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7. Adsorption under Partially-Saturated Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . body sizes are taken from uncorrelated truncated lognormal distributions, and pore throat sizes are correlated to the pore body sizes. Probability 0.2 0.15 0.1 0.05 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 x10 −1 Effective radius [cm] Figure 7.1: Distributions of pore-body sizes within the pore network model. 7.2.2 Determination of the pore cross section and corner half angles A key characteristic of real porous media is the angular form of pores. It has been demonstrated that having pores with a circular cross section, and thus single-phase occupancy, causes insufficient connectivity of the wetting phase and as a result poor representation of experimental data [Zhou et al., 2000a]. In the present work, pore bodies are considered to be cubic in shape. Pore throats are assigned a variety of cross sectional shapes including circular, rectangular, and scalene triangular, as it was explained in Section 6.2.2. 7.2.3 Coordination number distribution in MDPN One of the main features of the MDPN is that pore throats can be oriented not only in the three principal directions, but in 13 different directions, allowing a maximum coordination number of 26, as shown in Figure (2.1). Then, to get a desired coordination number distribution, we fallow an elimination procedure to rule out some of the connections. The elimination procedure is such that a pre-specified mean coordination number can be obtained. A coordination number of zero means that the pore body is eliminated from the network, so there is no pore body located at that lattice point. A pore body with a coordination number of one is also eliminated except if it is located at the inlet or outlet boundaries (so it belongs to the owing fluid backbone). This means that no dead-end pores are included in the network. Details of network 164
7.3 Unsaturated flow modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . generation can be found in Chapter (2). In this study, we have chosen to make a MDPN with an average coordination number of 4.5. This value corresponds to the sand packing [Talabi and Blunt, 2010, Talabi et al., 2008]. The distribution of coordination number is given in Figure (7.2). 0.25 Normalized frequency 0.2 0.15 0.1 0.05 0 1 2 3 4 5 6 7 8 9 10 11 12 Coordination number Figure 7.2: The coordination number distribution of the MDPN model. The mean coordination number is equal to 4.5. 7.2.4 Pore space discretization To take into account the effect of limited mixing within the drained pores we follow our approach which was explained in Section 6.2.4, i.e., under unsaturated conditions, we consider each corner of the pore, occupied by the wetting space, as a separate element with its own pressure and concentration. In addition, since we take into account adsorption process, We also calculate separate adsorbed mass concentration for each of these elements. Thus, for a cubic pore body, 8 different corner elements exist with 8 different pressure and concentration of solution and adsorbed mass assigned to them (see Figure 6.3a). 7.3 Unsaturated flow modeling We wish to simulate drainage in a strongly water wet porous medium, initially saturated with water. The non-wetting phase is assumed to be air, which can flow under negligibly small pressure gradients. To simulate drainage in our network, the displacing air is considered to be injected through an external reservoir which is connected to every pore-body on the inlet side of the network. The displaced water escapes through the outlet face on the opposite side. 165
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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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REFERENCES D.F. Yule and W.R. Gardn
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