longitudinal dispersion in nonuniform isotropic porous media

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145 Table 5.3 Computed Results for the Average Number of Steps Required before the Asymptotic Theory is Valid J!HUQRM Mt;D;rUM NONUNIFORM MEDIUM Pec1et iF DL/D n Pec1et iF DL/D n 58.0 45.5 80 52.0 67.6 688 165. 165. 902 215. 460. 25400 365. 427. 4880 525. 1470. 187000 670. 873. 17300 2450. 9770. 2660000 Table 5.4 Average Number of Steps to Each Probe J!NJ,FORM MEIUUM NONUNIFORM MEDIUM Probe n Probe n 1 350 1 170 2 2100 2 1000 3 4200 3 2100
146 of the required number of steps for the asymptotic dispersion coefficient to apply to the actual average number of steps downstream to each of the probes indicates that the experimental measurements have not been made sufficiently far downstream to reach this criterion for the asymptotic condition, particularly for the higher Pec1et number experiments. This fact may explain the increase in the calculated dispersion coefficient compared to measured values at the higher Pec1et numbers. It is difficult, however, to determine the necessary downstream distance for the longitudinal dispersion coefficient to approach the asymptotic value. This difficulty centers on the inability to say what difference is expected between the asymptotic dispersion coefficient and measured dispersion coefficient when the asymptotic distance requirement is not met. In the Saffman (1959) model for uniform media, the relation derived for the "near-field" longitudinal dispersion coefficient shows a logarithmic growth in time. This type of slow variation in the dispersion coefficient would suggest that the measured dispersion coefficients will be close to the asymptotic value long before the asymptotic distance is reached. The discrepancy found at the higher Peclet numbers in Figure 5.3 was not expected, based on the experimental results and theoretical predictions shown in Figure 2.5. In this figure, the asymptotic dispersion coefficient compares well over a range of Peclet numbers from 10 to 10 6 , although the typical experiment (using water) will lie outside Darcy's regime when Pe > 10 4 • Based on equation (3.23), the required number of steps at Peclet = 10 3 is n > 3.4x10 4 or a distance
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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
Page 152 and 153: 137 Monte Carlo integration techniq
Page 166 and 167: where a m £ m total porosity 151 =
Page 169 and 170: 154 number flows since the advectio
Page 175 and 176: 160 homogeneous packing is not to b
Page 182: 167 f( £) = probability density fo
Page 190 and 191: 175 to a known distribution functio
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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