Document Type


Date of Award

Fall 10-31-1995

Degree Name

Doctor of Philosophy in Civil Engineering - (Ph.D.)


Civil and Environmental Engineering

First Advisor

Paul C. Chan

Second Advisor

John R. Schuring

Third Advisor

Edward G. Dauenheimer

Fourth Advisor

C.T. Thomas Hsu

Fifth Advisor

George Y. Lei

Sixth Advisor

Dorairaja Raghu


A mathematical model that simulates the process of contaminant removal from a pneumatically induced fracture within a porous medium is presented. It includes: (1) model development; (2) parameter evaluation; (3) statistical sensitivity analysis; and (4) model validation.

Based on the dual porosity approach, a mathematical model for a fractured porous formation is developed for both two dimensional and axial symmetrical cases. This model constitutes a pair of coupled partial differential equations for the porous medium and discrete fracture, respectively. The initial and boundary conditions have been determined based on field considerations of a soil vapor extraction system. By means of Laplace transforms, analytical solutions of the equations are obtained in explicit forms of exponential and error functions.

The four principal physical parameters used in the model include tortuosity, retardation factor, fracture aperture, and extraction flow rate. Fracture aperture and flow rate are related to the characteristics of geologic formation and operational system, while tortuosity and retardation factor are related to geochemical characteristics. Guidelines for determination of these parameters are provided. In addition, a statistical analysis is performed to evaluate the sensitivity of mass removal to variations in these parameters. A linear relationship between the standard deviations of mass removal and tortuosity or retardation factor is obtained. The sensitivity of mass removal to the fracture aperture is found to be minimal; however, aperture affects mass removal indirectly through extraction flow rate. Mass removal is determined to be sensitive to flow rate in low flow ranges only.



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