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Appendix C average velocity: ṽ = v − v (C.5) The term nc i ṽ represents the mixing of the solute within an REV as a result of pore-scale velocity fluctuations within the pores. Together with the diffusive flux nj i , it is known as macro-scale hydrodynamic dispersion and is denoted by J i J i = nc i ṽ + nj i (C.6) substituting Equation (C.6) into Equation (C.4), the final form of averaged mass transport equation is obtained ∂nc i ∂t + ∇ · (nc i v ) ( + ∇ · nJ i) = nr i − 1 V ∫ A fs [ c i (v − w) + j i] · ndA (C.7) 208
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES L.M. Abriola and G.F. Pinder. A multiphase approach to the modeling of porous media contamination by organic compounds: 1. Equation development. Water Resources Research, 21(1):11–18, 1985. 4 R.C. Acharya, S.E. van der Zee, and A. Leijnse. Porosity-permeability properties generated with a new 2-parameter 3D hydraulic pore-network model for consolidated and unconsolidated porous media. Advances in Water Resources, 27(7):707–723, 2004. 35, 73 R.C. Acharya, S. van der Zee, and A. Leijnse. Transport modeling of nonlinearly adsorbing solutes in physically heterogeneous pore networks. Water Resources Research, 41(2):W02020, 2005a. 93, 136, 142, 162, 179 R.C. Acharya, S. van der Zee, and A. Leijnse. Transport modeling of nonlinearly adsorbing solutes in physically heterogeneous pore networks. Water Resources Research, 41(2):W02020, 2005b. 6, 43, 68, 69 R.C. Acharya, A.J. Valocchi, C.J. Werth, and T.W. Willingham. Pore-scale simulation of dispersion and reaction along a transverse mixing zone in two-dimensional porous media. Water Resources Research, 43(10):W10435, 2007a. 68 R.C. Acharya, M.I.J. van Dijke, K.S. Sorbie, S. van der Zee, and A. Leijnse. Quantification of longitudinal dispersion by upscaling brownian motion of tracer displacement in a 3d pore-scale network model. Advances in Water Resources, 30(2): 199–213, 2007b. 178 P.M. Adler. Porous Media: Geometry and Transports. Butterworth-Heinemann, 1992. 93 209
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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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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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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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5.5 Conclusion Our approach is also
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6. Dispersivity under Partially-Sat
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