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CONTENTS
5.3.3 Regular hyperbolic polygons . . . . . . . . . . . . . . . 106
5.3.4 Calculation of relative permeability curves . . . . . . . . 108
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.4.1 Flow field in the MDPN model . . . . . . . . . . . . . . 110
5.4.2 Calculation of relative permeabilities using MDPN model 111
5.4.2.1 Generic pore networks . . . . . . . . . . . . . . 112
5.4.2.2 Relative permeability for a carbonate rock . . 116
5.4.2.3 Pore Network model of Fontainebleau sandstone 118
5.4.3 The concept of equivalent pore conductance . . . . . . . 120
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6 Dispersivity under Partially-Saturated Conditions; Pore-Scale
Processes 125
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.1.1 Dispersion under unsaturated conditions . . . . . . . . . 126
6.1.2 Experimental works and modeling studies . . . . . . . . 128
6.1.3 Objectives and computational features . . . . . . . . . . 131
6.2 Network Generation . . . . . . . . . . . . . . . . . . . . . . . . 133
6.2.1 Pore size distributions . . . . . . . . . . . . . . . . . . . 133
6.2.2 Determination of the pore cross section and corner half
angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.2.3 Coordination number distribution in MDPN . . . . . . 135
6.2.4 Pore space discretization . . . . . . . . . . . . . . . . . . 136
6.3 Unsaturated flow modeling . . . . . . . . . . . . . . . . . . . . 138
6.3.1 Drainage simulation . . . . . . . . . . . . . . . . . . . . 138
6.3.2 Fluid flow within drained pores . . . . . . . . . . . . . . 139
6.4 Simulating flow and transport within the network . . . . . . . . 140
6.4.1 Flow simulation . . . . . . . . . . . . . . . . . . . . . . . 140
6.4.2 Simulating solute transport through the network . . . . 142
6.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.5.1 Advection-Dispersion Equation (ADE) . . . . . . . . . . 145
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