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3. Upscaling of Adsorbing Solutes; Pore Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) (b) Figure 3.6: The relation between macro-scale katt ∗ as a function of pore-scale (a)κ and (b) P e p. pendent of Peclet number. It is, practically, a linear function of the pore-scale distribution coefficient, κ, as shown in Figure (3.7). The linearity of the upscaled distribution coefficient, K D , as a function of the 60
3.4 Discussion of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 3.7: The relation between upscaled distribution coefficient (K D = katt/k ∗ det) ∗ as a function of the pore-scale dimensionless distribution coefficient, κ for the Single-Tube Model. pore-scale distribution coefficient, κ, also shows the validity of our upscaling process. Both K D and κ are a measure of the capacity of the porous medium to absorb mass and thus they should be linearly related. 3.4 Discussion of results Equations (3.40a) and (3.40b) can be converted to dimensional forms using Equations (3.31) and (3.37). This gives and k att = 4.0(1 − k D e−3 R0 ) v 0.05 D0 0.95 R0 1.95 k det = 9.0 v0.05 D0 0.95 (0.5 + 4.5 k D R0 )R0 1.95 (3.42a) (3.42b) We observe that k att and k det are only weak functions of velocity but they depend strongly on the geometry of the pore space and the diffusion coefficient as well as the pore-scale distribution coefficient. We could compare Equations (3.42) with corresponding equations derived using the averaging method in Section 3.2.2. For the case of the Single Tube, it is plausible to assume that c i∣ ∣ pore , at a position somewhere between the pore center and pore wall (denoted by w R0 , where 1.0 > w > 0) will be equal to the average fluid concentration, c i . This means that in Equation (3.19) we may set 61
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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 . . . . . . . . . .
Page 30 and 31: 1. Introduction . . . . . . . . . .
Page 37: Part I Generation of Multi-Directio
Page 40 and 41: 2. Generating MultiDirectional Pore
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Page 63 and 64: 3.1 Introduction . . . . . . . . .
Page 67 and 68: 3.2 Theoretical upscaling of adsorp
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Page 91 and 92: 4.2 Description of the Pore-Network
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Page 121 and 122: 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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5.4 Results . . . . . . . . . . . .
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5.5 Conclusion Our approach is also
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6. Dispersivity under Partially-Sat
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7. Adsorption under Partially-Satur
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8. Numerical scheme . . . . . . . .
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8. Numerical scheme substituting fo
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9. Summary and Conclusions . . . .
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Appendix A . . . . . . . . . . . .
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Appendix A . . . . . . . . . . . .
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Appendix B . . . . . . . . . . . .
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Appendix C average velocity: ṽ =
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REFERENCES . . . . . . . . . . . .
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REFERENCES D.F. Yule and W.R. Gardn
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