UNLV Retrospective Theses & Dissertations
1-1-1993
Exchange of oxygen and hydrogen isotopes between water and water vapor: Experimental results
Michael Willem Slattery University of Nevada, Las Vegas
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Repository Citation Slattery, Michael Willem, "Exchange of oxygen and hydrogen isotopes between water and water vapor: Experimental results" (1993). UNLV Retrospective Theses & Dissertations. 295. http://dx.doi.org/10.25669/z6nr-dvzi
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Exchange of oxygen and hydrogen isotopes between water and water vapor: Experimental results
Slattery, Michael Willem, M.S.
University of Nevada, Las Vegas, 1993
UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106
EXCHANGE OF OXYGEN AND HYDROGEN ISOTOPES
BETWEEN WATER AND WATER VAPOR:
EXPERIMENTAL RESULTS
by
Michael Willem Slattery
A thesis submitted in partial fulfillment of the requirements for the degree of
Master of Science
in
Geoscience
Department of Geoscience University of Nevada, Las Vegas M ay 1993 The thesis of Michael Willem Slattery for the degree of Master of Science in
Geoscience is approved.
L . X Chairperson, Neil L. Ingraham, Ph.D.
ining Committee Member, John W. Hess, Ph.D.
’Examining Committee Member, David Kreamer, Ph.D.
1/ m LAZZ G radual Faculty Representative* Spencer St4i*fe/erg, Ph.D
Graduate Dean, Ronald W. Smith, Ph.D.
University of Nevada, Las Vegas
May 1993
i i A b stra ct
The exchange of 818 0 , S D , and tritium between water and water vapor was investigated with two experimental methods. The first was quiescent equili bration of water samples having widely contrasting isotopic compositions, surface areas, volumes, and temperatures, but similar salinities. The transfer of water was quantified with an exchange coefficient k , as identified by [Criss, Gregory and Taylor, 1987] for water and minerals in a closed heterogeneous system. Rates of exchange depended on surface area and vapor pressure, while the end-point equilibrium was controlled by volume and isotopic composition of the exchanging waters. Over a 76 day period, shifts as large as 12.8 °/0o <518 0 and 60 %o <*> D were observed for two exchanging waters with initial volumes of 475 ml, identical sur face areas, and initial isotopic differences of 13.4 %o oxygen and 71 °/0o deuterium.
One water, with initial tritium activity of 95,077 TU, underwent a reduction of
60,000 TU. Values of k ranged from 0.09 to 0.19 cm/day at 22 °C and from 0.86 to 0.92 cm/day at 52 °C .
The second method involved sparging 30 1 of tritiated water (5,000 and 630,000
TU) with a constant 15 1/min flux of water-saturated air (TU <10). Half of the tri tium was exchanged into the vapor effluent over 40 days; itranged from 0.025/day to 0.030/day. Equilibration with 630,000 TU was observed over a bubble path of 20 cm, suggesting an alternative method of tritium remediation. The value of k for 180 / 160, D/H, and 3H was found to be the same for each trial using both experimental methods.
The process of isotopic exchange with the atmosphere is argued to occur in the hydrologic cycle, and as an example a 40 °/00 discrepancy in 6 D between the observed isotope composition of Pyramid Lake, Nevada (-35 %o $ D ) and the value calculated assuming a perfectly terminal lake (+5 %o S D ) is suggested to be caused by isotopic exchange. Table of Contents
A B S T R A C T ...... iii
LIST OF FIGURES ...... vii
LIST OF TABLES ...... ix
ACKOWLEDGMENTS ...... x
INTRODUCTION ...... 1 Isotopes in H ydrology ...... 9 Stable Isotopes ...... 10 T r itiu m ...... 12 Fractionation ...... 13 Theory of Isotope Exchange ...... 15 Bubble-mediated isotope exchange ...... 22 METHODOLOGY ...... 31 Box Experiments ...... 31 Equipm ent ...... 32 Sam pling ...... 33 Procedures ...... 35 Bubble-Mediated Exchange ...... 39 Equipm ent ...... 40 Sam pling ...... 43 Procedures ...... 45 Bubble parameters ...... 46 R E S U L T S ...... 48 Box Experiments ...... 48 Experiment 1 ...... 48 Experim ent 2 ...... 52 Experiment 3 ...... 61 Experim ent 4 ...... 63 Experiment 5 ...... 65 Bubble Mediated Exchange ...... 68 Isotopic Results ...... 69 DISCUSSION ...... 76 Box Experiments ...... 76 Rate Constant Summary ...... 87 Bubble-Mediated Exchange ...... 94 APPLICATION TO HYDROLOGY AND FUTURE RESEARCH ...... 99
SUMMARY AND CONCLUSIONS ...... 107
REFERENCES ...... 110
APPENDIX A 3H vapor extraction ...... 114
APPENDIX B Exchange equation derivation ...... 116
APPENDIX C Isotopic analysis ...... 118
APPENDIX D Humidification calculations ...... 120
vi List of Figures
1 Schematic of the Craig-Gordon boundary layer model ...... 7
2 Schematic of isotope exchange for similar surface areas and volumes. 19
3 Vapor concentration profiles for bubble diameters of 1 to 4 mm. . 24
4 Vapor concentration profiles for bubble diameters of 5 to 8 mm. . 25
5 Schematic of concentration changes over a short bubble rise .... 27
6 Schematic of the bubble-mediated tritium exchange experiment. . 41
7 Bubble rise velocity and bubble diameter for small bubbles in tap
w ater...... 47
8 <5180 -<5D relations for Experiment 1 ...... 50
9 (5180 - d)D relations for Experiment 2, Box 1 ...... 57
10 <5180 - 6D relations for Experiment 2, Box 2 ...... 58
11 <5180 - 6 D relations for Experiment 2, Box 3 ...... 60
12 <518 O - 6 D relations for Experiment 2, Box 4 ...... 61
13 £18 O - 6 D relations for Experiment 3 ...... 63
14 618 0 - 6 D relations for Experiment 4 ...... 65
15 <518 0 - 6 D relations for Experiment 5 ...... 67
16 Fractionation factor, time and temperature relations for Run 1. 71
17 5180 -d>D graph of the bubble-mediated exchange experiments. . . 72
18 Mean vapor temperature and observed values of fractionation factor
alpha for Run 1 ...... 75
vii 19 G raph of 6180 versus time for waters A, B, and C in Experiment 1. 77
20 <5180 versus time for Waters A and B in Box 1, Experiment 2. . . 78
21 Sl80 versus time for Waters A and B in Box 2, Experiment 2. . . 79
22 <5180 versus time for Waters A and B in Box 3 , Experiment 2. . . 80
23 6180 versus time for Waters A and B in Box 4, Experiment 2. . . 81
24 <518 0 and 6 D exchange curves for Experiment 3 ...... 82
25 Normalized <518 0 exchange curves for Experiment 3 ...... 83
26 27 Normalized 618 O exchange curves for Experiment 4 ...... 86 28 618 O exchange curves for Experiment 5 ...... 87 29 Influence of surface area/volume relationship on the value of k . . 90 30 Influence of temperature on the value of k ...... 91 31 Results of Experiment 1 as a function of F / ...... 93 32 Results of Experiments 3 and 4 as a function of F ; ...... 93 33 <518 0 -6D graph of the bubble-mediated exchange experiments. . . 95 34 Variation in tritium concentration over time for Runs 1, 2, and 3. 96 35 Variation of fractional approach to equilibrium for three bubble- mediated experiments ...... 97 36 Schematic of Pyramid Lake isotope system ...... 104 viii List of Tables 1 Worldwide abundances of hydrogen and oxygen isotopes ...... 10 2 Initial Conditions of Box Experiments ...... 36 3 Results for Box Experiment 1 ...... 49 4 Results for Box Experiment 2 ...... 53 5 Results for Box Experiment 3 ...... 62 6 Results for Box Experiment 4 ...... 64 7 Results for Box Experiment 5 ...... 66 8 Stable isotopic results of the bubble-mediated exchange experiments. 70 9 Tritium results of bubble-mediated exchange experiments ...... 74 10 Exchange Coefficient Summary for Box Experiments ...... 88 11 Changes in water content, evaporation and inflow, Pyramid Lake. 102 Acknowledgments My sincere thanks and appreciation are given to my thesis committee chair man Dr. Neil L. Ingraham, whose support and guidance has been invaluable. Many thanks also to the other members of my committee, Dr. John W. Hess, Dr. David Kreamer, and Dr. Spencer Steinberg. I am indebted to Craig Shadel, whose interest in this work extended past his duties as Isotope Laboratory Man ager at the Water Resources Center, Desert Research Institute (DRI)-Las Vegas. Mr. Shadel performed all stable isotope analyses reported in this work. I respect fully acknowledge Dr. Bob Criss of UC-Davis for his willingness to divulge and discuss his intimate knowledge of things isotopic. I appreciate and credit all my fellow students, as well as faculty and researchers at DRI-Las Vegas, DRI-Reno, and UNLV Geoscience. In particular, I would like to recognize my student colleagues Linda Urzendowski and Gary Icopini at UNLV, as well as Igor Jankovic at the University of Minnesota for their support, suggestions, and manuscript reviews. Thanks also to A1 Benincasa of the DRI-LV computer support staff for his visionary postscript prowess. This research was funded by DOE Grant No. DE-AC08-90NV10845. Further financial support from the George B. and Jane C. Maxey Fund, the Bernada E. French Scroungers Fund, and the UNLV Geoscience Graduate Student Association Fund is gratefully recognized. A final note of thanks to my parents, Marijke and Bill, and to my good friend William Peters, whose support and encouragement over the years contribute directly to any success I may achieve. Introduction Understanding the partitioning of hydrogen and oxygen isotopes in nature is important because their distribution can reveal the physical history of a given water parcel. The conservative nature of light stable isotopes provides a solid framework for water-balance and recharge studies. The conservation of mass of stable isotopes within the hydrologic cycle can be expressed as a summation of the mass balances for each control volume and its associated isotopic measurement. This simple concept allows mixing ratios, origin, and history of a water parcel to be accurately assessed. Isotope exchange has been shown to be important in di verse areas of earth sciences such as the study of mineral-water interactions [ Criss, Gregory and Taylor , 1987], deposition of aerosols to various surfaces [Chamber- lain, 1991; Chamberlain and Eggleton, 1964], the isotopic composition of rainwater [Friedman, Machta and Soller, 1962], and the implications of crustal isotope bal ances on paleoclimates [Schrag, DePaolo and Richter, 1992]. In this work, isotope exchange between water and water vapor is evaluated under controlled conditions to better understand isotope systematics of low-temperature air-water systems. Numerous transport models have been derived for the isotopes of oxygen and hydrogen using wind velocity, humidity, and water vapor and energy fluxes [Brut- saert, 1975; Craig and Gordon, 1965; Dansgaard, 1961; Merlivat and Conantic, 1975]. Most models which describe the movement of an isotopic species from 2 liquid water to the atmosphere are based on an evaporative (net) loss of water from the liquid phase [ Horton, Corey and Wallace , 1971; Prantl, 1974]. For this case the isotopic enrichment of the water is reasonably well constrained, and has been shown to be proportional to the logarithm of the fraction of liquid remain ing [Craig, Gordon and Horibe, 1963]. Less understood and docum ented are the dynamics of the natural reflux (deposition) of atmospheric water vapor to the liq uid phase, and its implication on the isotopic evolution of both vapor and liquid phases. The isotopic flux to and from a body of water is governed by humidity and isotopic exchange with the ambient vapor [Craig, Gordon and Horibe, 1963; Gat and Bowser, 1991]. The term isotope exchange, as used in this work, is defined as the two-dimensional flux of isotopes between water and water vapor, and the attendant isotopic evolution of each phase. Correct interpretation of isotopic data depends on understanding the mech anism and knowing the rates of the exchange process. The buffering effects of an isotopic return flux complicate the interpretation of isotopic data from water- budget studies because the observed isotopic shifts are normally evaluated with evaporation as the dominant process. Possibly for this reason, the isotopic equi libration of water under non-evaporative conditions has received relatively little attention in the literature. These considerations have prompted several questions. Can pure end-member isotopic exchange be isolated (from the isotope effects of evaporation/condensation) and identified? What are the rates of exchange? 3 O bjectives The goal of this work was to investigate isotope exchange through experi ments which are designed to circumvent the kinetic effects of evaporation on the fractionation of stable isotopes and tritium between liquid and water vapor. This was achieved by experimentation at near-saturation conditions. Rates of exchange are evaluated for different surface areas, volumes and temperatures. Two experimental methods were used to evaluate the exchange rates of water isotopes between liquid and vapor. In addition, a qualitative application of isotope exchange to the hydrologic cycle is presented. The three main objectives of this work are: 1 Evaluate the rates of isotope exchange for a closed system (quiescent conditions). 2 Evaluate the rates of bubble-mediated isotope exchange (turbulent conditions). 3 Evaluate the implications of findings on the hydrologic cycle. The first objective was achieved utilizing sealed boxes to allow waters of dif ferent initial isotope compositions to equilibrate via the vapor phase over time, while tracking the isotopic evolution of the waters. Humidity and temperature were held constant, and air flow was minimized to produce controlled conditions that should mimic end-member isotope exchange and dampen the effects of evapo ration. These are known as the box experiments; since the vapor and liquid phases were kept undisturbed, the exchange was passive in nature (quiescent conditions). The second objective employed isotopic exchange by air-sparging. The goal of these experiments was to estimate the magnitude of bubble-mediated isotope exchange between a water-saturated air stream, and a tritated water. The rates of mass flux are estimated, and compared to the results of the quiescent closed- system findings. Air sparging (aeration, or air stripping) is widely used to modify the chemistry of bulk water by adding or removing selected components. Typical applications to waste water and drinking water are the addition of oxygen or ozone and the removal of hydrogen sulfide, ammonia, or volatile organics. While a large literature base exists for the extraction of volatile and semi-volatile components from bulk water, little work has been done concerning the exchange of water iso topes during sparging. These sparging experiments thus represent the application of standard stripping methods to a non-standard component of water, namely tri tium. The analysis of these experiments will emphasize isotope systematics rather than optimization which is typically the goal of the chemical engineer. The third objective is to evaluate the implications of isotope exchange on the hydrologic cycle. The case of a terminal lake is discussed, in which the hypothesis of exchange is argued to explain the discrepancy between observed isotope com positions and those calculated based on hydrologic parameters. Suggestions are m ade for further isotope exchange research within natural systems. Background The movement of water molecules across an air-water interface is not a static process. The kinetic theory of gases describes the dynamic equilibrium that exists when the number of water molecules passing into the vapor phase equals the number that recondense on the liquid surface. At this point of equilibrium, the 5 vapor phase is saturated with water. If the number of molecules leaving the liquid is greater than those recondensing, the process is termed evaporation, and a net loss of water from the liquid phase occurs. Molecules are in constant motion upwards out of the liquid (isotopic flux) regardless of whether or not the water is evaporating. Thus, water molecules enter and exit the liquid phase as an isotopic flux first; this flux may or may not be enhanced by evaporation or condensation, depending on environmental conditions. In nature, the two cases of flux into saturated and under-saturated atmospheres combine to produce a spectrum of isotopic relations between the liquid and vapor phases. In principle, evaporation is proportional to the moisture deficit in the atmosphere, and was proposed by Dalton (ca. 1800) to be a function of vapor pressure: E = C(p0 — pa), where C is an empirically determined constant which accounts for wind speed and surface conditions, p0 is the vapor pressure at the surface, pa is the vapor pressure at some point above the surface, and E is the rate of evaporation. This formulation is the basis for a suite of evaporation equations [.Blaney and Criddle, 1950; Penman, 1948; Thornthwaite and Holzman, 1942] which predict water loss as a function of solar radiation, wind speed, albedo, etc. A model of isotopic evaporation was deduced for an isolated liquid [ Craig and Gordon, 1965], which by analogy is the transport resistance of Ohm’s Law: 1) Evaporation begins when water molecules (in isotopic equilibrium with a well mixed liquid) move into a saturated sublayer at the air-water boundary. This layer is non-mixing with the atmosphere and produces the isotopic fractionation. 2) The vapor then enters a laminar layer, in which molecular diffusion is the dominant transport mechanism. At low relative humidities, the vapor phase is further depleted of heavy isotopes (kinetic effect). 3) The water vapor then migrates into a fully turbulent layer which is non fractionating because the resistance to transport for the various isotopic species is the same throughout. 4) The water vapor in the atmosphere may, in return, penetrate the molecular diffusion layer as an isotopic flux in the case of exchange, or as water gain in the case of condensation, thus completing the process of cycling between the liquid and vapor phases. Exchange rates, molecular diffusion, and vapor pressures for the different iso topic species are interrelated in a complex fashion across the various boundaries along a vertical cross section of the liquid-vapor interface. It is the fourth step which outlines the return flux to the liquid phase, and is of particular importance to this study. The four-step process described above is known as the Craig-Gordon model, and is shown schematically in Figure 1. The left hand y-axis of Figure 1 shows the humidity (h) components, the right-hand y-axis the isotopic (6) com po nents, and the interior p expressions are the transport resistances for the various sections. In this figure, Z denotes the thickness of the laminar boundary layer; D is the coefficient of diffusion for water vapor in air; C* and C l are the mole fractions of water for the vapor and liquid phases, respectively. The subscripts 7 h a 9 © (5a Turbulent Section □O' p Q. C > h Mo - o (5m /0 = D Laminar^S.ection h \Jz V v Interface 1 7T\ s P=^L Laninar Section L D C l 1 O" o (5l i—i 3 GS Turbulent Section Figure 1: Schematic of the the Craig-Gordon boundary layer model showing hu midity (h), isotopic (5), and transport resistance ( p ) components at an air-water interface (modified from [Craig and Gordon, 1965]). The heavy lines represent the isotopic values of that phase; Z is the thickness of the laminar boundary layer; D is the coefficient of diffusion for water vapor in air; C* and Cl are the mole fractions of water for the vapor and liquid phases, respectively. The subscripts A, M, V, S, and L denote the bulk air, vapor laminar layer, vapor interface, liquid interface, and bulk liquid, respectively. A, M, V, S, and L represent, respectively, the bulk air, vapor laminar layer, vapor interface, liquid interface, and bulk liquid. If liquid-vapor equilibrium exists, then hy=l, and the distribution of a particular isotope is defined by the ratio of the saturation vapor pressure of the heavy isotope to the saturation vapor pressure of H 2O16. This is the condition on which the experiments in this work are predicated. 8 The implications of isotope exchange were discussed by Craig, Gordon, and Horibe, [1963] in terms of humidity and batch distillation for a suite of evaporation experiments. One of these experiments was similar to the box experiments of this work; the main differences are that in the 1963 work, evaporation was the dominant process studied, and no attempt was made to quantify the observed exchange. The work of Craig, Gordon and Horibe, [1963] was furthered in terms of application to hydrology, and lake-air interaction in particular, in a study of lake dynamics [Gilath and Gonfiantini, 1983]. This investigation sets forth isotope systematics in terms of limnological parameters, and also the isotope evolution of lake waters expected under conditions of variable humidity. The predictions of lake water isotope evolution are important to this study because they represent the actual trends observed in nature under evaporative conditions, as opposed to the end-member case of pure exchange (the saturated vapor pressure conditions modeled in this work). For example, the findings of Gilath and Gonfiantini [1983] indicate th at at 50 percent relative humidity, the expected enrichment of a terminal lake (in- flow=evaporation) is approximately linear. For humidities above about 50 per cent, and isotopic stationary state will be reached through rapid molecular ex change between the liquid and vapor phases for an isolated body of water [Craig, Gordon and Horibe, 1963]. These researchers showed that such an equilibrium may be attained long before the water mass has totally evaporated. End-member cases occur at zero percent humidity (batch distillation, maximum enrichment) 9 and 100 percent relative humidity (no evaporation, pure exchange). Thus at 50 percent relative humidity the effects of evaporation and exchange are approxi mately equal. Conditions of non-zero humidity have previously been found to cause a depres sion of the expected liquid isotope enrichment for natural waters. This limitation is thought to be caused by a return (isotopic) flux, and is not completely under stood in either magnitude or mechanism. The study of the end-member case of isotope exchange within a vapor saturated atmosphere is the main objective of this work. Isotopes in Hydrology Since their discovery during 1929-1932 [Gat, 1980], the isotopes of hydrogen (3H, 2H, 1H) and oxygen (180 ,17 O,16 O) have received more and more interest from hydrologists. These isotopes, in various combinations, make up the water molecule. Thus they directly reflect the natural water’s history, and are a means of fingerprinting the identity and tracing the movement of a parcel of water in the hydrologic cycle. Other common isotopes used in hydrologic and hydrogeo chemical studies are those of carbon, sulfur, strontium, and those in the U-Th series. 10 Stable Isotopes Relative worldwide abundances of hydrogen and oxygen isotopes are given in Table 1.; values are bulk percentages. About one atom of 180 exists for every 500 atom s of 160 ; similarly, about one atom of 2.//(deuterium or D) exists for every 6700 atoms of 1//(hydrogen). Although oxygen has three isotopes, the abundance of 17O is about 20 percent lower than that of 180 and 160, thus its effective use is limited (see Table 1.). Tritium (3H ), the cosmogenic isotope of hydrogen, has special properties and uses, and does not appear in Table 1., but will be discussed later. Table 1: Worldwide abundances of hydrogen and oxygen isotopes Element Isotope Percent Hydrogen lH 99.98 Hydrogen (Deuterium) 2H(D) 0.015 Hydrogen (tritium) - - Oxygen 160 99.67 Oxygen 170 0.0375 Oxygen 18 0 0.20 Modified from Fritz and Fontes, 1980. A convenient cjuantitative expression for hydrogen (excluding 3H) and oxygen isotopes is given by a ratio of the heavier isotope to the lighter isotope [Friedman et al., 1964; IAEA, 1981]. Since relative isotopic concentrations can be measured more precisely than the absolute concentrations, these isotope ratios are typically presented relative to an standard-either Standard Mean Ocean Water (SMOW), 11 or Vienna Standard Mean Ocean Water (V-SMOW). These standards are designed to represent the average isotopic composition of the ocean since the oceans are the sink and source for all waters in the hydrosphere. Thus the 8180 and SD values for ocean water are, by definition, zero [ Craig , 1961]. The relative concentrations are expressed in 8 units (delta units), and represent the deviation in parts per thousand (‘per mil’ or %o) of the sample ratio from the standard ratio. 618 O and 8 D are given by: ( 18 0 / 16 O ) standard ( 1) P#/1H ) standard where standard is SMOW or V-SMOW. Each laboratory has its own standards which are calibrated against SMOW so that a stable in-house standard is obtained. The isotopic ratio of a standard is then measured and compared to the lab standard; this intermediate result is then re-calculated against SMOW to produce the final measurement. Thus it is the isotopic stability of ocean water which provides a basis for the measurement and interpretation of water samples. The use of stable isotopes in hydrologic studies relies on the fact that the stable isotopic composition of waters can be related to some physical process through which the water has undergone. Inherent to the stable isotopes of hydrogen and 12 oxygen are several properties which permit interpretation of these processes: 1) these isotopic species are part of the water molecule, and thus are inseparable from the history of that water parcel; 2) additions and subtractions to isotopic compositions are due chiefly to fractionation; there are no sources or sinks per se for the species, and 3) stable isotopes are conservative, i.e., they generally do not undergo chemical, electrical or radiative change. Due to the conservative nature of the isotopes, they are commonly used to perform mass-balance calculations for water budgets. Tritium Tritium is the radioactive isotope of hydrogen (half life = 12.26 years), and is produced both in nature and artificially. Natural production of tritium occurs by bombardment of atmospheric nitrogen with cosmic radiation. Artificial pro duction of tritium is achieved through nuclear reactions with deuterium, lithium, boron, nitrogen or beryllium [ Jacobs , 1968]. Both natural and synthetic tritium lose an electron by soft (weak) beta decay, and thus only pose a significant health risk if absorbed internally (liquid or vapor phase) [ Murphy, 1990]. Most of the tritium found in nature (artificial or natural) resides in the form of water (HTO), since at standard temperature and pressure the reaction HT + H20 = * HTO + H2 (2) is thermodynamically favored [ Atkins, 1990]. 13 The amount of tritium in a particular sample can be described in various ways. The unit used in this work is the Tritium Unit (TU), defined as the ratio of tritium atoms to hydrogen atoms in a sample. Thus, a TU is not a concentration, but rather a specific activity, and is defined as [Jacobs , 1968] 1 TU = °ne at°m 3R 131 lx lO 18 atoms 1H The transfer of tritium from the liquid phase to the vapor phase is of interest for two reasons. First, understanding non-evaporative interphase transport of 3H can elucidate the extent to which a body of water is isotopically modified for a given change in tritium concentration. Second, HTO cycling through the hydrosphere from losses in nuclear power plants and research facilities necessitates basic remediation research for compliance with increasingly stringent air and water quality standards. Fractionation Any mechanism which causes a preferential separation of isotopes between phases is termed a fractionating process. When the vapor pressures of the various isotope species are in equilibrium between phases, their ratio describes equilib rium fractionation which is denoted by a equ;i. Further fractionation is possible through physical processes such as evaporation, to which is ascribed a kinetic addition to the process of equilibrium fractionation [Craig, Gordon and Horibe, 1963; Dansgaard, 1961]. 14 Fractionation is thus a natural separation of isotopes between coexisting phases, and is typically dominated by a physical processes such as evaporation. The most fundamental property which forces an inter-phase deviation from equilibrium in isotopic composition is the frequency of vibration exhibited by the lighter molecule compared with the heavier molecule [Ferronsky and Polyakov, 1982] W ithin a molecule or crystal structure, atoms of a light isotope vibrate at slightly higher frequencies, and are thus less tightly bonded than atoms of a heavier isotope. These differences in bond strength (and length) are appreciable only for ele mental isotopes whose relative mass difference is large. Differences in vibrational frequencies of isotopes become smaller at higher temperatures and changes in iso topic composition become less pronounced. Thus relative differences in isotopic ratios in low-temperature environments are especially detectable. The different vapor pressures of pure isotopic solutions is a reflection of their unequal atomic masses. The magnitude of fractionation has also been shown to be greater for covalent bonds [O ’Neil, 1986]. Upon evaporation or exchange, instantaneous isotopic partitioning is con strained for an isotopic species to a degree known as the fractionation factor, defined as [Dansgaard, 1961]. _ Ra Q A - B = ~ s ~ K b This definition may be restated in terms of delta values for the phases A and B, provided they are reported against the same standard: 15 _Z2l _ 1000 + £l aL~V ~ Rv ~ 1000 + 8V ^ where L and V refer to the liquid and vapor phases, respectively. This equality allows an apparent fractionation factor to be calculated from the measured 8 values between two related phases at equilibrium, or to predict the 8 value for a given phase based on the 8 value for the other phase and an appropriate fractionation factor. As a first approximation, tritium behaves like ordinary water in the hydro sphere. However, the large mass differences between the isotopes of hydrogen produce significant changes in how these isotopes behave physically. Since tritium (as HTO) has a lower vapor pressure than deuterium (as HDO) its fractionation factor is larger, i.e., (HTO/H\°0)L iq _ (H D O /H «0)LI9. (HT0/H?0)var > (llD O /U fO )VM, 1 ' The fractionation factor for tritium at 20 °C is 1.11 [Sepall and Mason , 1960] and predicts that at equilibrium, the liquid phase will hold approximately 11% more HTO than will the vapor phase. This distribution reflects the lower vapor pressure of tritiated water compared with HDO and H^O. 16 Theory of Isotope Exchange Isotope exchange processes have been identified as a dominant control on the natural distribution of isotopic species for a diverse group of earth materials. The transport of HTO and H 2O vapor to and from various surfaces in wind tunnel experiments was studied on the basis of aerosol deposition [ Chamberlain , 1991; Chamberlain and Eggleton, 1964]. The analysis of removal and deposition of these species reported by this researcher suggests that the transfer is controlled by eddy diffusion in the free air, and molecular diffusion across the viscous boundary layer near the air-water interface. While molecular diffusion in the liquid phase is the limiting factor for the transfer of sparingly soluble gases such as H 2 and O 2, across a viscous boundary, the liquid-side resistance for H20 and HTO is negligible [Slinn et al., 1978]. Gas-phase controlled exchange coefficients for water vapor are reported about 5 times greater their liquid-phase counterparts and thus control the transfer of water vapor [Tiss, 1972]. Chamberlain [1991] provides an analysis for the deposition of HTO to various surfaces which utilizes an apparent exchange coefficient termed the velocity of deposition. The deposition velocity is commonly used in analysis of bulk evap oration and in studies of isotope equilibration rates of rain drops [ Chamberlain , 1991; Friedman, Machta and Soller, 1962]; the concept is especially appropriate for use here because of the quiescent conditions within the box experiments. The following section describes a model for transport and exchange of stable isotopes in an idealized closed system of finite volume. All components of the 17 system are assumed well mixed, with no losses to evaporation. In analogy to the rate equations developed for mineral-water oxygen isotope exchange [ Criss, Gregory and Taylor, 1987], transfer rates within a closed sys tems (e.g. box experiments) can be evaluated beginning with a standard isotope exchange equation of the form Ai6 + B i s ^ Ai8 + B i s (7) where A and B denote different phases, and the subscripts refer to the 180 and l60 compositions of the phases. Rate coefficients describe the tendency for the system to fall to one side or the other of equation (7), and in the case of water isotopes in a closed system under equilibrium conditions, will differ as described by the fractionation factor a. The exchange rate law for equation (7) can be expressed [Criss, Gregory and Taylor , 1987] ^ = ka(A16)(B18) - k(A18)(Bie) (8) As applied to equation (8), the rate constant k proceeds to the right and k •a to the left. These are defined as overall mass transfer constants, and provide information on the bulk mass transfer within a heterogeneous system. Units of concentration for the use of (8) in a heterogeneous system such as for mineral-water interactions are typically moles of water and mineral present. However, the use of extensive properties has the disadvantage of making the resulting expressions dependent on the size of the system. Criss, Gregory, and Taylor [1987] suggest 18 the simplification of redefining the terms A j6 and Bie to unity; this makes Ais and i?i8 equal to the isotope ratios of that phase so that: A18= R^i, Ai6=l, Bis= R b , Bx6=1. This normalization is justified on the grounds that the natural abundance of the common isotopes of oxygen and hydrogen are sufficiently close to unity (e.g. 160 ~ 0.998, JH ~ 0.9999). When the substitution a=R, 4 /RB=Rz,/Rv, where subscripts L and V refer to the liquid and vapor phases, is combined with the above assumption, the rate law of (8) becomes [CVfss, Gregory and Taylor , 1987] ^ = -k(RL - a R v ) (9) This equation states that, for any given instant, the rate of change of R^ is proportional to the difference between the value of R^ (t), and the value it would have if in isotopic equilibrium with its vapor phase. Thus the term a Ry is the instantaneous equilibrium isotope ratio written Ra/. The composition of the vapor phase, Ry, is controlled by the composition of the liquid phases present, the appropriate isotope fractionation factors, and the available surface areas. The composition of the liquid phase, however, is a gradual function of the changes in Ry. In the case of identical surface areas and volumes of water samples in the box experiments, Ra/ is a constant. The rate of isotope exchange of the liquid phase is also proportional to the volume and surface areas of the liquids which leads to the expression [Ingraham and Criss , in prep.] 19 ^ = -k(Rx - RM (10) where R^ is the isotope ratio of the liquid phase X at time t, Sx and Vx are the surface area and volume of this water, respectively. A schematic of this case is pictured in Figure 2. In this figure, both Rx and Ry are applicable to investigation by equation (10). R = isotope ratios S = surface area V = volume Rx/a Ry/a Sx Rx, Vx Ry, Vy Figure 2: Schematic of isotope exchange for similar surface areas and volumes. Application of equation (10) requires integration over time and the variable R a' • For the case of identical surface areas and volumes, the equality R^f=Roo=common isotope end point is justified since the liquids respond to an unchanging vapor 20 composition. The solution of (10) for this case is Rx ~ Roo ( ,, Sx = exp R i — R oo V( - »Vx £ ■ ) <“> where R,-, R^, and R* refer to the isotope ratios of the liquid X at the initial, equilibrium states, and at any time t, respectively. The derivation of equation (11) is presented in Appendix B. Conversion of the isotope ratios in the left hand term of (11) to the more practicable delta values is based on the relationship given in equation (5) Since values of a tend to be very close to unity, equation (5) can be written 8i-8y = 1000(a:£_v'-l). Consequently, the left hand term in equation (11) becomes Jtx-Ko = 1000 ( f c - 1 ) - 1000 (tST-i) = ) ll2) R i - R o o 1000 - l) - 1000 - l) \ 6 i - 6 o o ) where Rs is the isotope ratio of the appropriate standard, 6;, 6 and 8 are the delta values in per mil for the initial, equilibrium, and time t states, respectively. Combining equations (11) and (12) yields 8 ^ =exp(-kt^f) (13) A - W V Vx Equation (13) is used in the following sections to model the progression of isotope changes in the box experiments for the case of identical volumes and surface areas for two exchanging waters. The parameter k has units of velocity, and has been interpreted as a piston velocity when scaled to a wind speed, or as 21 a coefficient of stickiness. The lack of convection within the box systems allows a reasonably strict interpretation of the range of k ’s to be made. Isotopic gradients within the liquid phase are assumed negligible, and the liquid phases are considered well mixed. While this is not strictly true, self diffusion of the isotopes in water was not found to be rate limiting. For the case of same surface areas and volumes, then, the instantaneous isotope composition of the liquid phases will gradually change, but the composition of the vapor to which the liquids react remains constant (Rm)- For the case of differing volumes or surface areas, Rm is no longer constant, but becomes a function of the different values of Sx and Va'. Exchange between waters in a closed system where Sx or Vx differ is controlled by a more complex Rm, or end-point value, which can be w ritten [Ingraham and Criss , in prep.] o SxR-x + SyRy + SzRz + ••• n/)x R u = SX + Sr + Sz + ...------(14) The physical interpretation of this equation is that the instantaneous isotope composition of the vapor phase at any time is a function of the surface areas and isotope composition of the liquids for the case of differing surface areas and volumes. The vapor composition R m does not respond at any given instant to the volume of the liquid phases. The solution (analogous to equation [13]) for the case of two beakers of water with different surface areas and volumes is [Ingraham and Criss, in prep.] 22 Equation (15) is used for the Box experiments in which the surface areas and volumes were varied between trials. In addition to the exchange processes, the initial humidification of the boxes was studied to study the losses of bulk water to the vapor phase. Calculations of the water vapor flux for the initial humidification of the box atmosphere are presented in Appendix D. Bubble-mediated Isotope Exchange The dominant forcing agent in the case of bubble-mediated water-isotope exchange is the diffusion of water vapor in air. Superimposed on this mechanism are the actions of the isotope gradient and interfacial conditions. Diffusion forces the mass isotope concentration inside a bubble towards an equilibrium value equal to that at the surface of the sphere. The end-point concentration inside the bubble is bound to the constraint of isotopic fractionation, so that the equilibrium vapor composition (for any isotopic species i) of a bubble is related to the liquid phase by a,-. The aim of the bubble-mediated exchange experiments is to investigate whether or not vapor-phase equilibrium is reached over a small bubble path for a given experimental geometry, and how these rates of isotope exchange compare with the box values, and those calculated for moderate humidities. An estimate is first made of the time necessary for water vapor to diffuse 23 through a small, hollow, air-filled sphere. The governing differential equation in cylindrical coordinates which describes diffusion to and from a sphere where lines of equal concentration form concentric spheres is given by equation (16) [Carslaw and Jaeger, 1986] where r = the radius of the sphere, D0 is the coefficient of diffusion of water vapor in air, and the change in concentration is a function of v. (16) With the substitution u=vr this becomes 9 u _ d 2u (17) d t = °~d^ Equation (17), is adopted from derivations for radial heat flow within a sphere. Assumptions for applying these equations to the present case of small air bubbles rising in water include: • coefficient derivation is analogous with heat flow. • there is no internal turbulence or convection. • the system is isothermal. • bubbles are spherical with no surface effects. • evaporation at the free water surface is negligible. The solution for equation (17), where C0 is the concentration at the surface of the sphere, a is the radius, and r and C are the distance and concentration at time t, respectively, is given by [Carslaw and Jaeger , 1986]. 24 ^ ^ , 2aC0^ f . m r r \ ( - D 0n 2-K2t \ C — C0 -\------> s m ------exp ------(18) vr ^ i V a J \ a J C0 is assumed to be equal to the concentration at the surface, which is in turn 1mm 2mm C/Co 0.5 0.0 1.0 3mm C/Co 0.5 0.0 0.0 0.5 1.0 0.0 0.5 1.0 r/a r/a Figure 3: Water-vapor concentration profiles for four bubble diameters (one to four mm) and various values of dimensionless time ( D o t/a 2) as a function of r/a. Dimensionless times are determined by Do=2.39x-10~5 m2/second, a=sphere radius, and the following values of time in seconds: A=0.0003, B=0.001, C=0.003, D=0.006, E=0.01, F=0.03, G=0.06, H=0.1, 1=0.3. in equilibrium with the continuous (bulk) phase. Concentration profiles for various sphere diameters and exposure times (values of D0//a 2) are graphed in Figures 3 and 4 as a function of r/a. The coefficient of diffusion D0 for water vapor in air 25 is 2.39 a;10 5 m2/second at ambient temperatures. 5pim F 6mm C/Co 7mm C/Co 1.0 0.5 1.0 r/a Figure 4: Water-vapor concentration profiles for four bubble diameters (five to eight mm) and various values of dimensionless time (Dot/a2) as a function of r/a. Dimensionless times are determined by Do=2.39a;10-5 m2/second, a=sphere radius, and the following values of time in seconds: A=0.001, B=0.01, C=0.1, D=0.3, E=0.5, F=0.7, G=0.9, H =l.l. Figures 3 and 4 are interpreted by estimating the time necessary for C/Co to reach unity. The sweep of the time-lines across the graphs (from right to left) represent the diffusion of water vapor through the bubble from outer surface (r/a = 1) to the center of the bubble (C/Co = 1). For the purpose of estimating complete diffusion through the sphere, we define equilibrium in Figures 3 and 4 26 to be the point where the time line reaches 0.99 C/Co. From these graphs, the time required for equilibrium to be reached is found to range from 0.01 to 0.3 seconds for small (1-4 mm) bubbles, and from 0.5 to 1.0 seconds for medium (5- 8 mm) bubbles. The time-dependent concentration profiles in Figures 3 and 4 indicate that for the range of bubble diameters of interest (2-5 mm), diffusion of water vapor will force equilibration of the entire bubble volume within the time necessary for equilibration (residence time of bubbles). For these experiments the residence time was about 2 seconds. A schematic of the bubble-mediated transfer is shown in Figure 5. A model of this exchange must take into consideration the open-system nature of the vapor flux. Because little pressure is built up in the head space of the exchange vessel, and the exit vapors are swept out continuously, the system can be considered open. Thus if equilibrium is attained over the bubble path, the mass transfer will be proportional to the rate of air flow. At any instant, the dominant change in concentration occurs very near the interface; the distance over which k is applied is thus very small. However, it is usually impractical (if not impossible) to sample a moving liquid and measure C^;, the liquid-side interfacial concentration (Figure 5). An analogous Cv; exists within the vapor phase, as well as bulk vapor-phase Cl and C2 values, but are not pictured in Figure 5 for simplicity. 27 Vapor Free Water Surface C(TU,D,18—0) = equilibrium C(TU)=0 C(D,1B-0) = C(column vapor) apor Diffusors) Figure 5: Schematic of concentration changes over a short bubble rise Typical liquid and vapor sampling would more likely provide measurements of Cl and C2 within the chosen phase (Figure 5). Previous research suggests that the interfacial values are equilibrium concentrations, and that the resistances to mass transfer for the two phases are essentially independent and additive [W hitman, 1923]. This is the two-film theory (better termed the two-resistance theory), and implies equilibrium or equal chemical potential across the interface. The stable isotopic evolution of the vessel water in the bubble-mediated ex periments is modeled with equation (13). This method of analysis was chosen because it is the simplest model which correctly accounts for the observed vari 28 ations in composition. Since the input vapor has a constant near-zero tritium concentration (background), the tritium transfer is modeled based on the air flow rate. A mass balance expression of the system with the exchange vessel as the control volume relates the rate of change of mass in the control volume to the mass flux out of the system V ^ = %[Cvi) (19) where C l and Cv, are the concentrations of the liquid phase and the surficial vapor phase, respectively, qa is the air flow rate, and V is the volume of the liquid. If the saturated air behaves ideally, then the equilibrium condition C v, = H C l , (20) exists, where H is Henry’s Law constant for the gas of interest. This is justified since Raoult’s law is obeyed by mixtures of HDO and HTO [Smith and Fitch, 1963], in which the equilibrium partial pressure of each component is equal to the product of the vapor pressure of the pure component, and its mole fraction in the liquid phase. For water vapor, an apparent Henry’s Law constant can be closely approximated by converting the vapor pressure of water at the desired temperature to a molar concentration. For example, at the temperature of interest here (24.5 °C ), water vapor exerts a pressure of about 23.5 mm Hg, from which a vapor concentration of 1.23 xlO-3 M is calculated. The molar ratio of water vapor to liquid is thus 1.23 o,T0“3 M/55.5 M = 2.3a.T0“5, and can be thought of 29 as a dimensionless water vapor pressure. This value represents the equilibrium concentration of the vapor phase relative to the liquid phase. Inserting equation (20) into equation (19) yields 9JW = <2i> where the quantity q0V/H is proportional to the mass transfer coefficient k which has the units of 1/time. The integration of equation (21) is very similar to that presented in Appendix B for equation (12), using different initial conditions and limits of integration. It differs from equation (12) in that the partial pressure of tritium in the vapor phase is initially zero, hence Coo=0. Thus the use of equation (21) requires measurement of the air flow rate, liquid volume, and tritium concentration, and assessment of initial conditions. For typi cal applications of equation (21) to atmospheric gases, the resistance of one or the other phases tends to dominate the system, so that the total measured resistance is essentially equal to that of the resistance of the rate-controlling phase [ Treybal , 1968]. The major difference between the box experiments and water under more nat ural conditions (besides for isotopic composition) is the constant high humidity. Temperature gradients in nature across an air-water boundary will generally pro duce a flux of water into the vapor phase, resulting in a volume loss of the liquid phase. One model used to predict the isotopic composition of an evaporating liquid is the Rayleigh distillation equation. This model predicts the evolution of a dessicating liquid to be a function of the relative humidity raised to a power (some form of the fractionation factor). The application of the Rayleigh equation was found by Craig, Gordon and Horibe [1963] to be limited by molecular exchange between the liquid water and the atmosphere. The present work extends this concept in an attempt to quantify the resulting exchange for various end-member cases. 31 Methodology Two separate experimental designs were used to evaluate the exchange of iso topes between water and water vapor. In the first design, sealed boxes were used to create closed-system environments (boxes) in which waters of different isotopic compositions are allowed to isotopically equilibrate under isothermal conditions. This set of experiments is termed the box experiments, and is used to evaluate passive exchange, that is, exchange under quiescent conditions (with the excep tion of Experiment 3). The second design was an air-sparging experiment to study exchange under dynamic conditions in which the vapor phase is dispersed through the liquid phase in vertical bubble columns. In these experiments, the goal was to evaluate the rate of mass transfer of stable isotopes and tritium from the liquid phase to the vapor phase. Box Experiments The box experiments were designed to provide information on the isotopic transfer rates between liquid water and its vapor in a closed system based on the waters’ exposed surface area, volume, and temperature. Five experiments were conducted by allowing beakers of water of specific and known isotopic composition and salinity to equilibrate under controlled conditions within a closed system (box). Isotope exchange between beakers occurred through the vapor phase by removal and deposition of water molecules to and from the liquid surface. Under these conditions, the exchange and evaporation/condensation rates depend on the 32 isotopic and energy gradients existing between the phases, and the surface area to volume ratios of the liquid phase. Five experiments were conducted, (denoted Experiments 1 through 5), each with a specific set of initial conditions and water chemistries. The five experiments had the common attributes of high humidity, closed atmospheres, constant (but varied) temperatures, similar salinities, and waters with a wide range of stable isotope compositions and tritium concentrations to facilitate the exchange process. Both liquid (beaker) and vapor (box atmosphere) samples were taken over time to measure individual isotope exchange rates and liquid-vapor equilibria produced by the five experimental designs. Assumptions for the application of equations (13) and (15) to the box experi m ents are: • diffusion, transfer of water molecules is the dominant process. • the system is closed to energy gradients. • change in water content of the liquid phases is negligible. • the liquid and vapor phases are well mixed. Equipm ent Two box designs were used in these experiments; the first was used for Experiment 1, and the second was used for subsequent experiments. The first design employed was a glove box constructed of 1/2 inch thick Plex iglas screwed to a interior wooden frame (inside dimensions: 0.60 m length x 0.48 m width x 0.37 m height, interior volume ~ 107 liters). The box was sealed along 33 its frame with silicon sealant, and was fitted with a 0.08 m2 door for access. The second box design was used in Experiments 2 through 5, and differed from the box used in the first experiment in that 1) all acrylic construction removed the vapor sink effects of the wooden frame, 2) new dimensions (0.90 m length x 0.60 m width x 0.55 m height, interior volume ~300 liters) provided 2.8 times the volume of the first box, 3) no glove ports were installed, 4) 10 mm vapor ports were installed in the doors to allow vapor sampling. This design provided more control of water vapor loss resulting in a constant high humidity of greater than 95 % for Experiments 2 through 5. The boxes for Experiments 3-5 were modified by drilling two 15 mm holes into the top of each box for remote sampling access; this reduced loss and dilution of the box atmosphere by sampling through the door. This also allowed the doors to be sealed with silicone during the experiments to reduce loss of water vapor from the system, however, it was no longer possible to measure F/ (fraction of liquid remaining) at each sample time. All boxes were monitored with mercury thermometers and one of two hygrom eters, either a diaphragm or digital type. Sampling Liquid samples for stable isotope analysis of the exchange waters were taken for Experiments 1 and 2 by removing the beakers from the box and extracting four lOyuL aliquots from each water using micro capillaries. Each beaker was also 34 weighed on an analytical balance to provide a record of water loss (F/) during the experiments. Liquid samples for stable isotope analysis of exchange waters in Experiments 3 through 5 were taken remotely by lowering the capillaries into the box through the sampling ports set into the box tops. Liquid samples for tritium analysis requires larger sample volumes (~0.5 to 1 mL at the elevated tritium levels of these waters), and this sampling was consequently performed only at the beginning and end of each experiment. Vapor samples were taken for Experiments 2 through 5 only. Air samples for stable isotope analysis of the box atmospheres were obtained by connecting a one-liter glass globe (evacuated to 10-3 torr) with tygon tubing to the vapor port set in the door. The globe was fitted with a teflon stopcock to allow vacuum release and isolation of the unit after sample collection. Each one liter sample was allowed to equilibrate for several hours with the box atmosphere, and was then sealed and transferred to a laboratory vacuum line for extraction. The one-liter sample volume supplied sufficient condensed water vapor (~20 fj.L at saturation) for analysis of both <5 D and <518 0 which require 10 /iL each. Vapor samples for tritium analysis were taken for Experiment 5. This required the removal of about 8 liters of saturated air (providing ~0.8 ml of water), and was taken in one and two-liter glass globes. The water from each globe was condensed individually, and mixed before analysis. The analytical procedures used for stable isotope and tritium analysis from both vapors and liquids are presented in Appendix C. With the exception of 35 Experiment 3, excessive stirring and disturbance to the air-liquid boundary was avoided. Procedures The exchange waters were placed in cleaned, weighed Pyrex beakers for each of the box experiments. The beakers were put in the boxes, and the boxes sealed with dense plastic tape. All attempts were made to place the boxes in stable temperature environments, and disturb them as little as possible during equilibration. In Experiment 1 three beakers of water were equilibrated, and in Experiments 2 through 5, two aliquots of water were studied. The initial conditions for these experiments are given in Table 1. The beaker label heading in this table refers to the type of water contained in that beaker. Water A for all five experiments (Cambric water) was obtained from a post-shot well drilled near the core of the Cambric event on the Nevada Test Site, and was the source of tritium within all boxes. Waters B and C (Experiment 1) were specifically chosen so that they reflected the approximate mean center of isotopic mass, and a more depleted water, respectively (Table 1). Water B (Experiments 2-5) was distilled Pacific Ocean water chosen so that the relative isotopic difference between Waters A and B remained large, and so that solute effects on the vapor pressure of water were minimized. The initial salinity of each water for a given experiment is given in Table 2. The ocean water contained only background tritium values (<10 TU). 36 Table 2: Initial Conditions of Box Experiments Beaker f Water Surface L t EC £D 818 0 TU Label Volume Area (1 /cm ) (/tm hos) ± ± CH/'H) (m L) (cm 2) 1.0 %o 0.2 %o Experiment 1, still air, 21 ± 1.0 ° c , rel. hum. > 85 % A 457.47 71.25 0.156 420 -105 -12.8 95,077 ± 1138 Box 1 B 468.07 71.25 0.156 420 -34 +0.6 8.3 ± 3.6 C 468.99 71.25 0.156 420 +27.0 +9.0 6.8 ± 4 Experiment 2, still air, 21 ± 1.0°C , rel. hum. >95 % Box 1 A 529.99 71.25 0.134 455 -104 -13.0 86,690 ± 989 B 530.11 71.25 0.134 420 -7 -1.1 <10 Box 2 A 530.10 71.25 0.029 455 -104 -13.0 86,690 ± 989 B 530.04 8.70 0.029 420 -7 -1.1 <10 Box 3 A 132.22 71.25 0.336 455 -104 -13.0 86,690 ± 989 B 530.08 71.25 0.336 420 -7 -1.1 <10 Box 4 A 530.10 71.25 0.073 420 -104 -13.0 86,690 ± 989 B 132.5 8.70 0.073 420 -7 -1.1 <10 Experim ent 3, forced air, 22 ± 1.0° C , rel. hum . > 95 % Box 1 A 530.02 71.25 0.134 470 -50 -5.1 86,690 ± 989 B 530.56 71.25 0.134 425 -72 -10.1 <10 Experiment Jh still air, 50 ± 2.0 °C , rel. hum. >95 % Box 1 A 530.43 71.25 0.134 465 -103 -12.8 86,690 ± 989 B 530.28 71.25 0.134 400 -19 -2.8 <10 Experim ent 5, still air, 50 ± 2.0 °C , rel. hum. > 95 % Box 1 A 530.14 71.25 0.134 470 -105 -13.5 86,690 ± 989 B 530.06 71.25 0.134 420 -10.0 -1.7 86,690 ± 989 t Experiment 1: A = distilled ocean water, B = Cambric water, C = fog water Experiments 2-5: A= Cambric water, B= distilled ocean water } L = Surface area-volume relations calculated from equation (13) for Experiments 1,3,4,5, and Box 1 of Experiment 2, and from equation (14) for Experiment 2, Boxes 2,3, and 4. 37 Experiment 1 This is the only experiment in which three beakers of water were equilibrated; Experiments 2-5 used only 2 beakers. Communication between the waters took place through the vapor phase for 76 days. The box was held at a constant temperature of 21 ± 1.0 °C , and the relative humidity remained above 85 percent over the course of the experiment. The surface areas and volumes of these three waters were all the same (Table 1). The three waters contained contrasting stable isotopic compositions; two were diametrically opposed (Waters A and C), while Water B was chosen to have an isotopic composition close to the isotopic center of mass of the system. Water A initially contained all of the tritium. This isotopic contraposition allowed the process of exchange to be observed more readily. Experiment 2 Experiment 2 was designed to evaluate the effects of water surface area and volume on exchange rates between two waters; one tritiated and depleted in stable isotopes, the other with only background tritium, but more enriched in stable isotopes. Four separate boxes were used; the initial configuration for each box is given in Table 1. Box 1 of this experiment replicated the the surface area-volume relationship of Experiment 1, while boxes 2, 3, and 4 had varied surface-area relationships (Table 1). The sampling procedure was otherwise identical to the first experiment. 38 Experiment 3 Experiment 3 was designed to investigate the effect of a constant air flow on the isotope exchange rates for the similar surface area-volume relations. An air velocity of about 0.35 meters/second was produced by placing a small air fan in the box. By inducing turbulence within the saturated boundary layer, the exchange rates should increase. The air movement also reduced the surface tension of the water which would lead to higher exchange rates. Experiment 4 The goal of this experiment was to study the changes in isotope exchange rates produced when a constant temperature of 52 ± 1.5 °C was maintained within the box. Heat was applied through electrical resistance tape wrapped around the box which was then covered with insulating material to ensure constant temperatures. The possibility that hot spots existed within the box was considered, and in trial runs some localized differential heating was found. However, the speed at which isotopic equilibrium was reached suggested that if the box and the waters were thermally pre-conditioned, this effect could be minimized. This was done by pre heating the box and waters separately to the proscribed temperature, and then beginning the experiment. The door of this box was sealed with silicon sealant because of the increased vapor pressure. Experiment 5 The design of this experiment is much the same as Experiment 4, with the exception that 7.0 liters of water were placed on the floor of the box in order 39 to produce an isotopically buffered atmosphere. The water used was an equal mixture of the two exchange waters, so that the composition of the vapor was the same as it would have been without this application. Using the buffered atmosphere was only possible under similar surface area-volume conditions. The greater surface area of the flood water compared to the beakers severely lessened the initial evaporation of the beaker waters to produce high humidity within the box. The beakers were raised off the floor of the box to shield them from direct heat, but were still immersed in the water mixture. The box with the mixed water was allowed to equilibrate thermally and isotopically for 24 hours before the experiment was begun. Daily samples were taken because of the speed at which the waters equilibrated. Three 8-liter vapor samples were taken, once after initial equilibration with only the flood water, once halfway through the experiment, and once at the end. Eight liters of saturated vapor at ~52 °C provided ample liquid water for tritium analysis of the vapor phase. The flood waters were also sampled at the same three points. Bubble-Mediated Isotope Exchange Three separate experiments were conducted using this mode of isotope trans fer (Runs 1, 2, and 3). They were variable in length and initial isotopic composi tion of the liquid phase. The first run began with an exchange water containing ~ 5000 TU (Federal drinking water standard = 6154 TU), the second and third 40 trials were conducted with waters containing ~ 630,000 TU so that the exchange rates could be evaluated for more elevated tritium activities. The systematics of isotope transfer for bubble-mediated exchange is similar to those observed in the box experiments; the major differences are 1) the vapor phase was dispersed through the liquid phase in vertical bubble columns, and 2) the nature of the gas-liquid boundary was turbulent. Equipm ent Figure 6 shows a schematic of the experimental design which comprises two main parts. The first is a saturation system designed to modify the input air (compressed laboratory air) to a known isotopic composition and high absolute humidity for injection to the reaction vessel. The second is the exchange portion, which contains the water to be modified, an air diffuser and the exhaust system. The saturation columns were constructed of extruded acrylic 10 cm in diameter and 122 cm high, providing an effective volume of about 8 liters each. Each column is fitted with a removable lid secured by bolts set through a collar on the columns; an o-ring set into each lid provides a water- and pressure-tight seal. The lids were each drilled and tapped to accept two bore-through teflon tube fittings for the vapor input and output lines; flexible 1 cm (i.d.) plastic tubing was used throughout. Within the saturation system, stable vapor parameters were achieved by 41 SATURATION SYSTEM EXCHANGE SYSTEM Radioisotope Compressed Air Hood Vapor globe port Flow meter Vapors ^ 3 8 Liter Humidity meter Exchange Bubbles Thermometer Vessel W ater A W ater B i\ Saturation Columns Acrylic Containment Box (8 liter volume each) Figure 6: Schematic of the bubble-mediated tritium exchange experiment. The saturation system produces high (>95 %) relative humidity water vapor of known isotopic composition through evaporation and exchange with Water A. The tri tium transfer (liquid to vapor) is induced in the exchange vessel by a constant flux of saturated, zero-tritium air through the bulk liquid (Water B). passing a constant flow of compressed air (~ 15-20 % relative humidity) through the three columns which were filled with water of known isotopic composition to produce a vapor stream of consistent and known isotopic composition. The input air flow was dispersed in the columns through a 6 cm length of fibrous diffuser at the bottom of each column into a bubble swarm whose vapor was constantly modified by exchange along the length of the columns. The bubble regime in the columns was highly turbulent, and a certain amount of recirculation of bubbles occurred before they rose to the top and broke. As the bubbles within the first column broke the surface, the head pressure increased, and forced the airflow into the second unit. Measurements indicated that the initial air stream (~ 15-20 % rel. hum.) was saturated to about 85 % by the first column, and to 42 greater than 95 % after the second column. The first column, then, was evaporated to a greater degree than the second and third. As the vapor left the third column, temperature, relative humidity, and flow rate were monitored and recorded. Temperature and relative humidity measure ments were taken with either a Hanna Instruments 9065 or 9064 thermohygrom eter. Air flow was monitored with an Omega Instruments Fl-214 glass-float ro- tometer and controlled with an in-line gate valve. Line pressure on the input side of the columns was measured with a Wika pressure gauge. At this monitoring station, one liter vapor samples were also taken for stable isotope analysis of the saturated (column) air stream. The volume of water vapor condensed from these samples provided a secondary check on the absolute humidity of the air stream for a given temperature. The stable isotope composition of the vapor from the columns was forced to equilibrium with the column water (Water A, Figure 6); the column water was thus chosen so that its equilibrium vapor was isotopically enriched with respect to Water B in the exchange vessel; this dis-equilibrium in stable isotope composition facilitated the study of the exchange process. The column water contained only background tritium (<10 TU), so that the vapor introduced to the exchange vessel had a constant, high tritium gradient with respect to the exchange water. The second part of the experimental design was the exchange system which was completely enclosed in a radioisotope fume-hood, and consisted of a rectangular, acrylic reaction-vessel (38 liter volume) housed in a sealed acrylic containment 43 box (Figure 6). Within the exchange vessel, the modified air stream which exited the three columns was dispersed into the tritated water through a 50 cm flexible aerator attached to the floor of the vessel. The resulting bubbles rose vertically through the water column with no recirculation with the result that the effective bubble path was equal to the depth of water. The containment box was fitted with a exhaust stack (diameter = 7.5 cm) which allowed the vapor effluent to enter the fume hood. The vessel and containment box were continuously monitored for mass on a laboratory platform scale, and a record was kept of the daily loss of exchange water. Sam pling Sampling of both the reacting liquid and input and output vapors was con ducted at regular intervals. One-liter vapor samples for stable isotope analyses were extracted in glass globes (previously evacuated to 10~3 torr) by releasing the vacuum within the atmosphere of interest. The globes were then processed in the in-house isotope laboratory. Details of the extraction and sample analysis are given in Appendix C. Liquid samples of the reaction water were taken by pipette through the vent on the containment box for both stable isotope and tritium analysis. A typical liquid sample consisted of four 10 /zL micro-capillaries for stable isotopes and two 1 mL aliquots for tritium analysis. Acquisition of a Liquid Scintillation Counter midway through the second run allowed more tritium samples to be taken. 44 Direct tritium analysis of the exchange (exit) vapors was performed in Runs 2 and 3 to better evaluate the efficiency of the tritium exchange. Transfer rates for the first experiment were estimated based on the loss of activity over time of the reacting water. Measurement of the vessel vapor exhaust for tritium requires a larger volume of air than for stable isotope analysis. While a one liter sample of saturated air (providing ~ 20 fiL water) suffices for the stable isotopic measure ments, approximately 20 liters of air (~ 400 fiL water) at 21 °C are needed for tritium analysis. The problem posed is the capture of every water molecule within a specific volume of air to provide a 1 ml sample. If the condition of complete water capture is not met, the sample will be, by definition, fractionated. An in-line extraction technique was devised to sample the water vapor from the vessel exhaust for tritium analysis, and so better estimate the efficiency of the tritium exchange process. The isolation of the full fraction of water vapor from a moving air stream was achieved by a multiple cold-trap technique which utilizes a C02-acetone slush (temperature ~ -96 °C ) as the condensing agent. This method was chosen over other extraction techniques (e.g., molecular sieves, dessicants) because at high efficiencies, the cold-trap method is non-fractionating. The cold trap consisted of a series of glass finger tubes connected to a copper coil with vacuum tubing; this geometry provided a large enough surface area for com plete condensation of the water vapor. The vessel exit vapor was diverted into the cold trap by means of a plastic tee and gate valve in the exhaust line. The flow rate for the diversion was controlled by the gate valve and measured with a Fischer 45 and Porter low-flow rotometer; 1.5 liters/minute was found to be a sufficiently low flow to allow complete extraction of the water fraction. Procedures An experimental run consisted of passing a known flux of air through the saturation system until the vapor parameters reach steady state, and connecting this output to the reaction vessel filled with a water of known stable isotopic composition and tritium activity. Measurement of liquid, input and output vapor concentrations define the mass balance of the system. Initial conditions for the bubble-mediated exchange experiments are as follows: • air flow = 15 liters/minute. • relative humidity = 97to 99 %. • temperature = 22 ± 1.2 °C . • line pressure = 22 ± 2 psia. • volume of tritiated water = 30 liters. The stable isotopic composition of the input vapor was variable because of evaporation and isotopic enrichment of the column waters. The evaporation ne cessitated replenishment of the column waters (column one in particular). Vapor samples both before and after replenishment were taken so that a record could be kept of the change in the isotope composition of the input vapor. 46 Bubble Parameters The air bubbles were generated through a flexible multi-nozzle aerator fixed near the bottom of the exchange vessel (Figure 6, page 42). The bubbles released from the aerator were well behaved at the chosen flow rate. That is, there was lit tle recirculation or turbulence, although enough existed to maintain a well mixed liquid. It was not necessary to use optical or photographic methods to estimate bubble velocities; the shallow water depth (21 cm) and linear rise allowed rea sonably good estimates to be made with a stopwatch. Visually, the bubbles were found to move through the 21 cm depth of water in an average time of about 2 seconds, giving a first approximation of bubble velocity of between 10 and 11 cm/sec. Further, the shallow depth of water also allowed the changes in volume and pressure within each bubble to be ignored which simplifies the mass transfer calculations. For example, over a 29.5 cm bubble rise (bubble diameter = 0.7 mm) a total increase in volume of less than one-half of one percent was observed for single air bubbles in tap water [Motarjemi and Jameson , 1978]. The relationship between bubble rise velocity and bubble diameter for small rigid spheres (Stokes law) and results from Haberman [1956] and M otarjem i [1978] is shown in Figure 7. The bubble size-velocity relations from this work (diame- ter=3.1 mm, velocity=10.5 cm/sec.) are in good agreement with Figure 7. In dividual bubble volumes are estimated based on the average diameter (3.1 mm) giving an averaged bubble volume of 0.017 cm3, from which an aggregate surface area per second of exposure of 4700 cm2 is estimated. e ad a sn 17) Sld ie s tks a fr ml rgd spheres. rigid small for Law Stokes is line Solid (1978). eson Jam and i jem ube i tp ae. te ln i mdfe fo Haema (96 ad otar M and (1956) an aberm H from modified is line otted D water. tap in bubbles Figure 7: Relationship between bubble rise velocity and bubble diam eter for small small for eter diam bubble and velocity rise bubble between Relationship 7: Figure Bubble rise velocity (cm/sec) 100.0 10.0 0.1 1.0 0.0 Equivalent Bubble diam eter (mm) eter diam Bubble Equivalent 0.1 1.0 10.0 47 48 R esu lts The results of the Box experiments are presented in Tables 3-7 giving the isotopic evolution of the exchange waters for a particular experiment, in addition to a Box Experiments Experiment 1 The results for Experiment 1 are tabulated in Table 3. Approximately 30% of the total water mass was lost during this experiment, but high humidity within 0 the box lessened the effect of evaporation on the isotopic evolution of the exchange waters. As the three waters equilibrated isotopically over the 76 day period, Waters A and C asymptotically approached an isotopic stable state, close to that of Water B. Water A, the most depleted in both <5D and <5180 (-105 °/ooa,nd -12.8 °/0o, respectively) became enriched in <5D by 60 per mil, and increased 12.8 per mil in 8180 . However, this enrichment was caused by an isotopic flux rather than a net loss of vapor (evaporative enrichment) since the isotopic center of mass only changed by several per mil over the 76 day period. The relationship between the isotopic shifts for the three waters and the me teoric water line (MWL) [Craig, 1961] is shown in Figure 8. 49 Table 3: Results for Box Experiment 1 Same Volumes: ~470 ml Same Surface Areas: 71.3 cm2 Analytical error: ± 1.0 %o £ D , ± 0.2 °/oo 6180 . Day Water(ml) F\ 8T) 818 0 TU W ater A 0 475.47 100 -105 -12.8 95,077 ± 1138 5 455.01 96 -96 -11.0 — 8 445.53 94 -93 -10.1 — 19 419.95 88 -81 -7.2 — 29 402.28 85 -73 -5.1 — 39 387.22 81 -66 -3.8 — 49 373.43 79 -58 -2.5 — 57 363.12 76 -54 -1.5 — 67 352.24 74 -49 -0.6 — 76 342.76 72 -45 0.0 37,846 ± 492 W a te r 'B 0 468.07 100 -34 +0.6 8.3 + 4 5 448.35 96 -32 +0.7 — 8 439.72 94 -33 +1.4 — 19 415.56 89 -32 +1.2 — 29 398.12 85 -36 + 1.6 — 39 382.94 82 -35 +1.8 — 49 368.74 79 -34 +2.0 — 57 357.96 77 -34 +2.0 — 67 346.71 74 -33 +2.4 — 76 336.95 72 -34 +2.2 19,138 ± 307 W a te r C 0 468.99 100 +27 +9.0 6.8 ± 4 5 449.08 96 +20 +8.7 — 8 440.37 94 + 17 +8.3 — 19 415.54 89 +4 +7.0 — 29 397.07 85 -4 +6.3 — 39 380.44 81 -10 +5.3 — 49 364.99 78 -17 +4.7 — 57 353.22 75 -19 +4.4 — 67 340.39 73 -22 +4.0 — 76 329.25 70 -24 +3.7 19,169 ± 430 50 Water C -20 V/ -35 Water B a> a -50 -65 Water A -80 Analytical Error ± 1 .0 %o 8 D -95 ± 0 .2 %o 5 1 8 - 0 -110 -15.0 - 10.0 -5.0 0.0 5.0 10.0 Delta 18-0 Figure 8: Evolution of isotopic signature with time of three isotopically different waters under constant humidity and temperature conditions. A theoretical evap oration line (long dashes) is computed for the same initial isotopic composition as Water A, and a 30% water loss. The addition of a kinetic effect at 85% humid ity (short dashes) affects the slope and magnitude of this line only slightly. The arrows indicate the direction of the isotopic trends for waters A and C. Water A appears to have undergone an evaporative shift. However, the theo retical evaporation trend for this water (long dashed line), calculated with 20 °C fractionation factors at a net water loss of 30% for both species, suggests that exchange has appreciably affected this water. The tritium concentration of Water A decreased from 95,077 TU to 37,846 TU. The direction of change in tritium for Water A contradicts the expected evaporative enrichment of the liquid phase. This suggests that vigorous isotopic exchange with the ambient vapor occurred 51 even though the vapor initially contained no tritium. Waters B and C initially contained very little tritium (8.3 and 6.8 TU, respectively) and these values in creased to over 19,000 TU for both waters. T he 5 D and S18 0 values for Water C became more depleted by 51 per mil and 5.3 per mil respectively. Therefore the stable isotopic changes in Water C also revealed a non-evaporative shift, indicating that the 30% drop in F/ had little or no effect on the direction of isotopic shift. This is again caused by an isotopic return flux, rather than a water volume flux associated with an evaporative shift in A D /A 180. Water B was initially very close to the isotopic center of mass of the system and underwent only a slight enrichment in 6180 (1.6 per mil), while the 6D values remained essentially constant. The isotopic center of mass for the system was calculated by mass balance for each sampling time; this value deviated from the mean by only 3 per mil in <5D and 4 per mil in 6180 , indicating that evaporation did not cause an appreciable effect in the observed isotopic shifts. Even when the fractionation factors are adjusted for a kinetic effect at 82 per cent humidity (short dashed line, Figure 8), the magnitude of the actual data line is still about twice that of the line calculated for evaporation, indicating that exchange strongly influenced Water A. Clearly, the isotopic adjustment of this water to the surrounding atmosphere is caused by exchange, rather than a net loss of water. The theoretical lines can also be calculated for Waters B and C with similar results. Water C roughly parallels the MWL but trends in the opposite direction of Water A. Waters A and C trend inwards towards the isotopic center 52 of mass of the system, approximated by the position of Water B. Isotopic values for the steady state case are obtained by extrapolating the trends in Figure 8 towards the point of mutual intersection; for this experiment they are: 6D (%,) = -34, <5180 (%,) = +2.6, TU = 25,000 Experiment 2 The results for Experiment 2 are shown in Table 4 as separate data blocks for the four different boxes in this experiment. The evaporation was much better controlled in these experiments because of the improved box design. Within each box, Water A (<5D = -104, (S180 = -13.0, tritium concentration ~86,000 TU) was allowed to equilibrate with Water B (<5D = -7, <5180 = -1.1, tritium concentration <10 TU) over a 54 day period at 22.5 ± 1.0 °C . Box 1 contained beakers with the same volume and surface area for both waters, the same configuration as in Experiment 1. This was done to check the reproducibility of the experiment. Water A experienced an isotope shift of 34 per mil in <5D (-104 %oto -94 °/0o) and Water B underwent a 23 per mil shift in 5180 (-7 %0to -30 %0); these results are graphed in Figure 9. Water B, which initially contained no tritium, absorbed about 28 percent of the total tritium inventory of 86,690 TU for this box. These results compare well with those from Experiment 1. No appreciable differences in results were found because of the larger box volume. In general, the water losses were less than for the first experiment. 53 Table 4: Results for Box Experiment 2 B O X 1 Same Volumes: 530 ml Same Surface Areas: 71.3 cm2 Analytical error: ± 1.0 %o £D, ± 0.2 °/0o <5180 . Day W ater (ml Fi <5D <5180 TU W a te r A 0 529.99 100 -104 -13.0 86,690 ± 989 4 518.61 97.9 -98 -11.7 — 10 510.06 96.2 -95 -11.0 — IS 501.91 94.7 -89.5 -10.5 — 28 492.80 93.0 -82 -9.9 — 38 484.88 91.5 -79 -8.7 — 45 479.05 90.4 -76 -8.3 — 54 468.63 88.4 -70 -7.7 62,008 ± 412 W a te r B 0 530.11 100 -7 -1.1 <10 4 519.10 97.9 -10 -0.8 — 10 510.SO 96.4 -13 -1.6 — 18 503.24 94.9 -16 -2.3 — 28 495.12 93.4 -20 -2.3 — 38 488.28 92.1 -26 -3.2 — 45 483.30 91.2 -29 -3.1 — 54 473.91 89.4 -30 -3.0 24,512 ± 284 V a p o r 10 -131 -21.6 — 28 -136 -19.5 — 38 -137 -21.2 — 45 -132 -17.1 — 54 -134 -17.8 — C e n te r o ■ Isotopic Mass 0 -55.45 -7.04 — 4 -52.46 -6.39 — 10 -52.50 -5.90 — 18 -55.42 -6.64 — 28 -51.90 -6.09 — 38 -52.39 -5.94 — 45 -52.40 -5.69 — 54 -49.89 -5.34 — 54 T able 4 continued B O X 2 Same Volumes: 530 ml Different Surface Areas: Water A= 71.3 cm2, Water B= 8.7 cm2 Analytical error: ± 1.0 %0 Day Water(ml) Ft 6 D <5180 TU W a te r A 0 530.10 100 -104 -13.0 86,690 ± 989 4 527.74 99.6 -102 -12.7 — 10 525.77 99.2 -103 -12.3 — 18 523.97 98.8 -99 -12.4 — 28 521.39 98.4 -97 -12.1 — 38 519.53 98.0 -98 -11.8 — 45 518.77 97.8 -98 -11.6 — 54 515.77 97.3 -94 -11.1 79,507 ± 460 W a te r B 0 530.11 100 -7 -1.1 <10 4 519.10 97.9 -3 -0.7 — 10 510.80 96.4 -6.65 -0.0 — 18 503.24 94.9 -4.5 -0.6 — 28 495.12 93.4 -6 -0.2 — 38 488.28 92.1 -8 -0.1 — 45 483.30 91.2 -8 -0.3 — 54 473.91 89.4 -7 +0.6 6390 ± 193 V a p o r -110 -18.6 -110 -16.9 -118 -16.4 -107 -14.4 Isotopic Center of Mass 0 -55.50-7.05 — 4 -52.90 -6.75 — 10 -55.44 -6.24 — 18 -52.67-6.61 — 28 -52.66 -6.30 — 38 -54.39 -6.13 — 45 -54.57 -6.15 — 54 -52.35 -5.50 — 55 Table 4 continued B O X 3 Different Volumes: Water A= 132.5 ml, Water B= 530 ml Same surface Areas: 71.3 cm2 Analytical error: ± 1.0 °/00S D , i 0.2 °/00^18O. Day W ater(m l) F t 6D 6lsO TU W a te r A 0 132.22 100 -104 -13.0 86,690 ± 989 4 122.18 92.4 -88 -10.2 — 10 114.21 86.4 -71 -7.3 — 18 107.10 81.0 -53 -5.6 — 28 98.26 74.3 -38 -3.4 — 38 91.18 69.0 -30 -2.1 — 45 86.81 65.7 -24 -1.3 — 54 80.94 61.2 -22 -0.5 30,103 ± 349 W a te r B 0 530.08 100 -7 -1.1 <10 4 517.84 97.7 -7 -1.1 — 10 508.30 95.9 -12 -1.3 — 18 499.68 94.3 -14 -1.5 — 28 489.05 92.3 -15 -1.4 — 38 480.05 90.6 -18 -1.5 — 45 474.65 89.5 -16 -1.2 — 54 465.99 87.9 -17 -0.7 13,410 ± 232 V a p o r -127 - 21.0 -118 -17.5 -111 -13.4 -112 -14.3 -110 -13.6 Isotopic Center of Mass 0 -26.34 -3.47 — 4 -22.46 -2.84 — 10 -22.81 -2.40 — 18 -20.89-2.22 — 28 -18.84 -1.73 — 38 -19.91 -1.60 — 45 -17.22 -1.21 — 54 -17.74 -0.67 — 56 Table 4 continued B O X 4 Different Volumes: Water A= 530 ml, Water B= 132.5 ml Different Surface Areas: Water A= 8.7 cm2, Water B= 71.3 cm2 Analytical error: ± 1.0 %o 6D, ± 0.2 %, <5180. Day W ater (ml) Fi 6T> <5180 TU W a te r A 0 529.97 100 -104 -13.0 86,690 ± 989 4 527.10 99.5 -103 -12.3 — 10 524.77 99.0 -101 -12.2 — 18 522.68 98.6 -99 -12.3 — 28 520.25 98.2 -98 -12.0 — 38 518.12 97.8 -98 -11.6 — 45 516.54 97.5 -95 -11.3 — 54 513.59 96.9 -94 -10.6 66,007 ± 525 W a te r B 0 132.69 100 -7 -1.1 <10 4 117.49 88.5 -4 +0.1 — 10 104.57 78.8 -5 +0.5 — 18 92.06 69.4 -7 +0.7 — 28 75.96 57.2 -9 + 1.3 — 38 61.47 46.3 -11 + 1.6 — 45 49.24 37.1 -7 +2.4 — 54 26.66 20.1 +2 +4.4 21,217 ± 307 V a p o r 10 -106 -18.0 — 28 -111 -14.9 — 38 -109 -11.9 — 45 -112 -14.1 — 54 -105 -11.6 — Iso topic Center of Mass 0 -84.63 -10.62 — 4 -85.01 -10.05 — 10 -85.10 -10.10 — 18 -85.21 -10.35 — 28 -86.78 -10.32 — 38 -88.83 -10.21 — 45 -87.37 -10.11 — 54 -89.36 -9.87 — -10 -25 -40 Water B o o O -55 « a3 Q -70 Water A -85 Analytical Error ± 1.0 %c8D -100 ±0.2 %o6 18-0 -115 -15.0 - 10.0 -5.0 0.0 Delta 18-0 Figure 9: 618 0 - 6D relations for Experiment 2, Box 1. Waters A and B had similar surface areas and volumes. Box 1 underwent an evaporative loss of about 10 per cent total water mass compared to the 30 percent lost in Experiment 1 (same surface area-volume rela tions). In Experiment 1, the ratio of isotopic shifts A/B, when adjusted for the same time period (~54 days) were: ^ t eJr Q = 51/46 ~1.1 in <5D and 11.3/4.6 ~2.4 in 6180 . For Experiment 2, the same ratios are 1.4 in 6 D , and 2.8 in <5180 which agree reasonably well, and probably differ because of the slightly smaller initial volumes in Experiment 1, and because the evaporation rate for the second experiment was better controlled. 58 -20 Water B -35 o o Q -50 LU Q -65 -80 Analytical Error Water A ± 1.0 %o& D -95 ±0.2 %o8 18-0 -110 -15.0 - 10.0 -5.0 0.0 Delta 18-0 Figure 10: 618 0 - 8 D relations for Experiment 2, Box 2. Waters A and B had the same volumes, but different surface areas. For the case of same volume, different surface areas (Box 2, Figure 10), Water A underwent a 10 per mil shift in <5D (-104 °/00to -94 °/00), and shifted 1.9 per mil in <$18 0, while Water B, having one eighth the surface area of Water A, experienced no appreciable shift in either £180or <5D. Water A lost about one percent of its tritium activity to Water B over the 54 day period. It was not possible to resolve the expected 8:1 shift in <5D, 818 0, or tritium activities from these data. Water A experienced a total water loss of about 3 percent, while Water B lost about 10 percent of its initial mass. Vapor concentrations were generally found to be in isotopic equilibrium with the center of mass calculations. 59 In Box 3, the case of different volumes and same surface areas (Figure 11) forced a shift in water A of about 12.5 and 82 per mil in <518 0 and <5D, respectively, while Water B, at four times the volume, shifted only by 0.4 and 10 per mil for the same isotopes. The ending tritium distribution for this experiment (Table 3) confirms the 4:1 volume ratio, and indicates that the long-term distribution of isotopes for a closed system is a function of volume. The volume-distribution relationship is less clear for the stable isotope compositions because the center of mass shifted by 2.8 and 8.8 per mil in The mass of water lost from the system, however, also reveals a 4:1 volume ratio between Waters B and A (Table 4). The effect of the different volumes on the isotopic shifts is stark as shown in Figure 11. Water B follows a path opposite that of Water A in stable isotope shifts until reaching close to the mean isotopic composition of the system, and then turns away from the meteoric water line subparallel to the trend of Water A. The results for Box 4 reflect the combined effects of different surface areas and volumes (Water A = 530 ml, 8.7 cm2, Water B = 132.5 ml, 71.3 cm2), and are graphed in Figure 12. The surface area-volume ratios (A/B) were 4:1 and 1:8 respectively. Water A underwent 10 and 2.6 per mil shifts in deuterium and oxygen, respectively, while Water B experienced 9 and 5.5 per mil shifts for the same isotopes. The ending tritium inventory indicates that Water B accepted 24 percent of the total beginning activity. Water A lost about 4 percent of its initial water mass, while Water B lost about 80 percent. 25 Water B -20 o o o -35 Q a> -50 a -65 Water A -80 Analytical Error ±1.0 %o8D -95 ±0.2 % o 8 18-0 -110 -15.0 - 10.0 -5.0 0.0 Delta 18-0 Figure 11: <5180 - 6 D relations for Experim ent 2, Box 3. W aters A and B had different volumes, but similar surface areas. The combined effect of differing surface areas and volumes appears difficult to resolve with the observed data. From the 25 percent loss in tritium activity for Water A, it seems possible that the long-term effect of volume dependence (4:1) on the overall isotopic composition may dominate the more instantaneous effect of surface area (1:8) when these parameters compete with each other, but this is difficult to justify based only on these data. From Figure 12 it is clear that Water B shifted more in 618 0 and <5 D than Water A, even though its surface area was one-eighth that of Water A. This suggests that the shift was dominated by the -20 Water B -35 o o o -50 Q) Q -65 -80 Water A Analytical Error ± 1.0 %o5D -95 ±0.2 %o5 18-0 -110 -15.0 - 10.0 -5.0 0.0 5.0 Delta 18-0 Figure 12: <518 0 - 6 D relations for Experiment 2, Box 4. Waters A and B had different surface areas and volumes. differences in volume (Water A=530 ml, Water B=132.5 ml). Experiment 3 Experiment 3 was designed to estimate the effect of convection on the observed isotope exchange rates; the initial conditions for this experiment were identical to Experiment 1, and Box 2 of Experiment 2, with the exception of the air flow, and different initial water compositions. The results for this experiment are given in Table 5. Figure 13 shows the 6180 - 6D relations for this experiment. 62 Table 5: Results for Box Experiment 3 Same Volumes: Water A= 530 ml, Water B= 530 ml Same Surface Areas: Water A=71.3 cm2, Water B= 71.3 cm2 Air Flow ~0.3 meters/second Analytical error: ± 1.0 %o <$D, ± 0.2 °/00 S180. 00 O'! Day <5D o TU W a te r A 0 -71 -10.1 86,690 ± 989 5 -67 -8.3 14 -61 -7.4 19 -60 -7.1 33 -58 -6.9 45 -58 -6.8 56,034 ± 590 W a te r B 0 -50.0 -5.5 <10 5 -53 -6.7 14 -59 -7.3 19 -58 -7.3 33 -58 -6.9 45 -58 -6.9 31,040 ± 756 During Experiment 3, localized condensation of the box atmosphere onto the walls and floor of the box may have allowed droplets of water to fall back into the beakers. Also, the increase in surface area created by the skin of water on the box was a concern. Because this water was formed in equilibrium with Rv (a constant), its effect is not seen as shifts in isotopic composition (Figure 13). About 46 percent of the total water mass was lost from the beakers, two thirds of which was returned to the liquid phase in the form of condensation. 63 -45 Water B -55 o *S o5 a -65 Analytical Error Water A ± 1.0 %oSD ±0.2 %o 8 18-0 -75 - 10.0 - 8.0 -7.0 - 6.0 -5.0-9.0 Delta 18-0 Figure 13: <5180 - <5 D relations for Experiment 3. Waters A and B had similar surface areas and volumes under conditions of convecting air. Experiment 4 The stable isotope results of Experiment 4 are shown in Table 6. The addi tion of heat produced competing effects on the exchange rates within the boxes. First, the higher vapor pressure of water produced larger fluxes across the air- water boundary, increasing the exchange efficiency. Second, since the equilibrium exchange fractionation factor is inversely dependent on temperature (higher tem peratures cause lower fractionation factors), this to some degree counteracted 64 Table 6: Results for Box Experiment 4 Same Volumes: Water A= 530 ml, Water B= 530 ml Same Surface Areas: Water A=71.3 cm2, Water B= 71.3 cm2 Temperature = 52 ± 2 °C . Analytical error: ± 1.0 °/oo^D ,± 0.2 °/oo £18 0 . Day <5180 TU W a te r A 0 -103 -12.8 86,690 ± 989 5 -86 -10.1 14 -60 -6.3 19 -56 -5.8 33 -52 -4.2 45 -53 -2.8 44,354 ± 690 W a te r B 0 -19 -2.8 <10 5 -32 -4.0 14 -52 -5.3 19 -52 -5.1 33 -52 -3.7 45 -49 -2.1 39,669 ± 756 the increase in isotope transfer of the water. As with Experiment 3, localized con densation created a possible return path of condensing liquid back to the beakers. While this probably occurred to some extent, the effects of a return flux is not seen in the shifts in isotopic composition (Figure 14). Localized differential heating of the box caused Water B to be completely evapoi'ated by the end of the experi ment. Water A shifted 50 per mil in deuterium and 10 per mil in oxygen, while Water B underwent changes of 30 per mil and 0.7 per mil in the same isotopes (Figure 14). 65 -20 W ater B -35 -50 a> Q -65 -80 W ater A Analytical Error -95 ± 1.0 %«5D ±0.2 %o8 18-0 -110 -14.0 - 12.0 - 10.0 - 8.0 - 6.0 -4.0 - 2.0 Delta 18-0 Figure 14: S18 O - 8 D relations for Experiment 4. Waters A and B had similar surface areas and volumes at a constant temperature of 52 ± 2 degC. The shift in <51S 0 for Water B shows a reversed trend, becoming initially more depleted, and then becoming slightly more enriched. Additions of liquid to the beakers from condensation may also complicate these results. The tritium inventory for this experiment shows that the tritiated water gave up about 50 percent of its activity to the non-radioactive water. Experiment 5 The results for Experiment 5 are summarized in Table 7. 66 Table 7: Results for Box Experiment 5 Same Volumes: Water A= 530 ml, Water B= 530 ml Same Surface Areas: Water A=71.3 cm2, Water B= 71.3 cm2 Flood Water=3.5 liters of each Water A and B. Temperature = 52 db 2 °C . Analytical error: ± 1.0 %o <5D, ± 0.2 °/0o <5180 . Day SB Sl80 TU W a te r A 0 -102 -12.9 86,690 ± 989 1 -97 -12.2 2 -92 -11.6 3 -88 -11.1 4 -86 -10.5 5 -83 -10.1 6 -81 -10.0 7 -80 -9.6 9 -75 -8.4 14 -70 -7.9 17 -66 -7.8 24 -58 -7.0 27 -58 -7.2 47,889 ± 690 W a te r B 0 -13 -2.0 <10 1 -17 -2.5 2 -22 -2.8 3 -26 -3.0 4 -36 -3.5 5 -33 -3.8 6 -34 -4.0 7 -36 -4.3 9 -42 -4.8 14 -46 -5.0 17 -49 -5.6 24 -51 -6.0 27 -54 -7.0 44,354 ± 690 F o o d W a te r 0 -56 -7.4 43,325 ± 873 8 -55 -6.6 44,164 ± 892 18 -55 -7.0 43,980 ± 364 V a p o r 0 -19 -2.8 41,138 ± 570 8 -32 -4.0 42,574 ± 658 18 -52 -5.3 42,254 ± 355 Delta D lost 1.38 ml of water, while W ater B lost 0.99 nil of water. T he tritiu m inventory m tritiu he T water. of nil 0.99 lost B ater W while water, of ml 1.38 lost isotopes. same the °/0o in 5 and %o 41 of shifts showed and flood-water samples were taken, an assessm ent of the evolution of condensing condensing of evolution the of ent assessm an taken, were samples flood-water and aos s osbe a wl a a assmn o h fatoain atr o tii m tritiu 44 for factor shifted A ater W fractionation . the of °C 52 assessment at an as well as possible, is vapors two exchange trends have sim ilar m agnitudes and forms. In addition, since vapor vapor since addition, In forms. and agnitudes m ilar sim have trends exchange two ufc aes n vlms t cntn tmprtr o 5 ± dg. e t o atm the of he T floor the degC. on B ± and 52 A of aters W of perature ixture tem m liter 7.0 a constant a with box. at buffered was volumes sphere and areas surface iue 15: Figure - - Upon com pletion of this experim ent (27 days), W ater A was found to have have to found was A ater W days), (27 ent experim this of pletion com Upon T he buffering effects of the flood w ater are clearly seen in Figure 15, where the the where 15, Figure in seen clearly are ater w flood the of effects buffering he T 130.0 110.0 - - - - - 90.0 70.0 50.0 30.0 10.0 10.0 -17.5 - 518 0 - 0 Q -0 Vapor -0 Q o -o Water B Water -o o o—oFlood 6 D relations for E xperim ent 5. W aters A and B had sim ilar ilar sim had B and A aters W 5. ent xperim E for relations D Water AWater -12.5 °/00 in in 8 D n 57 /o n $8 wie tr B ater W while , <$180 °/°o in 5.7 and D Delta 18-0 Delta 75-2.5 -7.5 Analytical Error Analytical ± 0.2 ± 1.0 %a ohD % 5 18-0 67 2.5 68 of this experiment indicates that tritium was enriched in the liquid phase due to evaporation. Fractionation factors calculated from the vapor and liquid tritium concentrations listed in Table 7 yield the following values: day 0=1.053, day 8=1.037, and day 18=1.041, and their mean value is 1.044. Previous studies of the relative vapor pressure of HTO versus H 2 O at 50 °C indicate that the value ranges from 1.057 to 1.063 [Price, 1958; Sepall and Mason, 1960; Smith and Fitch, 1963]. The results of this work thus agree to within about 3 percent of the quoted values. Bubble-Mediated Tritium Exchange-Results Three separate extractions were performed with the same design and air flow rates, but with different initial tritium activities. Run 1 began with about 5,000 TU, and was in operation continuously for 43 days. Runs 2 and 3 began with about 630,000 TU, and lasted 57 days and 26 days, respectively. The air flow rate for all three trials was 15 liters/minute, and was accurate to ± 0.35 liters/minute. The column air stream was found to be at 97-99 percent saturation for all three trials. The total measured evaporation of column waters averaged about 0.34 liters/day. This agrees well with the value estimated from the daily air flow (21,600 liters/day) and the initial relative humidity of the laboratory air (20 percent), which yields about 0.3 liters/day. An average ratio of the water consumed (used to humidify the air stream) to the water treated (30 1) of 1/3 was recorded. The evaporation rate within the exchange vessel itself was 0.09 liters/day, and is attributed to 69 free surface evaporation, as well as transfer of aerosol sized water packets in the saturated effluent, and the slight undersaturation in the air stream. Isotopic Results Table 8 shows the stable isotope results for the three runs of this experiment. The stable isotope results indicate that the liquid phase and the exit vapors were in equilibrium at all times. The fact that equilibrium between the liquid and vapor phase for stable isotopes was observed over a relatively short bubble path length is consistent with the diffusion results of Figures 3 and 4. The calculated fraction ation factors are compared to accepted values of a p = \. 07990, and aiso^l-00923 at 24.5 °C [Baertschi and Thiirkauf ’ 1960; Craig, Gordon and Horibe, 1963]. Comparison of the mean stable isotope fractionation factors calculated for each run (Table 8) reveals only a one-half of one percent deviation from the accepted values for deuterium; the variations in Qie0 are even less. These results confirm that the flux out of the vessel was in stable isotopic equilibrium at all times, and that for a one-stage exchange column of this geometry, the efficiency of the system is at a m axim um . The observed fractionation factors a p and aie0 are graphed in Figure 16 A and B. The mean vapor and water temperatures are both scaled to be viewed on the same graph; little correlation between temperature and fractionation factor is seen. Figure 20 shows only the fractionation factors, and in this graph an overall 70 Table 8: Stable isotopic results of the bubble-mediated exchange experiments. All delta values are in per mil; the fractionation factor alpha is calculated from equation (4) between liquid and exit vapor values. Analytical error: ± 1.0 %o & D , ± 0.2 %> <518 O . Day 618 0 618 0 S180 ais0 6D 8 D <5D OiD col. vapor liquid exit vapor 24.5 °C col. vapor liquid exit vapor 24.5 °C Run 1, 24-5 ± 2 °C rel. hum. >95 % 0 -9.1 -13.0 -22.1 1.00931 -77 -102 -163 1.07288 6 -9.1 -12.2 -21.0 1.00900 -71 -92 -152 1.07075 15 -8.3 -10.8 -19.5 1.00890 -72 -78 -144 1.07710 22 -7.4 -8.7 -18.5 1.00998 -60 -67 -138 1.08237 29 -10.6 -7.2 -17.0 1.00977 -79 -56 -126 1.08009 43 -9.1 -5.0 -13.7 1.00882 -58 -37 -102 1.07238 Mean 1.00929 1.07593 St.Dev. 0.00048 0.0047 Run 2, 24-5 ± 2 °C rel hum. > 95 % 0 -8.9* -13.4 -22.2 1.00893 -79 -104 -170* 1.07356* 9 -9.5 -11.8 -20.6* 1.00899* -77 -90 -145 1.07996 23 -8.0 -9.3 -18.5 1.00972 -66 -71 -135 1.08321 Mean 1.00921 1.07891 St.Dev. 0.00044 0.0049 Run 3 , 24-5 ± 2 °C rel hum. > 95 % 0 -10.4 -13.1 -22.2 1.00931 -86 -102 -165 1.07545 7 -10.1 -12.2 -21.2 1.00919 -76 -91 -156 1.07701 8 - -12.0 -21.0* 1.00930* -77* -90* -155* 1.07710* 9 - -11.7 -20.7 1.00940 -76 -88 -153 1.07647 15 - -10.9 -19.7* 1.00898* -69* -81* -148* 1.07864* 16 -10.3 -10.7 -19.5* 1.00877* -69* -81* -149* 1.07991* 20 -9.1 -9.1 -18.4* 1.00947* -60* -73* -141* 1.07916* Mean 1.00920 1.07768 St.Dev. 0.0025 0.0016 Mean of 3 Runs= 1.00923 1.07751 * values calculated assuming equilibrium conditions, i.e. not measured. 71 1.30 ■ Alpha 0-10, this wortc ♦ Alpha D/H, this worfc ••• Alpha 18*0 at m aan vapor tam p (24.6 C) - Alpha D/H at maan vapor tamp (24.5 C) 1.20 0 0 vapor tamp. /0.0412 W watar tamp. /0.0412 ______ o ra 1.10 l l oc (0 c o o 2 1.00 LL 0.90 0.80 0.010.0 20.0 30.0 40.0 50.0 Time in Days 1.10 B 1.08 o 8 1.06 LL c .2 ■ Alpha 0-18, this work ro c ♦ Alpha 0 , this work o O 1.04 Alpha 0-18 at m ean vapor temp (24.5 C) — Alpha D/H at m ean vapor temp (24.5 C) 1.02 1.00 0.0 10.0 20.0 30.0 40.0 50.0 Time In Days Figure 16: Fractionation factor, time and temperature relations for Run 1 (A). Confidence interval for 6 D in graph B (solid lines) is proportional to mean vapor temperature variation for Run 1. sinusoidal trend in both a p and qib0 is readily apparent. These trends have apparent periods of about 40 days, which are probably related to long-term tern- 72 perature fluctuations within the laboratory. The two solid lines in Figure 16 (B) indicate the range of a o over two degrees C. This range represents the variation in temperatures (liquid and vapor) for the three experiments. The accuracy of the deuterium and oxygen data suggest that the fractionation factors can be measured with a high degree of accuracy. The fractionation factor for D/H can apparently be more accurately measured than that for 18O /160 because the analytical precision for hydrogen is greater. The stable isotope results for all three runs are plotted in Figure 17. -30 -50 -70 o— o Run 1,43 days -90 ►---- ■ Run 2,23 days a — a Run 3,20 days -110 Analytical Error -130 ± 1.0 %o5D ±0.2 %o8 18-0 -150 -15.0 - 10.0 -7.5 -5.0 -2.5-12.5 Delta 18-0 Figure 17: <5180 -<5D graph of the bubble-mediated exchange experiments. The isotopic trends for Runs 1 and 3 begin parallel to the Meteoric Water Line (MWL), and slope away after about 23 days, while the Run 2 data deviate from the 73 MWL at a constant slope of about 7.5. The deviation from a perfectly saturated condition probably indicates free surface evaporation and the lack of absolute saturation in the vapor phase. The relative humidity of the vapor phase ranged from 97-99 percent. Three percent undersaturation (mass flux of water vapor) and also surface evaporation would account the observed loss of water ( %). The tritium results for the three experimental runs are tabulated in Table 9. About 45 percent of the initial tritium of 5,000 TU in Run 1 was transferred to the vapor phase and released. For Run 2, the initial tritium inventory (~630,000 TU) was reduced by 42 percent over a 57 day period. The results for Run 3 (initial tritium concentration = ~630,000 TU) reveal a 24 percent loss over a 26 day period. These results indicate that the extraction efficiencies are a function of initial activity since the design parameters for all three runs were held constant (bubble size, vessel geometry, air flow rate). The results of the tritium analyses of the exit vapors (Table 9) confirm that the exhaust was in constant equilibrium in tritium with the liquid phase. The tritium fractionation factors in column 4, Table 9 each represents the analysis of one vapor-liquid pair using the vapor-extraction unit (Appendix A). The calculated fractionation factors for tritium range from 1.094 to 1.133, and agree to within 6 percent of the generally accepted value of 1.11 at 25 °C [ Jacobs , 1968]. The fractionation factor data in Table 9 confirm the precision achieved with the vapor extraction unit, and suggests that regardless of initial activity studied, the system so designed is in constant equilibrium with respect to tritium. 74 Table 9: Tritium results from bubble-mediated exchange experiments. Day 3H 3H aifi % loss (TU in liquid) (TU in vapor) (24.5 °C ) (3H) Run 1, 24-5 ± 2 °C rel. hum. > 95 % 0 4,492 ± 383 __ — 0 15 3,630 ± 597 —— 19.2 29 3,052 ± 485 —— 32.1 43 2,455 ± 304 —— 45.3 Run 2, 24-5 ± 2 °C rel hum. >95 % 0 626,641 ± 3066 —— 0 26 434,982 ± 2561 —— 30.5 33 388,293 ± 2417 351,043 ± 2106 1.107 38.3 49 376,002 ± 2385 337,827 ± 1501 1.113 40.0 57 361,298 ± 1654 326,645 ± 1950 1.106 42.3 Run 3, 24-5 ± 2 °C rel hum. >95 % 0 630,522 ± 1419 565,863 ± 1345 1.114 0 1 627,681 ± 1411 553,932 ± 1331 1.133 0.05 1.5 624,441 ± 1150 573,039 ± 2060 1.109 0.95 7 583,772 ± 919 — — 7.4 8 576,378 ± 940 — — 8.6 9 567,264 ± 1050 — — 10.0 15 531,789 ± 975 — — 15.7 18 520,117 ± 1112 — — 17.5 23 502,378 ± 702 — — 20.3 26 479,295 ± 670 — •— 24.0 Figure 18 shows the variation of fractionation factor for <518 0 and 6 D with the mean vapor temperature of Run 1. The good fit between the observed (open symbols) and the accepted values for alpha (dashed lines) indicates that the ef ficiency of water transport to the vapor phase can be accurately measured with 75 stable isotopes. 1.10 1.09 1.08 1.07 D/H 2 £ 1.06 •■§ 1.05 TO c o — 1.04 LL. 1.03 1.02 180/160 1.01 1.00 22.0 24.0 25.0 26.0 27.023.0 28.0 Mean Vapor Temperature (C) Figure 18: Correlation between mean vapor temperature and stable isotope frac tionation factors for Run 1. 76 D iscu ssio n The results of the box experiments have shown that the isotopic enrichment or depletion that a water undergoes is limited by the return flux from the ambient atmosphere. A similar condition was found in the dynamic (bubble) experiments in which the mass transfer was limited by the equilibrium observed within the vapor phase over the bubble path. In this section, equations (13), (15) and (21) presented in the introduction are used to calculate gas-side exchange coefficients for the individual waters in the box experiments, and also for the bubble-mediated exchange experiments. Box Experiments For passive exchange (box experiments), the composition of the vapor phase is a controlling factor in the isotopic evolution of waters inside the boxes. The time dependence of the exchange process is defined in equations (13) and (15), from which values for k can be calculated. Time-composition curves from these expressions are drawn for 518 0 trends of each water and are then used to estimate the exchange coefficients. For these graphs, a perfectly symmetrical curve set indicates an initial isotopic balance in composition and volume of waters for a given box. Skewed exchange curves are the result of the chosen variations in initial isotope composition and water volume. The time-518 0 plot for Experiment 1 is shown in Figure 19. 77 12.0 8.0 Water C 4.0 Water B £> CO i 0.0 0) o -4.0 - 8.0 Water A - 12.0 Analytical Error ±0.2 %o5 18-0 -16.0 0 9 18 27 36 45 54 63 72 Time in Days Figure 19: Graph of 6180 versus time for waters A, B, and C in Experiment 1. Water B is close to the calculated isotopic center of mass (dashed line); Waters A and C trend asymptotically towards this equilibrium state. Solid lines are equation (13). The exchange coefficients calculated from equation (13) for this experiment range from 0.12 cm/day to 0.14 cm/day for each isotope. This narrow range of coefficient values indicates the precision with which the exchange process can be monitored in the three-beaker system. The k values are independent of isotopic species, suggesting that the experiments are not sensitive to the small variations in vapor pressure of water molecules differing in isotopic mass. I The four time-618 0 plots for Experiment 2 (Boxes 1-4) are shown in Figures 20, 21, 22, and 23 respectively. Box 1 contained waters with identical surface 78 5.0 Analytical Error ±0.2 %o8 18-0 Water B -3.0 o —o ----- o ------00 -7.0 CD Q - 11.0 Water A -15.0 Vapor -19.0 -23.0 o 9 18 27 36 45 54 Time in Days Figure 20: Graph of #180 versus time for Waters A and B in Box 1, Experiment 2. Isotopic compositions at each sampling time (filled squares) are fitted to equation (13) (solid lines). The calculated isotopic center of mass is shown by the dashed line. Solid lines are equation (15).Vapor values are generally in equilibrium with the liquid at 20 °C . areas and volumes; the k values calculated from equation (15) for both waters and all isotopes ranged from 0.12 cm/day to 0.15 cm/day (Figure 20). The time- composition exchange curves for Box 2 (same volume, different surface areas) are shown in Figure 21, and fall between 0.09 cm/day for Water B and 0.14 cm/day for Water A, for each isotope. The low value for Water B in this experiment suggests a possible limitation of equation (15) at low surface area conditions. However, the exchange coefficients calculated are still extremely well constrained. The time-#18 0 concentration data for Box 3 (different volumes, same surface 79 5.0 Analytical Error Water B ±0.2 %o8 18-0 o.o -5.0 -o- -o — " - 10.0 -15.0 Water A Vapor L i_____ - 20.0 0.0 20.0 40.0 60.0 Time in Days Figure 21: G raph of li180 versus time for Waters A and B in Box 2, Experiment 2. Isotopic compositions at each sampling time are shown by the filled squares, and the calculated isotopic center of mass is shown by the dashed line. Solid lines are equation (15). areas) are graphed in Figure 22, along with curves generated through equation (15). The resulting exchange coefficients k are 0.16 for Water A and 0.14 for Water B. Figure 22 shows a skewed initial composition; since the model correctly accounts for the effects of surface area and volume differences, the underlying k values are the same. This result underscores confidence in k values to describe the exchange of water molecules, regardless of geometry or isotopic composition. The two exchanging waters in Figure 22 came to equilibrium after about 40 days, and then apparently follow a slight evaporation trend shown by the similar enrichment 80 Water B -3.0^•w <5 - 11.0 Vapor -15.0 -19.0 Analytical Error ±0.2 %c8 18-0 -23.0 0 9 18 27 36 45 54 Time in Days Figure 22: Graph of <5180 versus time for Waters A and B in Box 3, Experiment 2. Isotopic compositions at each sampling time are shown by the filled squares, and the calculated isotopic center of mass is shown by the dashed line. Solid lines are equation (15). in both waters. Figure 23 shows the time-^180 relations for Box 4, Experiment 2 (different surface areas, different volumes). From equation (15), a k value of 0.13 cm/day is obtained for all isotopes of Water A. The enrichment trend of Water B is the result of the high evaporation in this low volume (132.5 ml) beaker (80 % over 54 days). The solid line extending from the initial composition of Water B is the path predicted by equation (15) for a k value of 0.12. The convection in Experiment 3 produced very interesting results which are not clear from the 6180 - <5 D graph on page 64. The time-composition exchange 81 4.0 0.0 Water B -4.0 CO I - 8.0 Cl) Q —o -O' - 12.0 Water A -16.0 Vapor Analytical Error ±0.2 %oS 18-0 - 20.0 27 3645 54 Time in Days Figure 23: Graph of d)180 versus time for Waters A and B in Box 4, Experiment 2. Isotopic compositions at each sampling time are shown by the filled squares and the calculated isotopic center of mass is shown by the dashed line. Solid lines are equation (15). curves for Experiment 3 are graphed in both 6 D and 618 0 in Figure 24, from which it is apparent that the isotopic evolution of the two stable isotopes was independently affected, 618 0 being selectively enriched in the fluid phase relative to 6 D . This is emphasized by the dashed line plotted from the initial center of isotopic mass of the system (<5180 = -7.5%o) along a slope of 0.02 °/00618O /day (graph A, Figure 24). Little enrichment is seen is seen in the graph of deuterium (graph B, Figure 24). 82 The preferential enrichment of both waters in <518 0 is accounted for by a kinetic addition to equilibrium fractionation. While this effect is only about 13 percent -6.5 -7.0 O I CO a - 7 - 5 0 Q 0 - 0 W ater B W ater A - 8 . 0 -8.5 Analytical Error ± 1 . 0 % . 8D ±0.2 %«8 18-0 E -55 1 3 •*—'0 3 0 Q B -65 0 ■ Water A o o Water B -75 0 1 0 40 Time in Days Figure 24: <518 0 and S D exchange curves for Experiment 3. Solid lines in lower graph (B) are equation (13). 83 greater for oxygen than for deuterium, an identical kinetic addition will propor tionately affect oxygen more because of the smaller scale upon which the 61S 0 data are resolved. The rate constants for oxygen can still be calculated from these data (it is obtained directly for 6 D ). If the rate of enrichment is thought of as a steady flux, and this trend is subtracted from the data points (normalized to the x-axis) the exchange curves are effectively separated from the influence of evaporation, and are evaluated as before with equation (13). The result of this transform is shown in Figure 25 from which the coefficients of exchange 0.87 cm/day and 0.92 cm/day are calculated for Water A and Water B, respectively. -6 .5 o Water B -7 .0 ■ Water A O 00i © Q -8.0 Analytical Error ±0.2 %o5 18-0 -8 .5 4 0 Time in Days Figure 25: Normalized 618 0 exchange curves for Experiment 3. These values again compare well with the corresponding tritium exchange coeffi- 84 cients, as in previous experiments. The convection within this box clearly caused the seven-fold increase in k observed in Experiment 3 compared to the same surface area-volume trials (Ex periments l,and Box 2 of Experiment 2). Air currents in the laboratory in con junction with the interior convection caused localized condensation to form on the walls, sides and floor of the Plexiglas. This may have allowed water droplets to fall back into the beakers with the effect of returning water of composition Rv back into the exchange waters. The increase in liquid surface area created by the condensing water is not reflected in the isotopic shifts shown in Figure 25, and supports the conclusion that reflux of water in equilibrium with Rv to the beakers does not appreciably affect the mass balance of the system. The exchange curves for Experiment 4 are graphed in Figure 26. An evapo rative trend for the oxygen isotopes is again apparent, as in Experiment 3, and is shown by the dashed line in graph A, Figure 26. This effect is barely visible in the deuterium data (graph B, Figure 26). The slope of the oxygen trend (graph A, Figure 26) indicates that both waters were enriched by 0.13 %oin <5180 per day. These data are normalized to remove the evaporative trends as with Experiment 3, and the results are plotted in Figure 27. The rate coefficients for both waters in Experiment 4, calculated after subtrac tion of the evaporative trends are very similar to those measured for the previous (air flow) experiment. They are: k wafer/i= 0.86, k n/aferB=0.89. This similarity in exchange coefficients is thought to be fortuitous, because of the completely rp () r euto (13). equation are (B) graph Figure 26: 26: Figure ifrn cniin wihn hs to xei ns Te i -o oiin curves position e-com tim The ents. experim two these ithin w conditions different Delta Deuterium -150 0 1 1 -70 -30 0 1 - 15 618 5 0 0 and and 0 0 6 D exchange curves for E xperim ent 4. Solid lines in lower lower in lines Solid 4. ent xperim E for curves exchange D 0 1 i i Days D in e Tim 0 2 Wtr B Water o o - o ■ - « W ater A ater W « - ■ ■ Water A Water ■ W ater B ater W 30 Analytical Error Analytical ± 0.2 ± 1.0 40 %chD 8 18-0 50 85 86 ■ Water A o Water B O CO •*—Ito 0) Q -11 -13 Analytical Error ±0.2 %o5 18-0 -15 32 Time in Days Figure 27: Normalized S18 0 exchange curves for Experiment 4. for Experiment 5 are the most symmetrical of all, because of the flood water used to condition the box air. The overwhelming buffering effect of the flood water is apparent in Figure 28, in which the <518 0 exchange curves for Experiment 5 are shown. The symmetry of these curves about the indicated center of mass confirms that the observed exchange was controlled exclusively by the buffered vapor phase. Condensation of water vapor onto the box walls occurred in this experiment also. It is likely that some water did return, however, this is a random function of the dripping condensation related to the surface area available for the return. Since the surface area of the floor of the box is approximately 21 times the combined -20 Water B -40 2 — O------O =} Q) -60 <£--0 <><>-^>-0-O-<>._ _ 0------o------Q 4-*CO CD Q -80 Water A -100 Analytical Error ±1.0 %oSD -120 0 4 8 12 16 20 24 28 Time in Days Figure 28: 6180 exchange curves for Experiment 5. Solid lines are equation (13). surface area of the beakers, it probably had only a small effect on the bulk com position of the beaker liquids. Summary of Observed Passive System Rate Constants The exchange coefficients calculated for the oxygen data in all box experiments are summarized in Table 10. The values of k for Experiments 1 and 2 suggest excellent reproducibility of these experimental values. The anomalously low value observed for Experiment 2, is thought to be a function of the flat curves found in that experiment, and may be related to a limiting condition of Sx/Vx for which equation (13) is no longer applicable. The similarity between the k values calculated for the two high-temperature experiments (4 and 5) and the air flow 88 Table 10: Exchange Coefficient Summary for Box Experiments Experim ent Box W ater Lt k(cm/day)-f A 0.156 0.12 1 1 B 0.156 0.13 C 0.156 0.14 1 A 0.134 0.15 B 0.134 0.12 2 A 0.029 0.14 2 B 0.029 0.09 3 A 0.336 0.16 B 0.336 0.14 4 A 0.073 0.13 B 0.073 0.09 3 1 A 0.134 0.87 B 0.134 0.92 4 1 A 0.134 0.86 B 0.134 0.89 5 1 A 0.134 0.86 B 0.134 0.84 f Surface area-volume ratios calculated from equation (13) for Experiments 1,3,4,5, and Box 1 of Experiment 2, and from equation (15) for Experiment 2, Boxes 2,3, and 4. t quoted values are for 6180 ; <5Dand tritium values are similar. experiment (Experiment 3) is thought to be coincidence. However, since these three experiments all involved some degree of change at the air-water interface compared to the quiescent, low temperature trials, it is possible that the sim ilar values are a real indication that the exchange processes for these different situations were comparable from a kinetic point of view. T he k values for the high temperature experiments ( 4 and 5) are about 7 times larger than for the room temperature experiments. This is probably related 89 to the differences in vapor pressures. For example, the vapor pressure of water at 22 °C is ~22 mm Hg, and that at 52 °C is ~103 mm Hg, yielding a ratio of 5.2. The corresponding ratio of k values for the 52 °C and 22 °C cases is 6.8. These values compare reasonably well, and could be used to further investigate the dependence of transport on water vapor pressure for the individual isotopes. The rate constants calculated for the box experiments indicate that the process of isotope transfer under high humidity conditions is species independent. This may mean that the resolution of the experimental data is insufficient to discern the actual differences in equilibrium vapor pressures. Alternatively, these differences in vapor pressure may simply be insignificant under the conditions imposed within the boxes. Influence of Sa'/Vx and Temperature on k To summarize the discussion of k values for the box experiments it is helpful to quantify the influence of the two major parameters controlling the box envi ronments on the exchange coefficient k, namely surface area-volume relations and temperature. The process of isotope exchange as defined in this work is predi cated on a isotopic difference between the liquid and the vapor phase. Without a reasonable difference in isotopic composition, the exchange rates would simply not be measurable. Consider a dimensionless disturbance to be a proxy for the difference in isotopic composition driving the exchange process. When this dis turbance is plotted against time as a function of the parameter k for a given value of L = Sx/Vx, an indication of the relative influence of the surface area-volume 90 ratio on the parameter k is obtained. This situation is shown in Figure 29, in which the values of L=0.029, 0.073, and 0.336 are plotted over a 300 day time period. It is apparent from this graph that rates of exchange will increase the larger the surface area to volume ratio of a water body. — k=0.13, L=0.029 — k=0.13, L=0.073 k=0.13, L=0.336 0.0 0 50 100 150 200 250 300 Time in Days Figure 29: Influence of surface area/volume relationship on the value of k. The ratio of the smaller L values is about 2.5, and the time required to reach y=0.5 (50 percent equilibration) is about 2.7, indicating that the influence of these surface area-volume ratios on k is relatively small. The ratio of the two larger values of L is about 4.6, and their corresponding ratio of time of approach to y=0.5 is about 0.166, suggesting that once the surface area-volume ratio reaches 91 a certain threshold, its influence on the rate of equilibration increases. Similarly, a plot relating the influence of temperature on the observed differ ences in k is shown in Figure 30. The ratio of equilibration times for the two values of k of 300/5 ~6 is estimated. 1 — Temp.=22 C, k=0.13, L=0.134 — - Temp.=55C, k=0.88, L=0.134 oCD c JOas 3 4-»W 0 b 'c ID 0 50 100 150 200 250 300 Time in Days Figure 30: Influence of temperature on the value of k. However, the ratio of temperatures for the two values of k plotted is only 2, indicating that the increase in temperature has a profound effect on the rate of equilibration for the same surface area-volume relationship. While these results seem somewhat intuitive, they quantify the influence of temperature and L on the observed rates, and could possibly be used to further 92 investigate the rates at which the surface area-volume ratio of a body of water responds over time to different forcing agents. Also, with only two data points for the high temperature experiments, it was not possible to derive a rate equation which incorporates temperature. However, the direct correlation with temperature suggests a more fundamental relationship between the exchange coefficient and vapor pressure. Indeed, the ratio of k values to the ratio of vapor pressures is about unity. Comparison of Box Results with Rayleigh Distillation The deuterium results for Experiment 1 are plotted in Figure 31 against the Rayleigh distillation curve which indicates the isotopic evolution of a water for an open system in which the vapor phase is continually renewed. The comparison between the two end-member processes reveals little or no correlation. It is evident that batch distillation had little effect on the evolution of these three waters, and that the control of the observed isotopic shifts is a function of their common end point value, i.e. R^ = constant, in this case. Figure 32 shows a similar plot, except that the results of Experiments 3 and 4 are shown, along with the same Rayleigh curve. Figure 32 indicates that even for those waters undergoing appreciable evap oration (Experiments 3 and 4), the effects of exchange still produce trends not predicted by the Rayleigh curve. The comparison of the experimental results with the Rayleigh curve is a bit misleading, in that this curve is derived for a completely open system in which the developed atmosphere is continuously swept away. Figure 32: Results of Experim ent 3 and 4 as a function of F/. E xperim ent 4 was was 4 ent xperim E F/. of function a as 4 . and 3 °C 52 ent at Experim of conducted Results 32: Figure Delta Deuterium Delta D euterium - - 200.0 200.0 .0 0 0 4 600.0 200.0 200.0 .0 0 0 4 600.0 0.0 0.0 0.0 Figure 31: Results of Experim ent 1 as a function of F/. of function a as 1 ent Experim of Results 31: Figure 0.0 R ayleigh Distillation C urve at 2 1 .5 d e g re e s C. s e re g e d .5 1 2 at urve C Distillation ayleigh R yeg Dsilto Cuv at21. degr C. s e re g e d .5 1 2 t a urve C Distillation ayleigh R 0.2 0.2 . 0. . 06 0.7 0.6 0.5 .4 0 0.3 . 0. 5 06 0.7 0.6 .5 0 .4 0 0.3 rcin f iud maining em R Liquid of Fraction ato o Lqi maining em R Liquid of raction F O — O W ater B, Experiment 4 4 Experiment B, ater W O — O O O Water A, Experiment 4 Experiment A, Water O O A v ------A Water A, Experiment 3 Experiment A, Water A ▼ W ater B, Experiment 3 Experiment B, ▼ ater W 0.8 0.8 -o W ater C ater W -o -A A ater W -o W ater B ater W 0.9 0.9 93 94 However, the comparison does illustrate the idea that distillation for an evaporat ing body of water can be modified, limited, or even completely reversed depending on the magnitude of the isotopic disturbance and the water vapor concentration. The observed limiting forces within the box experiments are the end-point isotopic composition of the system, and the kinetics of the actual interfacial transfer. Bubble-mediated Exchange The increase in k for exchange processes at different vapor pressures implies that the water transfer is dependent on vapor pressure. Thus for the exchange by bubble aeration, isotope mass transfer should also be proportional to temperature. Isotopic equilibrium for the isotopes of hydrogen and oxygen was found be tween the exchange vessel liquid and the exiting vapor at all times during the three experiments. Measurements of 6 D and 8l80 in both liquid and vapor phases revealed that isotopic equilibrium was attained within the length of the bubble path, indicating that the exchange efficiency for these isotopes was at or near 100%. The changes in stable isotope composition of the vessel water during Run 1 are plotted in Figure 34. The curves were drawn using equation (13), to which the constant is not applied. Therefore, k has the units of 1/day, and is observed to range from 0.023/day to 0.027/day for both isotopes, which agrees well with the results from the box experiments when the same units of k are employed. The similarity in k values between the box and bubble-mediated experiments suggests that the 95 - 2 0 -40 -60 -80 cd Q -100 -120 - 3.0 O co - 7.0 CO CD - 15.0 0 10 20 30 40 50 Time in D ays Figure 33: <518 0 -6 D graph of the bubble-mediated exchange experiments. Solid lines in both (A) and (B) are equation (13). process of isotopic exchange is similar in both cases. Analysis of loss rates for the bubble-mediated exchange experiments indicates that for a given geometry, and once isotopic equilibrium is attained, the flow rate C/Co rkn ie ae qain 2) rw fr h idctd aus far lw rates. flow air of values indicated the for drawn (21) equation are lines Broken iue 4 Vaito i tii ocnrto oe tme o Rn 1 2 ad 3. and 2, 1, Runs for e tim over concentration m tritiu in ariation V 34: Figure at 15 liters/m in u te, while th e d a ta from Run 1 are in good agreem ent w ith this this ith w ent agreem good in are 1 (21) Run equation from by ta a d e th odel. predicted m while trend te, u the in from liters/m deviate 15 2 at Run for ta a d he T rate. flow Figure 34; the broken lines are equation (21) drawn for the indicated values of air air of values indicated the for drawn (21) equation are lines broken the (21). 34; Figure equation by predicted as transfer mass isotope the controls air of 0.0 0.2 0.4 0.6 0.8 1.0 e eito o Rn fo te is ad hr rn (n t t rdce by predicted at th (and runs third and first the from 2 Run of deviation he T T he difference in the rates of tritiu m removal for all three runs is graphed in in graphed is runs three all for removal m tritiu of rates the in difference he T 0 10 20 30 7 liters/min 70 . iei Days in Time 050 40 A— A Run 3, Go= 630,000 TU Go=630,000 Run A3, A— 0—0 ■— ■Run 2; Co= 630,000 TU 630,000 Co= 2; ■Run ■— Run 1; Co= 15,000 TU 15,000 Co= 1;Run 7 liters/min 7 5 liters/min 35 60 15 liters/min 15 70 96 80 97 equation (21) for 15 liters/minute, Figure 34) appears constant, and suggests a systematic error such as flow rate for this run. There may also be a threshold up to which equation (21) can be applied without some type of adjustment for the geometry or scale of the process. The late-time data for Run 2 trend along an apparent flow rate curve of about 12.5 liters/minute in Figure 34. Insufficient data are collected from the third run to assess the precision (comparison with Run 2) of extraction at high (>600,000 TU) initial concentrations. However, from Figure 34, Run 3 appears to have a slightly higher initial extraction rate than Run 2. Figure 35 shows the natural log relations between the fractional approach to equilibrium in tritium with the observed values for k . -0.52 Run 3 -0.54 Run 2 8 o c -0.56 -0.58 Run 1 -0.60 -1.50 -1.45 -1.40 -1.35 -1.30 -1.25 In k Figure 35: Variation of fractional approach to equilibrium for the three bubble- mediated experiments. The observed linear correlation indicates that the system behaves exponentially, and that the variation of the approach towards equilibrium appears steady even 98 with different initial isotopic compositions. 99 Applications to Hydrology and Future Research The results of this research clearly indicate that the process of exchange is an important mechanism which can control the isotopic evolution of water and water vapor. The application to hydrology centers on combining the two end-member cases of evaporation into a zero humidity environment and exchange at saturation so that environmental conditions can be modeled. It is possible then, to imagine a model which incorporates the necessary evap orative component of natural systems which is then modified by a bulk return flux term, analogous to the k parameter of the box experiments. This is the goal of a recent study, in which the evaporation from a single source is coupled through the atmosphere to a downstream or downwind water body [Gat and Bowser , 1991]. These researchers found that heavy isotope enrichment of the liquid phase re mains considerable at low humidities, but becomes increasingly overwhelmed by atmospheric return flux at humidities greater than 50 percent. Cave Systems The most direct application of this work to a natural system may be to a high humidity, low air flux situation, such as found in most caves. The process of isotope exchange between ambient vapor and a cave pool system was identified within Carlsbad Caverns by the stable isotope composition of drip water, pool water and vapor samples [ Ingraham, Chapman and Hess , 1990]. Measured conditions within the cave indicated maximum temperature fluctu 100 ations of ~6 °C , and relative humidities of between 90 and 95%. The reported deviations in stable isotope ratios from those expected at isotopic equilibrium be tween water and vapor within the cave (up to 6 %o depleted in 6D, and 2.5 %o more depleted in 618 O ) were interpreted as being caused by a kinetic addition to equi librium fractionation. The degree of stable isotopic enrichment reported in the cave pools was found to be limited by exchange of water vapor with the pools, which, in a feedback loop, is controlled by the liquid phase. A high degree of such control was observed in the box environments, and it can be expected that this control begins to fade the more open a system becomes. Terminal Lakes Lakes are complex water systems which are often valuable in isotopic studies because of the combinations of hydrologic relationships present. They and their surroundings are, in a sense, a microcosm of the hydrologic cycle, and may be chosen for study based on some unique characteristic such as high evaporation or unique chemical composition. A terminal lake is one for which water loss by evaporation equals total outflow, and represents an additional hydrologic system which may illustrate the importance of isotopic exchange. Losses to the groundwater system by seepage, pumping losses or other outflows are assumed negligible or non-existent. If a condition of isotopic steady state is assumed for the terminal lake scenario, then the inflow composition (river) should equal the outflow composition (evaporation). The composition of the lake is then related by the fractionation factor plus a kinetic addition, to the inflow 101 composition. The hypothesis that a given lake is indeed a terminal lake is tested here by a simple analysis of inflow and lake isotope compositions, and evaporation and water input estimates. As an example, Pyramid Lake is thought to be a terminal lake [ Galat et al., 1981; Peng and Broeker, 1980; Whitehead and Feth, 1961], and is situated in northwest Nevada. This lake is a descendent of Lake Lahonton, a major Pleis tocene lake of the Great Basin. The headwaters of the Truckee River, Pyramid Lake’s only permanent surface water source, arise in the Sierra Nevada moun tains of eastern California and western Nevada. The Truckee River starts at Lake Tahoe, then trends in a northeastern direction for 190 km until discharging into the south end of Pyramid Lake, which lies about 90 km east of Reno, Nevada. The lake is 40 km long and varies from 6.5 km to 16 km in width, having a surface area of about 450 km2. The mean depth of Pyramid Lake is 59 m, with a maximum of about 100 m, giving an estimated volume of 27 km3 [Galat et al., 1981], and a surface area-volume ratio of 17 m. An estimate of 120 cm/year evapo ration for this lake appears stable over the last 25 years [ Galat et al., 1981; Harding, 1965]. This gives a averaged volumetric evaporative loss of about 5.3aT08m3/yr based on the above surface area. In non-drought years, the area receives only about 15 cm of precipitation annually, which includes 25-30 cm of snowfall. The years 1986 through 1989 were drought years in which approximately one-half to two-thirds normal precipitation was recorded [Bostic et al., 1991; Pupacko et al., 1988; Pupacko et al., 1989; Pupacko et al., 1990]. 102 To test the hypothesis that Pyramid Lake is a terminal lake, estimates of the inflow of water to the lake for the years 1986-1989 are necessary. Direct discharge measurements at the staging station at Nixon, Nevada (16 km upstream from Pyramid Lake) are not considered representative because several dams exist between the station and Pyramid Lake from which agricultural water is diverted. A better estimate of the actual inflow to the lake is obtained by adjusting the known lake volume for precipitation and evaporation for the years of interest. The changes in Pyramid Lake volume for the years 1986-1989 are shown in Table 11, along with the estimated discharge of the Truckee River into Pyramid Lake (inflow). Table 11: Changes in water content, evaporation and inflow, Pyramid Lake. Year A l/ f E-P t inflow * (108m 3/y r) (108m 3/y r) (108m 3/y r) 89 4.7 5.0 0.3 88 4.2 5.0 0.8 87 5.0 5.0 0.0 86 2.6 5.0 2.3 t change in volume of lake t evaporation - precipitation * net inflow estimate of Truckee River to Pyramid Lake. From Table 11, it is seen that the evaporation is about 2-5 times that that of the influx of water to the lake. From these estimates, Pyramid Lake was appar ently dessicating, and did not represent a terminal lake over the years 1986-1989. For these years, a residence time of about 50 years is estimated. Larger inflow 103 values are obtained for earlier (non-drought) years, during which the condition of inflow=evaporation apparently holds. The stable isotopic composition of the Truckee River has been reported as -85 °/oo 8 D and -10 %o 6180 , while the lake itself measures -35 %o 6 D and -0.9 %o 618 0 [McKenna et al., 1992]. If Pyramid Lake is indeed a terminal lake then the condition E8 e = I8 i + P8p (22) where E denotes evaporation, I is the inflow, and P is the precipitation should hold true. For this condition then, the lake composition should be defined by the inflow composition and the appropriate fractionation factor. The condition for a terminal lake can be tested by applying equation (4), and using the known inflow composition and a reasonable fractionation factor (evaporation at 10 °C , a= 1.098). For these inputs, equation (4) yields a lake composition of + 5 %o 8 D . This value would be even more enriched if corrected with a kinetic addition, but for purposes of estimation, however, it is clear that the calculated isotopic composition of the lake (dD= +5 %o ) is ~40 %o more enriched that the observed values for the lake 8 D = -35 °/°o . The isotopic relations for the lake system are shown schematically in Figure 36; the upper part of this graphic shows the various isotopic components, and the lower is an isotopic composition line showing the observed values along with the composition calculated when equation (22) holds true. 104 It is apparent from Figure 37 that isotopically speaking, Pyramid Lake does not represent a terminal lake; nor does it represent a dessicating lake based on isotopic composition. i 6 , Inflow" “ 85 (^served) Lake - —35 (observed) t ______I + 5 = 6 Lake (calculated for lnflow = Evap) 40 per mil exchange hypothesis Figure 36: Schematic of Pyramid Lake isotope system. A dessicating lake would have isotopic compositions which follow some form of Rayleigh fractionation, and be possibly more enriched than the +5 %o calculated for the terminal condition. The discrepancy between the observed value of the 105 lake composition and that calculated based on equation (4) can be attributed to exchange with the atmosphere in which the expected composition for the lake (+5 °/oo in 8 D ) is never reached because of buffering effects of exchange. The loss of lake water to the groundwater system could contribute to the observed depletion in stable isotopes relative to a closed system. This analysis is simplified and subject to the typical errors of estimation and isotope analysis. However, explaining the very large (40 %oin 8 D ) discrepancy between the calculated and observed lake compositions clearly requires that more than estimation errors be invoked. Field Prototype for Tritium Remediation The results of the bubble-mediated exchange experiments confirm that the mass-transfer rates for tritium are a function of air flow. Any desired increase in the mass transfer rate would thus require a greater air flow rate, since the system is highly efficient in stable isotope and tritium equilibration. In order to increase the efficiency for field use, the air flux should be increased within a multi-stage extraction design. The design and implementation of a field pilot plant using this method of remediation is currently underway. Future Research Future research in the areas of isotope exchange, water-vapor transport and cy cling throughout the hydrosphere is a key element for being able to unify the end-member concepts of exchange and evaporation. The complexity of hydrody 106 namics and climatology at the various scales of interest must be clarified if current models of atmospheric chemistry and mechanics (e.g. Global Circulation Models) are to properly account for natural changes and variability within the hydrologic cycle. Listed below are current and possible research ideas which may further our understanding of exchange within the hydrologic cycle. 1 Experimentation to determine exact control of temperature on exchange. 2 Multi-season cave study. 3 Climatological and hydrodynamic study of water vapor and isotope transport through hydrosphere. 4 Tritium remediation pilot study (underway). 107 Summary and Conclusions This work provides new data on the transfer of isotopes between water and water vapor based on the available surface areas, volumes and temperatures. Two experimental methods have been used to evaluate the transfer of water isotopes between liquid and vapor using stable isotopic compositions (6180 and £D ) and tritium activities under controlled conditions. The rate of isotope transfer was modeled based on surface area, temperature, and initial composition for quiescent conditions at high humidities. Isotope exchange progresses via the vapor phase until the liquids reach isotopic equilibrium. The transfer of water was quantified with an exchange coefficient k [Criss, Gregory and Taylor, 1987] which ranged from 0.09 to 0.19 cm/day at 22 °C , and from 0.86 to 0.92 cm/day at 52 °C . The value of k for oxygen and hydrogen as well as tritium was found to be constant for each experiment indicating that for bulk analysis under quiescent, humid conditions, the three isotopes behave similarly. For the case of identical surface areas and volumes, exponential shifts toward an isotopic state of equilibrium are controlled by a constant isotopic composition of the vapor phase. For the case of different surface area-volume relations, the composition of the vapor at any time will change as equilibrium is reached. The mean end-point vapor composition in this case is controlled by the surface area and volumes of exchanging waters. The bubble-mediated isotope exchange method appears a promising alterna 108 tive to traditional approaches in the extraction or isolation of tritium from liquid water. Results of both stable isotope and tritium analysis indicate that the ex haust vapors were in isotopic equilibrium with the liquid at all times during the three experiments, suggesting isotopic equilibration times of about 2 seconds. This is consistent with the results of water vapor diffusion analysis within a small, hol low sphere in a continuous medium. Thus any increase in extraction efficiency must be derived from changes in the rate of air flow, and stage configuration. About 50 % of the tritium activity was removed from the (30 liter) liquid phase over a 40 day period. A constant 15 liter/minute flux of input air (water saturated, TU <10 ) was found to equilibrate in 618 0 , 8 D , and 3H over a 20 cm bubble path. Initial liquid tritium activities of 5,000 TU and 630,000 TU were both found to isotopically equilibrate with the vapor stream under identical conditions. The stable isotope evolution of the exchange water has been modeled mathe matically to show that the fractional approach to equilibrium is a function of the initial composition of the vapor phase, and the isotopic gradient between the two phases. The rate of tritium transfer was evaluated by mass-balance; these results confirm the dependence of mass transfer on the air flow rate. The efficiency of the exchange process is a function of isotopic equilibration between bubble and bulk water, and is dependent on bubble size, contact time, diffusivity of water vapor, and isotope gradients. Pyramid Lake presents an isotopic enigma; the hypothesis of isotope exchange with the atmosphere is argued to explain the discrepancy (40 °/00) between ob 109 served isotope compositions and those calculated for a terminal lake. Groundwater leakage from the lake is another scenario which could help explain this finding. A reasonable extension of the experimental work of this investigation would be the study of a natural system with humidity and temperature regimes similar to those of the laboratory conditions used here. For this purpose, caves in which air flow is minimized, and temperature and humidity are approximately constant are perfect natural laboratories. The goal of studying air-water interactions is to better understand the flux of water vapor and its role within the hydrologic cycle. Pure isotope exchange represents an end-member case of the larger process of evaporation. In order to apply the concept to hydrologic studies, the two pure processes (exchange and evaporation) must be combined to account for their individual contributions to water-vapor fluxes. 110 R eferen ces Atkins, P. W., Physical Chemistry (fourth edition), W. H. Freeman and Company, New York, 1990. Baertschi, P. and M. Thurkauf, Isotopie-EfFekt fur die Trennung der Sauerstoff- Isotopen 16-0 und 18-0 bei der Rektifikation von leichtem und schwerem W asser, Helvetica Chim. Acta, 43, 80-89, 1960. Blaney, H. F. and W. D. Criddle, Determining water requirements in irrigated areas from climatological and irrigation data , USDA Soil Conservation Service Technical Paper , No.96, 48, 1950. Bostic, R., D. Hitch, L. VanGordon and R. Swanson, Water Resources Data Nevada, Water Year 1990, U. S. Geological Survey Water-Data Report, NV-90-1, 357,1991. Brutsaert, W., A theory for local evaporation (or heat transfer) from rough and smooth surfaces at ground level, Water Resources Research, 11 , pp. 543, 1975. Carslaw, H. S. and J. C. Jaeger, Conduction of Heat in Solids, Oxford University Press, Oxford, 1986. Chamberlain, A. C., Radioactive Aerosols, Cambridge University Press, 1991. Chamberlain, A. C. and A. E. J. Eggleton, Washout of tritated water vapour by rain, International Journal of Air, Water Pollution, 8, 135-149, 1964. Craig, H., Isotopic variations of meteoric waters, Science, 133, 1702-1703, 1961. Craig, H. and L. Gordon, Deuterium and oxygen-18 in the ocean and the marine atmosphere, Spoleto, 165, 121, 1965. Craig, H., L. Gordon and Y. Horibe, Isotopic exchange effects in the evaporation of water: low temperature results, Journal of Geophysical Research, 68, 5079-5087, 1963. Criss, R. E., R. T. Gregory and H. P. Taylor, Kinetic theory of oxygen isotope exchange between minerals and water, Geochimica et C'osmochimica Acta, 51, 1099-1108, 1987. Dansgaard, W., The isotopic composition of natural waters, Spoleto, 165, 120, 1961. Ill Dugan, J. P., J. Borthwick, R. S. Harmon, M. A. Gagnier, J. E. Gahn, E. P. Kinsel, S. Macleod, J. A. Viglino and J. W. Hess, Guanidine hydrochloride method for determination of water oxygen isotope ratios and oxygen-18 fractionation between carbon dioxide and water at 25 degrees C., A nalytical Chemistry, 57, 1734-1736, 1985. Ferronsky, V. I. and V. A. Polyakov, Environmental Isotopes in the Hydrosphere, John Wiley and Sons, 1982. Friedman, I., L. Machta and R. Soller, Water-vapor exchange between a water droplet and its environement, Journal of Geophysical Research, Vol 67, No. 7, 2761-2766, 1962. Friedman, I., A. C. Redfield, B. Schoen and J. Harris, The variation of the deu terium content of natural waters in the hydrologic cycle, Reviews of Geo physics, 2, N o .l, 177-203, February, 1964. Galat, D. L., E. L. Lider, S. Vigg and S. R. Robertson, Limnology of a large, deep North American terminal lake, Pyrimid Lake, Nevada, Hydrobiologia, 82, 281-317, 1981. Gat, J., The isotopes of hydrogen and oxygen in precipitation, in Handbook of Environmental Isotope Geochemistry, I, 21-48, 1980. Gat, J. R. and C. Bowser, The heavy isotope enrichment of water in coupled evaporative systems, in Stable Isotope Geochemistry: A tribute to Samuel Epstein, The Geochemical Society, Special Publication No 3, 1991. Gilath, C. and R. Gonfiantini, Lake Dynamics, in Guidebook on Nuclear Tech niques in Hydrology, IAEA Technical Report Series No. 91, 1983. Harding, S. T., Recent variations in the water supply of the western Great Basin, University of California, Berkeley, Water Resources Center Archives Re port, 16, 226, 1965. Horton, J. H., J. C. Corey and R. M. Wallace, Tritium loss from water exposed to the atmosphere, Environmental Science and Technology, 5, 338-343, 1971. IAEA, Stable Isotope Hydrology: Deuterium and Oxygen-18 in the Water Cycle, in Technical Report Series No.210, Gat, J.R. and Gonfiantini (eds), Vienna, 1981. Ingraham, N. L., J. B. Chapman and J. W. Hess, Stable isotopes in cave pool systems: Carlsbad Cavern, New Mexico, USA, Chemical Geology (Isotope Geoscience Section), 86, 65-74, 1990. 112 Ingraham, N. L. and R. E. Criss, The effects of surface area and volume on the rate of isotopic exchange between water and water vapor , in preparation. Jacobs, D. G., Sources of Tritium and its Behavior upon Release to the Environ m ent, Atomic Energy Commission Critical Review Series, TID-24635, 90, 1968. Kendall, C. and T. Coplen, Multisample conversion of water to hydrogen by zinc for stable isotope determination, Analytical Chemistry, 57, 1437-1440, 1985. Liss, P. S., Process of gas exchange across an air-water interface, Deep-Sea Re search, 20, 221-238, 1972. M cKenna, S. A., N. L. Ingraham , R. L. Jacobson and G. F. Cochran, A stable isotope study of bank storage mechanisms in the Truckee River Basin, Journal of Hydrology, 134, 203-219, 1992. Merlivat, L. and M. Conantic, Study of mass transfer at the air-water interface by an isotopic method, Journal of Geophysical Research, 80 (24), pp. 3455, 1975. Motarjemi, M. and G. J. Jameson, Mass transfer from very small bubbles-the optimum bubble size for aeration, Chemical Engineering Science, 33, 1415— 1423, 1978. Murphy, C. E., The transport, dispersion and cycling of tritium in the environment (U ), Westinghouse Savannah River Company Report, WSRC-RP-90-462, 70, 1990. O’Neil, J. R., Theoretical and experimental aspects of isotopic fractionation, Rev. Mineral. , 16, 1-40, 1986. Peng, T. H. and W. Broeker, Gas exchange rates for three closed-basin lakes, Limnol. Oceanogr., 25(5), 789-796, 1980. Penman, H. L., Natural evaporation from open water, bare soil, and grass, Proc. Roy. Soc. A., 193, 120-145, 1948. Prantl, F. A., Isotope balances for hydrologic systems, Pure and Applied Geo physics, 112, 209-218, 1974. Price, A. H., Vapor pressure of tritiated water, Nature, 181, 262, Jan 25, 1958. Pupacko, A., R. J. LaCamera, M. M. Riek and J. R. Swartwood, Water Resources Data Nevada, Water Year 1987, U. S. Geological Survey Water-Data Re port , NV-87-1, 250, 1988. 113 Pupacko, A., R. J. LaCamera, M. M. Riek and J. R. Swartwood, Water Resources Data Nevada, Water Year 1988, U. S. Geological Survey Water-Data Re port , NV-88-1, 265, 1989. Pupacko, A., L. VanGordon, J. R. Swartwood and R. P. Collins, Water Resources Data Nevada, Water Year 1989, U. S. Geological Survey Water-Data Re port , NV-89-1, 332, 1990. Schrag, D. P., D. J. DePaolo and F. M. Richter, Oxygen isotope exchange in a two-layer model of oceanic crust, Earth and Planetary Science Letters, 111, 305-317, 1992. Sepall, 0. and S. G. Mason, Vapor/liquid partition of tritium in tritiated water, Canadian Journal of Chemistry, 38, 2024-2025, 1960. Slinn, W. G. N., L. Hasse, B. B. Hicks, A. W. Hogan, D. Lai, P. S. Liss, K. 0. Munnich, G. A. Sehmel and 0. Vittori, Some aspects of the transfer of atmospheric trace constituents past the air-sea interface, Atmospheric Environment, 12, 2055-2087, 1978. Smith, H. A. and K. R. Fitch, Determination of the separation factor for the vaporization of mixtures of protium and tritium oxides, Journal of Physical Chemistry, 67, 920-921, 1963. Thornthwaite, C. W. and B. Holzman, Measurement of evaporation from land and water surfaces, U. S. Dept. Agr. Technical Bulletin , No. 817, 75 pp., 1942. Treybal, R. E., Mass-Transfer Operations, McGraw-Hill, 1968. Whitehead, H. C. and J. H. Feth, Recent chemical analysis of waters from sev eral closed-basin lakes and their tributaries in the western United States, Geological Society of America Bulletin, 72(9), 1421-1425, 1961. Whitman, W. G., Chem. and Met. Eng., 29, 147, 1923. 114 A p p en d ix A Vapor Extraction for Tritium Analysis This appendix describes the design and use of the water-vapor extraction unit used to draw vapor samples from the exit vapors of the bubble-mediated tritium exchange experiments. Four glass finger tubes were connected in series by vacuum tubing to form the main trap. The tube lengths (20 cm.) and diameters (2.5 cm) provided a large surface area to allow condensation of the water vapor without ice clogging. The finger diameter within each tube was 1 cm. The unit was fitted at each end with teflon vacuum stopcocks for isolation of the unit after the sample extraction. Trial vapor extractions with the unit indicated that while no ice clogging oc curred, there was insufficient surface area to completely isolate the entire fraction of water from the air stream. To increase the surface area of the unit, a 230 cm length of 0.75 cm diameter copper tubing was coiled around a 4 cm form, and con nected to the main trap by means of vacuum tubing, to create a secondary trap. A small, single-bend glass U-trap was added (behind the two large traps) as a visual check for water that may have passed through the main traps. Throughout both the trial and actual extractions, little or no water was found to condense in the glass U-trap. The extraction unit had a total interior volume of approximately 0.56 liters, and an interior surface area of approximately 1000 cm2. A critical requirement for high efficency extraction of water vapor from a 115 moving air stream is a low flow rate across the unit. The constant 15 liters/min air flow rate would have overwhelmed the ability of the cold-trap unit to extract the total water fraction. Different air flow rates were tested; a flux of 1.5 liters/minute was found to be low enough for the extraction efficiency to remain high. The air flow across the unit was regulated by means of an in-line gate valve, and measured with a low-flow, glass-bead rotometer. A check valve fitted in at the outflow end of the unit maintained the integrity of the flow direction. To obtain a sample, the air flow through the system was reduced to 1.5 liters/minute, and the extraction unit attached to a reducer on the containment vessel exhaust vent. The unit was immersed in a C02-acetone slush, and then opened to the air flow for a period of about 50 minutes. After sample collection the unit was closed, connected to a vacuum extraction line, and the sample slowly isolated using a liquid nitrogen cold trap. The sample was then transferred to a pre-weighed glass ampule, flame sealed, and weighed on an analytical balance to determine the mass of the sample. 116 A p p en d ix B The derivation of equation (10) is as follows (notation is the same as in the text): After separation of variables, equation (10) can be written dRx — —K • dr Rx — Rm in which the substitution I<=k(p*-) is made for simplification since the surface areas and volumes are constants under the stated assumptions. After writing the integrals and applying limits of integration this expression becomes t Rx(t) d R x _ _ rl K ■ dr (23) JRi R x ~~ R m Jo Introducing the substitution u= R a -R m yields du=dR* and the following inte gration limits: for R a'= R 2, u= R ,-R m , and for RA=RA'(t)> u=Rx(t)-RM- Now, equation (23) can be written as R-xW-R-m du = - K f dr fJ r , R m u Jo and the solution is Rx(t)—R\t In u = —K • r Ri-Rm Introducing the limits of integration yields / Rx (Q ~ Rm 1 _ R x { t) - R m In —I< • (t - 0) = exp (—K ■ t) \ R i — R m R i — R m 117 Finally, substituting k(f*) for I< yields the final form of (10): Rx(t)_-R m _ ( k Sx\ R i- R M ~ P\ Vx)' 118 A p p en d ix C All stable isotopic analyses were performed at the Water Resources Center of the Desert Research Institute, Las Vegas. Hydrogen gas was extracted from 5/zL water aliquots using zinc as the reducing agent [Kendall and Coplen, 1985]. The H 2 gas is then analyzed on a Nuclide 3- 60HD mass spectrometer. Reproducibility for the hydrogen analysis is 1.0 per mil. Isotope concentrations are calculated using Vienna Standard Mean Ocean W ater (V-SMOW), and Vienna Standard Light Arctic Precipitation (V-SLAP). Oxygen isotope ratio determination was based on the conversion of the water sam ple to CO 2 by a guanidine hydrochloride method [Dugan et al., 1985]. The resulting carbon dioxide gas was then analyzed on a Finnegan Model Delta-E isotope-ratio mass spectrometer. Laboratory reproducibility for oxygen isotopes is 0.2 per mil. Standards used in calibration are V-SMOW. V-SLAP, and an internal standard (DIST). Tritium activities were determined both at the DRI-WRC Water Chemistry Laboratory in Reno, Nevada, and the DRI-WRC Stable Isotope Laboratory in Las Vegas. Analyses for tritium were performed by liquid scintillation counting on either a Beckman LS 1801 Liquid Scintillation Counter, or a Packard Minaxi 4300 Liq uid Scintillation Counter. Low-activity waters were enriched by an electrolytic method, while concentrated waters were counted immediately. Each sample was 119 typically counted five times (about 20-50 minutes each). 120 A p p en d ix D Humidification Assuming a well mixed vapor phase, the flux of water vapor which enters a finite (small) reservoir can be estimated by measuring the change in water vapor concentration over time. The assumption of well mixed separate reservoirs (water and vapor), as it turns out from the isotopic data, is a good one for the time scales of interest (minutes to days). The conditions for the following humidification calculations are: • air temperature: 28.3 °C • air volume: 300 liters • water volume: 1000 ml (in 2 beakers) • water surface area: 142.6 cm2 • vapor pressure of water @ 28.3 °C : 23.8 torr Expecting the amount transferred to be proportional to the concentration difference and the interfacial area we have Ji = k (c h - cl) (24) where Jj is the flux at the interface (mol/cm2-sec), cl, and cl are the concentra tions at the interface and in the bulk solution, and k expresses the proportionality. As with equation (9) this expression states that if the concentration difference is doubled, the flux will double, and that if the area is doubled, the amount of mass 121 transfer will double, but the flux per unit area will not change. The flux Ji is first calculated based on measurements of the change in water vapor concentra tion over time using equation (24). Several trials yielded fluxes which ranged from 4.65a:10~8 to 3.93a:10-8 mol/cm2 sec. As these calculations are performed on evaporating water, the fluxes can expected to be larger that those calculated under saturated conditions because of the high water vapor gradient. From equa tion (24), this range of fluxes yields the following range of transfer coefficients: k ~0.046 to 0.055 cm/second. These are thus the mass transfer coefficients ex pected under quiescent evaporative conditions at 15-30 percent humidity for early times in the box experiments. Liss et. al [1972] reported gas-side k values for water vapor ranging from 0.27 to 2.5 cm/second based on salinity changes in the liquid phase under wind conditions ranging from 1.6 to 8.2 m/second. The results of Liss et. al [1972] agree well with these calculations, and confirm the range of gas-side A'values for environmental conditions. It is helpful to estimate the flux of water vapor based on relative saturation for the case of evaporating waters in order to guage these values against those for the case of high humidity. Such calculations provide a range of k values which are important in low humidity environments. The magnitude of the water vapor flux at early times within the boxes can also be estimated. An evaporative water- vapor flux can be calculated by applying the same arguments as those developed for the case of end-member exchange equation (9) to different initial and boundary conditions.