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7. Adsorption under Partially-Saturated Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . We have introduced a new formulation of adsorptive solute transport within a pore network which helps to capture the effect of limited mixing within the pores under partially-saturated conditions. This formulation allows a very detailed description of solute transport processes within the pores by accounting for limitations in mixing within drained pore bodies and pore throats as a result of reduced water content. We have considered various types of adsorption such as i) two-site kinetic (at SW or AW interfaces), ii) two-site equilibrium, and iii) one-site kinetic and one-site equilibrium. Our results show that, even if there is equilibrium adsorption at the SW and AW interfaces at the pore scale, one may need to apply a nonequilibrium formulation for the adsorption process at the macro scale. We have found that the kinetic description of the adsorption process at the macro scale can accurately describe the results of pore network simulations. Using the kinetic description, we can employ dispersivity values obtained from tracer simulations. However, using the equilibrium macro-scale model, we needed to use higher values of the dispersion coefficient, modeled as a function of adsorption in addition to saturation. 7.1 Introduction 7.1.1 Major colloid transport processes Understanding colloid transport mechanisms in unsaturated porous media has always attracted significant attention in management of groundwater contamination, especially in the case of groundwater polluted by contaminants that could adsorb to colloids. Colloids presence can enhance pollutant mobility [Mc- Carthy and Zachara, 1989]; field results suggest the importance of colloids in the transport of low-solubility contaminants [Vilks et al., 1997, Kersting et al., 1999]. The enhanced mobility, together with the very limited acceptable concentration of hazardous solutes (in the range of few parts per billion), mean that we must pay more attention to modeling and accurate prediction of colloid (facilitated) transport processes. Since contaminants migrate and reach the groundwater through the vadose zone, the transport of adsorbing solute in the vadose zone becomes an important issue. Commonly the breakthrough curves (BTCs) for reactive/adsorptive solutes display earlier appearance, greater spreading, and more tailing compared to the solution of classical models with equilibrium adsorption. Even under saturated conditions, adsorption processes may cause non-ideal behavior in the BTCs. However, under unsaturated conditions, in addition to the adsorption processes, the non-ideal behavior of the BTCs could be a result of partial occupation of the pore space by the non-wetting phase. 158
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Under unsaturated conditions, various mechanisms may account for (non-ideal) behavior of colloids under different flow and transport conditions. Under low flow rates, diffusion may act as the rate-limiting process. Most of experimental studies which support this idea (e.g., Jacobsen et al. [1997], Laegdsmand et al. [1999], Schelde et al. [2002]) suggest a linear relationship between the cumulative mass of mobilized colloids and the square root of time. During transient conditions, such as drainage or imbibitions, colloid scavenging by airwater interfaces may be a dominant process [Jacobsen et al., 1997, Laegdsmand et al., 1999, Bradford and Torkzaban, 2008]. At high flow rates, however, hydrodynamic shear [O’neill, 1968] may be the dominant process [Kaplan et al., 1993, Laegdsmand et al., 1999, Weisbrod et al., 2002]. The induced shear force is opposed by an attractive force due to Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions [Bradford and Torkzaban, 2008]. Under very low saturations, due to the discontinuity of water films between grains, film-straining may be the dominant process [Lenhart and Saiers, 2002, DeNovio et al., 2004, Bradford et al., 2006, Torkzaban et al., 2008], and transport of suspended colloids can be retarded due to physical restrictions imposed by thin water films [Wan and Tokunaga, 1997]. 7.1.2 Experimental studies Experimental studies are a major source of information for adsorptive transport in porous media. They are also instrumental in guiding the development of mathematical models for colloid transport and deposition. Studies of reactive/adsorptive transport in porous media can be categorized into three groups: pore-scale studies, column-scale studies of ideal systems (mostly under uniform saturation and constant pore water velocity), and studies conducted on nonideal systems (such as natural vadose zone environments). Laboratory studies of colloid and colloid-facilitated transport have focused primarily on the interpretation of breakthrough of colloids (e.g, using latex microspheres, clays, oxides, or microorganisms, with or without other tracers) in sand or glass bead systems. While many studies have been carried out under saturated flow conditions [Weisbrod et al., 2003, Toran and Palumbo, 1992, Noell et al., 1998, Elimelech et al., 2000, Bradford and Bettahar, 2005, Bradford et al., 2007], some have examined unsaturated conditions [Wan and Wilson, 1994b,a, Wan and Tokunaga, 1997, 1998, Schafer et al., 1998, Thompson et al., 1998, Thompson and Yates, 1999, Jewett et al., 1999, Sim and Chrysikopoulos, 2000, Jin et al., 2000, Gamerdinger and Kaplan, 2001, Saiers and Lenhart, 2003b,a, Wan 159
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Reactive/Adsorptive Transport in (P
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text Reactive/Adsorptive Transport
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Promoter: Prof.dr.ir. S.M. Hassaniz
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My colleagues and other staff in th
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CONTENTS 2.2.3 Connection Matrix .
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CONTENTS 5.3.3 Regular hyperbolic p
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CONTENTS 8.3.1 Non-adsorptive solut
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LIST OF FIGURES 3.6 The relation be
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LIST OF FIGURES 6.5 Breakthrough cu
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LIST OF TABLES 2.1 Expressions for
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1. Introduction . . . . . . . . . .
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1. Introduction . . . . . . . . . .
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1. Introduction . . . . . . . . . .
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1. Introduction . . . . . . . . . .
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1. Introduction . . . . . . . . . .
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1. Introduction . . . . . . . . . .
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1. Introduction . . . . . . . . . .
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Part I Generation of Multi-Directio
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2. Generating MultiDirectional Pore
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Published as: Raoof, A. and Hassani
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3.1 Introduction . . . . . . . . .
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3.1 Introduction . . . . . . . . .
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3.2 Theoretical upscaling of adsorp
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3.3 Numerical upscaling of adsorbin
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3.4 Discussion of results . . . . .
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3.5 Conclusion . . . . . . . . . .
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Published as: Raoof, A. and Hassani
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4.1 Introduction . . . . . . . . .
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4.1 Introduction . . . . . . . . .
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4.2 Description of the Pore-Network
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4.3 Simulating flow and transport w
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4.3 Simulating flow and transport w
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4.4 Macro-scale adsorption coeffici
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4.5 Discussion . . . . . . . . . .
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4.5 Discussion . . . . . . . . . .
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4.6 Conclusions . . . . . . . . . .
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Raoof, A. and Hassanizadeh S. M.,
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5.1 Introduction . . . . . . . . .
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5.1 Introduction . . . . . . . . .
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5.2 Network Generation . . . . . .
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5.2 Network Generation . . . . . .
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5.3 Modeling flow in the network .
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Page 127 and 128: 5.3 Modeling flow in the network .
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Appendix C average velocity: ṽ =
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REFERENCES D.F. Yule and W.R. Gardn
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