Longitudinal dispersion in nonuniform isotropic porous media
Creators: name: Houseworth, James Evan
Publisher: name: California Institute of Technology
Year: 1984

description: 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 in terms of integrals of kinematic properties of solute particles flowing through individual, random capillary tubes. However, shear dispersion within individual capillary tubes 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 interface. 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. 

The material presented in this report is essentially the same as the thesis submitted by the author in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
description: This research project has enlisted the support of several people whom I would like to thank. 

Norman Brooks, my advisor, has provided an excellent environment for doing research. While allowing me the freedom necessary to explore different ideas, as well as providing essential, constructive criticisms during the course of the research, he has been a constant source of encouragement. His support is deeply appreciated. 

Many thanks are due Bob Koh, who has given generous assistance and advice concerning computational and data acquisition problems encountered. Bob's computer programs were used extensively for data processing and computer graphics, and his random number generator is the basis of the one used for this work. 

The assistance of Elton Daly, who has been instrumental in the design and construction of the experimental apparatus, is greatly appreciated. Consultation sessions with Elton were essential in translating concepts into actual experimental equipment. 

The help of all the shop staff members is also appreciated. Rich Eastvedt gave considerable assistance in the construction and installation of experimental apparatus. Joe Fontana also provided valuable assistance, particularly in the design and construction of the conductivity probes. Leonard Montenegro helped locate and assemble the components of the data acquisition system used for conductivity measurements. 

I wish to thank Rayma Harrison and Gunilla Hastrup, who have cheerfully tracked down a large number of books and papers needed for this research. 

Much appreciation is due the staff members who assisted in the production of this text. Joan Mathews and Mary Ann Gray efficiently handled the onerous task of typing the equations. The illustrations and graphics labeling were produced with great skill by Theresa Fall and Joseph Galvin. 

I am ever grateful to Pat Rankin for making sure my stipends and tuition support were not overlooked in the tangle of administrative paperwork. 

Finally, I thank my wife, Pat, for her assistance in putting together the text and, most of all, for her love and support through the years. 

This study was supported by the Caltech Environmental Quality Laboratory with gift funds from the Andrew W. Mellon Foundation and Southern California Edison Company (from the 1981 Tyler Ecology- Energy Prize received by S.C.E.).