PB82-230939
Volatilization of Organic Pollutants from Water
Toronto Univ. (Ontario)
Prepared for
Environmental Research Lab.
Athens, GA
April 1982
U.S. DEPARTMENT OF COMMERCE
National Technical Information Service
NIIS
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PBS2-230939
EPA 600/3-82-019
VOLATILIZATION OF ORGANIC
POLLUTANTS FROM WATER
by
Donald Mackay, Wan YIng Shi'u, Alice Bobra, Jim Billington,
Eva Chau, Andrew Yeun, Cecilia Ng and Foon Szeto
Department of Chemical Engineering
and Applied Chemistry
University of Toronto
Toronto, Canada M5S 1A4
Contract No. R805150010
Project Officer
Samuel W. Karickhoff
Environmental Processes Branch
Environmental Research Laboratory
Athens, Georgia 30613
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GEORGIA 30613
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/3-82-019
2.
3. RECIPIENT'S ACCESSION-NO. ,
ORD Report
4. TITLE AND SUBTITLE
Volatilization of Organic Pollutants from Water
5. REPORT DATE
April 1982
6. PERFORMING ORGANIZATION CODE
7. AUTHORIS)
D. Mackay, W.Y. Shiu, A. Bobra, J. Billington, E. Chau,
A. Yeun, C. Ng and F. Szeto
a. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Department of Chemical Engineering and- Applied Chemistry
University of Toronto
Toronto, Canada M5S 1A4
10. PROGRAM ELEMENT NO.
CCUL1A
11. CONTRACT/GRANT NO.
R805150010
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Research Laboratory—Athens GA
Office of Research and Development
U.S. Environmental Protection Agency
Athens, Georgia 30613
13. TYPE OF REPORT AND PERIOD COVERED
Final. 8/77-11/80
14. SPONSORING AGENCY CODE
EPA/600/01
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The volatilization of organic environmental contaminants from water bodies to the
atmosphere was investigated. The general aim was to elucidate the factors that control
the volatilization process and develop predictive methods for calculating volatiliza-
tion rates for various compounds from rivers, lakes and other water bodies under
various conditions of temperature and wind speed.
The report contains both theoretical and experimental studies and a comprehensive
review of the equilibrium physical chemistry and thermodynamics of systems involving
hydrophobic organic solutes and water. .A result of the thermodynamic analysis is the
development of the fugacity approach for calculating multi-phase equilibria applicable
to environmental, partitioning. The approach can also be applied to calculating multi-
resistance transfer as may occur in lakes. Correlations are developed for predicting
or checking consistency of data for aqueous solubility, vapor pressure, Henry's law
constant and octanol-water partition coefficient.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/GlOUp
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)
UNCLASSIFIED
21. NO. OF PAGES
232.
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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DISCLAIMER
This report has been reviewed by the Environmental Research Laboratory,
U.S. Environmental Protection Agency, Athens, Georgia, and approved for publi-
cation. Approval does not signify that the contents necessarily reflect the
views and policies of the U.S. Environmental Protection Agency, nor does
mention of trade names or commercial products constitute endorsement or
recommendation for use.
ii
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FOREWORD
Environmental protection efforts are increasingly directed towards
prevention of adverse health and ecological effects associated with specific
compounds of natural or human origin. As part of this Laboratory's research
on the occurrence, movement, transformation, impact, and control of environ-
mental contaminants, the Environmental Processes Branch studies the micro-
biological, chemical, and physico-chemical processes that control the transport,
transformation, and impact of pollutants in soil and water.
Environmental decisions regarding the control of toxic substances rely
heavily on information about the substances' partitioning between the atmos-
phere, water, soil, sediment, and biota and the effects of degradation processes
such as photolysis, chemical oxidation, and hydrolysis. An important factor
is the volatilization rate because some compounds that degrade slowly in water
are rapidly transformed in the atmosphere. This report examines the volatili-
zation process and presents a predictive method that can be incorporated into
evaluative models of compounds in aquatic environments.
David W. Duttweiler
Director
Environmental Research Laboratory
Athens, Georgia
iii
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ABSTRACT
The volatilization of organic environmental contaminants from water
bodies to the atmosphere was investigated. The general aim was to elucidate
the factors that control the volatilization process and develop predictive
methods for calculating volatilization rates for various compounds from
rivers, lakes and other water bodies under various conditions of temperature
and wind speed.
The report contains both theoretical and experimental studies and a
comprehensive review of the equilibrium physical chemistry and thermodynamics
of systems involving hydrophobic organic solutes and water. A result of the
thermodynamic analysis is the development of the fugacity approach for calcu-
lating multi-phase equilibria applicable to environmental partitioning. The
approach can also be applied to calculating multi-resistance transfer as may
occur in lakes. Correlations are developed for predicting or checking consis-
tency of data for aqueous solubility, vapor pressure, Henry's law constant
and octanol-water partition coefficient.
The experimental program developed a small-scale laboratory system that
is suitable for studying volatilization characteristics of solutes from water
under controlled conditions of temperature, concentration, and turbulence,
and in the presence of co-solutes or sorbents. The test may be used for
volatilization screening purposes. Tests in a 6-m-long by 60-cm-deep wind
wave tank were used to study the volatilization of 11 compounds covering a
wide range of Henry's law constant. The relevant hydrodynamic data were
also obtained. It was concluded that the two-resistance or Whitman model of
mass transfer adequately describes the volatilization process. Correlations
were developed for the liquid and gas phase mass transfer coefficients as a
function of wind speed and solute properties.
Henry's law constant data were obtained for a number of organic solutes
using a previously developed gas stripping system. A novel system was also
developed that is suitable for the measurement of Henry's law constants in
the range of 10~? to 10~^ atm m^/mole. The system essentially involves
batch distilling a solute-water mixture.
Determinations of Henry's law constant are also reported for solutes
in the presence of dissolved organic humic matter. It is concluded that the
dissolved organic matter will rerely be present at concentrations that will
significantly affect solubility and hence Henry's law constant.
This report was submitted in fulfillment of Contract No. R805150010 by
the University of Toronto under the sponsorship of the U.S. Environmental
Protection Agency. This report covers the period August 1977 to November
1980," and work was completed as of November 1980.
iv
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CONTENTS
Foreword • ill
Abstract iv
Figures vi
Tables viii
1. Introduction 1
2. Conclusions 3
3. Recommendations 6
4. Equilibrium Physical Chemistry 7
5. Mass Transfer Phenomena 57
6. General Model of Laboratory Volatilization Systems 82
7. Experimental and Results 88
8. Discussion 141
9. Calculation of Environmental Volatilization Rates 171
10. References 188
11. Symbols 195
12. Glossary 200
13. Index 201
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FIGURES
Number Page
1 Illustrative Pressure Temperature Diagram for a Pure Compound 13
2 Plot of Total Surface Area Versus Molecular Weight 25
3 Plot of Total Surface Area Versus Molar Volume 26
4 Plot of Total Surface Area Versus Carbon Number 27
5 Plot of Total Surface Area Versus Carbon Plus Chlorine Number 28
6 Relationship Between Vapor Pressure and Boiling Point for 31
Selected Solutes
7 Plot of Solubility, Vapor Pressure and Henry's Constant 41
8 Schematic Diagram of Relationships Between Physical Chemical 53
Properties, the Fundamental Quantities which are Inaccessible
by Direct Experimental Measurement Being in the Box
9 Schematic Diagram of Transport Processes 58
10 Illustrative Fugacity Transport Calculation 67
11 Schematic Diagram of an Element of Water Experiencing Exposure to 70
the Atmosphere and Hence Loss of Solute by Volatilization in a
"Roll Cell"
12 Diagram Illustrating the Non-additivity of Resistances during 73
Unsteady State Transfer in a Roll Cell
13 Diagram Illustrating a Possible Experimental Test of the Two 74
Resistance Theory for Compounds of Various H Values
14 Plot of G/A Versus H illustrating Approximately the Regimes 87
Which May Apply during Laboratory Volatilization Experiments
15 General Arrangement of the Small Scale Volatilization Apparatus 1QO
System
16 Plan View of the Small Scale Volatilization Tank 101
17 A Typical Plot of Log Concentration Versus Time for a Highly 102
Volatile Solute (Benzene)
vi
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Number Page
18 A Typical Plot of Log Concentration Versus Time for a 103
Solute of Intermediate Volatility (2 Butanone)
19 A Typical Plot of Log Concentration Versus Time for a 104
Solute of Low Volatility (1 Pentanol)
20 Plot of Mass Transfer Coefficients K Versus Turbulence for 105
the Small Scale Volatilization Apparatus Illustrating Dependence
on Volatility
21 Effect of Temperature on KQ_ for Benzene and Toluene 106
Volatilization in the Small Scale Volatilization System
22 Plot of Log ((C-C^/CC -C^)) Versus Time for Oxygen Transfer in 107
the Small Scale VolatiJization System
23 Diagram of the Wind Wave Tank 109
24 Typical Plot of Linear and Logarithmic Velocity Profiles 111
25 Variation of Surface Drift Velocity with Fetch in the Wind Wave H2
Tank
26 Plot of Final Water Surface Drift Velocity Versus Wind Speed 113
for the Wind Wave Tank Illustrating a Drift Velocity of 2.82%
of Wind Speed
27 Typical Plot of Log Concentration Versus Time for a Volatile 115
Compound (Benzene) in the Wind Wave Tank
28 Plot of Log Concentration Versus Time for Volatilization of a
Low Volatility Compound (1 Butanol) in the Wind Wave Tank
29 Plot of K Versus Wind Speed for Volatilizing Solutes of Various 117
H Values in the Wind Wave Tank
30 Schematic Diagram of the Relative Volatility System for 123
Measuring Henry's Law Constants
1 9Q
31 Diagram of Henry's Law Apparatus -"••"
32 Experimental and Correlated Values of K for Schmidt Number 0.60 16°
33 Experimental and Correlated Values of K. Connected to a Schmidt
Number of 1000 lbl
vii
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TABLES
Number Page
1. Illustrative Fugacity Calculation 14
2. Total Surface Area Correlations 22
3. Boiling Points, Melting Points and Literature Calculated 32
Vapor Pressures at 25 C
4. Henry's Law Constant Correlations 43
5. Physical and Chemical Properties of Selected Compounds 47
6. Solutes Used in the Volatilization Experiments 91
7. Solute Properties 92
8. Small Scale Volatilization Test Results 98
9. Volatilization of Mixtures 99
10. Mass Transfer Coefficients Fom the Wind Wave Tank 120
11. Volatilization Results of Mixtures in the Wind Wave Tank 121
12. Results from the Relative Volatility Apparatus 125
13. Solubility Results 127
14. Henry's Law Constants Results 131
15. Hydrodynamic Results 150
16. Wind Wave Tank Mass Transfer Rates for Benzene and Toluene 152
17. Wind Wave Tank Gas Phase Controlled Mass Transfer Coefficients 155
18. Environmental and Laboratory Values of K_ and K~ 156
19. Constants for Infinite Dilution Activity Coefficients 162
20. Calculated and Experimental Results from the Relative Volatility 164
Apparatus
viii
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SECTION 1
INTRODUCTION
This report contains a description of the results of a three-year research
program into the volatilization of environmental contaminants from water bodies
to the atmosphere. The general objective was to elucidate the dominant
factors controlling the volatilization process and develop a predictive method
by which volatilization rates can be calculated for various compounds under
various environmental conditions.
It is evident that the environmental management of toxic substances
requires a knowledge of the substances' partitioning properties between the
atmosphere, water, soil, sediments, and biota, and also the reaction rates of
processes such as biodegradation,photolysis, chemical oxidation and hydrolysis
which may occur in each environmental compartment. The overall rate of
reaction of the substance, which directly controls its half-life or persistence
in the environment is the sum of the various individual rates of reaction
in each compartment, which are each determined by concentrations of the sub-
stance and prevailing degradative rate constants as influenced by microbial
populations, incident solar radiation, temperature, pH, and other variables.
In many cases, contaminants are introduced into one compartment of the
environment, for example, water, in which there may be relatively slow
degradation. The primary degradative process for that compound may occur
in an adjacent compartment such as the atmosphere. The result in such cases
is that the overall persistence of the substance and the concentrations which
it achieves in the environment are controlled by the rate at which the material
can move from the compartment into which it was first introduced, to the comp-
artment in which it primarily degrades. For example, certain hydrocarbons
may be Introduced as effluents to the water environment in which they are
subject to very slow or zero rates of hydrolysis, oxidation and biodegradation.
Their physical-chemical properties are such that they volatilize into the
atmosphere where they become subject to photolytic degradation rates. In
such cases, the environmental rate of destruction of the compound may be
primarily controlled by the volatilization rate.
An adequate understanding of a substance's environmental dynamics can
thus only be obtained by assembling some form of model in which the accumu-
lation in, reaction in, and transfer between various compartments is taken
into account. The real environment is exceedingly complex and it is possible
to model only very limited sections of it with any degree of validity. An
example could be a stretch of river or a small pond. In such cases, for local
management purposes, it may be desirable to estimate the prevailing volatiliza-
tion rates of contaminants for that particular environment. For example,
attempts have been made to assemble mass budgets for contaminants in water
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bodies such as the Great Lakes of Lake Zurich (1,2). Of more general
applicability and of greater use for regulatory purposes are the "evaluative"
models first proposed by Baughman and Lassiter (3), which have been imple-
mented for 12 contaminants by Smith et al. (4). In this study, the dynamics
of the behaviour and movement of these toxic substances was calculated for
hypothetical aquatic environments consisting of defined volumes of ponds or
rivers. This concept has recently been extended to the "Exposure Analysis
Modeling System" developed at the U.S. Environmental Protection Agency's
Environmental Research Laboratory, Athens, Georgia (5).
In these modelling efforts it is apparent that accurate estimates of
volatilization rate are required for certain categories of compounds. The
object of this study was then to undertake an experimental program to elucidate
the nature of the volatilization process and develop a predictive method
which can be used in such evaluative models or in models of actual sections
of the environment.
In this report, the approach taken is first to discuss the equilibrium
physical-chemistry or thermodynamics of these substances. This is largely
the estimation of the Henry's Law constant or air-water partition coefficient,
which applies to a given substance. Relationships between this constant and
other quantities are explored. This is followed by a discussion of the kinetic
or mass transport phenomena aspects of the issue and is largely concerned with
measurements of mass transfer coefficients. Finally, a general approach towards
calcu^tion of volatilization rates in the environment is presented by combining
physical-chemical properties with transport phenomena information and
environmental data. Some validating experiments are also described.
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SECTION 2
CONCLUSIONS
An experimental and theoretical'study has been undertaken of the process
of volalilization of organic compounds from water bodies to the atmosphere.
Comprehensive reviews are presented of the relevant equilibrium physical den-
sity and mass transport phenomena from which the following conclusions are
drawn.
The fugacity concept which has been increasingly used in engineering
calculations of multi-phase equilibria has been extended to treat environ-
mental partitioning. It is believed that its use facilitates partitioning
calculations which are an important component of the assessment of compounds
of environmental concern. The use of the fugacity concept has also been suc-
cessfully applied to multi-resistance transfer problems as may occur in lakes.
From a consideration of the physical chemical principles underlying a-
queous solubility, vapor pressure, Henry's Law Constant (i.e., air-water par-
tition coefficient) and octanol water partition coefficient (i) forms of cor-
relation are suggested (based largely on previous work) for solubility as a
function of solute melting point, total surface area, molecular weight, molar
volume and carbon number; (ii) a correlation is presented for vapor pressure
as a function of boiling & melting point; (iii) correlations are presented
for Henry's Law constant and (iv) correlations are presented between solubi-
lity and octanol-water partition coefficient.
The equations governing the volatilization process in various configur-
ations of laboratory systems have been assembled and it has been shown that
they reduce to four limiting regimes of equilibrium control, liquid phase
resistance control, gas phase resistance control and non-volatile systems.
Some confusion has existed in the literature by applying equations applica-
ble in one regime to results obtained from another.
The experimental program has resulted in the development of a small
scale laboratory system suitable for the study of the volatilization charac-
teristics of solute under controlled conditions of concentration, tempera-
ture, turbulence and the presence of co-solutes or sorbents. Tests with a
series of twenty organic solutes (covering a wide range of Henry's Law Con-
stants) demonstrated the validity of the two resistance model of volatiliza-
tion and suggested that the preferred method of taking into account solute
molecular size as it influences the gas afed liquidmass transfer coefficients
is by use of the solute's dimensionless Schmidt number (i.e., phase visco-
sity divided by the product of density fcnd .diffusivity) raised to the power of
-0.67 for the gas and -0.5 for the liquid. This approach also incorporates
a temperature dependence.
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It was also concluded that in dilute solutions solute mixtures volati-
lize without significant interactions between the solutes, thus greatly fa-
cilitating multicomponent volatilization calculations.
The effect of temperature is complicated by the possible influence of
evaporating or condensing water which could not be adequately quantified in
this study.
A wind wave tank 6 meters long by 1.2 meters deep was constructed and
operated to study the volatilization of eleven compounds covering a wide
range of Henry's Law Constants. Relevant hydrodynamic data were also ob-
tained, especially velocity profiles from which full stream and function
velocities,surface roughness and roughness Reynolds Number were calculated.
It is concluded that function velocity is the primary determinant of mass
transfer coefficient in gas and liquid phases.
The liquid and gas phase mass transfer coefficients K^ and K m/s have been
correlated for both laboratory and environmental conditions as follows.
Laboratory B^ - 68.2xlO~6Uco1>5ScL"°'5
Environment K. = 34.1xlO~6(6.1-l-0.63U.A)°'5U1rtScT""°'5 (all *n units
-515 -0 67 °f m/s>
Laboratory KQ - 92.4x10 TjJ-^SCg U'0/
• Environment K,, = 46.2xlO~5(6.1-W.63n )°*5n Sc_~°'67
Or 1U ID b
where UM is the free stream velocity (m/s) (generally at a height of 30 cm),
U.. 0 is the 10 metre environmental wind velocity (m/s), Sc_ and Sc_ are the
dimensionless liquid and gas Schmidt Numbers i.e. (viscosity deviaed by density
and molecular diffusivity in consistent units).
More complex forms involving roughness Reynold's Number terms have also
been developed which give a slightly better fit of the data, but the extra
complexity is not regarded as justified at present. These equations which have
a sound basis in fluid mechanics predict that environmental mass transfer coef-
ficients will be lower than laboratory values because of the generally lower
drag coefficients which in turn cause lower friction velocities in the environ-
ment. It is believed that at short fetches when the wind is actively accelera-
ting the water surface layers there are higher drag coefficients and friction
velocities, greater turbulence and hence more rapid mass transfer. This obser-
vation is borne out from an examination of the few available environmental mass
transfer coefficients, which are reproduced well using the correlations.
There remains some doubt about the IL and K_ values at low wind speeds
(which were not studied in this work) and it is suspected that the correlations
will require some modification to be more accurate at these conditions.
The use of the Schmidt number quantifies the effects of molecular size
and temperature.
The data generated in the wind wave tank for eleven solutes covering a
range in Henry's Law Constants provide further evidence validating the two re-
sistance approach.
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A preliminary experiment into the effect of interfacial films on vola-
tilization is described and a theoretical framework is suggested (based on
previous work) which is believed to be capable of describing this phenomenon.
A novel system is described far the measurement of Henry's Law Conr-
stants in the range of 10 to 10 atm m /mol which involves measuring the
relative volatility of the solute and water. It is thus complimentary to
the gas stripping technique which is better applied to compounds of higher
Kenny's Law constant. Determinations are presented for the solutes alone
and in the presence of dissolved organic (humic) matter. The aqueous solu-
bility of selected organic compounds was also measured in the presence of
similar organic matter using a generator column technique. It is concluded
that dissolved organic matter present at concentrations likely to be encoun-
tered environmentally does not significantly affect solubility and hence Henry's
Law constant. Allowance must be made for sorbents and high concentrations
of electrolytes as may be encountered in certain environments.
The results of the program suggest that volatilization rates can be
calculated for most environmental conditions with an acceptable accuracy.
Some aspects of tliese calculations applied to rivers and lakes are reviewed.
It is suggested that when the environmental volatilization characteristics
of a solute are to be determined the optimal strategy is to obtain data for:
aqueous solubility
vapor pressure and boiling point
Henry's Law Constant
octanol water partition coefficient
molar volume (experimentally or by additive volumes)
(and hence Schmidt Numbers)
The physical chemical data should be subjected to an internal consistency
check. An example is given for naphtahlene.
Volatilization rates can then be measured in the small scale (6 liter)
system to obtain K^ estimates at the required temperature, preferably with simul-
taneous measurement of KQL for solutes of similar Henry's Law Constant (e.g.
toluene, an alcohol or oxygen; and the values again checked for consistency with
the two resistance model. If desired distilled water, salt water or other natural
waters containing organic or mineral matter can be used at any desired temperature
and humidity level.
The resistance to volatilization as characterised by K_ and Kfi combined with
the appropriate fugacity capacities can then be compared witn other resistances
as may for example be offered by depths of water column to establish an overall
resistance and hence a steady state flux.
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SECTION 3
RECOMMENDATIONS
For any compound of environmental concern, reliable aqueous solubility, vapor
pressure, Henry's Law Constant and octanol water partition coefficient data
should be sought and the values checked for internal consistency.
Of particular interest are data for highly hydrophobic compounds such as
PCB's which have apparently anomalous solubility-octanol water partition coef-
ficient relationships.
The correlations developed here for solubility, vapor pressure and hence
Henry's Law Constants should be improved to achieve higher accuracy by improving
(i) the activity coefficient - molecular area relationship and (ii) the boiling
point-vapor pressure relationship. To achieve this accurate vapor pressure data
are required for higher boiling organic solutes. Ultimately, it is believed that
these properties can be predicted with acceptable accuracy from molecular
structure.
The further systematic study of the effects of temperature, co-solutes and
turbulence on volatilization rates of various organic solutes is justified to
provide additional validation of the predictive equations derived here, especially
at low wind speeds.
A study of the effect of surface organic microlayers or films of various
compositions and various thickness is desirable to test the theoretical approach
suggested here.
In situ measurement of volatilization rates from ponds is desirable to vali-
date the predictions developed here.
Further experimentation using the "relative volatility" method for deter-
mining Henry's Law Constants is desirable, especially for solutes in which water
is quite soluble and for which the assumption that the Henry's Law Constant is
simply the ratio of vapor pressure to solubility is believed to be erroneous.
The magnitude of this error and corrective methods should be studied.
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SECTION 4
EQUILIBRIUM PHYSICAL CHEMISTRY
CRITERIA FOR EQUILIBRIUM BETWEEN PHASES
Volatilization of a substance from a water body to the atmosphere occurs
only when the concentration of the substance in the atmosphere is lower
than the (hypothetical) concentration which is in equilibrium with its
concentration in the water body. Determining whether or not volatilization
occurs and the direction of transfer between the two phases thus requires
knowledge of the equilibrium concentrations in the two phases. Further, in
kinetic expressions developed later, the conventional approach is to postulate
that the rate at which material moves between phases is proportional to the
displacement from equilibrium. Equilibrium data are thus critically important
in controlling the direction and rate of transfer.
When a solute, such as benzene, achieves equilibrium between air and
vater phases.it adopts different concentrations in each phase. The ratio of
these concentrations, i.e. the air-water partition coefficient can be
expressed in various forms, the most convenient being the Henry's Law constant
(H atm m /mol) which is the ratio of partial pressure in the atmosphere (P atm)
to concentration in water (C mol/m ).
In environmental studies, several such partition coefficients are useful,
for example, bioconcentration factors between water and aquatic biota,
octanol-water partition coefficient, and sorption coefficients. For each
solute, there can be therefore, a partition coefficient for each pair of
environmental phases. It is more illuminating and intellectually more
satisfying to discuss these equilibrium partitioning situations in terms of
the fundamental quantity which controls the differing concentrations. In
his classical studies of phase equilibrium thermodynamics, Gibbs showed that
diffusive equilibrium of a solute between two phases occurs when the system
is at maximum entropy, or for constant temperature and pressure conditions
is at minimum free energy, or when the chemical potential of the solute in
in both phases are equal. This topic is discussed fully in standard texts
in thermodynamics, for example that by Prausnitz (6). Later, Lewis intro-
duced the more convenient criterion for equilibrium between phases of
fugacity. Whereas chemical potential has units of energy per mole which is
conceptually difficult to grasp, fugacity has units of pressure and can be
viewed as the escaping tendency which a substance exerts from any given phase.
In the atmosphere, the fugacity is normally equal to the partial pressure of
the substance. Equilibrium is achieved between two phases when the escaping
tendency from one phase exactly equals that from the other. There is
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inevitably transfer or exchange between the two phases, however, the net
rate of exchange is zero. A most convenient property of fugacity is that
it is usually linearly related to concentration, at least at the low concen-
trations which normally apply to environmental contaminants. It is thus
possible to write a fugacity concentration relationship of the form
C = fZ
3
where C is concentration in (mol/m ), f is fugacity (atm) and Z is a
fugacity capacity with units mol/m atm.
It may be helpful for conceptual- purposes to consider the analogous
situation of equilibrium of heat between two phases. Heat achieves
equilibrium between two phases at different heat concentrations expressed
as J/m . The criterion of equilibrium in this case, is that the temperature
of the two phases are equal. Temperature, like fugacity, is a potential
quantity which determines the state of the phases with respect to equilibrium.
The relationship between heat concentration and temperature is the simple
heat capacity relationship,
CH " TZH
where C is heat concentration (J/m ) , Z.,is a volumetric heat capacity
(J/m K) (which is actually the product or the more commonly used mass heat
capacity and the phase density), and T is temperature (K).Whereas heat tends
to accumulate in the phases where its heat capacity is largest, mass tends to
accumulate in phases where its fugacity capacity is largest. It transpires
that hydrophobia organics thus tend to partition into lipid phases where
their Z value is large. This topic has been reviewed by Hackay (7).
If there are two phases, (subscripted 1 and 2) then equilibrium of a
solute will be reached when the fugacity of the solute is equal in both
phases
i.e. f. » f~
thus C1/Z1 - C2/Z2
or VC2 - Z;L/Z2 - K12
It is apparent then that the dimensionless partition coefficient controlling
the distribution of the substance between the two phases (K,-,) is thus
merely the, ratio of the fugacity capacities. The elegance of this approach
is apparent if one considers a ten phase system in which there are potentially
10 x 9 or 90 partition coefficients which may apply. These partition
coefficients are, of course, constrained in value with respect to each other.
There are, however, only 10 fugacity capacities, and the 90 partition coeffic-
ients are merely all possible ratios of these 10 values. Expressing equilib-
rium in terms of these fugacity capacities is also more convenient because
it separates the escaping tendencies of each phase and facilitates the
calculation of these quantities from other related thermodynamic data. Usually,
much of the uncertainty about the value of an air-water partition coefficient
lies in the value of Z in the water.
The approach taken here is to calculate Z values for solutes mainly in
the atmosphere* in aqueous solution, in sorbed state, in octanol
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solution, and in biota. The ratios of these quantities then give the required
partition coefficients, in particular, the related Henry's Law constant,
which is of primary interest in volatilization calculations.
It is believed that the "fugacity approach" for elucidating the parti-
tioning, reaction and transport characteristics of environmental contaminants,
which has been developed as part of this research program, may be of value in
the environmental management of toxic substances. It has the advantage of
being conceptually simple, of being applicable at various levels of complexity,
and of providing guidance as to the required accuracy of physical, chemical,
reaction and transport data which may be sought by regulatory agencies prior
to commercial manufacture and use. Most substances will partition into a few
environmental compartments, be degraded by a few processes and be subject
only to a few significant transport routes. Obviously then, relatively high
accuracy is required for only a few properties, but which few is not apparent
until a preliminary assessment has been undertaken. A particularly attractive
and economic option is thus to estimate physical property data,then refine
these estimates by experiment as the need for refinement is demonstrated.
It is hoped that this section will be of value in this subject area by
assembling a reasonably complete account of the phase equilibrium thermo-
dynamics of aqueous solutions of organic compounds, with some attempt at
correlation and estimation of environmentally relevant properties.
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FUGACITY CAPACITIES
The Atmosphere
In the vapor phase the fugacity is rigorously expressed by
f - y 4> PT ~ P
where y is the mole fraction, PT is the total pressure (atm) (here atmospheric
pressure) and is the fugacity coefficient which is dimensionless and is
introduced to account for non-ideal behaviour. Fortunately at atmospheric
pressure is usually close to unity and can thus be ignored. The exceptions
are solutes such as carboxylic acids which associate in the vapor phase.
The fugacity is thus equivalent in most cases to the partial pressure P (atm).
It should be noted here that this equation assumes the solute to be in trulv
gaseous form, not associated with particulates . Now concentration C (mol/m )
is related to partial pressure through the gas law as
C m n/v - p/RT = f/RT - fZ
Thus Z for vapors is simply 1/RT where RT has a value of about 24 atm/(mol/
liter) or 0.024 m atm/mol, corresponding for example to R of 82 x 10
m atm/mol K and T of 293 K or 20 C. Z> is independent of the nature of the
solute or the composition of the vapor (for non-association solutes and low
or atmospheric pressure condition) and. has a value of typically 41 mol/m atm.
The temperature dependence of Z is obvious.
Water Bodies
In aqueous solution the fugacity is given by
where x is the mole fraction, Ps is the vapor pressure of the pure liquid sol-
ute at the system temperature and y is the liquid phase activity coefficient
on a Raoult's Law convention (not a Henry's Law convention). By this
convention when x is unity y is also unity and f becomes the pure component
vapor pressure. Generally for non-ionizing substances y increases as x
decreases to an "infinite dilution" value as x tends to zero. This relation-
ship between x and y is often of the form
In y - K(l-x)2
In most environmental situations x is quite small thus In y can be equated
to K without serious error. This near-constancy in y leads to the very
convenient near linear relationship between C and f, reflected as a constant
value of Z.
10
-------
The relationship between £ and C to give Z can be obtained by writing
for infinite dilution conditions
Z = C/f = C/P - 1/H = x/vf = l/vyPS
3
where vis the molar volume (m /mol) of the solution which is approximately
18 x 10 m /mol. For water Z^ is thus simply the reciprocal of the Henry's
Law Constant H. This -is in accord with the definition of H which is the
constant by which liquid concentration is multiplied to give partial pressure
P, which is here equal to fugacity, i.e.
P - HC
Since H is of such importance in volatilization calculations it is desir-
able to elucidate certain conditions under which this simple approach may be
applied incorrectly.
First, these equations are applicable only if the solute is in truly
dissolved forms at a concentration less than or equal to saturation. Often
the solute is present environmentally in solution in a sorbed form associated
with biota or suspended mineral or organic matter. Very hydrophobia compounds
such as PCBs or PNAs may be present in colloidal form at a total concentration
in excess of their solubility. Such forms of solute are effectively in another
phase and do not contribute to the solution fugacity. It is thus essential
to ensure that a measured concentration is truly dissolved, or if this is not
the case, calculate the fraction which is dissolved.
Second, as discussed later, there are several methods of measuring or
estimating H (and hence Z for water). In principle these reduce to the
direct or indirect measurement of P and C at equilibrium or to the separate
calculation of P_as the saturation vapor pressure (Ps) and C the solubility
of the solute (C ). This latter method is very convenient since solubilities
and vapor pressures are widely available in the literature. Unfortunately the
pure solute may undergo a phase transition (melting, boiling or crystalline)
near environmental temperatures thus the published P and C data may refer
to different phases. For example the solubilities published for naphthalene
are usually of the solid, while the vapor pressures are of the liquid. In
the case of PCBs the solubilities are usually of the pure isomers, most of
which are solid, whereas the vapor pressures are of the liquid mixtures which
are essentially subcooled. Both measurements must refer to the same phase or
erroneous results will be obtained.
Techniques are emerging by which y can be calculated from molecular
structure. If such data are available H can be deduced as vyPS provided that
data are available for P , the liquid solute vapor pressure at the system
temperature. This vapor pressure may be experimentally inaccessible if the
solute is solid or gas at this temperature i.e. the system temperature lies
outside the range from triple point to critical point. In such cases P is a
hypothetical quantity whose value can be inferred by extrapolating the
liquid vapor pressure curve below the triple point or above the critical point.
It is erroneous to use a solid vapor pressure in this calculation.
11
-------
This issue is discussed in more detail later.
Sorbed Phases
The importance of calculating Z for sorbed phases lies in the necessity
of discriminating between truly dissolved and sorbed material as: are often
measured in total by environmental analyses. The approach taken below differs
from that presented previously by Mackay (7) and it is believed to be simpler
and more rigorous.
Sorption equilibrium are usually' expressed as equations or isotherms
relating dissolved to sorbed concentrations . Examples are the Freundlich,
Langmuir or Linear equations. For most hydrophobia compounds at concentrations
well below their solubilities the Linear equation is adequate (Karickhoff
et al, 8), namely
X - KyC
where X is the sorbed concentration, here expressed in moles solute per 10 g (Mg)
sorbeng (wet or dry) and 1C is a sorption coefficient with units of m water
per 10 g sorbent. The equation is often expressed in mass concentration units
(X in g/Mg or Ug/g and C in g/m or mg/L) in which case an identical numerical
value is obtained.
If the sorbent concentration expressed as volume fraction is S and its
density is p (g/cm or Mg/m ) then its concentration is Sp Mg/m (or g/cm ) .
This concentration is-typically 10" g/cm or 10 mg/L thus it is convenient
to record data as g/m or 10 Sp.
The concentration of sorbed material (c ) expressed as mol per m3 of
sorbent is thus Xp mol/m3, s
At equilibrium^ the fugacities of the sorbed and dissolved material must
be equal, thus if Z is the sorbed phase fugacity capacity
S
f - HC - C /Z
s s
thus Zg • Cg/HC - Xp/H(X/Kp)
the group Kpp is dimensionless and is actually the partition coefficient
expressed as a mols per unit volume ratio.
If in 1.0 m of solution containing a low concentration of sorbent of
volume fraction S the fugacity is f then the concentration of dissolved material
is Zf or f/H mol/m thus there are f/H mol dissolved. The sorbed concentration
is fZ or C mol per m of sorbent or a total of fZ S mol or fK_,pS/H. The
total8 amount is thus s
f/H + fKppS/H or f/ (1 + KppS)H
and the fractions dissolved and sorbed become
dissolved [(f/H)]/[f /(.I + K pS)H] - 1/0. + K pS)
12
-------
sorbed (fKppS/H)/£/a + K pS)H - KppS/(l
If the sorbent concentration is expressed as S1 g/m (or mg/1) this is
»o,, . ,
equivalent to 10 Sp and,the group K_pS in these equations becomes the more
conventional group 10~ K_S'.
This analysis can be applied also to sorption on atmospheric particulate
matter but caution must be exercised in situations when the sorbed solute is
physically trapped or enveloped in the particle. This may occur, for example,
to polynuclear aromatics formed during combustion and associated with (or
inside) soot particles. Such materials are unable to exert their intrinsic
fugacity outside the limits of the particle and thus are not in a truly
equilibrium situation.
For biota a bioconcentration factor K_ is used instead of the partition
coefficient. If it can be expressed as a ratio of the concentration in the
biota (e.g. fish) on a wet weight basis in which case it is identical to 1C,.
If expressed on a wet volume basis it is rigorously analogous to the group
Kpp where p is the fish density but since p is near unity the difference
is dimensional rather than numerical. If a dry weight or lipid content basis
is used a suitable concentration factor must be applied.
In summary the term Z for sorbing phases is *L,p/H and the problems
become that of estimating K_? usually some relationship being sought to
the solute's octanol-water partition coefficient.
Octanol Phase
The importance of Z for octanol (Z ) lies in the utility of the octanol
water partition coefficient K as an indicator of hydrophobicity as
documented in the many studies of Lea and Hansch (9, 10).
Following the example of water, it can be shown that Z is 1/v y PS
where y is the activity coefficient of the solute in octanSl and
Ps is the vapor pressure of the liquid solute at the system temperature
and v0 is the molar-volume of octanol saturated with water.
Of greatest interest is the octanol-water partition coefficient K
expressed as a concentration ratio (mol/m ) or (g/m) i.e. C /C when°w
the fugacities are equal ° w
K - C /C - Z /Z - v y /v y
ow o w o w w w o o
the vapor pressures cancelling. For most hydrophobic organic compounds
YQ appears to be fairly constant in the range 1 to 10 and of course v
and VQ are also constant. The value of K is thus dominated by y . wSince
y controls aqueous solubility it follows°?hat solubility and K ¥re closely
related. This issue is discussed in more detail later. ow
Pure Solid and Liquid Phases
For pure substances (solid or liquid) the fugacity is the vapor
pressure of the pure substance. This situation rarely occurs environmentally
13
-------
but is interesting thermodynamically and is included here for completeness.
The concentration C of the material is the inverse of the molar volume
v (m / mol). The saturation vapor pressure of the pure substance (solid or
liquid) P is approximately equal to the fugacity at environmental pressures,
except for some associating species such as carboxylic acids. Z is thus
given by
H = f/C
PS/v
C/f
l/PSv
The temperature dependence of Z arises primarily from the variation in
P which is conventionally quantified by Antoine Equations
In PS = A - B/(T + C)
The temperature dependence of v is slight and can be obtained from density-
temperature data.
Illustrative Calculation of Fugacities
- If a system of i phases is in equilibrium each phase having a volume V
m and a fugacity capacity Z, then the concentration in each phase C. is
fZ. where f is the prevailing common fugacity. The amount of material in each
phase M. is thus C.V or fZ.V and the total amount M_ is fIZ V . If the total
amount is known, trie fugacity can thus be calculated as
Hence the individual values of C. and M can be deduced.
For example if we consider a system consisting of air, water, suspended
solids and biota containing a fixed amount of a hydrophobic organic compound
it is possible to deduce the partitioning behaviour as illustrated below in
Table 1.
TABLE 1. ILLUSTRATIVE FUGACITY CALCULATION
Compartment
Air
Water solution
Suspended
solids
Aquatic biota
Total
Volume V
m3
10000
1000
0.015
0.005
Fugacity
capacity Z
3
mol/m atm
41
500
5 x 106
3 x 106
zv
mol/atm
410 x: 103
500 x 103
75 x 103
15 x 103
1000 x 103
C
mol/m
410 x 10"6
5000 x 10~6
50
30
M
mol
4.1
5.0
0.75
0.15
10.0
14
-------
Volumes are assumed as given in Table 1. If the substance has a vapor
pressure of 0.02 atm and an,,aqueous solubility of 10 mol/m, its Henry's Constant
H is 0.02/10 or 0.002 a'tm m /mol,thus Z becomes 500 mol/m atm. Z for the
atmosphere is typically 41 mol/m atm. WIf the suspended solids have a density_g
of 2 g/cm and are present at 30 mg/L or g/m the volume fraction S |s 15 x 10
thus V becomes SV or 0.015. -If the biota have a density of_£ g/cm and a
concentration of 5wmg/L or g/m the volume fraction is 5 x 10 and VB is
0.005. A substance of K equal to 50000 may have a 1C of approximately 5000
and a 1C of 6000, thus Zowis 5000 x 2/0.002 or 5 x 10 and ZB is 6000 x 1/0.002
or 3 x 10 . These K_ an! K_ data could be measured experimentally or deduced
from correlations.
The individual and total values of ZV can then be calculated. If the total
amount of :ma.terial M_ is 10 mols, the fugacity can then be deduced as
M_/£ZV or 10~ atm. The individual concentrations can then be deduced as
fz or C. and the individual amounts as C.M.. In this case the compound
partitions fairly equally in amount between the air and water, with the air
having a larger volume by a factor of 10. The concentrations in the suspended
solids and biota are very high but in amount they are |% of the total. , In
the aqueous phase the total concentration of 5.9 mol/m is 85% in solution 13%
sorbed on suspended solids and 2% bisorbed.
q
The concentration of 50 mol/m on the solids is equivalent to 25 mol/Mg,
a factor of 3 K_ (i.e. 5000) greater than the water concentration
of 5 x 10~-* mol/m . Likewise the biotic concentration of 30 mol/m is a
factor of K^ (i.e. 6000) greater than the water concentration.
Summary
This example illustrates the general procedure which can be followed when
calculating concentrations in environmental compartments. It is of fundamental
importance to volatilization calculations in several respects.
Before any estimate can be made of the rate or even direction of transfer
between air and water phases it is essential to have concentration data which
can be translated properly into the appropriate fugacities in order to determine
the phase of lowest fugacity into which material will tend to transfer.
A knowledge of the breakdown of the total aqueous (and indeed atmospheric)
concentrations into truly dissolved and sorbed forms is essential.
The actual amounts present in each phase provide a useful indication of
the importance of the partitioning. In this example the highest concentrations
on a mass per unit mass basis are in the biota from which an erroneous
deduction can be made that biota contain most of the solute. Generally it is
only in the case of highly hydrophobic compounds present in very turbid waters
that an appreciable quantity of the material in the water column is sorbed.
A useful rule of thumb is that the sorbed and dissolved forms are approximately
equal when the sorbent is at a concentration of 10 /K parts per million.
15
-------
AQUEOUS SOLUBILITY
Theoretical Background
It often seems strange that aqueous solubility plays such an important
role in volatilization calculations since most compounds are (fortunately)
present in the environment at levels well below their solubility limits.
The importance lies in the fact that the Henry's Law Constant or the
partitioning coefficient into the air is inversely proportional to solubility
i.e. H = PS/CS'
Compounds of low vapor pressure (such as DDT) can have high H values and
thus tend to volatilize despite their low vapor pressures because of their
low solubility. Certainly, a low vapor pressure impedes the absolute
volatilization rate but if the compound is sparingly soluble it is likely to
be present at a low concentration and very little of it may have to volatilize
in order that the concentration drops by a significant factor. The volagiliza-
tion "half life" of a substance thus tends to be reduced by increasing P and
decreasing CS. In a homologous series of increasing molecular weight there is
a tendency for Ps and CS to fall and the overall effect on H is not clear.
Conceptually it may be useful to regard solubility as the inverse of
hydrophobicity thus decreasing solubility or increasing hydrophobicity tends
to drive a solute out of solution by volatilization.
The solubility of a pure, non-ionizing, sparingly soluble liquid solute
can be expressed by 'writing the fugacity equation for the pure liquid and
the solution yielding
f - Ps - XY PS thus x * 1/Y
w w
where x is mole fraction, y is activity coefficient and P is vapor_greasure.
Converting to mol/m units using the water molar volume v (18 x 10 m /mol)
gives
Cs = x/v - 1/Y v
w w-w
It is assumed here that the concentration of solute in water is so low that
the molar volume of the solution equals that of water and that the solubility
of water in the liquid solute is negligible.
For solid solutes the equation is more complex since the fugacity is
that of the solid f whereas the vapor pressure P remains that of the liquid,
here termed f for convenience. It follows that
f-fg=xYwfR thus x-(fs/fR)/Yw
and Cs - (fs/fR)/Ywvw
The group (f /f_) is termed the fugacity ratio and is essentially the
ratio of the vapor pressures of the solid to the subcooled liquid. It is
unity at the triple point but less than unity below that temperature. Its
importance lies in the observation that it causes a marked reduction in
16
-------
solubility of solid organic compounds when compared to similar liquid compounds.
Further, the higher the melting point the lower the fugacity ratio (because
the slope of the solid P-T line is greater than that of the liquid P-T line
on a phase diagram as is illustrated in Figure 1.
It can be shown (Prausnitz 6 ) that the fugacity ratio (f /£ ) can
be expressed as
ln(fs/fR) - -AHF(1/T - 1/TM)/R
where AH is the enthalpy of fusion ( J/mol) , T and TM are the system arid solute
melting point temperatures (K) and R is the gas constant (8.3 J/mol K) . Since
the entropy of fusion AS at the melting point is AH /T and is found to be
fairly constant it is convenient to write
ln(fg/fR) * -AVTM -T)/RT
Yalkowsky (11) has shown that for many organic compounds AS^, is approximately
13.6 entropy units, thus ASp/R is approximately 6.8, thus
ln(f /fR) = -6-8(TM - T)/T = 6.8(1 -
or at 25°C,i~e.T =298 K,
ln.(f /£„) - -0.023(1 - 298)
S B. rt
or log(£fl/fR) = -0.01 (TM - 298)
Now since lnCSisln(f /£ ) -Iny -Inv it follows that solubility can be
estimated if data for T and y are available. Yalkowsky and Valvani (12) have
shown that IIVYW varies linearly with computed total surface area using the solu
bility data for polynuclear aromatics. Techniques for correlating activity
coefficients and hence solubility are discussed in more detail later in this
section. Such correlations are invaluable for predicting solubility and
checking experimental values.
As part of this work a similar approach was taken for PCBs using ISA data
kiridly supplied by Yalkowsky and Valvani, the method being given in .3 recently
published paper on this topic. (Mackay et alls ).
For gaseous solutes i.e. when the system temperatures exceed the triple
point, the vapor pressure becomes hypothetical and the pure solute has a
fugacity equivalent to its partial pressure. Solubility data are usually
reported as Henry's Law Constants, Bun sen or Ostwald coefficients.
In summary, the aqueous solubility of a non-ionizing sparingly soluble
compound is dependent on two quantities, its activity coefficient in aqueous
solution (y ) which is a measurement of its hydrophobicity and if the com-
pound is solid at the system temperature the solubility also depends on
melting point. Theoretically based methods are available to correlate
solubility as Influenced by these quantities. The final equation for C using
18 x m~ m /moj. for v is thus
In CS = 6.8(1 - TM/T) - In YW + 10.95
17
-------
FIGURE 1
ILLUSTRATIVE PRESSURE. TEMPERATURE
DIAGRAM FOR A PURE COMPOUND
co
V)
SOLID
PHASE
SUBCOOLED LIQUID
VAPOR PRESSURE OR
FUGACITY £„
£R--*
CRITICAL POINT
BOILING POINT
LIQUID VAPOR
PRESSURE OR FUGACITY
MELTING OR TRIPLE
POINT
VAPOR
PHASE
FUGACITY RATIO
o,,
w. K
SOLID VAPOR PRESSURE OR FUGACITY f.
TEMPERATURE
18
-------
If the solute is totally miscible or even quite soluble in water i.e.
greater than 5% mole fraction, this simple analysis breaks down because
the solute phase properties are influenced by the dissolved water. This
usually occurs when YW has a value less than 20. Fortunately, when consider-
ing environmental volatilization such compounds are rarely of interest be-
cause they volatilize very slowly as can be demonstrated by a simple
calculation.
If the compound is present at a concentration of 1 g/m3 and has a
molecular weight of 100 g/mol its molar concentration is 0.01 mol/m3
equivalent to a mole fraction (x) of 0.01/55000 or 2 x 10~7. If its
activity coefficient is 20 and its vapor pressure is 0.025 atm then its
fugacity f is the product of these three quantities or 1 x 10~7 atm. The
vapour pressure of water under these conditions may be 0.02 atm thus the
equilibrium ratio of solute to water in the air is 5 x 10~6 which is 25
times the aqueous concentration. It follows that to evaporate most of the
solute in a water body requires evaporation of about l/25th of the water
present, a process which will take a considerable time except in shallow
ponds. Further, compounds of this type, which include alcohols, phenols,
esters, ketones, etc. tend to be biodegradable or subject to hydrolysis
thus volatilization is usually a less significant environmental pathway.
If values for y are desired the best approach is to use vapor-liquid
equilibrium data as reviewed by Reid et al ( 14 ). Group contribution
methods outlined in that reference can be used to estimate y to a sufficient
degree of accuracy for most environmental purposes.
Effect of Co-solutes on Solubility
It is well established that the solubility of a compound is influenced
by the presence of other dissolved compounds. Suspended matter is best
treated as a sorption phenomenon.Of primary environmental interest are three
classes of compounds, electrolytes, other dissolved organics and surfactants.
Most electrolytes cause a "salting out" effect, i.e. they reduce the
solubility of the organic solute. The mechanism by which this occurs is
not entirely clear but it appears that these electrolytes alter the water
structure to reduce the volume of the "holes" available for incorporation
of organic solutes. The conventional approach for correlating this behaviour
is to use the Setschenow equation (15 ) to describe the relationship between
solubility and electrolyte concentration in terms of a single constant which
is essentially the slope of the plot of log of the ratio of solubility in
electrolyte solution to that in pure water against molarity. The constant
depends on the electrolyte and on the molar volume of the solute organic and
can be correlated using the McDevitt-Long approach ( 16 ). An example of
the use of these methods has been reported by Aquan-Yeun et al ( 17 ).
To give a general indication of the magnitude of this effect, most hydro-
carbons have a solubility in sea water (approximately 30 g/L electrolyte)
of 70 to 80% of their pure water values. This may be important in marine or
estuarine waters, the implication being that since the solubility is reduced
by some 25% the Henry's Law Constant will be increased by a similar amount,
thus possibly promoting faster volatilization. In practice this effect is
probably not very important for two reasons. Most compounds which volatilize
rapidly have high Henry's Law Constants and (as is discussed later) volatilize
under liquid"phase, diffusion controlwhich, proceeds at a^rate^independent of,
19
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that constant. Only when the compound volatilizes slowly under gas phase
control does this effect become significant. From an environmental quality
viewpoint the electrolyte concentrations necessary to significantly affect
solubility are so large that these electrolytes in themselves probably have
a more significant detrimental effect on environmental processes. Finally,
the concern is occasionally expressed that in estuaries the mixing of salt
and fresh water will reduce the solubility of a dissolved compound to a level
such that it precipitates. This is very unlikely since it requires that the
solute be present at close to its solubility (which fortunately rarely occurs)
and the dilution by sea water inevitably results in a drop in concentration.
Surface active materials "solubilize" organic solutes, which is of
course the principle of detergency as reviewed in the many texts on inter-
facial phenomena such as Davies and Rideal (18 ). This phenomenon is
perhaps best regarded as partitioning into a separate phase which is stabilized
by the surfactant and can act as a partitioning reservior. Such "phases"
tend not to form appreciably below a critical micelle concentration
(cmc). Below the cmc the solubility is only slightly increased, however
above the cmc when micelles form they are capable of accommodating solutes,
especially organic solutes similar in composition to the organic part of the
surfactant, thus apparently increasing the solubility. Th""s topic has been
reviewed by Makenjee and Mysels (19 ) and recent data given on solubili-
zation of aromatic hydrocarbons by Almgren et al ( 20 ).
The simplest approach is to assume that below the cmc, solubility (and
hence Henry's Law Constant) is unaffected by the presence of surfactants.
Above the cmc the situation is very complex and although it is possible to
assemble partition equilibria equations using what are essentially micelle-
water partition coefficients it seems unlikely that this appraoch could be
used for environmental modelling or prediction purposes because of the
doubtful nature, number and concentrations of the natural and anthropogenic
surfactant molecules and the various solutes present which will compete for
accommodation in the micelles. Fortunately the use of biodegradable
detergents has substantially reduced their environmental concentrations to
levels,usually below the cmc.
More difficult is the problem of assessing the effect on solubility of
other organic solutes. A common procedure for preparing an aqueous solution
of a sparingly soluble compound is to first dissolve it in an organic liquid
such as methanol or acetone and then mix this solution with water. It is thus
possible to obtain solutions in water at concentrations exceeding the water
solubility. It can be argued therefore that the solubility of say napththalene
in water can be increased by adding some methanol or acetone. The extension
of this argument to environmental conditions is that the presence of natural
or anthropogenic organic material will increase the solubility of the solute
and thus reduce the Henry's Law Constant. Most natural waters contain con-
centrations of dissolved and suspended organic matter, notably fulvic and
humic acids whose chemical structures are poorly characterised. It is sus-
pected that these compounds may enhance solubility although definitive
solubility determinations are lacking. The real issue is the magnitude of
this effect rather than its existence. Accordingly some experiments were
undertaken to measure the magnitude of this effect. This involved measuring
the solubility of organic solutes in the presence of low concentrations of
other organic compounds, including fulvic acid, using a modified "generator
column" technique. The results of this study and their implications are
discussed later.
20
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A final concern is the observation that when saturated solutions of
sparingly soluble organic solutes are prepared there may be solubilization
or "accommodation" of concentrations of the solute in the range up to 10 g/m3
in the form of colloidal or emulsified particles. This was first noticed by
Peake and Hodgson ( 21 ) for hydrocarbons. Membrane filtration removes
some (but not all) of this material and the apparent solubility depends on
the filtration efficiency. This effect is responsible for many erroneous
solubility data reported in the literature. Preparation of solutions of
such solutes is best done under conditions such that no colloid material
forms. Further, when very small organic particles are present the solubility
may be enhanced because of the interfacial curvature effect. Although
important in areas such as petroleum -reservoir engineering such effects are
of marginal environmental interest because they can only occur at saturation.
A system of unsaturated solution and a separate phase of organic solute in
particle form is inherently unstable and will tend to move towards true
solution. The effect is thus unlikely to be important in natural waters where
most solutes are present at concentrations several orders of magnitude below
their solubilities.
There has been a considerable amount of erroneous solubility data
published in the literature, especially for sparingly soluble compounds
such as hydrocarbons and halogenated hydrocarbons. The errors usually
arise from either analytical difficulties associated with the quantification
of small quantities of solute (which may sorb appreciably on glass surfaces)
or the improper preparation of saturated solutions. Fortunately modern
"generator column" techniques coupled to liquid chromatographic analysis
are capable of high accuracy. Such methods are described later.
Activity Coefficient Correlations and Predictions
As was discussed earlier in this section, the aqueous solubility of a
hydrophobic organic solute depends on two factors, its melting point and en-
tropy of fusion (which controls the fugacity ratios f /fR) and the activity
coefficient YW« The former quantity can be estimated using Yalkowsky's va-
lue for the entropy of fusion. The latter (Y ) is a function of molecular size
and the nature of the solute interaction withwwater. Estimation and corre-
lation techniques for^ are developing, the simplest approach being to exa- .
mine the variation in Y for a homologous series and develop equations or
'rules" in which molecular fragments are regarded as being responsible for
contributions. This approach has been successfully used to correlated octanol
-water partition coefficient and to estimate Y for some systems of engineering
interest, a review being given by Reid et al (14). Here we examine the status
of such techniques and undertake some further development.
Greatest success has been obtained in correlating In YW with total mole-
cular surface area (TSA, which is conventionally expressed in square angstroms)
using an equation of the type
In Y - A + B (TSA)
w
Table 2 lists values of A and B for various homologous series, the stu-
dies being reported in several publications by Yalkowsky and co-workers. Un-
fortunately, the computation of TSA is a relatively sophisticated procedure
and some doubt may arise as to actual values depending on the conformation of
the molecule. There is therefore an incentive to correlate Y with a more
w
21
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TABLE 2
TOTAL SURFACE AREA CORRELATIONS FOR AQUEOUS SOLUBILITY AND
ACTIVITY COEFFICIENT CORRELATIONS AS Iny = A + B (TSA) *
Solute Series
Alkanes
Alcohols
Polynuclear
aromatics
Halobenzenes
Polychlorlnated
biphenyls
Number of
Compounds
18
55
31
35
35
Kl
0.73
3.8
1.42
3.30
3.20
K2
0.0323
0.0317
0.0282
0.0423
0.354
K3
—
—
0.0095
0.0103
—
A
2.92
4.15
1.33
3.00
2.78
B
.0.0744
0.0730
0.0649
0.0974
0.0815
Reference
128
128
12
129
13
to
* See explanation on following page.
-------
Explanation of Table 2
For the first four series Yalkowsky and Valvani report the solubilities
as a function of total surface area (TSA) in square angstroms as follows
log S - KX - K2(TSA) - K3(MP)
where S is solubility at 25°C (mol/L), MP is melting point (°C), K^, K2 and K
are regression constants, the K, term being included only if the melting point
exceeds 25°C. K, is equivalent to the constant 6.8 developed here divided by
298 K and by 2.303 to convert to base 10 logarithms i.e. 0.0099.
Substituting 0.0099 for K. and converting S to CS, MP to TM> and using
natural logs gives
lnCS = 2.303(Kn+3) - 2.303K.(TSA) - 2.303x0.0099(TM-273)
1 / ft
- 2.303(1^+3) - 2.303K2(TSA) - 0.0228TM + 6.22
The equivalent form used here is
lnCS = -lnTw - lnVw + 6.8(1-TM/T)
which at 298 K and with Vw equal to 18 x 10~ m /mol gives
lnCS - - A - B(TSA) + 10.93 + 6.80 - 0.0228T..
It follows that
A =.
B * 2.303 K
A a. 11.51 - 2.303 (Kj+3)
2
A specimen calculation involving these quantities is given at the end of
Section 4.
23
-------
accessible quantity such as molecular weight, carbon number, molar volume
or some calculated combination of the contributions of the various groups
or molecular fragments present. Here we examine the feasibility of these
approaches by illustrating the correlation of ISA with such accesible quan-
tities.
Figure 2 is a plot of ISA versus molecular weight for selected homo-
logous series, which shows satisfactory correlation within a series, but
not between series. Figure 3 is similar and shows ISA plotted against mo-
lar volume, which is best expressed as molecular weight divided by liquid
density at the normal boiling point. .Additive atomic volumes can also be
used to calculate molar volume. Figure 4 shows TSA plotted against carbon
number which is again fairly successful provided that the number of atoms
such as chlorine or oxygen is zero or constant. Clearly for a series such
as the PCBs carbon number is a useless correlating quantity. The use of the
sum of carbon and chlorine number is then preferable as illustrated in Fi-
gure 5.
Regression equations can be obtained for each series, resulting in a net
correlation between y and the accessible quantity (Q) which may have the
form:
Inv » A + B (TSA)
V
TSA = C + D (Q)
ln^ = A + BC + DB (Q)
or more complex expressions can be used. From plots such as Figures 2,3,4
and 5 or the corresponding regression equations it is possible to estimate
Y and hence solubility for a compound for which no experimental data are
available.
An attractive sequel to this data compilation is to develop a group
contribution procedure which would be applicable to a wide range of compounds.
Some preliminary steps were taken towards this end as part of this study but
the results were not sufficiently accurate to justify publication. Further
work is planned and it is believed that the ultimate objective of calcula-
ting solubility from molecular structure and melting point is attainable with
accuracy sufficient for most environmental purposes.
24
-------
FIGURE 2
PLOT OF TOTAL SURFACE AREA VERSUS MOLECULAR WEIGHT
300 -
• alcohols
o alkanes
» PC3s
ycloalkanes and
:i I kv lben~enes
* chlorobenzenes
O PNAs
100
200 300
Molecular Weight (g/mol.)
-100
25
-------
FIGURE 3
PLOT OF TOTAL SURFACE AREA VERSUS MOLAR VOLUME
300 _
250
' 200 -
-
!H
a
•f.
-
:
150
100
cycloalUanes and
alkyIbenzenes
PCBs
100
150 200
^i
Molar Volume (cm°/mol.)
250
26
-------
FIGURE 4
PLOT OF TOTAL SURFACE AREA VERSUS CARBON NUMBER
300
250 -
<
~ 200
u
u
I
I*
^
3
150 -
100
cycloalkanes and
alkyIbenzenes
O PMAs
10
Carbon 'lumber
15
27
-------
FIGURE 5
TOTAL SURFACE AREA VERSUS CARBON PLUS CHLORINE NUMBER
300
250
. i
'.
•
-
CJ
w 20°
Ll
Y.
,
—
-
150
100
• chlorobenzenes
A PCBs
10 15
Carbon plus Chlorine Number
20
28
-------
VAPOR PRESSURE
The vapor pressure of a solute is clearly of considerable signifi-
cance in any assessment of volatilization and reliable data are very desirable
but unfortunately often lacking, especially if the solute has a low vapor pressure
which is difficult to measure accurately. A detailed treatment of correlating
equations for vapor pressure has been given by Reid et al ( 14 ) and only some
salient points are presented here.
Figure 1 is a typical pressure-temperature diagram for a pure solute. The
range of environmental temperatures may lie anywhere on this diagram relative
to the important phase transition points which are the triple point (which is
essentially the melting point, the critical point and the normal boiling point).
Ideally data should be available for vapor pressure of solid, or liquid over
the range of environmental temperatures but estimation is often necessary.
The Glausius-Clapeyron equation in its simple form relates vapor pressure
to temperature as a function of enthalpy of vaporization AHV
dlnP/dT • AHV/RT2
from which the Clapeyron equation can be derived by integration
InP - A - B/T where B is AHV/R
where A and B are constants. This equation assumes that AHV is constant with
changing temperature which is generally invalid and especially so near the
critical point where AHV becomes zero. A more accurate equation is that of
Antoine which has an additional constant C which usually has a value of -40 to
-60 K,
InP •- A - B/(T + C)
Several equations have been proposed for predicting vapor pressure,
usually as a function of critical temperature and pressure using corresponding
states theory which is based on the generalization that properties such as
vapor pressure are related to the critical property in similar ways for all
compounds. Critical property data are usually available only for those com-
pounds for which vapor pressure data are also available thus the better pro-
ceedure is to use vapor pressure data directly. Methods are available for
estimating critical properties by an additive structural contribution method
devised byLydersen (Reid et al 14 ). Unfortunately many higher molecular
weight compounds of enviromental interest decompose thermally before they
reach critical conditions thus experimental validation is impossible.
Boiling point data are often available which can be used as a basis for
extrapolation down to environmental temperatures, using for example the
Clapeyron equation. This requires an estimate of the enthalpy of vaporization,
AHV.Fortunately several methods are available for accomplishing this, the
simplest being Trouton's Rule that AHV/TB (i.e. the entropy of vaporization) is
approximately 21.2 cal/mol K at the normal boiling point Tg. More accurate
procedures have been suggested by Kistiakowsky and by Vetere (Reid et al 14) In
which additional terms involving boiling point or molecular weight are included.
For approximate calculations AlF can be assumed to be constant but if better
accuracy is desired, and an estimate is available of the critical temperaturei
29
-------
the Watson equation can be used to express AHV as a function of temperature
0 J 8
(AHj/AHj)
where subscripts 1 and 2 refer to the values at two temperatures T]_ and T2
and Tc is the critical temperature (K).
A simple approximation for vapor pressure (P atm) as a function of
temperature T and boiling point TB using Trouton's Rule and the Clapeyron
equation is,
InP - -B (1/T - 1/TB) =• -(AHV/R)(1/T - 1/TB)
- -(21.2 TB/R)(1/T - 1/TB) = 10.6(1 - TB/T)
or inPfo ~ 10.6 (1 - TB/TM)
This can be used to estimate the liquid vapor pressure down to its value P^
at the melting or triple point (Tjyj). Below this temperature the enthalpy of
sublimation should be used. This can be estimated approximately using
Yalkowsky's observation ( 11 ) which is essentially Waldeas1 Rule,that the
entropy of fusion of most rigid organic compounds is 13.5 cal/mol K. Long
chain molecules with n flexible links have higher entropies of fusion expressed
as 13.5 +2.5 (n-5).
Applying a similar equation to the solid-vapor pressure curve (below the
triple point) gives
ln(P/PM) - -(AH3/R)(1/T - 1/TM)
where AH8 is the heat of sublimation and is given approximately by
AHS - 21.2 TR + 13.5 TM
o n
or AHS/R = 10.6 TB + 6.8 TM
Combining these equations to eliminate PJJ yields
InP - 10.6 (1 - TB/T) + 6.8 (1 - TM/T)
The first term gives the liquid (and subcooled liquid) vapor pressure at
any temperature T and the second term (which is also negative) gives the
additional reduction in vapor pressure due to solid phase formation. The
second term is ignored if the environmental temperature exceeds the melting
point, i.e. T > TJJ. For correlation purposes a plot of InP versus TB/T should
thus be linear for liquids. Solids should also fall on the line if the vapor
pressure is connected to the higher subcooled liquid value by adding the term
6.8 (1 - TM/T) to -In P.
Figure 6 is a plot of this type for 30 compounds listed in Table 3
illustrating the general validity of the method.
30
-------
FIGURE 6
RELATIONSHIP BETWEEN VAEQR PRESSURE AND
BOILING POINT FOR SELECTED SOLUTES
-1 h
_ •
cyclopemane
.methyl cyclooentane
^?t carbon tetracrtlori^
cyclohexane
•benzer.e
ethyl e'/clopentar.i
-.oluene
cr.isrobeniene
etnyl benzene
n-ootar.a
i. t,'. .1- :e*.racr..ar3«t.n.ar.e
p. «thyl cyoL
-
1.3, 5 - .-.rime thy L —•
uronvl ber.ier.e
•. .2 ,^-'.ri.ir.9-.nvl ber.
isobu-.;,-: benzene
t \ l -Ti"ir.vL naphthalene
'. i.riiis
.solid vapor 3r=s.- i
visor
31
-------
TABLE 3. BOILING POINTS, MELTING POINTS AND
LITERATURE & CALCULATED VAPOR PRESSURES AT 25°C
Vapor Pressure (atm)
Compound
benzene
toluene
ethyl benzene
p-xylene
m-xylene
o-xylene
1,2,4-trimethyl
benzene
1,3,5-trimethyl
benzene
C-umene
propylbenzene
Isobutyl benzene
butyl benzene
n-octane
naphthalene (s)
CD
1-methyl naphtha-
lene
*biphenyl (s)
1,1,1,2-tetra-
chl or oe thane
trichlorohydrin
c hlorobenzene
o-dichloroben-
zene
cyclopentane
cyclohexane
methyl, cyclo-
pentane
ethyl cyclo-
pentane
Boiling Pt.
K
353.099
383.6
409.2
411.0
412.0
417.4
442.35
437.7
437.7
432.2
445.8
456
398.66
491.0
517.64
528.9
403.5
429.85
398.9
451.5
322.2
353.7
344.9
376.4
Melting Pt.
K
27S.5
178
178
286.2
225.1
247.8
229.2
228.3
176.4
171.4
221.5
185
216.4
353.2
251
34 A
202.8
258.3
227.4
196.0
179.12
279.55
130.6
134.56
Literature
0.125
0.037
0.013
0.0115
0.0109
0.0086
0.00267
0.00318
0.00605
0.00451
0.00271
0.00142
0.01855
1.08 x 10~*
3.06 x 10~^
9.21 x 10~5
7.5 x 10"5
0.0183
4.078 x 10~3
0.0155
0.00168
0.418
0.1286
0.1806
0.0526
Calculated
0.141
0.048
0.019
0.018
0.017
0.014
0.006
0.007
0.007
0.008
0.005
0.0036
0.028
2.96 x 10~4
4.05 x 10~4
9.488 x 10"5
0.0235
9.187 x 10~3
0.0276
0.0043
0.423
0.138
0.189
0.0615
32
(continued)
-------
1ABLE 3. (CONTINUED)
Vapor Pressure (atm)
Compound
ethyl cyclo-
hexane
carbon tetra-
chloride
*phenanthrene (s)
^anthracene (s)
*fluorene (s)
*acenaphthene (s)
Boiling Pt.
K
402.9
349.7
612
613
568
550.5
Melting Pt.
K
161. 68
250.0
374
489.2
389
369.2
Literature
0.01688
0.149
4.53 x 10~6
1.42 x 10"6
1.64 x 10"5
3.97 x 10~5
Calculated
0.024
0.159
2.489 x 10"6
1.73 x 10~7
8.46 x 10"6
2.476 x 10~5
* extrapolated vapor pressure
33
-------
Interestingly, Almgren et al ( 20 ) have recently shown that a degree
of correlation exists between aqueous solubility and boiling point,of aro-
matic hydrocarbons, most of which are solid, namely
- log S = 0.0138 TB + 0.76
where S the solubility has units of mol/L and T is in °C. This correlation
is not very accurate, having a typical error in S of a factor of 2 and
occasionally as high as 10 but it indicates that both solubility and boiling
point depend on molecular size.
The overall picture which emerges is that molecular size and structure
and the presence of interactive group£ such as alcohol or amine groups control
the molecular's critical properties, larger molecules having higher critical
temperatures and pressures. These properties in turn control the vapor
pressure of the liquid. Molecular shape also plays a strong role in controll-
ing melting point and hence the solid vapor pressure. Molecular area appears
to control the aqueous activity coefficient and hence directly controls
solubility of liquids and jointly with melting point controls the solubility
of solids. It is thus not surprising that a correlation exists between
boiling point and solubility since both depend on the same molecular properties.
Finally,it is worth commenting on experimental methods for determining
vapor pressure. Little difficulty is encountered if the vapor pressure exceeds
1 mm Hg since an isoteniscope can be used. For lower vapor pressures effusion
rate or evaporation rate methods have been used but they are now regarded as
excessively complex and unreliable. The preferred approach is to flow a
stream of gas through a vessel containing the volatile solute either as liquid
or as a solid coated on packing under conditions such that saturation is
achieved. The effluent gas is then analysed for the concentration of the
solute by one of several methods including trapping on a sorbent column,
absorption in a liquid or combustion to yield C02 which is subsequently
analysed by IR spectrometry. Such methods have been described by Spencer and
Cliath ( 22 ), Sinke ( 23 ) and Macknick and Prausnitz ( 24 ).
It must be emphasized that the foregoing analysis applies only to non-
electrolytes.
34
-------
HENRY'S LAW CONSTANT
UNITS AND SYSTEMS
In this report H is consistently presented in units of atm m3/mol, but
other systems are used, for example, pressure can be expressed in mm Hg or Pa
and concentration in g/m3, mg/L or mole fraction. The correct SI unit is
Pa mVmol which reduces to J/mol. It is often convenient to calculate H as
the dimensionless ratio of concentrations (e.g. (mol/m3)/(mol/m3)) which can
be derived from H simply by dividing by the group RT thus converting pressure
into concentration using the gas law
i.e. n/v - PS/RT
The gas constant is 82 x 10~6atm m3/mol K thus RT is typically 0.024 atm mVmol.
If H is expressed in Pa m3/mol or J/mol, R is 8.3 J/mol K.
Another system of expressing H is as the ratio of partial pressure to
mole fraction or
P - %X
Examination of the fugacity equation shows that HJJ is equivalent to Yw^R (atm).
At low concentrations the molar volume of watervw is 18 x 10~6m3/mol thus at
a concentration C mol/m3 the mole fraction of solute X is C vw thus H is
equivalent to (HMVW).
Gas solubilities are occasionally reported as the Bunsen or absorption
coefficient which is the volume of gas at 0°C and 1 atm which is dissolved in
one volume of water. It can be shown to be 273 R/H. The Ostwald co-
efficient is similar except that the gas volume is at the system temperature
and the solute partial pressure. It is thus RT/H or the reciprocal of the
partition coefficient.
A final and unusual system is to express H as a relative volatility with
respect to water. This is later shown to be useful experimentally. The
relative volatility a is usually expressed for a binary system as.
a - y (1 - x)/x(l - y) * y/x
where x and y are the liquid and vapor mole fractions of solute. In dilute
solution this reduces to y/x which can be shown by the fugacity equations to be
YwfR/Px °r Yw PS/PT where fR is the reference fugacity, equivalent to the liquid
vapor pressure Ps (possibly subcooled) and Pip is the total pressure. -As was
shown earlier H is equal to vwYw^R or VWYWPS thus ct equals H/PT Vw. Consider-
ing for simplicity an air-free system, the H for water between pure water and
35
-------
Q
the vapor phase is P W/C^, i.e. the ratio of water vapor pressure to its
concentration G» which is 55,000 mol/m3 or l/vw. The group PT;VW is thus
the Henry's Law Constant for water Hw and a is the ratio of the solute to
water Henry's Law Constants, i.e.
Addition of air to the system does not alter this conclusion since air
merely increases the total pressure Pj and correspondingly reduces the mole
fraction y, leaving the vapor phase fugacities of water and solute unchanged.
The usefulness of this approach is that for systems of relatively low H,
water provides a convenient "benchmark" since if H is lower than Hw,
i.e. a < 1, volatilization will tend to increase solute concentration (as
occurs with ethylene glycol) . Only if Ct exceeds 1.0 will volatilization
cause a concentration drop. Knowledge of ot thus provides a convenient
method of rapidly estimating volatilizating tendency.
CALCULATION OF H.
Although H is commonly referred to as the ratio of vapor pressure to
solubility, it is more correct to express it as the ratio of partial pressure
to aqueous concentration thus allowing its value to change at undersaturated
conditions. Provided that the solubility is low, little change in H with
concentration is expected.
Temperature has a profound effect on H mainly because of its effect on
vapor pressure and to a lesser extent, because of the solubility effect.
Expressing H in logarithmic form yields ,
InH = lnPs,r lnCs
Applying a Clapeyron-type relationship to both Ps and Cs yields,
inH - ~AHV/RT + AHS/RT + constant
For naphthalene AHV the enthalpy of vaporization is approximately
10,000 cal/mol,(Reid et al 14 ), whereas the enthalpy of solution AH8 is
about 5000 cal/mol (Schwartz 25) thus the combined effect is about 5000
cal/mol or a (-AHV + AHS)/R value of 2500 K. An increase in temperature
from 0°C to°25 C corresponding to (!/TI - 1/T2> of 0.0003 thus results in an
increase in H by a factor of 2.2 corresponding approximately to a 4.6 fold
increase in Ps and a 2.2 fold increase in Cs. A convenient "rule of thumb"
is thus that H approximately doubles over a 25° temperature rise.
An aspect of calculating H which has been briefly referred to earlier,
and has been the cause of erroneous deductions is the possibility of
combining a solid vapor pressure with a liquid solubility or an activity co-
efficient calculated from molecular size with a solid vapor pressure. This
issue is clarified below.
When H is expressed as PS/CS it is essential that both Ps and Cs refer
to the same state of solid or liquid, ideally solid state data should be
used below the triple point and liquid state data above. Extreme care must
be taken when using literature vapor pressure correlations since these may be
36
-------
for liquids extrapolated to below-melting temperatures. Occasionally liquid
mixtures exist below the melting point temperature of either pure substance,
the classic example being PCBs. Most PCB solubility data are for pure solid
isomers but the vapor pressures are for liquid mixtures.
If an activity coefficient yw is used to calculate H the correct pres-
sure to use is the reference fugacity or the liquid or subcooled liquid
vapor pressure.
H is usually a smooth, continuous function of temperature through the
melting point whereas Ps and Cs experience abrupt changes in slope, the
gradients of both increasing by an amount corresponding to the enthalpy of
fusion. But since H is the ratio (or difference in logs) it does not
experience this abrupt change.
A final pitfall in the calculation of H arises when the solute is ^
appreciably soluble in water or when water is soluble in the liquid solute.
The assumption that H equals P /C is valid only if the solute vapor
pressure Ps is not appreciably reduced by water dissolving in the pure
liquid solute phase. For example, considering a system in which the pure
solute vapor pressure is 0.100 atm and the aqueous solubility is 100 mol/m ,
the value of H is apparently 10" 3 atm m-Vmol. It is possible that the
solute phase contains dissolved water to the extent of a mole fraction of
0.1 in which case the solute will not exert the full vapor pressure Ps of
0.100 atm thus H may be lower, possibly 0.9x10"^ atm m-Vmol.
If subscripts s and w apply to the solute activity coefficient y and
mole fraction x in the solute and water phases respectively then it follows
that at equilibrium
Vs " Vw
Writing the 2 suffix Margules equation for Y as a function of mole
fraction (Reid et al 14) gives in terns of a constant K
lnys -K(l-xs)2
lnyw-K(l-xw)2
Here x and y are close to unity, xw is small and y is large. The
group of interest is y x which is the factor by which th¥ vapor pressure
is reduced. Eliminating K and y in favor of y yields after rearrangement
W • S •
lnxg + lnyg •« lmxw + (1-x^) 2 I«YS/ U-XB) 2
thus lnyg - (lnsw-lnxg)/(l-(l-xw)2/(l-xs)2)
(1-x )2lnx - (1-x )2lnx
and iny + Inx - - - - £ - =-* - * - F •
2
or ln(x y ) - F and x y - exp(F)
So S S
*
|n |he case of a solute such as ethanol which is miscible with water, the group
P /C gas no meaning and H must be measured experimentally or calculated from
v Y P , the value of Y being obtained from another source.
w w w 37
-------
The quantity F is normally small and negative and becomes zero when x
becomes unity, ie the water content of the solute phase becomes zero. F can
be calculated from a knowledge of x the mole fraction solubility of the
solute in water and x , where (1-x ; is the mole fraction solubility of water
in the solute For example if x Sis 0.1 and x is 0.9 then F is-0.07 and
x y, is 0.93 resulting in a 7% reduction in vapor pressure and hence in H.
s s
When x approaches unity the equation can be approximated as
F « (l-xw)2lnxg « (l-xw)2(l-xs)
and ultimately if x is very small
F «t Inx
from which x y = exp(F) ss 1+F ft x
s s s
The most important influence on x y is thus x with the y effect
being secondary.
In the case of solutes such as alcohols x may be small e.g. 0.01 but
(1-x ) may be quite large e.g. 0.3 in which case F may become apparently pos-
itive (e.g. 0.073) and the Henry's Law constant is increased (i.e. by a factor
of 1.073). Such systems can not be represented by a Margules one constant
equation and the best approach is simply to reduce PS by the factor x».
This approach is used later in the experimental section of this report.
In summary, for solutes which have an appreciable miscibility with
water the simplest approach is to assume that Ps is reduced by the factor
x , If x is less than 0.95, ie water achieves a solubility greater than
53mol percent, it is advisable to calculate x y more rigorously.
METHODS OF DETERMINING H
Two methods are discussed here, the first being an approach discussed
earlier in which the relative volatility c*. is measured to give the ratio
of H for the solute to that of water (H ).
At 15 C, for example, the vapor pressure of water is 0.0168 atm and its
molar volume is 18 x 10"^ m^/mol thus H is 3.03 x 10"? atm m^/mol. Only if
H is significantly greater than this iswvolatilization likely to be important^
It is very easy to measure a for dilute systems since all that is
required is that a volume of solution be distilled at the temperature of
interest and the concentration change measured. Specifically,if a solution
of YI m3 of water containing solute of concentration Ci mol/m is distilled
to leave a residue of V2 m3 and concentration €2 mol/m thus yielding a
distillate of D m3 of concentration CD mol/m3 then a mass balance yields,
V-L « V2 + D (total)
vlcl = V2C2 + D:CD (solute)
If the vapor leaving the solution is in equilibrium with the liquid its
concentration will be a C where C is the liquid concentration.
38
-------
Writing the differential equation for the concentration decay gives,
dV (a C) = d(VC) = VdC + GdV
thus dV/V - dC/C(ct -1).
Integrating between limits of V]_, C^ and V2,C2 yields,
ln(V1/V2) - ln(C1/C2)/(a -1)
or ct = 1 +ln(C1/C2)/lti(V1/V2)
This has the correct properties that if the solute is involatile (a = 0)
CD is zero and 0;^ equals C2V2 thus (C]_/C2^ etluals (V2/V,) and the log term
becomes -1. When a is unity there is no concentration change and C^ equals
C2 making the log term zero. Usually a exceeds unity and may typically have
a value of 5 thus when (V;iyv2) is 2.0 (i.e. half the liquid is distilled),
CI/GO' is 16 °r the concentration drops to 6.2% of its initial value.
If the concentrations of the initial solution (C^) the residue C2 and the
distillate (Cjj) are measured along with the respective volumes a mass balance
can be done to validate the distillation. The value of a can then be
calculated accurately. If a is high, only a small fraction of the volume V,
should be distilled. Highest accuracy is probably attained when C2 is about
half C which implies that
« exp [- 0.69/(a - 1)]
Thus if a is 3, i.e. H is 10~6,V2/V1 should be 0.71
if a is 10, i.e. H is 3 x 1Q-6, V2/V]. should be 0.93
if a is 30, i.e. H is 10"5, V2/Vi should be 0.97.
As a becomes large,
1 - 0.69/(a - 1)
thus the fraction distilled becomes very small and only a small amount of
water need be evaporated in order to substantially deplete the solution of
solute. This phenomenon was noticed by Acree et al (26 )for aqueous
solutions of DDT and at that time was wrongly attributed to a "codist illation"
phenomenon. In fact DDT has a fairly high Henry's Law Constant relative to
water thus a is large and only slight water evaporation is necessary to
remove most of the DDT. This was demonstrated by Mackay andWalkoff ( 27 )
who first elucidated the physical chemical principles which in modified form
are detailed here.
In view of the simplicity of this method compared to the difficulty of
measuring Henry's Law Constants for these relatively involatile compounds by
conventional methods, some experimental work was done to develop a suitable
test method. This method described later as the "relative volatility
method" is a simple method of obtaining an estimate of H for compounds which
have H values in the range 10-7 to 10 atm m3/mol range.
A second "gas stripping" method is also described which is more suitable
for compounds of higher H values. Details of this method have been
described previously by Mackay et al ( 28 ) but it has been extended in this
study. The principle is to sparge a gas stream of G m3/s through a volume
39
-------
Vm3 of water containing an initial concentration C^ mol/m3 of solute under
conditions such that the exit gas stream is saturated with solute,the partial
pressure being HC atm and the concentration HC/RT mol/m3. A differential
equation for the volume yields,
GHC/RT = -VdC/dt
This includes the assumption that HC is small compared to atmospheric pressure.
Integration yields,
C - G! exp(-GHt/RTV)
A plot of I
-------
FIGURE 7
PLOT OF SOLUBILITY. VAPOR PRESSURE AND HENRY'S CONSTANT
gmol/m3
-------
Combining these expressions.to give one for In H. eliminates the fuga-
city ratio term giving
In H = 10.6 (1 - T_/T) - 10.93+ A+ B(TSA)
D
The significance of this elimination is that H can be correctly defined
as the ratio of the solid vapor pressure to solid solubility or liquid vapor
pressure to solid solubility or liquid vapor pressure to liquid solubility,
but not a mixture of solid and liquid values. Although P and C show discon-
tinuities in slope at T , H has a continuous slope.
The values of A and B presented earlier in the solubility section can
be used or TSA can be related to molar volume, molecular weight or carbon
number for a homologous series. Finally, Almgren's correlations (20) for
solubility can also be used thus yielding a correlation for H in terms of
only melting and boiling points. Writing Almgren's equation in units of K,
mol/m •* and natural logarithms yields
In CS = -0.0318(1, - 273) + 5.15
is
Thus In H = 10.6(1 - TB/T) + 6.8(1 - TM/T) + 0.0318(TB - 273) - 5.15
This equation can be used to give approximate values for H, however the pre-
ferred procedure is to obtains experimental data for the homologous series and
interpolate or extrapolate. It is unlikely that a sufficiently accurate cor-
relation can be established for H for a wide range of compounds.
As a test of these correlations, data were gathered for a selected group
of compounds for which reliable H data and TSA data are available. Values of
H were then calculated from the TSA, boiling point correlation and from Alm-
gren's correlation and presented in Table 4. The mean factor by which the
(TSA and BP) value differs from the experimental value is 3.2, the corresponding
number for the Almgren correlation being 13,0. Neither is accurate enough for
any but the most approximate purposes. This expression of the results is some-
what "pessimistic" since much of the error is attributable to a few compounds
(especially first six). A better approach is to use TSA and BP as a mechanism
of interpolation or extrapolation from data for homologs. It is believed that
such an approach will give values consistently within a factor of two of the
correct value. Occasionally a fortuitously high P and low C combine to give
a large error in H.
42
-------
TABLE 4
HENRY'S LAW CONSTANT CORRELATIONS
Compound
naphthalene
1-rcthyl
naphthalene
1-ethyl
naphthalene
2-aethyl
naphthalene
blphenyl
acenaphthene
fluorene
phenanthrene
o-dlchloro
benxene
n-dlchloro-
benzene
p-dlchloro-
benzene
brombenzene
1,2.3,5-tetra-
chlorobenzene
fluorobenzene
lodobenzene
n-octane
2.2-dlaethyl-
butane
n-pentane
2, 24- tr 1-ethyl
pentane
2.2,5-trlmethyl
pentane
H.W.
g/«ol
128.19
142.2
156.2
142.2
154.21
154.21
166.2
178.23
147.01
147.01
147.01
157.02
215.9
96.11
204.01
114.23
86.17
72.15
114.23
114.23
Solubility Vapor Pressure
•ol/.3 at.
0.27
0.20
0.07
0.18
0.05
0.03
0.011
6.6xlO~3
0.99
0.84
0.57
2.61
0.017
16.16
0.88
5.78xlO~3
0.214
0.534
0.0214
0.0101
1.1 xlO~*
7.8 xlO~5
2.5 xlO"5
8.9 icUf5
7.4 xlO"5
4.0 xlO"5
1.63xlO~5
4.5 xlO"6
1.9 xlO~3
3.0 xlO~3
8.9 x!0~* ,
5.0 xlO~3
-
0.10
1.3 JtUf3
1.86xlO~2
0.420
0.675
6.49xlO~2
2.18xlO~2
Boiling Point
K
491
517.6
531.7
514.6
528.9
550.5
568
612
453.5
446
447
429
519
358.1
461.3
398.66
322.74
309.07
372.24
397.1
Melting Point
K
353.2
251
259.2
307.6
344
369.2
389
374
256
248.3
326.1
242.18
327.5
231.8
241.79
216.21
173.13
143.3
165.62
167.22
*
155.8
172.5
187.4
176.3
182.0
175.0
193.6
193.0
142.7
144.7
144.7
133.1
175.8
113.6
141.9
178.4
1*5.1
124.0
163.1
186.6
Henry's Law
Literature*
4. 8x10"* (e)
-4
3.9x10 (c)
-4
3.6x10 (c)
4.9xlO"*(c)
-4
4.1x10 (e)
L
1.5x10 (e)
1.5xlO~3(c)
—A
3.9x10 (e)
1.9xlO~3(e)
_
3.6x10 (c)
2.4xlO~3(e)
2.4xlO"3{e)
1.6xlO~3(e)
612x10 (c)
1.4xlO"3(e)
3.219(c)
1.967(c)
1.265(c)
3.038(c)
2.165(c)
Conetant-atH
TSA and BF
1.74x10
-3
2.0 xlO
,
3.2x10
2.8xlO~3
-3
2.5x10
-4
7.3x10
_3
1.3x10
-4
3.6x10
3.84xlO"3
_3
6.1x10
5.9xlO~3
3.6xlO"3
9.4xlO~3
6.7xlO~
2.7xlO"3
5.4
3.2
2.3
4.4
10.46
Almgren
1.76x10
1.6 xlO~2
-2
1.3x10
4.6xlO~3
, -3
1.9x10
-4
9.8x10
-4
5.8x10
-4
6.9x10
1.9xlO"2
-2
2.3x10
.
3.9xlo"3
2.8x10
-2
2.8x10
_2
4.6x10
iy
2.5x10
5.7xlO"2
2-OxlO"1
4.2xlO"A
2.0X10"1
_«
1.7x10
* c - calculated; e - experimental
-------
OCTANOL-WATER PARTITION COEFFICIENT
It is universally accepted that a knowledge of octanol water partition
coefficient (K ) is essential for predicting the environmental fate of
organic contaminants. The pioneering work of Hansch and Leo and co-workers
(9, 10, 30 ) and other groups have demonstrated that K can be used
as an indicator of hydrophobicity or llpophilicity and thus serves to
quantify the tendency for solute partitioning into cell membranes where the
solute may have some-physiologicaleffect. It has thus been widely used in
drug design. Its application to environmental prediction has been success-
fully developed by Neely et al ( 31 ) to bioaccummulation or bioconcentration
in fish, by Karickhoff et al ( 8 ) -to characterise sorption to organic
matter in sediments and by many other workers.
An attractive feature of K is that methods are available for
QIJ
calculating it from a knowledge of molecular structure by adding increments to
log K attributable to various functional groups. Such calculations can be
quite accurate when the process is essentially interpolation or modest extra-
polation but it is suspected that significant extrapolation is inaccurate.
This latter issue is unfortunately of considerable environmental relevance
since many compounds of environmental interest have high molecular weights ,
are sparingly soluble in water and have high KQW values which are very
difficult to measure experimentally.
The purpose of considering K here is to demonstrate that its value
can be closely related to aqueous solubility using the fugacity equations
derived earlier. It is thus a useful physical chemical property which can
help to validate (or invalidate) other property data and the ability
to calculate it from a knowledge of molecular structure may make it possible to
estimate other physical chemical properties.
The relationship between solubility 0' mol/m3 and K was first noted by
Hansch et al ( 30 ) and later Chiou et al ( 32 ) correlated the approximately
inverse relationship between Cs and K . The issue has also been discussed
by Mackay ( 33 ), Tulp and Hutzinger ( 34 ) and Kenega and Goring (35).
Recalling the equations derived earlier
C - 1/Cy v ) for liquid solutes
s w w
C m exp ( 6.-8(l-T /T )/Ywvw for solid solutes
K => v Y./(v Y )
OW W W rt n
Equating Ywv in these equations yields
K - I/ C? Y v for liquids
ow o o
K = exp( 6.8 (1-T../T )/Csy v for solids
OW M O O
Writing in logarithmic form gives
8 -InC -Iny -Inv for liquids
ow 'o o n
44
-------
= 6.8 (1 - T IT<\ -InC3 -lirv - Inv for solids
ow M ° °-
The molar volume of pure octanol is 157 x 10 6 m3/mol. In K determinations
the octanol is water saturated to a mole fraction of approximately 0.26, thus the
molar volume of the mixture is lower, ^-e H5 x 10 6 m3/mol, thus In v is
-9.07. If K and CS data are available Y can thus be calculated.
. ow. o
Correlation
Data for 56 compounds are presented in Table 5 . From the K and
Cs data y was calculated for each compound. The tabulated y results are
remarkably constant for most compounds but there are two exceptional groups.
The aromatic carboxylic acids and 2,4-D ( regarded as suspect) have low
Y values which indicates some form of solute association in octanol solution.
Tn"e mean Y value of approximately 0.48 is an order of magnitude smaller than
those of tne other compounds. The second group is of compounds of molecular
weight greater than 290 including some PCBs and DDT in which Y *s larger.
Segregating these groups for separate treatment gives a mean value of Y for
the remaining 45 compounds of 4-835 thus In Y« is 1.576. The overall °
correlations become
In K = 7.494 - lnCS for liquids
ow
In K - 7.494 - InC3 +6.8 (1-T /T) for solids
The root mean square of the deviation in log K for the 45 points is ^0. 216
corresponding to a factor of 1.64 in K . TheWcorrelation coefficient for
the calculated and literature values of Tog K is 0.988.
ow
Discussion of the Correlation
A useful procedure for calculating K or Cs emerges from these equations.
Structurally similar molecules such as phertin threne and anthracene should
have similar Y values. Eliminating Y from the equations yields at 298 K.
Kowi/Kow2 = «/<) «P(-0.023 (TM1 - TM2))
If either or both are liquids TM: and/or T 2 is replaced by the system
temperature, usually 25°C. The ratio of solubilities (Cf /Ci) for
anthracene (1) and phenanthrene (2) is 17.7 but the melting point difference
(TMI - T ) is 115° thus the exponential term becomes 0.071 and the
expected^ ratio is 17.7 x 0.071 or 1.26. close to the observed value.
ow
An important implication is that in correlating the partitioning
behaviour of organic solutes from water or its subsequent toxic effects it is
best to use K since it is a more direct measurement of Y • Solubility
should only biWused if the fugacity ratio term is also incYuded, i.e, the
correlation should be with (Csf /f ) not Cs. This better correlation has
been observed for sorption by Kirickhof f et al ( 8 ) . The preferred units
of solubility are mol/m3 or mole fraction not g/m3 or ppm. For long chain
flexible molecules the entropy of fusion will be higher resulting in a larger
coefficient on the melting point term, and the rules devised by Yalkowsky can
be used to estimate this effect ( 11 ) .
The K , C relationship for carboxylic acids is best treated by assign-
45
-------
ing a value of 0.48 to y thus the coefficient 7.494 in the equations should
be replaced by 9.804.
The higher molecular weight compounds present a more serious problem
which may have significant environmental implications. Several authors have
speculated that very high molecular weight compounds do not show the expected
lipophilicity that is indicated from their calculated K values. Examples
are high molecular weight chlorinated alkanes reported by Zitko ( 36 ) and
squalene reported by Albro and Fishbein (37 ), as discussed by Tulp and
Hutzinger ( 34 ). it has been speculated that lipophilicity is related to
calculated K by a near linear equation at low K , i.e. below log K of
OW ' OW OW
5 or 6 but a negative quadratic term becomes dominant thereafter depressing
the lipophilicity. There is pharmacological support for this claim (Hansch
38 ). An alternative explanation suggested by the data is that the
calculated K values are in error and that above a molecular weight of
approximatelyW290, K. tends to level off because both y an^ y increase
with increasing molecular size. It is possible that y shows a tendency to
increase as a result of the solute molecule becoming "?ess soluble" in octanol.
An equation relating y to molecular weight could be easily devised if suf-
ficient accurate data were available.
The most significant implication is that if high molecular weight solutes
display this unusual behaviour with octanol they may also display it with
lipids, but to a different degree. If this is the case, the K -lipophibicity
relationship may break down above log K of about 6. Sugihara et al (39) re-
ported evidence of such an effect. Whether this is due to kinetic or thermo-
dynamic effects is not known. Clearly this is an area requiring further study
since if very high molecular weight compounds do not bioconcentrate to the
extent expected they may prove to be safer environmentally than is expected
from extrapolation of the behaviour of lower molecular weight compounds.
46
-------
Table 5 Physical and chemical properties of selected compounds
Compound
benzene
toluene
ethyl benzene
o-xylene
1,2,4-triraethyl
benzene
propyl benzene
isopropyl benzene
naphthalene
1-methyl
naphthalene
2-methyl
naphthalene
1,3-dimethyl
naphthalene
1,4-dimethyl
naphthalene
1,5-dimethyl
naphthalene
2,3-dimethyl
naphthalene
2,6-dimethyl
naphthalene
M.W.
78.12
92.15
106.17
106.17
120.20
120.20
120.20
128.19
142.20
142.20.
156.23
156.23
156.23
156.23
156.23
M.P.
5.5
-95.0
-94.97
-25.18
-43.8
-99.5
-96.0
80.55
-22.0
34.58
<25
7.66
81.0
105
108.0
S Solubility Cs
g/m3 mol/m3 fg/fR '
1780i.
515
152
175
57
55
50
31.7
28.5
25.4
8.0
11.4
3.38
3.0
2.0
22.79
5.59
1.43
1.65
0.47
0.46
0.42
0.25
0.20
0.18
0.05
0.07
0.02
0.02
0.013
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.28
1.0
0.80
1.0
1
1.0
0.28
0.16
0.15
Literature
log k
ow
2.13
2.69
3.15
3.12
3.65
3.68
3.66
3.37
3.87
3.86
4.42
4.37
4.38
4.40
4.31
Y0
2.83
3.18
4.30
4.00
4.14
3.95
4.53
4.15
5.87
5.36
6.46
5.08
4.60
2.94
5.01
Calculated
log k
ow
1.90
2.51
3.10
3.04
3.58
3.59
3.63
3.30
3.95
3.90
4.55
4.39
4.35
4.18
4.32
-------
Literature
Calculated
co
J.£LU-LC J L,*Jlli-J-lA*-lt-VA *
1-ethyl
naphthalene
1,4,5-trimethyl
naphthalene
b iphenyl
ace naph th en e
fluorene
phenanthrene
anthracene
9-methyl -
anthracene
9,10-dlmethyl-
anthracene
pyrene
fluoranthrene
1,2-benzofluorene
chrysene
triphenylene
tetracene
1,2-benzo-
anthracene
3,4-benzopyrene
perylene
M.W.
156.23
176; 2
154.21
154.21
166.23
178.24
178.24
196.3
206.3
202.26
202.26
216.28
228.3
228.3
228.3
228.3
252.32
252.32
M.P.
-13.88
64.0
71.0
96.2
116.0
101.0
216.2
81.5
182.0
156.0
111.0
187.0
255.0
199.0
357.0
162.0
176.5
277.0
S
10.7
2.1
7.0
3.93
1.98
1.29.
0.073
0.261
0.056
0.135
0.26
0.045
0.002
0.043
5.7 x 10~"
0.014
0.0038
0.0004
cs
0.068
0.012
0.045
0.025
0.012
7.2 x 10~3
4.1 x 10~*
1.33xlO~3
2.7 x 10"11
6.7 x 10~"
1.3-x 10~3
2.1 x 10~"
8.8 x 10~6
1.9 x 10~"
2.5 x 10~6
6.13xlO~5
1.5 x 10~5
1.6 x 10~6
fS/fR
1.0
0.41
0.35
0.20
0.13
0.18
" 0.01
0.28
0.03
0.05
0.14
0.02
0.005
0.019
0.0005
0.04
0.03
0.00.3
log k
& ow
4.39
4.90
4.09
4.03
4.18
4.46
4.45
5.15
5.67
4.88
5.22
5.75
5.91
5.45
5.91
5.91
6.50
6.50
Y°
5.21
3.75
5.30
6.40
6.06
7.36
9.63
12.96
1.91
8.66
5.72
1.85
6.47
3.10
2.23
7.68
5.87
5.50
log k
& ow
4.42
4.79
4.14
4.15
4.27
4.64
4.73
5.65
5.25
5.12
5.29
5.32
6.01
5.24
5.54
6.10
6.57
6.53
-------
Table 5 continued:
Literature
Calculated
3-methyl
cholanthrene
benzo (ghi)
perylene
Indan
chloroform
tetrachloro-
ethylene
carbon
tetrachloride
fluorobenzene
chlorobenzene
br omob en zene
iodobenzene
p-dichlorobenzene
4,4'-dichloro-
biphenyl
M.W.
268.36
276. 34
118.18
119.38
165.83
153.82
96.11
112.56
157.02
204.01
147.01
223.11
M.P.
178.0
277.0
-51.4
-63.5
-19.0
-22.99
-41.2
-45.6
-30. 82
-31.27
53.1
149
S
0.0029
0 .00026
109.1
7950
400
800
1553
472
410.6
340 (30°)
79
.062(20°)
C"
1.1 x 10~5
9.4 x 10~7
0.92
66.6
2.41
5.20
16.16
4.19
2.61
1.67
0.54
2.8 x 10~*
VfR
0.03
0.003
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.53
0.05
log k
ow
7.11
7.10
3.33
1.97
2.60
2.64
2.27
2.84
2.99
3.25
3.38
5.58
Yo
1.91
"
2.35
4.41
1.40
9.06
3.83
2.89
3.00
3.41
2.93
3.54
4.31
log k
6 ow
6.69
6.77
3.29
1.43
2.88
2.54
2.05
2.63
2.84
3.03
3.24
- 5.57
high activity coefficient compounds
2,4,5,2'5'~penta-
chlorobiphenyl
2,4,5,2', 4', S'-hexa-
chlorobiphenyl
methoxychlor
P.p'-DDT
malathion
326.4
360.9
345.66
354.49
330.36
77
103
94
109
2.85
0.010(24°)
0.00095(24
0.12
0.0031
145(20°)
3.1 x 10~5
°) 2.6 x 10~6
3.5 x lO"1*
8.7 x 10~6
0.44'
0.30
0.17
0.21
0.13
1.0
6.11
6.72
5.08
6.19
2.89
65.87
104.01
43.15
84.10
25.52
*
7.24
8.06
6.03*
*
7.48
*
3.61
-------
Table 5 continued:
Literature
Calculated
parathion
low activity
2,4-D
M.W.
291.
27
M.P.
6.1
S
24
c1
0
»
.08
VfR
1.0
log k
6 ow
3.81
Yo
16.42
log k
6 ow
*
4.35
r
coefficient compounds
221.
salicylic acid , 138.
ben zoic acid
phenyl acetic
phenoxyacetic
122.
acid 136.
acid 152.
04
12
13
16
16
141
159
122.4
77
99
890
1800(20°)
2700(18°)
16600(20°)
12000(10°)
4
13
22
121
78
.03
.03
.11
.92
.86
0.07
0.04
0.09
0.27
0.13
2.81
2.26
1.87
1.41
1.26
0.24
0.15
0.49
0.76
0.79
1.50
0.75
0.86
0.60
0.47
(2.49)
(1.75)
(1-87)
(1.60)
(1.47)
( ) values in bracket are calculated log kQW using the preferred value of 0.48 for y
* °
values in which poor agreement between correlated and experimental data is evident,
-------
RELATIONSHIPS BETWEEN PHYSICAL CHEMICAL PROPERTIES
The elucidation and regulation of the environmental behaviour and effects
of existing and new contaminants is a fascinating scientific and social
problem. There is no doubt that before any assessment can be made for a
particular compound, sufficiently accurate physical chemical data must be
available. Most toxic substance regulatory schemes thus require information
on solubility, vapor pressure, boiling and melting point, KQW> sorption
coefficients, as well as reactivity or degradability data. Essentially,
the required physical chemical data are fugacity capacities. Interestingly,
it is not clear how accurate these data must be until some general indication
of environmental behaviour is obtained in which the important processes or
compartment s are identified. This issue has been discussed in some detail
by Mackay ( 7 ).
The establishment of procedures for calculating these data from solely
a knowledge of molecular structure would be invaluable for two reasons. It
would permit economies in that certain properties of certain compounds
need only be calculated rather than measured. It would enable experimental
data to be checked for validity and any obviously erroneous data could be
identified. Part of this procedure would undoubtedly involve relating one
measured quantity to another, for example vapor pressure to boiling point or
solubility to K as have been discussed earlier.
ow
This brief section is an exploratory review of the state of the art in
this area whichlhas the purpose of elucidating some of the existing and
potential procedures. It is first useful to list the properties which are
directly and readily accessible or inaccessible by experiment.
Directly and Readily Accessible Properties
Molecular Structure
Solid and Liquid Vapor Pressure, melting and boiling points
Aqueous Solubilities
K
ow
Henry's Law Constant
Properties which are not directly accessible
Activity coefficients in water, octanol or lipid phases
Fugacities
Properties which are potentially accessible but present difficulties in
direct measurement
Critical Properties (Temperature and Pressure)
Enthalpies and Entropies of fusion and vaporization
Other Phase Transition properties e.g. crystalline transitions
The linkages between these properties is illustrated in Figure 8
which shows that the fundamental physical chemical quantities are the activity
coefficients in water and in an organic phase (such as octanol or lipid)
51
-------
and the solid and liquid fugacities and their ratio » which are essentially
the vapor pressures. If these data are known as a function of temperature
it is possible to calculate all the experimentally measurable quantities
using established thermodynamic relationships. Conversely, it is possible
(and necessary in practice) to estimate these inaccessible properties from
experimental measurements.
The important conclusion is that most of these quantities are mutually
dependent, thus not all quantities need be measured. For example only two
of -vapor pressure,solubility and Henry's Law Constant need be measured
since the third can be calculated, or better, all three can be measured and
checked for consistency.
Consistency checks are also possible between K and solubility or
between vapor pressure and boiling point.
A very significant development would be the ability to calculate the
activity coefficient and fugacities from molecular structure. This would
enable data to be validated and avoid the necessity for some experimental
measurement, although it is accepted that there is ultimately no substitute
for experimenal data. This capability is emerging. Examples are the
correlations of activity coefficient with molecular surface area by
Yalkowsky and Valvani (12 ), the calculation of K from molecular structure
by Hansch and Leo ( 10 ). Ultimately the developmentf this predictive
ability could be a step towards further structure -property-activity deductions
involving estimation of sorption (from K and organic content), reactivity
using linear free energy relationships (e?g. hydrolysis) and ultimately even
biological processes such as biodegradation or toxicity. In the long term
it is possible that the environmental behaviour and effects of contaminants
will become predictable from molecular structure. To achieve this a sound
foundation of verified physical chemical property data is essential.
52
-------
FIGURE 8
SCHEMATIC DIAGRAM OF^RELATIONSHIPS BETWEEN PHYSICAL CHEMICAL PROPERTIES, THE FUNDAMENTAL
QUANTITIES WHICH ARE INACCESSIBLE BY DIRECT EXPERIMENTAL MEASUREMENT BEING IN THE BOX
01
.IQUI1
'RESSl
I
SOLII
PRES£
) VAPOR LIQUID HENRY'S LAW
JRE CONSTANT
c S LIQUID AQUEOUS
PT / L , L SOLUBILITY
\ / \ \
\ /
f L ,.
ASp & T
fS °r fR
/ \
/ v
S
) VAPOR SOLID 1
JURE CO
V
M ^
\/
/\
/ \
5
flENRY'S LAW
NSTANT
Y, .
0
\
,,§ SOLID AQUEOUS
"s SOLUBILITY
Kow
/«
/ 7i
C(
E
L
OCTANOL-WATER
PARTITION
COEFFICIENT FOR
EITHER SOLID OR
LIQUID
-------
SPECIMEN CALCULATION AND CRITICAL.REVIEW OF AQUEOUS PHASE PROPERTIES
To illustrate the concepts discussed in this section a calculation for
naphthalene is outlined below.
Properties (experimentally obtained)
Molecular weight 128.2 g/mol.
Total Surface Area 155.8 sq. angstroms
Melting point (T ) 353.2K (80.2°C)
Boiling point 491 K (218°C )~ .
Aqueous solubility at 25°C 34.4 g/m (0,268 mol/m )
Vapor Pressure at 25°C solid 1.14 x 10 ,atm (f.)
liquid 3^08 x if atm (IL)
Henry's Law Constant 4.8 x 10 atm m /tnol
Octanol Water Partition Coefficient 2300
(1) Fugacity ratio at 25°C (298K)
f /f = exp(6.8(l-TM/T)) - 0.28
(experimental = 0.35)
(2) Activity Coefficient
Iny - A + B(TSA) = 11.44
thus Y = 93100 (Table 2)
(3) Aqueous solubility
CS =
-------
(5) Henry's Law Constants
s s —4 3
H calculated from P and C is 4.25x10 atm m /mol
-4,
(experimental = 4.8 x 10 )
InH = 10.6(1 1L/T) - 10.93 + A + B(TSA) = -6.36
o
—3 3 —3
H = 1.7 x 10 atm m /mol (experimental 0.48 x 10 )
The discrepancy here is due to a combination of an overestimated
vapor pressure and an underestimated solubility.
Almgren's correlation
InH - 10.6(1 - TB/T) + 6.8(1 - TM/T) + 0.0318(TB - 273) - 5.15
= 8.13 + 6.93 - 5.15
= 6.35
-3 3
H o 1.76 x 10 atm m /mol
(6) Solubility-Octanol Water Partition Coefficient
lnKATT - 7.494 - InC8 - 0.023(TV - T)
OW « '«.
here CS is 0.0268 mol/m thus
InK
OW
7.54
3.27
(experimental 2300)
Discussion
It is apparent from this example that correlated values of solubility,
vapor pressure, Henry's Law Constant and octanol-water partition coefficient
can be in error by factors of two or more. At the present state of the art
such correlations must be used with caution. Since experimental values are
also suspect in many cases there is a compelling incentive to check the experi-
mental data by comparing values of fg, f"L> YW and YQ obtained by different methods
and critically reviewing their likely errors.
For example, naphthalene is judged on the basis of the accuracy of the de-
terminations and correlations to have the following basic values.
quantity
fL
YQ
VfL
units
atm
atm
-
-
recommended
value
1.14 x 10~4
4.0 x 10~4
59100
4.02
0.285
lower
limit
1.00 x 10"4
2.5 x 10"4
57400
3.82
0.25
upper
limit
1.40 x 10~4
4.5 x 10"4
60900
4.22
0.31
55
-------
quantity
cs
Kow
H
units
mol/m
2
atm m /mol
recommended
value
0.268
2300
4.25 x 10~4
lower
limit
0.260
2200
3.90 x 10~4
upper
limit
0.276
2400
4.83 x 10~4
A compilation of this type is invaluable in highlighting the quantities
which are less accurately known. A judgement can then be made as to whether
or not more accurate values are required for environmental assessment purposes.
As data in this form become available,better correlations can be developed
thus facilitating the calculation of properties of other solutes in the series
with greater accuracy.
56
-------
SECTION 5
MASS TRANSFER PHENOMENA
MECHANISMS OF TRANSFER
Figure 9 illustrates the processes which may occur when a solute trans-
fers from a water body to the atmosphere.
• First it may be incorporated in sediments or biota and require some
time for desorption into the water column.
Second, it may have to diffuse vertically through the water column
until it reaches the near surface layer, i.e. within a mm of the inter-
face. In fast flowing shallowurivers this process is probably fairly rapid
but in deep quiescent water it is slower. The solute may encounter strati-
fied regimes during its vertical journey in which there are different dif-
fusive velocities. This occurs particularly in lakes where there may be
a well defined fairly well mixed surface layer or epilimnion and a deeper
more quiescent hypolimnion. Such stratification is normally the result
of density differences arising from temperature variation but in sea water
and estuaries there may be contributions arising from the differing salini-
ties, and hence densities, of the water.
Third, the solute must pass through the near-interfacial liquid layer
to the interface.
Fourth, it must penetrate the interface.
Fifth, it must pass through the near-interfacial gas layer.
Sixth, it must then diffuse to the bulk of the atmosphere.
In addition to these processes the solute may be carried vertically by
rising bubbles generated for example by anaerobic processes or it may rise
or fall in association with suspended mineral, organic or biotic matter.
This gives rise to a possibly complex situation in which the material is
moving up and down simultaneously by differing mechanisms and at different
rates and it is not immediately clear what the net effect will be.
At the surface it is possible that the material may accumulate in a sur-
face organic nicrolayer containing organic material of natural and anthro-
pogenic origin. This layer may influence the transfer rate in several res-
pects. If coherent, it can damp turbulence in the form of capillary waves
thus reducing transfer rates, (Davies & Rideal 18 ). It may also block
57
-------
FIGURE 9
SCHEMATIC DIAGRAM OF TRANSPORT PROCESSES
WET AND DRY DEPOSITION
BULK ATMOSPHERIC DIFFUSION/DISPERSION
ATMOSPHERE
GAS SURFACE
LAYER OR
"FILM"
oo
SURFACE LAYER DIFFUSION
- ^NTERFACE PENETRATION __ _
7_LLQUiD
-------
the transfer process by forming a layer of less penetrable surface active
materials. This layer is probably in motion relative to the water column
at approximately 3% of the prevailing wind speed. As a result, a solute
may diffuse vertically through the water column at one location, enter the
microlayer and be swept horizontally to another location at a velocity of
typically 0.1 to 1.0 km/h. The result may be the transfer of the solute
preferentially to the banks of rivers or small lakes.
As bubbles arrive' at the surface they tend to form a thin skin con-
sisting primarily of the interfacial .material which ruptures as the bubble
bursts through the surface, generating a number of small droplets which may
be propelled permanently into the atmosphere. This occurs particularly in
situations such as aeration vessels where exceptionally high rates of bub-
bling are induced. This mechanism serves to introduce involatile materials
such as electrolytes and microorganisms into the atmosphere in addition to
volatile material. Only in locations where there is abnormal bubbling
activity is this likely to be important for the volatilizing compounds con-
sidered here.
Finally, it should be noted that the solute may become associated with
particulate matter in the atmosphere and be redeposited in the water. It
may also dissolve in rain water or associate with snow and return to the
water in the form of wet deposition. It is most unlikely that there are
high rates of exchange in both directions. A substance which volatilizes
generally does so because of its tendency to partition into air rather than
water. Having volatilized it will tend to achieve a lower atmosphere con-
centration because of dilution. If then contacted with water in the form
of rain it can not then achieve an aqueous concentration equal to that of
the water body it left. Rain must thus contain a lower concentration of the
volatilized solute than that of the water from which volatilization took
place. Rainfall will thus lend to dilute the water body concentration, pos-
sibly approximately making up for the concentrating effect of evaporation.
In the event that the solute enters the system primarily by air, as is
the case with S02, there may of course be substantial wet deposition, but one
would then expect negligible volatilization. The situation with substances
such as PCBs which have poorly defined sources and partition characteristics
is less clear.
There is a possibility that a solute may sorb on to atmospheric parti-
culate matter and then be deposited either naturally by gravity or by wash-
out. Only if the rate of deposition is high is this likely to be important.
Generally, particulate matter is at much higher concentrations in water than
in air thus if the compound has a strong sorbing tendency it will tend to
remain in the water rather than volatilize since it will be associated with
the suspended aquatic matter.
The general conclusion is that it seem unlikely that a substance will
undergo simultaneously significant transfer rates in both directions. Rain- .';
fall should have a negligible effect on a volatilizing compound, especially
because of the low rates and its intermittent nature. Movement by associa-
59
-------
tion with suspended matter will tend to be either consistently vertically
down in the case of compounds which sorb strongly, the ultimate destination
being sediments, or it will be unimportant for other compounds.
From a thermodynamic viewpoint the overall tendency will be to equalize
fugacity or chemical potential and in a closed system no natural process can
appreciably delay that process..
DIFFUSION PROCESSES
Diffusion Within A Phase
Within a single phase, diffusion tends to transfer material from regions
of high to low concentration which corresponds to high and low fugacity.
This is essentially a manifestation of the tendency of any fluid to mix,
ultimately reaching a homogeneous composition. The simplest mathematical
representation of diffusion is Pick's first law which applies to steady
state (i.e. time independent) conditions. It is analogous to Fourier's law
for heat transfer, Ohm's law for electricity transfer, and Newton's law for
momentum transfer, in that it postulates that the flux is proportional to
the gradient in the driving force. For mass diffusion, concentration is
the driving force and the proportionality constant is the mass diffusivity.
The equation can be expressed in differential or intergrated form as shown
below.
N = - D dC/dy - - DAC/Ay
2 2
where N is mass flux (mol/m s), D is diffusivity (m /s), C is concentration
(mol/nr) and y is distance in the direction of diffusion (m). The mass flux
is thus the product of two types of terms. The diffusion and distance terms
express the kinetics of the system and can be regarded as characterizing the
rate of mixing or the velocity which with the elements of the fluid move.
The concentration difference term is an expression of the departure of the
system from equilibrium conditions and is therefore thermodynamic in nature
and time independent.
In a stagnant fluid, in which there is no bulk motion (a condition
which is achieved only with difficulty in the laboratory and rarely in the
environment), the diffusivity is the molecular diffusivity which is typically
10-5 Cm2/s for liquids and 10-1 cm2/s for gases. It can be shown from the
kinetic theory of gases that the gas diffusivity equals 1/3 of the root
mean square velocity times the mean free path. . As a result, high diffusivi-
ties result from high molecular velocities (which are caused by high tempera-
tures) and large internal spacing between the molecules, which arise from
low pressures. For liquids, no such simple relationship can be devised. For
solids, the diffusivity is normally regarded as negligible. Diffusivity is
thus dependent upon the nature of the diffusing molecule. Larger heavy mole-
cules tend to have lower velocities and thus have lower diffusivities. This
is important environmentally in calculating diffusion rates of one compound
from that of another, for example, in calculating the diffusion rate of PCS
molecule from that observed for oxygen. Diffusivities are temperature and
pressure dependent and are influenced by the presence of other species in
solution.
60
-------
Correlations are available for calculating these diffusivities as re-
viewed in the text by Reid, Sherwood and Prausnitz (14 ). Usually the
Wilke-Chang correlation is used for liquids and the Chapman-Enskog correla-
tion for gases.
In environmental and industrial situations, the fluids (air or water)
are normally in motion thus diffusion can occur by two distinct and additive
mechanisms, molecular diffusion as described above, and turbulent diffusion
which can be regarded as transport of material by means of an element or
eddy of fluid which moves from one region to another. There is relatively
poor information about the size and velocity and frequency of these eddies,
largely because they vary greatly in size and configuration and are very
difficult to observe because of their intermittent nature. Eddies may range
from a fraction of a millimeter to many meters in dimension and they may be
superimposed upon each other. There is a considerable amount of literature
in atmospheric and oceanographic physics on turbulent diffusion processes
and many empirical approaches have been used to calculate these diffusivities,
(for example, Csanady,40 )•
It is noteworthy that in the bulk of environmental fluids turbulent
diffusivities are normally several orders of magnitude greater than molecular
diffusivities, thus, in many situations, the molecular term can be ignored.
Turbulent diffusivities are virtually impossible to predict from theoretically
first principles. They can only be measured by simultaneously measuring mass
fluxes and concentration gradients and correlating the results.
Fortunately there is a close linkage or analogy between turbulent dif-
fusion of mass, heat and momentum thus generalised correlations are possible
in which data from one transport process can be used to predict the behaviour
of another (Bird, Stewart and Lightfoot 41 ).
The source of turbulence or eddies is of considerable importance, since
if the strength of the source can be measured it may be possible to predict its
effect in generating turbulence elsewhere. The source is usually a region
of relatively high fluid velocity gradient. Examples are the interaction of
a river current with the bottom in which the roughness at the bottom induces
eddies, which move upwards towards the surface tending to decay as they pro-
gress. Even smooth surfaces induce turbulence above a certain critical velo-
city, usually characterized by the Reynolds number. Only at low velocities
does flow become nonturbulent or laminar. In the atmosphere, pressure and
thermal effects cause winds which are variable in direction and velocity.
The turbulent diffusivity in the atmosphere depends on wind velocity and
particularly on the thermal structure near the ground. The turbulence exper-
ienced at, for example, a lake surface, is thus very dependent on the temp-
erature and velocity conditions in the overlying air. In lakes most turbu-
lence may be formed by the interaction of wind with the water surface result-
ing in the formation of waves and surface currents. Residual currents arising
from rivers may also play a significant role. Estuaries and tidal regions,
may also contain significant currents which induce turbulent motion. Finally,
under some conditions, the turbulence induced by biota may be, significant,
for example, in sediments benthic' organisms may play a significant role in
in transporting material between the sediment and the water column.
61
-------
When mass diffuses close to a phase boundary, for example, at a solid-
liquid or air-liquid interface, gravitational and interfacial forces prevent
eddies from moving directly across the interface vertically*although an eddy
in one phase may induce eddying in the other phase. For example, wind may
induce turbulence at and below the surface of a lake. The result is that
turbulent vertical diffusivities tend to approach zero at an interface, thus
much of'the resistance to mass transfer (the resistance being inversly pro-
portional to the diffusivity) tends to be located within a few millimeters
of phase boundaries. From the viewpoint of the diffusing molecule, it finds
that it can move relatively easily from the bulk of the phase to a region a
few millimeters from the interface having been carried by relatively large
turbulent eddies but its subsequent journey to the interface is made on
smaller and slower eddies and may ultimately be made by slow molecular dif-
fusion. In calculating the rate of flux, it is often possible to ignore
the time taken to get to the near-interfacial region and concentrate on
interfacial transfer in both phases. Unfortunately then, the interfacial
region is often the most critical and where it is most difficult to make
precise measurements of concentration, distance or even position. This is
particularly true in air-water systems, where the interface may be moving
vertically as a result of wind and wave action. In applying Pick's law,
there is thus no accurate data for D, the diffusivity or Ay, the diffusion
path length. It is then convenient to lump these two unknown quantities
together in a single unknown term, called a mass transfer coefficient, which
can be regarded as D/Ay, and is defined as follows:
N - D AC/Ay = K AC where K » D/Ay
A considerable volume of data exists on mass transfer coefficients in various
phases, geometries, turbulence levels and for various compounds. Ultimately
any volatilization rate predictions depends heavily on such correlations.
It is noteworthy that there remains considerable doubt about the actual
microscopic mechanism during mass transfer between air and water phases. It
is generally accepted that eddies of fluid move to the surface, are exposed
to unsteady state molecular diffusive mass transfer for some unknown time,
and then move back to the bulk. This model is consistent with observations
that the mass transfer coefficient depends on the molecular diffusivity, but
the dependence is not linear as one would expect if K was simply D/Ay.
Empirically, K is often expressed as a power of D, usually D to the power in
the range 0.5 to 0.8. This is regarded as evidence that the diffusion process
is a combination of turbulent transport of the eddy (which is independent of
D) followed by an unsteady state diffusion at the surface dependent on D,and
possibly even a steady state period. This unsteady state transfer can be
characterized by Fick's second law, which essentially gives the differential
relationship between the concentration, time and distance. Solutions of
this equation suggest that the mass transfer should be proportional to the
square root of diffusivity. The full details of such considerations are
given in texts on mass transfer, for example, by Sherwood et al (42).
A further complication is that turbulent diffusion is not necessarily
or even usually isotropic, i.e. it is not equal in all directions. If eddies
were spherically symmetrical, one would expect diffusion to be equal in all
62
-------
directions, however, the eddies are subject to gravitational forces and tend
to move horizontally with a greater ease than vertically, especially if the
fluid is horizontally stratified or confined. Vertical diffusion is thus
often an order of magnitude less than horizontal diffusion in water. Similar,
but not as profound differences, exist in atmospheric diffusion. Vertical
diffusion may be particularly slow under conditions where the fluid has a
temperature (and hence a density) gradient. In most fluids, as temperature
increases, density decreases (water below 4°C being the notable exception),
thus, an element of fluid propelled vertically upwards into a fluid region
of higher temperature tends to be slowed and fall back by virtue of its
greater density. Such fluids in which temperature increases with height
tend to be very stable and even stagnant, the buoyancy effects damping out
any tendency for vertical diffusion. Examples of this are thermoclines in
lakes and temperature inversions in the atmosphere. In the opposite situation
in which temperature falls with increasing height, an eddy moving vertically
tends to be assisted by buoyancy forces and thus, vertical diffusion may be
enhanced. The net result is that the mass transfer processes are strongly
influenced by the thermal condition of the fluid in which transfer is taking
place. This thermal condition may be a result of recent temperature history,
but may also be influenced by evaporation of water.
In summary, diffusion within a phase is readily characterized by Pick's
law by which fluxes can be calculated from diffusivities, concentration dif-
ferences and diffusion path lengths. The diffusivity term can be regarded
as the sum of a molecular term (for which adequate correlations exist) and a
turbulent term which is very complex and can only be measured experimentally
and correlated empirically. In the near interface regions, there is consider-
able doubt about the value of diffusivity path length and indeed position,
thus it is conventional to lump the diffusivity and distance terms into a mass
transfer coefficient. These diffusivity or mass transfer coefficient terms
depend on turbulence level, the molecules properties, including its molecular
diffusivity, and the only approach available is to develop an empirical
procedure for calculating them from easily measurable quantities such as wind
speed or river depth, which are essentially characterisations of the strength
of the turbulence source.
Diffusion Between Phases
When a solute diffuses through a region of different phases or of one
phase in which it experiences different diffusivities (and hence velocities)
it is essential to develop a method of determining how each zone affects
the overall diffusion rate. Often one process is so fast that it affects
the overall rate to a negligible extent. This is illustrated schematically
in Figure lOwhich shows a solute diffusing at steady state from a high ter-
minal fugacity f^ to a low terminal fugacity f^ through three zones which
may be different phases (eg. air and water) or stratified layers.
There is presumably a continuous trend in fugacity between f]_ and f^
which must be linear in regions of constant diffusivity if steady state
applies.
63
-------
An important assumption here is that at the boundary between phases or
regions within a phase the fugacities are equal i.e. there are no fugacity
discontinuities. This is regarded as a reasonable assumption since if a
fugacity difference did exist over a microscopically small distance diffusion
would be very fast because of the large gradient. This assumption is equiva-
lent to the "equilibrium existing at the interface" assumption made in the
Whitman Two Resistance Theory and elsewhere.
Fick's Law can be written for each phase as
N = - DiACi/Ayi or -
But in each zone C^ = Z^f j_
Thus N = - DZAf/Ay or -
It is convenient to replace the "conductivity" terms V±Z±/hyi and
by their reciprocals or "resistances" r^ i.e.
r±= Ay-iD.^ or
thus N = Afi/ri
N - (f1-f2)/rA- (f2-f3)/rB= (f3-f4)/rc
from which rA = (f1-f2>/N, rB » (f 2-fa)/N etc.
hence (rA+rB+rc) - (fi-f4)/N
and N - (fi-
If each resistance can be predicted, the total can be obtained, the domi-
nant resistance determined and the flux calculated. The values of intermed-
iate fugacities can than be determined.
The most important feature of this analysis is that the resistance terms
depend not only (as is obvious) on the dif fusivities or mass transfer coef-
ficient but also (and less obviously) on the Z values or fugacity capacities.
The reason for this latter dependence is that in regions of low Z only a low
concentration is necessary to achieve the required fugacity^thus only on low
concentration gradient is achievable, thus the mass flux tends to be constrain-
ed to a low value. Mass diffuses most rapidly where it can achieve high
concentrations and hence concentration gradients. Low Z values thus cause
high resistances. The importance of this effect lies in the observation
that in many cases Z is sufficiently high in a phase that the resistance
becomes small and hence can be neglected. Control of the overall diffusive
process then lies in another phase.
This general conclusion reduces to the Whitman Two Resistance Theory
( 43 ) for air-water exchange. If rL and rG are liquid and gas resistances
equivalent to l/K^and 1/KgZQthen since fL is C^/Z^nd fQ is PQ
N - (CL/ZL-PG)/(1/KLZL4-1/KGZG)
64
-------
But ZL is 1/H and ZG is 1/RT thus
N = (CLH-PG)/(H/KL+RT/KG)
This equation is conventionally written in the equivalent forms
N = KoL(CL-PG/H) where
or N =KQG/ (CLH-PJ/RT) where I/KQQ = 1/Kg+H/RTKL
The terms KQL and KQG are overall liquid and gas mass transfer coefficients
which are related since
compounds of high Rvalues which tend to partition into the air phase because
of their high vapor pressure and/or low solubility usually have negligible
gas phase resistances (RT/HK(j) because they are able to establish high gas
phase concentrations. Such systems are termed liquid phase controlled. Con-
versely compounds of low H are usually gas phase controlled. The resistances
are equal when
1/KL => RT/HKc or when H/RT - KL/K(;
Illustration Of Multiphase Diffusion
Consider a solute diffusing through a system of (A) a water body of
depth Y of 2 m and diffusivity D of 0.001 m2/s, (B) a liquid film of mass
transfer coefficient KL of 0.0001 m/s and (C) a gas film of mass transfer
coefficient KQ of 0.01 m/s. The concentration at the bottom is 0.1 raol/m^
and in the atmosphere it is 10-6 atm. The temperature is 10°C at which the
solute solubility Cs is 20 mol/m^ and 'its vapor pressure P** is 0.002 atm.
Then Henrys constant H is Ps/Cg or 0.0001 atm. m^/mol, thus ZL is 10000.
ZQ is 1/RT or 1/82x10-6x283 or 43.
The resistances are thus
rA " Y/DZL a 2/0.001x10000 =0.20 atm. m2s/mol
rB - 1/KLZL - 1/0.0001x10000 - 1.00 atm. m2s/mol
re - l/KcZG - I/. 01x43 - 2.33 atm. m2s/mol
The total resistance r? is thus 3.53
The total fugacity difference is from the bottom value fi of C/Z^ or
0.1/10000 or 10" 5 atm to the atmospheric value f£ of 10~" atm i.e. a change in
Af of 9xlO"6 atm.
The flux N is thus Af/ri - 9x10-6/3.53 or 2.55xlO-6mol/m2s
65
-------
The intermediate fugacities can also be calculated from Af « Nr
i.e. AfA " 2.55xlO-6x0.2 or 0.51x10-6 atm
AfB = 2.55x10-6x1.0 or 2.55x10-6 atm
Afc = 2.55xlO-6x2.33 or 5.94x10-6 atm
Total 9.00x10-6 atm
The intermediate fugacities are thus
Between the water column and the water film 9.49xlO~6 atm
Between the water film and air film 6.94xlO~6 atm
In this case most of the resistance (66%) lies in the air film, 28% lies
in the water film and 6% lies in the bulk of the water phase. The calculation
can be done for any number of phases with little increase in complexity.
These quantities are illustrated in Figure 10. Note that the fugacity
profile varies continuously over the diffusing regions whereas the concentration
profile undergoes a discontinuity at the air-water interface.
66
-------
FIGURE 10
ILLUSTRATIVE FUGACITY TRANSPORT CALCULATION
Concentrations Fugacities atm
— 1 x 10~6 atm
~6
/
> film
\
/
V '
i
^ f
/
Kp = 0.01 m/s Z =43 r = 2.33
U (66.0%)
\
\
6.94 x 10~ atm
0.0694 mol/m3
1 x 10
-6
6.94 x 10
o\
B Liquid
film
1L = 0.0001 m/s ZT = 10000 r = 1.00
^ L . B (28%)
f\
A Bulk
Liquid
____ 0.094mol/m
9.49 x 10 6 atm
Y = 2m
D = 0.001 m /s
ZT = 10000
L
0.20
(6%)
N
2.55 x 10
A
-6
0.1 mol/m 10 x 10
/:
~
rT = 3.53
-------
PREDICTION AND CORRELATION OF ENVIRONMENTAL MASS TRANSFER COEFFICIENTS
(a) Mass^ Transfer Coefficients
There have been numerous studies in which mass transfer coefficients
have been measured in various contacting geometries. Much of the incentive has
been to assist the design of chemical process equipment such as distillation
columns where the size and efficiency are directly controlled by these
coefficients. A convenient review of this topic is the text by Sherwood
et al (42 )t Less effort has been devoted to environmental mass transfer
and the predictive capability is somewhat poorer, partly because environmental
systems have more complex and variable fluid flow characteristics. Reviews
relevent to this area have been compiled by Csanady (40 ) and Thibodeaux
( 44 ).
Since the 1920's several approaches towards predicting and correlating
mass transfer coefficients have been advanced, all based on a conceptual
model of the physical processes which control mass transfer. One of the
principal difficulties is that for environmental conditions the physical
mechanism of transfer is still not clear, and until this is clarified it is
doubtful if a comprehensive, accurate predictive capability will emerge.
The film theory presented by Whitman ( 43 ) and by Lewis and Whitman
( 45 ) was the earliest model to quantify the absorption of gases into
turbulent liquids. They postulated that laminar or stagnant films of gas
and liquid exist at the interface between the two phases. These films
experience little convective motion while turbulent motion and rapid mixing
keep the concentration of the solute uniform in the bulk phases. It follows
that the solute that transfers through one film must also pass through the
other and the two films can be considered as two diffusional resistances in
series. The rate of transfer at steady state can thus be calculated from
the film thickness (Z) and the molecular dlffusivity (D) and the mass transfer
coefficient K becomes D/Z. This approach is still used in some oceanographic
and limnology literature in which the mass transfer resistance is expressed as an
equivalent stagnant film thickness.
It is generally accepted that this sample model is invalid, principally
because there is insufficient time for steady state diffusion to be established.
This is manifested experimentally as a non linear relationship between K and
D, i.e. generally if D increases by a factor of four, K only doubles or
trebles.
This model is however invaluable as a means of combining the two phase
resistances to give an overall resistance. This "two resistance" version
of the model is generally accepted as valid in process equipment provided
that it claims no particular relationship between resistance and diffusivity.
It is less generally accepted in environmental situations partly because
of concern about the role of surface organic microlayers and accumulation of
certain solutes at the surface at concentrations different from the bulk.
For example the interface can be viewed as a temporary storage or sorption
region from which solute molecules may leave according to some form of thermal
activation process, as occurs on solid surfaces. Undoubtedly several con-
ceptual models of inter-phase transfer processes can be postulated and used
as a correlating or predictive tool by fitting appropriate constants to the
model equations. The evidence available suggests, however, that diffusion
68
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models most faithfully express the physical reality.
After Lewis and Whitman the next significant step was taken by
Higbie ( ^6 ) who postulated that elements of fluid moved to the surface,
experienced unsteady state transfer for a short time t then moved back to
the bulk. Application of Fick's Second Law yields an expression for K
K = /4D/TTt
Dobbins pioneered the application of unsteady state mass transfer theory
to environmental conditions of oxygen transfer to water bodies (48). Danckwerts
(47) later introduced the concept of 'a surface renewal rate or frequency S
yielding
When t is large of S small these models reduce to the Whitman Two Film
model. Toor and Marchello (49) , King (.50), Harriot (51) and Ruckenstein
(52) have proposed models which are similar in concept. These models predict
that
K a D when exposure time is short
K a D when exposure time is long
Typically an intermedidate condition exists and a power of 0.67 is frequently
used. This dependence is very important environmentally since it is useful
to relate transfer rates of one compound to those of another, such as
oxygen.
One of the most appealing models is based on the "roll cell" concept
developed by Fortescue and Pearson (53 ) Euckenstein (52 ) and Ruckenstein
and Sucier (54 ). A version of this model is illustrated in Figure 11.
It oan be regarded as a microscopic version of the Langrauir circulations which
result from the interaction of wind and waves and cause clearly defined down-
welling regions. An element of fluid at the water surface moves at a few
percent of the wind speed (say 15 to 20 cm/s) when the wind speed is 5 m/s
or 18 km/h. The element is exposed to unsteady state transfer (volatilization)
losing solute to the atmosphere above. After some time t in which it may
have moved some centimeters or meters it is propelled back to the bulk of
the liquid to be replaced by another element. This propulsion may be
associated with internal circulation in waves. Horizontal movement of the
element is a factor of 10 to 100 faster than vertical movement thus the roll
cell is elongated. It is possible that several scales of roll cells exist
superimposed on each other. The relative ease of horizontal movement com-
pared to vertical movement results in a higher horizontal than vertical eddy
diffusivity as is observed experimentally in dye tracer studies (Csanady 40 ).
The nature and dimensions of environmental roll cells are not known and
it seems likely that it is impossible to simulate then precisely in the •'
laboratory. It would not be surprising if over a large fetch a stable
relatively long roll cell pattern developed which would not be observed at
short fetches as inevitably apply to laboratory systems. This would result
in laboratory tests overestimating mass transfer rates since the exposure
time is shorter in the laboratory and the average mass transfer coefficient
69
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FIGURE 11
SCHEMATIC DIAGRAM OF AN ELEMENT OF WATER EXPERIENCING EXPOSURE TO THE
ATMOSPHERE AND HENCE LOSS OF SOLUTE BY VOLATILIZATION IN A "ROLL CELL"
ATMOSPHERE
UNSTEADY STATE EXPOSURE AND VOLATILIZATION
S\ \) f FLUID ELEMENT
I \\A I PROPELLED TO
THE SURFACE
.ELEMENT PROPELLED
BACK IN WATER
COLUMN
DEPLETED OF SOLUTE)
MIXING
WATER
-------
correspondingly higher as is indicated by the Higbie .equation presented
earlier.
(b) Verification of the Two Resistance Model
The 5 conditions under which the additivity of individual phase resist-
ances is valid has been theoretically treated by King (55 ). They are:
1. H must be a constant.
2. There must be no significant resistance present other than those
represented by K, and K . .
3. The hydrodynamic conditions for the case in which the resistances
are to be combined must be identical to the measurements of the
individual phase resistances.
4. The mass transfer resistances of the two phases must not interact.
5. The ratio H K-/IL must be constant at all points of the interface.
Most of these conditions are intuitively obvious but the last two de-
serve some discussion. If unsteady state exchange from roll cells exists this
implies that the flux from the water is greatest from the freshly exposed
element, and least just before the "aged" element returns to the water bulk.
The local VL thus varies along the roll cell. If there is negligible gas
phase resistance an average 1C will apply. If there is an air phase resist-
ance equal in magnitude to that of the average water phase resistance then it
will add equally to all points of the roll cell. This is illustrated in Figure
12 with hypothetical quantities for a compound of H/RT of unity. If the
first half of the roll cell (A) has a K_of 10, doubling it will give an
average 1C of 7.1 (by penetration theory) thus K..B must be 4.2. Assuming
a unifonnKp of 7.1 and adding the resistances (i.e. reciprocals of K)
to give an overall K yields 4.15 for A, 2.64 for B, the average of which is
3.39. This is less than the value calculated by merely adding the average
IL and K . The reason is that when K_'drops (at the end of the cell) the
overall resistance does not drop in proportion. The net effect is a 5% error
in flux, i.e. the actual flux is 5% less than is expected from adding the
resistances. This effect is thus relatively small given the uncertainties in
the values of K but it does indicate that conditions may exist when additivity
is not precisely correct. One implication is that deducing K of K. from
K or K for a two phase resistant system may give different values from
that of one phase resistant systems.
The closest experimental verification of the additivity of resistances
has been by Goodgame and Sherwood ( 56 ) who studied transfer of COa.NHs and
acetone to water in an agitated vessel . The experimental design with gas
and liquid stirring was quite removed from an environmental air-water
interface thus it is unwise to assume that the two resistance concept has
been verified for environmental conditions. • Accordingly a small scale
apparatus was designed, built and operated in this project to provide
additional verification. Although it can be argued that the evidence
supporting the two resistance concept is overwhelming it was judged to be
worthy of further verification in this project because its validity is the
key assumption in volatilization calculations -and any discrepancies should
be exposed. In addition a small scale test apparatus can be used to test
the dependence of K on diffusivity under various turbulence conditions as
71
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well as the effects of temperature and extent and direction of evaporation.
A convenient method of verifying the two resistance concept is to measure
the mass flux and hence K for compounds of a wide range of H. Rearranging
the transfer coefficient equation yields.
(1/KQL) = (1/1^) + (RT/H)(1/KQ)
If 1C and K are constant, a plot of (1/K ) versus (RT/H) should yield a
line of slope (I/Kg) and intercept (at RT7H = 0) of (1/IL) as illustrated
in Figure 13. . L
(c) Effect of Waves
As has been indicated, considerable difficulties have been experienced
quantifying interphase transfer rates even from solids to fluids in which the
interface is well defined. In air-water systems the presence of a mobile
wavy interface introduces an additional dimension of complexity. The
characteristics of wind waves have been reviewed in the test by Kinsman (57 )
and only a brief account is possible here in which some of the more relevant
references are cited.
When wind blows across a solid surface its velocity at the surface must
be zero i.e. there is "no slip". This implies that a steep velocity
gradient exists immediately above the surface. Since air has a small but
finite viscosity there is thus transfer of momentum and thus a force or stress
exerted by the wind on the surface, tending to drag it in the wind direction.
If the surface is liquid it will be dragged by the wind thus creating a
surface current which is generally observed to be 2 to 5% of the wind speed.
Above a wind speed of about 3 m/s waves develop of a few centimeters in length.
These waves provide a roughness which further increases the drag resulting in
growth of waves to a steady amplitude and wavelength. This process of wave
build up may occur over hundreds of kilometers resulting in large gravity
waves. A typical large lake or ocean surface is covered with multiple wave
spectra which are remnants of wind action in remote locations. At higher
wind speeds whitecapping may occur as the wave crests are blown over and at
very high wind speeds waves may break and generate spray. No mathematical
description of these processes is entirely satisfactory.
An important point is that it is believed that is is the small "capillary"
waves which are most important from a mass transfer viewpoint. Large waves
of period 5 to 10 s are probably not important in this respect because the
air "rides" with them. There is no doubt that the wind influences the water
which in turn influences the air phase etc., a complex equilibium being
reached and a level of turbulent mixing achieved dependent on wind speed and
fetch. There is also an area increase but this is quite small since the ratio
of wave height to length is usually about 0.143 (Kinsman 57 ) thus the
factor increase in area is approximately /(!* + 0.1A32) or 1.01 i.e. 1%. In
breaking wave conditions this may be considerably higher.
The commonest method of defining the velocity of the air is the logari-
thmic velocity profile
U - (U*/K)ln(Z/Z )
o
72
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FIGURE 12
DIAGRAM ILLUSTRATING THE NON-ADDITIVITY OF RESISTANCES
DURING UNSTEADY STATE TRANSFER IN A ROLL CELL
SECTION A
SECTION B
-4
U>
AIR
WATER
., MEAN
"OLA
K
OLA
K
_.
10 7.1 4.15
AVERAGE KQL = 3.39
7.1
KOLB
KOLB
KG
1 .1
4.2 7.1
2.64
2.64
BUT
OL
K
G '
AVERAGE KQL = 3.55
-------
FIGURE 13
DIAGRAM ILLUSTRATING A POSSIBLE EXPERIMENTAL TEST OF THE TWO
RESISTANCE THEORY FOR COMPOUNDS OF VARIOUS H VALUES
K.
•OL
SOLUTES OF HIGH H
i.e., LIQUID PHASE
RESISTANT
VOLATILIZE RAPIDLY
SOLUTES OF LOW H
i.e., GAS PHASE
RESISTANT
VOLATILIZE SLOWLY
sv
pt*
vl%
INTERCEPT
(RT/H)
74
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where U is velocity (m/s), K is the von Karman constant (taken as 0.4), Z is
the height, Z the "surface roughness" and U* is the "friction velocity"
which is equivalent to
U*
where T is the stress of the air on the surface (N/m2) and p is the air
density (kg/m3)., A plot of velocity versus ln(Z) generally gives a straight
line of slope (U/K ) and intercept In Z when U is extrapolated to zero. For
example Z may be 0.001 m, U may be 1.0 m/s thus at various heights Z the
following°velocities will apply.
U
0.001m (1 mm) 0
0.003m (3 mm) 2.75
0.01m (1 cm) 6.32
0.03m (3 cm) 8.50
0.10 (10 cm) 11.5
1.0 17.3
10.0 23.0
Clearly most of the velocity gradient lies in the few centimeters above the
water surface. A height of 10 m is the standard for wind speed measurement
but there is little gradient above 2 m.
The friction velocity U* is best conceived of as being related to the
force which the air exerts on the water rather than as a velocity. The
surface roughness Z0 can be conceived of as being related to the height of
the small capillary waves on the water surface which are caused by the wind
and tend to assist the wind to drag the water surface. Both quantities are
thus indicative of the degree of turbulence or mixing induced at the water
surface by the air and it seems reasonable that their product should
correlate well with mass transfer coefficients. Cohen et al (58 ) combined
these quantities with the air density PA and viscosity (UA) to give the
dimensionless roughness Reynolds Number lie*
Re - ZQ U* PA/UA
and correlated it with K.. Schlichting ( 59 ) has shown that for Re*
exceeding 2.3 the surface can be regarded as aerodynamically rough whereas
below 0.17 it is smooth, with a transition region between. Environmental
conditions are in the transition and rough region except at very low wind
speeds where the water surface becomes glassy.
It is not feasible to measure U* orZ routinely in the environment
thus a method must be sought of relating these quantities to a conveniently
measurable quantity such as the 10 meter wind speed UIQ. Two approaches
are possible, both of which use the dimensionless drag coefficient (or wind
stress coefficient) CD which is defined from
75
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T - CD PA ufo
But since T = p. U*2
CD = (u*/u1Q)2
A considerable literature exists on values of CQ at various wind
velocities. Typically it has a value of 10~3 under oceanic conditions
thus a typical friction velocity will be 3% (i.e. /10~3) of the 10 meter
wind speed. This is usually close to-the actual water surface drift velocity.
The available data indicate that C- tends to increase slightly with wind speed
and several correlations have been attempted, for example Wu ( 60 ) has sug-
gested that
CD = 5.0 x 10"4(U10)°'5
-4
with the value of C levelling off above 15 m/s at a value of 26 x 10
Smith ( 61 ) has recently suggested that
CD = 10~4(6.1 + 0.63U1Q)
for winds from 6 to 22 m/s, which has the merit that C does not become zero
at zero wind speed.
Unfortunately, C-. is also dependent on fetch, i.e., the distance from the
point at which the air flow meets the water surface. This distance can be a
few meters in a laboratory tank or hundreds of kilometers at sea. The reason
for this dependence is that when an air flow meets a water surface the air
starts to drag the water and to generate waves. This process continues with
wave height building up until a steady or equilibrium condition is reached.
During the acceleration phase more energy is transmitted from air to water.
This results in a higher value of U*and hence a higher value of C... Wu (62 )
has suggested that CD can be correlated as a function of the dimensionless
Froude Number F whicn is a function of the wind speed Uz at height Z above the
water surface, and the gravitational constant g (m/s^)
F - U /C%Z)°'5
Z*
Laboratory systems tend to have smaller values of Z than do oceanic
conditions thus the Froude numbers are higher, resulting in higher values of
C_. The effect of low fetch at constant wind speed is thus to alter the
velocity profile generally increasing the velocities near the surface and thus
probably increasing IL.
Charnock (63 ) argued on dimensional grounds that Z should be pro-
protional to U*z or equivalently that the group °
ZQ g/U*2 or "a"
will be constant. This can be tested by plotting Z versus U*2/g to obtain a
76
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slope of a. Wu ( 62 ) has suggested a value of 0.0156 for a and other workers
have obtained similar values, for example Smith (61 ) obtained 0.010.
The implication of this assumption is to establish a relationship between
CD and F since,
CD = (U*/U1Q)2 = [K/ln(Z/ZQ)]2
- [K/ln(Zg/aU*2)]2
- [K/ln(Zg/CD a U2Q)2] = [K/ln(l/aF2CD)]2
where F = U10/(Zg)°'5
This relationship is implicit in CD but can be plotted to facilitate
solution. Wu1 s correlation between CQ and F is essentially this equation.
Its usefulness is that under laboratory conditions measurements can be made
of U_ and Z at various values of Z and CD, & U* and Z deduced from the logar-
ithmic velocity profile. The Charnock relationship can then be tested, which
is equivalent to testing the C^ - F relationship. If these relationships
hold it can be argued that the laboratory conditions can be related to
environmental conditions since the same underlying principles apply. Further,
it becomes necessary only to measure TJ at Z of say 10 cm, calculate F, then
C and hence U*, Z and Re*. If K^ and KG data are available for both
laboratory and env?ronment they can be tested to determine if they are the
same function of Re*.
This lengthy procedure can be shortened by substituting the Charnock
relationship directly into Re* i.e.
Re* - PAU*ZQ/yA - PAU*3a/gyA
But U* -U
Thus Re* - PA
where C.. can be estimated from one of the correlations and a can be taken as
0.0156.
An alternative approach suggested by Cohen et al (58 ) is to use the
logarithmic velocity profile to calculate ZQ from U* and C^ namely
ZQ = Z exp(-K UZ/U*) - Z exp(-KCD°'5)
The difference between these equations is relatively small given the
uncertainties in the variables. For example when UIQ is 15 m/SjC.. from the
Wu correlations is 1.9 x 10~3 with the Smith correlation yielding 1.6 x 10~3.
Taking 1.8 x 10~3 as C_ gives U* of 0.64 m/s. The Charnock equation gives
Z to be 6.5 x 10"1* m whereas the logarithmic profile value is 8.5 x lO""4 m.
77
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The effect Is to change Re* by some 30%. Since It, is a fairly weak function
of Re* (for example Cohen et al ( 58 ) found it to be to the power of 0.195)
the effect is tolerable. The important requirement is that Re* be calculated
and correlated consistently. These equations are very simplified expressions
of exceedingly complex phenomena and can only be used as correlating guides
for treating experimental data.
The Charnock relationship is an attractive approach since it has been
supported by environmental observations and its use is thus preferred here.
In summary, the approach adopted here is to measure velocity profiles
K, and KG, test the Charnock relationship, calculate U*, Z and CD and hence
Re*, correlate Re* with K. and KG and examine if this correlation agrees with
other data.
Since a dimensionless number approach is used it is preferable to render
IL and K_ dimensionless either as a Stanton Number ( St) (by dividing by a
velocity)1 or as a Sherwood Number by dividing by a diffusivity and multiply-
ing by a length. It is tidier to use diffusivity only once in the Schmidt
Number (Sc) thus the Stanton Number is preferred. Two velocities can be
selected, the friction velocity U* or the free stream velocity U_. Both can
be tested and the better approach used.
The ultimate correlating equation is thus
B
St - A Re*
where St^ - ^/U* or
StG - KG/U* or
Re - PAU*ZQ/y
and Sc,. » uw/p D
T, w w
SCA " VPADA
This approach is regarded as being hydrodynamically justifiable but it
suffers from a practical disadvantage in that few environmental scientists
(who are equally concerned with other processes such as reactions, sorption
and accumulation by biota) have the necessary background in fluid mechanics
to appreciate these subtleties. It is thus convenient to transpose these
equations into simpler versions containing only 10 meter wind speed, possibly
at the expense of loss of some rigor and accuracy. Thus simpler versions
also have a useful role in that they will tend to be more readily used.
78
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A final problem is the effect of fetch on K_, as a result of the air
stream gradually building up a concentration of the volatilizing substance.
Previous work by Mackay and Matsugu ( 64 ) showed that fetch influences Kp
albeit weakly and they suggested, based on earlier work, a dependence of
the type
where X is the fetch (m). To verify this power requires data from systems
of widely varying fetch, in fact to generate a two fold reduction in K_
requires a 545 fold increase in X which is difficult experimentally. Tne
only feasible approach is to compare laboratory water evaporation data with
oceanic data at similar wind speeds. This system is entirely gas phase
controlled since there is no need for water to diffuse to the liquid surface.
The series of wind wave tank experiments described later thus had the
objective of providing volatilization data which could be used to generate
expressions for IL and Kfi from which K-.. can be calculated. Clearly it is
desirable to test this hypothesis by measuring volatilization rates over a
range of. Henry's Law Constants and compare the experimental values and those
calculated from the correlating equations.
79
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(d) Surface Films
It is well established that most environmental water bodies are covered
with a thin layer of organic-rich material consisting of proteinaceous and
lipid material. To. extreme cases this layer may be augmented by surfactants
or oil of anthropogenic origin. Such layers can have a profound effect on the
fluid mechanics of the interface, they may accumulate organic and metallic
contaminants and depress volatilization rates_.
The role of surface films in altering volatilization rates is complex
and difficult to study and quantify. No attempt is made here to review the
subject comprehensively or to undertake experimental investigations. The
aim is merely to assemble a multiple resistance model based on the fugacity
capacity concepts developed earlier and speculate on its possible future
application to studies of surface films. The subject merits more detailed
consideration than can be given here.
Liss ( 66 ) has comprehensively reviewed recent literature of the effects
of surface films on gas exchange across the air-sea interface. Liss and
Martinelli ( 67 ) have described laboratory experiments involving oil films.
The general conclusions are that natural (glycoprotein and polysaccharide)
material petroleum and surfactants to retard air-water exchange. The extent
of retardation is very dependent on the coherence or coverage of the film and
its thickness. Most natural films are unable to achieve the coherence neces-
sary to retard transfer significantly. Even a 1 mm oil film only reduces
oxygen transfer to 40% of its oil free value but a 30 ym has the same effect on
water transfer. The conclusion is that when the transfer resistance is vapor
phase controlled (as in the case of water) the effect of surface films is lar-
ger. In essence, the film creates an additional or enhanced liquid phase
resistance which adds (slightly) to the already present liquid phase resistance
for oxygen and substantially to the previously vapor-only resistance for water
vapor. Whether or not this effect will apply to all vapor phase resistant sys-
tems is not clear.
Nguyen Ly et al ( 68 ) have developed a model in which the film is consi-
dered as a separate layer with a finite thickness, diffusivity and solubility
(i.e. fugacity capacity). Typically, for detergent films the calculated thick-
ness was 10 5 cm and the diffusivity 10~9 cmz/s. The resultant mass transfer
coefficient K^ is 10 3 cm/s or 3.6 cm/h which is of the same order of magnitude
as KL.
Writing the transfer equation in the form of series resistances using
fugacity capacity (2) shows that the film will have the most profound effect
when Z is small, i.e., the solute is relatively insoluble in the film and thus
unable to establish a substantial concentration gradient specifically the total
resistance r_ is
rF + rV
6/DFZF + 1/KVZV
where subscripts L, F and V refer to liquid, film and vapor phases and 6 is the
film thickness.
The ratio of transfer rates with and without the film present is thus the
inverse of the corresponding resistances or
V'V+'V
80
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For water transfer rL is negligible thus this ratio becomes
and a value of 15 cm'1 is indicated for (tZ./Z-D,) since the ratio becomes 0.4
when 6 is 0.1 cm. ' u ^ * *
A set of reasonable values which would reproduce the experimental data
are
D,, 10~5 cm2/s • or 10~9 m2/s
r
K. 3 x lO'1* cm/s or 3 x 10~6 m/s
Ky 1 cm/s or 10~2 m/s
For water Z_ « 101* mol/m3atm, Z~ * 41 mol/m3atm
For oxygen Z_,/Z.. • 2 corresponding to an oil-water partition coefficient of 2,
oxygen being more soluble in oil than water. ZT is approximately 1.5 corres-
ponding; to H for oxygen in water of 0.65 atm m"/mol thus Z*, is approximately
3.0.
If these estimates are close to the correct values it becomes clearer why
oil retards water transfer more than oxygen transfer. For water ry is appro-
ximately 2.4 m2s/mol. For oxygen r_ is approximately 2.5 x 105, a factor of
105 greater thus a much thicker oil film is necessary to establish a comparable
resistance. This is compensated for, however, by the much greater solubility
of water in the oil compared to oxygen resulting in a low H and a higher Zj
by a factor of some 300. The net result is that an oil film a factor of only
30 greater is necessary to create a resistance equal to that experienced by the
.oxygen in the water in the absence of oil.
It follows that surface films will have their greatest effect when the
liquid resistance is low i.e., when Z^ is large or the solute Henrys Law
Constant is low and the solute can establish high concentrations in water. The
retarding effect will be enhanced if ZF is low, i.e., the solute is less solu-
ble in the surface film. Since most compounds of interest here are organic
they will probably partition preferentially into a surface film resulting in
high ZF values, necessitating very thick films to achieve significant retarda-
tion. From a knowledge of the partition properties of the solute and an .
indication of the composition of the surface film it should be possible to
estimate Z^. Dp_apparently varies from its molecular diffusivity value of -
10"5 cm2/s to 10~8 cm2/s for close packed surfactant films. The thickness 6
is amenable to measurement. In principle, it may be possible to develop a
method of calculating the film resistance but this is presently not feasible.
In summary, there may be two quite different mechanisms of surface film
retardation, introduction of a diffusive resistance as discussed, above and
damping of capillary waves resulting in hydrodynamical changes. Only /some
preliminary experiments could be undertaken here in which an attempt was made
to determine if a surface film significantly reduced benzene volatilization
rates.
81
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SECTION 6
GENERAL MODEL OF LABORATORY VOLATILIZATION SYSTEMS
There has been some confusion in the literature about the relationsnip
between laboratory volatilization systems with different geometries and air-
water contacting arrangements. Some systems involve beakers which may or may
not be stirred, over which air may or may not be blown by a fan. Others
involve wind tunnels or sparged systems in which a bubble swarm is directed
through a pool of water. It is the purpose of this section to develop a
general volatilization rate equation and demonstrate that it reduces to
simplified forms describing specific types of contacting. The danger is that
an equation for one type of system may be wrongly applied to another.
If we consider a water volume of V m3 and area Am2 contacted with a flow
of air of G m3/s and containing a solute of concentration C mol/m3 and a
Henry's Constant H atm m3/mol, the partial pressure of the solute in the gas
is an average of P atm. In cases of interest here the direction of transfer
is water to air thus C exceeds P/H, i.e. the fugacity of the solute is greater
in the water than in the air. Using the mass transfer relationship derived
earlier with overall mass transfer coefficients, KQL and KQG m/s the mass flux
N mol/m2s can be related to the concentration driving force, to the increase
in solute partial pressure in the gas (P - Pj) xrfiere P: is the inlet and P the
outlet partial pressure and to the change in solute concentration with time.
NA - G(P - Pi)/RT = -V dC/dt = AKOG(CH - P)/RT
- AKOL(C - P/H)
This contains the inherent assumption that all the area experiences the
same concentration driving force which is to a first approximation valid in
most cases. In the interests of simplicity, the derivation is continued with
the assumption that PI is zero, i.e. the incoming air contains no solute.
These equations can be rearranged to eliminate P, i.e.
P - -(RTV/G) dC/dt - (RTV/AKQG)(dC/dt) + CH
Rearranging yields,
dC/dt - GHC/((RTV)(1
Integrating from C = Co at time zero yields,
C - C0 exp( - GHt/((RTV)(l
or in terms of the individual coefficient KL and KQ
C - C0 exp( - GHt/((RTV)(l + G/KGA + GH/KLART))
82
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The relative magnitudes of the three summed terms in the denominator
control which of four regimes may apply. The principal determinants are
the prevailing values of H (which is controlled by the value of the solute),
G the gas flow rate and A the interfacial area. Although K^ and Kg vary
they do not vary over as wide a range. The following simplified or limiting
versions apply.
(a) Near-equilibrium conditions
If G/KQQA « 1 the general equation simplifies to
C - C0 exp (-GHt/RTV)
Under this condition mass transfer is essentially complete and P equals
HC. This condition occurs when the transfer area and coefficients are large
thus promoting fast and complete transfer but the gas rate G is restricted
such that the gas becomes saturated prior to leaving the system.
When H is large, i.e. there is marked preferential partitioning into the
vapor, it may be difficult to achieve equilibrium except with a very small
gas rate G. This corresponds to a condition in which head space analysis or
gas purging are very effective. Intermittent rather than continuous operation
may be preferable. Such solutions obviously volatilize very quickly and
volatilization is a significant environmental pathway.
The system of this type has been described by Mackay et al (28 ) ±n
which air is sparged into a column of water at a slow rate such that the exit
gas is saturated. It is a useful method of measuring H directly,particularly
for solutes such aromatic hydrocarbons for which solubility and vapor pressure
data may not exist or may be suspect because of the low values. A plot of the
logarithm of concentration versus time will have a slope of'-GH/RTV from
which H can be calculated from the known values of the other terms.
It is essential to confirm experimentally that the inequality assumption
is valid. This can be done by reducing A thus increasing G/KOGA. This may
involve a change in V if for example, the height of the liquid is reduced, thus
the test should be if the apparent H as obtained from the slope is dependent
on height.
(b) Liquid Phase Diffusion Control
If GH/KLART » (1 + G/KGA) the general equation simplifies to
C - C0 exp (-KLA t/V)
Under these conditions the volatilization rate is controlled by the
diffusion rate through the liquid layer immediately below the interface.
Interestingly, the rate becomes apparently independent of H which gives rise
to the possibility of the erroneous conclusion that even very involatile
(low H) solutes (such as NaCl) will be volatilized according to this equation.
In practice when H is small the inequality stated above cannot be achieved
83
-------
thus this condition will never apply.
This condition will tend to occur when H is fairly large, i.e.
H » KTRT/KQ or about 0.0002 atra ra3/gmol, which implies a fairly volatile,
insoluble solute. It is also favoured by large values of G, resulting in
the volatilized solute becoming very rapidly diluted in the exit gas stream.
This is most easily accomplished in a wind tunnel and applies for example to
the conditions described by Cohen et al (58 ). This is an ideal method of
measuring KL under various turbulence (wind speed) conditions, where A is
well-defined. The rate of concentration drop is controlled by area, KL and
the volume of water.
Convenient solute systems for measuring K^ are by oxygen transfer (in
either direction) or by volatilization of a solute such as benzene or toluene.
(c) Gas Phase Diffusion Control
If G/KfiA » (1 + GH/KLART) which is essentially equivalent to
H/RT « KL/KQ, the general equation reduces to
C = C0 exp (-KGAHt/RTV)
Under these conditions the volatilization rate is controlled by the
diffusion rate through the gas layer immediately above the interface. It
tends to occur for systems of very low H implying high solubility and/or low
vapor pressure. Since the ratio KL/KG is typically 0.01 and RT is 0.024 for
this situation to apply, H « 0.0024. This results in a very low value for
the entire term in the exponent and thus very slow volatilization. Indeed,
the water may volatilize faster than the solute unless the inlet gas is
saturated with water. The "half life" for volatilization is likely to be
many hours or even days in a small laboratory apparatus. This condition or
conditions close to it may occur during volatilization of ionizing gases such
as S02, lower molecular weight soluble organics such as alcohols and possibly
some pesticides such as dieldein.
In view of the experimental difficulties associated with operating
under these conditions it may be preferable to measure the reverse process,
i.e. absorption from the vapor, by introducing the solute vapor into a re-
cycling gas stream and monitoring the increase in concentration in the water.
This could be done easily for SOz or acetone. The form of the equation
describing the absorption process can be obtained by solution of the mass
flux equation with appropriate boundary conditions.
A convenient method of measuring KQ or KgA for a given apparatus is to
measure the water evaporation rate which is totally vapor phase controlled,
there being no necessity for the water to diffuse to the interface.
84
-------
(d) Non-Volatile Systems
When H becomes smaller than H for water, i.e. less than approximately
6 x 10"7 the group in the exponent becomes very small and evaporation under
environmental conditions will tend to increase rather than decrease the
solute concentration.
The Henry's Law Constant for water thus forms a convenient criterion
for determining if volatilization is significant environmentally.
An instructive method of illustrating these simplied versions is on a
plot of G/A against H or H/RT as illustrated in Figure 14. The four
regions correspond to the inequality assumption. It is essential when
designing and interpreting volatilization experiments to have a clear concept
of where the conditons will be on this "map". Apparently anomalous results
can be obtained by misapplication of these equations.
For example, it is convenient to use oxygen transfer rate (reaeration)
data as a means of estimating KL for other solutes in rivers since a
considerable literature on reaeration rates exists. Tsivoglov . (69,70)
demonstrated that the inert gases could be used as "tracers" or "surrogates"
for oxygen transfer estimation. Rathbun ( 71 ) later used volatile hydro-
carbons in a similar manner. The advantage of using these solutes instead
of oxygen is that their presence at the experimental concentrations is
"unnatural" whereas oxygen is ubiquitous and is generated and consumed by bio-
logical processes thus masking the concentration changes attributable to
air-water exchange. Smith et al ( ?2 ) have also measured ratios of trans-
fer coefficients of other solutes to that of oxygen. Normally the ratio of
the solute and oxygen transfer coefficients is 0.2 to 0.5 reflecting the
slower diffusion of the larger solute molecule. For some solutes very low
ratios were obtained, i.e. less than 0.1 or 0.01 which cannot be attributable
to diffusion differences.
Examination of these cases in the light of these equations,shows clearly
that when H becomes low the term (GH/KLART) becomes small thus the implicit
assumption that (GH/KLART) » 1 + G/KgA becomes invalid and the rate of
volatilization falls because a gas phase resistance becomes significant. It
is clearly incorrect to estimate the volatilization rate of such solutes from
reaeration rate data because the controlling processes differ.
A popular and simple method of estimating volatilization tendency is to
follow the concentration decay of a solute experienced in a water solution of
a solute from a beaker. Depending on the presence or nature of induced
agitation or mixing and air flow over the surface, the values of G,KG and KL
can vary considerably and it is not immediately clear which regime applies.
Increasing the air flow rate can cause a change from equilibrium control to
diffusion control corresponding to a vertical movement .in Figure 14.
85
-------
Finally, there is interest in calculating volatilization rates in
"artificial" environments such as lagoons, aerated lagoons,spray towers and
biological oxidation units. The general equations derived here can be
applied to such systems but care is necessary to ensure that the correct
equations are applied. Perhaps the safest approach is to apply the general
equation initially, using one of the simplified forms as experience demon-
strates its validity.
86
-------
102
W
CD
10
10
10~6
1
1
1
SOLUTE |
IS LESS i
VOLATILE '
- THAN 1
WATER
1
1
1
L.
1
i
1
I
i
1
I
1
I
1
1
1
1
i
• i
i
I
BOTH j LIQUID
VAPOR PHASE AND . VAPOUR LIQUID PHASE
DIFFUSION PHASE RESIS- DIFFUSION
CONTROL TANCiJs CONTROL CONTROL
G ' „ , . GH G I GH GH G
K A ' RTI^A KgA RTI^A RTI^A " ' KgA
1
e.g., WATER e.g., tkpHTHALENE e.g., BENZENE
EVAPORATION VOLATILjIZATION VOLATILIZATION
' OR 02 TRANSFER
1
1
1
-V.
X
\
\
S
S
\
s
\
\
EQUILIBRIUM CONTROL \
\
^v4"*™? s\
V
e.g. GAS STRIPPING ^^
i • | I i i
10
10"6 10"1* 10*"2
HENRY'S LAW CONSTANT (ATM.M3/MOL)
87
-------
SECTION 7
EXPERIMENTAL
INTRODUCTION AND ORGANIZATION
This section consists of a description of several experimental systems
used in the study. For each, the apparatus is described with appropriate
diagrams followed by the experimental procedures used. Analytical procedures
were common to several of the studies and are thus grouped at the end. The
results including assessment of errors and unusual difficulties are also
discussed. It should be noted that much of the experimental effort was de-
voted to improving and adapting the systems often by trial and error in
order to obtain precise experimental data. Details of these less productive
but essential efforts are generally omitted in the interests of brevity.
The approach adopted is to describe the small (30 cm diameter) volati-
lization system, the wind wave tank, the relative volatility system, the
measurement of Henry's Law Constants, the measurement of solubility and final-
ly the analytical techniques.
There were several objectives of this experimental program.
In the case of the small volatilization system the aim was toistudy the
volatilization rates of compounds with a wide range of Henry's constant to
determine whether the two resistance approach is valid. Although the evidence
is substantial that this is so, the assumption is so important that further
validation is believed to be justified. The effect of solute molecule "size"
was also investigated to develop a procedure for taking this factor into ac-
count. Other variables examined include temperature and whether solute-
mixtures behave independently or interact. A final objective was to devise a
simple test for screening the volatilization characteristics of new solutes.
Work in the wind wave tank emphasized higher velocities for which there
are few data published. Again the two resistance model was tested. The pri-
mary aim was to develop equations which can predict both laboratory and en-
vironmental mass transfer coefficients in a rigorous manner. This requires
novel interpretive analyses of these and other data since no entirely satis-
factory theoretical framework exists with which to approach this problem.
The aim in the relative volatility and Henry's Law Constant work was to
devise, methods for measuring H reliably over the range of interest above
5x10 atm m /mol, and obtain new data.
The solubility measurements and some Henry's Constant measurements sought
to elucidate the extent to which the presence of natural organic matter in-
fluences these properties at typical environmental levels.
88
-------
SHALL- SCALE- VOLATILIZATION.APPARATUS
Volatilization tests were carried out in a small scale system in which
the process of environmental air-water transfer was simulated. It is shown
schematically in Figure 15 and is similar in principle to an apparatus developed
by Mackay et al (73) for dispersant effectiveness.
The core of the apparatus testing was a 30 cm ID, 30 cm deep glass tank
containing 6.0 L of water (approximately 10 cm deep) containing, in solution,
the compound under study. The tank was covered by a 1.25 cm thick, 40 x 40 cm
plexiglass lid with a rubber gasket to prevent air leakage. It was immersed
in a constant temperature bath.
Three thermometers were inserted at the centre of the tank through the
lid. One was placed in the water, giving the bulk water temperature. The
other two-were used to measure the air humidity, one giving the air dry-bulb
temperature and the other, which was wrapped with a piece of cotton cloth
continuously soaked by dipping it in a small beaker of water, giving the wet-
bulb temperature. A sampling port was located 2 cm from the tank wall to
enable water samples to be taken by a syringe.
Wind-induced waves were generated at the air-water interface by blowing
air from a blower into the tank. The air flowrate and thus the turbulence
level was controlled by a 3.2 cm diameter gate valve and measured by passing
the air through an orifice meter 2.54 dm in diameter connected to a water manometer.
Air entered the tank through a 5 cm diameter PVC 90 elbow inserted through
the lid and at a height of 10 cm above the water surface, and flowed tangentially
along the wall of the tank in a swirling motion. It left the tank through a
5 cm diameter pipe located vertically beside the elbow and extending 6 cm
below the lid. The exit air was directed to a fume hood by a 3.2 cm flexible
plastic hose. The relative locations of the pipes, thermometers and sampling
port are shown in a plan view of the tank in FigurelS.
The evaporation of water at the air-water interface in the tank may
influence the mass transfer behaviour of the compounds under study, thus
provision was made for humidity control. In most tests the air was saturated
with water vapor by passing it through a humidification column prior to entering
the tank. This 20.3 cm ID plexiglass column was packed with 3.8 cm ceramic
Raschig rings to a height of 1.2 m. The blower was located at the bottom of
the column. Air having a maximum flowrate of 17,000 cm3/s passed up the column.
Simultaneously, water was injected at the lap in a spray located 24 cm above the
packing at a flowrate of 100 cm3/s. The water collected at the bottom of the
column drained into a 40 cm x 20 cm x 25 cm reservoir from which it was
returned to the top of the column by a pump.
To prevent any increase in air temperature due to heat generation in the
blower, it was wrapped with copper cooling coils through which cold-water was
passed! A second coil was immersed in the water reservoir. The-air- (and water)
temperatures of the column were adjusted by varying the cooling: coil water
flowrate. ,
89
-------
The saturated air leaving the top of the column was passed through the
gate valve and the orifice meter to the tank, where the flowrate was controlled
and measured.
In some experiments, the mass transfer process was studied using unsaturated
air, in which case, instead of passing the air through the humidification column,
it was directly blown into the tank.
The volatilization rates of twenty organic compounds across the air-water
interface were determined. The compounds_listed_in Table 6 and Table 7 covered
a wide range of Henry's Law Constants (10 2 to 10 e 'atm.m3/molj.
The overall liquid phase mass transfer coefficients (KQ^) for each compound
were determined individually with air saturated with water vapor at four dif-
ferent turbulence levels and at ambient temperature (22 ± 2° C) . The experimental
procedure for a typical run is outlined below.
The saturated solution of the compound under study was prepared by
stirring an excess quantity of the compound in distilled water for a minimum
of four hours. Six liters of distilled water having a low concentration (less
than 100 ppm) of the compound was prepared in the glass tank by diluting the
saturated solution. The degree of dilution (10, 100, or 1000 times) depended
on its response factor in the gas chromatograph.
The plexiglass lid with the rubber gasket was immediately fitted in place
to minimize the loss of the compound. A stirring rod was then used to stir
the diluted solution to ensure homogeneity of the aqueous solution. Water was
then passed through the cooling coils around the blower and in the reservoir
to maintain the air flow at ambient temperature. The pump and blower were
then switched on and the tank and the plexiglass lid were checked to ensure
a complete seal at the rim. The air flowrates were adjusted by the gate valve
to the required value.
Five minutes were allowed for the air. flow and water waves in the tank
to stabilize, after which water samples were taken at selected times. Sampling
intervals depended on the rate of volatilization of the specific compound and
varied from ten minutes to two hours. Duplicate water samples of 5.5 ml were
obtained by syringes through the sampling port and stored in 5.5 ml sampling
bottles. The samples were analyzed immediately by gas chromatography or if
analyzed later were stored in a refrigerator with tightly sealed caps to avoid
vapor loss.
A typical experiment lasted for two to ten hours depending on the rate of
volatilization. To reduce experimental error, a concentration drop of at
least 80% (i.e. a factor of 5) was desirable. Thus, a preliminary run was
performed for each compound to determine the sampling time and the length of
the experiments.
When the mass transfer rates of two or more compounds were studied
simultaneously, the same procedure described above was followed. Compounds
were used in mixtures only when gas chromatographic analysis was capable of
detecting and quantifying them separately.
90
-------
TABLE 6
SOLUTES USED IN THE VOLATILIZATION EXPERIMENTS
Small Scale Wind Wave H at p°C
Apparatus Tank atm m /mol
Carbon Tetrachloride
Toluene
Benzene
Chorobenzene
1 , 2-dichloropropane
0-dichlorobenzene
Bromobenzene
l-Choro-2-Methylpropane
1 , 2-dibromoethane
Bromoform
1 , 3-dibromopropane
3-heptanone
2-heptanone
4-methyl-2-pentanone
2-butanone
2-pentanone
2-butanol
1-pentanol
Acetophenone
Cyclohexanol
2-methyl-l-propanol
1-butanol
/ / 1.6 x 10~2
/ / 6.7 x 10~3
/' / 5.5 x 10~3
. ... /' .'".' . .". . './........ .3.7 x 10~3
/ / 2.1 x 10~3
/ 1.9 x 10~3
/ 2.1 x 10~3
V .1.2 x 10~3
/ / 6.3 x 10~4
/ 6.2 x 10~4
/ 3.2 x 10~4
/ 1.5 x 10 ~5
/ / 1.0 x 10~4
/ 3.1 x 10~5
/ 4.3 x 10~5
/ • / 3.7 x 10~5
/ 3.9 x 10~5
S / 1.5 x 10~5
^ 1,1 x 10~5
/ 8.7 x 10"6
/ 5.6 x 10~5
^ 1.1 x 10~5
Note. Further physical property data are given in Table 7.
91
-------
PART 1
TABLE 7
PROPERTIES OF THE SOLUTES USED IN THIS STUDY
Compound
Benzene
Toluene
Chlorobenzene
Bromobenzene
o-Dichlorobenzene
Carbon-
tetrachloride
1,2-Dichloro-
propane
l-Chloro-2-methyl
propane
1 , 2-Dibromo ethane
1 , 3-Dibromo-
propane
Bromoform
1-Butanol
2-Butanol
1-Pentanol
2-Methyl-l-
propanol
Cyclohexanol
2-Pentanone
2-Heptanone
Molecular
Weight
78.11
92.13
112.56
157.02
147.01
153.84
113.0
92.57
187.9
201.9
252.7
74.12
74.12
88.15
74.12
100.16
86.14
114.18
ESTIMATED VALUES ARE DESIGNATED WITH AN ASTERISK*
Vapor Pressure Aqueous Solubility Solubility of water
(atm) mol/m in solute at 25 C
20°C 25 C 20 C 25 C (mol frn)
0.100
0.029
0.012
0.00132
0.118
0.052
0.0144
0.0060
0.0058
0.0158
0.0079
0.00132
0.016
0.0034
0.125
0.0374
0.0156
0.056
0.00193
0.148
0.118
0.066
0.119
0.0143
0.0027 '
0.00737
0.010
0.023
0.0034
0.0095
0.00145
0.016
22.4
5.39
4.44
0.68
5.20
25.0
23.0
1040
1686
2712
307 (22°)
1280
1260
500
38.0
22.8
4.85
4.19
2.61
0.99
7.54
5.10
99.0
22.94
8.4
12.0
1040
500
38.0
-4
7x10
5xlO~4
2xlO~3
2xlO~3
-4
4x10
7xlO~4
2x!0"3 •
4xlO~3
4xlO"3
2xlO"3
IxlO"3
0.5
0.76
0.33
0.51
0.58
0.14
0.11
Henry's Law Constant
atm m /mol.
20°C 25°C
_3
4.39x10
5.18xlO~3
2.61xlO"3
2.0 x!0r3
•3
1.8 xlO
2.27xlO~2
2.07xlO~3
1.0 xlO"3
5.0 xlO~4
3.0 xlO~4
5.0 xlO~4
7 xlO"6
6 xlO~6
8 x 10~6
1.0 x 10~5
— ft
2.5 x }0
_ 5
3.67x10
l.OlxlO"4
-3
5.49x10
6.71xlO~3
3.72xlO~3
2.08xlO~3
_3
1.95x10
1.56xlO~2
1.2 xlO~3
6.32xlO~4
3.18xlO~4
6.15xlO~4
1.65xlO~5
-5
4.88x10
-------
PART 1
TABLE 7 CONTINUED
Compound
3-Heptanone
4-Methyl-2-
pentanone
Acetophenone
2-Butanone
(Methyl ethyl ketone)
Oxygen
Water
Air
Carbon dioxide
Radon
I
ss
1
Molecular Vapor Pressure Aqueous Solubility Solubility of water Henry's Law Constant
Weight (atm) mol/ra in solute at 25 C atm m /mol.
20°C 25°C 20°C 25°C (mol frn) 20°C 25°C
114.18 0.00184 125.2 0.047 2.0 xlO~4
100.16 0.0079 0.0095 190 0.097 4.60xlO~5
-4 -5
120.16 4.87x10 45.8 0.01 1.06x10
-5 -5
72.12 0.102 0.129 3702 3134 0.055 2. 92x10^ 4.35x10
3328 3.23xlO~
32.0 - - - -
18.0 - - - -
29---- - --
44 __ __ -.-
-------
PART II
TABLE 7
PROPERTIES OF THE SOLUTES USED IN THIS STUDY
ESTIMATED VALUES ARE DESIGNATED WITH AN ASTERISK*
Compound
Benzene
Toluene
Chlorobenzene
Bromobenzene
o-Dichlorobenzene
Carbon-
tetrachloride
1,2-Dichloro-
propane
l-Chloro-2-methyl
propane
1 , 2-Dibromoe thane
1,3-Dibromo-
propane
Bromoform
1-Butanol
2-Butanol
1-Pentanol
2-Methvl-lT
propanol
Cyclohexanol
2-Pentanone
2-Heptanone
20°C
0.0797
0.0732
0.0705
0.0691
0.0643
0.0695
0.0716
0.0719
0.0724
0.0663
0.0710
0.0778
0.0778
0.0703
0.0778
0.0693
0.0723
0.0591
Diffusivities (cm /s) fi
air in water x 10
25 C 20°C 25°C
0.0817
0.0751
0.0724
0.0709
0.0659
0.0713
0.0734
0.0739
0.0742
0.0680
0.0728
0.0798
0.0798
0.0721
0.0798
0.0711
0.0741
0.0606
9.57
8.45
8.05
7.95
7.704
8.22
8.09
8.04
,
8.92
7.9
8.87
8.65
8.65
7.70
8.65
7.71
7.99
6.26
10.9
9.63
9.69
9.58
8.78
9.90
9.75
9.69
10.8
9.52
10.7
10.4
10.4
9.62
10.4
9.29
9.62
7.54
20°C
1.892
2.060
2.139
2.182
2.345
2.169
2.106
2.097
2.083
2.275
2.125
1.938
1.938
2.145
1.938
2.176
2.086
2.552
Schmidt
in air
25°C
1.898
2.065
2.142
2.187
2.353
2.175
2.113
2.104
2.090
2.281
2.130
1.943
1.943
2.151
1.943
2.181
2.093
2.559
Numbers
in water
20°C 25°C
1049
1188
1247
1263
1303
1221
1241
1249
1126
1271
1132
1161
1161
1304
1161
1302
' 1257
1604
827
931
925
936
1021
906
920
925
830
942
838
861
861
932
861
965
932
1189
Molar Volume
at_N. BP.
cm /mol
96
118.2
116.9
119.3
137.8
112.8
115.8
117.1
98.4
120.6
99.5
103.6
103.6
125.8
103.6
125.6
118.4
177.6
-------
PART II
TABLE 7 CONTINUED
Diffusivities (cm /s)
Schmidt Numbers
Molar Volume
Compound in air
20°C 25°C
3-lleptanone 0.0591 0.0606
4-Methyl-2- 0.0661 0.0678
pentanone
Acetophenone 0.0649 0.0666
2-Butanone 0.0805 0.0825
(Methyl ethyl ketone)
Oxygen
Water
Air
Carbon dioxide
Radon
in water
20°C
6.26
7.21
7.21
9.05
18.0
18.0
17.7
x 10
25°C
7.54
8.68
8.683
10.9
20°C
2.552
2.281
2.32
1.866
0.77
in air
25°C
2.559
2.287
2.329
1.880
0.60
in
20°C
1604
1393
1393
1109
558
570
water
25°C
1189
1033
1033
823
at3N.BP.
cm /mol
177.6
140.6
140.4
96.2
25.6
18.9
29.9
34.0
-------
Experiments in which the effects of temperature and humidity were examined
involved blowing air directly into the tank instead of through the humidification
column. The temperature of the water bath in which the glass tank was immersed
was adjusted by an immersion heater or a cooler as required. The dry-bulb
temperature of the unhumidified air was kept at 25° C. The experimental pro-
cedure was identical to that described previously. During the run, water
temperature, wet and dry-bulb temperatures were checked and adjusted if necessary.
The oxygen transfer rate across the air-water interface was studied by first
depleting the water of oxygen by bubbling nitrogen gas. A YSI Model 53 Oxygen
Monitor connected to a Heath-Built Model EUW-20A Servo-Recorder was used to
indicate the percent saturation of oxygen in water. The instruments were
first calibrated by immersing the oxygen probe in a beaker of water saturated
with air. After calibration the oxygen probe was inserted through the plexiglass
lid and Immersed 5 cm below the water surface to monitor the decrease in oxygen
concentration. When oxygen saturation was less than 20% (about 2 ppm),
nitrogen bubbling was stopped and the blower was switched on, the flowrate
adjusted and the increase in oxygen concentration was recorded. The concentration
was at least 80% of saturation before the experiment was terminated. At the
end of the'test, the oxygen concentration was allowed to reach a steady value
to confirm the saturated concentration calibration. These tests were repeated
at four different flowrates.
The air flow geometry was designed to simulate wind effects on water in the
environment. Above a critical air flowrate, water waves were observed. This was
found to occur at a turbulence level of 2 to 3 cm H.O pressure drop across the
orifice meter. Below this turbulence level, a flat water surface moving along
with the air flow was observed. At turbulence levels of 3 to 7 cm H 0, steady
and smooth waves having heights of 4 to 7 cm were noted. At still higher
turbulence levels (> 7 cm H20) the water surface was rough, waveheight did not
increase significantly, a small quantity of air bubbles was found in the bulk
of the water. It is believed that this contacting geometry is the best small
scale simulation that can be obtained, being more typical in turbulence intensity
than stirred systems and more reproducible than beaker-fan systems.
The conditions were selected to study mass transfer within the ikinetic area
in Figure 14 . The non-volatile region has been omitted because experiments
conducted in this regime are of little interest and are of long duration. The
turbulence levels were chosen largely on the basis of oxygen transfer rates to
cover the range of environmental interest. Taking the gas flowrate (G) from the
flowrate through the orifice meter and the surface area (A) as the flat water
surface area, the ratios G/A were calculated and found to be 0.15 to 1.00 m/s
which indicates equilibrium was not reached in these experiments. For a given
G/A ratio or turbulence level, when compounds of different Henry's Law Constant
(H) values were tested in the apparatus, the volatilization process moved from
vapor phase diffusion control for low H to liquid phase diffusion control for
high H. Between is a transition region in which resistances in both phases
were significant.
The twenty organic compounds were tested at four levels of turbulence of
3, 4, 6 and 8 cm HO pressure drops across the orifice meter. For compounds
with high Henry's taw Constant, such as benzene, samples were taken every 10-20
96
-------
minutes over two hours. For compounds with low Henry's Law Constants, for
example, acetophenone samples were taken every 1-2 hours over 10 hours.
During the experiments, slight variation of water, air temperatures was unavoid-
able but were kept at 20 i 2 C. The wet and dry-bulb thermometers indicated
that the air was essentially saturated with water vapor.
Applying an overall mass balance on the system assuming negligible solute
oncentration in the bulk of the vapor phase, results in the equation (as
detailed earlier) where Co is the initial aqueous solute concentration and C the
concentration at time t; A and V are the surface area and volume of water
respectively. Due to wave motion at the surface of the interface, determination
of the actual surface area is difficult, thus A was taken as the flat water
surface area.
The overall mass transfer coefficients (KQL) were determined by plotting
In (C/C0) against t, the slopes of these plots being obtained by linear
regression. A typical plot of 111 C/C0 versus t is shown in Figures 17 to 19 for
compounds of high, intermediate and low volatility. Table 8 groups all the
experimental mass transfer coefficients, the compounds being listed in order
of decreasing Henry's Law Constants. The dependence of transfer coefficients
on turbulence levels is shown in Figure 2Q.
Five different groups of organic compounds were selected and studied in
mixtures. The tests were conducted at air and water temperatures of 20 ± 2 C
with saturated air and at two different turbulence levels, corresponding to
4 and 6 cm HO. The results are shown in Table 9. The mass transfer coefficients
were calculated individually.
The effects of temperature and humidity were studied by keeping the air dry-
bulb temperature constant at 25° C for all runs. QA wet-bulb temgerature of
16 - 1° C was measured. Water temperatures of 25 C, 20 C and 15 C were tested
using a mixture of toluene and benzene as volatilizing solutes at a turbulence
level of 4 cm H 0. The experimental data were analyzed as described above, the
mass transfer coefficients being presented graphically in Figure 21.
The transfer of oxygen in the laboratory was tested at water and air
temperatures of 20 - 2° C using air saturated with water vapor transfer at four
different turbulence levels as illustrated in Figure 22.
As oxygen was transferred from air to the water phase, the following
equation results from an overall mass balance:
in[(c - cs)/(c0 - cs)] = -KOL At/v
where CQ is the initial concentration at time zero and Cs is the final saturation
concentration at infinite time.
97
-------
TABLE 8
MASS TRANSFER COEFFICIENTS IN THE SMALL SCALE VOLATILIZATION SYSTEM.
UNITS ABE cm/h. VALUES IN PARENTHESES ARE CORRELATED.
Compound
carbon tetrachloride
toluene
benzene
chlorobenzene
1 , 2-dichloropropane
0-dichlorobenzene
bromobenzene
l-chloro-2-tnethyl-
propane
1 , 2-dibromoethane
bromofora
1 , 3-dibromopropane
3-heptanone
2-heptanone
4-methyi-2-pentanone
2-butanone
2-pentanone
2-butanol
1-pentanol
acetophenone
cyclohe::anol
oxygen
K.T values at stated orifice plate pressure drop
\JLt
3 cm H20
10.07 (8.54)
8.31 (8i59)
10.48 (9.12)
10.48 (8.28)
5.59 (8.26)
8.19 (8.01)
12.41 (8.18)
10.22 (8.0)
9.94 (7.91)
7.46 (7.90)
7.60 (6.93)
7.20 (5.72)
6.33 (4.66)
7.22 (3.40)
5.40 (2.92)
7.52 (3.16)
1.90 (3.4 )
1.64 (1.66)
1.10 (1.17)
0.35 (0.33)
17.3 (13.4)
4 cm H20
14.50 (15.5)
19.72 (15.6)
19.8 (16.6)
22.83 (15.0)
13.58 (14.9)
15.40 (14.5)
20.35 (14.8)
17.87 (14.5)
16.98 (14.4)
11.09 (14.3)
12.82 (12.6)
13.96 (10.4)
11.44 (8.45)
13.37 (6.18)
7.78 (5.30)
9.81 (5.72)
3.30 (6.22)
2.44 (3.02)
2.28 (2.12)
0.44 (0.59)
32.0 (24.3)
6 cm HO
27.73 (28.1)
30.28 (28.3)
32.25 (30.0)
24.13 (27.3)
25.47 (27.2)
22.47 (26.4)
31.67 (26.9) '
28.43 (26.3)
25.34 (26.0)
23.46 (26.0)
25.12 (22.8)
19.96 (18.9)
14.22 (15.3)
16.45 (11.2)
11.73 (9.61)
14.18 (10.4)
4.10 (11.3)
3.21 (5.48)
2.95 (3.85)
0.47 (1.07)
46.0 (44.0)
8 cm HO
36.71 (39.9)
36.35 (40.1)
44.15 (42.6)
31.54 (38.7)
34.06 (38.6)
31.03 (37.4)
40.35 (38.2)
41.66 (37.3)
33.35 (36.9)
32.48 (36.8)
34.00 (32.4)
23.00 (26.7)
22.93 (21.7)
20.00 (15.9)
15.92 (13.6)
17.99 (14.7)
4.49 (15.9)
4.84 (7.77)
3.76 (5.47)
0.68 (1.52)
5^.0 (62.4)
vO
oo
-------
TABLE 9
VOLATILIZATION OF MIXTURES
Compounds
benzene
toluene
benzene
toluene
bromoform
benzene
bromoform
1, 2 dichloropropane
3 heptanone
2 pentanone
2 butanol
1 pentanol
K™
OL
at h =
Single
19.8
19.7
19.8
19.7
11.1
19.8
11.1
13.6
14.0
11.4
3.3
2.4
(cm/h)
4 cm H_0
Mixture
19.0
19.1
19.0
19.1
10.5
10.5
13.4
8.1
7.0
1.7
2.0
KOL
at h =
Single
32.2
30.3
32.2
30.3
23.5
32.2
23.5
25.5
20.0
14.2
4.1
3.2
(cm/h)
6 cm H20
Mixture
29.0
28.9
29.0
28.9
22.4
29.0
22.4
20.4
14.0
11.0
2.8
2.4
99
-------
FIGURE 15
GENERAL ARRANGEMENT OF THE SMALL SCALE VOLATILIZATION APPARATUS SYSTEM
o
o
humidity
column
water
(low
air
flow
air -{--
blower
n't
air
X
/
' /
f
packing /'
s
•'/•
x
x'
"' '•
^
wdtcr
H — 20 em— H
MM*
pump
0
M
1
water
h
~j we
1 rtv
gala valve
orifice
meter
IT]
water
manometor
lOcin
JL
10 cm
1
to (mm hood
sampling
port
»
roservolr
water
30 crn ------ H
JO ciri
-------
FIGURE 16
PLAN VIEW OF THE SMALL SCALE VOLATILIZATION TANK
ir in
!r cut
wst-bulb
\
\
O dry-bulb hermcmstsrj
30 cm
101
-------
FIGURE 17
A TYPICAL PLOT OF LOG CONCENTRATION VERSUS
TIME FOR A HIGHLY VOLATILE SOLUTE (BENZENE)
1.C
60 £c
Tin* lrr.in)
102
-------
FIGURE 18
A TYPICAL PLOT OF LOG CONCENTRATION VERSUS TIME FOR
A SOLUTE OF INTERMEDIATE VOLATILITY (2 BUTANONE)
C.CC1
Tin-.* (K-!
103
-------
FIGURE 19
A TYPICAL PLOT OF LOG CONCENTRATION VERSUS TIME
FOR A SOLUTE OF LOW VOLATILITY (1 PENTANOL)
C.01.
104
-------
FIGURE 20
PLOT OF MASS TRANSFER COEFFICIENTS KQL VERSUS TURBULENCE FOR THE SMALL
SCALE VOLATILIZATION APPARATUS ILLUSTRATING DEPENDENCE ON VOLATILITY
105
-------
FIGURE 21
EFFECT OF TEMPERATURE ON K^ FOR BENZENE AND TOLUENE
— - - - - - —T UL " ' ' "~r
VOLATILIZATION IN THE SMALL SCALE VOLATILIZATION SYSTEM
20
J=> 10
10
OBENZENE
•TOLUENE
J_
20 30
WATER TEMPERATURE °C
106
-------
FIGURE 22
PLOT OF LOG ((C - CJ/(C - C^)) VERSUS TIME FOR OXYGEN
TRANSFER IN THE SMALL SCALE VOLATILIZATION SYSTEM
107
-------
WIND WAVE TANK
The wind-wave tank system used for the volatilization study is shown in
Figure 23 . It consisted of an upwind or air-entry section, a water tank, and
a downwind section in which an Aerovent LS-248 fan was located. One side of
the water tank was made of steel plate while glass sheet was used for the front
side to permit viewing of waves and taking other measurements. The top of
the tank was removable and was constructed of acrylic sheet to facilitate
observations. Air gaps were taped to prevent leakages.
The upwind section was equipped with a dif fuser to decrease the turbulence
of the air flow at the entrance. A honeycomb structure consisting of glued
thin wall paper tubes, 4 cm in diameter and 23 cm in length, was installed
at the inlet converging section and just upstream of the outlet dif fuser to
even out the swirling motion of the fan. An aluminum plate 50 cm long was
attached to the end of the upwind section and inclined at an angle of 5°
to the water surface to provide a smooth transition between the adjoining
air and water flow. Air speed was varied by inserting screens of different
porosity in front of the fan.
A fibre mat wave absorber was attached to the downwind end of the tank
to dissipate the wave energy and minimise reflection. It also acted as a
barrier to stop water spilling out from the tank during high wind speed runs.
To maintain a uniform concentration along the tank, a recirculation
system consisting of a 1.5 HP pump (Dayton, Teel pump) and a gate valve for
adjusting the recirculating rate was connected to the two ends of the
water tank. Two stirrers (Canlab high-torque stirrers) were mounted on the
tank to enhance the mixing process. A stirrer speed of 400 r.p.m. was
found to give satisfactory mixing with minimum disturbance and no surface
vortex formation. The propeller shafts were made of 316 stainless steel, were
40 cm in length and were. 9 mm in diameter. The propellers used were axial
flow three bladed marine-type propellers, type 316 stainless steel, placed
30 cm below the water surface.
Air velocity profiles were measured at two locations, A and B which
were 1.5 m and 4.2 m from the leading edge of the tank, using a pitot-static
tube of Prandtl design which was mounted on a motor driven transverse
mechanism. The height of the pitot tube from the water surface was measured
by a cathetometer. The pressure differential was measured using a
differential pressure transducer (Decker 306) and a recorder (Honeywell,
Electronik 196). The pressure transducer was calibrated using a zero dis-
placement type micromanometer (Airflow Development Ltd., portable Airflow
Testing Set Mark IV).
The drift velocity of the wind driven current was measured using pieces
of wax paper 5 mm in diameter. The tank was divided into thirteen sections
and the time for the wax paper to travel through each of them was measured
using an electronic stop-watch.
The transfer rates of eleven organic chemicals at various wind speeds
were measured. Tap water was used for the experiments. A sump pump was used
to dissolve the chemicals. For compounds which were denser than water saturated
solutions were first prepared in large vessels and then diluted in the water
108
-------
FIGURE 23
DIAGRAM OF THE WIND WAVE TANK
l-82cm-j-—2U cm
I. Diriitsc-r
2 . llmniili Ly Mcnsurumcnl
3. Air Flo* Grid
•1. Doach
91 cm
-4- 80cm-l
it. Stlrrur
O. Drain
10. Hecirculation Pump
11. Air Flow Controlling Screen
14. Wind Tunnel
15. Water Tank
5. Interfacial Temperature Measurement 12. Aerovent LS-248 Fan
6. H«clrculntion System 13. Wave Absorber
7. Samp I tuts Port
109
-------
tank. Direct mixing in the tank was feasible for soluble compounds which
were less dense than water. Water samples (50 mL) were siphoned from the
tank usually at one hour intervals however the duration between sampling was
increased up to four hours for experiments of less volatile compounds which
ran over 50 hours. The analytical procedure is described later.
The evaporation rate of water at different wind speeds was measured
using a constant water level apparatus which operated on the "chicken-
feeder" principle i.e. the volume of water added to the tank to maintain a
constant level was measured. Air humidity was measured at the upwind and
downwind ends of the tank and the interfacial temperature was estimated
using a thermometer (accurate to 0.1°C) dipped just below the water surface.
The length of the experiments was usually 48 hours to give a reasonable esti-
mate of the transfer coefficient.
Velocity profiles were measured in the wind wave tank for speeds from
5 to 13 m/s. A steep increase in velocity adjacent to the air-water inter-
face was found and a uniform velocity occurred in most parts of the profile.
A typical velocity profile is shown in Figure 24 . The profiles indicate that
the air flow generally develops the behaviour characteristic of turbulent
flow in a boundary layer over roughened surfaces.
The velocity profiles were fitted to a logarithmic law as described
"earlier, the values of the free stream velocity if, the friction velocity
D and the surface roughness ZQ being calculated. Figure 24 also gives a
typical logarithmic profile.
Longitudinal profiles of surface velocity for different flow conditions
are plotted in Figure 25. The drift current appears to increase linearly
with the wind speed and a ratio of 0.0282 can be established from the data.
A plot of drift velocity versus wind speed is shown in Figure 26.
The development of wind waves with fetch can be distinguished into
several regions. The fist part is the wave generation section which con-
sisted of the glassy surface near the leading edge of the tank in which
two-dimensional waves are formed at the end of the section. The second
region of linear instability followed in which the amplitude increases while
the frequency is approximately constant. The third section is the non-linear
growth region in which the growth in amplitude takes place at a slower rate
while the frequency of dominant waves decreases with fetch. For still larger
fetches white caps and water droplets may form and an equilibrium wave pattern
110
-------
FIGURE 24
TYPICAL PLOT OF LINEAR AND LOGARITHMIC VELOCITY PROFILES
50
<.o
!3°
H
X
o
IJ
20
10
0
\o
\
Screen 2
Position A
c
U., 9.95 m/s
0
3
)
O
f
A
/
i i i i '
10
E
O
****
H-
I
CD
•x
1
1
O
y
7
/
/
t /
9
w Uo, 995 m/s
/U" 63.8 cm/ s
Z^ 'O.O3O1 cm
o
- '
till
6 7 6 9 10
iAiiMr~\ cncrcrr* / rv^ ,«- \
u
WIND SPEED (m/s)
-------
FIGURE 25
VARIATION OF SURFACE DRIFT VELOCITY WITH FETCH IN THE WIND WAVE TANK
1100 m/s
11.67 «
* 10.31 •
O 8.57 •
€ 7
5.96
100
200 300
FETCH (cm)
too
500 600
-------
FIGURE 26
PLOT OF FINAL WATER SURFACE DRIFT VELOCITY VERSUS WIND SPEED FOR THE
WIND WAVE TANK ILLUSTRATING A DRIFT VELOCITY OF 2.82% OF WIND SPEED.
Slope 0.0282
5 10
WIND SPEED (m/s)
113
-------
is established.
The first two stages of wave formation could be easily identified in the
tank but the small fetch of the wind wave tank prohibits the transition into
the non-linear growth region. A glassy surface could be identified only at
low wind speed (< 5 m/s). Dp to a wind speed of 3 m/s, no waves appeared on
the water surface. As the wind speed increased, small ripples appeared and
were separated by relatively calm water. When the wind speed reached 5 m/s
significant waves developed from the small ripples and the amplitude in-
creased with fetch. Wave heights up to 4 cm were observed and small ripples
could be seen riding on the dominant waves at higher wind speed. Although
the air speed U^ reached values exceeding 13 m/s, breaking waves i.e.
.white caps, were not observed. At high air velocities small droplets of
spray were observed to be shedding from crests of the larger waves on the
downwind end but the waves did not become sharp-created,- as is found in a
"fully developed" sea.
Volatilisation Tests
A component mass balance -during volatilization from the tank gives,
KOLA(C - P/H) = - V f
where C is the average concentrations in the water phase (mol/m3), P is the
air partial pressure (atm), H the Henry's Constant, A and V are the surface
area in m2 and the volume in m3 of the water in the tank respectively.
Integrating the differential equation gives
(c-p/H) - (CO-P/H) exp (-KQLA t/v)
where Cn is the initial concentration. '
Recalling the equations derived earlier for various laboratory air-
water contacting systems it is clear that conditions are either liquid or
gas phase diffusion controlled since 6/A is of the order of 2 m/s thus
assuming a K of 0.01 m/s the group G/K A is of the order of 200. Inclusion
of a liquid phase resistance adds to this group thus it exceeds unity (the
criterion for near equilibrium conditions by at least two orders of
magnitude). It follows that the exit gas is at the most 1% saturated
i.e. P/H < 0.01C thus P can be assumed to be zero without significant error
and
C = CQ exp(-KQLA t/v) - CQ exp(-KQL t/h)
114
-------
FIGURE 27
TYPICAL PLOT OF LOG CONCENTRATION VERSUS TIME FOR
A VOLATILE COMPOUND (BENZENE) IN THE WIND WAVE TANK
20.7 °C
13.29 cm/h
7.09 mxs
3 U
TIME(h)
115
-------
FIGURE 28
PLOT OF LOG CONCENTRATION VERSUS TIME FOR VOLATILIZATION OF
A LOW VOLATILITY COMPOUND (1 BUTANOL) IN THE WIND WAVE TANK
10
05
c
c.
0.1
L
17'C
169 cm/h
13.2 m/s
10 20 30
TIME (h)
50
60
116
-------
FIGURE 29
PLOT OF K VERSUS WIND SPEED FOR VOLATILIZING
'" UJ-* " -•••-••••----
SOLUTES OF VARIOUS H VALUES IN THE WIND WAVE TANK
o Benzene e 1-Pentanone
-o- Toluene + l-3utancl
'•O h * i,2-Dichlcropropcne G 2-Fentanol
® 1,2-Dibrcmoethane A 2-Methyl-1-Propanol
C3 Chlcrobenzene
A Carbon Tetracl-Joride
O 2-Heptanone
a
30
&
©
u
*
o
20
o
O
©
©
a
o
o o
* O
3 1C 12
WIND SPEED (m/s)
117
-------
where h is V/A and is the mean height of water in the tank. The. data from the
mass transfer runs were analyzed using linear regression to calculate the
overall mass transfer coefficient from the ln(c) versus t graph. The fitted
line was not forced through the origin and the intercept can have values
greater or less than the concentration measured at time zero. Figure 27
shows the results of a typical benzene run.
The data obtained for less volatile compounds show more scatter, Figure
28 being the results of a n-butanol run. The reason for this is believed
to be %he difficulties encountered in analytical techniques, and since
the stripping efficiency for alcohols and ketones at room temperatures is
low and more variable. The accuracy was however sufficient for the present
purposes.
During a volatilization run, the temperature of the water and the humidity
of the room were reasonably constant. However, a temperature difference of
5°C between runs carried out in the winter and in the summer necessitated
some correction. The temperature dependence of KQ. on temperature is normally
represented as,
v /v m Q(TZ ~ TI>
KOL2/KOL1 6
Dobbins ( 48 ) reported that the range of 6 varied from 1.017 to 1.044.
Metzger ( 74 ) has shown that the numerical value of 6 depends on the mixing
conditions in the water, with values being generally in the range 1.005 to
1.030. A value of 1.016 was suggested by Thackston 'and Krenkel ( 75 ) and
was employed by Cohen ( 58 ) to make the adjustment. The same value is used
in the present study to correct all the mass transfer data to 20°C.
Exchange coefficients obtained for the solutes at different wind speeds
are plotted in Figure 29. Their properties are given in Table 7.
In setting up the mass balance equation a uniform concentration in the
tank is assumed. Mixing experiments with dye showed that water was recircula-
ting at a speed about 1 cm/s which was relatively fast compared to the time
between sampling. Mixing in the vertical direction was enhanced by the
two stirrers located along the tank. Preliminary runs indicated that the
concentrations taken in three positions of the tank were all within the accuracy
of experimental measurements, and the value of mass transfer coefficients ob-
tained were relatively close. At wind speeds greater than 3 m/s, the wind
drags the surface water to the downwind end of the tank and piles it up
which produces a hydraulic head which causes a bottom flow to occur in the
opposite direction. The experimental evidence showed that uniform mixing
was attained in the tank at a time scale much shorter than the duration of
the experiment.
Several runs were carried out using a mixture of compounds in which the
individual mass transfer coefficients were measured to study if any inter-
actions between the compounds exist. The results are listed in Table 11
along with the individual KQ^ for comparison. The difference is within ex-
perimental error and no significant deviation can be detected.
118
-------
The evaporation rate of water is controlled by the water in air con-
centration difference between the air close to the interface (which is
assumed to be saturated with water vapor ), and the bulk air phase. The
water content of the air phase was measured fay monitoring the humidity
both at the upwind and the downwind ends of the tunnel. By measuring
the flux of water vapor and the concentration difference in the air,
K for water may be calculated. A total mass balance of water in the tank
gives the following equation,
where v is the molar volume of water (.18 x 10 6 mol/m3) C. and C, are the
interfacial and bulk air concentrations of water (mol/m3) and K is the
gas phase mass transfer coefficient of water (m/s) . During a short interval,
this eqaation can be rewritten in the form,
KG = AV/(vA(C. - Cb)AVAt)
from which K can be calculated. Water evaporation experiments were carried
out over 40 nours due to the fair amount of scattering that occurred between
each individual measurement. The measured K., (which have been corrected to
20 °C) are reported in Table 10.
Surface Film Tests
Decyl alcohol (Fisher Scientific 98% purity) was used to form a monolayer
on the water surface. Initially, a benzene volatilization run was carried
out at a wind speed of 8.5 m/s. After the experiment had run for four hours
and a concentration drop was established, a layer film was formed by dripping
10 ml of the alcohol continuously onto the water surface through tubing
located at the upwind end of the wind wave tank. This would give a film of
average thickness 3xlO~5 cm or 0.3 ym, ignoring dissolution. The wind and
spreading forces caused the film to drift toward the downwind end of the
tank and multilayers of surplus alcohol could have been formed. No special
precaution was taken to remove the excess alcohol and avoid the possible
accumulation due to the constraints of the tank. The experiment was con-
tinued for another three hours during which observations were made and samples
were taken to establish a new concentration - time curve.
The water surface turned glassy smooth immediately after the addition of
decyl alcohol which could be attributed to the damping effects of the layer.
The surface stayed calm for over 8 minutes then waves of much smaller ampli-
tude started to form. However, the appearance of waves only lasted for a
short duration and the surface returned to the glassy state afterwards.
This cyclic behavior continued for the rest of the experiment. The reason
was probably the periodic suction of the alcohol accumulated at the downwind
end into the recirculation system. When the alcohol came out at the other
(upwind) end, it formed a more coherent layer and damped out the wave forma-
tion more effectively.
The mass transfer coefficient was observed to be 16.6 cm/h prior to addi-
tion of the alcohol, then it fell to approximately 3.3 cm/h, a factor of five
drop. The effect on the hydrodynamics was obviously very significant.
It is impossible to separate the effects of "blocking" and "damping."
119
-------
TABLE 10
MASS TRANSFER COEFFICIENTS FROM THE WIND WAVE TANK
fi *
EXPRESSED IN m/s x 10 WITH CORRELATED VALUES IN PARENTHESES.
Air Speeds (m/s)
Compound
Benzene
Toluene
1,2 dichloro-
propane
chlorobenzene
1,2 dibromo-
methane
carbontetra-
chloride
2 pentanone
2 heptanone
1 pentanol
2 methylpropanol
n butanol
Water
13.2
94.4
(99.1)
93.6
(93.4)
93.9
(89.2)
89.7
(89.7)
77.2
(83.1)
33.1
(28.6)
42.7
(44.9)
8.11
(8.06)
7.30
(10.5)
4.69
(7.64)
71100
11.67 .
73.3
(82.4)
79.4
(77.6)
78.0
(74.6)
79.4
(77.5)
29.7
(23.8)
31.6
(37.3)
55200
10.31
62.5
(68.4)
68.9
(64.4)
63.9
(61.6)
54.7
(57.4)
63.3
(64.4)
5.75
(7.28)
39200
8.57
51.1
(51.8)
51.6
(48.9)
55.0
(46.9)
45.3
(43.5)
51.1
(48.8)
21.1
(14.9)
23.0
(23.5)
5.75
(4.22)
3.58
(3.99)
29700
7.09
36.9
(39.0)
46.9
(36.7)
35.8
(35.1)
41.9
(35.3)
39.1
(36.7)
3.81
(4.15)
22200
5.96
31.6
(30.0)
26.6
(28.3)
28.9
(27.0)
23.6
(25.2)
13.3
(8.67)
16.9
(13.6)
3.80
(2.45)
2.02
(2.31)
19400
evaporation
See later discussion of correlating equations.
120
-------
TABLE 11
VOLATILIZATION RESULTS OF MIXTURES IN THE WIND WAVE TANK
VALUES IN PARENTHESIS ( ) ARE FOR COMPOUNDS ALONE.
Mixture Wind Speed
Run m/s
1 6.0
2 8.6
3 6.0
4 8.6
5 10.7
K values
UL
i 2-Butanol
0.820
(0.724)
1.36
(1.26)
Benzene
12.50
(11.40)
16.7
(18.4)
Benzene
24.6
(22.5)
(cm/h) for stated
2-Methyl-Propanol
1.06
(ca 1.2)
1.66
(ca 1.6)
Chlorobenzene
11.50
(ca 11.0)
15.7
(19.8)
Toluene
24.1
(24.8)
compounds
2-Heptanone
5.71
(6.07)
8.77
(8.26)
1,2 Dichloropropane
11.20
(10.35)
15.6
(ca 18.0)
-------
RELATIVE VOLATILITY APPARATUS
As is outlined earlier in Section 4,this apparatus operates on the
principle that if a solution of a slightly volatile solute is distilled to a
known extent the relative concentrations in the residue and distillate can be
used to calculate the relative volatility and hence the ratio of solute to
water Henry's Law Constants.
Several systems were designed and tested. The first and simplest was a
direct batch distillation of a volume of solution. Unfortunately this
necessarily occurs at a temperature of 100°C at atmospheric pressure and
yields data which must be extrapolated down to environmental temperature
conditions. This extrapolation may be inaccurate because of uncertainties
about the temperature dependence of solute vapor pressure and solubility.
Distilling at low temperatures requires vacuum or low pressure operation
with the possibility of vapor loss. Finally it was decided to operate at
atmospheric pressure and induce distillation by recirculating air through
the solution in a "scrubber" and condensers using a sealed metal bellows
pump.
The apparatus used is illustrated in Figure 30 . The first vessel in
which the feed solution is placed, has a narrow section of 10 cm long and 2
cm in diameter, a wider section of 8 cm long and 3.5 cm in diameter, with
gas inlet tubing of 0.5 cm diameter. It was Immersed in a Neslab Tamson
constant temperature bath. The second vessel was a condenser 24 cm long,
3.5 cm in diameter and had gas inlet tubing of 0.75 cm in diameter. It was
immersed in an ice bath. The cold finger trap in the third vessel was
32.5 cm long, 6.5 cm inside diameter and 8 cm outside diameter. It was cooled
with liquid nitrogen. The collecting bottle was 10 cm long, 2.8 cm in
diameter and had a teflon stopcock at the side and was immersed in a liquid
nitrogen bath. Teflon sleeves were used instead of grease on the glass
ground joints to avoid contamination. The air flow was provided by a Metal
Bellows Corp., Model MB-21 pump. The units were connected with tygon
tubing. The electrical heating tape at the front section was used in order
to avoid condensation and restore the air to the required temperature.
The feed solution of normally 20 to 40 g of 10 to 30 g/m3 concentration
was obtained by serial dilution of a standard solution prepared gravometrical-
ly. A known mass of the feed solution was introduced into the first vessel.
The initial level of the solution was in the lower part of the wide section
to ensure a larger interfacial area. The solution was then stripped by a
moderate flow of air of approximately 2 cm3/s. Most of the water content in
the air stream was condensed in the ice condenser. The remaining moisture
and remaining chemical content was solidified on the wall of the cool-finger
trap using liquid nitrogen. The air was then warmed up to room temperature
and was recycled. The residue and the distillate were collected after 3 to
5 hours depending on the properties of the compound, warmed to room
temperature, combined and diluted prior to analysis.
Analysis was by either purge and trap gas chromography as described
later or by total organic carbon analysis using a Beckman Instrument.
122
-------
FIGURE 30
SCHEMATIC DIAGRAM OF THE RELATIVE VOLATILITY
SYSTEM FOR MEASURING HENRY'S LAW CONSTANTS
VENT
U)
SOLUTION
\
J I
CONSTANT TEMPERATURE
WATER BATH
s
X
s
f
tf
/
f
f
'
/
«
Cc
/
t
"™* ^*
•<-
%/v^
^
/
/
/
/
/
1
T-
/
' , x /
CONDENSATE
TRAPS
ICE
BATH
CONDENSATE
DISTILLATE
-------
The materials used were ACS Reagent Grade (or equivalent) methanol
ethanol, n propanol, n butanol, n pentanol, 2 butanol, isobutanol, 2
butanol, 2 pentanone, 2 heptanone, 3 heptanone and acetophenone. This
range of compounds have Henry's Law Constants in the range of interest, i.e.
up to a factor of 100 times that of water. It was normally necessary to alter
the extent of distillation to obtain satisfactory concentrations.
A mass balance on the compound was determined and any obviously un-
satisfactory results discarded. This mass balance check is a particularly
useful feature of the technique. Generally the mass balance results were
within 5%.
A sample calculation with n propanol at 25°C illustrates this procedure.
Feed 25.15 g (or m3 x 10~6) concentration 24.7 g/m3 (621 yg solute)
Residue 21.83 g concentration 6.65 g/m3 (145 yg solute)
Distillate 3.20 g concentration 155 g/m3 (496 yg solute)
Total solute recovered 641 yg or 103.2% of initial amount
a = 1 +ln(Ci/C2)MVi/V2) - 10.27
The Henry's Constant of n propanol is thus 10.27 times that of water
at 25°C. The vapor-pressure of water at 25°C is 0.0313 atm (Weast 76 )
and its density is 0.997 g/cm3 thus its molar concentration is 55400 mol/m3
and H is 5.65 x 10~7. It can thus be inferred that H for n proponol at 25°C
is 5.8 x 10~6* atm m3/mol. Note that this value can not be obtained accurately
from solubility and vapor pressure data.
A series of determinations were done at 25°C, there being 3 or 4 repli-
cates per compound. The results are summarized in Table 12 and show the
steady increase in a as molecular weight increases.
A series of tests was undertaken at 15,25 and 35°C with 2 butanol and
2 butanone which showed that a increases slightly as temperature increases
due, it is believed, to the reduction in y (corresponding to the increase
in water solubility). This is offset to some extent by the increase in the
ratio of water to solute vapor pressure, the solute always having a lower
enthalpy of vaporization.
124
-------
TABLE 12
RESULTS FROM THE RELATIVE VOLATILITY APPARATUS AT 25°C
Compound
methanol
ethanol
n propanol
n butanol
2 butanol
isobutanol
n pentanol
2 butanone
2 pentanone
2 heptanone
3 heptanone
acetopheno ne
2 butanol (15°C)
2 butanol (35°C)
2 butanone (15 C)
2 butanone (35°C)
Mean Solute Mass
Balance Percent
- 0.8
+ 1.6
- 1.0
+ 7.3
- 2.3
+ 3.3
+ 3.9
- 1.4
+17.2
+18.6
+26.0
+20.0
+ 9.0
+ 4.7
-11.4
-14.8
Experimental
Relative Volatility
9.62
7.66
10.7
16.3
17.5
22.7
22.0
62.9
51.8
35.8
28.8
31.8
14.0
24.5
51.5
54.1
125
-------
SOLUBILITY MEASUREMENTS WITH CO-SOLUTES
As was indicated earlier there remains some doubt about the extent to which
a co-solute such as ethanol influences the solubility (and hence Henry's Law
Constant) of a hydrophobic organic solute such as phenanthrene. Accordingly,
a series of experiments was undertaken to determine the magnitude of this effect
using phenanthrene as a model hydrophobic solute and ethanol, butanol, hexanol,
octanol, and fulvic acid as co-solutes. Under the experimental conditions
applicable here the solute and co-solute are truly in solution, there being
no micelle or suspended phase^ Concentrations of co-solutes used were mainly
in the range below 5000 g/m3 which is high environmentally but low compared
to concentrations used in analytical procedures to "solubilize" the hydrophobic
solutes.
The experimental procedure used was essentially that of May et al (77) in
which double distilled water or a co-solute solution was pumped through a generator
column containing glass beads coated with phenanthrene. The column was 6 mm out-
side diameter by 10 cm long containing 40-60 mesh beads. The pump was a Beckman
Solution metering Pump Model 746 operated at 5 cm3/min. The column was
thermostatted at 23 C - 0.5 C. Samples of the effluent were weighed, extracted
with spectro-grade cyclohexane and analysed .for phenanthrene content using an
Aminco-Bowman Spectr photometer by measurement of fluorescence intensity in the
linear response region.
The co-solutes used were of the purest grade commercially available and
were used without purification. The fulvic acid which was obtained from Aldrich
Chemical was dissolved in double distilled water and filtered prior to use, the
dissolved fulvic acid content being measured by difference of amount introduced
and the filter residue.
The absolute solubility of phenanthrene was determined to be 1.03 ± 0.03 g/m3
which compares well with 1.002 ± 0.011 measured by May et al (77). Results are
reported here as the ratio of the solubility in the co-solute solution to that
in pure water, the object r^ being to determine the magnitude of this ratio as
a function of co-solute concentration. The results are given in Table 13 for the
five co-solutes at various co-solute concentrations. It should be noted that
since there is an absolute error in the two solubilities comprising the ratio of
3%,-the absolute error in the ratio is quite high . Since the experiments were
done at the same time with the same instrument settings the precision is better
than the accuracy and is believed to be approximately - 0.02 of the ratio.
The results show that as expected there is generally a solubilizing effect
which amounts to approximately 102 at co-solute concentrations of approximately
2000g/m3 of alcohols. The limited solubility of octanol and fulvic acid prevented
such concentrations being reached.
It is concluded from these results that at typical environmental concentrations
of dissolved organic natter of 10 g/m3, possibly reaching 100 g/m3 in exceptional
cases, that the solubilizing effect is negligible. At 1000 g/m3 an 8% increase
in solubility is indicated. It is of course possible that other solutes and
co-solutes behave differently but this seems unlikely in the absence of specific
interactions such as ionization or complexing. A further analysis of these data
is presented later.
126
-------
TABLE 13
SOLUBILITY RESULTS
Ratio of solubility of phenanthrene in solution to that in pure water at 23° (R ),
experimentally and calculated from
log Rs = 0.10 M x 10~6 C
where C is co-solute concentration (g/m3) and M is co-solute molecular weight,
a value of 1000 being assumed for fulvic acid.
C
0
7
14
24
60
80
100
270
540
800
1000
1600
3000
16000
32000
48000
64000
80000
Ethanol
exp. calc.
1.0 1.0
-
-
-
-
1.01
1.001
-
-
1.06
1.01
1.08
-
1.18 1.15
1.36 1.3
1.53 1.6
1.70 1.9
2.00 2.3
Butanol
exp. calc.
1.0 1.0
-
-
-
-
1.04
1.002
-
-
1.07
-
1.08
-
1.35 1.31
1.72 1.72
-
2.83 2.97
-
Hexanol
exp. calc.
1.0 1.0
1.02
1.01
1.01
1.02
1.03
1.002
-
1.02
-
1.02
-
1.08 1.05
-
-
-
-
-
Octanol
exp. calc.
1.0 1.0
-
-
-
-
-
1.003
1.01
1.01
-
1.03
-
-
-
-
-
-
-
Fulvic Acid
exp. calc.
1.0 1.0
1.05
1.05
-
1.05
-
1.02
-
-
-
1.25
-
-
-
-
-
-
-
127
-------
HENRY'S LAW CONSTANTS
The apparatus used here for measuring Henry's Law constants was
essentially that described previously by Mackay et al. (28 ) and is shown
in Fig. 31 . Nitrogen was introduced -through a sintered glass disk into
the bottom of the gas stripping vessel filled with an aqueous solution
of the compound of interest. Two versions of the system were built: one
with a water jacket for coolant circulation and a second which could be
immersed in a temperature bath. In the second system, samples were with-
drawn from a sampling port near the top. Originally the glass vessel was
made to contain 4.5 L of liquid in order that the total liquid volume change
would be insignificant with larger samples taken for liquid extraction. It
was later found that since the rate of concentration change was inversely
proportional to the volume of liquid, a larger liquid volume tended to make
the concentration change smaller and thus subject to greater error.
Consequently the volume of the glass vessel was reduced to 1 L and more
satisfactory results were obtained. In both cases, the system was main-
tained at 25° * 1°C. The exit gas flow rate was measured by a soap bubble
flow meter. The concentration of the solute in water was determined by
either gas chromatography or fluorescence depending on the characteristics
of the solute.
Experimental procedure:
Aqueous solutions were prepared by stirring an excess amount of the
compound in a 1 L Erlenmeyer flask containing doubly distilled with a
Teflon coated magnetic stirring bar for 1 day. Since it was not necessary to
use a.-saturated solution for the experiment, a certain amount of the
aqueous solution was drawn off from the flask and added to the stripping
vessel,usually diluted with water. The amount was determined previously
by determining an appropriate GC response or fluorescence intensity.
After the desired experimental temperature and gas flow rate were
obtained, samples were taken periodically for analysis. When using the
fluroescence method, the fluorescent intensities of the aqueous poly-
nuclear aromatic hydrocarbon solutions or their cyclohexane extracts were
measured. Since the fluorescent intensity is linearly related to
concentration (a calibration line was prepared prior to the experiment
to ensure that the concentration in the stripping apparatus was in the
linear region), a plot of logarithm of fluorescent intensity versus time
gives a straight line,and the Henry's law constant can be calculated from
the slope. For halogenated hydrocarbons, alcohols and ketones the
concentration of the aqueous solution was determined by the vapor extrac-
tion technique followed by gas chromatographic analysis. Similarly, a
plot of logarithm of peak area versus time yields a straight line.
To study the effect of sorption, a sorbent, such as humic acid, fulvic
acid or bentonite, was added to the stripping vessel after enough experi-
mental points were obtained to determine the Henry's law constant of the
pure solute in water. Since the sorbent materials are insoluble in water
and were obtained in powder form, they formed cloudy suspensions in water.
Any larger heavier particles tended to sink to the bottom in a few minutes
while the smaller ones remained in the water column for a long time (a few
128
-------
FIGURE 31
DIAGRAM OF HENRY'S LAW APPARATUS
gas exit
water jacket
inlet
o'°-2
O e»
*'* *
\s.**
° o
0 ' o
• «•• * a
o
*
• *
•.'•'
• • «.•
'•'."''
: -;..;,-
water jacket outlet
gas inlet
cm.
129
-------
hours) before settling, leaving a slightly opaque solution. To prepare a
humic acid solution, 5 g of humic acid was added to 1 L of water. At the
start of the experiment, the prepared humic acid solution was shaken
vigorously then allowed to settle. Approximately 10 mL of the cloudy
solution was introduced to the stripping vessel. Aqueous samples were
taken immediately for 10 minutes every two minutes after addition to
observe the sudden drop in concentration due to sorption. Afterwards
samples were collected at the same time intervals as previously.
After the experiment, the aqueous solution in the vessel was drained
and collected. This solution was then filtered through a preweighted
5.0 ym Millipore filter and the filter paper dried and weighted. By taking
account of the loss due to sample collection and handling, the amount of
sorbent added could be estimated.
It should be noted that as samples of the aqueous solution were
removed, the total volume was reduced, hence the latter part of the log
(concri) - time plot became nonlinear.
The experimental difficulties involving compounds with Henry's law
constant less than lxlO~4 atm-m^/mol, as discussed in Section 4, were the
small concentration changes which were comparable to accepted experimental
errors when samples were taken four hours or even eight hours apart during
high flow rates. It is believed that the Henry's law constant thus obtained,
for example with pyrene, have higher error. For the more hydrophilic
compounds, the situation was more complex since stripping efficiency, prior
to GC, was low even at elevated temperature and long purging time. However,
it was possible to follow the concentration change reproducibly using a
specified purged time at ambient temperature.
The set of results obtained with this apparatus are given in Table 14.
130
-------
TABLE 14
RESULTS OF HENRY'S LAW CONSTANT DETERMINATIONS USING THE STRIPPING APPARATUS WITH DISTILLED WATER
AND IN THE PRESENCE OF FULVIC ACID (FA) , HUMIC ACID (HA) AND BENTONITE (B) SORBENTS
Compound Literature Data Experimental
Henry's Law Constants
3
atm m /mol
Water Water + Sorbent
-4
Naphthalene MW=128.2 4.40x10
P8= 1.08xlO~4atm 4.43xlO~4 3.73xlO~4
CS=31.7g/m3 4.31xlO~4 4.24xlO~4
=0.247mol/m3 4.38xlO~4 3.93xlO~4
H =4.37xlO~4atm m3/mol 4.66xlO~4 4.18xlO~4
H =4.83xlO~4atm m3/mol (28) 4.13xlO~4 4.18xlO~4
-4 -4
4.47x10 3.70x10
-4 -4
4.38x10 3.87x10
-4 -4
4.18x10 3.58x10
4.42xlO~4 4.35xlO~4
-4 -4
4.68x10 4.63x10
-4 -4
4.56x10 4.24x10
-4 -4
4.44x10 4.22x10
-4 -4
4.50x10 4.28x10
4.85xlO~4 4.49x10-4
-4 -4
4.34x10 4.18x10
AT 25°C.
Sorbent
Concentration
3
28.6 FA
10.0 FA
14.3 FA
28.6 FA
14 HA
14 HA
28 HA
7 . 71HA
19.14HA
22.3 HA
36.7 HA
54.1 HA
20 B
100 B
50 B
-------
TABLE 14 CONTINUED
Compound
Literature Data
c
Experimental
Henry's Law Constants
3
atm m /mol
Water Water + Sorbent
Sorbent
Concentration
g/m
Biphenyl
o-Dichlorobenzene
p-Dichlorobenzene
MW-154.21 ^
Ps-7.45xlO~5 atm
CS-7.1g/m3
3
-0.0460mol/m
H -4.08xlO""4atm m3/mol (28)
MW-147.01
Ps-0. 00193 atm
C3-145g/m3
-0.986mot/m3
H -1.95xlO~3atm m3/mol
MW-147.01 a
Ps-8.9xlO"4 atm
CS-83.1g/m3
-0.565 mol/m3
3.0 xlO~4
2.95xlO~4 2.96xlO"4
3.23xlO~4 2.75xlO"4
3.12xlO~4 2.82xlO"4
1.90xlO~3
1.89xlO~3 1.88xlO"3
1.98xlO"3 2.01xlO~3
2.40xlO~3
2.34xlO~3 2.44xlO~3
2.48xlO~3 2.44.10'3
12.0 HA
12.14 HA
12.0 HA
1.36 HA
9.52 HA
20.6 HA
13.6 HA
,* extrapolated values
-------
TABLE 14 CONTINUED
Compound
Literature Data
U)
CO
Experimental
Henry's Law Constants
3, ,
atm ra /mol
Water Water 4- Sorbent
Sorbent
Concentration
g/m
1,2,3-Trichlorobenzene
1,2,3, 5-Tetrachlorobenzene
Bromobenzene
MW=181.5 A
P8=5.23xlO~4 atm
CS=31.5g/m3
= 0.170 mol/m3
MW=215.9
P8=1.836xlO"'4*atm
CS=3.57 g/m3
=0.0165 mol/fli3
MW=157.02
PS=5.45xlO~3 atm
C8=410 g/m3
=2.61 mol/m3
-3 ^
H = 2.06x10 atm m~/mol
1.25 xlO"3
1.245xlO"3 1.195.10"3
1.26 xlO~3 1.12 xlO~3
1.57xlO~3
1.59xlO~3 1.49xlO"3
1.57xlO~3 1.55xlO~3
2.48xlO~3
2.51xlO~3 2.53xlO~3
2.44xlO~3 2.37xlO~3
41.3 HA
63.03 HA
11 J 6 HA
31.8 HA
10.71 HA
13.6 HA
* extrapolated values
-------
TABLE 14 CONTINUED
Compound
Literature Data
Experimental
Henry's Law Constants
3
atm m /mol
Water Water + Sorbent
Sorbent
Concentration
g/m
2-Pentanone
2-Heptanone
Acetophenone
MW-86 . 14
PS-1.58xlO~2atm
Cs-43070 g/m3
3
-500 mo,l/m
H - 3.16x10* atm m /mol
MW-114.18
Ps-3.42xlO~3atm
Cs-4340 g/m3
3
-38.0 mol/m
-5 3
H - 9.0x10 atm m /raol
MW-120.16
P8-1.32xlO~3atm
C8-5500 g/m3
3
-45.8 mol/m
-5 "i
H -2.87x10 atm m /mol
8.80xlO"5
8.71xlO"5
1.74xlO~4
1.81xlO~4
1.75xlO"4
1.02xlO"5
l.llxlO"5
1.07xlO"5
-------
TABLE 14 CONTINUED
Compound
Literature Data
Experimental
Henry's Law Constants
3
atm m /raol
Water Water + Sorbent
Sorbent
Concentration
g/m
2-Methyl-l-propanol
1-Heptanol
Acenaphthene
MW=74.12
o -2
pa= 1.32x10 atm
CS=94875 g/m3
= 1280 mol/m3
-5 3
H = 1.3x10 atm m /mol
MW=116.2
s -3
P =1.32x10 atm
C8=1975 g/m3
=17 mol/m
5 3
H "7. 6x10 atm m /mol
MW=154.2 £
PS=3.97xlO~5 atm
C8=3.88 g/m3
3
=0.0252 mol/m
H =1.46xlO~4 atm m3/mol (28)
2.67X10"15
-5
2.58x10
2.81xlO~5
5.3x!0"5
-5
5.82x10
1.55xlO"4
1.60xlO~4
1.58xlO~4
1.50xlO~4
1.67xlO~4
1.51xlO~4 10.71 HA
1.59xlO~4 21.3 HA
1.64xlO~4 15.0 HA
1.52xlO~4 25.3 HA
* extrapolated values
-------
TABLE 14 CONTINUED
Compound
Literature Data
Experimental
Henry's Law Constants
3
attn m /mol
Water Water + Sorbent
Sorbent
Concentration
g/m3
Fluorene MW-166.2 ^
P8-1.64xlO"5 atm
M
C -1.90 g/m
-0.
0114 mol/m3
Phenanthrene MW-178.23 '4
P8-4.
C8-l.
H
-0.
-3.
53x10 atm
29 g/m3
00724 mol/m3
93xlO"5atm m3/mol (28)
Anthracene MW-178.23 ^
P8
c8
H
=5.
•0.
-4.
- 6
04xlO~ atm
075 g/m3
2xlO"4 mol/m3
-3 3
.67x10 atm m /mol (28)
1
9
9
9
9
3
3
3
3
3
7
7
8
6
.0 xlO"4
.47x10"^
. 52x!0"5
.68xlO~5
.45xlO~5
.6 xlO"5
,55xlO"5
.71xlO~5
.52xlO~5
.55xlO~5
.20xlO~4
.50xlO~4
.8 xlO"4
.67xlO~3
9
9
9
8
6
5
6
8
2
4
.53x10
.48x10
. 58x10
.8 xlO
.42x10
.38x10
.88x10
.29x10
.46x10
-5
-5
-5
"5
•
-5
-5
-5
-5
-4
.89xlO~4
22
10
25
24
17
15
34
46
14
14
.8
.5
.6
.0
.4
.3
.86
.0
.0
HA
HA
HA
HA
HA
HA
HA
HA
HA
HA
* extrapolated values
-------
TABLE 14 CONTINUED
Compound
Literature Data
to
Experimental
Henry's Law Constants
3
atm m /mol
Water Water + Sorbent
Sorbent
Concentration
g/m
Pyrene
1-Methylnaphthalene
1 , 5-Dimethy Inaphthalene
1-Chloronaphthalene
MW=202.3
C8=0.135g/m3
3
=0.00067 mol/m
MW=142.2
P8=7.8xlO~5 atm
CS=28.5 g/m3
3
=0.20 mol/m
/ *^
H =3.54xlO~ atm m /mol
MW=156.23
C8=3.38 g/m3
2 3
=2.16x10 mol/m
MW=162.6
CS=22.4 g/m3
3
=f».138 mol/m
l.lOxlO"5
2.6 xlO~4
2.22xlO"4
2.27xlO~4
2.49xlO~4
3.5 xlO~4
3.73xlO~4
3.81xlO~4
3.62xlO~4
3.55xlO~4
3.67xlO~4
3.54xlO~4
pts scattered
2.01x!074 9.43 HA
2.19xlO~4 20.3 HA
18.7 HA
3.38xlO~4 28.7 HA
3.62xlO~4 14.0 HA
3.54xlO~4 25 HA
3.76xlO"4 15.7 HA
3.65xlO~4 25.7 HA
-------
TABLE 14 CONTINUED
oo
Compound Literature Data
Experimental
Henry's
Law Constants
atm m /mol
2-Chloronaphthalene MW-162 . 6
C8-11.67 g/m3
-7.18 mol/m3
Chlorobenzene MW-112 . 56
P8-0.0156 atm
C8-472 g/m3
-4.19 mol/m3
—3 3
« «^ 71-vin at-m m /mol
Water
3.20xlO~4
3.10xlO"4
3.24xlO~4
3.28xlO~4
3.77x!0"3
3.1 xlO"3
3.14xlO~3
3.04xlO~3
3.17x!0"3
Water + Sorbent
3.57xlO"4
3.25xlO"4
3.40xlO"4
3.0 xlO"3
3.07xlO"3
3.02xlO"3
Sorbent
Concentration
g/m
27.4 HA
20.43 HA
23.6 HA
32.0 HA
19.9 HA
15.6 HA
H -3.77xlO~3 atm m3/mol (28)
-------
ANALYTICAL METHODS
The determination of the concentration of the aqueous solution was
obtained by several methods. Previously UV absorption was employed to
measure the concentration change of some aromatic hydrocarbons in a flow
system. However, the addition of sorbents interfered with the UV adsorption,
hence other methods were tested which were mainly static in nature in which
small samples were removed at specified time intervals. Liquid scintilla-
tion counting was considered but rejected because of the availability of the
instrument, chemicals.and the disposal problems of the aqueous solution
after experiments.
Fluorescence method was chosen for the analysis of polynuclear aromatic
hydrocarbons because of its high sensitivity (1000 times higher than that
of UV adsorption) and the sorbent did not interfere with the fluorescent
intensity in the wavelength range (250 to 350 nm) and amount added ( <50 ppm) ,
Gas chromatographic analysis following vapor extraction (purge and trap
technique) was used for the halogenated and more hydrophilic compounds. It
was the obvious choice for the former groups of compound because of their
relatively high vapor pressure and is a much simpler technique than solvent
extraction for ketones and alcohols. The experimental details are given
below.
1. Fluorescence
The analysis was performed on an Aminco-Bowman Spectrophotofluorometer
(American Instrument Ltd). As stated earlier, the fluorescent intensity of
most aqueous solutions (except pyrene) was measured using the compound
specific excitation wavelength. It was not always necessary to prepare
calibration solutions although the solubility of the compound under investi-
gation should be known so that a suitable concentration giving a proper
signal could be prepared before starting the experiment. 1-2 mL samples
were taken from the stripping apparatus after the experiment had started,
and their emission fluorescent intensity was recorded.
Since the light source of the instrument was a xenon lamp with a
variation in lamp intensity sometimes greater than 10% during the course
of the entire experiment (even when the light source was equipped with a
magnetic arc stablizer), a standard solution was then required to use as
a reference to correct for the unstable light intensity resulting in a
fluctuation of fluorescent intensity. In the case of a sparingly soluble
compound, such as pyrene, the fluorescent spectra of the aqueous solution
was significantly different than that in a solvent, possibly due to
impurities which were more soluble in water. Therefore the fluorescent
intensity of cyclohexane extracts were measured for the determination
of Henry's Law constants.
2. Gas chromatography
A conventional method of analyzing aqueous solution is by solvent
extraction which involves several extracts and subsequent concentration
of solvent until the concentration reaches a level suitable for gas
139
-------
7-53
chromatography. Vapor extraction is more convenient when applied to the
more volatile compounds.
A Hewlett-Packard GC Model 5840A with a 7675A Purge and Trap Sampler
was employed for this analysis. The GC was equipped with both dual flame
ionization detector and an electron capture detector. The analytical
column was a 50 m long, 0.5 mm I.D. glass open tubular column coated with
SE 30. Nitrogen was used both as carrier and purge gas. Initially,
nitrogen bubbled the aqueous sample carrying the purgable content onto a
Tenax-GC trap. After the purge cycle, the Tenax-GC column was heated to
200°C and the sorbed material was swept directly onto the analytical column
by the carrier gas. The oven temperature was determined by the physical
properties of the compound under investigation. For single compound
analysis the isothermal mode was used, while for multicomponent mixture, the
temperature programming mode was used if the isothermal mode did not give
satisfactory resolution. The FID detector was set at 300°C.
The concentration of the sample was recorded as an area count in the
chromatogram. With suitable calibration the concentration could be obtained.
140
-------
SECTION 8
DISCUSSION
INTRODUCTION AND ORGANIZATION
This section consists of a discussion of the experimental results
obtained
(i) in the small scale volatilization apparatus where the aims were
to verify the two film model by studying 20 compounds covering a wide range
in Henry's Law Constants, and to devise a test procedure which may be useful
for testing the volatilization behavior of compounds of unknown volatility.
(ii) in the wind wave tank, where the primary objective was to develop
correlations for mass transfer coefficients as a function of wind speed,
fetch, and molecular properties.
(iii) by the relative volatility systems which is believed to be suitable
for measuring Henry's Law Constants for involatile compounds.
(iv) by the measurement of Henry's Law Constants by gas stripping, which
is essentially an extension of a previously devised system.
(v) by the measurement of solubility in the presence of co-solutes.
It should be noted that in the discussion of (i) and (ii) the aim is
to develop correlations for 1C and K as a function of wind speed or turbulence
solute properties and temperature. The experimental K^ and K values discussed
apply to the specific solutes used and the initial correlations obtained apply
only to these solutes. Later, general correlations are developed which, it
is believed, apply to all solutes.
141
-------
SMALL SCALE VOLATILIZATION APPARATUS
Characteristics as a Test Apparatus
The first objective was to devise and test a relatively simple small scale
system which could be used in the laboratory to study the air-water exchange
rates of compounds under various conditions of temperature, turbulence and in
the presence of other dissolved and suspended materials. It is believed that
the nature of the interfacial turnbulence generated by stirrers or shakers may
be quite different from that which occurs at natural air-water interfaces and
thus it is inherently better to generate the turbulence using air flow. If the
air flow is directed linearly over a water surface it causes water drift and
circulation at a rate dependent on the depth and configuration of the containing
vessel. Any surface films tend to be driven to the downwind end where they are
trapped. It becomes impossible to generate waves because of the short fetch.
The circular swirling geometry overcomes many of these problems, permits waves
to develop and turbulence levels to be achieved such that oxygen transfer rates
can be achieved in the apparatus equivalent to those in the environment under
various wind and fetch conditions. The 10 liter volume is convenient in that
only small quantities of solute are required but substantive sample volumes can
be taken without disturbing the system. Since the apparatus is closed there
is minimal-risk to operators of exposure to toxic substances.
The disadvantages include the inability to specify a meaningful air velocity
since it varies radially, the possibility of volatilization from liquid splashed
on the vessel walls and a degree of non-reproducibility of wave action which was
observed between tests. This may be due to the presence of trace quantities of
surface active materials which act to damp capillary waves (Davies and Rideal (18 ))
or to inadvertant changes in the location of the entry and exit pipes. Apparently
minor changes in the flexible piping from the apparatus appeared at times to
influence wave characteristics and it is possible that some acoustic resonance
phenomena controlled by the nature of the upstream and downstream flow resistances
may influence air flow in the apparatus. An obvious approach is to define the
dimensions of the apparatus and its connecting piping in great detail such that
it could be reproduced between laboratories. This may not be necessary if the
transfer rates of a common solute such as oxygen are measured along with the
solute of interest.
It is believed that with some refinement and closer definition the system
could be used as a standard volatilization test, designed to yield kinetic
information. It would thus be complementary to the thermodynamic (Henry's Law
Constant) information obtained in the gas stripping or relative volatility
systems. Because of the radial variation in velocity the apparatus is inherently
unsuited for fundamental studies of turbulence pheonomen. The mass transfer
coefficients are averages of undoubtedly varying local values.
142
-------
Correlation of the Results
The results presented earlier in Table 8 show that the overall mass transfer
coefficient is a strong function of the orifice plate pressure drop A P and hence
of the air velocity. Although the actual air.velocity in the pipe can be calcu-
lated the velocity over the water surface varies radially and no single value can
be established. It is thus convenient to characterise the level of turbulence by
the orifice plate pressure drop alone. This value depends on the dimensions of
the orifice which would have to be reproduced exactly to obtain similar turbu-
lence levels in different sets of apparatus.
It is also apparent that the lower Henry's Constant compounds volatilize
more slowly as the gas phase resistance becomes significant. The effect of solute
diffusivity is entirely masked by these larger effects. To analyse the data it is
first convenient to fit an expression for the effect of turbulence level. This
was done using a regression program to fit constants C., C , n, m and q
equations of the form given below.
1/KOL = 1/KL + RT/HKG
^ = CjD^CAP - 2.0)q
KG = C2DGmUP - 2.0)q
Here DT and Dfi are the solute molecular diffusivities. This equation implies
that 1L and Kp are zero when P is 2.0 cm HO which is outside the experimental
range. The constant q was found to have a value of 0.86. Actually a slightly
lower value may be appropriate for q in the Kp equation but it can not be deter-
nined precisely. The values of n and m were determined to be 0.70 and 0.59 but
the sum of squares deviation is quite insensitive to variations in the range
0.5 to 0.8 in both. Examinations of the data suggests that the variance in the
data attributable to changes in D and D is so small compared to the turbulence
and H effects that no accurate values can be assigned. Fortunately there are
other experimental studies and theoretical predictions which strongly suggest
that n should be 0.50 and m should be 0.67.
Inserting these values gives a correlation which is entirely consistent
with the data. The constants C and C_ can then be determined yielding finally
KL = 2990 DL°'5( AP - 2.0)°'86
Kr = 19500 D °'67( AP - 2.0)°'86
O U 2
In these equations 1C. and K are in cm/h and D and D are in cm /s. The calcu-
lated Km values are given earlier in Table 8 in which the experimental and
correlated values can be compared. The satisfactory fit of the data indicates
that the two resistance model is valid. Another approach would be to plot 1/KQL
versus RT/H as discussed earlier. Such a plot is not as illustrative as had
been hoped because of the effect of turbulence level and solute diffusivity. A
precise fit in such a plot is impossible because of (i) experimental error
(ii) errors in H especially for the alcohols and ketones (iii) variations in
IL and K between solutes because of the diffusivity effect and (iv) wave
damping effects of the nore polar solutes. There is clearly no need to invoke
a resistance for the interface. If such a resistance exists, it can not be
measured with this system. This is supported by results quoted by Sherwood et al
(42) to the effect that the interfacial resistance for water evaporation
143
-------
(equivalent to the "delay" as the solute leaves the liquid phase) exceeds the
K_ values reported here by a factor of 1000, thus when the reciprocals of the
transfer coefficients are added the interfacial resistance term is negligible.
Although it may appear that this validation of the two resistance model is
unnecessary in view of the overwhelming evidence, it is believed to be justified
since it is the key assumption in all volatilization calculations.
For experimental purposes it is suggested that a series of solutes including
cyclohexanol, 1 pentanol, 4 methyl 2 pentanone, 2 butanone, bromof orm, chlorobenzene,
toluene and oxygen provide a good range of H values.
• t
The oxygen transfer results are puzzling in that the rates are higher than
are predicted from the solute data. The water diffusivity of oxygen is approxi-
mately twice that of benzene, thus one would expect an increase in IL. by a factor
of 1.41 ie/TI In fact the factor is about 1.7 at low turbulence levels but
falls to about 1.4 at high turbulence levels. This may be experimental error or an indi-
cation of a fundamental dependence of the power or turbulence level as is suggested
by unsteady state theory. In principle, this uncertainty can be avoided by measuring
the solute volatilization rate directly add not relying on ratios to oxygen transfer
rates. It is probably better to use a solute such as toluene for volatilization
studies and ratio transfer rates to it, rather than use oxygen which has an un-
usually high diffusivity. Admittedly ouch oxygen transfer data apparently exists
for environmental conditions but there are few reliable in situ measurements be-
cause of oxygen's formation and consumption biologically.
A noteworthy observation during the data analysis was that some Henry's Law
constants calculated from published data were exposed as,.being erroneous. For
example a literature value for 3 heptanone of 1.54 x 10~ is clearly a factor
of about 10 too low. A determination was made yielding a value of 2.0 x 10
which gives much better agreement. Likewise cyclohexanol appears to have_a value
of 1.2 to 2.5 x 10 instead of the initially estimated value of 8.7 x 10~ based
on a suspected low published solubility. The Implication is that although the
system is kinetically controlled it can be used to some extent to validate thermo-
dynamic data. This suggests that when elucidating the volatilization characteris-
tics of new compounds it is useful to obtain kinetic data from a system such as is
described here and check the consistency of the data against predictions based
on correlations, which include an assumed value for H. If an error has been made
in determining or calculating H by a factor of about two this will become apparent
provided that H is in the gas phase controlled regime.
Multicomponent Results
Within the experimental error, it appears that solutes in mixtures behave
as they would individually. A test of the validity of this claim would require
a series of tests using solutes alone and in mixtures with a high degree of
precision between tests. The results obtained are sufficient to indicate that
any interacting effect, if present, is fairly small and certainly there is no
possibility of "additive" effects. This conclusion is not surprising and
greatly simplifies environmental volatilization calculations since each com-
pound can be treated individually.
144
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Effect of Solute Molecular Size, Diffusivity and Temperature
In these results, the effect of solute molecule size has been characterised
by using the molecular diffusivity in each phase raised to an empirically de-
termined power. Other approaches are possible, for example Tsivoglou (69,70)
Rathbun (71) Smith et al (72), and Paris et al (78) have used molecular diameter.
Liss and Slater (79) used molecular weight. Frequently Schmidt number is used
for engineering applications to similar geometries. A brief review of the re-
lationships between these quantities is useful.
Gas Phase
In the gas phase there is a clear relationship between molecular weight, molar
volume and diffusivity which is expressed in the various correlations by Gilliland,
Chapman and Enskog or Slattery and Bird as reviewed by Sherwood et al (42) . The
Gilliland correlation (97) is probably most convenient and is used in this study,
details being given later. The diffusivity is proportional to absolute tempera-
ture to the power 1.5. When the gas Schmidt Number (Sc or u/pD) is calculated
as a function of temperature, fortuitously it is relatively insensitive to temp-
erature since the viscosity y is proportional to..T " and the density p is pro-
portional to T ' thus when combined with the T ' dependence of D the tempera-
ture effect tends to cancel.The molecular weight or volume effect thus dominates.
Liss and Slater (79) suggested using the inverse square root of molecular
weight to account for solute effects on K_ but this can be criticised on two
counts. First the dependence of D on molecular weight is not precisely to the
power -0.5 since the size (cross sectional area) of the solute also affects the
diffusivity. Second a considerable volume of experimental mass transfer coef-
ficient data suggest a power of 0.5 to 1.0 on D, averaging approximately 0.67
hence a more accurate dependence is probably the inverse cube root of molecular
weight. For example Tamir and Merchuk obtained a value recently of 0.684 for
the power dependence of K on D (95,96).
The best overall approach to both solute molecular size and temperature is
believed to be to use the Schmidt Number. This implies that K is relatively
insensitive to temperature. Experiments to test this sensitivity are very diffi-
cult because varying temperature causes large changes in vapor pressure and hence
in evaporation rate thus any effect on Kr will be swamped by the larger vapor
pressure effect.
Liquid Phase
For liquid diffusion the most convenient correlating approach is to use
the Stokes-Einstein equation as a basis and correct it for solvent differences,
as for example in the Wilke-Chang correlation (Sherwood et al 42 ) which for
dilute water solution has the form
DAB = (Consta*1*)1/^ VA°*6
where yR is the viscosity of water and V is the solute molar volume. For
relating D between solutes the molar volume is the best quantity. The
temperature effect is best estimated using published data for water viscosity,
which approximately halves from 1.79 cp at 0°C to 0.89 cp at 25°C. This is
usually expressed in the form of an "activation energy" expression
145
-------
V = p exp(E (1/T - 1/T ))
o o
where E is an activation energy divided by the gas constant (approximately 2250 K
for water) and the subscript refers to a reference temperature.
Diffusivity is thus a very strong function of temperature since the term
X increases and V decreases as temperature rises. A factor of approximately
2.18 applies between 0°C and 25°C. If a power function in T is forced, then
D is proportional to T to the power 9. If an exponential function is used E is
approximately -2540 when the extra dependence on T is included.
The liquid phase Schmidt number is also useful, however, unlike the gas
phase Schmidt number it is very temperature dependent, the values falling
rapidly with increasing temperature as y falls and D increases, the overall
effect being equivalent to an activation energy quantity E of 4790 K, i.e.,
the sum of 2250 for u and 2540 for D.
Again the difficulty lies in the dependence of K. on D,a similar power exp-
ression being invoked usually of the form
where n is generally believed to lie between 0.5 and 1.0 but usually lies in
the range 0.5 to 0.67.
There is oftenjsome difficulty in determining the exact value of powers
in expressions of this type as is illustrated below. If experimental measurements
are made for two solutes differing in molar volume bj a factor of 4 then D will
differ by a factor of 2.3 and IL by a factor of 1.7^ when the power is 0.67 and
by a factor of 1.52 when the power is 0.50. Accurate determination of the power
thus requires very accurate values of K. preferably over a wide range of molecular
sizes .
For KL , Li ss and Slater ( 79) suggested that the dependence be expressed as
square root of molecular weight. Tsivoglou showed that ratio of molecular dia-
meter gave an adequate correlation for the inert gases, a result found by Paris
et al (ygj) to fit PCB data. Penetration theory suggests a power of -0.5 on
Schmidt number or the equivalent 0.5 on diffusivity. Since diffusivity is
proportional to molar volume to the power -0.6 and molar volume is proportional
to molecular diameter to the power 3.0 it follows that diffusivity is propor-
tional to diameter to the power -1.8 (i.e. 3.0 times -0.6). It follows that
Tsivogolou's observation is in close agreement with penetration theory since
it predicts a power of -0.9 (i.e. 0.5 times -1.8). The Liss assumption implies
that the power on Schmidt number is near unity which could occur only during
steady state near stagnant- diffusion. The experimental data obtained here
support a power of 0.5 on diffusivity and it is thus concluded that the
evidence favors adoption of this value, at least until evidence to the con-
trary is forthcoming. It is possible that more refined experimentation
involving simultaneous volatilization of compounds with a wide range of
diffusivitles could .produce a more accurate value. Further, it should be
noted that there are theoretical fluid mechanical reasons for suggesting that
the power may be a function of level of turbulence.
146
-------
The effect of temperature on 1C. is more easily measured than that of K
and such data indirectly give an indication of the likely value of the power
on D or Sc. In this study the values of K_ for benzene and toluene fell from
15 cm/h at 25 C to 12 cm/h at 15 C, a variation of 2.2% per degree around the
mean temperature of 20°C. Downing and Truesdale (80) in a more exhaustive
study of temperature found that IL varied by from 1.52 to 3.12% per degree
around 20 C and with an average of 2.21% with a standard deviation of 0.5%.
A solute with a liquid Schmidt Number of 1000 at 20°C will have a Schmidt
Number at 19°C of
1000 exp(-4790(l/293 -(1/293 - 1/292)) = 1058
i.e. a 5.8% increase. Raising Sc to the power -0.5 thus reduces 1L. by a factor
equivalent ot 2.8% for this one degree change. This is in excellent agreement
with the present work and that of Downing and Truesdale thus it is concluded
that the use of the Schmidt Number characterises both molecular size and the
temperature effect. No separate temperature correction is thus necessary.
There remains a possibility that temperature may influence volatilization
under conditions of water condensation from the atmosphere as may occur at
night when the relative humidity rises due to surface radiative cooling. This
effect has not been investigated here.
147
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WIND WAVE TANK.
The general aim In this section is to interpret the experimental results
in the light of recent observations of wind-wave hydrodynamics and develop
reliable prediction procedures for environmental volatilization calculations.
Specifically, the aim is to obtain equations for IL and Kg as a function of
wind speed, fetch and solute Schmidt Number.
It is believed that a dual approach is required. Many environmental
scientists undertaking volatilization calculations are primarily concerned
about the processes which comprise the overall fate of the solute, thus there
is insufficient time to obtain a deep* understanding of the fluid mechanics
at the air-water interface. For them a simple expression in terms of 10 m
wind speed is sufficient. To oceanographers this approach is excessively
simplistic and an adequate understanding requires evaluation of drag coef-
ficients, friction velocities, Reynolds and Froude Numbers. An attempt is
made to satisfy both.
The hydrodynamic results are examined first. Velocity profiles were
measured at wind speeds from 5 to 14 m/s free stream velocities. Profile
differences were encountered with distance along the tank and to accommodate
this effect the individual profiles were fitted to the logarithmic velocity
profile by plotting velocity against logarithm of height to obtain the fric-
tion velocity U* and Z the surface roughness as was described earlier in
the experimental section. The values of U* and Z were then averaged as
shown in Table 15. The drift velocities were measured as the final values at
the end of the tank. Examination of these velocities showed that they were an
average of 2.82Z of the wind speed in excellent agreement with other studies.
The 10 cm drag coefficient C_ as calculated from the free stream
velocity U^ and U* show a distinct trend of becoming smaller at low
velocities, in general agreement with oceanic observations. The absolute
values are high compared to oceanic values (which rarely exceed 3 x 10~3)
due, it is believed, to the short fetch.
2
The constant "a"" in the Charnock relationship calculated as Z g/D*
shows remarkable constancy apart from the lowest wind speed point which is
possibly in error due to a low value of Z . It appears that above a wind
speed of 6 m/s a mean value of 0.0093 applies. This is in excellent agree-
ment with Smith's (61) suggestion of 0.01 and is somewhat lower than the
value of 0.0156 suggested by Wu (60). The accuracy here is probably no
better than 20Z. An implication of these results is that the Froude
scaling law appears to apply.
The roughness Reynolds Numbers are in the transition and rough regions
(the boundary being at approximately 2.0) thus it is possible that this
analysis breaks down at lower velocities when the water surface becomes
very smooth. This transition to another regime was suggested by Cohen
et al (58).
Hidy and Plate (81) proposed a relationship between U and U* for
148
-------
laboratory tanks of the form
U* = (3.41 x 10~4 U )°'5 U
OO CO
-4
which is equivalent to„the statement that C is given by 3.41 x 10 U^.
This is in satisfactory agreement with the values obtained here.
Consideration of these results leads to the conclusion the wind wave tank
results are consistent with other studies in that the drag coefficients C cal-
culated from the friction velocity and the free stream velocity U^ (which is
close to the 10 cm velocity) are in range 2 x 10 to 6 x 10 , values which
are higher than oceanic or lake values. A correlation of CD for these results
is .4
CD = 4.0 x 10^ U^
It is thus possible to estimate U* from U as
U* = U C °'5 = 2.0 x 10"2 U 1>5
08 JJ W
Using a value of 0.01 for the Charnock constant "a", the surface roughness
Z can thus be deduced as being
o
Z - 0.01 U*2/g = 4 x 10~6 uJVg = 4,08 x lO'7!^3
2
since g is 9.81 m/s .
The only serious ^discrepancy is at low wind speeds where Z appears to be
lower than expected, possibly due to a more "glassy" surface. In a similar
study with a smaller tank Cohen et al (58) obtained larger roughness heights
which may be attributable to different aerodynamic conditions. When the wind
speed is below 5 m/s it appears that the roughness height becomes negligible
and thus probably can not be measured accurately.
The roughness Reynolds Number Re in the tank can be estimated as
Re* = pU*ZQ/y = 8.16 x 10~^'Vv-S.WJ x lO"4!^4'5
For air at 2Q°C is 0.00120 g/cm3^ and y is 181 x 10~ poise (g/cm.s)thus p/y
is 6.62 s/cm or 6.62x10 s/m .
Under lake or oceanic conditions it is necessary to use another expression
for the drag coefficient, Smith's (61) correlation being suitable namely
It follows that
= 10"4(6.1 + 0.63
U* = 10~2(6.1 + 0.63
and
Z = a U*2/g = 1.02 x 10~5 U 2(6.1 + 0.63) U °<5
O -LU -LU
2
since g is 9.81 m /s and
149
-------
TABLE 15. HYDRODYNAMIC RESULTS FROM THE WIND WAVE TANK
Screen
No.
0
1
2
3
4
5
Position A (1.4 n)
U. U* S
m/s m/s mxlO
12.84 0.884 0.522
11.59 0.737 0.355
9.95 0.638 0.301
8.59 0.422 0.185
6.89 0.357 0.084
-
Position B (4.2 m)
U» U* Zo«
m/B in/8 mxlO
13.53 1.102 1.290
11.78 0.960 1.070
10.66 0.712 0.556
8.55 0.487 0.232
7.28 0.406 0.169
5.96 0.271 0.044
Drift
Velocity
rn/s
0.395
0.344
0.290
0.222
0.200
0.158
Average
Uw U* Zo3
a/a m/s mxlO
13.20 0.993 .906
11.67 0.849 .713
10.31 0.675 .429
8.57 0.455 .209
7.09 0.381 .127
5.96 0.271 .044
CD1Q
Re* xlO
54.2 5.66
36.5 5.29
17.5 4.29
5.73 2.82
2.91 2.89
0.72 2.06
a
0.00900
0.00970
0.00924
0.00990
0.00858
0.00587
K
o
-------
Re* = 1.02 x 10~7 U1Q3(6.1 + 0.63 U10)1'5p/p
= 6.75X 10~ 3U1Q3(6.1 + 0.63 U-^)1'5
In principle it should be possible to relate mass transfer coefficients in
the tank to those in the environment using U*, Z and Re* as defined above.
Liquid Phase Controlled Mass Transfer
The liquid phase mass transfer data can be interpreted in isolation by
examining the K^ values for benzene and toluene volatilization which are almost
totally liquid phase resistant systems. Table 16 gives these data. The benzene
and toluene values are within experimental error of each other which is not
surprising given their similar molar volumes. To assist interpretation, the
mean value of K^ is calculated, converted to m/s and its ratio to U* calculated.
These values are tabulated and show remarkable constancy in the range 94 to 110.
An important inference from this is that the friction velocity U* is the primary
determinant of K_. There is an apparent tendency for IL /U* to increase at low
velocities which implies that there will be a small but negative power on the
roughness Reynolds Number in a Stanton Number correlation.
The simplest correlation is
St* = I^/U* = 1.02 x 10"4
Table 16 gives the correlated values which compare well with the experi-
mental values especially in the mid range but there are deviations at the high
and low wind speeds. An improved correlation, obtained at the expense of
another term is
St* = ^/U* = 1.09 x 10~4 Re*"0'03
Table 16 gives the correlated values for this equation. Use of the Re
equation tends to give higher IL. values at low wind speeds but the maximum
difference between the correlations is 8% which is not large considering the
experimental error and the uncertainty about mean environmental wind speeds.
Which correlation is preferable is a matter of judgement.
The mean Schmidt Number SCL. for these systems is 1118 thus forcing a -0.5
power on Sc and gives the general correlation
Li
St* = 34,.l x 10~4 ScL-°'5
or * - , -4 *-0 03sc_~°*5
StT = 36.4 x 10 Re L
LI
These correlations can be converted to forms involving U.. -. by substituting
the equations for U* and Re* in terms of U1& for the environment or U^ for
experimental tanks.
151
-------
to
TABLE 16
WIND WAVE TANK MASS TRANSFER RATES FOR BENZENE AND TOLUENE
u
CO
m/8
13.2
11.67
10.31
8.57
7.09
5.96
U*
m/s
0.993
0.849
0.675
0.455
0.381
0.271
Re*
54.2
36.5
17.5
5.73
2.91
0.72
Benzene K.
cm/h m/sxlO
34.0
26.4
22.5
18.4
13.3
11.4
94.4
73.3
62.5
51.1
36.9
31.6
Equation (1)
Equation (2)
Toluene Hi,
cm/h m/sxlO
33.7
28.6
24.8
18.6
16.9
9.6
KL " lt02
K. - 1.09
93.6
79.4
68.9
51.7
46.9
26.7
-A *
x 10 U
-4 *
x 10 U
Mean ,
KL/U*xlOb
94.7
90.0 .
97.3
112.9
101.1
107.6
Re"0'03
Correlated
xlO
(1)
101.3
86.6
68.9
46.4
38.9
27.6
6Vm/8)
(2)
96.0
83.1
67.5
47.1
40.2
29.8
-------
Environmental Conditions, U is 10 metre wind speed
U* = 10~2(6.1 + 0.63 U)°>5 U
Simple version
Re* = 6.75 x 10~3 U1Q3(6.1 + 0.63 D^)1'5
= 34.1 x 10~4 U* ScL~°'5
= 34.1 x 10~6 (6.1 + 0.63 U..)0'5 Uin Sc."0''5
-LU J_U i_i
Reynolds Number version
^ = 36.4 x 10"6 U* -Re*'0'03 Sc ~0-5
= 42.3 x 10-6 (6.1 + 0.63 Uin)°'455 U°-91Sc
since Re*'0'03 = 1.16 U^0'09 (6.1 + 0.63 V
Laboratory conditions, U^ is free.. stream velocity
U* = 2.0 x 10~2 U
CO
Re* = 5.4 x 10~4 U^4'5
Simple version ,
1^ - 34.1 x 10 U* ScL
= 68.2 x 10"6 vJ-5Sc^°
Reynolds Number version
^ = 36.A x 10-4 U* Re-0-0
= 91.0 x 10-6
since Re*-°-03 = l. 25
Strictly, the temperature variation of Re* should be included but the effect is
negligible because of the low power.
Table 17 gives calculated environmental values of K_ using these equations
for a compound of Schmidt Number 1000. The effect of lower temperature is to
increase Sc.. thus reducing IL. . The magnitude of this effect has been discussed
, . J_i lit
earlier .
These equations are markedly different in form from those of Bank (82,83)
and Sivakumar (84) which were developed from data at lower velocities. They are
in good agreement with the form suggested by Deacon (85) .
153
-------
Gas Phase Controlled Mass Transfer
The Kr data obtained from water evaporation measurements given earlier in
Table 11 are presented in Table 17 in which the ratios of K to U*, U , and
U^O.78 are also calculated. The KG/U* group shows no significant trend the
average value being 65.0 x 10~ with a maximum deviation of 7.3 x 10 or 11%.
The other groups show what is believed to be a significant trend for the ratio
to be lower at low wind speeds. Following the procedure used for K^ it is
proposed that the data be represented by an equation of the type
St* = K.,/U* = 65.0 x 10~3 for water (Sc., = 0.6)
VI U (3
or St* - KG/D* = 46.2 ScG"°-67 x 10*8
The reason for introducing the U^O-78 term was that Mackay and Matsugu(64)
developed a correlation for gas phase controlled evaporation which included this
term, however the data were obtained at lower wind speeds and that correlation
severely underestimates K_ at high wind speeds, probably due to the wave action.
That correlation also included a fetch term which is necessary in any correla-
tion using 0 to take into account the change in evaporation rate as the flow
becomes steady and C_. falls at high fetch. It is postulated here that includ-
ing the variable C_ term (for calculating U* from U^) removes the necessity to
include a fetch term. "*
The values of K_ calculated from the above correlation are given in Table is.
IT
The correlation can be expressed in terms of U._ and U as follows
10 <»
U* - 10"2(6.1 + 0.63 U10X°*5U10
KG - 46.2 U*ScG-°'67xlO-3
KG - 46.2 x 10~5(6.1 + 0.63 D10)°"5D10ScG"0'67
Laboratory conditions, U^ is free stream velocity.
D* - 2.0 x lO'^ 1'5
-5 1.5- -0.67
K = 92.4 x 10 3U bCG
154
-------
Ul
01
TABLE 17
WIND WAVE TANK GAS PHASE CONTROLLED MASS TRANSFER COEFFICIENTS FOR WATER
u
oo
13.20
11.67
10.31
8.57
7.09
5.96
Eq(l)
*
U
0.993
0.849
0.675
0.455
0.381
0.27
KG/U* =
Re*
54.2
36.5
17.5
5.73
2.91
0.72
65.0 x 10~3
KG
m/sxlO 3
71
55
39
29.7
22.2
19.4
KG/U*
xlO3
71.5
64.8
57.7
65.3
58.3
71.8
G o°
xlO4
53.8
47.1
37
34.6
31.3
32.5
yu.°-78
xlO4
94.9
80.9 '
63.2
55.6
48.2
48.2
KG(Eql)
xlO3
64.5
55.2
43.9
29.6
24.8
17.6
-------
Cn
TABLE 18
ENVIRONMENTAL AND LABORATORY VALUES
u» or uio
0
2.0
5.0
8.0
10.0
13
15
20
25
30
OF K. AND K
— — if
environmental
m/sxlO ctn/h
0
5.8
16.4
28.8
37.9
52.9
63.7
93.2
126
161
0
2.1
5.9
10.4
13.7
19.1
22.9
33.6
45.3
58.2
„ FOR A COMPOUND OF Sc,
u •"
u-
KL
laboratory
m/sxlO cm/h
0
6.1
24.1
48.8
68.2
101
125
192
269
354
0
2.2
8.7
17.6
24.5
36.4
45.1
69.4
97.0
127
• 1000 AND
Sc^ - 0.6
KG
envirdnment
m/sxlO cm/h
0
3.5
9.9
17.4
22.9
32.0
38.5
56.3
76.0
97.6
0
1270
3560
6250
8250
11500
13900
20300
27400
35100
KG
laboratory
tn/sxlO cm/h
0
3.68
14.5
29.4
41.1
61.0
75.6
116
162
213
0
1325
5236
10600
14800
22000
27200
41900
58500
77000
-------
Entire K^T Data Set
— —— "— — OLi
Having established the two equations for K_ and K. it is possible to apply
m to the entire set of K data, for
ry's Law Constant. This is essentia
resistance model. The equation used is
them to the entire set of K data, for the compounds of various values of
Henry's Law Constant. This is essentially a. test of the validity of the two
1/KOL = 1/KL
^ = 68.2
K. = 92.4
(3
+ RT/HK_
\J
xlO-6U ^S
xloA ^Sc
-0.50
-0.67
The correlated K values are given earlier in Table 10 in the experimental
section. Comparison of these experimental and correlated values is a test of the
IL. and K correlations both as a function of Schmidt number and wind speed and
or the two resistance theory. Agreement is excellent for the compounds of higher
volatility. Somewhat poorer agreement is apparent for the alcohols, partly it is
suspected because the Henry's Law Constants are in error and partly because of
wave damping. The agreement is regarded as sufficient to lend further confidence
to using the two resistance model in volatilization calculations.
Comparison with Other Studies
A number of studies have reported K_ and K values obtained in wind wave tanks
and in the environment. It is instructive to compare the correlations derived
here with these data notably those in wind wave tanks by Liss(86), Downing and
Truesdale (80), Kanwisher (87), Hoover and Berkshire.(88) and Cohan et al (58)
and for the environment by Broecker and coworkers (89,90,91), Emerson (92,93,94)
and Schwartzenbach et al (2).
Gas Phase Resistance (K )
^———— u
Liss (86) measured K for water and K^ for oxygen in a wind wave tank
and reported friction velScities, the conditions being at lower wind speeds
than were used in this study.At a 10 cm velocity of 6.0 m/s Liss obtained a
friction velocity of 0.31 m/s which compares well with the 0.27 m/s obtained
in this study. Under these conditions,and as shown in Figure 32, Liss obtained
a K of 7451 cm/h or 20 x 10 m/s which compares well with the 19.4 x 10 m/s
in ?his study. The ratio of K /U* obtained by Liss from 1.6 to 8.2_m/s averaged
63 x 10 which is in remarkable agreement with the present 65 x 10 . Again
there was no trend in KR/U* with wind speed.
Sverdriip (98) reported oceanic evaporation fates"-.over a range of velocities^
The trend was for K to rise from 6 x 10 m/s at 3 m/s wind speed to 14 x 10
m/s at 8.5 m/s. Pond et al (99) also obtained data which agree with these
values, being 8.7 x 10 m/s at 6.8 m/s wind speed. Applying t|e correlation
to these environmental conditions yields KQ values of 5.5 x 10 m/s at 3 m/s
to 18.6 x 10 m/s at 8.5 m/s in very satisfactory agreement. Pond's velocity
of 6.8 m/s should yield a friction velocity of 0.22 m/s.(0.256 was obtained
experimentally) and a K of 14.2 x 10~ m/s (8.7 x 10~ m/s was observed).
Clearly the correlation agrees well with both other wind wave tank studies and
oceanic data although at very low wind speeds, ie below 3 m/s the laboratory
data seem unusually high. The most important point is that analysing the data
in this way predicts a considerable difference between laboratory and oceanic
data which is borne out by observation. These data are shown in Figure 32.
157
-------
Liquid Phase Resistance (K.)
The laboratory data are plotted in Figure 33 corrected to 20 C and a
Schmidt Number of 1000. Essentially this involves multiplying the 0 and CO
data by 0.75, the benzene and toluene data by 1.06. There is a fairly wide
scatter in the data attributable to differences in tank geometries, the smaller
tanks tending to have larger coefficients, probably as a result of larger drag
coefficients. The line given by the equation gives a good fit of the present
data but tends to underestimate the high velocity data and overestimate the
low velocity data, especially those of Liss. A better fit to all these data
could be obtained by making the drag coefficient fetch dependent and forcing a
lower drag coefficient at low wind speeds . A one-constant equation for C is
thus too simple and it is necessary to use different expressions at high and low
wind speeds. The most serious discrepancy is between the present work and that
of Liss (79) at 6 to 8 m/s where there are similar friction velocities but the
mass transfer coefficients differ by a factor of two. For example at 8 m/s
Liss obtained coefficents of about 30 x 10~ while in the present work a value,
of about 50 x 10 m/s was obtained, Cohen et al (58) obtaining about 60 x 10
m/s and Kanwisher (87) 85 x 10 m/s, the values being corrected for Schmidt
Number. The reasons for this discrepancy are not known although it may be
related to the shallowness of Lisa's tank (10 cm) but: the weight of evidence
favours the higher values as Suggested by the correlation. It seems likely that
the correlation overestimates K_ in the low wind speed range of 0 to 4 m/s when
the water surface is fairly calm.
The best available environmental data are from radon flux measurements in
Atlantic (BOMEX) , Pacific (Papa) by Broecker and Peng (89) , Peng et al (91) ,
for small lakes by Emerson (92,93) and for p dichlorobenzene in Lake Zurich by
Schwartzenbach_et al (2). The oceanic radon data give values of K_ of approxi-
mately 40 x 10 ra/s at 12 m/s and 21 x 10~ m/s at 7 m/s which are in good
agreement with the environmental prediction. Emerson's lake data range from
0.07 to 0.25 m/day (0.8 to 2.9 x 10 m/s) at a probable wind speed of 1 to
2 m/s. At 1 m/s the environmental correlation predicts 3 x 10~ m/s which is in
fair agreement.
Parad±chlorobenzene_has a water solubility of approxima tely. 8 3 g/nu and a
vapor pressure of 9 x 10 atm thus fl is approximately 1^6 x 10 atm m /mol.-
At a wind speed of 2 m/s JL will be approximately 5 x 10 m/s and K 3.3x10 m/s
thus with RT equal to 0-025
1/KOL = 1/KL
- 0.20 x 106 + 0.02 x 106 - 0.22 x 106
and K » 4.5 x 10 m/s or 1.6 cm/h,
with the system being 90Z liquid phase resistant. SchwartzftnbacB et al (2)
obtained a value of 1 cm/h but did not quote on average wind speed for this long
but narrow lake. The discrepancy could be due to wind speed, diurnal effects,
mass balance errors or of course the correlation. It is also possible that
an appreciable water column resistance may be present. Given these uncertainties
the agreement is encouraging.
158
-------
The principal concern is that the laboratory and environmental equations
overestimate K_ at low wind speeds. It appears that at low function velocities
the relationship suggested here may break down because of onset of smooth condi-
tions in a manner analogous to the laminar-turbulent transition in pipe flow.
Support for this is found in the observation that the environmental prediction
equation yields higher IL values at 2 to 4 m/s than are found in tanks. Further
careful IL measurement at low wind speed is required in long tanks and in ponds
to resolve this problem. Given this uncertainty the error limits on the pre-
dicted environmental values are placed at +10% and -40% i.e. a predicted value
of 10 is believed to lie between 6 and 11.
The general conclusion is that these equations provide satisfactory methods
of correlating both laboratory and environmental mass transfer coefficient data.
The apparent discrepancy between laboratory and environment is attributed to a
difference in drag coefficient which is higher in small tanks. • The key scale-up
variable is believed to be the friction velocity for which a K^ and K relation-
ship is suggested. It is possible that roughness Reynolds number "corrections"
may be necessary but given the present level of accuracy it is doubtful if they
are needed. The most useful data to improve these correlations are
(i) further tank measurements of YL at low wind speeds where there is
an apparent discrepancy
(ii) pond measurements with varying wind speed
(iii) a systematic study of the effect of Schmidt number for a range of
solutes including oxygen, inert gases, CO. and organic solutes
over a range of temperature
(iv) studies of the effects of additional resistances provided by organic
microlayers, as discussed earlier.
159
-------
FIGURE 32
EXPERIMENTAL AND .CORRELATED VALUES OF
FOR SCHMIDT NUMBER 0.60
tn
O
X
W
la
w
8
&
e
0LISS
TTHIS WORK
SVERDRDP
FOND
WIND SPEED M/S
160
-------
FIGURE 33
EXPERIMENTAL AND CORRELATED VALUES OF K
CORRECTED TO A SCHMIDT NUMBER OF 1000
150
100 -
X
en
--.
e
u
M
Px
E*
M
O
fa
CO
H
03
6 LISS 02
O LISS C02
X COHEN et al
HOOVER & BERKSHIRE
KANWISHER
DOWNING & TRUESDALE
THIS WORK
Q BROECKER & PENG
T EMERSON
WIND SPEED M/S
161
-------
RELATIVE VOLATILITY APPARATUS
The results given earlier in Table 12 suggest that the method is capable of
yielding solute mass balances better than 10% in most cases, but for higher
molecular weight sparing soluble compounds there is less satisfactory recovery
of the solute. The reasons for this are not clear and it is believed that
further investigation could result in improved techniques and correspondingly
better recoveries.
Since most- of these compounds are fairly soluble in water the solute
Henry's Law Constant (H ) can not be expressed meaningfully as a ratio of vapor
pressure to solubility. The fundamental definition of H is the ratio of solute
partial pressure to concentration which, it has been shown is given by:
H =Y'PS = Ha = oPSv
s s w s w w w
and a « y PS /PS
's s w
where y is the infinite dilution activity coefficient of the solute in water,
v is tne molar volume of water (18 x 10 m /mol), P and P are the solute
and water vapor pressures (atm), a is the relative volatility and Hw is the
Henry's Law constant for water between air and pure water.
Values of Y can be obtained from vapor liquid equilibrium data and have
been correlated Sy Pierotti et al as reviewed by Reid et al (14). The usual
approach is to use an equation of the form
log YS - A + BN + C/N
where N is the carbon number and A,B and C are constants applicable to a homolo-
gous series. Selected values of these constants are given in Table 19 below
(Reid et al 14).
TABLE 19
CONSTANTS FOR INFINITE DILUTION ACTIVITY
COEFFICIENTS IN WATER AT 25°C
Solute ABC
n Acids -1.00 0.622 0.490
n Primary alcohols -0.995 0.622 0.448
n Secondary alcohols -1.220 0.622 0.170
n Tertiary alcohols -1.740 0.622 0.170
Aldehydes -0.780 0.622 0.320
Ketones -1.475 0.622 0.500
Ethers (20 ) -0.770 0.640 0.195
Esters -0.930 0.640 0.260
Using these correlations it is possible to estimate o if vapor pressure data for
the solute and water are available. This is done in Table 20 which shows that
162
-------
a tends to increase with increasing carbon number. This effect is not clear
since a- depends on y (which increases with carbon number by about a factor of
3 per carbon added) but also on the vapor pressure of the solute P (which tends
to decrease by a similar factor) thus the net effect is not large or immediately
obvious.
Also given in Table 20 are the experimental values reproduced from
Table 12. Agreement is good for compounds of a less than 20 but there are
severe descrepancies for the Ketones. The reasons for this are not clear but
probably are associated with the poor mass balances. There is also a possi-
bility that there are errors in the calculated values. It can be concluded
that the method is satisfactory for compounds which have a values up to 20 which
corresponds to H lying in the range of 5 x 10~ atm m /mol (i.e. that of water)
to 10 atm m /mbl. It should be noted that for compounds of higher H the ratio
of vapor pressure to solubility is a satisfactory method of determination. The
relative volatility method is satisfactory for solutes which are miscible with
water. It can also be used to give a rapid, qualitative estimation of H which
may show that H is so small that volatilization is unimportant.
s
The effect of temperature is interesting in that it is experimentally
more convenient to measure ct at atmospheric pressure, and hence higher tempera-
tures than ambient.
Taking n pentanol as an example, the vapor pressures at 25, 60 and
100°C are respectively 0.0034, 0.034 and 0.25 atm (Reid et al 14) while the
Y values are relatively unchanged at 168, 178 and 162. Since the water vapor
pressures are respectively 0.031, 0.20 and 1.0 atm, the values of a become 18.4,
30.3 and 40 i.e. doubling in the range from environmental temperatures to 100 C
where the solution can be boiled at atmospheric pressure. This behaviour is not
generalizable to other compounds and depends on the solute enthalpy of vaporiza-
tion which controls the variation of vapor pressure with temperature. It is
thus unwise to use high temperature atmospheric data to estimate a,and hence H.,
at the lower environmental temperatures. If this estimation is attempted it is
probably best to use the value of a at 100°C to estimate y at 100°C then assume
Y to be equal at 25 C. This is true for athermal solutions (i.e. those of zero
excess enthalpy of mixing). The other extreme approach is to assume that the
solution is regular (zero excess entropy of mixing) in which caselnY varies
inversely with absolute temperature. Thus if Y is 100 at 100 C (373 K), Iny
will increase from 4.61 at 100°C to 5.76 at 25 (298 K) giving an Y of 319.
The aqueous solubility of such a solute should decrease from a mole fraction of
0.01 (i.e. 1/100) to 0.0031 (i.e. 1/319) over this temperature range. A con-
venient method of estimating the change in Y with temperature is thus to measure
the variation in solubility and apply the same factor to Y but inversely. Un-
fortunately this approach is of greatest relevance to miscible systems for which
solubility data are of cours not available. The principal merit of the method-is. as
a rapid screening approach to H determination for solutes which are suspected to
be involatile relative to water.
163
-------
TABLE 20
CALCULATED AND EXPERIMENTAL RESULTS FROM
THE RELATIVE VOLATILITY APPARATUS AT 25°C
Compound
methanol
ethanol
n propanol
n butanol
2 butanol
isobutanol
n pentanol
2 butanone
2 pentanone
2 heptanone
3 heptanone
acetophenone
Vapor Pressure
(atm) at 25°C
0.15
0.072
0.026
0.010
0.023
0.016
0.0034
0.13
0.016
0.0019
0.0018
0.0005
CO
Y
1.53
3.37
11.4
42.9
20.4
42.9
168
13.7
54.3
892
892
-
Calculated
a
7.3
7.8
9.5
13.7
14.9
21.9
18.4
57
28
54
51
-
Experimental
a
9.62
7.66
10.7
16.3
17.5
22.7
22.0
62.9
51.8
35.8
28.8
31.8
water
0.0313
164
-------
SOLUBILITY MEASUREMENTS WITH CO-SOLUTES
The experimental data presented earlier in Table 13 indicate that, as
expected, the presence of an organic co-solute tends to increase the aqueous
solubility of a hydrophobic organic compound such as phenanthrene but the
effect is unlikely to be significant. Exceptions may occur if the co-solute
is a strong complexing agent such as EDTA, a surfactant, the co-solute is not
truly in solution or ionization occurs. Such exceptional cases can be treated
using conventional procedures. It is interesting to examine the theoretical
basis for suspecting a solubilizing effect.
It-may bs convenient to-visttaliza triangular diagrams of ternary systems
consisting of water, a hydrophobic solute (here phenanthrene) and a co-solute
such as an alcohol. The co-solute may not be tatally miscible with water, as oc-
curs with higher alcohols but the solubility of alcohol in water greatly exceeds
that of the phenanthrene. In the case of fulvic acid there is a solid phase
region which is not of direct interest here. The area of interest is the water
apex and particularly how the phase envelope corresponding to the cloud point or
solubility lies as the co-solute concentrations rises. If it is parallel to
the water-co-solute side there will be no effect on solubility. If it diverges
from the side there will be solubilization, as of course must occur eventually
at high co-solute concentrations when the co-solute and water are miscible.
The basis for suspecting solubilization is that the presence of co-solute mole-
cules, of largely organic character, will reduce the hydrophobic solute activity
coefficient and thus increase its solubility, i.e. it will become more soluble
since the matrix which it encounters has more organic character. The difficulty
lies in determining the magnitude of this effect at low co-solute concentration.
One approach is to attempt to quantify the degree of non-ideality using
an excess Gibbs Free Energy Equation for the ternary system, the simplest of
which is the symmetrical or two-suffix Margules equation (Hala et al 100)
For a ternary system the activity coefficient y becomes
log YI = x/A^ + *32A13 + X2X3
with similar symmetrical expressions for y. and y_. The constants A „. A _
and A. _ are binary interaction parameters, the possible existence of a
ternary constant being ignored here for simplicity. If subscript 1 refers to
the hydrophobic solute, 2 to water and 3 to the co-solute, the region of inter-
est is that where x is very small thus (x + x ) is essentially unity.
Rearranging yields
log YX = x2A12(x2 + x3) + X3A13(X2 * X3^ ~ X2X3A23
= X2A12 + X3A13 " X2X3A23
Now the solubility of compound 1 will be approximately (1/y.^) on a mole frac-
tion basis or (M /18y ) on a mass/volume (g/cm ) basis where MI is the molecu-
lar weight of the compound and 18 is the molecular weight of water.
The ratio (Rg) of the solubility in the presence of co-solute to that in
pure water (where x, is zero and x_ is unity) is thus the inverse ratio of
activity coefficients
thus log Rg = A12(l ~ X2^ ~ X3^A13 ~ X2A23^
165
-------
But since x_ and (1 - x») are nearly equal and x» is nearly unity
log R_ = X3(A-J9 ~ Ai3 + A?3^ = X3A
This suggests that co-solutes with the greatest solubilizing effect will
be those which cause Y- to be reduced rapidly as x increases which occurs
when A-_ is small i.e. the co-solute is similar in organic character to the
hydropnobic compound and thus miscible with it and when A2_ is large, i.e. there
is relatively high nonidsaiity between the co-solute and water. This latter
effect suggests that higher molecular weight organic co-solutes will be more
effective solubilizers than low molecular weight compounds, i.e. they should
have higher A values.
The form of these equations suggests plotting logR against the co-solute
concentration, which should yield straight lines of slop! A dependent on the
A values. Interestingly this is the same form as the Setchenow Equation for
electrolytes in which the group consisting of the summed A values is termed
the salting-out parameter.
Writing the equation in terms of mass concentration units as used here
yields at high dilution
log Rg - x3A - 18 x 10~6C3A/M3 - A^
where 18 is the molecular weight of-water^ M. is the molecular weight of the
co-solute and C, is in units of g/m and A,, has units of m /g. The molecular
weight dependence of A is thus the combination of two competing trends; high
molecular_weights leadmto high C. values at equivalent x, values thus if A is
constant A., should fall with increasing molecular weightf however as indicated
earlier it is probable that the greater jthe organic character of the co-solute
the greater the value of A and hence of A...
An approximate value for A., can be estimated from the present data using
the higher co-solute concentration values. Forexample for ethanol, A^ is _
approximately 3.8_x 10 , for butanol 7.1 x 10 m /g, for hexanol 1.3 x 10~ ,
for octanol 3 x 10~ and for fulvic acic 3.5 x 10 , all in units of m /g.
There is a trend of increasing A,, with molecular weight approximately expressed
as *
1^ = 0.10 M3 x 10"6 m3/g
Using this simple relationship R values were calculated for the data in
Table 13 assuming (arbitrarily) a molecular weight of 1000 for fulvic acid.
Fairly good agreement is obtained especially at higher co-solute concentrations,
the significant conclusion being that at co-solute concentrations of 100 g/m
and lower no appreciable solubilization occurs. The agreement at low concen-
trations of co-solute is less satisfactory probably as a result of experimental
error, however non adherence to the equation can not be ruled out. An interest-
ing observation is that although compounds such as octanol and fulvic acid are
more effective per gram they are less soluble thus it is impossible to achieve
high degrees of solubilization with them. For example the highest achievable
concentration of fulvic acid was 60 g/m .
166
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It is interesting to compare these results with those of Ueda et al (101,
102) who determined the effect of the polyhydric alcohols sorbitol and inositol
on toluene solubility. These co-solutes decreased the solubility of toluene,
typically by 25% at a concentration of 0.4 to 1.0 mol/liter. Urea on the
other hand increases solubility by about 10% at 1 mole Aiter. Boehm and Quinn
(103)reported data on hydrocarbon solubilization in seawater and concluded that
the effect was due to association of the hydrocarbon with organic matter,
possibly in micellar form. That the effect is some form of sorption into a
separate phase is indicated by the dependence of the magnitude of the effect
on the hydrophobicity of the hydrocarbon, isoprenoids having a greater effect
than aromatics. Phenanthrene showed little solubilization at the dissolved
organic carbon levels from 0 to 17.5 g/in but n hexadecane solubilities varied
by about a factor of 50 over this range reaching .535 g/m at 17.5 g/m of dis-
solved organic matter, the pure water solubility being estimated to be
0.0009 g/m (Sutton and Calderl04) . This six hundred fold increase must be
due to partitioning into a separate phase. Boehm and Quinns' data can be in-
terpreted as indicating that truly dissolved organic matter does not increase
solubility significantly but colloidal organic matter, submicron in size, can
sorb approximately 5% of its-own mass of hydrophobic organic material. This
amount of sorbate (e.g. Ig/m ) may be very large compared to the solubility in
the case of a substance such as hexadecane but is relatively smaller in the
case of aromatic compounds such as phenanthrene or naphthalene which thus do
not display a significant increase in solubility.
The conclusion is that at normal environmental concentrations of organic
matter there is no significant effect on solubility. The effect may be to in-
crease or decrease solubility depending on the nature of the oo-solute. Any
solubilizing effect is likely to be small compared to sorption into suspended
organic matter, some of which may be non-filterable and thus wrongly designated
as being truly dissolved.
167
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HENRY'S LAW CONSTANTS
This work had two primary objectives, the determination of Henry's Law
Constants (H) for selected compounds including those used experimentally in the
volatilization studies and the determination of the extent to which H is likely
to be reduced by the presence of dissolved and particulate natural organic
matter .
The data presented earlier in Table 14 for the hydrophobic compounds show
good agreement between calculated and experimental values for those compounds
for which reliable vapor pressure and solubility data are available. The
deviations are approximately: naphthalene 3%, chlorobenzene 2%, o dichloroben-
zene 3Z and bromobenzene 20Z. This, coupled to the satisfactory agreement
obtained earlier (Mackay et a!28) indicates that the method is fundamentally
reliable and can be used to
(i) estimate H in isolation
(ii) estimate H and vapor pressure if the solution is known
(iii) estimate H and solubility if the vapor pressure is known or
(iv) estimate H and check reported values of solubility and vapor
pressure.
Clearly the last approach is preferred.
The data for the ketones and alcohols are less satisfactory, although it
is clear that the values are reasonable i.e. generally within a factor of two.
It is suspected that some of the vapor pressure data are suspect and since water
is appreciably soluble in the solutes this effect tends to change the solute
vapor pressure and H is not simply the ratio of pure solute vapor pressure to
solubility. The discrepancy appears to be highest for the more soluble solutes.
Because of the low H values the stripping method is inconveniently slow and it
is possible that there is an error in the procedure in that the exit gas is not
fully saturated with the solute. This seems unlikely as is discussed below.
Consider a bubble of gas of diameter DH,, initially containing no solute,
rising during time t ^s through perfectly mixed water containing solute of
concentration C mol/m" . The bubble, if spherical, will have an area A of
ED m and a 'volume V of IID /6. If the overall mass transfer coefficient is
and the solute partial pressure is P atm then during time 7
the amount transferred will be
K_-,
die
A(HC - P)dt/RT - VdP/RT
thus dP/(HC - P) = I^Adt/f
integrating from P « 0 to P - P at time t gives
HC - P -
HC
P - HC(1 -
Now A/V - 6/D
thus P - HC(1 - expC-eK^t/D))
The critical group is 6 K«fit/D which should be at least 3.0 to ensure a 95%
approach to equilibrium. This is best achieved by having D small (finely
168
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dispersed bubbles) and t large (a deep pool of water) . As H becomes very low
should approach K- since
I/KQG = I/KG + H/RTK,
Li
For example if the system is "calibrated"with a substance such as benzene
with a H value of approximately 5 x 10 atm m to assure a 98% approach to
equilibrium then the group 6 KOGt/D will be 3.9 which may consist of values of
2s for t, 0.002 m for D and thus K is 6.5 x 10~ m/s. Since the system is
liquid phajse controlled K_ is approximately equivalent to RTIL./H and K_ is
1.36 x 10 m/s. This is a reasonable value for JL (Sherwood et al 42 ) . It
seems likely that K_ will be higher, possibly 10~ m/s. It follows that
• -4
1/K.., = 1/K_ + H/RTK_ = 100 + 1532 = 1632 = 1/6.5 x 10
\J\J \J Jj
illustrating that only 100/1632 or 6% of the resistance lies in the gas phase.
-4
If H is reduced to 5 x 10 (e.g. naphthalene) but IL and K remain con-
stant, as is likely given the constant fluid mechanical conditions, the K
breakdown becomes:
l/Kn_ = 100 + 153 = 253 = 1/4 x 10~3
Uli
and 63C_-,t/D becomes 24 thus an even closer approach to equilibrium is achieved.
It thus appears that as H falls the system should give more accurate re-
sults. The only difficulty here may be if the less hydrophobic solutes cause
changes in interfacial tensions and thus affect the flow conditions in the
vicinity of the bubbles. Comparison of the calculated and experimental results
for the five solutes shows that in three cases the experimental results are
higher than calculated and in two cases they are lower, thus no systematic
error is apparent. Further, the reproducibility is much better than the dis-
crepancy between experimental and calculated data.
It is recommended that the gas stripping method be validated for compounds
with H in the range less than 10 atm m /mol.
The tests with fulvic and humic acids in the concentration range up to
54 g/m showed a significant reduction in H following addition of the acid.
These tests involved measuring the change in slopes of the concentration -
time curve before and after addition. The precision between experiments was
insufficient to permit the change in H to be determined between tests. The ,
naphthalene results showed that the reduction in H was an average of 1.7 x 10
atm m /mol per g/m of sorbent. The error on this quantity is no better than a
factor of three but it is significantly greater than zero.
—6 3
Taking an average value for H of 440 x 10 it appears that at 1 g/m
sorbent there is 0.39% sorption which is equivalent to a partition coefficient
of 3900 (pg solute per g sorbent) per (g solute per m water or mg solute per
liter water).
It is interesting to compare these results with the sediment sorption
work of Karickhoff et al (8 ). -Naphthalene has a KQW of 2300 and a KQC of 1300.
In a suspension containing Sg/m of organic carbon sorbent in equilibrium with
169
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3
a dissolved solution of concentration C g/m the sorbed concentration will be
1300 C pg solute/g organic carbon or 1.3 x 10 CSg solute/m .. The ratio of
sorbed to dissolved solute is thus 1.3 x 10 S.
Assuming that the sorbents have 65% carbon, the ratio becomes 0.85 x 10 ST
where ST is the tetal sorbent concentration.
Taking H for naphthalene as 440 x 10 , it is expected that at a low con-
centration S of say 10 g/m the ratio would be 8.5 x 10 and H would be re-
duced by that ratio i,e. by 3.7 x 10 . The experimental data indicate a
reduction of 17 x 10 or 4.6 times the amount calculated above. The conclusion
is that reduction in H is attributable to a partition coefficient which is
greater than K by a factor of 1.7. It must be emphasized that the accuracy
of this "Kp" determination is no better than a factor of three thus it is
possible that the experimental results are consistent with Karickhoffs. It
had been hoped that other solutes with higher KQW values such as pyrene would
permit the "Kp" to be determined more accurately but this proved to be impos-
sible because of the low concentrations.
The implications of these results is that the presence of high molecular
weight natural organic matter in suspension andjbr solution apparently causes
a reduction in H but the effect is small at normal environmental concentrations.
A procedure for calculating the likely magnitude of the effect is to assume that
the sorbent is octanol then calculate the extent of sorption using K „ as Kp
This will probably give a result within a factor of three of the correct value.
3
For example at a sorbent concentration S_ g/m the fractional reduction in
H will be approximately 10 S-K.,,. This "rule" should not be used when the
fraction sorbed exceeds 10%.
This result is in accord with the results of the solubility measurements in
the presence of co-solutes in that it is very unlikely that concentrations of
dissolved organic matter can be achieved which will significantly enhance solu-
bilities or reduce Henry's Law Constants. The most effective organic matter
is probably material such as fulvic or humic acids which have high molecular
weights and structures which can incorporate molecules of hydrophobic solutes
thus reducing the water cavity area requirements. Precise measurement of this
effect is desirable, especially for high K compounds but this is difficult
experimentally since the magnitude of the effect is of the same order of mag-
nitude as the error.
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SECTION 9
CALCULATION OF ENVIRONMENTAL VOLATILIZATION RATES
The primary purpose of this work was to devise procedures for calculating
environmental volatilization rates. Some general features of this procedure
are reviewed below. The required data fall into several categories.
PHYSICAL CHEMICAL DATA
A knowledge of the Henry's Law Constant is essential, but the required
accuracy varies depending on the absolute value. In the liquid phase control
regime only an approximate value is necessary, provided that the atmospheric
concentration is low. If experimental solubility and vapor pressure data are
available, they can be used to calculate H provided that they refer to the same
state. Ideally the "May-Wasik" generator column method should be used for
solubility and the "Spencer-Cliath" method for vapor pressure. KQ^ data can be
used to check the solubility. If solubility and vapor pressure data are not
available, one of the correlation techniques can be used. If experimental
determination is necessary either the gas stripping or relative volatility
approaches can be used to measure H or the small scale volatilization system
can be used to measure KQL and from it infer H.
Examination of the H value with others for a homologous series provides
a useful check. Experimental values should be checked against the correlation.
A partition coefficient to any suspended(mineral or organic matter in the
water phase should be estimated either directly or from KQW and used to esti-
mate the fractions of dissolved and sorbed material as discussed earlier. Only
the dissolved material exerts a driving force for volatilization.
A similar calculation may be necessary for atmospheric participates.
ENVIRONMENTAL CONCENTRATIONS
Estimates of the temperature and water and air concentrations and their
breakdown into solution (or gaseous) and sorbed forms are required. When
juxtaposed with the Henry's Law Constant, the direction of transfer will be-
come apparent as will the sensitivity of the flux estimates to the concentra-
tions and H. This calculation can be done using concentrations or fugacities.
In many cases the air phase fugacity will be negligible but in cases where
the air and water phase solute fugacities are close, accurate values of both
171
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concentration and H may be necessary. Examination of the absolute values
enables the required accuracy to be estimated*
MASS TBANSFER COEFFICIENTS
Depending on the value of H, either or both of KG and IL may be required.
The correlation equations derived earlier for these quantities as a function
of wind speed, fetch, current (for rivers), and Schmidt Number (or diffusivity)
can be used.
If surface films are present, an' allowance may be made for their presence
although quantifying this effect may be difficult.
A time average mass transfer coefficient is most useful. This requires
an estimate of the diurnal variation of temperature and wind speed, possibly
in 4 or 6 hour increments. The relevant temperature is that of the water
surface, not the bulk. This temperature may fall during the night due to
radiative cooling. In principle it is better to calculate 1C. and Kr rather
than average temperature and wind speed. It should be noted that temperature
influences K_, KG and H, and thus K™, and it also affects (C-P/H) the driving
force for volatilization.
The correlation equations presented in Section 8 can be used to calculate
mass transfer coefficients, using either the versions in which 10 meter wind
speed is used directly or the dimensionless groups (Reynolds and Stanton
numbers) are evaluated. Both methods require use calculation of the Schmidt
number which includes the effect of solute molecular size or diffusivity and
temperature. For most purposes the simpler wind speed correlations are
probably preferred.
Although in most cases the partial pressure P of the solute in the
atmosphere is small and can be assumed to be zero, there may be situations
(for example PCB's) where this is not valid. The simplest test is to
calculate the fugacities of the solute in the water and in the atmosphere
and compare their magnitudes and difference. In certain cases, volatilization
may create a significant solute concentration in the atmosphere above a lake,
especially if the ventilation rate is slow. An approximate mass balance-
atmospheric dispersion calculation can be done to elucidate the influence of
such an effect.
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CALCULATION OF SCHMIDT NUMBERS
The. calculation of Schmidt numbers for atr and water is straightforward
but procedures: are reviewed here for completeness.
The water Schmidt number Sc is given by
w
Sc = y /p D
w www
where y is the viscosity of water, p is the density of water and D is the
diffusivity of the solute in water. Rarely does the solute concentration
reach a level that y and p are significantly different from that of pure
water. The values or y and p are of course temperature dependent and can
be obtained from Handbooks. The preferred SI units are Pas for viscosity
and kg/m3 for water.
The diffusivity D is best obtained by the Wilke Chang correlation
which is given by Sherwood et al (42) for water systems as
Dw = 7.4 x 10"8 [(M)°'5T/uwVs°-6]
D has units of cm Is
Here M is the molecular weight of water.
4 is an association parameter which is 2.6 water
T is temperature (K)
y is water viscosity (cp)
V is solute molar volume at its normal boiling point
s
This reduces to
= 5.06 x 10~7 T/ywVs°'6 cm2/s (yw in cp)
Since 1 cp is equivalent to 10~3 P this becomes
clS
D - 5.06 x 10~10 T/y V °'6 crn^s (y in Pas)
w w s w
Finally, if D is required in m /s to be consistent with the other SI
quantities the equation becomes
5.06 x
0-6 m2/
A typical diffusivity is 10~5 cm2/s or 10~9 m2/s which, when combined with
a density of lO^g/m3 and a viscosity of 10~3 Pas yields a dimensionless
Schmidt number of typically 10 3.
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The air Schmidt Number Sc. is given similarly as
SCA = VPA DA
where v is tfie viscosity of air, p. is the density of air and D. is the
diffusivity of tfie solute in air values of p. and p. are available in
Handbooks.
The air diffusivity D can he obtained from one of several correlations as
reviewed by Reid et al (14J for example the Fuller Schettler and Giddings
correlation is often used. Although regarded as somewhat obsolete the Gilliland
correlation (97) is attractive in that it uses the same molar volume as the
Wilke Chang correlation.
DA - 4.3 x lO'V^d/*^ + 1/Mg)0'5
o
where D has units of cm Is
£L
P is total pressure (atm)
MA and Mg are the molecular weights of air and the solute
VA and Vfi are the molar volumes at the normal boiling point.
When expressed in SI units of m2/s the constant 10 3 is replaced by
10~7.
A typical diffusivity is 0.1 cm^/s or 10~£ m2/s which when combined with
a density of 1 kg/m3 and a viscosity of 2 x 10~5 P (i.e. 2 x 10~2cp) yields
a Schmidt number of 2.0. Water vapor has a lower fchmidt number of 0.6 at 0°C
because of its unusually high diffusivity of approximately 0.3 cm2/s.
An attractive feature of the Schmidt Number is that it combines in a
rigorous manner the effect of both molecular size (i.e. diffusivity) and of
temperature in the correlation for mass transfer coefficients. It is more
theoretically justified than equations invoking fictitious activation energies
or power dependencies of temperature. Since correlating equations are avail-
able, or can be easily devised for densitites, viscosities and diffusivities
in air and water it is relatively easy to incorporate the Schmidt Number in
computer programs used for environmental prediction purposes.
OTHER TRANSFER PROCESSES
The possibility of other transfer processes such as sedimentation or wet
or dry atmospheric deposition should also be examined since these processes may
counteract or enhance that of volatilization. The role of sedimentation is
discussed briefly in a later section.
174
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Of particular interest are the processes of volatilization from lakes and
rivers which are also discussed in more detail separately. In these cases,the
hydrodynamic regimes strongly influence volatilization processes.
ROLE OF SEDIMENTATION AND SORPTION
If a diffusing solute is present in dissolved and sorbed forms in water
the calculation of water column transfer rates becomes more complex. This has
been discussed by Mackay et al (105 ) in some detail and only the salient
points are reviewed here.
If the suspended matter has a negligible settling (or rising) velocity the
sorbed material will diffuse with the water, equal diffusivities apply,and
Pick's First Law can be used with the total (dissolved and sorbed) concentra-
tion. The fugacities are reduced by sorption but the resistances are also
reduced.
If the suspended matter has a velocity with respect to the water column,
the net velocity becomes the algebraic sum of the diffusion and particle velo-
cities. These velocities are best calculated as the invidual mass flux
(mol/m2.s) divided by the relevant concentration (mol/m ). It is possible
for upward diffusion to be exactly balanced by downward sedimentation. The
diffusive velocity is N/C where the mass flux N is EL.AC/AY where DV is vertical
diffusivity, C is concentration and Y is depth. The sedimentation velocity is
simply the particle velocity which can be estimated from sedimentation or par-
ticle size observations.
SORPTION-DESORPTION KINETICS
In this analysis, we have assumed that equilibrium exists between the dis-
solved and sorbed forms, but this may not always apply. Sorption experiments
generally show a fairly fast initial "outer surface" or "labile" sorption (half
life of minutes) superimposed on a slower penetration of solute into intersti-
cies (half life of hours). Desorption is similar with fast "labile" desorption
with slower release of the solute trapped more deeply in pores. These rates are
of importance in volatilization since they may control whether or not the sorbed
solute is volatilized from an element of water which eddies to the surface and
remains there for a short time. If the "volatilization exposure half life" at
the surface is much shorter than the desorption time, it can be assumed that only
the dissolved solute will volatilize during exposure; thus the "driving force"
for volatilization is derived only from the dissolved state. If desorption is
fast the sorbed material could also be volatilized after having been desorbed.
Unsteady state theory suggests that the mass transfer coefficient KL will be
related to diffusivity D and exposure time t by an equation of the form
A typical diffusivity is 10~5 cm2/s and typically ^ is 0.003 cm/s; thus the
exposure time t is typically 1.4 s. It seems unlikely that appreciable desorp-
tion will occur during this short period. Under quiescent conditions when K.
is smaller, i.e., 0.001 cm/s, t will be approximately 13 s and some desorption
may occur.
175
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The general conclusions are (i) that usually only the dissolved solute
will volatilize at the surface with the sorbed material desorbing later in the
bulk of the water column to establish a new equilibrium, and (ii) the sorbed
material will probably not influence the transfer rate in the water "film",
i.e., it will not lower the resistance as may occur in the water column.
Kinetics may also influence the behaviour of solids falling through
the water column. If the falling velocity is low,it is likely that the sorbent
will maintain close to its equilibrium amount of sorbate;whereas if the velo-
city is high (as may occur with mineral particles), there may be insufficient
time for equilibrium to be reached.
The role of sedimenting sorbents is thus usually to act counter to
upward diffusion (or to enhance downward diffusion) at a rate depending on
sorbed concentration and settling velocity and to some extent on the sorption-
desorption kinetics.
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VOLATILIZATION FROM RIVERS
The issue of volatilization rates from rivers has been discussed by
Mackay and Yuen ( 106 ) as part of this project. The following is a review
and expansion of that material.
Rivers are a particularly important component of the aquatic environment,
being widely used as a source of drinking water, they provide commercial and
sport fisheries and recreational ecosystems as well as supporting intrinsically
valuable eeosystems. It is very desirable that the extent of contamination
be known and controlled to an acceptably low level.
Examples of contamination problems include; the presence of haloforms
(notably chloroform) generated during chlorination of wastes and of electrical
and other plant cooling waters; contaminants introduced by groundwater in-
flitration from nearby landfill or industrial sites, and especially from
leaking storage tanks or pipelines; chronic emissions from industrial and
domestic sources; water runoff containing pesticides from agricultural land;
hydrocarbon and other product contamination from accidental and chronic spills
including releases from submerged oil and product pipelines, outboard motor
exhausts, and from vessels which have been accidentally holed. In many of
these cases volatilization is an important, or even the most important, pathway
for decontamination.
Of some concern is the issue of the extent to which ice alters the
volatilization rate. It is suspected for example that an oil or chemical
spill into an ice-covered river could have a greater impact than a spill into
an ice-free river because the rapid loss of toxic volatile compounds is
inhibited, resulting in greater exposure in the water column.
Fortunately the problem of oxygen depletion or "sag" in rivers has lead
to a considerable volume of information on transfer rates of oxygen between
the atmosphere and the river. Many correlations have been developed to quantify
this rate.
The usual approach is to express the oxygen uptake rate as a first
order rate constant or reaeration constant termed K2 . Thus if C is the
oxygen concentration in the river and Cs is the saturation value (approximately
10g/m3) then the flux N into unit area of water is expressed as
N = K2(CS-C) - dC/dt
hence C = CS - (CS - CQ) exp(-K2t)
where t is time (usually hours or days) and C is an initial concentration.
K2 has units of reciprocal time and is typically 0.1 to 0.2 h"1 for aim
deep river. Comparison of this equation with the mass flux equation derived
earlier shows that K2 is equivalent to K^/Y where Y is the river depth. It is
perhaps unfortunate that K2 was used as the correlating quantity in the early
reaeration literature because it is "less constant" than K2. As is discussed
later, it is found that K2 is approximately inversely proportional to depth.
It is worth laboring this point by an example because there has been an
unfortunate tendency to apply K2 to lakes. Suppose that ^ is 0.1 m/h in a
river of depth 2m. K2 then becomes 0.05 h~J. If this water flows into a
-------
region where the depth decreases to 1 m it is likely that K2 will increase
slightly to say 0.12 m/h because of the closer proximity of the bottom to the
surface. K2 then becomes 0.12 m/h, which is a substantial increase. If this
water enters a lake of depth 10 m it is probable that K.2 will drop to say
0.05 m/h and if a K2 is to be defined it will be 0.005 h"1. Since lakes are
very variable in depth it is unwise to express "average" or "typical" K2
values since it can vary by orders of magnitude. It is better to use ^
which is relatively more constant.
For rivers it is likely that in moving from the bulk of the water to the
atmosphere, the contaminant experiences three diffusive processes, each with
a resistance. Normally one of these resistances will dominate.
The first resistance (ri) is that of diffusion from the bulk of the river
to the interface. This is approximately Y/D where Y is river depth (m) and
D is the vertical diffusivity (m2/s). In a reasonably turbulent river the
dif fusivity can be approximated as Y2 divided by the average time t (s) for
an element or eddy of water to move from bottom to surface. In a river of
depth 2 m, it is likely that this time is of the order of 100 s, thus n
is t/Y or 50 s/m. In shallow fast flowing rivers ri may be as low as 1 s/m
and in deep sluggish rivers it may be as large as 1000 s/m.
The second resistance r2 is that for diffusion through the near-surface
liquid to the interface. Typical reaeration constants K2 are 0.1 to 0.2 h"1
for 1 m deep rivers thus K_ is typically 4 x 10~s m/s and r2 is thus 25,000 s/m.
It thus appears that except in deep slow moving rivers the resistance r\ will
usually be negligible compared to r2 and can thus be neglected.
The third resistance r3 is that for diffusion through the atmosphere in the
layer close to the water surface. From the considerable body of information on
water evaporation this resistance can be estimated as corresponding to a mass
transfer coefficient K of approximately 0.01 m/s. It has been shown that the
tern r3 is given by
r3 - RT/HKG
The overall resistance r is thus approximately
rx - ri + r2 + r3 £ 50 + 25000 + 2.4/H
It follows that a number of regimes can be identified in which differing
resistances dominate.
If H is greater than 10 3, r2 will dominate by a factor of approximately
10, i.e. the overall rate is controlled by the diffusion rate through the
water film at the interface. The substance will generally volatilize rapidly.
This is the regime in which oxygen diffuses (since H for oxygen is
approximately 0.65 atm m3/mol) thus an estimate can be made of volatilization
rate of substances in this class from reaeration data. The simplest (and
rather Inaccurate) approach is to assume that K2 or KL are equal for solute
and oxygen. A correction for the usually slower diffusivity of the solute
should be applied as is discussed later.
If H lies between 10~3 and 10~s both resistances r2 and r$ are important
and volatilization will be less rapid but still possibly significant.
Reaeration data can not be used alone to estimate solute volatilization.
178
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In the regime where H is 10~7 to 10~5 the substance will volatilize
slowly and at a rate dependent on H. The gas phase resistance r3 will
dominate by a factor of over 10 and the rate is controlled by the slow
diffusion through the air phase. Reaeration data become irrelevant.
In the regime of H less than 10 7 the compound can be regarded as
involatile or less volatile than water.
The driving force for volatilization is the difference between the
water column concentration C (mol/m3) and the water concentration in
equilibrium with the atmospheric concentration or partial pressure (P)
of the contaminant, and is thus (C-P/5). The overall mass flux (N) equation
becomes
N = (C-P/H)/(ri + r2 + r3) mol/m2.s
River Concentration Profiles
It is instructive to set up and solve the steady state differential
equation which applies to the decay of concentration in a river both
attributable to volatilization and to other processes. The easiest situation
is that of a continuous point source. If the average river depth is Y(m),
the velocity is V (m/s) and the concentration C is homogeneous laterally
(being C at the source point) then a mass balance on a volume of water of
area 1 m moving downstream in time t (s) gives
YdC/dt - -H - -(C-P/H)/rT
Usually P/H will be negligible compared to C thus
Integrating gives
YdC/dt = -C/rT
C - CQ exp (-t/YrT) = CQ (-L/YVrT
where L (m) is the distance downstream and is equal to t/V.
If the contaminant is subject to another first order decay process of
rate constant K_(s *) then it can be included yielding
dC/dt = -C(l/YrT +
thus
c=coexp (-
The group (1/Yr ) .for oxygen transfer is the reaeration constant Ka« Since
oxygen has a high H value in this case 12 dominates thus TT is TZ and
becomes l/, and (l/Yr> becomes KY which is K2 .
A plot of logarithm of concentration ratio (C/C ) against distance
downstream should thus give a straight line as illustrated in Figure 34.
The slope is (1/Yr + K_) which becomes steeper the lower the resistance
r_;, the shallower the river, and the greater the value of Kp. Comparison
of the values of K^ and (1/Yr ) indicates whether or not volatilization
is a significant competitive process.
-------
It may be useful to calculate a volatilization "half life" or "half
distance" in which the concentration drops by half. It can be easily shown
that this is
half life = 0.69 YrT s
half distance = 0.69 YVr m
For example a volatile hydrocarbon such as benzene (H = 5 x 10 3) with
a typical K. value of 4 x 10 m/s in a river of depth 1 m of velocity
1 m/s will nave a half life of 4.7 hours and a half distance of 17 km.
Clearly very shallow rivers have the potential to lose volatile contaminants
very rapidly.
It is instructive to examine the plot of half life or half distance as a
function of H for the river described above. Ignoring the resistance ri and
adopting the typical values r2 of 25000 and r3 of 2.4 /H the expression becomes
as illustrated in Figure 35.
half life - 0.69Y (25000 + 2.4/H) s
half distance - 0.69YV (25000 + 2.4/H) m
Clearly only if H is greater than 10~5 is volatilization likely to be
significant except in very shallow rivers where the lower limit of interest
is 10-6.
This analysis suggests that the critical quantities necessary for the
determination of volatilization rates from rivers are: -
(i) r2, the liquid phase near surface resistance (which can be
obtained from reaeration coefficient data);
(ii) H, the Henry's constant
and of lower priority and needed only in certain situations
(iii) ra the gas phase resistance (which can be obtained
from existing correlations such as that of Mackay and
Matsugu ( 64 ) or those developed earlier in this report.
(iv) T\ the river bulk resistance (which is needed only in
very deep slow moving waters which can almost be regarded
as lakes)
Review of Reaeration Data
There is a considerable literature on reaeration rates of rivers with
numerous correlations as a function of river velocity, depth and slope.
Excellent, comprehensive, critical reviews have been compiled by
Rathbun G.07) ,Holley (108) ,Lau(109)and Bennett and Rathbun (llO )• Studies
by Mattingly (111 ) and Downing and Truesdale ( 80 ) have shown that wind
also has a significant effect of reaeration rates, a result entirely in accord
with the present work which has shown that these rates are influenced by
180
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wind speed, which generates near-surface turbulence. This wind effect is
difficult to characterise because it depends on fetch which in turn depends
on the wind direction relative to river direction and on river width.
Rathbun ( 107 ) after a detailed review of some 19 equations showed that
the equations of Tsivoglou-Wallace ( 112 ), Parkhurst-Pomeroy ( 113 ) and
Churchill et al ( 114 ) gave the best overall predictions although it must
be recognized that other equations may give better predictions for specific
streams. These equations are
Tsivoglou-Wallace K2 = 638VS
Parkhurst-Pomeroy K2 = 1.08 (1.0 + 0.17F2) (VS)0-37'
Churchill et al K2 - 0.00102V2.695Y-3.085S-0.823
where S is the river slope (m/m) and F is the Froude Number V/(gY)°'5.
If no slope data are available the similar Isaacs-Gaudy ( 115 ) or
Langbein (116) equations can be used.
Isaacs Gaudy K2 = 0.223VY"1'5
Langbein Durum K2 = 0.241VY"1'33
It is likely that for a given river application of these equations would
give an estimate of K2 with an average error between 10 and 50%. One
practical approach is to apply all the equations, discard the outlying result
and take an average of the remainder.
From the oxygen transfer coefficient or resistance it is then necessary
to calculate the effect of the difference in molecular size or diffusivity
preferably using the Schmidt number approach.
Tracer Techniques
Of particular interest and relevance is the recent development of tracer
techniques for measurement of stream reaeration capacity. Tsivoglou (70 )
used radioactive krypton as tracer, but this presents licensing difficulties.
Rathbun et al ( 71 ) have developed an ingenious technique using ethylene or
propane as indicator of volatilization and Rhodamine WT dye as indicator of
dispersion and dilution. Any change in the ratio of hydrocarbon to the non-
volatile dye concentration is largely attributable to volatilization. In
essence this technique provides a direct measurement of the volatilization
rate of high H contaminants from rivers. The solubilities of ethylene and
propane at 1 atm are 131 and 62 g/m3 (4.7 and 1.5 mol/m3) thus the H values
are 0.21 and 0.67 atm m3/mol, well in the liquid phase control range. It is
interesting to note that the tracer technique was developed to enable oxygen
transfer data to be predicted whereas in this case it is the reverse which is
being attempted.
Ice, Aeration and Volatilization
In their comprehensive review of the literature on ice behaviour in
rivers and lakes Ficke and Ficke (117 ) have described several situations
in which ice cover has significantly altered water quality including by oxygen
181
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depletion. It seems very likely that volatilization will be severely reduced,
if not eliminated, when a continuous ice cover is present. Of particular
concern is the situation which may exist when there is an accidental release
of a toxic compound into an ice covered river. In such cases it may prove
beneficial to break the ice cover or bubble air under it in order to promote
volatilization. There may be a case for installing permanent submerged
bubbling or aerating systems in locations such as pipeline river crossings.
This raises the issue of whether or not situations may exist in which
artificial aeration and thus volatilization may be feasible or desirable.
In many oxygen depleted rivers it may be advantageous to install
artificial aerating devices such as surface diffusers, submerged bubblers or
even artificial weirs . Such devices would also serve to increase volatili-
zation rates. The following order of magnitude analysis illustrates the
feasibility of this approach.
If air is bubbled into water at any significant depth (i.e. > 1m )
it is likely that it will become nearly saturated with any dissolved
volatilizing gas of reasonably high H. If an increament of air rate dG m3/s
is introduced then the exit volatilization rate will be dGHC/RT mol/s
when the water concentration is C mol/m3. If the river volumetric flowrate is
Fm3/s then
FdC - - dG HC/RT
integrating gives
C - Co exp(-GH/RTF)
A reasonable target would be to reduce C to 27% of Co which would occur when
GH/RT is unity or when G/F - 0.024/H. If it is feasible to bubble air into
a river at a rate equal to the volumetric river flow than a reduction to
37Z is possible only if H is 0.024 or greater. This suggests that the mini-
mum condition at which artificial aeration could be contemplated is when H
is 10~2. At 10"1 and above it becomes very attractive. Examination of solute
H values indicates that alkanes and haloforms are attractive candidates but
aromatics such as benzene are marginal, and the polynuclear aromatics are
definitely not feasible.
Another method of viewing an artificial aerating device is to consider
the natural river length to which the device is equivalent. This length is
obtained by equating L/IVrT to GH/RTF i.e.
L - GHYVrT/RTF
but since ZVW is F where W is the river width (m)
L - GHrT/RTW - G'HrT/RT
where G1 is the air rate in cubic meters per meter width per second. Since
r_ is typically 25000 s/m and RT is 0.024 this length becomes 106 G'H m._^
To achieve 1 km of natural volatilization for a compound with an H of 10
would require 0.1 m3/m$.s which seems feasible. Higher values of H would
require correspondingly smaller values of G'.
It is concluded that situations may exist for toxic compounds of high
182
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Henry's Constant in which artificial voltatilization is a feasible approach
to stream decontamination. Since the artificial volatilization efficiency
increases steadily with increasing H (whereas the natural rate becomes
independent of H above 10 3) the most attractive situations are those in
which H is largest, i.e. low solubility highly volatile compounds.
Comparison with Literature Data
The most accurate reported data are those of Rathbun et al (71 ) and
Rathbun and Grant (118 ) who obtained dye, ethylene and propane concentration
profiles over river lengths in the U.S. from 4 to 9 km. The results were plotted
by Mackay and Yuen(106) astheratio of volatile tracer to dye concentration
as a function of flow time, which is approximately proportional to distance.
The drop in concentration of a factor of 2 occurs in approximately 200
minutes or 3 to 4 km, indicating that Zr has a v ue of 17400 s, which for a
depth of 1 m corresponds to a mass transfer coefficient of 5 x 10 5 m/s and
a reaeration constant Ka of approximately 5 days 1, in good agreement with
the earlier theoretical predictions.
Zurcher and Giger (H9) and Giger et al (!20) have presented some precise
data on trichlorethylene tetrachloroethylene, 1,1,2,2 tetrachloroethane, 1,4
dichlorobenzene, benzene and other contaminant profiels for a 30 km stretch
of the Glatt river in Switzerland which flows from the Greifensee to the
Rhine. In the 12 km stretch after Dubendorf the concentrations of
trichlorethylene, tetrachloroethylene and 1,1,2,2, tetrachloroethane showed
reductions of factors of approximately 8, 50 and 20, all probably attributable
to volatilization. These data are broadly consistent with the earlier
predictions. The 1,4 dichlorbenzene and benzene profiles showed little drop
possibly because of the low H values and the presence of continuous inputs.
It is interesting to note that the disagreement between predicted and observed
concentrations may indicate the presence of unknown sources. Data reported
by Helz (121) on haloform concentrations in the estuary of the Back River,
Maryland also suggest that this class of compounds may be useful as tracers.
Finally, the comprehensive laboratory and computer prediction work of
Smith et al ( 4 ) on eleven contaminants provides an interesting assessment
of the importance of volatilization in rivers, relative to other processes.
In two cases (benzo (b) thiophene and mirex) volatilization was judged to be
the most significant pathway. In the case of benzo (a) pyrene volatilization
was second in importance after photolysis., assuming summer sunlight conditions.
Agreement with the available literature data is clearly satisfactory and
lends support to the methodology developed here.
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VOLATILIZATION FROM LAKES
The simplest approach for calculating volatilization rates from lakes is
to assume that the water volume is well mixed in a time scale which is short
compared to the volatilization tine, and that the resistance to volatilization
lies at the interfaclal region. Mathematically, if V is the lake volume (m3),
A is the area (m2), thus the mean depth is (V/A)m, T is the water inflow and
outflow (m3/h), KQL is the overall liquid phase mass transfer coefficient (m/h),
C is the solute dissolved concentration (mol/m3) and the total solute input
rate is I mol/h it follows that for a nonreacting solute
I - FC - K^ A(C-P/H) = V dC/dt
The atmospheric concentration P can usually be assumed to be zero.
Two solutions are of interest, the first being the steady state value when
the derivative becomes zero at which
C - I/(F +
The relative magnitudes of F and K L A control the solute fate, i.e., by outflow
if F dominates and by volatilization if K-, A domeinates. A reaction term
could also be included in the denominator which would have the form K_ V where
KR is the total first order reaction rate constant. The mean residence time T
of the solute in the lake becomes
T - VC/I - V/(F + KA) (h)
If F is small compared to Kfl, A, T becomes V/KflL Z or Y/KQL where Y is the mean
depth.
Second, is the first order decay equation corresponding to an initial
concentration C with no subsequent input.
-FC - K_T A C = V dc/dt
OJj
or C = CQ exp (-(F + KQIA)t/v)
The half life for small values of F becomes 0.69 V/K-.A or 0.69 Y/K^A, similar
to the mean residence time introduced earlier.
In assessing the role of volatilization compared to flow (advection) and
reaction the characteristic half lives or residence times are thus useful indi-
cations. These are
Volatilization
Flow V/F all in units of hours
Reaction ^*-R
Examination of thier magnitudes provides a useful indication of relative
inctortance.
184
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This simple approach is likely to break down when the lake is sufficiently
deep that there is some thermal stratification and thus vertically restricts
diffusion. Calculation of volatilization rates from water bodies with signi-
ficant vertical diffusive resistance is very difficult since it requires knowledge
about the exact vertical variation in diffusivity and the vertical location of
solute introduction. A comprehensive analysis is probably best done using
finite difference solution of equations set up for a multi-layer system. In
many cases it is suspected that relatively simple expressions can be derived
which elucidate where the dominant resistance lies. To do this it is first
desirable to discuss briefly the magnitudes and dependencies of vertical and
horizontal diffusivities.
Horizontal Diffusion
The usual approach is to assume that Pick's Law applies horizontally and
attributes any departure from that Law to a variation in diffusivity. In fact,
the departures are so large that horizontal diffusivities become very scale
dependent. In a typical determination a volume of dye is injected into the
water and its horizontal expansion followed with time. It tends to spread in a
Gaussian manner with a standard deviation S (or width L = 3S) at time t. The
diffusivity DH is then given as S2/2 t or L2/18 t. Results are usually expressed
in a logarithmic diffusion diagram of DH versus L and a typical relationship is
(Murty and Miners 122 )
1 2
D = 0.02 L (units of cm and s)
The implication is that for a small lake of diameter 100 m Dg will be
approximately 103 cm2/s whereas for a larger 1000 m lake DH will be 101* cm2/s
and at 10 km DH will exceed 105 cm2/s. Oceanic values reported by Okubo (123 )
have reached nearly 106 cm2/s.
This marked dependence of DH on L indicates that simple diffusion does not
apply. A better conceptual model may simply be to assume a constant spreading
velocity (dL/dt) which can be estimated as follows:
D = 0.02 L1'2 = L2/18 t
thus L0'8 = 0.36 t
and (dL/dt) = 0.45 L°'2° = 0.35 t0'25
The powers on L and t are quite low indicating that constant velocity is
a better assumption than constant diffusivity. For a 1 km lake (L = 105 cm) the
velocity becomes 4.5 cm/s with a characteristic diffusion time of 2.2 x 10 s
or 6 hours. A useful "rule of thantoT is then that horizontal diffusion occurs
at a rate of the order of 1 km/day. This rate is very rapid compared to that
of vertical diffusion discussed below, the implication being that in most lakes
it can be assumed that horizontal concentration gradients in surface waters are
eliminated quite rapidly.
185
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Vertical Diffusion
The vertical diffusivity Dy is controlled by the presence of currents (which
tend to induce eddying and thus promote diffusion) and the dainping effect of
density differences which arise from temperature and occasionally salinity varia-
tions. When the fluid density decreases with increasing height any eddy pro-
pelled upwards will tend to sink back because of its negative buoyancy. The
balance between these tendencies is characterised by the Richardson Number which
can be used to correlate Dy as reviewed by Thibodeaux (44 )• Thibodeaux also
discusses the work of Koh and Fan (124 ) who correlated Dy with vertical
density (p) gradient ft where
n = (dP/dY)/P (nf1)
yielding
Dv - (cm2/s) = lO'Vn
A form which does not give infinite Dy at 8 = 0 is
Dy - 10~V (10~6 + n)
At 10°C the density of water varies by approximately 0.0001 g/cm3 per °C
thus a 1°C temperature difference over a 1 mdepth corresponds to ft * 10 **
with a resultant Dy of 1 cm2/s which is orders of magnitude smaller than D.,.
For surface waters (epilinmdon) Dy may be 1 to 100 cm2/s with a mean value of
10 cm2/s being a useful estimate. The characteristic diffusion time in surface
waters is thus Y /Dy. A typical epilimmion depth in late summer may be 10 m
thus this time is 105 s or 1 day. A mean mass transfer coefficient KQL may be
10 cm/h thus the characteristic volatilization time is ?/KpL or 100 h or 4 days.
It follows that vertical mixing will generally be faster than volatilization
thus in an epilimmion the usual situation will be that of a vertically well
mixed layer with little concentration gradient. Expressed in another but
equivalent form introduced earlier, the vertical diffusive resistance (AY/DyZ)
is small compared to the interfacial resistance (!/KQL Z) where Z is the fuga-
city capacity which for water is (1/H).
At the thermocline temperature gradients_of 5 to 10°C may exist over
depths of a few meters thus Q may reach 10~3 m"1 resulting in Dy falling to
0.1 to 0.01 cm.2/s. If this applies over 2 m the characteristic diffusion time
becomes 10s s to 106 s or 4 to 10 days which implies a significant resistance.
It is probably better to combine the uncertainties in Dy and AY over the
thermocline into a single term K_ the exchange coefficient equivalent to Dy/AY
which can be compared directly with the volatilization mass transfer coeffic-
ient KQ^. Snodgrass (125 ) for example has shown that thermocline vertical
exchange coefficients for Lake Ontario have varied from 0.07 to 0.15 m/day which
corresponds to a mean diffusivity of say 0.05 cm2/s over a 3 to 6 m diffusion
distance. From thermal observations Snodgrass has deduced that Dy varies from
0.1 to 0.4 cm2/s in this region. The thermocline usually acts as a significant
barrier to diffusion thus the simplest approach may be to assume negligible
diffusion during the time that it applies.
In the hypolimmion below the thermocline there is usually negligible cur-
rent action and very low verticaldiffisivities apply. Thibodeaux (44 ) quotes
186
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values of 0.73 m /day (0.08 cm2/s) but values as low as 0.01 cm2/s may occur.
Snodgrass and O'Melia ( 126 ) have reviewed data on mean vertical diffusivities
in various hypolimnetic waters and obtained the correlation
D = 0.0142 Y1*49 (D in m2/day, Y the depth in m)
or D = 0.00164 Y1'49 (D in cm2/s, Y in m)
Thus for lakes of depth 10 to 30 m diffusivities in the range 0.05 to 0.26 cm2/s
are expected. For a hypolimmion of depth 20 m with a Dv of 0.05 cm2/s the
characteristic diffusion time is 2.5-years implying that the mixing process is
very slow.
The topic of modelling stratified lakes has been reviewed more fully by
Imboden and Lerman ( 127 ) and Thibodeaux ( 44 ) who give details of more complex
modelling approaches.
In summary, for estimating the volatilization rate from a lake it is
essential to first obtain an approximate picture of its annual vertical strati-
fication characteristics using temperature data as a guide. If dissolved oxygen
or phosphorus data are also available these may also be useful. The simplest
approach is to first regard the surface waters (which may be variable in volume
as the thermocline descends) as a vertically and horizontally well mixed volume
into which solute flows and from which solute is depleted by volatilization,
advection and reaction. Exchange with deeper waters can be considered if nec-
essary. It is unlikely that the transport, reaction, concentration and flow
quantities will be known to a sufficiently high degree of accuracy to justify
complex numerical models. For most purposes a simple intuitive model quantify-
ing the dominant process will be adequate. The analysis by Schwartzenbach et
al ( 2 ) for Lake Zurich is a good example of such an approach.
187
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19A
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SYMBOLS
The symbols used in this report are given below with dimensions,
which are generally in SI units. Pressures were expressed in atm
rather than Pascals. In some cases where an existing correlation is
quoted, for example for diffusivity or reaeration constant, the original
units used by the author have been retained, thus the dimensions may
differ from those stated below. Where this occurs, it is noted in the text.
A
a
C
H
F
F
area
Charnock constant
concentration
solubility
drag coefficient
heat concentration
initial concentration
molecular diffusivity
" in film
" in gas
" in liquid
horizontal turbulent diffusivity
vertical turbulent diffusivity
Froude Number
water flow rate
m
dimensionless
mol/m
mol/m
dimensionless
J/m3
mol/m"
m Is
m /s
m Is
m Is
m /s
m /s
dimensionless
m /s
195
-------
F
f
f
G
g
H
H
w
AH
AH
AH
I
K
K
'OG
OL
In (XSYS)
fugacity
liquid fugacity
reference fugacity (of subcooled liquid)
solid fugacity
volumetric flow rate
gravitational constant
Henry's law constant
Henry's law constant of water
enthalpy of fusion
enthalpy of sublimination
enthalpy of vaporization
input rate
various constants
partition coefficient
decay constant
sorption .coefficient
octanol water partition coefficient
mass transfer coefficient
" in gas
" in liquid
" overall gas
" overall liquid
dimensionless
atm
atm
atm
atm
m /s
9.81 m/s2
atm m /mol
atm m /mol
J/mol
J/mol
J/mol
mol/h
dimensionless
-1
m3/Mg
dimensionless
m/s
m/s
m/s
m/s
m/s
196
-------
K
K2
L
M
M
N
n
P
PS
PT
R
Re
r
S
s
AS
SC
SC
St
T
TB
ISA
t
Von Karman constant
reaeration constant
distance downstream
amount
molecular weight
mass flux
amount
partial pressure
saturation vapor pressure
total pressure
gas constant
Reynolds' Number
mass transfer resistance
solubility
surface renewal rate
entropy change
Schmidt Number in air
Schmidt Number in liquid
Stanton Number
temperature
boiling point temperature
critical temperature
melting point temperature
total surface area
time
197
dimensionless
IT1
m
mols
g/mol
mol/m s
mols
atm
atm
atm
(82 x 10 6 atm m3/mol K)
dimensionless
2
atm m s/mol
mol/L
s
J/mol K
dimensionless
dimensionless
dimensionless
K
K
K
K
-------
u
u
u
10
u
V
V
V
V
w
X
x
Y
y
y
z
z
wind velocity
wind velocity at 10 m height
free stream velocity
friction velocity
volume
river velocity
molar volume
molar volume
river width
fetch
mole fraction in liquid
water or river depth
diffusion path length
mol fraction in vapor
fugacity capacity in air
fugacity capacity in film
fugacity capacity in octanol
fugacity capacity in sorbed state
fugacity capacity in water
volumetric heat capacity
length dimension in Froude Number
height above water surface
surface roughness
m/s
m/s
m/s
m/s
3
m
m/s
3
m
m /mol
m
m
dimensionless
m
m
dimensionless
mol/m atm
mol/m atm
o
mol/m atm
mol/m atm
3
mol/m atm
J/m3 K
m
m
m
198
-------
Y
Y,
w
P
y
T
n
relative volatility
activity coefficient
activity coefficient in octanol
activity coefficient in solvent
activity coefficient in water
density
viscosity
fugacity coefficient
association parameter
stress
density gradient
dimensionless
dimensionless
dimensionless
dimensionless
dimensionless
kg/m
Pa s
dimensionless
dimensionless
N/m2
kg/m
199
-------
GLOSSARY
Activity Coefficient(Y) A dimensionless factor applied to a solute's
"ideal" or Raoult's Law fugacity or vapor pressure to correct it to the
observed experimental value. It is thus the ratio of the actual pressure
to that "predicted" by Raoult's Law.
Drag Coefficient (C_) A dimensionless quantity relating the drag or
stress on a surface to the speed of the wind passing over the surface.
Fetch Distance over water which wind has passed and thus has had an
opportunity to establish waves. Low fetch situations are sheltered from
wind and wave action.
*
Friction Velocity(U ) A hypothetical velocity which is a measurement of
the force, stress, or "friction" which air exerts when flowing over water.
Froude Number (F) A dimensionless number (velocity)/(length x g)
used to scale-up velocities over a range of system sizes.
Fugacity (f) The "escaping tendency" of a solute from a phase and thus
an Indication of equilibrium in multiphase systems. It has units of
pressure.
Fugacity capacity (Z) A constant relating fugacity to concentration
analogous to a volumetric heat capacity.
Logarithmic Velocity Profile A commonly used equation relating velocity
of air to height above a surface. It contains the von Karman constant and
two empirical constants, the friction velocity and surface roughness.
Mass Transfer Coefficient (K) A constant expressing the ease with which
mass diffuses in a defined region. It can be regarded as the piston
velocity with which the solute in solution diffuses near an interface.
Reynolds Number (Re) A dimensionless number (velocity x density x
length/viscosity) used to correlate turbulent flow conditions.
Schmidt Number (Sc) A dimensionless number (viscosity/[diffusivity x density])
which can be regarded as the ratio of the ease with which a fluid transports
momentum and mass by diffusion. It is used to introduce diffusivity into
correlation.
Stanton Number (St) A dimensionless number which is a ratio of a mass
transfer coefficient to a velocity.
Surface Roughness (ZQ) A constant obtained from a logarithmic velocity
profile. It can be regarded as an indication of the roughness of the surface.
Total Surface Area (TSA) A calculated area of a molecule in units of
square Angstroms used to correlate solubility.
200
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INDEX
Activity Coefficient, 4-15, 4-45, 8-22
Aeration, 9-11
Alcohols, 4-20
Antoine equations, 4-8
Aqueous solubility, 4-10, 4-45
Bioconcentration, 4-7
Charnock constant, 5-20, 8-9
Consistency tests, 4-45
Oo-solutes, 4-13, 8-25
Diffusion processes, 5-4
Diffusivity, 8-5
Drag Coefficient, 5-19, 8-8
Epilinmion, 9-16
Fetch, 5-20
Fick's first law, 5-4
Froude number, 5-20
Fugacity in atmosphere, 4-4
Fugacity in biota, 4-7
Fugacity capacity, 4-2
Fugacity in octanol, 4-7
Fugacity ratio, 4-10
Fugacity in sorbed phases, 4-6
Fugacity in water, 4-4
Henry's law constant, 4-29, 4-45, 8-28, 9-1
Horizontal Diffusion, 9-15
Hypolimmion, 9-16
Ice, 9-11
Lakes, 9-14
Logarithmic velocity profile, 5-16
Mass transfer coefficient, 5-6, 5-12
Mass transfer coefficient Kp, 8-14
Mass transfer coefficient IL, 8-11, 8-18
Mass transfer coefficient overall, 8-17
Mass transfer mechanism, 5-1
Molecular size, 8-5
Octanol-water partition coefficient, 4-38, 4-45
Reaeration constant, 9-7, 9-10
Relative volatility, 4-29
Resistances, 5-8
Rivers, 9-7
Roll cell, 5-13
Small scale volatilization apparatus, 7-2
Solubility, 8-25
Stanton Number, 5-22
Surface active, 4-14
Surface films, 5-24
Surface roughness, 5-19
201
-------
Temperature, 8-5
Thermocline, 9-16
Total surface area, 4-11, 4-15
Tracer techniques, 9-11
Turbulence, 5-5
Two resistance, 5-15
Vapor pressure, 4-23
Vertical Diffusion, 9-16
Volatilization systems, 5-25
von Karman constant, 5-19
Waves, 5-16
Whitman, 5-12
Whitman Two Resistance Theory, 5-8
Wind Velocity, 5-16
Windwave tank, 7-21
202
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