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Longitudinal Dispersion in Nonuniform, Isotropic Porous Media


Houseworth, James Evan (1984) Longitudinal Dispersion in Nonuniform, Isotropic Porous Media. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0vtp-g766.


A theoretical and experimental investigation has been made of the longitudinal dispersion of chemically and dynamically passive solutes during flow through nonuniform, isotropic porous media. Both theoretical and experimental results are limited to the high Peclet number, low Reynolds number flow regime. The goal of the theoretical investigation is to provide a quantitative method for calculating the coefficient of longitudinal dispersion using only measurable structural features of the porous medium and the characteristics of the carrying fluid and solute. A nonuniform porous medium contains variations in grain scale pore structure, but is homogeneous at the macroscopic level for quantities such as the permeability or porosity.

A random capillary tube network model of nonuniform porous media is developed which uses a pore radius distribution and pore length distribution to characterize the grain scale structure of porous media. The analysis gives the asymptotic longitudinal dispersion coefficient flowing through individual, random capillary tubes. However, shear dispersion within individual capillary tubes (discussed in Appendix C) is found to have negligible impact on the overall longitudinal dispersion in porous media. The dispersion integrals are evaluated using a Monte Carlo integration technique. An analysis of the permeability in nonuniform porous media is used to establish a proper flow field for the analysis of longitudinal dispersion.

The experimental investigation of longitudinal dispersion is carried out by measuring (with conductivity probes) the development of an initially sharp miscible displacement surface. The experimentally determined longitudinal dispersion coefficients are found to be greater in nonuniform media than in uniform media when compared using Peclet numbers based on the geometric mean grain diameter. The experimental breakthrough curves also display highly asymmetrical shapes, in which the "tail" of the breakthrough is longer than would be expected from advection-diffusion theory.

Although the theoretical model does not predict the tailing behavior, it is found that the leading portion of the breakthrough curve is described by advection-diffusion theory. The theoretically determined longitudinal dispersion coefficients lie roughly within a factor of 1.35 of the measured values.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Environmental Engineering Science
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Environmental Science and Engineering
Awards:Richard Bruce Chapman Memorial Award
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Brooks, Norman H.
Thesis Committee:
  • List, E. John (chair)
  • Saffman, Philip G.
  • Flagan, Richard C.
  • Herbolzheimer, Eric
  • Brooks, Norman H.
Defense Date:3 May 1984
Funding AgencyGrant Number
Andrew W. Mellon FoundationUNSPECIFIED
Record Number:CaltechETD:etd-01122007-131711
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:142
Deposited By: Imported from ETD-db
Deposited On:30 Jan 2007
Last Modified:19 Apr 2021 22:26

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