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Using the Dusty Gas Model to investigate reaction-induced multicomponent gas and solute transport in… Molins Rafa, Sergi 2007

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USING THE DUSTY GAS MODEL TO INVESTIGATE REACTION-INDUCED MULTICOMPONENT GAS AND SOLUTE TRANSPORT IN THE VADOSE ZONE  by SERGI MOLINS RAFA Eng. de Camins, C. i P., Civil Engineering, Technical University of Catalonia, 2001  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE STUDIES (Geological Sciences)  THE UNIVERSITY OF BRITISH COLUMBIA  December 2007  © Sergi Molins Rafa, 2007  Abstract Biogeochemical reactions and vadose zone transport, in particular gas phase transport, are inherently coupled processes. To explore feedback mechanisms between these processes in a quantitative manner, multicomponent gas diffusion and advection are implemented into an existing reactive transport model that includes a full suite of geochemical reactions. Multicomponent gas diffusion is described based on the Dusty Gas Model, which provides the most generally applicable description for gas diffusion. Gas advection is described by Darcy's Law, which in the current formulation, is directly substituted into the transport equations. The model is used to investigate the interactions between geochemical reactions and transport processes with an emphasis to quantify reaction-induced gas migration in the vadose zone. Simulations of pyrite oxidation in mine tailings, gas attenuation in partially saturated landfill soil covers, and methane production and oxidation in aquifers contaminated by organic compounds demonstrate how biogeochemical reactions drive diffusive and advective transport of reactive and non-reactive gases. Pyrite oxidation in mine tailings causes a pressure reduction in the reaction zone and drives advective gas flow into the sediment column, enhancing the oxidation process. Release of carbon dioxide by carbonate mineral dissolution partly offsets pressure reduction, and illustrates the role of water-rock interaction on gas transport. Microbially mediated methane oxidation in landfill covers reduces the existing upward pressure gradient, thereby decreasing the contribution of advective methane emissions to the atmosphere and enhancing the net flux of atmospheric oxygen into the soil column. At an oil spill site, both generation of CH4 in the methanogenic zone and oxidation of CH4 in the  ii  methanotrophic zone contribute to drive advective and diffusive fluxes. The model confirmed that non-reactive gases tend to accumulate in zones of gas consumption and become depleted in zones of gas production. In most cases, the model was able to quantify existing conceptual models, but also proved useful to identify data gaps, sensitivity, and inconsistencies in conceptual models. The formulation of the model is general and can be applied to other vadose zone systems in which reaction-induced gas transport is of importance.  iii  Table of Contents Abstract ^  ii  Table of Contents ^  iv  List of Tables ^  vii  List of Figures ^  viii  Acknowledgements ^  xiii  Co-Authorship Statement ^  xiv  Introduction ^  1  1.1. Motivation ^  2  1.2. Previous Work ^  4  1.3. Objectives ^  7  1.4. Organization ^  7  1.  References ^ 2.  10  Coupling between Geochemical Reactions and Multicomponent Gas and Solute  Transport in Unsaturated Media: A Reactive Transport Modeling Study ^ 16 2.1. Introduction ^  17  2.2. Model development ^  22  2.3. Numerical implementation ^  29  2.4. Gas transport mechanisms and model verification ^  31  2.4.1. Non-reactive binary transport in the molecular and transition regimes ^ 32 2.4.2. Non-reactive multi-component transport in the molecular regime ^ 32 2.4.3. Methane attenuation and multi-component transport in landfill cover soils33 2.5. Investigation of interactions between transport and reactions ^ 35  iv  2.5.1. Production and consumption of methane at a crude oil spill site ^ 36 2.5.2. Acid mine drainage generation and attenuation ^  40  2.6. Conclusions ^  44  References ^  55  3.^Transport and Reaction Processes Affecting the Attenuation of Landfill Gas in Cover Soils ^  64  3.1. Introduction ^  65  3.2. Methods ^  68  3.2.1. Model Formulation ^  69  3.2.2. Model Parameters and Calibration ^  73  3.3. Results and Discussion ^ 3.3.1. Concentrations of CH4, CFCs and HCFCs ^  75 75  3.3.2. Relative Contribution of Transport Mechanisms ^ 75 3.3.3. Variable Inlet Flow Experiments ^  77  3.3.4. Sensitivity to Variable LFG Composition ^  78  3.3.5. Sensitivity to Moisture Content ^  79  3.3.6. Sensitivity to Local Changes in Moisture Content, Porosity and Permeability ^  79  3.3.6.1. H2O Production^  80  3.3.6.2. EPS Production ^  82  3.4. Summary ^  84  References ^  96  v  4.  Vadose Zone Attenuation of Volatile Organic Compounds at a Crude Oil Spill  Site - Interactions Between Multicomponent Gas Transport and Biogeochemical Reactions ^  101  4.1. Introduction ^  102  4.2. Methods ^  106  4.2.1. Model description ^  106  4.2.2. Site description, conceptual model and model set-up ^ 107 4.3. Results and discussion^  113  4.3.1. Transient evolution and discussion of uncertainties and limitations ^ 118  5.  4.4. Summary and conclusions ^  122  References ^  138  Summary and Conclusions ^  145  5.1. Model summary ^  146  5.2. Coupling between reactions and gas transport ^  147  5.3. Diffusive and Advective Contributions ^  149  5.4. Sensitivity to saturation and tortuosity ^  151  5.5. Model limitations ^  152  5.6. Future work ^  153  References ^  154  Appendices ^ Appendix Al. Physical relationships (from Section 2) ^  155 156  Appendix A.2: List of parameters used in the simulations in Section 4 with range of observed and literature values from previous studies ^  158  vi  List of Tables Table 2.1. Summary of parameters and equations used in section 2.4. ^ 47 Table 2.2. Viscosity and binary diffusion coefficients used in the simulations in sections 2.3.2, 2.3.3 and 2.4 (T = 298 K). ^  47  Table 2.3. Summary of parameters and equations used in section 2.5. ^ 48 Table 2.4. Initial and boundary conditions in the simulation of methane attenuation in the crude oil spill site. ^  49  Table 2.5. Initial and boundary conditions in the simulation of pyrite oxidation' ^ 49 Table 3.1. Reaction stoichiometry and rate expressions ^  87  Table 3.2. Simulation parameters ^  88  Table 4.1. Soil parameters ^  125  Table 4.2. Crude oil composition for vadose zone simulations ^ 125 Table 4.3. Reaction stoichiometries, rate expressions and constants used for reactions in the simulations^ Table A2.1. Parameters for the physical domain and time.......... Table A2.2. Parameters for the geochemical system and transport ^  126 158 .159  vii  List of Figures Figure 2.1. Methane concentrations as a result of (a) diffusion in the molecular regime, (b) diffusion in the transition regime and (c) advection-dominated transport in the molecular regime. Model results in solid lines; results from Fen and Abriola (2004) in symbols ^  50  Figure 2.2. Comparison between model results (solid lines) and results from Thorstenson and Pollock (1989) (symbols) for the concentrations of N2, 02, and CH4. ^ 50 Figure 2.3. Advective, diffusive, non-equimolar components of the net flux for (a) N2(g) and (b) C1-14(g). Model results in solid lines; results from Thorstenson and Pollock (1989) in symbols ^  51  Figure 2.4. Comparison between model results (solid lines) and results from De Visscher and Van Cleemput (2003) (open symbols) for the concentrations of N2, 02, CO2, and CH 4 . Filled symbols are experimental data. (a) Stefan Maxwell equations (b) Dusty Gas model ^  51  Figure 2.5. (a) Velocity and pressure in the landfill cover soil column simulated using the equimolar Stefan-Maxwell equations. (b) Advective, diffusive, non-equimolar components of the net flux of CH 4 simulated using the equimolar Stefan-Maxwell equations ^  52  Figure 2.6. Molar fractions of 02, CO2, CH4, N2 and Ar along the section. Solid lines are model results; symbols are field data. A relative enrichment of N2 and Ar and depletion of atmospheric 0 2 is observed around the reaction zone. ^ 52 Figure 2.7. Simulated aqueous saturation profile. ^  52  viii  Figure 2.8. Advective, diffusive, non-equimolar components of the net flux for (a)  N2,  (b)  CO 2 , (c) CH 4 , and (d) 02. ^  53  Figure 2.9. pH and concentrations of Ca 2+ , and of the carbonate aqueous species (a) in the presence of calcite, and (b) in the absence calcite. Lysimeter data measured near well 601 is presented in symbols: pH (squares) and Ca2+ (diamonds). ^ 53 Figure 2.10. Simulated total and partial pressures during pyrite oxidation in (a) a carbonate-rich system and (b) a carbonate-depleted system. ^ 54 Figure 2.11. pH and concentrations of the carbonate aqueous species in (a) a carbonaterich system, and (b) a carbonate-depleted system ^  54  Figure 2.12. Advective, diffusive, non-equimolar components of the net flux for 02 in (a) a carbonate-rich system and (b) a carbonate-depleted system during pyrite oxidation. 54  ^  Figure 3.1. Experimental column set up (adapted from Scheutz and Kjeldsen, 2003) ^ 89 Figure 3.2. Gas concentrations: (a)  N2, 02, CO2  and CH4; (b) trichlorofluoromethane  (CFC-11) and dichlorodifluoromethane (CFC-12); and (c) chlorodifluoromethane (HCFC-21) and chlorofluoromethane (HCFC-22). Experimental data in symbols, simulated results in solid lines 89 Figure 3.3. Simulated oxidation rates: (a) CH4; (b) trichlorofluoromethane (CFC-11) and dichlorodifluoromethane (CFC-12); and (c) chlorodifluoromethane (HCFC-21) and chlorofluoromethane (HCFC-22). ^  90  Figure 3.4. Simulated flux components for (a) CH4, (b) CO2, (c) 02, and (d) N2 ^ 90 Figure 3.5. Simulated pressure and advective velocity^  91  ix  Figure 3.6. Concentrations of N2, 02, CO2 and CH 4 (a) at low and (b) high gas influxes. Experimental data in symbols, simulated results in solid lines ^ 91 Figure 3.7. Simulated fluxes at top of column for variable gas fluxes for (a) CH4 and (b) 02 ^  92  Figure 3.8. Simulated fluxes at top of column for constant gas influx rate (0.24 m (1 -1 ) for 02 ^  92  Figure 3.9. Simulated gas concentrations at influx rate of 0.24 m d -1 for a 70/30% v/v CH4/CO 2 mixture^  93  Figure 3.10. Simulated 02 flux at top of column for variable column saturation ^ 93 Figure 3.11. Simulated cumulative consumption of CH4 for different saturations. ^ 94 Figure 3.12. (a) Simulated aqueous saturation at 180 d and (b) CH 4 gas fluxes at 180 d, compared with CH4 net flux at steady-state conditions for the case with no water production^  94  Figure 3.13. Simulated effect of the accumulation of exopolymeric substances (EPS) on (a) gas pressure and advective gas flux at 180 d and (b) CH4 gas fluxes ^ 95 Figure 4.1. Cross section of contaminated aquifer (adapted from Delin et al., 1998).... 128 Figure 4.2. Schematic with relevant processes included in the conceptual model for (a) early times and (b) late times. Shaded area indicates the presence of oil at different saturations  129  Figure 4.3. Cross-sections of aquifer showing vapor-phase gas data collected in 2007 ^ Vapor-phase contours are in % mole fractions. Well numbers for each vapor well are shown. Note the vertical exaggeration with the ratio between vertical and horizontal axes being 20:3 is used in this and following figures. ^  130  Figure 4.4. Initial and boundary conditions for variably saturated flow and reactive transport model^  131  Figure 4.5. Cross-sections of aquifer showing simulated vapor-phase gas at 2007 for the heterogeneous case. Vapor-phase contours are in % mole fractions. ^ 132 Figure 4.6. Simulated rates of CH 4 aerobic oxidation and NVDOC anaerobic oxidation. ^  133  Figure 4.7. Most probable number at location A (upgradient) and B (downgradient) for methanotroph populations. Adapted from Bekins (pers. comm.) ^ 133 Figure 4.8. Simulated gas pressures in 2007. Shaded areas indicate zone of elevated (dark) and lowered (light) pressure. ^  134  Figure 4.9. Simulated N2 (a) advective and (b) diffusive fluxes in 2007. Vector head at point of estimation. Vertical exaggeration applies only to spatial coordinates not to vectors, which show true directions.  134  Figure 4.10. Simulated CH4 and 02 (a) advective and (b) diffusive fluxes in 2007. Vector head at point of estimation. Vertical exaggeration applies only to spatial coordinates not to vectors, which show true directions. ^  135  Figure 4.11. Simulated pH and calcite dissolution rates in 2007. ^ 135 Figure 4.12. Evolution of gas concentrations over time. Data for 1985 and 1997 has been interpolated from nearby ports. The brackets for the 1985 C4H10 data point include a range of concentrations corresponding to different average molecular weights for the VOC mixture (total VOC concentrations were reported in g 111 -3 in Hult and Grabbe [ 1988]). The upper bound corresponds to propane (C 3 H 8 ), and the lower bound to hexane (C6H16). ^  136  xi  Figure 4.13. Simulated depletion of Fe(III) and Mn(IV) minerals in 1994. ^ 136 Figure 4.14. Cross-sections of aquifer showing simulated vapor-phase gas in 1979 for the heterogeneous case. Vapor-phase contours are in % mole fractions. ^ 137  xii  Acknowledgements I would like to thank my thesis supervisor Dr. Uli Mayer for his continued support and guidance throughout this research, and for what I have learned during my PhD. I would also like to thank committee members Dr. Leslie Smith and Dr. Roger Beckie for their advice during my time at UBC, and the external and university examiners. I am also grateful to Dr. Rich Amos and Dr. B. Bekins for helpful discussions on modeling the Bemidji site, and to Dr. Peter Kjeldsen and Dr. Charlotte Scheutz for their help in modeling the landfill cover soil experiment. Funding for this research was provided by a University Graduate Fellowship awarded to S. Molins and through an NSERC (Natural Sciences and Engineering Research Council of Canada) discovery grant held by K. Ulrich Mayer. Additional financial support was provided by a Thomas and Marguerite MacKay Memorial Scholarship funded by Mr. David MacKay, and an Egil H Lorntzsen Scholarship funded by Mr. Charles Burge. I would like to thank everybody that has contributed to make these years in Vancouver a truly great experience. Thanks for the good times and the hand when I needed it in the office and elsewhere to Bruno, Ted, Angus, Alex, Rich, Tom, Payam, Yaming, Cindy, Randi, Craig, Cathy, Karin, Joe, Mark, Mario, Scot, Katie, Parisa and Murthy. Als meus pares, per tot el que han fet i han deixat de fer per mi. I a la Marta i al Xavier, per ser els millors. To Neda, for the support to finish this thesis successfully, and the love and disorder necessary for happiness.  Co-Authorship Statement  This thesis has been prepared as a collection of manuscripts either published, accepted for publication or in preparation. Although these manuscripts have been coauthored with individuals other than myself, I am the first author in each case and have conducted the research and manuscript preparation. The objectives of each chapter and research approach are based on my initiative in consultation with my thesis supervisor Dr. U. Mayer. The actual research work including model development, implementation of the Dusty Gas Model, and numerical simulations has been entirely done by myself My advisor provided guidance towards content and structure of the manuscripts. Only limited support was provided by coauthors other than my thesis advisor, as outlined below. Chapter 3 presents the modeling of column experiments conducted previously by Dr. C. Scheutz and Dr. P. Kjeldsen of the Technical University of Denmark. Charlotte Scheutz and Peter Kjeldsen supplied the data for the modeling study and also provided advice regarding interpretation of the raw data obtained from the column experiments. Peter Kjeldsen also offered minor comments on the manuscript. Chapter 4 presents the modeling of a site contaminated by a crude-oil spill. Dr. R. Amos of the University of Waterloo and Dr. Barbara Bekins of the United States Geological Survey, provided input for the development of the site-specific conceptual model and offered advice regarding the modeling approach. Field data have been collected over the years by a number of researchers including my co-authors. Data collection was not part of my project.  xiv  1. Introduction  1  1.1. Motivation Contamination of groundwater resources is a major environmental problem at many sites. Sources of subsurface contamination include disposal of urban, industrial and mining waste, leaking underground storage tanks, accidental spills from pipelines among others (Metcalfe and Farquhar, 1987; Falta et al. 1989; Mendoza and Frind, 1990; Elberling and Nicholson, 1996; Fischer et al., 1996; Ritchie, 2003; Binning et al., 2007; Scheutz and Kjeldsen, 2003; Linklater et al., 2005). The vadose zone is the first environment encountered by contaminants on their way to the water table. The vadose zone can also contribute to the attenuation of volatile contaminants that are released from subsurface sources or are produced in the soil environment through biogeochemical reactions (Hilger et al., 1999; Stein et al., 2001; Scheutz and Kjeldsen, 2003; Klusman, 2003). In the vadose zone, transport of contaminants can take place in different fluid phases and reactions can occur between mobile and immobile phases. For volatile contaminants, transport in the gas phase is of particular interest since it is much more rapid, and contributes to the spread of contamination in the subsurface (Thorstenson and Pollock, 1989; Massmann and Farrier, 1992; Popovicova, and Brusseau, 1997). Gasphase contaminants are often present in multicomponent gas mixtures (Sleep, 1998). Homogeneous and heterogeneous reactions that occur in the vadose zone may degrade contaminants to less harmful substances, thereby limiting the extent of the contamination (Gaganis et al., 2004; HOhener et al., 2006). However, biogeochemical reactions can also result in the mobilization of contaminants, or the production of secondary contaminants such as methane (Xu et al., 2000; Ritchie, 2003; Amos et al.,  2  2005). In general, consumption and production of gases during reactions can generate pressure and concentration gradients that drive advective and diffusive fluxes (Sleep, 1998; Amos et al., 2005). The interplay between gas transport, solute transport, and biogeochemical reactions results in a dynamic and inherently coupled system (Xu et al., 2000). Reactive transport models can be used to investigate flow, transport and reaction processes in subsurface environments in both the saturated and unsaturated zones. Most of the existing reactive transport models focus on the saturated zone (e.g. White, 1995; Steefel, 2004; Lichtner et al., 2004), while modeling of reactive transport in the unsaturated zone is still a fairly new area of research (Simunek and Suarez, 1994; Mayer et al., 2002; Saaltnik et al., 2004). Some published studies propose simplified models, which describe diffusive gas transport using Fick's law, neglecting multicomponent effects (Simunek and Suarez, 1994; Mayer et al., 2002; Saaltnik et al., 2004) and advection (Simunek and Suarez, 1994; Mayer et al., 2002), or they simply couple existing multiphase flow to a multicomponent transport models. This latter approach implies that no direct coupling is provided between flow, transport and reactions, and the effect of compositional changes on transport is not considered. The most rigorous description of transport in multicomponent gas mixtures is provided by the Dusty Gas Model (DGM). The Dusty Gas Model is the application of the Stefan-Maxwell equations for multicomponent transport to systems with pore walls, in which these pore walls are likened to large immobile dust particles (Mason and Malinauskas, 1983; Krishna and Wesselingh, 1997). The Stefan-Maxwell equations are derived mechanistically from a balance of the forces acting on the diffusing gas molecules: driving forces (i.e.  3  concentration gradients) and friction forces (i.e. interactions between particles) (Krishna and Wesselingh, 1997). The basic concepts behind the Stefan-Maxwell equations were put forward independently by James Clerk Maxwell (1866) and Josef Stefan (1871). When applied to a system with walls in addition to molecule-molecule interactions (molecular regime), the Stefan-Maxwell equation account for interactions between molecules and walls (Knudsen regime). Therefore, the DGM includes all relevant mechanisms of gas diffusion in multi-component mixtures in both the molecular and Knudsen diffusion regimes (Thorstenson and Pollock, 1989). In contrast, Fick's law is strictly only applicable to binary mixtures, but it has also been shown to be valid in multicomponent systems where advection is dominant or when diffusing gas species are dilute in the bulk gas phase (Fen and Abriola, 2004). Advective gas transport can be described with Darcy's law for moderate pressure gradients. Darcy's equation is not applicable, if the compression of the gas phase is significant due to high pressures.  1.2. Previous Work Gas transport and reaction processes in the vadose zone have been investigated at sites contaminated by volatile organic compounds (Falta et al., 1989; Mendoza and Frind, 1990), including those with buildings affected by the intrusion of contaminated soil gas (Garbesi et al., 1993; Fischer et al., 1996), and sites affected by generation of acid mine drainage (Ritchie, 2003, Binning et al., 2007). Additional motivation to study reactive transport processes in the vadose zone originates from the growing concern about emission of greenhouse gases to the atmosphere from sanitary landfills (Metcalfe and Farquhar, 1987; De Visscher and Van Cleemput, 2003) or leaking from reservoirs for  geologic CO 2 sequestration (Klusman, 2003; Altevogt and Celia, 2004). Models that consider coupled gas transport and reactions have been developed previously, but are designed for the solution of specific problems. In the following, modeling efforts in three environments of interest are reviewed. These include sulphide mineral oxidation in mine tailings and waste rock piles, CH4 oxidation in landfill cover soils, and attenuation of organic contamination. In mine tailings, pyrite oxidation is often limited by the availability of 02 supplied into the soil by transport from the atmosphere (Elberling and Nicholson, 1996). Most previous model developments assumed that diffusive transport dominates 02 ingress (Elberling and Nicholson, 1996; Davis and Ritchie, 1986; Wunderly et al., 1996; Mayer et al. 2002). Binning et al. (2007) showed recently that gas advection due to 02 consumption by sulfide mineral oxidation can significantly contribute to 02 ingress and affect gas transport as a whole. However, in Binning et al. (2007), pyrite oxidation was not explicitly included as a geochemical process, but was considered in a simplified manner through 02 depletion at the model boundary. The effect of other reactive gases such as CO2 on 02 transport was also not included in this study. The study of CH4 oxidation and gas migration through transport in landfill covers has also involved the use of numerical models (Hilger et al., 1999; Stein et al., 2001; De Visscher and Van Cleemput, 2003). Although some employed a multi-component formulation for gas transport (Hilger et al., 1999; De Visscher and Van Cleemput, 2003), all models included only the gaseous phase and were designed to deal exclusively with CH 4 oxidation.  5  Multiphase flow and transport models have been developed to investigate migration of NAPL phases, oil recovery, vapor injection-extraction at sites affected by organic contamination. Multiphase flow and transport models have also been used to study the fate and attenuation of volatile organic compounds (e.g. Falta et al, 1989, Mendoza and Frind, 1990). Although multiphase and compositional models allow simulating aqueous and gaseous flow and transport in a coupled manner, they do not include a wide range of geochemical reactions, but typically focus on inter-phase mass transfer, with reaction capabilities limited to first order decay and linear sorption (Abriola and Pinder, 1985; Corapcioglu and Baehr, 1987; Falta et al. 1989; Sleep and Sykes, 1989; Sleep, 1998). In a recent review of public domain codes for modeling the fate of VOC mixtures in the unsaturated zone, Karapanagioti et al. (2003) recognized that only a small number of codes consider vapor advection and even fewer models include reaction processes such as biodegradation. General-purpose models that couple gas transport, solute transport and a wide range of geochemical reactions in the vadose zone have been developed previously (Simunek and Suarez, 1994; White, 1995; Xu et al., 2000; Mayer et al., 2002; Steefel, 2004; Saaltink et al., 2004; Lichtner et al., 2004; Linklater et al., 2005). Although some of these models considered gas advection (White, 1995; Xu et al., 2000; Saaltink et al., 2004; Lichtner et al., 2004; Linklater et al., 2005), none of these models incorporates multi-component gas transport (e.g. the Dusty Gas Model) into a rigorous description of the feedback between geochemical reactions and gas transport processes.  6  1.3. Objectives  The objectives of this work are 1) the development of a reactive transport model that includes geochemical reactions, advective-diffusive transport in the aqueous phase, and a comprehensive formulation for gas transport, including diffusion in the molecular and Knudsen regimes, non-equimolar diffusion, and advection. In contrast to multiphase models, this model only considers the aqueous and gaseous phases; 2) the evaluation of the importance of feedback mechanisms between transport in the gas phase and homogenous and heterogeneous reactions; 3) the evaluation of the contribution of the different transport mechanisms to gas fluxes in the unsaturated zone, with a focus on reaction-induced transport; 4) the study of the effect that hydrogeological factors such as moisture content and permeability have on gas transport in the vadose zone; and 5) the application of the model to study three systems of environmental interest: pyrite oxidation in mine tailings, attenuation of CH4 emissions in landfill cover soils, migration and attenuation of organic contaminants at a crude oil spill site.  1.4. Organization  This thesis has been organized in three main chapters (chapters 2-4). Chapter 2 contains a description of the model, verification examples, and 1D example applications of the model. Model development is based on the existing reactive transport code MIN3P (Mayer et al., 2002) and focuses on the derivation and presentation of the equations accounting for the contributions of multicomponent gas advection and diffusion to the mass balance equations. The model is applied to investigate gas transport in mine tailings. Focus is placed on the feedback processes between mineral reactions and gas  7  transport. The role of sulfide mineral oxidation and calcite dissolution in determining diffusive and advective fluxes is analyzed. Chapter 3 presents an investigation of the performance of an experimental soil column designed to simulate the attenuation of CH 4 , CFCs and HCFCs in landfill cover soils. The evaluation of the contributions of various gas transport mechanisms and the effect of oxidation reactions on the overall gas transport regime are the main points in this chapter. In addition, the model is used to illustrate the effect of physical, chemical and environmental factors on the attenuation of CH4 and trace gases. Processes such as production of water and the accumulation of exopolymeric substances (EPS) associated with methanotrophic activity are considered, and their effect on moisture content and permeability is analyzed. In Chapter 4, the feedback processes between VOC transport and degradation are studied in 2D simulations of an oil spill site located near Bemidji, Minnesota. This site has been the focus of extensive work to study the natural attenuation of petroleum hydrocarbons since an underground pipeline ruptured in 1979. The processes that drive gas-phase plume formation and attenuation are analyzed using the model developed in this thesis. Volatilization, aerobic and anaerobic oxidation of VOC's, production and fate of reaction products such as CH4 and CO2 are included. Advective and diffusive contributions to gas fluxes are quantified and the model is used to reproduce the transient evolution of the unsaturated contaminant plume at the site. Various hypotheses are developed to provide possible explanations for the present day and past distribution of gases in the vadose zone. Parameters considered in this analysis include layered sediment  8  structure (heterogeneity), water content, and ebullition of gases produced in the saturated zone into the unsaturated zone.  9  References Abriola L., and G. Pinder (1985), A multiphase approach to the modeling of porous media contamination by organic compounds. 1. Equation development. Water Resour. Res., 21(1), 11-18. Altevogt, A.S., and M.A. Celia (2004), Numerical modeling of carbon dioxide in unsaturated soils due to deep subsurface leakage, Water Resour. Res., 40(3), W03509 10.1029/2003WR002848. Amos, R., U. Mayer, B. Bekins, G. Delin, and R. Williams (2005), Use of dissolved and vapor-phase gases to investigate methanogenic degradation of petroleum hydrocarbon contamination in the subsurface. Water Resour. Res., 41(2), W02001 http://dx.doi.org/10.1029/2004WR003433. Binning, P., D. Postma, T.F. Russell, J. Wesselingh, and P. Boulin (2007), Advective and diffusive contributions to reactive gas transport during pyrite oxidation in the unsaturated zone, Water Resour. Res., 43, W02414, doi:10.1029/2005WR004474. Corapcioglu, M.Y., A.L. Baehr (1987), A Compositional Multiphase Model for Groundwater Contamination by Petroleum Products. 1. Theoretical Considerations, Water Resour. Res., 23(1), 191-200. Davis, G., and A. Ritchie (1986), A model of oxidation in pyritic mine wastes: part 1. Equation and approximate solution, Appl. Math. Modell., 10, 314-332. De Visscher, A., and 0. Van Cleemput (2003), Simulation model for gas diffusion and methane oxidation in landfill cover soils. Waste Management, 23, 581-591. Elberling, B., and R. V. Nicholson (1996), Field determination of sulphide oxidation rates in mine tailings, Water Resour. Res., 32, 1773-1784.  10  Falta, R.W., I. Javandel, K. Pruess, and P. Witherspoon, (1989), Density-driven flow of gas in the unsaturated zone due to evaporation of volatile compounds. Water Resour. Res., 25(10), 2159-2169. Fen C.-S., and L.M. Abriola (2004), A comparison of mathematical model formulations for organic vapor transport in porous media, Adv. Water Resour., 27,1005-1016. Fischer, M.L., A. Bentley, K. Dunkin, A.T. Hodgson, W.W. Nazaroff, R.G. Sextro, and J.M. Daisey (1996), Factors Affecting Indoor Air Concentrations of Volatile Organic Compounds at a Site of Subsurface Gasoline Contamination, Environ. Sci. Technol., 30,2948-2957. Gaganis, P., P. Kjeldsen, and V.N. Burganos (2004), Modeling Natural Attenuation of Multicomponent Fuel Mixtures in the Vadose Zone: Use of Field Data and Evaluation of Biodegradation Effects, Vadose Zone Journal, 3,1262-1275. Garbesi, K., R.G. Sextro, W.J. Fisk, M.P. Modera, and K.L. Revzan (1993), Soil-gas entry into an experimental basement: model measurement comparisons and seasonal effects. Environ. Sci. Technol. 27(3), 466-473. Hilger, H.A., S.K. Liehr, and M.A. Barlaz (1999), Exopolysaccharide control of methane oxidation in landfill cover soil. Journal of Environmental Engineering, 125, 1113-1123. HOhener, P., N. Dakhel, M. Christophersen, M. Broholm, and P. Kjeldsen (2006), Biodegradation of hydrocarbons vapors: Comparison of laboratory studies and field investigations in the vadose zone at the emplaced fuel source experiment, Airbase Vxrlose, Denmark, J. Contam. Hydrol., 88: 337-358.  11  Karapanagioti, H.K., P. Gaganis, and V.N. Burganos (2003), Modeling attenuation of volatile organic mixtures in the unsaturated zone: codes and usage, Environmental Modelling & Software, 18, 329-337. Klusman, R.W. (2003), Computer modeling of methanotrophic oxidation of hydrocarbons in the unsaturated zone from an enhanced oil recovery/sequestration project, Rangely, Colorado, USA. Applied Geochemistry, 18, 1839-1852. Krishna, R., and J.A. Wesselingh (1997), The Maxwell-Stefan approach to mass transfer, Chemical Engineering Science, 51(6), 861-911 Lichtner, P.C., S. Yabusaki, K. Pruess, and C.I. Steefel (2004), Role of Competitive Cation Exchange on Chromatographic Displacement of Cesium in the Vadose Zone beneath the Hanford S/SX Tank Farm, Vadose Zone Journal, 3, 203-219. Linklater, C., D. Sinclair, and P. Brown (2005), Coupled chemistry and transport modelling of sulphidic waste rock dumps at the Aitik mine site, Sweden, Applied Geochemistry, 20, 275-293. Mason, E.A., and A.P. Malinauskas (1983), Gas transport in porous media: The dusty-gas model, Chemical engineering Monographs 17. Elsevier Science Publishers, Amsterdam. Massmann, J., and D.F. Farrier (1992), Effects of Atmospheric Pressures on Gas Transport in the Vadose Zone, Water Resour. Res., 28 (3), 777-791. Maxwell, J.C. (1866), On the dynamical theory of gases, Phil. Trans. R. Soc., 157, 49-88. Mayer K.U., E.O. Frind, and D.W. Blowes (2002), Multicomponent reactive transport modeling in variably saturated porous media using a generalized formulation for kinetically controlled, Water Resour. Res., 38(9), 1174, 10.1029/2001WR000862.  12  Mendoza, C., and E. Frind (1990), Advective-Dispersive Transport of Dense Organic Vapors in the Unsaturated Zone. 1. Model Development, Water Resour. Res., 26(3), 379-387. Metcalfe, D.E., and G.J. Farquhar (1987), Modeling gas migration through unsaturated soils from waste disposal sites. Water, Air, and Soil Pollution, 32, 247-259. Popovicova, J., and M.L. Brusseau (1997), Dispersion and transport of gas-phase contaminants in dry porous media: effect of heterogeneity and gas velocity, J. Contam. Hydrol., 28, 157-169. Ritchie, A.I.M. (2003), Oxidation and Gas Transport in Piles of Sulfidic Material in Environmental Aspects of Mine Wastes, eds. J.L. Jambor, D.W. Blowes and A.I.M. Ritchie, Mineralogical Association of Canada, Short Course Series, Volume 31, Vancouver, BC, 2003. Saaltink, M.W., F. Batlle, C. Ayora, J. Carrera, and S. Olivella (2004), RETRASO, a code for modeling reactive transport in saturated and unsaturated porous media, Geologica Acta, 2(3), 235-251. ‘S'imilnek, J., and D.L. Suarez (1994), Two dimensional transport for variably saturated porous media with major ion chemistry. Water Resour. Res., 30(4), 1115-1134. Scheutz, C., and P. Kjeldsen (2003), Capacity for Biodegradation of CFCs and HCFCs in a Methane Oxidative Counter-Gradient Laboratory System Simulating Landfill Soil Covers, Environ. Sci. Technol., 37(22), 5143 - 5149; doi:10.1021/es026464+ Sleep, B.E., and J.F. Sykes (1989), Modeling the Transport of Volatile Organics in Variably Saturated Media, Water Resour. Res., 25(1), 81-92.  13  Sleep B.E. (1998), Modeling transient organic vapor transport in porous media with the Dusty Gas model, Adv. Water Resour., 22(3):247-56. Steefel, C.I. (2004), Evaluation of the field-scale cation exchange capacity of Hanford sediments in Proceedings of the 11th International Symposium on Water-Rock Interaction, R.B. Wanty and R.R. Seal (eds.), Taylor and Francis Group, London,  999-1002. Stefan, J. (1871), Ober das Gleichgewicht and die Bewegung insbesondere die Diffusion von Gasgemengen, Sitzber. Akad. Wiss. Wien, 63,63-124. Stein, V.B., J.P.A. Hettiaratchi, and G. Achari (2001), Numerical Model for Biological Oxidation and Migration of Methane in Soils, Practice Periodical of Hazardous, Toxic, and Radioactive Waste Management, 5(4), 225-234.  Thorstenson D.C., and D.W. Pollock. 1989. Gas Transport in Unsaturated Zones Multicomponent Systems and the Adequacy of Fick's Laws, Water Resour. Res., 25(3): 477-507. Xu, T., S.P. White, K. Pruess, and G.H. Brimhall (2000), Modeling of Pyrite Oxidation in Saturated and Unsaturated Subsurface Flow Systems. Transport in Porous Media, 39,25-56. White S.P. (1995), Multiphase Nonisothermal Transport of Systems of Reacting Chemicals. Water Resour. Res., 31(7), 1761-1772. Wunderly, M. D., D. W. Blowes, E. 0. Frind, and C. J. Ptacek (1996), Sulfide mineral oxidation and subsequent reactive transport of oxidation products in mine tailings impoundments: A numerical model, Water Resour. Res., 32,3173-3187.  14  15  2. Coupling between Geochemical Reactions and Multicomponent Gas and Solute Transport in Unsaturated Media: A Reactive Transport Modeling Study  A version of this chapter has been published;  Molins, S., and K.U. Mayer (2007), Coupling between geochemical reactions and multicomponent gas and solute transport in unsaturated media: a reactive transport modeling study, Water Resour. Res., 43(5), W05435. Copyright [2007] American Geophysical Union. Reproduced by permission of American Geophysical Union.  16  2.1. Introduction  The investigation and modeling of gas transport and reaction processes in the vadose zone has received increasing interest in recent years through studies of sites contaminated by volatile organic compounds (Falta et al., 1989; Mendoza and Frind, 1990), including those with buildings affected by the intrusion of contaminated soil gas (Garbesi et al., 1993; Fischer et al., 1996), and sites affected by generation of acid mine drainage (Wisotzky, 1994; Ritchie, 2003, Binning et al., 2007). Additional motivation stems from the growing concern about emission of greenhouse gases to the atmosphere from sanitary landfills (Metcalfe and Farquhar, 1987; Scheutz and Kjeldsen, 2003) or leaking from reservoirs for CO 2 sequestration (Klusman, 2003; Altevogt and Celia, 2004). The vadose zone plays an important role because it can act as a buffer zone for contaminants on their way to the water table, but can also attenuate the emission of contaminants leaving the subsurface environment through the gas phase. In many cases, these contaminants are present as part of a multi-component mixture of gases and tend to react with atmospheric gases to produce chemical species with different chemical and physical properties. As a result, both transport processes and chemical transformations affect the composition of the gas phase, resulting in a dynamic and inherently coupled system. Examples include gas production and release in partially saturated landfills (De Visscher et al., 1999; Scheutz and Kjeldsen, 2003), methanogenesis and methane oxidation in aquifers contaminated by organic compounds (Amos et al., 2005), and the oxidation of sulfide minerals in mine waste deposits (Ritchie, 2003). In many cases, diffusion is considered the most relevant gas transport mechanism, and it is often the only mechanism included in models of vadose zone gas transport  17  (Elberling et al., 1994; Mayer et al., 2002). Gas diffusion as described by Fick's law affects each gas in a mixture differently because diffusion is driven by the concentration gradient of each individual gas and is therefore defined as a separative transport process (Thorstenson and Pollock, 1989). However, in multi-component mixtures diffusion of each gas component is also a function of the concentration of all other gas components and may include a non-separative component (Thorstenson and Pollock, 1989). Multicomponent diffusion in porous media is therefore better described by the Dusty Gas Model (DGM) (Thorstenson and Pollock, 1989, Massmann and Farrier, 1992), although in advection-dominated systems or when diffusing gas species are dilute in the bulk gas phase, a transport model incorporating Fick's law may give similar predictions to those of the DGM (Fen and Abriola, 2004). Mechanical dispersion is negligible in many gas transport applications, because its contribution to dispersion is typically small (Massmann and Farrier, 1992). However, for cases involving high velocities, such as air injection/extraction systems, the inclusion of mechanical dispersion may be required. Gas advection is non-separative in nature because it affects all gases in a mixture equally and is often a relevant gas transport process, in particular because even small pressure gradients (<1 Pam i ) can cause significant viscous fluxes (Thorstenson and Pollock, 1989). Despite its potential significance, gas advection has only been included in a limited number of models. These models show that viscous gas transport can be caused by a variety of processes including the injection and extraction of air or vapor (e.g. Massmann, 1989; Falta et al., 1992), the volatilization of organic compounds (e.g. Falta et al., 1989, Mendoza and Frind, 1990, Gaganis et al., 2004), sustained underpressurization relative to atmospheric conditions in basements of buildings and the  18  adjacent sediments (e.g.; Hers et al., 2002; Abreu and Johnson, 2005), barometric pumping (e.g. Massmann and Farrier, 1992), displacement due to infiltrating recharge water (e.g. Celia and Binning, 1992), and temperature changes (e.g. White, 1995). In low permeability media (permeabilites smaller than 10 3 -10 44 m 2 ), moleculesoil interactions become relevant and diffusive and advective fluxes are intrinsically coupled through Knudsen diffusion (Thorstenson and Pollock, 1989). Knudsen diffusion has been considered in the characterization of the composition and movement of gases in the unsaturated zone through the use of the DGM; examples of applications include the simulation of transport and consumption of atmospheric oxygen near a lignite mine (Thorstenson and Pollock, 1989), the effects of temporal variations of atmospheric pressure on gas composition (Massmann and Farrier, 1992), and forced advection and removal of benzene and toluene in a soil venting system (Sleep, 1998). In addition to gas transport, inter-phase mass transfer processes, solute transport, and biogeochemical reactions also affect the composition of the gas phase. Mass transfer between the gaseous phase and the aqueous phase is often sufficiently fast that an equilibrium approach is valid (White, 1995; Saaltink et al, 2004). At equilibrium, the ratio between gaseous and aqueous concentrations is known and equal to Henry's Law constant. Chemical reactions are described using aqueous species as primary variables in almost all multi-phase reactive transport models (e.g. Mayer et al., 2002; Saaltink et al., 2004). Mass in the aqueous phase is also exchanged with the solid phase through surface and precipitation-dissolution reactions. Biogeochemical reactions affect the composition of the gas phase by transforming reactive gas species into product species with properties such as molecular weight or  19  aqueous solubility different than those of the reactants. In consequence, chemical transformations change the composition and properties (e.g density, viscosity, and diffusion coefficients) of the gas mixture affecting the variables that control the transport processes such as pressure and concentrations. Therefore, a two-way coupling exists between gas transport and biogeochemical reactions that affects the composition of the gas phase. For instance, aerobic oxidation of methane mediated by methanotrophic bacteria produces gaseous species (carbon dioxide) with a larger aqueous solubility than the reactants. The diffusive flux of nitrogen is also affected because the binary diffusion coefficient is reduced from 2.1.10 m 2 s -I for N2 -CH4 to 1.6.10 m 2 s -I for N2-0O2. In addition, a decrease in gas volume caused by this reaction also contributes to a decrease in gas phase pressure and hence causes viscous gas transport into the reaction zone. Oxygen supplied by this flow may aid in sustaining the reaction and will contribute to maintaining the dynamic balance between transport and reaction processes. Models that consider coupled gas transport and reactions have been developed previously, but are designed for the solution of specific problems. For example, models of coupled methane oxidation and transport in landfill covers include only the gaseous phase and were designed to deal exclusively with methane oxidation (Hilger et al., 1999; Stein et al., 2001); De Visscher and Van Cleemput, 2003). Recently, the role of sulfide mineral oxidation on gas transport of 02 and N2 has been investigated by Binning et al. (2007). Multiphase flow and transport models have been developed mostly for simulating the fate and attenuation of volatile organic contaminants in the vadose zone (e.g. Falta et al, 1989, Mendoza and Frind, 1990). Although multiphase and compositional models  20  allow simulating aqueous and gaseous flow and transport in a coupled manner, they do not include a wide range of geochemical reactions, but typically focus on inter-phase mass transfer, with reaction capabilities limited to first order decay and linear sorption (Abriola and Pinder, 1985; Corapcioglu and Baehr, 1987; Falta et al. 1989; Sleep and Sykes, 1989; Sleep, 1998). In a recent review of public domain codes for modeling the fate of VOC mixtures in the unsaturated zone, Karapanagioti et al. (2003) recognized that only a small number of codes consider vapor advection and even fewer models include reaction processes such as biodegradation. Only a limited number of models exists that couple gas transport, solute transport and geochemical reactions in the vadose zone (Simunek and Suarez, 1994; White, 1995; Xu et al., 2000; Mayer et al., 2002; Steefel, 2004; Saaltink et al., 2004; Lichtner et al., 2004; Linklater et al., 2005). Although some of these models considered gas advection (White, 1995; Xu et al., 2000; Saaltink et al., 2004; Lichtner et al., 2004; Linklater et al., 2005), none of these models incorporates multi-component gas transport (i.e. DGM, Stefan-Maxwell) into a rigorous description of the feedback between geochemical reactions and gas transport processes. Here, the effect of geochemical reactions on multi-component gas and solute transport in the vadose zone is investigated through the development and application of a reactive transport model. This model is the first attempt to introduce the Dusty Gas Model into a multi-component reactive transport code that considers a full suite of geochemical reactions including intra-aqueous reactions and mineral dissolutionprecipitation. The focus of this work is on investigating the role of reaction-induced gas transport. The model is applied to several relevant problems including methane oxidation  21  in unsaturated sediments and its release to the atmosphere and interactions between sulfide mineral oxidation, ingress of atmospheric oxygen, carbonate mineral dissolution, and CO 2 release to the atmosphere.  2.2. Model development  The present model builds on the existing reactive transport model MIN3P (Mayer et al., 2002). The model description given here focuses on the development of the equations that account for the contributions of multicomponent gas transport to the mass balance equations. Other aspects of the model are only briefly described and the reader is referred to Mayer et al. (2002) for details. The mass balance equation for component k present in the aqueous and gaseous phases and written in terms of total component concentrations takes the form: a ES OT k ]-1-a [S OT k ]+V • k a Tak ]+V • [q g Tgk at a a^at g — [So D V Tak V V. N kT ,^—Qak, — Qak,ext — Qgk ,ext = 0  (1)  where t [s] is time, 0 is the porosity [m 3 void 111 -3 porous medium], Sa [m 3 H2O 111 -3 void] is the saturation of the aqueous phase, and Sg [m 3 gas 111-3 void] is the saturation of the gaseous phase. q a and q g [m s - 1 ] are the Darcy flux vectors in the aqueous and the gaseous phases, respectively, while D a [m2 s- 1 ] is the dispersion tensor for the aqueous phase, and N krg [mol m dm -3 porous medium s -1 ] is the total diffusive flux vector for component k in the gaseous phase. Tak [mol L -1 H2O] defines the total aqueous component concentration for component k, while T: [mol L -1 gas] is the total gaseous concentration for component k. These total concentration terms implicitly include 22  equilibrium reactions such as hydrolysis, aqueous complexation, aqueous phase oxidation-reduction, and mass transfer between the aqueous and gas phases (Mayer et al., 2002). Ion exchange and surface complexation reactions can also be considered as equilibrium reactions (e.g. Mayer et al., 2001a, 2001b). On the other hand, slow intraaqueous reactions and mineral dissolution-precipitation are described using a generalized kinetic formulation (Mayer et al., 2002). These reactions contribute to the mass balance equations through source-sink terms. Q ak, [mol dm -3 porous medium s -1 ] and Q"`,, [mol dm-3 porous medium s-I ] in equation (1) represent the internal sources and sinks toward the total aqueous component concentrations due to intra-aqueous kinetic reactions and kinetically controlled dissolution-precipitation reactions, respectively. A detailed description of the geochemical reaction network can be found in Mayer et al. (2002). The model is database-driven (Ball and Nordstrom, 1991) and its flexibility to include a wide range of geochemical processes has been demonstrated previously (e.g.: Mayer et al., 2001a,b, 2002, Jurjovec et al., 2004, Mayer et al., 2006). ^ext [mol dm -3 porous medium s -I ] and^Qgk ext[mol dm -3 porous medium s -1 ] are external source and sink terms for the aqueous and gaseous phase boundary fluxes, respectively. Equation (1) has been modified from Mayer et al. (2002) by the addition of the term V • [q g Tgk ] to account for gas advection and the replacement of the Fickian diffusion term in the gas phase by a multi-component diffusion term defined by V • N kTg Mechanical dispersion in the gas phase is not included in the model. Popocovicova and Brusseau (1997) report for an experimental study of methane migration, that mechanical dispersion can be neglected, unless advective velocities are large (>288 m d -1 ). Although  23  the experiments were conducted with glass beads, characterized by medium properties that are quite different from natural sediments, the maximum velocities for the examples presented in this work (ranging from 0.0016 - 5.6 m d -1 ) justify the omission of dispersive transport in the gas phase. Despite the fact that both advective flux terms in (1) have the same form, q a and q g are calculated differently. Assuming steady state flow conditions in the aqueous phase and a passive gas phase, the Darcy flux in the aqueous phase is obtained by solving the variably saturated flow problem by means of Richard's equation and Darcy's law (Mayer et al., 2002): sa ss — aaht +0 aa8; V [k a KVh]–Qa = 0^ q a = –Ica l(Vh^  (2)  (3 )  where S, [m -1 ] defines the specific storage coefficient and km [-] is the relative permeability of the porous medium with respect to the aqueous phase, h [m] is the hydraulic head, and Qa is a source-sink term [s -1 ]. K =(p a gkIp a ) [m s -1 ] is the hydraulic conductivity tensor, with p a [kg m -3 ] being the aqueous phase density, g [m 2]  being the gravitational acceleration, p a [kg m -1 s -1 ] being the aqueous phase viscosity,  and k [m2 ] being the intrinsic permeability tensor (Bear, 1972). Possible boundary conditions include specified head (Dirichlet), specified flux (Neumann), and a seepage face boundary condition.  24  The advective flux in the gaseous phase, on the other hand, is directly substituted in the mass balance equation (1). It is calculated using Darcy's law as a function of the total pressure in the gas phase ( p g [Pa])  kg k  qg  (Vpg + pg gVz)  fi g  (4)  where krg H is the relative permeability of the porous medium with respect to the gaseous phase (A1.4), pg [kg m -3 ] and fig [kg m -1 s -1 ] are the gaseous phase density and viscosity, respectively. Gas density and viscosity are calculated as a function of the gas composition according to equations (A1.1) and (A1.2) (see Appendix 1). Total pressure in the gas phase is related to the sum of the partial pressures of all gas species (  pig  [Pa]):  Ng  P g = E Pg  (5)  By means of the ideal gas law, partial pressures relate to the molar concentrations of gas species ( c'g [mol L-1 gas]): pig  = RTc' ^(6) g  with R [J Kl] being the ideal gas law constant, and T [K] the temperature of the system. For the range of pressures and temperatures usually encountered in the shallow subsurface environment, the use of the ideal gas law for real gases is not expected to lead to significant errors (Falta et al., 1989). Since concentrations of the gas species are obtained from the solution of the reactive transport equation (1), gas phase velocities adjust to compositional changes in the gas phase. In contrast to the formulation used for advection in the aqueous phase, advection in the gas phase is fully coupled with the processes that modify gas 25  concentrations. This approach ensures that a direct link between gas transport processes and chemical reactions is provided: any change in gas concentrations caused by chemical reactions has a direct effect on the gradient that drives gas transport, as described by equations (4), (5), and (6). First type boundary conditions can be applied in the aqueous phase (specified concentrations) or in the gas phase (specified partial pressures). In addition, second type boundary conditions (specified fluxes) can be defined separately for the aqueous and gas phases; and a free exit boundary condition can be used for the aqueous phase. Diffusive fluxes in the gas phase can be calculated using the Stefan-Maxwell equations within the framework of the Dusty Gas Model (Mason and Malinauskas, 1983): 1S1ix'^N i^M'c' g =^g g Oz^=1,...,N g^(7) 44 1^ gSgOr RT 1 j=.^ gDu^ g^13 Kg^ NR  X^ g^g g^.g  j^i  where x g [-] is the molar fraction of gas species i, Mg [kg mol -1 ] is the molecular weight of gas species i, and Ng [mol m dm -3 porous medium s -1 ] is the diffusive molar flux of gas species i. The right hand side of (7) must be viewed as the driving force for diffusive transport of gas species i (Thorstenson and Pollock, 1989), which includes the gravitational field in the second term (Sleep, 1998). The driving force is balanced by the friction between gas species i and all other gas species and the sediment particles as expressed by the left hand side of (7). The species concentrations and diffusive fluxes can be related to the components by means of the stoichiometric coefficients (vg)) (Mayer et al., 2002):  26  ^ ^  A1 Tk^irik .g^g i=1 Ng ivk T,g^g g =1  In equation (7), the first term on the left hand side accounts for molecule-molecule interactions, with D: [m2 s -1 ] being the free phase binary diffusion coefficient between gas species i and j, and '1- , the gas tortuosity coefficient (see equations A1.6 and A1.7 in Appendix Al). The second term accounts for molecule-sediment interactions, with  DK g '  [m2 s- 1 ] being the Knudsen diffusion coefficient for species i. The Knudsen diffusion coefficient can be calculated as a function of the Klinkenberg parameter (b, [Pa]) (Thorstenson and Pollock, 1989; Massmann and Farrier, 1992; Sleep, 1998; Fen and Abriola, 2004): =  k k^kr k M ref rg b i - ^ b ref^ef r^A i P gi g^g  (10)  where M ref [Kg mol l ] is the molecular weight of the gas of reference. The Klinkenberg parameter of the reference gas (b re, ) can be measured or estimated using expressions (A1.8) or (A1.9) (see Appendix 1). When D: » DK g , the first term in equation (7) becomes negligible, and the 1  system is said to be in the Knudsen flow regime. In this regime, gas molecules do not interact with each other but only with the sediment particles. On the other hand, when gas molecules interact only with other gas molecules (D: << D'„ g ), the system is in the  27  molecular regime and equations (7) can be simplified to the basic form of the StefanMaxwell equations (Thorstenson and Pollock, 1989): ^ M'c'g ^ — Vc i ^g g Oz lI 2C gg S g Or gDgi/ RT  Ng^-j  j ;  _1\T  j  =1,...,Ng^(11)  ^  In this form, equations (11) are linearly dependent. To make them a linearly independent set of equations, one equation in (11) needs to be replaced by an additional constraint. For example, the constraint of equimolar counter-diffusion can be used, which states that the sum of diffusive fluxes of all species is zero: Ng ND =  N i =0  g^g  (12)  In general, however, the so-called non-equimolar flux (N g° ) is not zero. The nonequimolar flux occurs in systems with walls (soil particles) because diffusing species have different molecular weights: lighter molecules move faster than heavier molecules (Cunningham and Williams, 1980). Although diffusive in origin, the non-equimolar flux results in a non-separative flux in the same direction as the diffusive flux of the lightest gas species in the mixture. In conclusion, the diffusive flux of gas species i (Ng) can be split in two components: a separative flux (J' g ) and a non-separative flux (zgN°g ) (Thorstenson and Pollock, 1989) such that: N' Ng^ =J'g^gg +xN D^(13) The use of the constraint expressed by (12) implies that the non-equimolar component of the diffusive fluxes is not included (Ng =Jig ) (Fen, 1993). For a non-equimolar  28  formulation of equations (11), the additional constraint can be set by Graham's law of effusion/diffusion (Fen, 1993): Ng  E (mg, ) ./2 Nig =0  (14)  i=1  If one adds the DGM equation for each gas species (7) over all gas species, the first term on the left hand side cancels out, and the right hand side can be rearranged as a function of bulk phase properties using equations (5) and (A1.1): Ng ED g 1=1^K ,g  RT  (Vp + p g  gVz) g  (15)  Having in mind that Knudsen diffusion coefficients are inversely proportional to the square root of the molecular weights of the gas species (equation 10), comparison of equations (14) and (15) shows that the DGM formulation implicitly includes the nonequimolar flux component. Further, in the isobaric case ( Vp g + pg gVz = 0 ), equation (15) simplifies to (14). Finally, when in and DK' g have similar magnitudes, the system is in the socalled transition regime, and both free phase and Knudsen diffusion processes contribute to the diffusive fluxes.  2.3. Numerical implementation  The different formulations presented in the previous section have been implemented in a modular fashion into an existing computer code for the simulation of multi-component reactive transport problems in variably saturated porous media (Mayer et al., 2002). The resulting code now allows the user to select the model of gas diffusion:  29  the Stefan-Maxwell equations in the form of the DGM (7), the basic Stefan-Maxwell equations (11), or the standard Fickian description (as implemented in Mayer et al., 2002). The model also includes a gas advection term (4). The domain is discretized spatially using the finite volume method, and an implicit scheme is employed for time discretization. To increase the efficiency of the solution, avoid oscillations, and to ensure its physical correctness when sharp concentration fronts are present, an upstream weighting scheme has been employed for solving the advective component of the transport equations. Although this standard Eulerian formulation can lead to poor accuracy when simulating the advective-diffusive migration of concentration fronts (Daus et al., 1985), the systems investigated in this work are characterized by rapid gas transport under quasi-steady state conditions with concentration gradients mostly controlled by boundary conditions and geochemical reactions. Under these conditions, Eulerian methods provide adequate accuracy, even for large time steps (Saaltink et al, 2001). The implementation is unconditionally stable, and in the simulations presented in the next section, no stability issues have appeared. The concentrations of the components as species in solution ( ) have been chosen as the primary variables (Mayer et al., 2002). Concentrations of aqueous complexes, gases, surface complexes and secondary redox species in equilibrium are dependent variables (Mayer et al., 2002). In the current implementation, the diffusive flux equations (9, 7, and 11) and the advective flux equations (4, 5 and 6) are substituted directly into the mass balance equations (1). Although there is no consensus about the relative merits of the various coupling approaches for reactive transport problems (e.g. Bell and Binning, 2002), some  30  authors have favored the direct substitution approach (DSA) over sequential approaches for problems involving a high number of flushed pore volumes. The DSA allows for the use of relatively large time steps without loss of accuracy, while the use of sequential approaches in such systems often requires small time steps leading to long computation times (Saaltink et al., 2001, Calderhead and Mayer, 2004). In the case of gas transport, low viscosities of soil gas and large diffusion coefficients lead to short transport time scales, and the solution of the governing equations can benefit from the direct substitution approach, as implemented here. The code uses an adaptive time stepping scheme, which determines the size of the time increment based on the relative change in aqueous concentrations and the number of Newton iterations in the previous time step. The size of the time steps is limited by a user-specified maximum value or, if smaller than that value, by the stiffness of the set of equations. In the systems of interest, stiffness originates in the fact that the processes involved have very different time scales: rapid gas transport compared to relatively slow reactions.  2.4. Gas transport mechanisms and model verification The model was verified by comparison to literature examples of gas transport modeling. These examples are also used to highlight the capabilities of the code including transport in binary and multi-component mixtures by molecular diffusion, Knudsen diffusion and advection. A validation of the model's capability to couple gas transport and geochemical reactions is provided by the example of methane oxidation in landfill  31  cover soils. The geochemical module has been verified previously applied to a number of studies (e.g. Mayer et al., 2001a,b; Mayer et al., 2002; Mayer et al., 2006).  2.4.1. Non-reactive binary transport in the molecular and transition regimes  The model presented in the previous section can simulate advective-diffusive transport in both molecular and transition regimes. The results obtained with the DGM presented in Fen and Abriola (2004) (hereinafter FA) for the transport of  N2 and  CH4 in a  1D horizontal domain under three different sets of conditions are compared to results obtained using the present DGM formulation (equation 7). Simulation parameters are presented in Table 2.1. For all cases, the pore space is initially filled with  N2.  At time  zero, the methane mole fraction is set to 1 at the left boundary. In the absence of an imposed pressure gradient, diffusion-dominated transport occurs in the molecular regime when a high permeability porous medium is considered (case 1, Figure 2.1a). The model is also able to simulate Knudsen diffusion in low permeability media (case 2, Figure 2.1b), which results in reduced diffusive fluxes with respect to those in the molecular regime (Figure 2.1 a). On the other hand, advection-dominated transport occurs under an imposed pressure gradient of 10 Pa m -1 that drives advective flux away from the methane source (case 3, Figure 2.1c). For all cases, the results obtained using the DGM implemented in the present model agree well with results obtained by FA (Figure 2.1).  2.4.2. Non-reactive multi-component transport in the molecular regime  In addition to binary transport, the present model incorporates multi-component diffusion and advection. Example 1 in Thorstenson and Pollock (1989) (hereinafter TP)  32  presents the simulation of steady-state multi-component gas transport in a 10-meter column of unsaturated porous medium with a permeability of 10 -12 m2 (Table 2.1). Whereas the top boundary is kept at atmospheric conditions ( g2 = 0.78, p g°2 = 0.20 ,  pC°2^Ar = 0. 01 , p = 0.01,p g = 0.0), methane is being produced at the bottom at a rate cH4  of 10 4 mol m -2 s 1 . In TP, the effects of gravity on gas transport are included; however, gravity gradients are not reported individually but lumped together with pressure gradients: Vp g i= Vp g + p g g\7z^  (16)  Results from the present DGM model compare well with those of TP (1989) in terms of concentrations (Figure 2.2), fluxes (Figure 2.3) and gradients ( Vp g '=24.4 Pam 1 ). The implementation of the DGM also allows accounting for the non-equimolar flux component of diffusion. Methane, which constitutes most of the gas phase in the column, has a smaller molecular weight than gases in the atmosphere, and causes an upward nonequimolar component in the diffusive fluxes (Figure 2.3).  2.4.3. Methane attenuation and multi-component transport in landfill cover soils  In order to study the capacity of a landfill cover soil to attenuate the emissions of contaminant gases to the atmosphere, De Visscher et al. (1999) conducted a column experiment with artificial landfill gas. A constant flux of CI-14 (13.4 mol m 2 d -I ) and CO2 (13.4 mol rri 2 d -1 ) was applied at the bottom of the column while the top was kept at atmospheric conditions (  p = 0.78, p° = 0.21, p c o2 = 0.01, pgcH4 = 0.0). The column gN2  2  33  was microbially reactive after being filled with landfill top cover soil and methane was oxidized by atmospheric oxygen diffusing into the column. The capability of the model to couple a wide range of geochemical reactions, as well as gas and solute transport makes it adequate to simulate these experiments. Simulation results are compared to experimental data and to modeling results by De Visscher and Van Cleemput (2003) (hereinafter DV), who developed a model based on the Stefan-Maxwell equations specifically designed to simulate the experimental results. Of two possible stoichiometric relationships for the oxidation of methane in the column explored in DV, equation (17) provided a better fit to experimental data, and is used in this work: CH 4 +1.5 02 —> 0.5 CO2 +1.5 H 2 0 ± 0.5 CH 2 0  (17)  In DV, the reaction rate was modeled with a kinetic expression that accounted for variable methanotrophic activity. However, it was found that model results were relatively insensitive to it. Therefore, in the present work the following hyperbolic expression is used: (  R CH4 = —k CH4  CH4  Ca v  C 02  (^  , „cH4 ",  K2^a + c °2  (18)  where K1 and K2 are the half-saturation constants for CH4 and 02, respectively. The reaction rate constant (^) is set equal to 7.5.10 -7 moles kg t- DRY WEIGHT 4 in accordance with the maximum oxidation rate reported by DV. Permeability was not reported in DV, and it is estimated at 2.10 13 m2 corresponding to a loamy sand. The parameter values used in the simulation are summarized in Tables 2.1 and 2.2.  34  Model results obtained with the present model (using the equimolar StefanMaxwell equations (11, 12)) are shown in Figure 2.4a together with DV's model results and experimental data (De Visscher and Van Cleemput, 2003). The present model produces almost identical results to DV's model; small discrepancies encountered mostly near the reaction zone can be attributed to the slightly different reaction rate model used that leads to differences in the calculated reaction rates of less than 3% with respect to those of DV's model (not shown). Results obtained using the DGM (7) (Figure 2.4b) are slightly different than those obtained using the equimolar Stefan-Maxwell equations (11, 12) because the DGM includes a non-equimolar flux component as well as Knudsen diffusion. A more detailed comparison between the two formulations is beyond the scope of this paper; the reader is referred to other works (Massmann and Farrier, 1992; Sleep, 1998; Fen and Abriola, 2004). It can be observed that the oxidation of methane leads to a decrease in pressure gradient in the reaction zone, which in turn results in a decrease in the advective velocity (Figure 2.5a). As a result, advection is not a relevant process for methane emission to the atmosphere (Figure 2.5b).  2.5. Investigation of interactions between transport and reactions  In this section, the interactions between multi-component gas transport, solute transport, and geochemical reactions are investigated for two systems of relevance in environmental earth sciences. Special attention is paid to the effects of reactions on gas advection, and multi-component gas diffusion as well as the effects of inter-phase mass transfer processes on the composition of the gas phase. Aqueous phase flow and transport is also included and flow is assumed at steady state; moisture content thus remains fixed  35  over the simulation time. In addition, atmospheric pressure fluctuations are excluded. Such fluctuations are superimposed on the reaction-induced behavior, but it is assumed that their effects average out over time, while reaction induced transport is a unidirectional process. The DGM is used to calculate diffusive fluxes for both examples, as it provides the most comprehensive representation of gas diffusion in porous media.  2.5.1. Production and consumption of methane at a crude oil spill site Gas data collected by Amos et al. (2005) to study the natural attenuation of petroleum hydrocarbons at an oil spill site near Bemidji, Minnesota, suggest that biodegradation reactions cause gas advection in unsaturated contaminated sediments. Directly above the water table, measured concentrations of non-reactive gases such as argon and at this site also nitrogen, were lower than atmospheric levels, suggesting that advective gas transport towards the ground surface takes place. It was hypothesized that biodegradation by methanogenesis in the zone near the water table may cause an increase of the gas pressure driving gas advection upward, which would explain the decrease of nitrogen and argon pressures in this zone (Figure 2.6). However, higher above the water table, a region of enrichment of Ar and N2 was observed relative to atmospheric composition. This zone coincides with a region of methanotrophic activity, i.e. the oxidation of methane by oxygen. These data suggest that the decrease in gas pressure in the reaction zone drives advective gas transport into this zone. Results obtained in the landfill cover soil example (section 2.4.3) also suggested that the decrease in gas pressure caused by methane oxidation affects advective and diffusive fluxes (Figures 2.5a and 2.5b). Bemidji field data shows that while gases consumed in the reaction become  36  depleted in the methanotrophic zone, gases that do not participate in the reaction such as nitrogen and argon become enriched due to non-separative transport processes into the reaction zone. Here this conceptual model is tested in a simplified manner using 7 components (02(aq), CH4(aq), CO2(aq), Ar(aq), N2(aq), Ca 2+ , and Fr), 5 gases (02(g), CH4(g), CO 2 (g), Ar(g), and N2(g)), 2 aqueous carbonate complexes (HCO3 - , and CO 3 2 ), and the mineral phase calcite. For the simulations, it is assumed that pore water is in equilibrium with calcite, because the native aquifer material contains approximately 4-6% carbonates (Bennett et al., 1997). The system is approximated using a one-dimensional vertical section, in which CH4 and CO2 are produced at the bottom due to anaerobic degradation of the oil. Methane oxidation along the section is simulated using the rate expression given in equation (18) and according to the following stoichiometry: CH 4 + 202 ---> CO2 + 2H 2 0  (19)  The measured concentration profiles indicate significant concentration changes around 2-2.5 m of depth (Figure 2.6), which suggests the presence of a zone with inhibited gas mobility, possibly due to increased water content. The location of this zone coincides with a layer of fine-grained sediments observed in core samples from the site near the location of well 601 (USGS, 1987, unpublished data). In the simulation, a layer of lower permeability (10 13 m2 ) has been considered between 2.0 and 2.5 m depth, while it is 2.101 2 m2 above and 5.10-12 m 2 below. A recharge rate of 160 mm yr 1 results in the simulated aqueous saturation profile shown in Figure 2.7. Porosity is 0.30 in the finer grained zone and 0.38 elsewhere; aqueous advection and dispersion are included. A summary of model parameters is given in Table 2.3.  37  The influx of CH4 and CO 2 at depth and the rate of methane oxidation within the sediment column are used as calibration parameters. The parameter values that provide good agreement to observed data are 0.09 mol m -2 (1 1 and 0.009 mol t11 -2 d -1 for the influxes of CH4 and CO 2 , and 10 -7 moles L-1 s -1 for the reaction rate ( k cH4 ) respectively. The relatively high CH4 to CO2 ratio may be attributed to a range of processes including the preferential release of CH4 from the saturated zone by ebullition (Amos and Mayer, 2006); the reduced nature of carbon in crude oil (Hunt, 1979), and sequestration of CO2 in the sediments, e.g. by the precipitation of siderite (FeCO3) (Mayer et al., 2002). The simulations intend to represent the current steady-state conditions at the oil spill site. Results are shown at 3.17 years, at which time steady state was reached when the initial and boundary conditions provided in Table 2.4 were used. The reasonable agreement between observed and simulated data that could be obtained (Figure 2.6) supports the validity of the conceptual model proposed by Amos et al. (2005). As a result of methane oxidation (equation 19), 3 moles of gases (CH4 and 02) are transformed into 1 mol of CO 2 . As recognized by Scheutz and Kjeldsen (2003), this transformation causes a decrease in total gas pressure in the reaction zone. At the Bemidji site, a reversal of the gradient ( ') is observed in the reaction zone: it is upwards in the bottom 3 meters (0.21 Pam'), and downwards in the top 2.5 m (0.55 Pam'). This causes a reversal of the advective fluxes in the upper part of the section (Figure 2.8). Atmospheric 02 is supplied at the top of the section not only by diffusion (92.6 %) but also by advection (7.4 %) (Figure 2.8d). The N2 concentration profile in Figure 2.6 can only be explained by considering this downward advective component. The concentration gradient drives diffusive fluxes away from the reaction zone (upwards above 2.77 m and  38  downwards below 2.77 m). As it is assumed that  N2  is non-reactive, the net flux of N2 at  steady state must be zero; therefore, an advective flux of the same magnitude as the diffusive flux but in opposite direction must develop (Figure 2.8a). The non-equimolar N2 flux component also contributes to counteract diffusion except in a very thin layer near 2.75 m where it has the same direction as the diffusive flux (Figure 2.8a). Comparing these results with those obtained for the landfill cover soil simulation, one can observe that at the Bemidji site the emission of methane to the atmosphere is effectively shut off by both methane oxidation and reversal of gas flow (Figure 2.8c). On the other hand, in the landfill cover example, there is a significant reduction in gas flow in the top 20 cm of the column; however, the pressure gradient is not completely reversed (Figure 2.5a), and methane emissions are not completely averted (Figure 2.5b). This implies that methane oxidation contributes to the reduction of methane emissions to the atmosphere directly by removing methane and indirectly by decreasing gas advection (landfill cover soil, Figure 2.5b) or by completely shutting it off (Bemidji, Figure 2.8c). These results indicate that the significant difference in the magnitude of the gradients generated to accommodate the influxes of CH4 and CO2 in the landfill cover soil column (655 Pa m -1 or 6.2 mbar m -1 ) and at the Bemidji site (0.21 Pa  211 -1  or 2 x 10 -3 mbar m -1 )  may be responsible for the different transport regimes in these systems, both affected by methane oxidation. At the Bemidji site, the production of CO2 by oil biodegradation as well as by methane oxidation causes acidity to increase. However, the presence of calcite maintains pH values at around 6.5 in the lower part of the section (Figure 2.9a) with bicarbonate being the most abundant carbonate species (Figure 2.9a). Simulated pH values are in  39  good agreement with those measured in lysimeter samples collected at the Bemidji site (pH=6.7) (Figure 2.9a). If calcite is not included, simulated pH drops to values below 5 (Figure 2.9b). Although the simulated low pH conditions are unrealistic, this simplification would have little effect on the gas transport regime, because the dissolution of calcite contributes mostly to increase the concentration of bicarbonate but not CO2 (compare Figures 2.9a and 2.9b). Lysimeter data also show that aqueous concentrations of Ca2+ increase with depth to a maximum of 3.3.10 -3 mol L-1 H2O, which is again in agreement with simulated concentrations of Ca 2+ (Figure 2.9a). Aqueous flow does not appear to contribute significantly to the transport of chemical components into the column. For example, the net aqueous flux of total inorganic carbon (TIC) in the recharge water into the column is less than 1% of the net flux of CO2(g) out of the column. The relevance of aqueous fluxes of the other gases is even smaller as their solubility is significantly smaller.  2.5.2. Acid mine drainage generation and attenuation  A hypothetical example of acid mine drainage generation and attenuation is studied using a 2-m one-dimensional variably saturated column that initially contains pyrite with a volume fraction of 0.04. Atmospheric oxygen that is transported into the column leads to the oxidation of the pyrite present according to the following stoichiometry: 7  FeS 2 + — 02 ± H 2 0 -> Fe 2+ +2SO 42- +2H +  2  (20)  A simple irreversible dissolution model has been employed for the reaction rate:  40  R FeS 2  =  min  —  kFes2  1 ^ 0 K Fes 2  (21)  where k Fes 2 = 10" 8 mol dm -3 bulk s -1 , which is consistent with literature rate data for pyrite oxidation (Williamson and Rimstidt, 1994; Gleisner et al., 2006) for surface areas found in fine grained mine waste materials. This rate coefficient leads to conditions under which the rate of pyrite oxidation is limited by the rate of oxygen supply into the reaction zone rather than by the reaction kinetics, as is often observed in mine tailings environments (Jaynes et al., 1984; Blowes et al. 1991; Elberling et al., 1994). IAP is the ionic activity product of the species in the reaction (20) and K F,s2 is the equilibrium constant. Consumption of oxygen by pyrite oxidation (20) creates a decrease in the 02 concentration that drives diffusive transport of 02 into the reaction zone. In addition, the depletion of oxygen also leads to a reduction in total gas pressure that drives advective transport of atmospheric gases towards the reaction zone (Wisotzky, 1994; Andersen et al., 2001). The water table represents a no-flow boundary for gas phase transport at the lower end of the column. Aqueous flow is included but dispersion in the aqueous phase is neglected to avoid non-physical results due to the application of macro-dispersivities at local-scale reaction zones (Table 2.3). If calcite is present in the column, acidity produced by reaction (20) is neutralized, leading to the production of carbon dioxide, which partially compensates total pressure reduction by oxygen depletion: CaCO 3 +2H + +--> Ca 2+ + CO2 + H 2 O  (22)  The simulations include 8 components (Fe2+ , H + , SO4 2- , CO3 2- , Fe3+ , 02(aq), N 2 (aq), and Ca 2+ ), 12 secondary aqueous species (including HCO3 - , and H2CO3), 3 gas species (02 , CO2, and N2), pyrite and calcite as primary minerals, and ferrihydrite and gypsum as 41  secondary minerals. Table 2.3 summarizes the parameters used for this simulation, including initial mineral volume fractions and reactions rates, and Table 2.5 presents initial and boundary conditions for the 8 components. Two different cases are considered in order to investigate the role of calcite dissolution and precipitation on gas transport in this environment. In the first case, calcite is included with a volume fraction of 30% to represent mine tailings consisting of a carbonate-rich rock (e.g. skarn). In the second case, a carbonate-depleted rock (e.g. granite) is considered and calcite is therefore not included in the simulation. Results are shown at 50 years. For both scenarios, simulation results show that as 0 2 is consumed at depth, N2 and CO2 concentrations increase relative to atmospheric conditions to compensate for depletion of 02 (Figure 2.10). However, in the carbonate-rich sediment, the increase in CO2 is more significant, indicating an increase in the amount of inorganic carbon present in the aqueous and gaseous phases. As a result of acidity production during pyrite oxidation (20), calcite dissolves according to (22) producing CO 2 . Additionally, some of the CO2 produced remains in the aqueous phase, and undergoes aqueous complexation (Figure 2.11 a). The presence of calcite buffers the pH at values around 7, making bicarbonate the most abundant carbonate complex, while its absence results in very low pH values (Figure 2.11b). In the carbonate-rich system, advection accounts for 9.5% of the net flux of atmospheric oxygen into the column, while diffusion accounts for the remaining 90.5%, with the non-equimolar component being 3.7% of the net flux (Figure 2.12a). If the nonequimolar flux component were not considered (i.e. using equations (11) and (12) in lieu  42  of (7) for gas diffusion), the advective flux would be greater to compensate for the nonseparative flux that is accounted for by the non-equimolar component of diffusion in the simulations presented here. Therefore, the relative importance of advection is reduced by the existence of the non-equimolar flux. For the carbonate—depleted system, advection is greater than in the carbonate-rich system and it gains relative importance in the distribution of flux components: 15.8% for advection, 84.2% for diffusion, with the non-equimolar component being 4.2% of the net oxygen flux (Figure 2.12b). Very similar results are obtained for the carbonate-rich system when CO2(g) is not included in the simulation (16.4-83.6-3.6%) although calcite is present. This indicates that the CO2(g) build-up is caused partially by advective transport, but mostly by calcite dissolution. Overall, the results compare well with findings by Binning at al. (2007) for a binary system including  N2  and 02; and confirm  that reaction-induced gas advection can significantly contribute to supply oxygen for pyrite oxidation. At quasi steady-state, oxygen diffusive fluxes into the column are approximately 4 times larger than non-separative fluxes; the non-equimolar and advective fluxes account for 20% of the net oxygen flux. Aqueous flow also contributes to the transport of chemical components in the column. For gases with low solubility such as 02, the contribution of the aqueous flux is small in comparison with the gaseous flux. For example, in the carbonate-rich system, at the top of the column, aqueous influxes represent 0.11% of net gaseous influxes. However, for gases with high solubility such as CO2, which in the aqueous phase speciates as CO3 2- , HCO3 - , and H2CO3, aqueous contributions can be relevant. In the carbonate-rich system, aqueous advective influx of total inorganic carbon reaches 23% of  43  the advective gas influx at the top of the column. It is, however, overwhelmed by the diffusive outflux of CO2, which is two orders of magnitude larger than gas ingress in the aqueous phase. In the calcite-depleted system, diffusion and advection in the gas phase approximately balance each other, and aqueous advection is the only mechanism that supplies inorganic carbon into the column at a rate of 1.94.10 4 mol d -1 . Only aqueous fluxes occur across the water table at the lower end of the column. In the carbonate-rich system, the aqueous flux at the water table contributes 12% to the total outflux of inorganic carbon across both boundaries.  2.6. Conclusions  This paper has presented the development of a reactive transport model that integrates multi-component gas diffusion and advection into a multi-component reactive transport code. The resulting model facilitates the investigation of interactions between geochemical reactions, rapid gas transport, and solute transport in the vadose zone. The use of the direct substitution approach allows relatively large time steps and solutions can be achieved with reasonable computational cost. It was found that reaction-driven advection can contribute significantly to gas transport. This is in agreement with previous studies of pyrite oxidation (Binning at al., 2007), where depletion of oxygen induces gas flow into the reaction zone. In addition, it was found that methane oxidation in unsaturated porous media contributes to the reduction of methane emissions to the atmosphere not only directly by removing methane but also indirectly by changing the gas flow pattern. A reduction in total gas pressure caused by methane oxidation may lead to the reduction of the advective gas flow  44  component (landfill cover soils) or even a reversal in the flow direction (e.g. oil spill site). A model for multi-component diffusion is required to simulate gas transport adequately and in a comprehensive fashion. Firstly, the assumption, necessary for Fick's law, that diffusing gas species are dilute in the bulk gas phase is not satisfied in any of the case studies. Secondly, reactions change the gas composition and product species have different diffusion properties than reactant species. Therefore, considering a single diffusion coefficient for all gases using Fick's law may lead to errors in the calculation of diffusive fluxes in systems where reactions occur. Knudsen diffusion does not appear to play a significant role in the systems studied here. Given the range of permeabilites encountered in the examples (10 -11 -10 -14 m2 ) this ,  ,  result is in agreement with results from other works (Massmann and Farrier, 1992; Sleep, 1998). Nevertheless, the use of the Dusty Gas Model equations allowed to account for the non-separative transport mechanism associated with diffusion: the non-equimolar flux component. This flux component depends on the composition of the gas mixture and is therefore affected by changes brought about by chemical reactions. For example, oxidation of CH4 with a molecular weight of 16 g mo1 -1 to CO2 with a molecular weight of 44 g moi l can change the magnitude or even reverse the direction of the nonequimolar flux component. In systems where sulfide mineral oxidation plays a role, the non-equimolar flux component can also be significant because oxygen consumed by the reaction has a higher molecular weight relative to air. The inclusion of the aqueous phase, as well as of a number of homogeneous and heterogeneous reactions, allows for the consideration of processes such a pH buffering  45  and aqueous speciation, which were not included in previous gas transport models. Such processes may also affect gas transport. In the case of pyrite oxidation, the presence of calcite accounts for higher CO 2 concentrations, and decreases the contribution of advection to the net oxygen flux into the soil column. Aqueous advection can be a relevant transport mechanism for gases with high solubility such as CO 2 , although in general gas fluxes tend to overwhelm aqueous fluxes. On the other hand, at the oil spill site, concentrations of gas species are not significantly affected by calcite dissolution although measured pH values and solution composition cannot be simulated satisfactorily without the inclusion of calcite and carbonate speciation in the model.  46  Tables Table 2.1. Summary of parameters and equations used in section 2.4.  Fen and Abriola^Thorstenson^De Visscher and Van and Pollock^Cleemput Fig.2.1a Fig.2.1b Fig.2.1c Fig.2.2, and ^Fig.2.4a^Fig.2.4b Fig.2.3^& Fig.2.5 Porosity [m 3 void m 3 porous^0.4^0.4^0.4^1.0^0.5878^0.5878 medium] (0 ) Gas saturation [m 3 gas m-3^1.0^1.0^1.0^1.0^0.7^0.7 void] (Sg ) Permeability^ 10 -10^10-16^10-10^10-12^2.10-13^2.1013 [m2 ](k) Diffusion (7)^(7)^(7)^(7)^(11, 12)^(7) equations Gas tortuosity^0.736 (Millington, A1.6)^0.1^0.1854 (Moldrup, A1.7) (D g ) Klinkenberg^ Reinecke parameter^Heid et al (1950) (A1.8)^bN2 = 1.35 .10 4 N/A^&Sleep [Pa] (bref )^ (2002)(A1.9) Reaction rate constant N/A^ N/A^4.43.10-6 [mol L -1 H2O Grid size [m] 0.047  0.62^0.026  Table 2.2. Viscosity and binary diffusion coefficients used in the simulations in sections 2.3.2, 2.3.3 and 2.4 (T = 298 K).  Viscosity [Pa s] Binary diffusion coefficients [m 2 s -1 ] (^) (P g )^02^CO2^CH4^Ar  N2^1.76.10-5^2.083.10-5^1.649.10-5^2.137.10-5^1.954.10-5 02^2.05.10-5^ 1.635.10-5^2.263.10-5^1.928-10-5 CO2^1.47.10-5^ 1.705.10-5^1.525.10-5 CH 4^1.09.10-5^ 2.045.10-5 Ar^2.23.10-5  47  Table 2.3. Summary of parameters and equations used in section 2.5.  Bemidji Fig.2.8, Fig.2.9, and Fig.2.10a a  Acid mine drainage Fig.2.1 la, Fig.2.12a, and Fig.2.13a b  Porosity [m 3 void 3 porous 0.30-0.38^0.50 medium] (0 ) Gas saturation [m 3 0.0-0.5 gas m -3 void] (Sg)^0.4-0.6 Permeability [m2] m2 '^10 43 -2-10 42 -5.10 42 (k) Diffusion equations (7)^ (7) Gas tortuosity (r g ) Millington (A1.6)^Millington (A1.6) Aqueous 0.1^ 0.0 dispersivity [m] Klinkenberg Heid et al. (1950)^Heid et al. (1950) parameter (A1.8)^(A1.8) [Pa]( bre ) 0.04 (pyrite) Initial mineral 0.3 (calcite) volume fractions 0.06 (calcite) 0.0 (ferrihydrite) [m 3 mineral 111 -3 bulk] 0.0 (gypsum) Reaction rate 10 -8 (pyrite), 10 -7 (calcite), constant le (methane oxidation) 10 -7 (ferrihydrite), 10 -8 (gypsum) [mol L-1 s -1 ] Solution time [yr]^3.17 (steady state)^50 Grid size [m]^0.15^ 0.05 Maximum Courant 1.39^ 14.34 number [-] Values also apply to simulation results shown in Fig.2.10b except for the initial calcite volume fraction (0 m 3 calcite 111-3 bulk). a  Values also apply to simulation results shown in Fig.2.11b, Fig.2.12b, and Fig.2.13b except for the initial calcite volume fraction (0 m 3 calcite 111-3 bulk). b  48  Table 2.4. Initial and boundary conditions in the simulation of methane attenuation in the crude oil spill site.  Recharge water  (atmosphere)  ^  Ca2+ 10 -4 mol L -1 ^ 0.778 atm N2 ^ 0.194 atm 02 ^ 0.018 atm CO2  CH4 0.000 atm ^ Ar ^0.009 atm 7.0 pH  Groundwater  Background Methanogenic zone 10 -4 mol L -1 0.778 atm 0.194 atm 0.018 atm 0.000 atm 0.009 atm 7.0  10 -4 mol L -1 0.729 atm 0.018 atm 0.149 atm 0.111 atm 0.009 atm 6.5  In-fluxes at lower end of columns  0.009 mol m -2 d -1 0.09 mol m -2 C1 -1  a Only gas fluxes are reported. The lower end of the column is a free exit boundary for dissolved species.  Table 2.5. Initial and boundary conditions in the simulation of pyrite oxidation'.  Recharge water  Tailings water  1.00.10 -4 2.03.10 -13 1.81-10 -6 4.82.10 -5 0.01 0.20 0.79 5.0  1.00.10 -4 1.00-10 -4 1.65.10 -n 3.19-10 -3 0.01 0.00 0.80 7.0  (atmosphere) Ca2+ [mol L -1 ] Fe2+ [mol L -1 ] Fe3+ [mol L -1 ] 504 2- [mol L-1 ] CO2 [atm] 02 [atm] N2 [atm] pH [-]  a The water table is the lower boundary. The water table is a free exit boundary for the aqueous phase  transport and a no-flow boundary for gaseous phase transport.  49  Figures  0.3^0.5^0.7  Distance [m]  09  0.3^0.5^0.7  Distance [m]  0  ea U  0 5-  0 2 0  0.1  ^ 0.3^0.5^0.7 0.9  Distance [rn]  Figure 2.1. Methane concentrations as a result of (a) diffusion in the molecular regime, (b) diffusion in the transition regime and (c) advection-dominated transport in the molecular regime. Model results in solid lines; results from Fen and Abriola (2004) in symbols.  0^0.25^0.5^0.75  Mole Fractions [-]  Figure 2.2. Comparison between model results (solid lines) and results from Thorstenson and Pollock (1989) (symbols) for the concentrations of N2, 02, and C114.  50  ^  A  net  non-eq  1>  )7  diffusion advection  ra 6  -  (b) ^upwards (+) 10 —0^ 0^4^8  ^I 0  Fluxes [mol m -2 d -1 ]  Fluxes [mol m -2 c1 -1 ]  Figure 2.3. Advective, diffusive, non-equimolar components of the net flux for (a) N2(g) and (b) CH4(g). Model results in solid lines; results from Thorstenson and Pollock (1989) in symbols.  0.1  0.4 0.5  0.4  (a) 0^0.2^0.4^0.6^0.8  Mole Fractions [-]  0.5  0^0.2^0.4^0.6^0.8  Mole Fractions [-]  Figure 2.4. Comparison between model results (solid lines) and results from De Visscher and Van Cleemput (2003) (open symbols) for the concentrations of N2, 02, CO2, and CH4. Filled symbols are experimental data. (a) Stefan Maxwell equations (b) Dusty Gas model.  51  Pressure [atm] 1.001^. 1.002 ^1.003  1.004  0.2^0.4  10  Velocity [m c1 -1 ]  Fluxes [molm" 2 cr]  Figure 2.5. (a) Velocity and pressure in the landfill cover soil column simulated using the equimolar Stefan-Maxwell equations. (b) Advective, diffusive, non-equimolar components of the net flux of CH4 simulated using the equimolar Stefan-Maxwell equations.  Argon Mole Fraction [-] 0.01 CH41  TO2  Art ^N2  13 4-  C O2 50.25^0.5^0.75  Mole Fractions [-]  Figure 2.6. Molar fractions of 02, CO2, CH4, N2 and Ar along the section. Solid lines are model results; symbols are field data. A relative enrichment of N2 and Ar and depletion of atmospheric 02 is observed around the reaction zone.  0  2  12 3 a) 0 4-  50  0.25^0.5^0.75  Aqueous Saturation [-]  1  Figure 2.7. Simulated aqueous saturation profile.  52  0  non-eq  diffusion I net  2  advection  0- 3 CI 4 5  (a) N 2  II (-) downwards  0.08 Fluxes [mol m 4 di  -0.05^0^0.05 2  Fluxes [molm" cl -1 ]  0  I^.^. 'diffusion net  5-  0^0.04^0.08  1\ non-eq  (d) 02^(-)  -0.2  2  Fluxes [molm" 6 1 ]  advection  downwards  0  -OA Fluxes [mol n1 2  Figure 2.8. Advective, diffusive, non-equimolar components of the net flux for (a) N2, (b) CO 2 , (c) CH4, and (d) 02.  pH  4  5  0  6  7  HCO'\ ,^I^3^pH 2  6.  4  cD  3  4 5  0^0.004^0.008  Concentrations [mol L -1 H 2 O]  CO 3 Ca t  I <>^  0  ! 0 H 2 CO3 *!^(b) 0^0.004^0.008  Concentrations [mol L -1 H 2 O]  Figure 2.9. pH and concentrations of Ca 2+ , and of the carbonate aqueous species (a) in the presence of calcite, and (b) in the absence calcite. Lysimeter data measured near well 601 is presented in symbols: pH (squares) and Ca 2+ (diamonds).  53  Total Pressure [atm] 0.99  Total Pressure [atm]  0.995  0  0.99  0.995  0  P  2  1  )02  N2  0.5-  E 1-  a)  CO 2  1.5 -  CO2  (a)  (b)  2  0.25^0.5^0.75  0^0.25^0.5^0.75  Partial Pressures [atm]  1  Partial Pressures [atm]  Figure 2.10. Simulated total and partial pressures during pyrite oxidation in (a) a carbonate-rich system and (b) a carbonate-depleted system.  pH  7  3 pH  1  5  0  7  0.5 -  E .c 0.  1-  a)  1.5 -  2  (a)  (b)  ^2 ^ 0^0.005^0.01^0^0.005^0.01  Concentrations [mol L -1 H 2 O]^Concentrations [mol L -' H 2 O]  Figure 2.11. pH and concentrations of the carbonate aqueous species in (a) a carbonate-rich system, and (b) a carbonate-depleted system  -0.15  -OA^-0.05^0  Fluxes [mol m -2 d -1 ]  -0.15  ^  -0.1^-0.05  Fluxes [mol m -2 d -1 ]  Figure 2.12. Advective, diffusive, non-equimolar components of the net flux for rich system and (b) a carbonate-depleted system during pyrite oxidation.  02  0  in (a) a carbonate-  54  References Abreu L.V., and P.C. Johnson (2005), Effect of Vapor Source-Building Separation and Building Construction on Soil Vapor Intrusion as Studied with a ThreeDimensional Numerical Model, Environ. Sci. Technol., 39, 4550-4561. Abriola L., and G. 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Olivella (2004), RETRASO, a code for modeling reactive transport in saturated and unsaturated porous media, Geologica Acta, 2(3), 235-251. Scheutz, C., and P. Kjeldsen (2003), Capacity for Biodegradation of CFCs and HCFCs in a Methane Oxidative Counter-Gradient Laboratory System Simulating Landfill Soil Covers, Environ. Sci. Technol., 37(22), 5143 - 5149; doi:10.1021/es026464+ imiinek, J., and D.L. Suarez (1994), Two dimensional transport for variably saturated porous media with major ion chemistry. Water Resour. Res., 30(4), 1115-1134. Sleep, B.E., and J.F. Sykes (1989), Modeling the Transport of Volatile Organics in Variably Saturated Media, Water Resour. Res., 25(1), 81-92. Sleep B.E. (1998), Modeling transient organic vapor transport in porous media with the Dusty Gas model, Adv. Water Resour., 22(3):247-56. Steefel, C.I. 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Rimstidt (1994), The kinetics and electrochemical ratedetermining step of aqueous pyrite oxidation, Geochim. Cosmochim. Acta, 58, 5443-5454. Wisotzky, F. (1994), Untersuchungen zur Pyritoxidation in Sedimenten des Reinischen Braunkohlenreviers and deren Auswirkungen auf die Chemie des Grundwassers, Ruhr-Universitat Bochum, Essen, Nr. 58.  63  3. Transport and Reaction Processes Affecting the Attenuation of Landfill Gas in Cover Soils  A version of this chapter has been accepted for publication; Molins, S., K. U. Mayer, C. Scheutz And P. Kjeldsen (2007), Transport And Reaction Processes Affecting The Attenuation Of Landfill Gas In Cover Soils, J Environ. Qual., accepted. From Journal of Environmental Quality, with permission, JEQ manuscript Q07-0250 (2007).  64  3.1. Introduction The anaerobic degradation of organic waste in municipal landfills results in the production of a gas mixture that contains methane (55-60 vol %), carbon dioxide (40-45 vol %), and numerous trace compounds such as halogenated and aromatic hydrocarbons as well as sulfur- and oxygen-containing aromatic compounds (Scheutz and Kjeldsen, 2003; Scheutz and Kjeldsen, 2005). Methane is an important greenhouse gas contributing to approximately 22% of the greenhouse effect (Lelieveld et al., 1998), with landfill sources accounting for 9-70 Tg yr -1 , out of an estimated annual global emission of 600 Tg of methane to the atmosphere (Bogner et al., 1997; Lelieveld et al. 1998). Column counter-gradient experiments have shown that landfill cover soils can play an important role in attenuating emissions of methane and other trace compounds to the atmosphere. Attenuation is significantly affected by ingress of atmospheric oxygen into the soil, which generates conditions suitable for aerobic methane oxidation. Methane removal efficiencies of up to 81% have been reported in column experiments (De Visscher et al., 1999; Bogner et al., 1997; Stein and Hettiaratchi, 2001; Scheutz and Kjeldsen, 2003). Column and batch experiments demonstrated the capacity of cover soils to also attenuate to different extents trace compounds such as trichlorofluoromethane (CFC-11), dichlorodifluoromethane (CFC-12), chlorodifluoromethane (HCFC-21), chlorofluoromethane (HCFC-22), tetrachloromethane (TeCM), trichloromethane (TCM), dichloromethane (DCM), trichloroethylene (TCE), vinyl chloride (VC), benzene, and toluene (Scheutz and Kjeldsen, 2003; Scheutz et al., 2004, Scheutz and Kjeldsen, 2005). Furthermore, compost biofilters have also been investigated as an alternative to attenuate  65  methane emissions from low intensity sources, where the use of methane as fuel for energy production is not viable (Park et al., 2002; Wilshusen et al., 2004). Numerical models of column experiments have provided a tool to investigate transport and oxidation processes occurring in landfill cover soils (Hilger et al., 1999, Stein et al., 2001; De Visscher and Van Cleemput, 2003). Typically, gas transport in landfill cover soils involves a multi-component mixture of gases. Thus, multicomponent diffusion models such as the Stefan-Maxwell equations provide the most adequate framework to describe the relevant gas transport mechanisms taking place in landfill cover soils (Hilger et al., 1999; De Visscher and Van Cleemput, 2003). In permeable porous media (e.g., silts, sands, and coarser grained materials), molecule-molecule interactions dominate and diffusion occurs in the molecular regime. However, in low permeability porous media, molecule-soil particle interactions become significant and the Stefan-Maxwell equations need to be cast in the form of the Dusty Gas Model (DGM) to account for diffusion in the Knudsen regime (Thorstenson and Pollock, 1989). In addition, the DGM includes the non-separative flux component that develops as a result of diffusion of non-equimolar gas mixtures: lighter molecules move faster than heavier molecules (Thorstenson and Pollock, 1989). The DGM has not been included in previous modeling studies (Hilger et al., 1999; Stein et al., 2001; De Visscher and Van Cleemput, 2003). Commonly, Fick's law has been used to simulate diffusive gas transport in cover soils (Stein et al., 2001; Wilshusen et al., 2004), although its applicability is limited to diffusion of dilute species in relatively permeable material or in advection-dominated systems (Thorstenson and Pollock, 1989; Fen and Abriola, 2004). Wind-induced gas advection can be significant under high soil moisture content (Poulsen and Moldrup,  66  2006). Other models have also included advection, but the contribution of advection to gas transport in landfill cover soils was not investigated (Stein et al., 2001). Numerical models can be used to identify the sensitivity of cover soils to physical, chemical, and environmental factors in the attenuation of methane and trace gases. Increased moisture contents result in low methane oxidation due to a decrease in oxygen supply into the column (Christophersen et al., 2000; De Visscher and Van Cleemput, 2003; Wilshusen et al., 2004). Both advection and diffusion can be affected by higher moisture due to the associated decrease in gas relative permeability and gas tortuosity. Higher moisture contents can be the result of high infiltration, production of water during methane oxidation (Scheutz and Kjeldsen, 2005), and are also affected by the soil type (Kightley et al., 1995). Soil permeability has been found to have little effect on simulations of methane attenuation (Stein et al., 2001). This result may not be generally applicable since permeability is a function of soil type and changes in permeability are associated with changes in moisture content, which profoundly affect the diffusive flux regime. In turn, reaction processes can have a direct effect on gas advection since the pressure decrease caused by the consumption of methane can change the magnitude of advective fluxes (Scheutz and Kjeldsen, 2003; Amos et al., 2005). In addition, the accumulation of exopolymeric substances (EPS) associated with methanotrophic activity can act as a barrier to transport at different scales. At a micro-scale, EPS biofilms limit the diffusion of substrate to methanotrophs (Hilger et al., 1999). At a macro-scale, EPS accumulation can change the effective porosity and hydraulic conductivity of the porous medium (Baveye et al., 1998). For example, Wilshusen et al. (2004) observed a decrease in macro-scale diffusion in compost biofilters. Such macro-scale barriers may result in a  67  decrease in the efficiency of a cover soil to attenuate methane and other trace components of landfill gas due to a limitation of 0 2 supply. The aim of this study is to investigate the gas transport and degradation processes occurring in landfill cover soils with the aid of a reactive transport model that includes both the aqueous and gaseous phases. The focus is on evaluating the contributions of various gas transport processes and the effect of oxidation reactions on the overall gas transport regime.  3.2. Methods  The analysis is performed using the results of counter-gradient column experiments conducted by Scheutz and Kjeldsen (2003) to investigate the capacity of landfill cover soils to attenuate methane, CFC (i.e., CFC-11, CFC-12), and HCFC (i.e., HCFC-21, and HCFC-22) emissions. In addition, a sensitivity analysis is conducted to evaluate the effect of local changes in physical, and environmental factors on short- and long-term gas transport in landfill cover soils. For this purpose, a reactive transport model that includes flow in the aqueous phase by means of Richard's equations, and transport in both the aqueous and gas phases is used. Aqueous concentrations are the primary variables of the model, which are assumed to be in equilibrium with gas phase concentrations by means of Henry's law. The use of the Dusty Gas Model for gas-phase transport allows for the consideration of transport mechanisms that have been neglected in previous landfill cover studies. A detailed description of the model is provided in Mayer at al. (2002) and Molins and Mayer (2007). Here a brief description is given that  68  ^  focuses on introducing the concepts of relevance to this work, in particular, the formulation for gas transport and relevant reactions.  3.2.1. Model Formulation  Diffusion of gases in the soils can be described by the Stefan-Maxwell equations within the framework of the Dusty Gas Model (Mason and Malinauskas, 1983):  E  ^11/1 gg 1 g ^= .^ VC i Vz^i =1,..., Ng^(1) RT O r^i/ D DK' g g Sg^ d g g  Ng Ni ^Xj—Nj; ' g)(Ig N  ^g  ja i  where xg (-) is the molar fraction of gas species i, c g is the concentration of gas species i (mol L -1 gas),  Mg (kg mol -1 ) is the molecular weight of gas species i, and Nrdg (mol m  dm -3 porous medium s -1 ) is the diffusive molar flux of gas species i. The first term on the left hand side accounts for molecule-molecule interactions, with D: (m 2 S -1 ) being the free phase binary diffusion coefficient between gas species i and j, 0 is the porosity (m 3 void 111 -3 porous medium), Sg (m 3 gas I11 -3 void) is the saturation of the gaseous phase, and r g is the gas tortuosity coefficient (-) (Moldrup et al., 2000): = v3/2,41/2 g " g  (2)  The second term in (Eq.[1]) accounts for molecule-sediment interactions, with D K g (m2 1  s -1 ) being the Knudsen diffusion coefficient for species i. The Knudsen diffusion coefficient (m 2 s -1 ) can be calculated as a function of the Klinkenberg parameter (b, [Pa]), soil permeability (k [m 2 ]), relative gas permeability (k g H), and viscosity of gas  69  species i (^[Pa s]) (Thorstenson and Pollock, 1989; Massmann and Farrier, 1992; Sleep, 1998; Fen and Abriola, 2004): (  .^k k^k k D' — rg^ b. = rg 0.11(k rg k) -° 39 K ,g^i Pg  ref  fi g ref^ Al m g^g  (3)  where ref indicates the gas species that is used as reference for the calculations. The relative permeability in the gas phase k, g (-) is calculated as follows (Parker et al., 1987): k,g = (1— S ea ) h/ 2 (1 — S ela/ 11/ )2m  ^  (4)  with m =1-11n, where n and m are soil hydraulic function parameters. The effective saturation of the aqueous phase, Sea(-), is defined as a function of the residual saturation in the aqueous phase, S ra (1— AS = sea^  (-):  ) — Sra g  1— S ra  (5)  A non-separative component may be present as part of the diffusive flux when gases in the mixture have different molecular weights. The non-equimolar flux occurs in systems with walls (soil particles) because diffusing species have different molecular weights: lighter molecules move faster than heavier molecules (Cunningham and Williams, 1980). Although diffusive in origin, the non-equimolar flux results in a non-separative flux in the same direction as the diffusive flux of the lightest gas species in the mixture. If one adds the DGM equation for each gas species (i.e., Eq.[1]) over all gas species, the first term on the left-hand side cancels out, and the right-hand side can be rearranged as a function of gas-phase pressure ( p g [Pa]) and gas density ( pg [kg m -3 ]):  70  Ng Nig  DIKg  = 1 (Vp g p g gVZ) RT  (6)  The magnitude of the non-equimolar flux depends on the Knudsen diffusion coefficient; in particular, it is a function of permeability and the molecular weight of a gas species (Eq•[3]). Diffusion is not the only mechanism contributing to gas transport in the system. Gas fluxes applied in the experiments range from 0.24 m d -1 to 4.09 m d -1 and are large enough to generate significant pressure gradients. Darcy's law is used to describe advective fluxes in the gas phase: =  k  Nia^ rg ^g  k  Pg  (Vp g + p g gVz)  (7)  where N iag, (mol m dm-3 porous medium s -1 ) is the advective flux in the gas phase, p g (kg m -1 s - 1 ) is the gas phase viscosity. The ideal gas law is used to calculate the partial pressure of each gas species (p g ), which are then added up to obtain the total pressure in the gas phase (Molins and Mayer, 2007). Biogeochemical transformations attenuate the emissions of landfill gas (LFG) to the atmosphere. The presence of methanotrophic bacteria results in the oxidation of methane and consumption of atmospheric oxygen, and the co-oxidation of HCFC-11 and HCFC-21 (Scheutz and Kjeldsen, 2003). These reactions take place in the aqueous phase and are formulated accordingly. During methane oxidation, oxygen is consumed and carbon dioxide, water (H2O), and organic carbon (CH2O) are produced according to the following stoichiometric relationship (De Visscher and Van Cleemput, 2003): CH 4 (aq) + 1.5 02 (aq) --> 0 .5CO 2 (aq) +  1.5 H2 O + 0.5 CH2 O  ^  (8)  71  It is assumed that the aerobic oxidation of HCFC-21 and HCFC-22 proceed to completion according to the stoichiometry of these reactions (Table 3.1). In addition, CFC-11, CFC-12, HCFC-21, and HCFC-22 are assumed to undergo reductive dehalogenation under anaerobic conditions (Table 3.1). Methane oxidation rates are calculated using the following Monod-type expression: RcH4 02 = — k CH4 -  CH,^17 C^ a^a  C°2  K i +c  ^ acH4 ‘ 2 + C a02  „, ,K  (9)  where k c.H4 (moles L -1 H 2 O s -1 ) is the reaction rate constant, and K 1 and K2 (M01 L -1 H2O) are the half-saturation constants for CH4 and 02, respectively. Aqueous concentrations of methane and oxygen are denoted with c acH4 and c a°2 , respectively. Similarly, Monod-type expressions are employed for the aerobic oxidation rates of HCFC-21 and HCFC-22 (Table 3.1). Anaerobic oxidation of the halogenated compounds is described with a Monod-type expression for the concentration of each compound, and an inhibition term for the concentration of oxygen to account for the fact that the reaction is hindered under aerobic conditions. Stoichiometry, rate expressions, and half-saturation constants for these reactions are given in Table 3.1. For simplicity, it is assumed that  H2 concentrations  are not rate limiting and H2 is left out of the model. Diffusive and advective gas fluxes (N'dg and 1■11 g ) and reaction source-sink terms contribute to the mass balance of each component in the aqueous and gas phases. The equations expressing this mass balance are solved simultaneously for all components (Molins and Mayer, 2007).  72  3.2.2. Model Parameters and Calibration The simulations are constrained by experimental data from Scheutz and Kjeldsen (2003) who conducted column experiments using soil collected at the Skellingsted Landfill south of Holbxk, Western Sealand, Denmark. The soil consists predominantely of loamy sand and a value of 10 -12 m 2 was used for average soil permeability, which is assumed to be representative for this material (Iversen et al., 2001). A detailed description of the soil analyses can be found in Scheutz et al. (2004). The soil was packed in tubes made of rigid PVC and the resulting average porosity was determined to be 0.52 m 3 void 111 -3 porous medium (Figure 3.1). The PVC tubes were closed at both ends to form gas-tight columns. The columns were fed from opposite ends with LFG and air through inlets situated at the bottom and top of the columns, respectively. An outlet positioned at the top was used to allow air to pass freely through the top chamber. Artificial LFG consisted of a mixture of 50/50% v/v CH4/CO2 and trace concentrations of CFCs and was injected into the bottom inlet of the column at a rate of 0.76 m d -1 for 3 weeks (Scheutz and Kjeldsen, 2003). For the simulations, this translates to specified methane and carbon dioxide molar fluxes of 15.6 moles L -1 gas m2 , which were used as boundary conditions at the bottom of the column. Specified gas concentrations applied at the top of the column were equal to atmospheric concentrations (i.e.,  p ; = 0.78 , 12  p° = 0.21, pgc02 = 0.01, and pgcH4 = 0.0001). Simulation parameters are summarized in 2  Table 3.2. A detailed description of the experimental setup can be found in Scheutz and Kjeldsen (2003). Simulations are conducted for both an active column and a sterilized control column. The maximum zero-order rate constants calculated for the batch experiments  73  conducted by Scheutz and Kjeldsen (2003) were used for initial simulations of the active column. Parameter adjustment was required for the anaerobic degradation of CFC-11 and the aerobic oxidation of HCFCs to provide a better fit to measured concentrations, and thus, these values were used for the remaining simulations (Table 3.1). Experimental results for the control column were also simulated by setting all reaction rate constants to zero. Pore water saturation was used as a fitting parameter for model calibration. Initial simulations were conducted with depth-dependent water saturations, which were determined from experimental porosity and bulk density data. However, consideration of a depth-dependent saturation profile was not warranted because the fit to observed gas concentrations could not be improved relative to simulations with constant water saturations. As a result, pore water saturations were assumed to be constant along the column and over the simulation time. In the active column, an aqueous saturation of 0.22 -3 m 3 H2O III  void provided the best fit between experimental data and simulated results,  which falls in the range of measured water saturations in the soil. In the control column, an aqueous saturation of 0.34 m 3 H2O void provided the best fit to experimental data. The differences in simulated water saturations between active and control columns are consistent with the experimental design. In the control column, higher saturations are the result of the sterilization treatment consisting of the addition of an average of 0.13 m 3 of HgC1 solution per m 3 of soil.  74  3.3. Results and Discussion 3.3.1. Concentrations of CH4, CFCs and HCFCs  Model results are in good agreement with the observed concentrations in the columns (Figure 3.2). Supply of atmospheric oxygen into the column contributes to the aerobic degradation of CH 4 , HCFC-21, and HCFC-22 (Figure 3.3 a,c), which results in the production of CO2. Organic compounds CFC-11, CFC-12, HCFC-21, and HCFC-22 also degrade in the anaerobic portion of the column (Figure 3.3 b,c). Although results presented are profiles after 3 weeks, concentration profiles obtained as early as after 3 days are almost identical to those obtained at steady state, which is an indication that steady-state transport is reached very rapidly. For selected compounds (i.e., CH4, CO2, CFC-12, and HCFC-21), statistical analyses were conducted to further evaluate the model performance. Modeling efficiency is 0.960 for CO2, 0.988 for CH4, 0.935 for CFC-12, and 0.997 for HCFC-21, while the d-index is 0.997 for CO2, 0.999 for CH4, 0.986 for CFC-12, and 0.999 for HCFC-21 (Legates and McCabe, 1999). This analysis confirms the very good agreement between observed and simulated data.  3.3.2. Relative Contribution of Transport Mechanisms  An analysis of the fluxes shows that advection is the most relevant transport mechanism for CH4 and CO2 near the base of landfill cover soils (Figure 3.4a). However, advection loses in importance with increasing proximity to the ground surface and diffusion becomes most relevant. As a result, advection does not play a significant role in gas emissions to the atmosphere, contributing only 0.6% of the total methane flux, and 3.5% of the carbon dioxide flux. Supply of oxygen into the column is driven by diffusion, 75  while an outward advective component offsets 15% of the 02 diffusive influx (Figure 3.4c). Nitrogen supplied into the column by diffusion is present at the bottom of the column at a mol fraction of 0.11 (Figure 3.2a). Since N2 is non-reactive in this system, at steady state, the downward diffusive flux must be balanced by the upward advective flux resulting in a zero net flux (Figure 3.4d). During methane oxidation, 2.5 moles of gases are transformed to 0.5 moles of gases (Eq. [8]). This results in a decrease in the gas pressure gradient and the gas flux near the reaction zone (Figure 3.5). The pressure gradient required to sustain the methane flux in the lower end of the column is 0.16 kPa m -1 (Figure 3.5); this gradient is nearly constant with depth except near the main reaction zone, where it decreases significantly to a minimum of 0.07 kPa m -1 near the top. Methane emissions are reduced mostly by methane oxidation but also partly because of the decrease in the advective component of the net methane flux (Figure 3.4a), indirectly caused by the oxidation reaction. As methane, a relatively light gas, is consumed to produce carbon dioxide, a relatively heavy gas, the average molecular weight of the gas mixture increases. This results in the development of a non-separative component of the diffusive fluxes from the bottom of the column (30.9 g mol l ) towards the reaction zone (31.7 g mol -1 ). However, the contributions of the non-equimolar component of the diffusive fluxes of CH4 and CO2 are small and become insignificant in the upper quarter of the column (Figure 3.4). At the top of the column, the non-equimolar component of diffusion is reversed, since the atmospheric mixture of gases (28.9 g mol -1 ) has a smaller molecular weight than the gas mixture in the reaction zone.  76  3.3.3. Variable Inlet Flow Experiments In addition to the 3-week experiment at a constant rate, Scheutz and Kjeldsen (2003) carried out column experiments with inlet flows varying between 0.82 and 14.25 mL min -I , which correspond to gas fluxes ranging from 0.24 to 4.09 m d-I . These values encompass the range of gas fluxes observed in landfills covers (Scheutz and Kjeldsen, 2003). Gas fluxes of 0.24 m d -I are representative for older landfills or sites with gas collection systems, while new and active landfills with high gas production rates can have gas fluxes of up to 5 m d -I (Scheutz and Kjeldsen, 2003). A series of simulations was carried out to reproduce the results of these experiments. Simulations for each inlet flow were run for 5 days, consistent with the duration of the experiment. The parameters used for the constant inlet flow simulation (Table 3.2) were also used in these simulations, and provided a good match between measured and simulated data (e.g., Figure 3.6 a,b). Results show that for increasing inflow rates, efficiencies of the soil column to remove CI-14 decreases from 99.8% at 0.24 m d -I to 8.7% at 4.09 m d -1 (Figure 3.7a). This decrease in efficiency is accompanied by an increase in the relative contribution of advection to methane emission (Figure 3.7a). At high LFG flux rates (e.g., 4.09m d -I ), advection dominates in the lower end of the column, as indicated by flat concentration gradients (Figure 3.6b), while diffusive fluxes dominate in a thin area at the top of the column driven by steep concentration gradients. For increasing gas fluxes, oxygen supply into the column increases at rates below 0.76 m d -I , and decreases slightly above it (Figure 3.7b). The net oxygen supply into the column is approximately the same at 0.37 m d -1 as at 4.09 m d -I . As a result, the consumption of methane in absolute value shows a  77  maximum at 0.76 m d -1 . The results suggest that above this threshold, methane emissions increase in a linear fashion for the range of fluxes covered in the experiment.  3.3.4. Sensitivity to Variable LFG Composition  The composition of LFG depends on the makeup of the waste in the landfill and may vary with time. The composition of artificial LFG used in the experiments (50/50% v/v) is within the range of typical compositions of LFG. However, methane concentrations as high as 70% have been measured in landfill cover soils (Kallistova et al., 2005). Furthermore, some column experiments designed to study the ability of filters to attenuate methane emissions were performed using methane as the sole gas (Wilshusen et al., 2004). For a constant gas influx, increasing methane concentrations result in a reduction of the efficiency of methane oxidation (De Visscher and Van Cleemput, 2003). A series of additional simulations were conducted to analyze the effect of the composition of the LFG on the transport of methane. These simulations were conducted at a LFG influx rate of 0.24 m (1 -1 . Oxygen fluxes into the column become less dominated by diffusion as advection at the top of the column decreases (Figure 3.8). For a CH4 fraction of 0.57, the direction of advection is inverted at the top of the column. This reversal is the result of the pressure drop created during methane oxidation. As a consequence, oxygen fluxes into the column occur not only by diffusion but also by advection. However, this was only observed at low LFG fluxes. Pressure gradients in simulation at higher LFG influx rates are not reversed; neither are they in simulations at low LFG influxes with high CO2 concentrations. Reversal of advective fluxes results in a  78  relative increase in N2 concentrations (Figure 3.9). This peak has been observed in column experiments conducted with methane as the sole LFG (Wilshusen et al., 2004).  3.3.5. Sensitivity to Moisture Content  Increasing moisture content has been shown to decrease the attenuation of methane within landfill cover soil experiments. Simulation results at a constant LFG flux rate of 0.76 m d -1 with variable moisture content show that for saturations below 0.34 m 3 H 2 O 111 -3 void, oxygen supply into the soil column is unchanged (Figure 3.10). As a result, methane attenuation at these saturations in the column is approximately constant. However, for saturations above 0.34 m 3 H2O m -3 void, diffusion of oxygen into the column becomes inhibited, while 02-advection out of the column remains relatively constant (Figure 3.10). Methane and oxygen concentration gradients become steeper, which decreases the width of the zone with active methanotrophic activity (Figure 3.11). As a result, for constant CH 4 release rates, the simulations suggest that CH4 consumption in landfill covers decreases with increasing moisture content (Figure 3.11).  3.3.6. Sensitivity to Local Changes in Moisture Content, Porosity and Permeability  A number of processes associated with methane oxidation can affect gas transport in a soil column. As expressed by Eq.[8], in the oxidation of methane, water (H 2 O) and organic carbon (CH 2 O) are produced, where the organic carbon fraction consists of biomass, but mostly of exopolymeric substances (EPS) (Thullner et al., 2004). Increased water content and EPS accumulation have been shown to affect attenuation of methane by reducing the supply of oxygen into the column. In addition, both processes can reduce  79  permeability of the gas phase and therefore change the balance between advection and diffusion. In order to study the effects of H 2 O and EPS production on gas transport and methane oxidation in a hypothetical fashion, short-term (i.e., 3 weeks) and longer-term (i.e., 180 days) simulations were conducted by adding these processes to the model presented herein. The short-term simulations can be used to evaluate if the exclusion of these processes in the assessment of the column experiments is justified, while the longterm simulations provide insight into the potential impact of these processes on the future performance of covers.  3.3.6.1. H2O Production  Water produced during methane oxidation has not been included in previous models of landfill cover soils. The model can be used to estimate water production during oxidation of methane and calculate its effect on the water budget in a soil column. Water produced contributes to the water balance expressed by Richard's equation (Mayer et al., 2002) through the source-sink term Qa (s -1 ): Qa =E0.018S a q5v H20 ,1? a,  (10)  m=1  where S a is the aqueous saturation (-), N km is the number of oxidation reactions, and v H20m is  the stoichiometric coefficient of H2O in a generic oxidation reaction m (in  particular, reactions T 1 , T2, and T3 in Table 3.1). Water produced during aerobic oxidation does not accumulate in the reaction zone but, as described by Richard's equation, water flows from regions of high soil moisture potential to areas of lower soil  80  moisture potential. Loss of the water may also occur by evaporation if methane oxidation takes place at shallow depth. The rate of H 2 O production integrated over the length of the column due to methane oxidation is 93 mm yr-1 , a magnitude comparable to that of infiltration at the Skellingsted site (180 mm yr -1 , estimated as 30% of average precipitation, Frich et al. [1997]). This rate of water production from methane oxidation activity increases the water saturation from 0.22 to 0.26 m 3 H2O 111-3 void at a depth of 9.6 cm in three weeks of experiment. This increase has a small effect on methane transport and oxidation, which justifies the exclusion of this process from the calibration simulation. Simulation results after 180 days show a larger increase in aqueous saturation to a maximum of 0.365 m 3 H 2 O m -3 void at 13.8-cm depth (Figure 3.12a). This increase in saturation results in a very small increase in methane release at the cover surface from 5.5 mol I11-2 C1 -1 to 5.6 mol m -2 (1 -1 (Figure 3.12b). The drop in methane oxidation efficiency would be more significant if initial saturations in the column were higher so that resulting saturations would be greater than 0.5 where changes in efficiency are greater (see discussion in section 3.3.5). Because of high water saturation, relative permeability in the gas phase decreases (Eq. [4]), but for a specified landfill gas production rate, pressure gradients in the high saturation zone increases, thus resulting in no significant changes in the advective fluxes. This result is partially a consequence of the boundary conditions used, which assume constant concentration at the top and constant influxes at the bottom. Measurement of pressures that develop in the column as response to permeability changes would be necessary to constrain simulation results.  81  3.3.6.2. EPS Production  It is assumed that 95% of the biomass produced (CH2O) during methane oxidation is EPS (Thullner et al., 2004) and that this EPS has a density of 0.065 g C  T11 -3 ,  which falls  within the range of values reported by Christensen and Characklis (1990). The accumulation of EPS results in a decrease in porosity, and therefore, in permeability according to the normalized Carman-Kozeny relationship (MacQuarrie and Mayer, 2005): 03^1[0 0initial \ 2 k initial + 0)2^(initial )3 .  k =[  ^  where Om'', and kil"" 1 are the initial porosity (m 3 void T11 -3 porous medium) and initial permeability (m2 ), respectively. Simulation results show that the accumulation of EPS results in a small decrease in porosity after 3 weeks of experiment. The maximum decrease is observed at a 10-cm depth from 0.52 m 3 void 111 -3 porous medium initially to 0.47 m 3 void 111 -3 porous medium. As a consequence, a decrease of diffusive fluxes is observed near the top of the column, while no change is observed in the advective fluxes. This results in a small decrease in methane oxidation from 63% in the base case to 55%, suggesting that EPS production may have an effect on cover performance, even for short time period column experiments. After 180 days, the decrease in the methane oxidation is more significant, in agreement with the effects observed by Wilshusen et al. (2004) for EPS accumulation in a compost column. As aerobic oxidation reactions occur closer to the top of the column because less oxygen diffuses into the column, EPS accumulation also occurs at shallower depths. As a result the maximum decrease in porosity (from the initial 0.52 to 0.13 m  3  82  void I11 -3 porous medium) occurs at a depth of 5.2 cm (Figure 3.13a). The loss of pore space causes a decrease in diffusive properties of the column (Eq.[1], Eq.[2], and Eq.[3]), and results in a significant decrease in methane oxidation from 63% in the base case to 11 %. Despite a significant decrease in permeability from 10 -12 m2 to 5.10 5 m2 , advective fluxes of methane are only slightly different assuming a constant methane production rate and due to compensation in predicted pressure gradients. Advection dominates the transport of methane and trace gases to the surface, with diffusion being the dominant transport mechanism only in the top 10 cm (Figure 3.13b). However, the composition of diffusive fluxes near the reaction zone is significantly different than at earlier times because of the decrease in permeability. The non-equimolar component of diffusion becomes significant at this permeability (Figure 3.13b), and makes up 18.1% of the net CH 4 flux at 9.3-cm depth. In the low permeability area, diffusion occurs in the transition regime between molecular and Knudsen diffusion. Since Knudsen diffusion coefficients in the Knudsen regime are smaller than in the molecular regime, a more significant decrease in permeability can result in further decreases in  02  supply into the column and  in the capacity of the cover soil column to attenuate CH4 emissions. Model results were found to be very sensitive to EPS density in agreement with previous studies (Thullner et al., 2004). Furthermore, the model did not include decay of EPS and subsequent oxidation of this organic material. Further studies are required to constrain model simulations and to investigate the effect of EPS on the oxidation of methane and other trace gases in landfill cover soils.  83  3.4. Summary  The role of all transport mechanisms relevant to the attenuation of the emission of methane, CFC-11, CFC-12, HCFC-21, and HCFC-22 in landfill cover soils has been analyzed using a multicomponent reactive transport model that includes the Dusty Gas Model for gas diffusion, and Darcy's law for gas advection. Transport in the lower end of the column is dominated by advection controlled by specified CH 4 and CO 2 fluxes, while diffusion is the mechanism that drives gas fluxes near the top of the soil column. For increasing LFG influxes, the portion of the column dominated by advection is larger, and diffusion is constrained to a shallower section of the column. In consequence, concentration gradients near the top of the column become significantly steeper. The net supply of oxygen into the column does not change significantly but the efficiency of the column in oxidizing CH 4 decreases, as methane influxes are larger. For a LFG influx of 0.76 m d -1 , the contribution of advection to methane emissions is small (less than 1% of net fluxes), in part, because methane oxidation results in a decrease in pressure gradients in the reaction zone. The contribution of advection grows slightly with increasing LFG influxes. Model results show that advective fluxes can be reversed near the top of the column, promoting increased 02 ingress and methane oxidation. However, this possibility is limited to cover soils subject to small LFG influxes and mixtures rich in methane. In addition to the direct effect on gas pressure, methane oxidation can indirectly affect transport of gases in the system by the production of water or accumulation of EPS. Simulations show that both processes could result in a decrease of the diffusive properties of the soil. However, in the 3-week duration of the experiment, these changes have a  84  relatively small effect on gas concentrations. Long-term simulations showed that EPS accumulation could decrease diffusive 02-ingress significantly, and thus, decrease oxidation of methane. The results suggest that EPS accumulation affect diffusive transport properties through a decrease in effective porosity that affects diffusion in the molecular regime, and partly through a decrease in the Knudsen diffusion coefficients due to reduced permeability that brings diffusion closer to the Knudsen regime. Water production rate is significant (93 mm yr -I ) and comparable to recharge at the site. However, water production did not cause a decrease in methane oxidation in the simulation presented. Water accumulation could potentially have a more significant effect for lower permeability soils, i.e., if saturated hydraulic conductivity of the cover soils are not significantly larger than water production rates within the cover. Generally, the production of EPS seems to have a more important effect than water production since EPS accumulation is concentrated in the reaction zone, while water produced is distributed along the entire column following Richard's equation. Investigation of the accumulation and decay of EPS is necessary to better constrain models of methane oxidation in landfill cover soils.  85  ^ ^ ^  •^  ^cS  ▪^ ▪  ▪ -7'^  •^  7'^7'  "5  --,'^.^ 7'^'7'^v)^v) v)^ v)^v) -.' 7'^7'^..4^oo-^1-•  .--.^o—i^  -  -  75^E -.'^E -^E^75^ 4-4^--.^o^E^E 7' b 46 _ —.^ c.) .7,^c) 6- 7, .7, x. E^6 - ^ . E^8 '•-^ x .--1^x^E 71-.^ ci ->" -6 O ^.^ 5^c•1 -c5 kr;^ 7 :) , (.1 75' 1-- J::5 6^—4^ c, II^ '..; b.^11^ ^II^E °°6^I I^E^ E^ '7<^ E —4^ xII^II^v—I ,  --  --  7r^ x^4.-1.4;4. r 4 ' cS r7 L, — ■c5 tr1 ^q `'l^ 1 c)^c=>^c:2:^ 1 c)^4,1 ° ,, 7—I^r•I /—I ,,:..,4 —4^I^4-4^I^WV^'-" II 4-4 r -;^4.44; M  t  N  +  (5  t C.)  e c2  NI  N^N u^c.) C4^f:4^g=4  C;^c.)^4.  I  .-k -k^-k^I I^I II II^I I  i^ ,^4._,.., c^c.,^c.,  c..) + -^.. k k ...^ ,^..,  C.)^' . C.)^C)^'e.-.)^Q^ C.)^ ^C-), n-I-^r--  Lt,^,.,,,, z..-,^4,- Ei^uc:i 47,^c_.^.. .,^-^u ^..4_  ..  c:t.) k + O 4,,^ ,...) k" + k + ^k" - \_/ k ,..,^4,.....-N  /--^.. \^ P. ^... \^  N^Cr) 'Cr  6'  6 z^ c.1 +^  C.)C.)  /-^ /-^- \  6 ^k  C.)^C.)  /-^\  C.) II c^ C)^I I 4., E^H^ w II II^II^LY,^II 4.^II C.)^ 4..^4.,^C.)^C.) U^-.''' k" ,..,k k^ --k k^...`)^ - --ku^''° ,-k^ i-^:^ c'c'  " kL) k" -  e—.I H^  t"^N  ....^_....,^,._^  ^. ,,^,--^--,^7c) ..44.4^k),4  kr.)^k  O , +^ .c...; C)^-CD^ ..^L'7, C.) t, t -(:). z.--., C.)C.)^ C.) \-..^,..../^C) c, +^C.) n + / 'N^C.)^C.)^ ,:r  ,. ., ^■^ ^C.)^\ C.) .,, + cS' cS'^ ^ 1 C.)i^ U_ N N -,--si ^ U^ C.) -  k^ k  -  c4^I^  ^0^ C.)^1^I ... v)^.k II^II 1--,^II^o"^o" al., 474^N  0.)^q^,..) L., ^C^ci.)^ 4.^4. ,..,^, 2^t-zi^L.,  ^-  ^4.,^r=4^cz^cg 1.r a. o.e C14  ^ao^C) .4., et V^C.)^ C)^C.) + : et^tr? ;..,^0^cf)^cr) .... ^± ± ^  ^,.-.N  .0^  E^+ + + ^E0^ '..:.-r.‘ I^'..; ' ^2^...., z 4,b—44 .  ^.  ^.2^t-I^+^c \I  ^2  a)^c:1 tr?^6^6 + ........ ^, = 0^0+^6 '-.)^kr)^,  P  6 .4) (-NI ":4^ ±^ ± ^In'7:;-■^ ±^± co ...^ z:3^ ett '7:1;-■ ^ 0^,--.1^,...., ± Ci^"";1 cn^ C:3  CS ^,-4^8^1::r c)"^4.,^. . . . .^ 4.7 --'1 .... ,...;^ ..._.. (..)^ tn 0.,^..-^ .3 6^..) T^c)^T^c...)^T  ^CLO^(..)^cr -2 C.)^L) ,.__ =^=^Ct^ 0..,..,^CD^C..)^ W..;^. ^'''g HCO^(1) El r:4^  N ,ftoo,  87  Table 3.2. Simulation parameters  Parameter  Values in base case  Porosity, 0 (-) Permeability, k (m2 ) Van Genuchten, a (m 1 ) Van Genuchten, n (-) Residual saturation, S ra (-) Aqueous saturation (calibrated), S a (-) Time (d)^  0.52 10 12 3.5 1.3 0.05 0.22 21  88  Figures Pump l Outlet  -1==L  ^ Chamber  Air  Landfill Gas Pump Gravel Net  4^  Leachate drainage  Figure 3.1. Experimental column set up (adapted from Scheutz and Kjeldsen, 2003)  ^ 0.5^1^0^0.25 0.5 0.75 0.2^0.4^0.6^0 8 ^ ^ Relative conc. (C/Co ) Mole fraction (-) Relative conc. (C/C o )  Figure 3.2. Gas concentrations: (a) N2, 02, CO2 and CH4; (b) trichlorofluoromethane (CFC-11) and dichlorodifluoromethane (CFC-12); and (c) chlorodifluoromethane (HCFC-21) and chlorofluoromethane (HCFC-22). Experimental data in symbols, simulated results in solid lines  89  ^  Anaerobic Oxidation Rate 0^2E-07 4E-07 6E-07 0 '  (b)  HCFC-22 \ (aerobic 0.2  o  CFC-11 (anaerobic)  (aerobic) HCFC-22  0.6- °-`' (anaerobic)  0.6-  CFC-12 (a)  0.8- (anaerobic)  HCFC-21 (anaerobic) (c)  0.81  0^5E1-08^1E -07  0.02^0.04 CH 4 Oxidation Rate (mol n1 -3 soil d i )  0^2E-06 4E-06 6E-06 Aerobic Oxidation Rate (mol m -3 soil d -1 )  CFC Oxidation Rate (mol m -3 soil d 1 )  Figure 3.3. Simulated oxidation rates: (a) C114; (b) trichlorofluoromethane (CFC-11) and dichlorodifluoromethane (CFC-12); and (c) chlorodifluoromethane (HCFC-21) and chlorofluoromethane (HCFC-22). (a) CH 4  diffusion,./ / 0.2- rion-e  0.2-  1  o  :non-eq.  I advection^net 0.8-  0.8-  Fluxes (mol m-2 d-1 )  Fluxes (mol rri 2 d-1 )  0^  advection 0.2  0.2-  diffusion  r  0^5 ^10 15  5^10^15  net \.  1 (b) CO 2^  210  // non-eq.\ diffusion  advection  non-eq. — 0.4_c  net  0.6-  ■ 0.8-  (c) 02 -10^0^10 Fluxes (mol m 2 c1-1 )  0 . 8-  (d) N 2 -10^0^10 Fluxes (mol m -2 d 1 )  Figure 3.4. Simulated flux components for (a) CH 4 , (b) CO2, (c) 02, and (d)  N2  90  0  Pressure (kPa) 101.35 101.4 101.45 '  0^0.2 0.4 0.6 0 8 Advective Gas Flux (m d -1 )  Figure 3.5. Simulated pressure and advective velocity  (b) 4.09 m cf' 0.2^0.4^0.6^0 8  Mole fraction (-)  0.2^0.4^0.6^0 8 Mole fraction (-)  Figure 3.6. Concentrations of N2, 02, CO2 and CH 4 (a) at low and (b) high gas influxes. Experimental data in symbols, simulated results in solid lines.  91  80 ^ \Consumption 70 net -o 60 50 diffusion E 40 - (a) CH 4 \ advection 30 emission (+) non-eq. X 20 10 0 1^2^3 Gas Influx at bottom of column (m c1 -1 ) 30 (b) 02 advection 20 "C3 E 10 emission (+) non-eq. 15 0 net -10 -  -20 6-30 - supply -40 2  100  80 0  -60  0  - 40 a u)  0  -20 0  0  ------,_^diffusion (-)  2^3^ Gas Influx at bottom of column (m )  4  Figure 3.7. Simulated fluxes at top of column for variable gas fluxes for (a) CH 4 and (b) 02  advection E  (7) E -5 6-1 0  net  02  non-eq.  supply (-)  30^40^50^60 CH 4 in mixture (%)  ^  70  Figure 3.8. Simulated fluxes at top of column for constant gas influx rate (0.24 m (1 -1 ) for 02  92  0.2  ..c  0.4 0.6 08 1^I 0.2^0.4^0.6^0.8  Mole fraction (-)  Figure 3.9. Simulated gas concentrations at influx rate of 0.24 m d -1 for a 70/30% v/v CH4/CO2 mixture  5 E  0  o -5 E -10  emission (+) ^  advection  non-eq. supply (-) ^  net  6-15 -20  02  0.3^0.4^0.5^0.6^0.7 Aqueous Saturation (SO ( )  ^  08  -  Figure 3.10. Simulated 02 flux at top of column for variable column saturation  93  ^ Sa = 0.21 ^ Sa = 0.34 = 0.47 = 0.65 -^- - Sa = 0.77  0^0.005^0.01 CH 4 Cumulative Consumption (mol m- 2 Figure 3.11. Simulated cumulative consumption of CH 4 for different saturations.  0.2 0.4 a) 0  0.8 0.1 0.2 0.3 0.4 05^0^5^10^15 Aqueous Saturation (-)^Fluxes (mol m-2 d-1 ) Figure 3.12. (a) Simulated aqueous saturation at 180 d and (b) CH 4 gas fluxes at 180 d, compared with CH4 net flux at steady-state conditions for the case with no water production  94  Pressure (kPa) 102^103^104  101 0^  flux  0^  et  pressure 0.2 -  0.2 — 0.4-  non-eq.  I 0.60.8  0.8-  (a) I  ,  I^advection i!  (b) CH 4  T^  0^0.2 0.4 0.6 0 8 Advective Gas Flux (m d 1 )  0^5^10^15 Fluxes (mol m -2 d-1 )  Figure 3.13. Simulated effect of the accumulation of exopolymeric substances (EPS) on (a) gas pressure and advective gas flux at 180 d and (b) CH4 gas fluxes  95  References  Amos, R., U. Mayer, B. Bekins, G. Delin, and R. Williams. 2005. Use of dissolved and vapor-phase gases to investigate methanogenic degradation of petroleum hydrocarbon contamination in the subsurface. Water Resour. Res. 41(2):W02001. Baveye, P., P. Vandevivre, B.L. Hoyle, P.C. DeLeo, and D. Sanchez de Lozada, (1998), Environmental impact and mechanisms of the biological clogging of saturated soils and aquifer materials, Crit. Rev. Environ. Sci. Technol, 28(2):123-191. Bogner, J.E., K.A. Spokas, and E.A. Burton (1997), Kinetics of methane oxidation in a landfill cover soil: Temporal variations, a whole landfill oxidation experiment, and modeling of net CH4 emissions, Environ. Sci. Technol., 31:2504-2514. Christensen B.E., and W.G Characklis (1990), Physical and chemical properties of biofilms. p 93-130. In W.G. Characklis, and K.C. Marshall (eds) Biofilms. Wiley, New York. Christophersen, M., L. Linderod, P.E. Jensen, and P. Kjeldsen (2000), Methane oxidation at low temperatures in soil exposed to landfill gas, J. Environ. 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Poulsen, and P. Moldrup (2001), In situ, on-site and laboratory measurements of soil air permeability: boundary conditions and measurement scale, Soil Science, 166(2):97-106. Kallistova, A. Yu., M. V. Kevbrina, V. K. Nekrasova, M. V. Glagolev, M. I. Serebryanaya, and A. N. Nozhevnikova (2005), Methane oxidation in landfill cover soil, Microbiology, 74(5):608-614. Kightley, D., D.B. Nedwell, and M. Cooper (1995), Capacity for methane oxidation in landfill cover soils measured in laboratory scale microcosms, Appl. Environ. Microbiol., 61:592-601. Legates, D. R., and G. J. McCabe (1999), Evaluating the use of "goodness-of-fit" measures in hydrologic and hydroclimatic model validation, Water Resour. Res., 35:233-241. Lelieveld, J., P.J. Crutzen and F.J. Dentener (1998), Changing concentration, lifetime and climate forcing of atmospheric methane, Tellus, 50B:128-150. MacQuarrie, K.T.B., and K.U. 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Rolston (2000), Predicting the gas diffusion coefficient in repacked soil: Water-induced linear reduction model, Soil Sci. Soc. Am. J., 64:1588-1594. Park, S., K.W. Brown, and J.C. Thomas (2002), The effect of various environmental and design parameters on methane oxidation in a model biofilter, Waste Manage. Res., 20:434-444. Parker J.C., R.J. Lenhard, and T. Kuppusamy. 1987. A Parametric Model For Constitutive Properties Governing Multiphase Flow In Porous Media. Water Resour. Res., 23(4): 618-624. Poulsen, T.J., and P. Moldrup (2006), Evaluating effects of wind-induced pressure fluctuations on soil-atmosphere gas exchange at a landfill using stochastic modelling, Waste Management Res., 24(5):473-481.  98  Scheutz, C., and P. Kjeldsen (2003), Capacity for biodegradation of CFCs and HCFCs in a methane oxidative counter-gradient laboratory system simulating landfill soil covers, Environ. Sci. Technol., 37(22):5143-5149. Scheutz C., H. Mosbaek, and P. Kjeldsen (2004), Attenuation of methane and volatile organic compounds in landfill soil covers, I Environ. Qual., 33(1):61-71. Scheutz, C., and P. Kjeldsen (2005), Biodegradation of trace gases in simulated landfill soil cover systems, J. Air Waste Manage. Assoc., 55:878-885. Sleep B.E. (1998), Modeling transient organic vapor transport in porous media with the Dusty Gas model, Adv. Water Resour., 22(3):247-56. Stein, V.B., J.P.A. Hettiaratchi, and G. Achari (2001), Numerical model for biological oxidation and migration of methane in soils, Practice Periodical of Hazardous, Toxic, and Radioactive Waste Manage., 5(4):225-234. Stein, V.B., and J.P.A. Hettiaratchi (2001), Methane oxidation in three Alberta soils: Influence of soil parameters and methane flux rates, Environ. Technol., 22:101111. Thullner, M., M.H. Schroth, J. Zeyer, and W. Kinzelbach (2004), Modeling of a microbial growth experiment with bioclogging in a two-dimensional saturated porous media flow field, J. Contam. Hydra, 70:37-62. Thorstenson D.C., and D.W. Pollock (1989), Gas-transport in unsaturated zonesMulticomponent systems and the adequacy of Fick's law, Water Resour. Res., 25(3):477-507.  99  Wilshusen, J.H., J.P.A Hettiaratchi, and V.B. Stein (2004), Long-term behavior of passively aerated compost methanotrophic biofilter columns, Waste Management., 24(7):643-653.  100  4. Vadose Zone Attenuation of Volatile Organic Compounds at a Crude Oil Spill Site - Interactions Between Multicomponent Gas Transport and Biogeochemical Reactions  A version of this chapter will be submitted for publication; Molins, S., K. U. Mayer, R.T. Amos, and B.A. Bekins (2007), Vadose Zone Attenuation of Volatile Organic Compounds at a Crude Oil Spill Site - Interactions Between Multicomponent Gas Transport and Biogeochemical Reactions, in preparation.  101  4.1. Introduction Accidental spills of hydrocarbon fuels from underground storage tanks or pipelines are a common cause of subsurface contamination at many sites around the world. In the vadose zone, volatilization of liquid-phase organic compounds retained in the soil by capillary forces, or perched on the water table, contributes to the spreading of contaminants. Additionally, degradation of both volatile and non-volatile compounds causes contaminant attenuation, consumes oxygen, and generates product species such as CO 2 or CH4, profoundly affecting the gas composition in the vadose zone. Transport of volatile organic compounds in the unsaturated zone has been identified as an important mechanism contributing to the contamination of groundwater (Baehr, 1987; Falta et al., 1989; Baehr et al., 1999) and contaminant release to the atmosphere (Metcalfe and Farquhar, 1987). Diffusion is commonly considered the dominant transport process for migration of VOCs in the unsaturated zone (Jury et al., 1984; Baehr and Corapcioglu, 1987; Silka, 1988; Mendoza et al., 1996; Conant et al., 1996; Pasteris et al., 2002). Pressure-driven advection may also be significant at early times of plume evolution due to the overpressure generated in the source area by rapid volatilization of organic compounds (Gaganis et al., 2004). Soil parameters such as moisture content and soil layering have been shown to strongly affect transport processes and gas-phase concentrations (Johnson and Perrott, 1991, Fischer et al., 1996, Davis et al., 2005). The fate of volatile contaminants is also affected by biogeochemical reactions, which cause contaminant attenuation. In particular, organic vapors can be degraded in the vadose zone in the presence of oxygen supplied from the atmosphere (Revesz et al.,  102  1995; Lahvis and Baehr, 1996; Lahvis et al., 1999; Lahvis et al., 2004; Amos et al., 2005) or anaerobically through interactions with solid phase electron acceptors (Anderson et al., 1998) and degradation under methanogenic conditions (Bekins et al., 1999; Anderson and Lovley, 2000). Methane produced by anaerobic degradation processes, in turn, is also subject to gas transport and aerobic oxidation (Amos et al., 2005). The interplay and coupling between transport and biogeochemical processes will determine the gas and solute composition in the vadose zone (Molins and Mayer, 2007), contaminant degradation rates and mineral weathering, and ultimately the longevity of the contaminant source. In 1979, the rupture of an underground pipeline near Bemidji, Minnesota spilled crude oil over a wide area. A large amount of oil infiltrated into the subsurface and accumulated above the water table of the glacial outwash aquifer forming three large oil bodies. The comprehensive data set collected at the Bemidji site provides an excellent opportunity for assessing the long-term evolution of vadose zone natural attenuation through numerical analysis. For example, the gas-phase composition in the area known as the north pool has been monitored since 1984 (e.g. Hult and Grabbe, 1988; Chaplin et al., 2002; Amos et al., 2005). In addition, several studies have been conducted that focus on sediment characteristics and moisture content distributions (Baehr and Hult, 1991; Dillard et al., 1997), the initial distribution of the oil and oil weathering (Dillard et al., 1997; Baedecker et al., 1984; Hostettler and Kvenvolden, 2002), and microbial ecology associated with degradation reactions (Bekins et al., 1999). Gas analyses showed that at early stages, elevated hydrocarbon concentrations were observed near the oil body (Hult and Grabbe, 1988), but these concentrations  103  decreased relatively rapidly (Chaplin et al, 2002). In contrast, methane concentrations were relatively low initially, but increased significantly over time, and presently account for 15-20% of the gas phase near the oil body (Baedecker et al., 1993; Chaplin et al., 2002; Amos et al, 2005). In recent years, non-reactive gases such as Ar and  N2 have  been  included in the analyses and show substantial deviations from atmospheric levels indicating that advective transport contributes to gas migration (Amos et al., 2005). Both aerobic and anaerobic degradation reactions including the reductive dissolution of Mnand Fe-oxides, as well as methanogenic degradation have been identified at the site (Anderson et al., 1998, Bekins et al., 1999). Previous studies have indicated that CH4 production in the saturated zone is significant enough to cause gas exsolution resulting in the formation of gas bubbles (Revesz et al., 1995; Amos et al., 2005). The vertical transport of gas bubbles driven by buoyancy forces, i.e., ebullition, has been suggested as an additional source of methane for the unsaturated zone (Amos and Mayer, 2006). Although 1 D-simulations of unsaturated zone natural attenuation and gas transport have been conducted previously for this site (Chaplin et al, 2002, Molins and Mayer, 2007), and preliminary integrated modeling of vadose and saturated zone natural attenuation was carried out (Amos, 2006), a quantitative analysis of interactions between gas migration, solute transport, and biodegradation reactions involving both dissolved and solid phase electron acceptors has not been conducted for the vadose zone. In particular, the transient evolution of contaminant degradation under consideration of site geometry, heterogeneities, and initial oil distribution has not been investigated to date. Furthermore, the contributions of advective and diffusive gas transport mechanisms to  104  contaminant migration and rates of contaminant degradation were not studied in an integrated manner and are not well quantified. Reactive transport models have been used to investigate processes occurring at sites affected by soil gas contamination where gas transport typically involves multicomponent mixtures (Gaganis et al., 2004). Fen and Abriola (2004) demonstrated that only formulations based on the Stefan-Maxwell equations or the Dusty Gas Model (DGM) are appropriate to rigorously describe multicomponent gas diffusion and advection in these systems. To date, models that are based on the Stefan-Maxwell equations or the DGM often neglect aqueous phase transport (De Visscher and Van Cleemput, 2003), and commonly are limited in terms of the reaction networks that can be considered (Sleep, 1998, De Visscher and Van Cleemput, 2003). Molins and Mayer (2007) recently presented a reactive transport model that incorporates the multicomponent gas framework provided by the Dusty Gas Model into the general description of the feedback between geochemical reactions and gas transport processes. The objective of this paper is the quantitative evaluation of the existing conceptual model for unsaturated zone natural attenuation at the Bemidji crude oil spill site (Chaplin et al, 2002, Amos at al, 2005) with the aid of the multicomponent reactive transport model developed by Molins and Mayer (2007). Specifically, this work attempts to reproduce past and present-day pore gas distributions including the transient evolution of contaminant degradation and gas transport processes. In addition, the contribution of diffusive and advective fluxes to gas transport during periods dominated by volatilization and methanogenesis will be evaluated. The objectives are accomplished by conducting 2D-reactive transport simulations and varying some of the less certain parameters within  105  bounds constrained by field evidence. The role of low permeability layers and methane ingress from the saturated zone by ebullition to explain the gas distribution observed in the unsaturated zone are evaluated. The benefits of a complete suite of gas analysis including the non-reactive gases N2 and Ar to constrain the model simulations are discussed. Uncertainties associated with the simulation results are evaluated and used to identify critical data gaps.  4.2. Methods 4.2.1. Model description  The analysis is conducted with a general-purpose reactive transport model that includes multicomponent transport and can consider a wide range of geochemical reactions (Molins and Mayer, 2007). In this section, only a brief summary of the model is provided, while a more complete description can be found in Molins and Mayer (2007). The model is applicable to multi-component reactive transport problems in variablysaturated porous media involving kinetically controlled redox and mineral dissolutionprecipitation, along with equilibrium reactions such as hydrolysis, aqueous and surface complexation, ion exchange, and mass transfer between the aqueous and gas phases (Mayer et al., 2002). Transport of geochemical components occurs in the aqueous and gas phases, with both advective and diffusive fluxes contributing to the migration of chemical species. Aqueous and gas advection are described using Darcy's law, while Fick's law is used for aqueous diffusion-dispersion. Gas diffusion is described with the Dusty Gas Model (DGM). The DGM describes gas transport of multi-component mixtures in both the molecular and Knudsen diffusion regimes. The DGM also includes a non-separative  106  flux component that develops as a result of the non-equimolarity of the gas species in the mixture: lighter molecules move faster than heavier molecules (Cunningham and Williams, 1980). Binary diffusion coefficients are calculated according to the Chapman and Enskog theory using the Lennard-Jones potential parameters (Reid et al., 1977). The model does not include NAPL migration, and in the simulations presented in this paper, it is assumed that crude oil is immobile. However, the reduction of pore space available for water flow and gas transport due to the presence of oil is included in the model as well as its effect on permeability and tortuosity coefficients for both the aqueous and gaseous phases. Gas data used in this study was collected in August 2007 following the experimental techniques described in Amos et al. (2005) and references therein. Additional data used in the modeling analysis has been obtained from previous published studies.  4.2.2. Site description, conceptual model and model set-up  The oil spill took place in a glacial outwash aquifer near Bemidji, Minnesota, which consists of moderately to poorly sorted sandy gravel, gravely sand, and sand with thin interbeds of fine sand and silt (Franzi, 1988). The observed permeability distribution is bimodal corresponding to the two predominant lithologies: coarse glacial outwash sand and fine-grained interbedded lenses (Dillard et al., 1997). The area that is the focus of this work, known as the north pool, originally contained from 80,000 to 160,000 L of oil (Bennett et al., 1993). The oil is present as a pool on the water table at 6-9 m below the land surface, and at residual saturation between the water table and approximately 1 m  107  below the ground surface. Figure 4.1 shows a cross section of the contaminated aquifer parallel to the direction of groundwater flow that outlines the location of the oil body and saturated and unsaturated contaminant plumes. Comprehensive site overviews can be found in Bennett et al. (1993), Baedecker et al. (1993), Bekins et al. (1999, 2005), Cozzarelli et al. (2001), and Chaplin et al. (2002). At the present time, the contaminant plume in the saturated zone is anoxic with methanogenesis being the dominant pathway for oil degradation (Bekins et al., 1999; Cozzareli et al., 2001). Here, the focus is on the description of the processes that are relevant for the development of vadose zone contamination, which are summarized in Figure 4.2. At early stages, the most volatile compounds evaporated stripping the area near the oil body from atmospheric gases (Figure 4.2a). These volatile organic compounds were partially oxidized in the presence of atmospheric oxygen (Hult and Grabbe, 1988). Over time, the oil body became depleted of its most volatile fraction, and degradation processes became more significant. Labile oil fractions degraded under aerobic and anaerobic conditions. The electron acceptors for anaerobic degradation are Fe(III) and Mn(IV) present at the site as oxide and hydroxide mineral phases (Anderson et al., 1998). Progressive depletion of Fe(III) and Mn (IV) lead to development of methanogenic conditions in the oil body with methanogenesis becoming the main pathway for attenuation of organic contamination (Figures 4.2b, 4.3a). As a result, methane concentrations increase both in the saturated and unsaturated zones. In the unsaturated zone, the vapor plume near the oil body is currently characterized by low 02 concentrations and high levels of CO2 and CH4 (Chaplin et al., 2002, Amos et al., 2005, Figures 4.3a, 4.3b, 4.3c). Amos et al. (2005) hypothesized that methanogenic degradation  108  in the zone near the water table may cause an increase of total gas pressure driving gas advection upward, which would explain the decrease of nitrogen and argon pressures in this zone. However, higher above the water table, a region of enrichment of Ar and N2 was observed relative to atmospheric composition (Figure 4.3d, 4.3e). This zone coincides with a region of methanotrophic activity, where methane is oxidized in the presence of oxygen. These data suggest that the decrease of total gas pressure in the reaction zone drives advective gas transport into this zone (Amos et al., 2005). In addition to methanogenesis in the unsaturated zone, methanogenesis in the saturated zone may explain concentrations of methane in the vadose zone. In the saturated zone, production of significant amounts of CH 4 causes gases to exsolve, form gas bubbles, and possibly ebullition (Revesz et al., 1995; Amos et al., 2005). For this work, a two-dimensional model of the vadose zone is constructed to investigate the interplay between reactions and transport processes. The origin of the horizontal axis is set at the center of the oil body. The domain comprises a 175 m-long section of aquifer along the direction of groundwater flow (Figure 4.4). The right and left boundaries are assumed to be impermeable. The ground surface is at an elevation of 430 masl downstream of the oil body, and at an elevation of 432.5 masl upstream (Figure 4.2), while the lower boundary is at 423.5 masl of elevation located approximately 20 cm above the water table. Groundwater recharge in the topographic low (0.2 m yr -1 ) is slightly above the average value of 0.18 m yr -1 , while recharge downgradient of the oil body is assumed to be 0.16 m yr -1 . The model represents average conditions over a year; aqueous flow is assumed to be at steady state, with seasonal fluctuations of the water table and in groundwater recharge omitted. This study focuses on long-term evolution  109  over a time period of more than 20 years, which justifies the previous assumption. Fluctuations in atmospheric pressure on gas transport were also neglected as it is assumed that their effects average out over time, in contrast to reaction-induced transport, which is a unidirectional process. Temperature fluctuations at depth are assumed to be small enough to be neglected. For initial simulations, the porous medium was assumed homogeneous with an average porosity of 0.38 and an average permeability in the horizontal direction equal to 10 -11 m2 , which is in agreement with observed and estimated values (Dillard et al., 1997; Baehr and Hult, 1991). Permeability in the vertical direction (3.10 -12 m2 ) is smaller than the horizontal value, an anisotropy ratio estimated from air permeability tests (Baehr and Hult, 1991). Soil parameters (Table 4.1) fall within the range of values measured in cores taken at the site (Dillard et al., 1997), and were chosen to reproduce observed aqueous saturations (Dillard et al., 1997). The crude oil spilled in the aquifer is of light paraffinic nature consisting predominantly of aliphatic and volatile aromatic hydrocarbons in the range C1-C35 (Eganhouse et al., 1993). For the simulations, the oil phase is represented by three fractions, following the approach of previous modeling studies (Essaid et al., 1995): volatile dissolved organic carbon (VDOC), non-volatile dissolved organic carbon (NVDOC), and a residual fraction. The most volatile oil fraction is represented by butane (Gallo) that constitutes 15 % of the oil present initially. This oil component represents the source for volatile hydrocarbons (VDOC) that were found to dominate the vapor plume during early stages (Hult and Grabbe, 1988; Chaplin et al., 2002). The second oil component represents a relatively non-volatile, yet soluble fraction (NVDOC) that is responsible for methane generation at later stages. This compound encompasses a wide  110  range of the oil constituents from n-alkanes and cyclo-alkanes to aromatics (C6-C35) that make up at least 25% of the initial oil (Hunt, 1979). The degradation of these compounds is represented by methylcyclohexane (C7H14) based on typical average oil compositions (Hunt, 1979). These oil fractions (i.e. VDOC, NVDOC) degrade under both aerobic and anaerobic conditions. Anaerobic degradation of these components occurs initially by reductive dissolution of Fe(III)- and Mn(IV)-minerals and, after these phases become depleted, by methanogenesis. The main products of anaerobic degradation processes are methane, carbon dioxide, Fe(II), Mn(II), and water. Under aerobic conditions, methane can in turn be oxidized to carbon dioxide. Stoichiometry, kinetic expressions and rate constants for all reactions included in the model are given in Table 4.2. The third oil fraction is considered insoluble over the duration of the simulations and does not degrade. A summary of the oil composition is provided in Table 4.3. The geochemical system that is necessary to describe the geochemical processes taking place at the site includes 11 aqueous components (HCO3 - (aq), 02(aq), CH4(aq), Ar(aq), N2(aq), Ca2+ , C7H14, Calm, Fe2+ , Mn2+ , and H ± ), 7 gas species (02(g), CH4(g), CO2(g), Ar(g), N2(g), and C 7 1-1 14 (g), C4Hio(g)), 15 aqueous complexes (OH - , H 2 CO 3 (aq), Ca0H + , CaHCO3 + , CaCO3(aq), CO3 2 , Fe0H + , Fe0H 3 , FeOH2(aq), FeHCO3 ± , FeCO3(aq), MnCO3(aq), MnHCO3 ± , Mn0H + , and Mn(OH)3 -), and 5 minerals (calcite, siderite, FeCO3, MnCO 3 , FeOOH, and Mn02). For the simulations, it is assumed that pore water is in equilibrium with calcite, since the native aquifer material contains approximately 4-6% carbonates (Bennett et al., 1997). The presence of Mn0 2 with an initial volume fraction 5.10 -5 m 3 111 -3 bulk inhibits the occurrence of oil degradation by FeOOH and methanogenesis at early stages. Reductive dissolution of FeOOH, with an initial volume fraction of 2.5.10 4 m 3 111 -3 bulk,  111  after partial Mn02 depletion, while near complete reductive dissolution of Mn0 2 is required for the onset of methanogenic conditions (Table 4.3). Loss of sediment Fe(III) is consistent with the reduction of sediment Fe(III) coupled to the degradation of hydrocarbons observed in the field (Anderson et al., 1998) and demonstrated in microcosms (Tuccillo et al., 1999). In addition to methane being produced in the unsaturated zone, methane produced in the saturated zone and capillary fringe region is modeled as a boundary flux specified for the region between -50 m and 50 m. The occurrence of ebullition is still subject of ongoing research, and magnitude and composition of this flux remain a matter of speculation. In this study, flux rates are used as model calibration parameters and compared to previous estimates (Chaplin et al., 2002). Concentrations of gases in the atmosphere are used as surface boundary conditions for the reactive transport problem, together with a pH value of 7 and a Ca 2+ concentration of 2.10 mol L -1 (Figure 4.4). The lower boundary is a free exit boundary for aqueous species and a no-flow boundary for gases. Initial pristine conditions are used for the vadose zone; thus, the same values used for the boundary conditions at the top boundary have been used as initial conditions (Figure 4.4). Simulations were run for 28 years (i.e. 1979-2007) and are intended to reproduce the evolution of the degradation processes and resulting gas plumes over time. A large number of parameters was included in this model resulting in a complex calibration process. A list of parameters and the values used in the model simulations are presented in Appendix 2. Well constrained parameters were maintained constant and fall within the range of observed and literature data, limiting model uncertainty. Sensitive and  112  poorly constrained parameters were calibrated using a trial-and-error approach. It must be acknowledged that these model parameters introduce uncertainties and non-uniqueness in the current set of simulations. A discussion on the uncertainties associated with simulated results and a comparison with the range of observed and literature values are provided in section 4.3.1. Limitations and shortcomings of the model with respect to these uncertainties are also discussed.  4.3. Results and discussion  Initial simulations were conducted assuming a homogeneous permeability throughout the region of interest. Although a good match between measured and simulated results could be obtained down gradient from the oil body during methanogenic stages (not shown), results in the upgradient area significantly differed from observed concentration gradients, which are focused on a narrow zone between 426 masl and 427 masl (Figure 4.3). Steeper concentration gradients can be explained by a zone of reduced transport properties, resulting in a limited supply of oxygen into the deeper vadose zone. This zone is consistent with the presence of a low permeability lens observed in the upgradient zone with its permeability being two orders of magnitude smaller than surrounding materials (Baehr and Hult, 1991; B. Bekins, unpublished data). This layer is considered in the simulations by the inclusion of a 36 cm-thick lens at 426.5 masl between -75 m and 0 m with a porosity of 0.30 and a permeability of 10 43 m 2 and 3.10 -14 m 2 in the horizontal and vertical directions, respectively. The presence of this finegrained lens has two effects on gas transport: diffusive fluxes decrease via tortuosity  113  reduction due to higher water contents, and advective fluxes decrease via effective permeability reduction due to higher water saturations and a lower intrinsic permeability. The comparison of simulated results to observed data focuses on present day conditions, because the available data set is most comprehensive. Unlike the homogeneous case, simulation results including the low permeability lens provide a good agreement to observed concentrations in the upgradient area (Figures 4.3 and 4.5). In addition, model results confirm concentration patterns explained by the conceptual model outlined earlier. Concentrations of methane increase near the oil body (Figures 4.3a, 4.5a) both due to methanogenesis occurring in the oil body and methane fluxes generated in the capillary fringe and saturated zone, while they decrease to atmospheric values towards the ground surface. The extent of the methanogenic zone as delineated by the 1% concentration contour of measured data (Figure 4.3a) is captured well by simulated results (Figure 4.5a). Within the methanogenic zone, simulated concentrations also agree well with measured values, especially near the region where oil is present with peak CH4 concentrations in the 15-20% range. In the upgradient area, high methane concentrations spread over a larger area than in the downgradient area, because oxygen transport to this zone is hampered by the presence of the low permeability lens. Concentrations of CO2 follow a trend similar to that of CH4 (Figures 4.3b, 4.5b), although high CO2 concentrations spread over a larger area downgradient of the oil body. The region with high CH 4 and CO 2 concentrations is also characterized by very low 02 concentrations that increase to atmospheric values towards the ground surface (Figures 4.3c, 4.5c). Oxygen contours in the area upgradient of the oil body are tightly spaced due  114  to the presence of the low permeability lens (Figure 4.5c) again in agreement with observed patterns (Figure 4.3c). Gases assumed to be non-reactive in the simulations also show spatial variations. Both Ar and N2 show zones of concentrations higher than atmospheric values (shaded areas in Figures 4.3d, 4.5d and Figures 4.3e, 4.5e) and concentrations below atmospheric values near the oil body and zone of CH4 and CO2 ingress. Location and patterns of enrichment and depletion of Ar and N2 are reproduced well by simulated results (Figures 4.5d, 4.5e). In the zones where methane production occurs relatively near the ground surface, or where gas transport is hampered by the high moisture lens, enrichment occurs in a narrow region of sediment (zones upgradient and immediately above the central part of the oil body in Figures 4.5d, 4.5e). On the other hand, where methane is produced deeper in the vadose zone, and gas transport has no significant obstructions, enrichment occurs in a wide region as observed downgradient of the oil body (Figures 4.5d, 4.5e). The magnitude of enrichment and depletion is in good agreement with measured concentrations (Figures 4.3d, 4.3e). Only slight differences exist in the size of zones of Ar and N2 enrichment, which larger than those observed at the site. In addition, lack of data in the zones immediately downstream of the leading edge does not allow for confirmation of high enrichment (>0.98% Ar, and >83% N2) extending to the water table as shown by simulated data. Likewise, due to lack of data upstream of well 604 (Figure 4.3), the location of the upstream edge of the methanogenic zone cannot be constrained. For example, simulations show that CH 4 concentrations decrease rapidly upstream of —30 m, which would suggest that the edge of the methanogenic zone does not extend further upstream. Overall, the good agreement between observed and simulated data indicates  115  that the conceptual model is adequate and representative for site conditions, and that reaction induced advective gas transport is occurring. As discussed in the following paragraphs, measurement of reaction indicators such as the spatial distribution of methanotrophs may aid in further supporting these simulation results. Figure 4.6 shows methanogenic rates for the NVDOC fraction in the unsaturated zone. The 10 -5 mol 1. -1 H2O c1 -1 contour delineates the zone under anaerobic conditions where significant oil saturations are present and methanogenic degradation is taking place. This is in agreement with elevated populations of methanogens observed in the unsaturated zone near the low permeability lens (Bekins et al., 1999). Away from the zone of methanogenesis, methane is oxidized in the presence of oxygen at rates shown in Figure 4.6. The region with highest oxidation rates is constrained to the zone of mixing between CH4 and 02 and corresponds to the location of high populations of methanotrophic bacteria measured in 2005 using the most probable number (MPN) method (Figure 4.7). The MPN method was previously used at the Bemidji site to characterize the spatial distribution of 6 different microbial physiologic types (Bekins et al., 1999). The zone of high methane oxidation rates coincides with the zone of high Ar and N2 concentrations), while the zone with high methanogenic rates coincides with the zone  of low Ar and N2 concentrations (Figures 4.3d,e; 4.5d,e). The distribution pattern of Ar and N2 reflects the coupling between advection and diffusion. Near the water table and the oil body, pressure increases due to the production of methane and ebullition from the saturated zone (Figure 4.8). In the methanotrophic zone, methane and oxygen consumption causes the gas pressure to decrease below atmospheric levels (Figure 4.8).  116  As a result, a pressure-driven flow develops between the zone of methanogenic zone (elevated pressure) and the methanotrophic zone (lowered pressure). Because advective gas fluxes originating from reactive processes equally affect all gases in the mixture, advective fluxes of the non-reactive gases Ar and  N2  (Figure 4.9a) must be offset by  diffusive fluxes (Figure 4.9b) under quasi-steady state conditions. These diffusive fluxes are driven by the concentration gradients that ultimately show the enrichment and depletion patterns observed at the site (Figure 4.3d, 4.5d and Figure 4.3e, 4.5e). Pressure gradients necessary to sustain advective fluxes between the two zones are very small. A maximum pressure gradient of 0.07 Pa m' m between the zone with highest methanogenic rates and the methanotrophic zone downgradient of the plume was calculated in the simulations. Pressure gradients of this magnitude cannot be measured and can only be constrained by flux measurements and modeling. However, as suggested previously, measurement of Ar and N2 and interpretation of their concentration patterns can serve as a good indicator for the occurrence of advection. Both advection and diffusion contribute to the transport of methane in the vadose zone. While advection contributes up to 15% of the magnitude of net CH4 fluxes, diffusion is still the dominant transport mechanism. Advective and diffusive fluxes tend to act in different directions, with diffusive fluxes being mostly vertical, driven by concentration gradients that exist between the atmosphere and the contaminated deeper vadose zone Figure 4.10b. Advective fluxes have larger horizontal components as low pressure zones develop upgradient and downgradient of the oil body and due to the anisotropy of the porous medium (Figure 4.10a).  117  Aerobic and anaerobic oxidation of organic compounds generates acidity that is buffered by the minerals present in the aquifer. In particular, dissolution of carbonate minerals included in the simulations maintains the pH at circum-neutral values (Figure 4.11 a). The decrease in pH is relatively more significant in the zone of methane oxidation because methane produced both in the saturated and unsaturated zone is oxidized there. Calcite dissolution is consequently more pronounced in this zone (Figure 4.11b). The capability of including mineral dissolution-precipitation in the modeling is important, because it affects the subsurface CO2 budget, and in carbonate mineral-poor systems, pH may also have a feedback on the rate of degradation reactions.  4.3.1. Transient evolution and discussion of uncertainties and limitations  Figure 4.12 shows the transient evolution of gas concentrations at a selected location near the centre of the oil body (i.e. port 3 of vapour well 9014 at 7.33 m depth) compared to available data collected in 1985 (Hult and Grabbe, 1988), 1997 (Chaplin et al., 2002), 2003 (Amos et al., 2005), 2004, 2005, 2006 (USGS, unpublished data), and 2007. These data have been used in the calibration process. Shortly after the oil spill, VOC-concentrations increase dramatically displacing atmospheric gases with nitrogen concentrations declining to mol fractions of 0.5 (Figure 4.12). As VDOC volatilizes with time, concentrations decrease, while N2 return to atmospheric values after 10 years. At this point, methane concentrations start to increase slowly as Mn02 is progressively depleted in the oxidation of oil compounds (Figure 4.13b). Oil degradation under anaerobic conditions by Fe(III) reduction starts after partial depletion of MnO2 (Figure 4.13a) and takes place simultaneously with methanogenesis, the onset of which occurs at  118  later times (progressively between 10-16 years) when near complete depletion of Mn02 has occurred (Figure 4.13b). In the simulations, the increase of methane occurs rapidly due to the contribution from the saturated and capillary zones. These contributions were simply modeled as a constant boundary flux that is included after 16 years. The increase in methane generation in the capillary fringe region and ebullition likely occurred in a more gradual manner at the site. The flux attributed to ebullition and degradation in the capillary fringe was calibrated to 0.13 mol CH4  111 -2 d i .  The consideration of this flux was necessary to obtain  agreement between observed and simulated concentration distribution data (Figures 4.3, 4.5) with the magnitude of this flux being slightly larger than fluxes reported previously (0.07 mol m -2 d -1 , Chaplin et al., 2002). The flux rate is equivalent to a rate of methane production in the saturated zone of 2.0-4.10 -9 mol CH4 L -1 H 2 O s -1 , assuming methane production occurs over a thickness of 1-2 m (Bekins et al., 1999). This rate falls in the same range than maximum calibrated methanogenic rates for the unsaturated zone in this work (2.0.10 -9 mol CH4 L -1 H 2 O s -1 , Table 4.3), but is higher than simulated rates (7.10 -1° mol CH4 L -1 H 2 O s -1 ) in Essaid et al. (1995). Rates in Essaid et al. (1995) may be low since the study did not include degassing or ebullition, and calibration was performed on the basis of aqueous concentrations of CH4. Methane generation causes slightly elevated gas pressures, and as discussed above, displaces nitrogen as shown by decreasing nitrogen concentrations. In comparison to CH4 at later stages, VOC concentrations at early stages are larger and can potentially produce larger pressure increases.  119  Figure 4.14 shows gas concentration in the vadose zone one month after the spill. The role that CH 4 assumes presently, is played at early times by the volatile oil fraction. Volatile compounds represent over 40% of all gases near the oil body. This large volume of VOCs displaces atmospheric gases away from this zone. These gases are partially degraded aerobically as indicated by the enrichment of Ar and N2 concentrations in the downgradient and upgradient areas. Also, an increase of CO2 is observed in those areas, since CO2 is produced in the oxidation reaction. However, the volume of VOCs that evaporate from the oil body is large enough that most of the volatiles are emitted to the atmosphere without undergoing degradation, as indicated by steep concentration gradients near the ground surface in the area directly above the main oil body, and the absence of the zones of Ar and N2 enrichment. Simulated results for C41410 underestimate reported values for 1985 (Figure 4.12). Volatile compound concentrations for 1985 are available in terms of g I11-3 ; thus, a range of volume fractions is possible for different average molecular weights of the VOC mixture. If it is assumed that the VOC mixture had an average molecular weight equivalent to that of hexane (82.15 g VOC fractions in the mixture are those in the lower bound given in Figure 4.12. Since the sum of partial pressures of gases should be approximately equal to the atmospheric pressure, concentration data for other gases in the mixture could be used as a check for the accuracy of the VOC value. Of special importance is N2 data, since it is relatively non-reactive and is present at high concentrations. However, N2 data is not available for 1985 and the actual mol fraction for volatiles cannot be constrained well. Other uncertainties are associated with the 1985  120  concentration data because contours reported in the former reference are based on a limited number of measurements (Hult and Grabbe, 1988). Alternative sources of model uncertainty originate in the moisture contents and tortuosity model (Millington, 1959) used in the simulations. It is well known that these parameters have a dominant influence on unsaturated zone gas transport. Higher water saturations would explain a slower rate of depletion of C4H 10 , since it would hinder transport of C4H 10 away from the zone of volatilization through tortuosity and relative permeability reduction. However, water contents specified for the simulations were constrained by data from Dillard et al. (1997). Likewise a tortuosity model that produced smaller tortuosity values for the same water content would also slow down the rate of C4H 10 depletion. It can be hypothesized that the tortuosity model used may be inadequate for the sediments present at the site. The presence of small-scale low permeability lenses or micro-layers such as those observed at the site (Franzi, 1988; Dillard et al., 1997) with high water saturations may control diffusion at the macro-scale. As a result, transport of both contaminants to the ground surface and atmospheric oxygen to the lower vadose zone would become inhibited. This hypothesis is also supported by the fact that most methane degraded aerobically is due to this flux, with the unsaturated zone contribution limited to a relatively small fraction (19%). Calibrated methane release rates from the saturated zone and capillary fringe are larger than those used in the unsaturated zone, which is in disagreement with MPN data that shows lower numbers of methanogens in saturated zone samples (Bekins et al., 1999). Again, this result points to an overestimation for the ingress of oxygen to the oil body that tends to maintain aerobic conditions, and decrease effective methanogenesis rates in the vadose zone.  121  If a tortuosity model that generates smaller tortuosity coefficients were more representative of site conditions, diffusive fluxes, as currently simulated, would overestimate actual diffusive fluxes; in particular, the flux from the saturated and capillary fringe zones would need to be recalibrated. Anaerobic and aerobic oxidation rates estimated with the current would also be overestimated. These discrepancies point to an inconsistency in the current conceptual understanding that could be revealed by the modeling. As suggested by previous results, a tortuosity value that reduced diffusive fluxes by a factor between 2 and 4 would also reduce rates by a similar factor; the estimated rates thus are expected to be correct within factor of 2-4. Other constraints in this modeling effort are model limitations, which include lack of multi-phase capabilities, and the inability to include saturated zone and capillary fringe processes such as bubble generation and ebullition that involve gas transport in a discontinuous phase in an integrated saturated-unsaturated approach. In addition, the spatial and temporal variability of microbial populations is neglected, limiting the model's capability to assess the impact of microbial growth and decay on biodegradation rates. However, these limitations are not believed to influence the main conclusions of this work and inclusion of these processes would not likely remedy the inconsistencies discussed above.  4.4. Summary and conclusions Simulations of gas transport and biogeochemical reactions have been performed to quantify the processes that contribute to the attenuation of volatile organic contaminants at a crude oil spill site near Bemidji, Minnesota. The reactive transport  122  model used for the simulations includes transport in the aqueous and gaseous phases, with gas-phase transport described using the Dusty Gas Model equations (Molins and Mayer, 2007). The model was able to quantitatively reproduce the distribution of gas concentrations observed at the site at different times and provide an evaluation of the uncertainties that remain with respect to fluxes and rates. Simulation results support the model proposed by Amos et al. (2005) in that the distribution of the non-reactive gases such as  N2  and Ar reflects the interplay between diffusive and advective flux  mechanisms. The zones of gas production and ingress are characterized by high gas pressures and low concentrations of N2 and Ar. On the contrary, zones of methane consumption by aerobic degradation are characterized by low gas pressures and high concentrations of N2 and Ar. As a result, non-reactive gases such as  N2 and  Ar have been  successfully used to constrain the model simulations. These patterns are also reproduced at initial stages of plume evolution when large volumes of volatile compounds evaporate from the oil body. Diffusion is the most significant transport mechanism of gases in the vadose zone. However, advection contributes significantly to the net fluxes of organic vapors evaporating from the oil at early stages and adds up to 15% of net fluxes of methane produced under anaerobic conditions at late stages. While the direction of advective fluxes depends on the anisotropic ratio kh/k v , diffusive fluxes are mostly vertical. The direction of net fluxes is a composition of both contributions. The presence of a low permeability lens has a significant effect on gas concentrations in the vadose zone, and its inclusion in the model was necessary to explain  123  observed concentration upgradient of the oil body. Higher water contents observed in these lenses can effectively control supply of oxygen into the zone of methane production. Concentration patterns resulting from this decrease in transport properties are significantly different than those resulting in homogeneous media. As a result, concentration gradients occur in a narrow zone. In the down gradient area, the assumption of homogeneity is sufficient to achieve a good match between simulated and observed data. The transient evolution of the system cannot be fully captured with the current model due to its complexity and a number of uncertainties partly associated with lack of data at early stages, and possibly affected by the use of a tortuosity model that is not appropriate for heterogeneous media. Rates may be overestimated, but they are expected to be correct within a factor of 2-4. Although a more quantitative analysis appears to be hampered by these uncertainties, the model has also proved useful to identify data gaps, sensitivity, and inconsistencies in the conceptual models. Additional measurements may help in providing better quantitative estimates. In particular, measurements of CO2 fluxes at the ground surface would provide a means to constrain rates the rates of aerobic and anaerobic contaminant degradation, including depth-integrated methane oxidation.  124  N  O  <=>^en *^.-. d  ^kr) b  CL)  0 U^cv 0./ 00 ,7-. b^N 10 (-,-)^6 7. 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O Z 0^ C1-' ..4 Z 4-) Cj -4^C:5 --:^ oo +^C.5 (:)^(5- C). `r) '+^ 0 00 ..,^N 'K, 0 —^ q) — co) ec; 0^c-A ..^co ■.o -I-^tr) +  )  .-•^ 0 --'^ :$ 6 U^6 (...)^r- . ,^tr) . , Z ± ^6 0 6 0 .t ±^ 71-^° ^o c) + z ir)^ ^.to Z 71Z GN^+ z^ • 0 ^C5 08^6 oc,^0 ^0 00 0 1:3 0 o 0 cf.) 4 a. T^a). T^ 6 6  X  11  Ys  127  Figures 4451E—Spray Zone —)1 Unsaturated ^Land Surface Zone g 'Unaffected by Spill conin tain 1^I Cru de Oil  -  44073435E  g  Zone  It 425w  Methano4eirk.444 _  :,  420 Flow  415  ^ -200^-100^0^100 200 Distance from Center of Oil Body (m)  Figure 4.1. Cross section of contaminated aquifer (adapted from Delin et al., 1998).  128  ^  432 Ground Surface  ra 430 -  E  Advection Diffusion  Volatiliza^,  0  c 428  01:‘ ,/  Fu 426  •  Advection Diffusion  vac Volatilization  424 -50^0^50  ^  Distance from Center of Oil Body (m)  432 = 4;430  -  b  11  Ground Surface  E ^02 c 428 o  \if^  07  100  A/  ,...." ..,„ .:.??6,0^ Advection  Diffusion CH ^'..... 0^ 0 • ..^CO,^,—:.... 1'0'0.  ". ...../ . 1f........ mom^...,...... .., .4.  ^....^* P° ./ ..,,,, ,..; „,. ^Anaerobic^ 426 ^?  424  ^WM= Degradation 077.fie;k2(1),- \ s. Ebullition from W.T. CH,^.........410" \.. + Degradation^ 1, in Capillary Fringe^.^CO2  I n so Distance from Center of Oil Body (m)  100  Figure 4.2. Schematic with relevant processes included in the conceptual model for (a) early times and (b) late times. Shaded area indicates the presence of oil at different saturations.  129  435^  a) CH 4  5  a E 430  a co  ■-•^Co  gt 5  X  O lO . r)  in  m  435  435  435  430  a 430  430  N CO  LL)  0  0  5 425  -50^0^50 Distance from Center of Oil Body (m)  425^425  100^-50^0^50 Distance from Center of Oil Body (m)  425  100  435  430  g 430  430  5 425^425  425  ^ ^ -50^0^50 100^-50^0^50 100 ^ Distance from Center of Oil Body (m) Distance from Center of Oil Body (m)  ^ -50^0^50 100 Distance from Center of Oil Body (m)  Figure 4.3. Cross-sections of aquifer showing vapor-phase gas data collected in 2007. Vapor-phase contours are in % mole fractions. Well numbers for each vapor well are shown. Note the vertical exaggeration with the ratio between vertical and horizontal axes being 20:3 is used in this and following figures.  130  434432-  P(02 ) = 0.21 atm [Cal= 2-10-3 M P(f1 9 )= 0.78 atm pH = 7.0  q 0.16m yr-1  P(Af)= 0.01 atm q = 0.2 m  7  oil saturation  g 430c^- ^impermeable 0 boundary Tff 428426-  h = 422.8 m  0.3 0.2 ^ 0.1  impermeable boundary  free exit boundary  (aqueous phase)  424 -50^0^50  Distance from centre of oil body (m)  100  Figure 4.4. Initial and boundary conditions for variably saturated flow and reactive transport model.  131  435 435^ b) CO2  435  c430 a 430 c 0 TO 2. e 425 W 425  -50^0^50^100 Distance from Center of Oil Body (m) 435^ C) 0 2 =.• a a E 430  -50^0^50 Distance from Center of 011 Body (m)  435 435  430  425  100  435  co 430 ; 430 c 0 TO 2. a 425 W 425  ia › 0  at  W 425  0^50^100 Distance from Center of Oil Body (m)  430  425  -50^0^50^100 Distance from Center of Oil Body (m)  435  430  425  -50^0^50 Distance from Center of Oil Body (m)  100  Figure 4.5. Cross-sections of aquifer showing simulated vapor-phase gas at 2007 for the heterogeneous case. Vapor-phase contours are in % mole fractions.  132  435  Log Rates (mol^H2O c1 -1 )  435  5, E 430  430  0 z TT;  425  -5  425  NVDOC anaerobic oxid. (methanogenesis)  -50^0^50 Distance from Center of Oil Body (m)  100  Figure 4.6. Simulated rates of CH 4 aerobic oxidation and NVDOC anaerobic oxidation.  430 429E c 4280 176 427a.) Lu 426425 ^ I ^I 3 4 5 6 7 8 Log MPN Figure 4.7.  Most probable number at location A (upgradient) and B (downgradient) for methanotroph populations. Adapted from Bekins (pers. comm.)  133  ^  435^  435  E 430  430  0  W 425  425  ^ -50^0^50 100 Distance from Center of Oil Body (m)  Figure 4.8. Simulated gas pressures in 2007. Shaded areas indicate zone of elevated (dark) and lowered (light) pressure.  ^435-  a)  N 2 : Advective Fluxes^ 0.25 moles if^  -  b) N 2 : Diffusive Fluxes 435^435-^ 0.25 moles if'  -435  1_4^ , I^ ^f t tt t t L i4 i i^,^ '411 i 1 s E 430^ 430 -^(E3 430^ 430 ^ 4 1/^0^ 4 4 4 i^ / ft t^t t ti l t f t t t f t t t 4 4^4 ^  ^4 ^tt o^  4^t/004,t,0^ 4^ 4 4^1^ t \t.‘^.^ p; t r.^t ^ f t t t/ ,  w 425-4,"N^■,,,,`"\.,  - t t t t^t t t 1  -430  4 01 ,t t t .  14, 4 41 1 14 1 P:it?: -  -425^425-i^),^'3^•i 4 • 4 •  4 4 4^4 4^ i1 .• -50  ^  go  100^-50  Distance from Center of Oil Body (m)^  ^  go  Distance from Center of Oil Body (m)  425  100  Figure 4.9. Simulated N2 (a) advective and (b) diffusive fluxes in 2007. Vector head at point of estimation. Vertical exaggeration applies only to spatial coordinates not to vectors, which show true directions.  134  435  b) Diffusive fluxes  a) Advective fluxes  435 435-  0.05 moles d  —  •  -435  0 5 moles d CH,  —a 0.5 moles cl -t 0 2  0.05 moles d  a  430 E 430 C c)  E 430 0  a  425 W 425-  W 425 ^i  4 04Y4 44 4 4^4 1^1/4^44 14^,ottf  -430  ,^I I t yt t i t t ft;f t tot ttff f it^t^ttt ^t tkft t^,t^it t  -425  ,  1  -50^0^50  ^  Distance from Center of Oil Body (m)  ^  100^-50^0^50 ^ Distance from Center of Oil Body (m)  100  Figure 4.10. Simulated CH 4 and 0 2 (a) advective and (b) diffusive fluxes in 2007. Vector head at point of estimation. Vertical exaggeration applies only to spatial coordinates not to vectors, which show true directions.  435 435  cz.  N.  a  E 430 — c  O  > W 425  7.6 7.3 7.0 6.7  Calcite Dissolution Rates (mol 1 -1 bulk s -1 )  ■NE=  435  10-7 10-8 10-9 10-1  (b)  430 E 430  430  C  0 a a)  425 W 425  425  ^ ^ -50^0^50 100^-50^0^50 100 ^ D istance from Center of Oil Body (m) Distance from Center of Oil Body (m)  Figure 4.11. Simulated pH and calcite dissolution rates in 2007.  135  0.015  0.8  E Ti  E"' co 0.6  0.01 E=  P.3  co  F, 0.4  co w Ili  c7i 'tco 0.2  0.005 2•t3-  an  a.  co  a. Ze  ci.  0^10^20  Time (year)  Figure 4.12. Evolution of gas concentrations over time. Data for 1985 and 1997 has been interpolated from nearby ports. The brackets for the 1985 C 4 H io data point include a range of concentrations corresponding to different average molecular weights for the VOC mixture (total VOC concentrations were reported in g 111-3 in Hult and Grabbe [1988]). The upper bound corresponds to propane (C 3 H8 ), and the lower bound to hexane (C6H16)•  435 c-.. a a E 430 — c 0 a w W 425  435 435  a) FeOOH Volume Fraction (m 3 M -3 bulk)  b) Mn0 2 Volume Fraction (m 3 m -3 bulk)  435  a  a 430 E 430 c 0 a 0 425 Ui 425  -50^0^50  430  425  ^  Distance from Center of Oil Body (m)  100^-50^0^50^100 ^ Distance from Center of Oil Body (m)  Figure 4.13. Simulated depletion of Fe(III) and Mn(IV) minerals in 1994.  136  435 435  co co  E 430  430 E 430  0  0  W 425  -50^0^50 Distance from Center of 011 Body (m) 435  76 Co 430  425 51 425  100^-50^0^50 Distance from Center of 011 Body (m) 435 435  CO  430  CO  430  430  425 1:5 425  425  0  0  1Co  co  W 425  -50^0^50 Distance from Center of 011 Body (m)  100^-50^0^50 Distance from Center of 011 Body (m)  100  ^ 100 -50^0^50 Distance from Center of OH Body (m)  Figure 4.14. Cross-sections of aquifer showing simulated vapor-phase gas in 1979 for the heterogeneous case. 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Summary and Conclusions  145  5.1. Model summary  A rigorous description of gas transport in unsaturated porous media has been implemented into an existing reactive transport model to study the effect of geochemical reactions on gas transport, and to evaluate the contribution of the different transport mechanisms to net gas fluxes in three case studies. These three case studies are pyrite oxidation in mine tailings, methane oxidation in landfill cover soils, and aerobic and anaerobic degradation of volatile and non-volatile organic compounds in a crude oil contaminated aquifer. To my knowledge, this is the first work to incorporate gas diffusion and advection based on a multi-component framework into a general-purpose reactive transport model. The StefanMaxwell equations in the form of the Dusty Gas Model (DGM) provide the most complete description of gas diffusion, which includes flux mechanisms in the molecular and Knudsen regimes. In addition, the model includes the feedback of reactions on gas advection with the direct substitution of Darcy's law in the mass balance equations. The inclusion of these processes has allowed for the evaluation of the significance of their contribution to gas transport in a variety of vadose zone settings of environmental interest. Such evaluation was not available in previous modeling studies because pre-existing models were formulated for specific problems and lacked generality. Only a limited number of reactive transport models include advection, and those that include Stefan-Maxwell equations include a very limited geochemical system.  146  5.2. Coupling between reactions and gas transport Case studies presented have shown that reactions and gas transport are coupled processes in the vadose zone. Consumption and production of gases caused by geochemical processes results in the generation of pressure and concentration gradients that drive gas fluxes. In addition, geochemical reactions can bring about other changes in the parameters that affect gas transport such as porosity, saturation and permeability by production of water and exopolymeric substances during methane oxidation. The flexibility of the model to include a wide range of reactions and the direct substitution approach of reaction terms in the mass balance equations allowed for the investigation of these feedback processes. Reaction-induced advection was shown to be a process of significance in the studied environments. Consumption of gas species in oxidation reactions reduces the gas-phase pressure, which may reduce or even reverse advective gas fluxes. The relative importance of the contribution of reaction-induced advection depends on the composition and magnitude of gas fluxes in the subsurface. Specific contributions will be discussed in section 5.3. Gases that do not participate in reactive processes provide an indication of the feedback of reactive processes on gas transport. At an oil spill site, concentrations of non-reactive gases are relatively high in zones where low pressures are generated by the consumption of gases during oxidation reactions in agreement with the conceptual model proposed for the site (Amos et al., 2005). In these zones, diffusion and advection of non-reactive gases act in opposite directions. Since there are no sources or sinks for non-reactive gases, advective fluxes, which originate from reactive processes and affect all gases in the mixture, are offset by diffusive fluxes. These diffusive fluxes are driven by the concentration gradients that ultimately show the  147  enrichment patterns observed in the reaction zone. On the other hand, low concentrations of nonreactive gases are observed in zones with high pressures. In cover soil columns, high  N2  concentrations indicate a reversal in the advective velocity  due to the pressure decrease caused by the methane oxidation reaction. In carbonate-depleted mine tailings, N2 concentrations at depth increase 24% from atmospheric values, in agreement with results obtained by Binning et al. (2007). However, in carbonate-rich tailings, only a 13% increase is observed, which was not obtained in the former study, because carbonate mineral dissolution was not considered. This example shows that the inclusion of the mineral weathering may have an important feedback on gas transport, and should be included to accurately calculate gas concentrations and fluxes in the vadose zone. Pressure gradients that develop as a result of reactions and that are required to drive the aforementioned advective fluxes are very small (up to 0.07 Pa 111 1 at the oil spill site, between 47 Pa 111 -1 and 77 Pa IT1 -1 in sulfide tailings). This supports conclusions from Thorstenson and Pollock (1989), who found that small pressure gradients in the gas phase (1 Pa m -1 ) could drive significant gas fluxes. Pressure gradients below 100 Pam 1 , such as the simulated values, are difficult to measure in laboratory experiments or in the field. Pressure gradients simulated for landfill covers caused by the large volumes of landfill gases entering the soil column are expected to be well in the measurable range. In addition to a direct effect on gas transport, reactions can have an indirect effect by changing porosity and water content. For example, methane oxidation in landfill cover soils results in the production of exopolymeric substances (EPS) and water. The model was enhanced to account for these processes in the landfill cover soil simulations. Long-term simulations showed that accumulation of EPS could decrease diffusive fluxes significantly, and thus, decrease oxidation  148  of methane. Simulated water production rate was significant (100 mm yr - 1 ) and comparable to recharge at the site. EPS production had a more significant effect than water production since EPS accumulation was concentrated in the reaction zone, while water produced was distributed along the entire column following Richard's equation. In the present study, available models derived for soils were applied to investigate the effect of EPS accumulation on the hydraulic properties and transport properties of porous media. These models may not be directly applicable to soils with EPS. The effect of EPS accumulation on the Van Genuchten parameters and water flow, as well as on Knudsen diffusion remains to be investigated.  5.3. Diffusive and Advective Contributions In general, diffusive fluxes were found to be larger than advective fluxes, but the latter are relevant when reactions produce or consume significant gas volumes. During pyrite oxidation in mine tailings, atmospheric oxygen is consumed and a low pressure is generated at depth. As a result, advection can contribute up to 16 % of atmospheric oxygen into the sediment column, if no carbonate minerals are present in the tailings. These results are in agreement with modeling results presented in Binning et al., (2007). While the model developed by Binning et al. (2007) did not include solute transport and mineral dissolution-precipitation reactions, and only considered pyrite oxidation implicitly through boundary conditions, the model developed in the current work allows the inclusion of a wide range of chemical reactions with mass transfer occurring between aqueous, gas and minerals phases. In carbonate-rich mine tailings, the advective contribution is smaller (9.5%) because the increase of CO2 during carbonate dissolution contributes to compensate the loss of volume caused by 02 consumption. Acidity in the pore water is buffered at values around 7 due to the dissolution of calcite. At a site contaminated with crude oil, advective fluxes account for 10-15% of CH 4 fluxes away from the  149  oil body under methanogenic conditions. In the landfill cover soil experiment, advection is dominant in the lower section of the column as a result of ingress of landfill gas at the base of the column, while diffusion dominates methane emissions to the atmosphere. Oxygen advective flux out of the column offsets 15% of the diffusive flux into the column. However, methane oxidation near the top of the column causes a decrease in gas pressure and decreases the magnitude of advective fluxes in the reaction zone. These results highlight the need for a gas transport model that includes all relevant diffusion mechanisms. For the range of permeability values representative for environments studied in this work, diffusion occurs in the molecular regime and Knudsen diffusion is not relevant. However, in cases where reactions result in the production of substances that reduce the pore space available for gas transport, and thus permeability, Knudsen diffusion may gain in importance. In landfill cover soils, where large amounts of methane are oxidized, accumulation of exopolymeric substances produced during methane oxidation can reduce permeability 3 orders of magnitude, which may cause Knudsen diffusion to become relevant. Likewise, in low permeability media (e.g. clays), Knudsen diffusion is also significant, but such low permeability values were not encountered in the case studies. Application of Fick's law requires that diffusing gas species are dilute in the bulk gas phase, which is not satisfied in any of the case studies. For example, diffusive flux of nitrogen depends on the gas species involved: the binary diffusion coefficient for N2-CH4 is 2.1.10 m 2 s -I while for N2-CO2 is 1.6.10 -5 m2 s 1 . For example, in the landfill cover soil simulations, using the same diffusion coefficient for all species resulted in an error of 1.5 % in the estimation of CH4 fluxes, and of 2.5 % in the estimation of CH4 concentrations. A priori estimation of the error for a particular system is not possible since it depends on the gases involved in the mixture and  150  interplay between geochemical reactions and gas transport. The non-equimolar component of diffusive fluxes was small in general, and only significant in low permeability regions. The exclusion of the non-equimolar component may result in the overestimation of advective fluxes and pressure gradients. A full description is required to study system dynamics.  5.4. Sensitivity to saturation and tortuosity The most important parameter in controlling diffusive fluxes is saturation since even small changes can have a significant effect on the space available for gas transport but also on the gas tortuosity correction. Aqueous saturation in the simulations was obtained by solving Richard's equation. In the landfill cover soil, where fluxes were specified, aqueous saturation was used as fitting parameter. Increasing aqueous saturations resulted in steeper concentration gradients. On the other hand, at the oil spill site, the presence of a finer-textured lens with lower permeability resulted in higher water contents, which helped explain gas concentrations in the vadose zone. High moisture observed in this lens effectively controlled the supply of oxygen into the zone of methane production. Estimation of diffusive fluxes is also hampered by uncertainties associated with the tortuosity model. Although different tortuosity models have been incorporated and tested in the present formulation (Millington, 1959; Moldrup et al., 2000), gas tortuosity correction has been a factor that introduced considerable uncertainty in the calculations of diffusive fluxes for the examples studied. In the simulation of landfill cover soils, saturation was used as a fitting parameter while the Moldrup model for repacked soil was employed (Moldrup et al., 2000). Resulting saturation values were on the lower range of measured values. High gas saturation allowed for larger tortuosity factors, and less steep concentration gradients. In the study of gas  151  transport at the oil spill site, the problem is the opposite. When using parameters constrained by field evidence (i.e. moisture content, oil composition), transport of atmospheric gases to the deeper vadose zone, and transport of contaminants towards the ground surface appears to be too rapid in nature. As a result, depletion of the most volatile fraction takes place more rapidly than what was observed at the site. For the simulation of gas diffusion, the tortuosity model must be chosen with care as it can result in different diffusive fluxes.  5.5. Model limitations Despite the inclusion of the direct feedback on gas transport from reactions, the model is not applicable to problems where multiphase flow processes are significant. This may include e.g. the displacement of water due to the effect of gas pressure changes. Assumptions made in the application presented in this model include an immobile NAPL phase, and relatively slow flow rates in the gas and aqueous phases. For multiphase applications, multi-phase and compositional models would be necessary. Limitations of the model include application with high gas fluxes (e.g. gas injection and extraction), and an active NAPL phase. For example, if pressure differences are significant, compressibility of the gas phase could be significant and Darcy equation would not be applicable. Another limitation of the model is the inability to simulate the production large quantities of gas under saturated conditions because it does not incorporate bubble formation and ebullition. Gas pressures generated under saturated conditions cannot be released because there is no pore space available for gas advection but would result in the formation of bubbles and subsequent ebullition.  152  5.6. Future work  Although the model has only been applied to the study of a limited number of settings, its formulation is general-purpose. The flexibility to specify the geochemical system through a database and to define the flow and transport problem through keywords makes it easily applicable to a variety of problems involving vadose zone reactive transport. Fick's law, the basic Stefan-Maxwell equations, or the full Dusty Gas Model can be used for gas diffusion, while the gas advection module can be disabled when this process is shown to be insignificant. For example, it can be envisioned to also use the model for simulating oxidation and gas transport in sulfur piles (T. Birkham, pers. comm.), groundwater remediation by vertical soil filters (Jenssen et al., 2005), and carbon sequestration in mine tailings (Wilson et al., 2007). Potential additions to the model include modeling of vadose zone processes and saturated zone processes that affect geochemistry and soil gas budget. Processes that may significantly contribute to the vadose zone gas balance are near surface processes such as root-rhizosphere interactions and evaporation and mass transfer processes with the saturated zones due to the formation of gas bubbles and ebullition of these bubbles to the unsaturated zone. Incorporation of these processes into the present model would enable a more comprehensive analysis of vadose zone transport and interactions with the saturated zone and the atmosphere.  153  References  Amos, R. T., K. U. Mayer, B. A. Bekins, G. N. Delin, and R. L. Williams (2005), Use of dissolved and vapor-phase gases to investigate methanogenic degradation of petroleum hydrocarbon contamination in the subsurface, Water Resour. Res., 41 W02001. Binning, P., D. Postma, T.F. Russell, J. Wesselingh, and P. Boulin (2007), Advective and diffusive contributions to reactive gas transport during pyrite oxidation in the unsaturated zone, Water Resour. Res., 43, W02414, doi:10.1029/2005WR004474. Jenssen P.D., T. Maehlum, T. Krogstad, L. Vrale (2005), High performance constructed wetlands for cold climates, J. Environ. Sci. Health — Part A-Toxic/Hazardous Substan. Environ. Eng., 40 (6-7), 1343-1353. Millington, R. J. (1959), Gas diffusion in porous media, Science, 130, 100— 102. Moldrup, P.,T. Olesen, J. Gamst, P. Schjonning, T. Yamaguchi, and D. E. Rolston (2000), Predicting the Gas Diffusion Coefficient in Repacked Soil: Water-Induced Linear Reduction Model, Soil Sci. Soc. Am. J., 64, 1588-1594. Park, S., K.W. Brown, J.C. Thomas (2002), The effect of various environmental and design parameters on methane oxidation in a model biofilter, Waste Management & Research, 20(5), 434-444. Wilson, S., I.M. Power, J. Thom, G.M. Dipple, M. Raudsepp, and G. Southam (2007) Microbial mediation of carbon dioxide sequestration in mine tailings. Frontiers in Mineral Sciences 2007, Programme and Abstracts Volume, Abstract B013, pp. 67-68.  154  Appendices  155  ^  Appendix Al. Physical relationships (from Section 2) Gas density is a function of gas concentrations and molecular weights: Ng  Pg  =EM i C i  ^  (A1.1)  i=1  The viscosity of the gas phase ( p g ) is computed using the following semi-empirical expression based on the kinetic theory of gases (Bird et al., 2002):  fi g  Xg  XII =^Ie  (A1.2)  x gjoi  ;  ^•N —1/2  ^i  where  q  1^Mi =1+ g V-8 ^M 'g / -  X1/2^. •\1/4  1+  M  Pg  —  2  (A1.3)  \ I" g  Relative permeability in the gas phase (keg ) is calculated using the relationship by Parker et al. (1987):  kg = (1— S en ) 112 (1_ s  ^ el aim )2m  (A1.4)  with m = 1 — 1/n, where n and m are soil hydraulic function parameters. Sen is the effective saturation of the aqueous phase defined by Se  S  (A1.5)  —  a Sra  a^1— S ea  where S,. a is the residual saturation in the aqueous phase [-]. Tortuosity r g [-] is expressed as a function of aqueous phase saturation and porosity based on the semi-empirical expression by Millington (1959): rg =  c7/3,A1/3 Y'  (A1.6)  156  or by the expression by Moldrup et al. (2000) for repacked soils: r g =AJ03/2,41/2 g  (A1.7)  The expression found by Heid et al. (1950) for dry consolidated materials has been widely used in the literature to estimate the Klinkenberg parameter: b,. = b a = 0 .11(k rg k) -° 39^(A1.8) „.  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