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Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Search algorithm in Multi-Directional Pore Network (MDPN) model In order to find the isolated clusters, we need to employ tracking.We have employed an algorithm based on the frequency of bonds. In order to illustrate the procedure, considering the network of Figure (2.2), we randomly eliminated some bonds by changing the states of them from open to block in the connection matrix of Figure (2.2). Figure (A.1) shows the network configuration after this random elimination. Figure A.1: A network of size: N i = 3, N j = 3, N k = 3 after random elimination. Site numbers are shown for some nodes; system of numbering is the same as in Fig. 1. N bond = 42, N site = 26. The connection matrix is a sparse matrix. Hence, we convert it in to compact form. This results in a matrix of the size 3N bond (N bond =number of bonds). Table A.1 shows the corresponding compact matrix for upper triangle part of connection matrix belonging to Figure (A.1). In the compact form shown in Table A.1, the first row (ROW in Table A.1) contains the row index of original sparse matrix, the second row (COL) contains the column index, and the third row (Entry) contains the corresponding nonzero direction numbers. Since this is compact form of connection matrix, it means that site numbers in ROW are connected in the forward direction to site numbers in COL. For example, first column of Table A.1 indicates that site number 1 is connected in the forward direction to site number 10 along lattice direction number 1. 202
A. Search algorithm in MDPN model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table A.1: Compact form of connection matrix for example of Figure (A.1). ROW 1 2 3 3 4 4 4 5 5 5 6 6 6 7 7 8 9 9 10 11 11 COL 10 10 12 11 13 11 14 10 12 18 15 17 14 16 14 13 14 17 19 14 19 Entry 1 11 1 11 1 8 10 6 8 9 1 7 11 1 8 6 6 11 1 3 11 ROW 11 12 12 12 13 13 13 13 14 14 14 14 15 15 15 16 17 17 17 17 18 COL 13 24 20 14 14 16 20 26 17 21 22 16 18 23 17 17 18 22 24 25 26 Entry 13 4 11 13 2 3 8 9 3 8 11 13 3 11 13 2 2 6 8 11 11 Table A.2: Frequency and cumulative matrix of the forward connections. Site no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Frequency 1 1 2 3 3 3 2 1 2 1 3 3 4 4 Cumulative 1 2 4 7 10 13 15 16 18 19 22 25 29 33 Site no. 15 16 17 18 19 20 21 22 23 24 25 26 27 Frequency 3 1 4 1 0 0 0 0 0 0 0 0 0 Cumulative 36 37 41 42 42 42 42 42 42 42 42 42 42 As we can see, the site numbers in the first row(ROW) of Table are sorted in increasing order. The number of times a site number appears in ROW of Table A.1 corresponds to the number of forward connections of that site. This information in taken up in a frequency table (see second row of Table A.2) together with its cumulative number of bonds (see third row of Table A.2). Table A.2 along with second row of Table A.1 can be used to determine to which sites a given site, N, is connected based on the following formula: Forward sites for site N = COL(cumulative(N) − frequency(N) + 1 : cumulative(N)) For example, for site number 12 (N = 12) we will have: Forward sites for site 12 = COL(cumulative(12) − frequency(12) + 1 : cumulative(12)) = COL(25 − 3 + 1 : 25) = COL(23 : 25) = [24, 20, 14] Hence, the sites to which site number 12 is connected forward are located in position 23 − 25 in the COL of Table A.1 which are sites number 24, 20, and 14. To find the backward connections, we need to replace ROW and COL of Table A.1 with each other (since in the connection matrix backward connections are 203
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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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5.4 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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