longitudinal dispersion in nonuniform isotropic porous media

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and Greenkorn (1970) use a nonuniform random capillary tube network to model permeability and dispersion in nonuniform media. The Haring and Greenkorn model is found to have the following deficiencies: 47 1) The permeability model neglects the fact that pores conduct fluid in proportion to the fourth power of the pore radius. 2) Neglect of molecular diffusion leads to an unbounded longitudinal dispersion coefficient for large times. 3) Pore radius distributions and pore length distributions must follow beta distributions. 4) No technique is developed to estimate pore length distributions from measurable structural features of porous media. 5) Experimental support for the model is very limited.
48 CHAPTER 3 A THEORETICAL MODEL FOR PERMEABILITY AND LONGITUDINAL DISPERSION IN NONUNIFORM POROUS MEDIA In this chapter, a theoretical method is developed for computing permeability and longitudinal dispersion in isotropic, nonuniform porous media based on structural features of the medium. As discussed in Chapter 2, the spectrum of length scales present in a nonuniform medium is important in determining the transport behavior of miscible solutes. Because of additional variables describing the distribution of length scales, there are more dimensionless groups to correlate through experimentation. Since the range of parameters is large, it would be helpful to have reliable models. Of the models presented in Chapter 2, the network model, statistical capillary tube model, and the volume-averaging model are capable of being extended to nonuniform media. The model to be developed here is an extension of the random capillary tube model proposed by Saffman (1959). No extensions were attempted with the network model or the volume-averaging model. As for the original model for uniform media (Saffman, 1959), the extended model is also limited to high Pec1et number flows. The model follows the original Saffman (1959) model closely, and is similar in some respects to the nonuniform media model proposed by Haring and Greenkorn (1970); however, there are some important differences: 1. Molecular diffusion is included as in the Saffman (1959) model such that an asymptotic longitudinal dispersion coefficient may be obtained, in contrast to the Haring and Greenkorn (1970) model.
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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)
Page 12 and 13: 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.1
Page 14: Table 3.1 3.2 4.1 4.2 4.3 4.4 4.5 5
Page 24: o en -o ::J o CD FLOW .. Solute Con
Page 33 and 34: porous medium and an unconsolidated
Page 35: 20 CHAPTER 2 LITERATURE REVIEW Tran
Page 43: (1/2) V yd s From experiments, they
Page 54: 39 governed by an effective advecti
Page 61: 2.4 SUmmary 46 Several different cl
Page 67: Q = 52 (3.1) where P'cos8 is the pr
Page 72: I 1 FLOW 3 PORE • JUNCTION 57 CAP
Page 81: shows a histogram of 10000 particle
Page 92: This expression gives the frequency
Page 97: PERMEABILITY where 82 TABLE 3.1 Sum
Page 107 and 108: 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
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137 Monte Carlo integration techniq
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145 Table 5.3 Computed Results for
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where a m £ m total porosity 151 =
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154 number flows since the advectio
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160 homogeneous packing is not to b
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167 f( £) = probability density fo
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175 to a known distribution functio
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177 Table A.2 Kolmogorov-Smirnov Te
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181 a change 1n source strength ove
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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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