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3. Upscaling of Adsorbing Solutes; Pore Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The CXTFIT curve-fitting program [Toride et al., 1995] was used for the purpose of solving Equations (3.35) and (3.36) and fitting to the breakthrough curves. Figure (3.4) shows an example fit to a breakthrough curves and the corresponding parameters. Through the fitting process, we have been checking the covariance matrix to make sure that parameters are not correlated. This procedure was repeated for a range of pore-scale parameters (1 < P e p < Figure 3.4: The resulting breakthrough curves for pore-scale (circles) and 1D upscale (solid line) models. In this illustration, at the porescale parameters are: P e p = 35 and κ = 5.0. And the corresponding upscaled parameters by fitting found to be: katt ∗ = 0.14 and kdet ∗ = 0.05. Using Equation (3.38), P e will be 1.3. 300, and 0.1 < κ < 20), and finding the corresponding upscaled k ∗ att and k ∗ det we could determine relations between these set of parameters. Figures (3.5) and (3.6) show the resulting plot of k ∗ att and k ∗ det as functions of P e p and κ. From the relations shown in Figures (3.5) and (3.6), we found the best fit formulas (through minimizing the least squares) for k ∗ att and k ∗ det k ∗ att = 4.0(1 − e−3κ ) P e p 0.95 (3.40a) k ∗ det = 9.0 (0.5 + 4.5κ)P e p 0.95 (3.40b) We define the upscaled distribution coefficient (K D ) by: 58
3.3 Numerical upscaling of adsorbing solute transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) (b) Figure 3.5: The relation between macro-scale kdet ∗ as a function of pore-scale (a) P e p and (b) κ. K D = k∗ att k ∗ det = 0.4 ( 1 − e −3κ) (0.5 + 4.5κ) (3.41) According to Equation (3.41), the upscaled distribution coefficient, K D , is inde- 59
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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 . . . . . . . . . .
Page 28 and 29: 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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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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