Diploma thesis in Physics submitted by Florian Freundt born in ...

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2.1. Noble gas temperatures 2 Theory � � � � � � � � � � � �� Figure 2.1: Temperature dependency of the Ostwald solubility L(T, S = 0) for the noble gases He, Ne, Ar, Kr and Xe, at atmospheric pressure. Plot data was calculated using the fit equation and parameters provided by Benson and Krause [1976]. 2.1.1 Solubility The partitioning of gas at the phase boundary between water and air at a constant temperature is described by Henry’s Law, formulated in 1803 by William Henry: C g i = Hi(T, S) · C w i (2.1) where C g i and Cw i are the concentrations of gas i in the gas and the water phase respectively. Hi is the gas specific Henry constant, a dimensionless constant that is a function of temperature T and salinity S. Influences on Hi by chemical interactions of solutes found in water can be neglected for meteoric and ground waters [Kipfer et al., 2002]. Since the Henry constant is dimensionless, its numerical value is defined by the units chosen for the gas concentrations C. The reciprocal of the Henry constant, called Ostwald solubility L, is a measure of solubility. Li(T, S) = 1 Hi(T, S) = Cw i C g i The temperature dependency of the solubility is described by a numerical approximation by fitting measured data to an equation like ln � Li(T, S = 0) � 1 1 = a0 + a1 + a2 T 16 T 2 (2.2) (2.3)
2 Theory 2.1. Noble gas temperatures where T is the temperature in Kelvin, leading to parameters ai as given Table B.1 [Benson and Krause, 1976]. The resulting functions for individual noble gases are shown in Figure 2.1 where the Ostwald solubility Li(T, S = 0) is plotted versus temperature. In ground water research it is usually more convenient to work with partial pressures pi of gas i. As described by Kipfer et al. [2002], using the equilibrium concentration Ci,eq, Henry’s Law is formulated as pi = Hi(T, S) · Ci,eq (2.4) The partial pressures of noble gases in atmospheric air, based on the assumption that the atmospheric noble gas composition is constant and usable as a standard [Porcelli et al., 2002], is calculated from ambient atmospheric pressure ptot: pi = zi · � ptot − p 0 � H2O with the volume fraction zi of the gas i in air (see Table B.3) and the saturated water vapor pressure p0 H2O as defined in Appendix A.1.1. Local conditions in the recharge area (e.g. elevation) may require some corrections of the total pressure as well as the equilibrium concentration due to the atmosphere’s barometric pressure profile: � ptot(h) = p0 · exp − h � (2.6) h0 � ptot(h) − p Ci,eq(T, S, ptot(h)) = Ci,eq(T, S, p0) · 0 H2O p0 − p0 � (2.7) H2O with h being the local height above sea level and h0 the local scale height, typically at around 8000 – 8300 m [Kipfer et al., 2002]. Henry’s Law is then expressed as Ci,eq(T, S, ptot(h)) = zi · (ptot(h) − pH2O) Hi(T, S) describing the gas concentration in water due to atmospheric equilibrium at the local site’s meteorologic parameters. 2.1.2 Noble gas fractions in ground water As shown above, noble gases enter the water phase by equilibration with air. In the case of ground water recharge this equilibration takes place within the vadose zone between the percolating meteoric water and the local soil atmosphere. The composition and similarity of soil air compared to atmospheric air is the main objective of this study. Isotopic fractionation occurs when this equilibration takes place due to mass differences of the different noble gas isotopes. Benson and Krause [1980] found that the solubility of 3 He and 4 He deviates by up to 1.8 %. Other studies [Aeschbach-Hertig, 1994; Beyerle et al., 2000] showed similar effects for Ne and Ar in an order of magnitude of per mil. The noble gas concentrations found in actual ground waters display additional influences as shown in Figure 2.2, originating from various other sources which shall be discussed below. 17 (2.5) (2.8)
Page 1: Faculty of Physics and Astronomy He
Page 5: Measuring annual variation of soil
Page 8 and 9: CONTENTS CONTENTS 3.1 Setup of the
Page 11 and 12: Chapter 1 Introduction Understandin
Page 13: 1 Introduction Molins and Mayer [20
Page 18 and 19: 2.1. Noble gas temperatures 2 Theor
Page 24 and 25: 2.2. Physical processes and propert
Page 26 and 27: 2.2. Physical processes and propert
Page 28 and 29: 2.3. Soil atmosphere composition 2
Page 35 and 36: Chapter 3 Sampling sites and method
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Page 43 and 44: Chapter 4 Measuring methods 4.1 Mas
Page 45 and 46: 4 Measuring methods 4.1. Mass spect
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Page 50 and 51: 5.2. Temperature profiles 5 Results
Page 52 and 53: 5.3. O2 and CO2 profiles 5 Results
Page 54 and 55: 5.4. Borehole sealing 5 Results 5.4
Page 56 and 57: 5.4. Borehole sealing 5 Results Fig
Page 58 and 59: 5.5. Noble gases 5 Results 8 days,
Page 60 and 61: 5.5. Noble gases 5 Results 5.5.3 So
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6 Discussion Table 6.1: Synthetic d
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Chapter 7 Summary The results of th
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8 Outlook Considering the manifold
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A.1. Gas sample size A Calculations
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A.3. Fractionation-Values A Calcula
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Table B.3: Noble gas volume mixing
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Table B.5: Calculated values of rel
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Table B.8: Precipitation record of
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Table B.10: Complete dataset of nob
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Appendix C Additional plots and fig
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C Additional plots and figures Figu
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C Additional plots and figures �
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C Additional plots and figures O 2
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C Additional plots and figures 4 He
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C Additional plots and figures 20 N
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C Additional plots and figures 10 1
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Appendix D Datasheets 107
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D Datasheets LogTag TREX-8 Technica
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Bibliography [Aeschbach-Hertig 1994
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BIBLIOGRAPHY BIBLIOGRAPHY [Friedric
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BIBLIOGRAPHY BIBLIOGRAPHY [Riveros-
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Acknowledegment At the end of this
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