Experimental Study on Retardation of a Heavy Napl Vapor in Partially Saturated Porous Media

Non-aqueous-phase liquid (NAPL) contaminants introduced into the unsaturated zone spread as a liquid phase; however, they can also vaporize and migrate in a gaseous state. Vapor plumes migrate easily and thus pose a potential threat to underlying aquifers. Large-scale column experiments were performed to quantify partitioning processes responsible for the retardation of carbon disulfide (CS 2) vapor in partially saturated porous media. The results were compared with a theoretical approach taking into account the partitioning into the aqueous phase as well as adsorption to the solid matrix and to the air–water interface. The experiments were conducted in large, vertical columns (i.d. of 0.109 m) of 2 m length packed with different porous media. A slug of CS 2 vapor and the conservative tracer argon was injected at the bottom of the column followed by a nitrogen chase. Different seepage velocities were applied to characterize the transport and to evaluate their impact on retardation. Concentrations of CS 2 and argon were measured at the top outlet of the column using two gas chromatographs. The temporal-moment analysis for step input was employed to evaluate concentration breakthrough curves and to quantify dispersion and retardation. The experiments conducted showed a pronounced retardation of CS 2 in moist porous media which increased with water saturation. The comparison with an analytical solution helped to identify the relative contributions of partitioning processes to retardation. Thus, the experiments demonstrated that migrating CS 2 vapor is retarded as a result of partitioning processes. Moreover, CS 2 dissolved in the bulk water is amenable to biodegradation. The first evidence of CS 2 decay by biodegradation was found in the experiments. The findings contribute to the understanding of vapor-plume transport in the unsaturated zone and provide valuable experimental data for the transfer to field-like conditions.


Introduction
Subsurface contamination is a major concern in industrialized as well as in developing and emerging countries. NAPL contaminants introduced into the unsaturated zone spread as a liquid phase; however, they can also vaporize and migrate in a gaseous state. In particular, vapor (gas) plumes migrate easily in the unsaturated zone (Barber and Davis, 1991;Davis et al., 2005Davis et al., , 200920 Höhener et al., 2006). Vapors heavier than air preferentially migrate downward, posing a potential threat to aquifers. When assessing the danger of groundwater contamination by migrating vapor plumes, retention effects on transport are of major interest. Processes such as partitioning to soil water or adsorption on sand grains affect the migration of vapors in the unsaturated regarding its potential to delay or prevent a contamination of an underlying aquifer is gained. Large-scale column experiments were designed and conducted to quantitatively characterize retardation of CS 2 with clearly-defined and controlled boundary conditions. The experiments were conducted in vertical columns (i.d. = 0.109 m) of 2 m length packed with a porous medium.
They were carried out under dry conditions and at static water saturations. Reproducible water saturations (initial conditions) 25 were obtained by saturation with water and subsequent drainage under controlled conditions at predetermined capillary pressures. A finite slug containing gaseous CS 2 as well as a non-retarding, conservative tracer (argon) was injected via an injection section at the bottom of the column. Effluent concentrations of CS 2 and argon were measured online at the top outlet of the column. Tensiometers installed along the column measured capillary pressures to monitor the drainage process and to obtain water-saturation profiles of the porous medium. Gas flow rates were controlled by mass-flow controllers and additionally mea-30 sured by a bubble flow meter. This novel experiment set-up enabled for the quantification of CS 2 retardation as a function of porous medium, water saturation, and seepage velocity.  Budavari (1996) Density of liquid (ρ), kg m -1 1263 Budavari (1996) Solubility in water (cw,sat), g L -1 2.1 Riddick et al. (1986) Henry coefficient (Hcc), dimensionless 1. 04 De Bruyn et al. (1995) Boiling point (TB),°C 46. 5 Budavari (1996) Vapor pressure (Psat), hPa 396.9 Wagner equation Saturation concentration in gas phase (ca,sat), kg m -3 1.239 Ideal gas law CS2-Air vapor mixture density (ρvap), kg m -3 1.971 Ideal gas law Diffusion coefficient in air (DCS 2 Air ), cm 2 s -1 9.71e-02 Chapman-Enskog

Materials and methods
This work focused on the experimental investigation into the retardation of CS 2 vapor in partially saturated porous media. This sections addresses the experimental set-up, the procedures, and data evaluation methods used in this study. Table 1 shows the physicochemical properties of the contaminant carbon disulfide (CS 2 ) at 20 • C, 1013.15 hPa.
2.1 Experimental set-up 5 The experiments were conducted in vertical, stainless steel columns of 2 m length packed with two different types of porous media ( Figure 1). The column (length = 2 m, i.d. = 0.109m) consisted of two custom-built, 1 m long sections. The ports along the column at a distance of 25 cm allowed for the installation of tensiometers to monitor capillary pressures. At the bottom of the column, the injection section with a base plate was installed. Into this base plate, a porous plate made of recrystallized silicon carbid was glued to act as a suction plate for the water drainage. The bottom of the column was realized as a constant- Two different types of porous media (Table 2) were used in the experiments: fine glass beads (soda-lime glass, Sigmund Lindner, Warmensteinach, Germany) and Geba fine sand (Quarzsande GmbH, Eferding, Austria). Their grain-size distributions as well as capillary pressure -water saturation relationships are shown in Figure 2. The columns were packed by dry pluviation using a sand rainer. The design of the rainer was adopted from Rad and Tumay (1987) with modifications according 15 to Lagioia et al. (2006). The columns consisting of two column sections were filled section after section, each with an overfill of around 30 cm. This prevented additional layering of the porous medium. The columns were sealed with cover plates equipped with 1/8" tube fittings (SS-6M0-1-4RT, Swagelok). The experiments were carried out under dry conditions as well as at irreducible, static water saturation. Comparable initial conditions for each experiment were guaranteed by a set-up controlling and monitoring saturation and drainage. The drainage of the porous media was realized by means of the porous plate at the bottom of the column exclusively permeable for water when fully saturated. This allowed for setting the water o.d. = 6 mm, i.d. = 4 mm). In addition, the column was placed on a scale to permanently monitor its weight and thus the total amount of pore water. The injection section at the bottom of the column allowed for the injection of a gas-mixture slug at a predefined mass flux and, in addition, for a controlled upward flow stabilizing the vapor front. The CS 2 vapor was prepared prior to injection. A predefined amount of liquid CS 2 was injected into a barrel (V = 50 L) and pressurized to an excess pressure of about 2 bar with nitrogen to ensure defined vapor properties. The tracer argon was provided from a gas cylinder (Westfalen AG, Münster, Germany). Constant mass fluxes of the injected CS 2 vapor and of the conservative tracer (argon) were critical to the experi-5 ment. Mass fluxes of argon, CS 2 vapor, and nitrogen were controlled by mass-flow controllers (EL-FLOW, Q max = 3, 50, and 10 mL m −1 , Bronkhorst High-Tech B.V., Ruurlo, Netherlands). Complete gas tightness of the entire set-up was ensured by using 1/8" stainless steel capillaries throughout. The slug of the gas mixture (CS 2 , argon, and the carrier nitrogen) was injected and then pushed through the column using a nitrogen chase at the same flow rate. Prior to injection into the column, argon (approximately Q Ar /Q total = 1.4 %) was added to the total flow. The mass balance was closed based on the measured flow rate, and the injection and effluent concentrations. The second objective of the nitrogen chase was to observe the recovery of the contaminant and reversibility of partitioning processes. In the case of moist experiments, the gas mixture slug was humidified with ultra-pure water (RH = 100 %) to avoid a drying-up of the moist porous medium. For the preparation of the gas-mixture  In the column outflow, CS 2 and argon concentration were measured to quantify retardation in dry and moist porous media.
Two gas chromatographs were directly connected in-line to the column outlet. CS 2 concentrations were determined using a gas chromatograph with a photoionization detector (GC-PID HE1, Meta Messtechnische Systeme GmbH, Dresden, Germany) and argon concentrations were determined using a gas chromatograph with thermal conductivity detector (GC-TCD, Multiple gas analyzer 8610-0270, SRI Instruments Europe GmbH, Bad Honnef, Germany). Single-point calibrations were conducted 15 prior to and after each run. Measurement intervals were set depending on the flow velocity such that a high temporal resolution (0.021 to 0.065 PV) of the breakthrough curves was obtained. Prior to the start of the slug injection, the concentration of CS 2 and argon in the slug mixture was measured as a base to normalize concentrations. A relative pressure transducer connected to the column inlet before the injection section was used to monitor the injection pressure. Since the top column outlet was open to the atmosphere (P atm ), this corresponded to the pressure loss caused by the flow through the porous medium. Temperature 20 sensors and absolute pressure transducer continuously measured and recorded ambient and water bath temperature as well as atmospheric pressure in the vicinity of the experiment.

Experimental procedure
Various experiment series were conducted in two different porous media (fine glass beads and Geba fine sand) under both dry and partially saturated (moist) conditions. Within each series the columns were not repacked and no saturation-and-drainage 25 cycle (SD) was carried out since first tests proved that the partitioning processes were fully reversible. The water saturation or total amount of pore water was monitored throughout the experiment. The slug of the gas mixture was injected with a The experiments were conducted in four steps. In the first step, the flow rates (slug and chase) were adjusted to match the target migration velocity. In the second step, the column was flushed with nitrogen. While maintaining constant flux, the inflow was switched to the slug injection of the gas mixture in the third step. After injecting 3.5 PV it was switched back to the nitrogen chase (fourth step).

Data evaluation
The objective of the experiments was to quantify the retardation of CS 2 vapor. Possible influences on the determined retardation factors due to experimental artifacts such as a deviation between theoretical and actual gas-effective pore volume had to be 5 taken into consideration. Hence, for each experiment the breakthrough curve of CS 2 was related to that of argon. Concentrations were normalized with respect to the steady-state concentrations (c = c exp /c ss ). Mass balance was calculated from concentration data and measured gas flow rates. Data was evaluated based on elapsed time and then correlated via flow rate, resulting from mass flux, to gas-effective pore volume. Moreover, both the slug itself and the nitrogen chase were considered which allowed for an separate evaluation of the slug front and tail (front of nitrogen chase). Breakthrough curves were evaluated using the 10 temporal-moment analysis (TMA) for a step input (slug) as proposed by Yu et al. (1999) and Luo et al. (2006). The advantage of TMA "is that no underlying physical model is needed for calculating the travel times" (Yu et al. (1999), p. 3571), and the breakthrough curves of the CS 2 -Ar mixture (slug front) as well as the nitrogen chase (or slug tail) can be evaluated individually.
Moreover, TMA can also be applied to asymmetrical BTCs resulting from non-equilibrium sorption processes during transport.
Hence, retardation of CS 2 in moist and dry porous media could be compared and the impact of water saturation on retardation 15 of CS 2 could be delineated.
TMA was applied to obtain transport parameters (seepage velocity [Eq. A9] and dispersion coefficient [Eq. A10]) and mean breakthrough arrival (Eq. A7) time from concentration breakthrough curves. The retardation factor R of CS 2 vapor was calculated from the ratio of the respective moments or mean breakthrough arrival time.
This ensured the independence from experimentally-induced deviations and thus allowed to quantify the influence of water saturation and migration velocity on retardation. Experimental retardation factors were compared with a theoretical factor. Brusseau et al. (1997) used carbon dioxide (CO 2 ) as a tracer whose predominant source of retardation was the partitioning into the aqueous phase. The similarity of CS 2 and CO 2 regarding solubility in water and Henry constant suggests a comparable retardation behavior for CS 2 . Hence, partitioning into the aqueous phase is considered the only contribution. Adsorption on 25 grains (3) and at the gas-water interface (4) (terms on the right hand-side of Eq. A11) will be neglected. This then yields the adapted theoretical retardation coefficient.
where θ w is volumetric water content, θ a is gas-filled porosity, K H (dimensionless) is Henry's constant.

Results and discussion
Column experiments were conducted with dry and moist porous media to characterize retardation of CS 2 vapor. Table 3 shows the experimental conditions of each series performed in fine glass beads and Geba fine sand. Several series of experiments were performed in each porous medium to quantify retardation. Series 1 refers to the experiments conducted in dry porous media while Series 2 to 4 refer to the experiments in moist conditions. A saturation-and-drainage cycle was performed prior to each 5 moist series. A slug of 3.5 PV of the gas mixture was injected ensuring, even for high flow rates, a sufficient residence time to reach equilibrium in the 2 m long column. Different seepage velocities (25, 50, 100, and 200 cm h −1 ) were applied, based on previously conducted experiments investigating density-driven vapor migration (Kleinknecht et al., 2015). Breakthrough curves under the prevailing experimental conditions were determined from concentration measurements at the column outlet. The temporal-moment analysis (Sec. 2.3) was applied to the breakthrough curves (BTC) to quantify diffusion/dispersion 10 and retardation as a function of the porous media, the water saturation, and the flow conditions. A detailed summary of all experiments (experimental conditions, injected mass, and mass recovery) is given in Tables 5 and 6 in the appendix.

Water saturations
The moist porous medium required for this investigation was obtained by saturation and subsequent drainage. The suction applied at the bottom of the column during drainage was responsible for the observed water saturation profiles. The capillary 15 pressure was measured with the tensiometers installed at the column ports to derive water saturations along the column (P c -S w , Fig. 2). Mean water saturations of the moist series are given in Table 3. toward the bottom from S w = 0.07 to 0.14. The very narrow and uniform grain-size distribution of the fine glass beads was responsible for a sharp transition from full to irreducible saturation (see P c -S w curve in Fig. 2), thus favoring a uniform saturation profile. In Geba fine sand, a constant water saturation of S w = 0.15 above a column height of 70 cm was measured.
However, both profiles showed a pronounced increase in the water saturation toward the bottom of the column, apparently reaching fully-saturated conditions according to the P c -S w relationship of Geba fine sand (Fig. 2). Still, capillary pressures 5 of P c = 55 and 65 hPa were measured at the lowest port. The suction applied via the porous plate was limited by its air entry pressure. A further decrease of pressure would have resulted in a breakthrough of air (continuous gas phase). The mean water saturation (Table 3) but also the observed profiles were expected to have an impact on the retardation behavior of CS 2 , as discussed in Sec. 3.3. Figure 3 (right-hand) shows an exemplary progression of water saturations measured in Experiment 28 of Series 2 with 10 Geba fine sand ( Table 6). The saturations were based on tensiometers along the column during the injection of the slug and the subsequent nitrogen chase. The tensiometers suggested an apparent change in water saturation during active gas flow through the porous medium. This was most likely provoked by the pressure increase due to the injection and the gas flow around the tensiometer. It is important to note that the tensiometers measured the suction at a very spatially-limited location in the porous medium due to the small size of their tips (o.d. = 6 mm, length = 8 mm). In addition, the pressure transducers of the 15 tensiometers showed periodic fluctuations as a result of daily temperature changes in the laboratory hall and due to varying ambient pressure. However, a drying-out of the porous medium was prevented by the humidification of all gases (slug and chase) prior to injection. This was confirmed by the water mass balance by means of the continuous weight measurement of the entire column throughout all experiments conducted within a series. Hence, the initial water-saturation profile could

Impact of velocity on breakthrough
The impact of the seepage velocity on the concentration breakthroughs of argon and CS 2 was investigated. Thus, different velocities were applied to characterize the transport. express dispersivity α of the respective porous medium. The theoretical coefficient D * t was determined according to the Chapman-Enskog theory and the approach by Millington and Quirk (1961) which accounts for tortuosity due to porous matrix and water saturation (see Sec. A1). Table 4    tortuosity tau). In fine glass beads, effective binary diffusion coefficients of argon were D * Ar = 0.0909 cm 2 s −1 compared to D * t,Ar = 0.0386 cm 2 s −1 and of CS 2 were D * CS2 = 0.0263 cm 2 s −1 compared to D * t,CS2 = 0.0213 cm 2 s −1 . In Geba fine sand, co- efficients of argon were D * Ar = 0.0966 cm 2 s −1 compared to D * t,Ar = 0.0284 cm 2 s −1 and of CS 2 were D * CS2 = 0.0332 cm 2 s −1 compared to D * t,CS2 = 0.0157 cm 2 s −1 . The experimental coefficients D * differed from the theoretical effective binary diffusion coefficient D * t calculated for the prevailing conditions. This could result from the choice of porous media, since both media were characterized by a uniform and narrow grain-size distribution, as well as the observed water-saturation profiles. Werner et al. (2004) reported that theoretical approaches are often sensitive since the majority of their parameters are raised 5 to a high power and do not apply satisfactorily to a wide variety of soils. Furthermore, the theoretical approach does not take into account material characteristics such as the pore-size distribution which may vary for similar porosities and hence affect the tortuosity factor. Dispersion coefficients shown in Figure 6 varied for a given velocity due to minor differences between the experiments and to variations arising from the temporal-moment analysis. The equation used to determine the dispersion coefficient (Eq. A10) from TMA raises the velocity to the power of three, thus minor deviations had a great impact on the final 10 values.
The increase in the dispersion coefficient in Figure 6 from the effective binary diffusion coefficient (at v = 0 cm h -1 ) with increasing velocity resulted from mechanical mixing due to flow through the moist porous medium. This was observed in all experiments. The increase is determined by the slope of the linear regression representing the dispersivity α which should be a parameter of the porous medium only and should be independent of the components (gases) and flow conditions. A slight 15 difference was found between CS 2 and argon for both materials, resulting in a mean dispersivity of α GBfine = 0.958 cm in fine glass beads and α Geba = 0.432 cm in Geba fine sand. The difference could be due to dispersivity transforming from a physical system to a lumped parameter, because of e.g. diffusional or nonequilibrium effects. This then results in a component-dependent dispersivity according to Costanza-Robinson and Brusseau (2002), who reported that dispersivity ranges from approx. 0.1 to 5.0 cm. Since argon is a conservative tracer and CS 2 is affected by retardation, greater reliability was attributed to the 20 dispersivity α Ar determined from BTCs of argon. The results of the experiments in this work demonstrate the impact of seepage velocities on the diffusion/dispersion of CS 2 vapor and of argon. Thus, an influence of the velocity on the retardation of CS 2 was expected.

Retardation of CS 2
Different series of experiments were conducted to quantify retardation of CS 2 as a function of water saturation and seepage 25 velocity. Figure 7 and 8 compare breakthrough curves (BTC) of argon and CS 2 in dry (black) and moist (red) porous medium for the same seepage velocity (v = 50 cm h −1 ). Two to three repetitions of each run in dry and moist conditions, respectively, are shown. The graphs show normalized concentrations as a function of effective pore volume (total pore volume minus water content after drainage).
The BTCs of argon showed excellent reproducibility in repetition experiments in both materials at the same conditions 30 (v = 50 cm h −1 ). In fine glass beads, argon showed very similar BTCs for dry and moist experiments. This thus confirmed that argon experiences no retardation and may be used as a conservative tracer and as a reference for CS 2 . In Geba fine sand, a different skewness was observed between dry and moist conditions as a result of the reduced pore space in moist conditions. Hence, a comparison of the BTCs revealed that the effective-flow region in fine glass beads was similar in dry and moist 13 Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2016-440, 2016 Manuscript under review for journal Hydrol. Earth Syst. Sci. conditions, whereas in Geba fine sand it was reduced in moist conditions. This resulted in BTCs which were less affected by diffusion due to a shorter residence time. Since the experiments were conducted with a constant-flow-rate boundary condition based on the calculated effective pore volume, a shorter residence time i.e. higher seepage velocity occurred when the actual effective pore volume available for gas flow is smaller than the calculated volume.
The BTCs of CS 2 showed, in general, good reproducibility for all experiments. In fine glass beads, a later breakthrough of 5 CS 2 compared to argon can be observed in Figure 7, demonstrating the retardation of CS 2 due to partitioning into the water phase. The different effective pore volume due to the pore water and possible reduced residence time (actual vs. calculated PV) resulted in less skewed BTCs compared to the dry experiments. In Geba fine sand, a more pronounced retardation of CS 2 was observed compared to experiments in fine glass beads. The later breakthrough becomes evident when comparing BTCs in dry (black) with moist (red) conditions in Figure 8. This could be ascribed to the overall higher water saturation and the 10 increase in saturation toward the bottom of the column (see Fig. 3). In two of the three BTCs in moist experiments (Fig. 8), CS 2 concentrations leveled at around c/c ss = 0.9 followed by an increase to steady-state (plateau) concentrations toward the end of the slug. This behavior might be a consequence of the water saturation over column height affecting the partitioning processes.
The retardation coefficients of CS 2 as a function of porous medium, water saturation, and seepage velocity were determined using the temporal-moment analysis ( and allowed for the comparison with theoretical values. Figure 9 shows retardation coefficients of CS 2 as a function of water saturation (upper) and seepage velocity (lower) in fine glass beads (black) and Geba fine sand (red). The coefficients of the slug (circle) and the chase (rectangle) are given and their size represents seepage velocity or water saturation. Note the broken x-axis (water saturation) between S w = 0.10 and 0.13 in the upper graph indicated by the vertical, dashed lines.
In fine glass beads, a non-linear increase in the retardation coefficient from R GBfine = 1.09 to 1.16 with increasing water 5 saturation from S w = 0.075 to 0.155 was observed. Of course, partitioning to the water phase is dependent on the gas-water interfacial area which should decrease with increasing water saturation. Thus an extrapolation of the retardation coefficient to higher water saturations might be difficult. The retardation of the slug and of the chase were different in fine glass beads, the chase being more prone to retardation than the slug. The breakthrough of the nitrogen chase (removal of the CS 2 vapor) showed a higher retardation by a factor (average) of 1.05 compared to the breakthrough of the slug throughout all experiments 10 in fine glass beads. This behavior can be also seen when comparing the BTCs of CS 2 in the upper graph of Figure 7.
In Geba fine sand, higher retardation coefficients compared to fine glass beads were measured in the experiments. These ranged between R Geba = 1.29 and 1.34 at a mean water saturation of S w = 0.162. This was due to the higher water saturation and its increase toward the bottom (discussed in Sec. 3.1), the different gas-water interfacial area, and the pore space available for gas flow. Series 3 in Geba fine sand had to be excluded from these graphs due to mass balance issues discussed later. Hence, results were only available for one particular water saturation in Geba fine sand. The ratio between the retardation coefficient of the slug and that of the chase did not show a clear trend as observed in fine glass beads despite the differences seen in Figure 9.
The retardation coefficients gained from the experiments were compared to a theoretical approach. The adapted theoretical retardation coefficient (Eq. 2) is shown as a line in the upper graph. The theoretical coefficient is calculated taking into account the porosity of the porous medium, the water saturation, and the Henry coefficient. Hence, only one function is shown in the upper graph of Figure 9, since the porosities of the fine glass beads and the Geba fine sand used were similar. In fine glass beads, the theoretical coefficient compared very well with the values from the experiments. It slightly overpredicted the retardation of the slug while it underpredicted that of the chase, however it reproduced satisfactorily the mean retardation coefficient and its increase with water saturation. In Geba fine sand, the theoretical coefficient significantly underestimated the observed retardation. This could be due to the fairly simple theoretical approach only taking into account the porosity of the porous 5 medium. It is obvious that the pore-size distribution depending on the grain-size distribution of the porous medium determines the gas-water interfacial area and thus has a significant impact on retardation. However, such material characteristics are not factored in by the theoretical coefficient. Moreover, the non-uniform water-saturation profile along the column height could be responsible for varying partitioning. Finally, deviations could occur due to adsorption processes or higher-order kinetics during partitioning which were neglected in the theoretical factor. These findings suggest that retardation may vary along the depth of 10 the unsaturated zone due to spatially-varying water saturations and especially around the capillary fringe in the vicinity of the groundwater level.
The experiments were conducted with different seepage velocities to evaluate their impact on retardation. The lower graph in Figure 9 shows the retardation coefficients as a function of seepage velocity. A mean retardation coefficient of R GBfine = 1.100±0.0096 and R Geba = 1.315±0.0152 was measured in the experiments with fine glass beads (S w = 0.088) and Geba fine 15 sand (S w = 0.162), respectively. In general, no significant change of the retardation behavior with increasing seepage velocity was observed. This confirmed that the mass transport rate was low enough and the residence time of the slug was sufficient for the partitioning processes to reach equilibrium. Concluding from the experiment with v = 200 cm h −1 it seems likely that there was a slight tendency toward a reduced retardation. In fact, retardation may reduce at higher seepage velocities due to limiting contaminant diffusion. If no equilibrium is reached in case of high velocities, the retardation coefficient reflects an apparent 20 coefficient since in this case it is a function of the experimental system used (i.e. length of the column). Additional experimental repetitions would have been required to provide proof. However, this experimental investigation aimed at characterizing retardation of CS 2 in the range of seepage velocities observed during vapor-plume migration experiments (v 200 cm h −1 ).
Hence, the focus laid on the velocities used and higher values were beyond the scope.
Mass balance analyses were performed to obtain mass recovery (r) from each breakthrough curve. Mass recovery was The results discussed above excluded Series 3 conducted in Geba fine sand. Series 3 was the second saturation and drainage cycle which was carried out to establish a different static water saturation than in Series 2. However, significant CS 2 mass losses became more pronounced with each experiment in this series, eventually leading to its exclusion from the results.
Recoveries of CS 2 decreased from r CS2 = 0.854 in the first experiment of Series 3 down to r CS2 = 0.010. This mass loss of CS 2 was caused by biodegradation which was confirmed by the smell of hydrogen sulfide in the column outflow. Cox et al. (2013) found carbonyl sulfide (COS) and hydrogen sulfide (H 2 S) as by-products during CS 2 biodegradation in their experiments. The mass balance analysis of the experiments enabled for determining mean degradation rates of CS 2 which were calculated from the CS 2 mass rate and the recovery. The mean degradation rates ranged from 0.12 to 1.28 mg h −1 depending on the respective 5 seepage velocity applied in the experiments. The experiments showed that biodegradation may have a considerable potential for mitigating the contaminant mass transfer by vapor migration to the underlying aquifer. However, the quantification of biodegradation of CS 2 was beyond the scope of this work but should be addressed in future research.

Conclusions
-The retardation of CS 2 vapor was quantified in 2 m long column experiments as a function of porous medium, water sat-10 uration, and seepage velocity. The novel set-up and methods applied additionally allowed for characterizing the transport of CS 2 and argon.
-The versatile temporal-moment analysis (TMA) was successfully applied to quantify diffusion/dispersion of CS 2 and argon as well as retardation of CS 2 from concentration breakthrough curves by comparison with the conservative tracer argon.

15
-Dispersion coefficients as a function of seepage velocity were obtained from the TMA for experiments in moist conditions. Linear regressions of these data sets yielded effective binary dispersion coefficients and dispersivity values at the prevailing experimental conditions. The effective binary diffusion coefficient at the given experimental conditions was found to be slightly higher than theoretical values based on the approach by Millington and Quirk (1961). The theoretical approach takes into account the porosity only and neglects material characteristics such as grain-size or pore-size distri-20 bution which affect diffusion/dispersion. Thus, the experiments confirm that theoretical approaches do not satisfactorily apply to a wide variety of porous media (Werner et al., 2004).
-The impact of different seepage velocities on the breakthrough curves and thus on the dispersion coefficient was observed. The experiments showed that the velocities affected diffusion/dispersion of the gases due to the corresponding residence time in the porous medium and due to mechanical mixing. This effect was illustrated by the skewness of the 25 breakthrough curves which were negatively correlated to the seepage velocity.
-The retardation coefficient of CS 2 increased with increasing water saturation and compared very well with the theoretical approach for fine glass beads. A slightly higher retardation of the chase by a factor of 1.05 compared to that of the slug was observed. A pronounced higher retardation was observed in Geba fine sand due to the different grain-size distribution and the particular water-saturation profile. Moreover, the theoretical coefficient underpredicted retardation in Geba fine 30 sand. Retardation coefficients as a function of (seepage) velocity revealed only a minor dependency and suggested a slight tendency toward a reduced retardation at higher velocities.
with D AB (cm 2 s -1 ), temperature T (K), pressure p (atm), the Lennard-Jones parameter σ AB (angstrom), and the collision integral Ω D,AB which can be approximated with the Lennard-Jones potential. Component-specific values to determine σ AB as well as Ω D,AB as a function of kT / can be found in Bird et al. (1960).
Porous media affect diffusion of gases since space is occupied by grains and possibly by additional fluid phases. Therefore, Fick's law is often modified by the factor β to account for these deviations.
while β is defined as where D * AB is the effective diffusion coefficient in porous media, φ is the porosity, S g the gas saturation (equal to 1 for all-gas condition), and τ is the tortuosity. According to Millington and Quirk (1961), tortuosity can be approximated by Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2016-440, 2016 Manuscript under review for journal Hydrol. Earth Syst. Sci. Published: 30 August 2016 c Author(s) 2016. CC-BY 3.0 License.

A2 Dispersion coefficient
Flow of fluids in a porous medium may vary significantly on a micro scale due to the velocity field in pores, irregularities of the pore size, flow restrictions, or dead-end pores resulting in additional spreading denoted as dispersion. These influences have to be taken into account in analytical or numerical solutions of flow in porous media. This is done by introducing the longitudinal dispersion coefficient with the dispersion coefficient D (cm 2 s -1 ), effective binary diffusion coefficient D * AB (cm 2 s -1 ) according to Eq. A2, gas-phase longitudinal dispersivity α (cm), and average gas velocity v (cm s -1 ).

A3 Temporal-moment analysis
The measured breakthrough curve (BTC) data had to be prepared to allow for the usage of the temporal-moment analysis 10 (TMA) generally applied to responses from dirac input. The breakthrough curves of the step-input boundary condition (1) were transformed to a dirac-input boundary condition (2) (Yu et al., 1999). This was achieved by using the derivative of the original step-input BTC data.
where c 1 (-) is normalized concentration of measured BTC and t (second or PV) is elapsed time. The second central moment µ 2 corresponds to the variance of travel times at the location of measurement and is given by These two moments can be used to directly infer seepage migration velocity v and dispersion coefficient D from BTC data for a one-dimensional system (Cirpka and Kitanidis, 2000). A4 Theoretical retardation coefficient Brusseau et al. (1997) defined the retardation factor to be the sum of various processes including adsorption and partitioning where θ w is volumetric water content, θ a is gas-filled porosity, K H (dimensionless) is Henry's constant, K Dsat (cm 3 g -1 ) is 5 the sorption coefficient for water-saturated conditions, ρ b (g cm -3 ) is the dry soil bulk density, K IA (cm) is the adsorption coefficient between gas and the gas-water interface and A IA (cm 2 cm -3 ) is the specific surface area of the gas-water interface.
The terms on the right-hand side describe retardation by the gas phase (1), partitioning into the aqueous phase (2), adsorption on the grains (3) and the last term accounts for gas-water interfacial adsorption (4).

Appendix B: Detailed experimental results
10 Tables 5 and 6 show the theoretical migration velocity, the injection duration (slug), the injected mass, and the normalized recovery of the components CS 2 and argon. The tables list all experiments in order according to the conducted series.