG COKPARTMEH'i DATA? '
14] LF,NAML, ' ( * ,{Sk NO) )' ,LF
Lb J n (KW2 ' \MOLECULAK HEIGHT: \ VAPOR PRESSURE: \SOLUBILITY IN WATER: \OC1AUOUhATHH COEFi ') ,f *+ 1 P Mw,VP.SOL,WPC
L6 j (/W2+ 'MOLECULAR WLIGHT: '
L7] (RW2i 'VAPOR PRESSUhE: ' ) ' (/)i>*.)»
La j (Rw2+ ' SOLUBILITY 1U WA TER: ' ) . (?£U£,) ,' (G/G)'
[y j UV2+ 'SOIL/WATER COEF: • )
Liu] -( 0=TB)/1+QLC 0 (AV2+ 'iWRMAL BOILlUG POINT: '), (t'TB) , ' (°x)'
Lll] ->(0 = l'C)/l+LiLC 0 (RW2i'MOLAL V0LW1E: ') ,(*VC)(C!4*3/G-NOL)'
L12 ] (RW2+ ' DIFb'USIVITY IN AZ7v:'),(0 5 T^/1) , • {M*2/SEC)X
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TECHNICAL REPORT DATA
(Please reod Instruction!, on the raene before completing
1 REPORT NO.
13. RECIPIENT'S ACCESSION NO.
4. TITLE AT.D SUBTITLE
PRESCREENING FOR ENVIRONMENTAL HAZARDS—A SYSTEM FOR
SELECTING AND PRIORITIZING CHEMICALS
7 AUTHORlSi
George H. Harris
5. REPORT DATE
September 1980 (Date of
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Arthur D. Little, Inc.
35 Acorn Park
Cambridge, MA 02140
10. PROGRAM ELEMENT NC.
|U. COMTR ACT/GRANT NC
! 68-01-3208
12. SPONSORING A G E N C v NAME AND ADDRESS
Office of Toxic Substances
Office of Pesticides and Toxic Substances
U.S. Environmental Protection Agency
Washington, D.C. 20460
13. TYPE OF REPORT AND PERIOD COVERED
FINAL PHASE 11,5/77-9/80
:ic. SPONSORING agencv code
15 suP?i.En»-:niAPy note;
IE
An objective system is described for ranking chemicals which may be released into
the environment in order of their hazard potential. Although the major focus is on
preliminary screening of new chemicals prior to full commercial manufacture
("premanufacturing"), the recommended scheme may also be applied to chemicals in pro-
duction. An important design criterion is that the system make minimal demands for data,
in recognition of the general paucity of available test data. Ranking is based on
the ratio of estimated future environmental concentration at a specified point in
time to the concentration level-of-concern causing deleterious effects.
The interactive computer model represents the air-land-water environment of the
United States as a system of 19 uniformly-mixed, interconnected reactors, each con-
taining the specified chemical at some compartment-average concentration. The temporal
distribution of the chemical among the various compartments is determined by the
initial concentrations, extent of direct emissions over time, and transformation
and transport processes that occur. The exact dynamic solution to the governing
vector-matrix differential equation is obtained. The resulting computer program
calculates the concentration of chemical in each environmental compartment over time
and at steady-state.
D- -T t.F.5
Ranking, Assessments, Environments, Water
Pollution, Air Pollution, Distribution,
Concentration, Mathematical Models,
Computer Simulation
pc. =
- ¦ r \ il A i - WEN"
RELEASE TO PUBLIC
Er"A r otp. (Re
77)
| Hazard potential, Risk : 07A
j assessment, Environmental ; 07D
| assessment, Chemical 12B
i transport and reaction, ; 08H
! Chemical system modelling,! 06T
| Chemical fate, Environ- ;
imental pathways j
UNCLASSIFIED
I'C
UNCLASSIFIED
_ 139
r I o N t s CH £ O _ E 7 E.
133
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A
CAMBRIDGE,
MASSACHUSETTS
SAN FRANCISCO
WASHINGTON
ATHENS
BRUSSELS
LONDON
MADRID
PARIS
RIO DE JANEIRO
SAO PAULO
TOKYO
TORONTO
WIESBADEN
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