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5. Pore-Network Modeling of Two-Phase Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2.2 Relative permeability for a carbonate rock In this section, we are applying the new formulation to a network which is based on the statistical properties of a carbonate rock. Al-Kharusi and Blunt [2008] applied a methodology to extract networks from pore space images of carbonate rock samples, in order to make predictions of multiphase transport properties. They started with a 2D thin-section image; then, converted it statistically to a 3D representation of the pore space. Using concept of maximal ball [Al- Kharusi and Blunt, 2008, 2007], they constructed a 3D pore-network model and simulated primary drainage, waterflooding, and secondary drainage processes [Valvatne and Blunt, 2004]. In that model, the resistance to flow was assigned to pore throats only. The simulated results were compared to the laboratorymeasured values obtained though centrifuge experiments. The good agreement for capillary pressure-saturation and intrinsic permeability implied that they had estimated pore and throat sizes correctly (Figure 5.13). However, the predicted wetting-phase relative permeability was overestimated compared to the experimental results, as shown in Figure (5.14). They mentioned the large coordination number (which was derived using imaging technics) as a potential reason for discrepancy between relative permeabilities. As another potential source of discrepancy, they mentioned the fact that the pore-network model did not capture all local heterogeneities of the sample due to the size of the network. All of these arguments could potentially explain the overestimation of the relative permeability. However, we believe that this discrepancy could have been minimized by taking into account the resistance to the flow within (partially-) drained pore bodies. To verify this explanation, we generated a network with similar properties to those used by Al-Kharusi and Blunt [2008]. The capillary pressure-saturation curves obtained from our network and the network model of Al-Kharusi and Blunt [2008] are shown in Figure (5.13), together with the P c −S w curve measured in the centrifuge experiments. There is good agreement between the two pore-network modeling results and measured values. There is also a good agreement between calculated values of absolute permeability using our network and that of Al-Kharusi and Blunt [2008] (Table 5.2). The relative permeability results of both pore-network models are shown in Figure (5.14) together with values obtained from the centrifuge experiments. It is clear that including the resistance to the flow within pore bodies improves the agreement between simulated and measured values of relative permeability. An important observation from Figure (5.14) is that the maximum discrepancy between results from Al-Kharusi and Blunt [2008] and experiments occurs at 116
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 5.2: Statistical properties of the Carbonate Network Model. Property value This study Al-Kharusi and Blunt [2008] Number of pores 641 643 Number of throats 2284 2623 Mean coordination number 7.7 7.9 Absolute permeability (mD) 2.80 3.1 Figure 5.13: Comparison between P c − S w curves obtained from two network models together with the measured values of capillary pressure-saturation during primary drainage experiment. higher saturations (0.75 < S w < 1). This can be explained by the fact that the largest pore bodies, which have the largest contribution to the flow under saturated conditions, are invaded first during drainage. The invasion of such large pores, and the subsequent corner flow along their edges, considerably decreases the permeability of the medium to the wetting phase, which can only be modeled by taking into account the resistance of pore bodies to the flow. As explained earlier, drained pore bodies could also considerably reduce the connectivity of saturated pore throats connected to them. The high coordination number in carbonate rock could increase the accessibility of the non-wetting phase to the larger pores. During recent years, the importance of coordination number distribution on flow and transport has been examined by some 117
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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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Published as: Raoof, A. and Hassani
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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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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 D.F. Yule and W.R. Gardn
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