longitudinal dispersion in nonuniform isotropic porous media

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137 Monte Carlo integration technique described 1n Section 3.5. The pore size distribution used for the calculations is shown in Figure 4.12. Although the same number of pores leading to and from a junction are required for a given unit cell (see Figure 3.2), it is possible to have a continuous range of junction connectivity for the network. This 1S accomplished by using the two nearest even connectivities, say C1 and C2, in proportion a, such that the connectivity for the network, C, is, C aC1 + (1-a)C2 Table 5.1 shows the computed and measured permeabi1ities using the "best fit" junction connectivity, C = 16. This parameter was set primarily to adjust the calculated permeability of the nonuniform medium, since the uniform medium was fairly insensitive to the junction connectivity parameter. Table 5.1 also shows the permeability calculations when network effects are ignored (C -+ (0). As expected, the permeability of the nonuniform medium is significantly higher when the network effects are not taken into account. Convergence of the Monte Carlo integration scheme for the nonuniform medium is slower than for the uniform medium, as shown in Figures 5.1 and 5.2. The nonuniform medium required 400,000 iterations (unit cells) , while the uniform medium permeability was calculated using 100,000 iterations to get within 2:1% of the final asymptotic value. Permeability as computed from equation (3.11) 1S seen in Table 5.1 to do reasonably well (within 15%) for both the uniform and nonuniform medium. The Haring and
Measured Calculated ( C = 16) (equation (3.15» Calculated ( C -+ 00) (equation (3.15» Calculated (equation (3.11» Calculated (equation (3.7» (a) d g (b) d g 0.382 mIn 1.26 mIn 138 Table 5.1 Heasured and Calculated Permeabilities (J g (J g . d' (a) Unl.form Me l.um (l0-5nun2) 5.55 5.94 6.29 6.18 5.02 1.15 (see Table 4.1) 2.93 (see Table 4.1) Nonuniform Medihk) (l0-5nun2) 5.94 5.64 16.0 6.71 3.31
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LONGITUDINAL DISPERSION IN NONUNIFO
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ii ACKNOWLEDGEMENTS This research p
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iv ABSTRACT A theoretical and exper
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ACKNOWLEDGEMENTS ABSTRACT LIST OF F
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viii TABLE OF CONTENTS (continued)
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4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.1
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Table 3.1 3.2 4.1 4.2 4.3 4.4 4.5 5
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o en -o ::J o CD FLOW .. Solute Con
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porous medium and an unconsolidated
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20 CHAPTER 2 LITERATURE REVIEW Tran
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(1/2) V yd s From experiments, they
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39 governed by an effective advecti
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2.4 SUmmary 46 Several different cl
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48 CHAPTER 3 A THEORETICAL MODEL FO
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Q = 52 (3.1) where P'cos8 is the pr
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I 1 FLOW 3 PORE • JUNCTION 57 CAP
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shows a histogram of 10000 particle
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This expression gives the frequency
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PERMEABILITY where 82 TABLE 3.1 Sum
Page 107 and 108: LITER RESERVOIR (FRESH OR SALINE) O
Page 115: 100 screens are needed to character
Page 120 and 121: VQ!gme-W@ight@d pistripgtiop(a) Gra
Page 123: 108 space in the medium, while the
Page 135: 120 When one fluid displaces anothe
Page 141: 126 medium type. This deviation of
Page 149: D v 134 Table 4.5 Longitudinal Disp
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Page 166 and 167: where a m £ m total porosity 151 =
Page 169 and 170: 154 number flows since the advectio
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Page 192 and 193: 177 Table A.2 Kolmogorov-Smirnov Te
Page 196: 181 a change 1n source strength ove
Page 201: 186 where P = vL/4D L and Ak are th
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B.3 Summary 194 Solutions for the m
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