longitudinal dispersion in nonuniform isotropic porous media

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193 max1mum error). The breakthrough curve for the exit concentration from a finite medium has a maximum error of about 4% relative to the other solutions when X = 80. The solution for a semi-infinite medium with a flux boundary condition is approximated to within 2% for X = 8.0 (Figure B.3) by the solution for an infinite medium. For high Peclet flows (Pe > 1.0), we can write for the dispersion coefficient 1n a uniform medium DL > vd/2 Using this in the expression for X we find, X < 2x/d which says that X is less than two times the number of grain diameters downstream. Thus, for Pe > 1.0, equation (B.6) approximates equation (B.12) within 2% maximum error for X = 8.0, which is less than 16 grain diameters downstream. This is probably well within the accuracy requirements for most situations. By 48 grain diameters downstream, equations (B.6), (B.ll), and (B.12) have less than 1% maximum error. For low Pee let number flows (Pe < 1.0), DL tends to a constant, which means X + 0 as v + 0 for a given x. Under these conditions, the different solutions according to the different boundary conditions may remain distinct far enough downstream to be significant.
B.3 Summary 194 Solutions for the miscible displacement of a resident fluid in infinite, semi-infinite and finite uniform porous media have been compared for downstream distances ranging from 0.8 < X < 80., where X = vx/D L • For a finite medium, the exit concentration is calculated with X = VL/D L , where L is the length of the porous medium. Under conditions of high Peclet number flow, Pe = vd/D L > 1, the solution for an infinite medium is found to approximate the solution for a semi infinite medium with a flux boundary condition at the inlet within 2% maximum error for X = 8. The error is found to decrease with increasing values of X. By X = 24, both solutions for the semi infinite medium are approximated within 1% maximum error by the infinite medium solution. All solutions discussed are seen to lie within 4% maximum error of each other wheri X = 80.
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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
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126 medium type. This deviation of
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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 =
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Page 192 and 193: 177 Table A.2 Kolmogorov-Smirnov Te
Page 196: 181 a change 1n source strength ove
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longitudinal dispersion in nonuniform isotropic porous media

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