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7. Adsorption under Partially-Saturated Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Norm malized interface 1.0 SW interface 0.8 AW interface 0.6 0.4 02 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 S w Figure 7.4: The solid-water, SW, and air-water, AW, total interfacial area as a function of average saturation, S w. The areas are normalized to the total area under saturated conditions (which only belongs to the solid-water surfaces). Interfaces associated with the water films are neglected. at fixed saturation values, we have also simulated the dispersion of a conservative (non adsorptive) solute under the same conditions. Doing so, for each saturation, we will have two dispersion coefficients, one for the tracer solute and the other one for the adsorptive solute. The ratio of dispersivity of adsorbing solute to the dispersivity of a conservative solute, as a function of the pore scale distribution coefficient is shown in Figure (7.5), obtained using the ADE model. The dispersivity of the adsorptive solute increases with the increase in pore-scale distribution coefficient (figure 7.5). In fact, under partially-saturated conditions, dispersivity is not constant and its value is a function of saturation [Raoof and Hassanizadeh, 2011b]. Figure (7.6) shows the resulting relationship between dispersivity and saturation (α − S w curve). A detailed discussion of this issue was given in Chapter 6 From Figure (7.6), it is clear that there is a relation between dispersivity and saturation. The relation is non-monotonic, with the maximum dispersivity (α max ) occurring at an intermediate saturation, which we refer to it as the critical saturation (S cr ). Figure (7.7) shows the BTC from pore network-model together with the BTC obtained from analytical solution of the ADE model. It shows that although increase in dispersivity for adsorptive transport would result in a better fit, however there is still discrepancy between BTCs. This means that the choice of the ADE model with equilibrium adsorption term is probably not appropriate. In addition to the adsorptive dispersivity, the solution of the ADE would pro- 172
7.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.52 s./α tracer α ad 1.48 1.44 1.4 0.0 1.0 2.0 3.0 4.0 k d Figure 7.5: The relationship between ratio of adsorptive solute dispersivity (α ads ) to tracer solute dispersivity (α tracer) obtained from ADE model, and pore scale distribution coefficient, k d . The results are shown for a pore network model with water saturation of 0.53. 4.0 Dis spersivity [cm] 3.0 2.0 1.0 0.0 0.2 0.4 0.6 0.8 1.0 S w Figure 7.6: S w. The relationship between solute dispersivity, α, and saturation, vides a macro-scale distribution coefficient. For saturated conditions, we found (in Chapter 4) a linear relationship between pore scale and macro scale distribution coefficients, with the average specific surface area as the proportionality constant [Raoof and Hassanizadeh, 2010a]. Under unsaturated conditions, the value of the average specific surface areas for SW and AW interfaces will change with saturation (Figure 7.4). Knowing average specific surface area for each saturation, we can calculate a value for the macro-scale distribution coefficient. Figure (7.8) shows the calculated and fitted values of macro-scale distribution 173
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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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5.4 Results . . . . . . . . . . . .
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5.4 Results . . . . . . . . . . . .
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5.4 Results . . . . . . . . . . . .
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5.4 Results . . . . . . . . . . . .
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5.4 Results . . . . . . . . . . . .
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REFERENCES D.F. Yule and W.R. Gardn
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