longitudinal dispersion in nonuniform isotropic porous media

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heterogeneities in the medium are large compared to the scale of the 19 problem being analyzed (Smith and Schwartz, 1978). A random capillary tube model has been developed for analyzing miscible transport phenomena during flow through nonuniform, isotropic, unconsolidated porous media. The analysis for a uniform porous medium is a special case of the general model. The solute is assumed to be chemically inert; i.e., no adsorption or reaction and dynamically passive in that its presence does not create significant density or viscosity deviations from the pure solvent state. In addition, the flow must be saturated, and is restricted to the Darcy regime (linear, laminar flow). A laboratory investigation of solute transport in nonuniform porous materials has been conducted. Previously, very little data existed regarding the relationship of solute transport characteristics and grain or pore size distribution data. Laboratory data characterizing pore structure are used as input to the solute transport model and results from model simulation and experiments are compared.
20 CHAPTER 2 LITERATURE REVIEW Transport phenomena during flow through porous media have been an active topic of research over the past 30 years. During this time, several distinct classes of porous media models have been developed. Considering the geometrical complexity of a porous medium, a crucial element in any model is the conceptual representation of the pore spaces. The different idealizations used to model a porous medium vary widely, ranging from simple capillary models which bear little resemblance to a porous medium to statistical models in which the complex geometry is modeled through probability density functions. The results of this effort at modeling solute transport 1n porous media are encouraging but far from complete. The problem in this type of modeling appears to be a reluctance to use more detailed information on the pore structure to define the medium. This reluctance is understandable for two reasons: 1. It is difficult to incorporate microscopic structural information into a solute transport model, particularly if one is interested in eventually using a macroscopic model such as the advection-diffusion equation. 2. Pore structural information 1S difficult to obtain and interpret. Despite the limitations of the theoretical models reviewed here, they provide reasonably accurate predictions for mass transport 1n
Page 1 and 2: LONGITUDINAL DISPERSION IN NONUNIFO
Page 4 and 5: ii ACKNOWLEDGEMENTS This research p
Page 6 and 7: iv ABSTRACT A theoretical and exper
Page 8 and 9: ACKNOWLEDGEMENTS ABSTRACT LIST OF F
Page 10 and 11: 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: porous medium and an unconsolidated
Page 43: (1/2) V yd s From experiments, they
Page 54: 39 governed by an effective advecti
Page 61 and 62: 2.4 SUmmary 46 Several different cl
Page 63: 48 CHAPTER 3 A THEORETICAL MODEL FO
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
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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
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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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