longitudinal dispersion in nonuniform isotropic porous media

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175 to a known distribution function. The values may be compared to tabulated values of K+ (or K-) which give the probability of the + ( - computed K or K). Table A.I shows 30 independent samples of N 1000 using the random number generator given by equations (A.2) and (A.3). The values of K+ (or K-) which correspond to the given place in the cumulative distribution when N = 1000 are shown at the bottom of Table A.I. By comparing the sample with the theoretical values, we see that no extraordinary behavior is detected. Table A.2 shows a similar calculation for a single linear congruential random number generator (equation (A.I». Again, acceptable random behavior is found. The Kolmogorov-Smirnov test may be applied to the sets of K+ and K- values displayed in Tables A.I and A.2. This is useful in detecting global nonrandom behavior in the original sequences. Global nonrandom behavior refers to deviation from expected random behavior over the entire sequence of random numbers (which is 30000 random numbers in this case). The theoretical cumulative distribution for the Kolmogorov-Smirnov coefficients (K+ and K-) is approximated by F(x) = 1 - exp(-2x 2 ). Table A.3 shows the global test as applied to the values in Tables A.I and A.2. We find that both generators display acceptable bahavior at the global scale (30000 random numbers). Table A.4 presents a summary of the constants and seed numbers used in the random number generators tested.
176 Table A.1 Ko1mogorov-Smirnov Test of the Dual Linear Congruential Method N K+ 1 - 1000 0.7254 1001 - 2001 - 3001 - 4001 - 2000 3000 4000 5000 0.1279 0.8831 0.6881 0.8464 5001 - 6000 0.6498 6001 - 7000 0.5952 7001 - 8000 0.4781 8001 - 9000 0.6586 9001 - 10000 0.4222 10001 - 11000 0.3533 11001 - 12000 0.7830 12001 - 13000 0.1789 13001 - 14000 0.7827 14001 - 15000 0.4602 15001 - 16000 0.8752 16001 - 17000 0.5086 17001 - 18000 0.6731 18001 - 19000 0.2417 19001 - 20000 0.6249 20001 - 21000 1.0093 21001 - 22000 0.3779 22001 - 23000 1.1243 23001 - 24000 0.4456 24001 - 25000 0.9829 25001 - 26000 0.3859 26001 - 27000 0.4626 27001 - 28000 0.1594 28001 - 29000 1.2748 29001 - 30000 0.0506 Theoretical Cumulative Distribution: Cumulative Probability 99% 95% 75% - K 0.5695 0.4951 0.2571 0.5165 0.1472 0.9749 0.8585 0.9395 0.1215 0.9876 0.6019 0.2979 0.9061 0.1527 1.1114 0.4569 0.7681 0.5046 0.8539 0.6061 0.4433 0.7720 0.3525 0.4906 0.5472 0.6732 0.6303 1.1121 0.1341 1.3684 50% 25% 5% 1% Value (K) 0.0661 0.1557 0.3746· 0.5840 0.8275 1.2185 1.5111
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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
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LITER RESERVOIR (FRESH OR SALINE) O
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100 screens are needed to character
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VQ!gme-W@ight@d pistripgtiop(a) Gra
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108 space in the medium, while the
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120 When one fluid displaces anothe
Page 141: 126 medium type. This deviation of
Page 149: D v 134 Table 4.5 Longitudinal Disp
Page 152 and 153: 137 Monte Carlo integration techniq
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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
Page 209: B.3 Summary 194 Solutions for the m
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longitudinal dispersion in nonuniform isotropic porous media

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