PEGN 513 Reservoir Simulation I Fall 2009 Homework #1 Solution Calculate the water fractional flow (fw) as a function of water saturation (Sw) and plot fw versus Sw for the following fluid system: krw* = 0.1 krow* = 0.7 nw = 1.5 no = 0.25 Sorw = 0.30 Swr = 0.25 µw = 0.6 cp µo = 2.4 cp The water fractional flow (fw) is calculated using the following expression, ()( ) ( )wowwwwwSSSfλλλ+= Where, mobility of water is, ( )()wwrwwwSkSµλ= and mobility of oil is, ( )()wwrowSkSµλ=0 The relative permeability is calculated as a function of saturation using the Corey correlation, wnwrorwwrwrwrwSSSSkk−−−=1* onwrorworwororoSSSSkk−−−=1* The Table 1 shows the values of water fractional flow as a function of saturation.PEGN 513 Reservoir Simulation I Fall 2009 2/3 Table 1. Values of Water fractional flow as a function of water saturation Water Saturation (fraction) Water Fractional Flow (fraction) 0.25 0 0.26 0.0019984 0.27 0.0059628 0.28 0.011553 0.29 0.018754 0.3 0.027626 0.31 0.038264 0.32 0.050784 0.33 0.065309 0.34 0.081967 0.35 0.10088 0.36 0.12217 0.37 0.14593 0.38 0.17224 0.39 0.20112 0.4 0.23257 0.41 0.26653 0.42 0.30287 0.43 0.34142 0.44 0.38189 0.45 0.42396 0.46 0.46722 0.47 0.51122 0.48 0.55544 0.49 0.59937 0.5 0.64245 0.51 0.68419 0.52 0.7241 0.53 0.76175 0.54 0.79682 0.55 0.82902 0.56 0.8582 0.57 0.88425 0.58 0.90717 0.59 0.92702 0.6 0.94394 0.61 0.95808 0.62 0.96967 0.63 0.97893 0.64 0.98612 0.65 0.99148 0.66 0.99528 0.67 0.99778 0.68 0.99922 0.69 0.99987 0.7 1PEGN 513 Reservoir Simulation I Fall 2009 3/3 A plot of water fractional flow as a function of water saturation is show in Figure 1. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100.10.20.30.40.50.60.70.80.91Water Saturation (fraction)Water Fractional Flow (fraction) Figure 1. Plot of water fractional flow as a function of water
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