Masters Theses

Date of Award

12-1996

Degree Type

Thesis

Degree Name

Master of Science

Major

Civil Engineering

Major Professor

Matthew Mauldon

Committee Members

Eric Drumm, Larry McKay, James Smoot

Abstract

Bed-normal permeability of a two-dimensional, fractured, stratified rock masses with steady-state, laminar, saturated flow is investigated. Fracturing is assumed to be orthogonal to stratification, and the permeability is assumed to be a function of fracture aperture and flow path length in an otherwise impermeable matrix. The flow path length through fractures takes the value of bed thickness for bed-confined fractures. Bedding planes are modeled as fictitious layers, termed interlayers, that conduct flow through "virtual" fractures. The aperture of virtual fractures in the interlayer is assumed equal to the bedding plane aperture. Fracture spacing in the interlayer is assumed equal to the fracture spacing in a fluid source layer. The interlayer thickness is a random variable derived from the mean length of the shortest paths from a fracture in a source layer to a fracture in a sink layer, along the bedding plane. Two fracture spacing assumptions are investigated, one where fractures have constant spacing, the other where fractures are negative exponentially spaced. An analytic expression, the interlayer equation, is found to quantify bed-normal permeability. Investigation of the interlayer equation indicates the fracture spacing in a layered rock mass influences bed-normal permeability more than previous derivations using tensor methods. The bed-normal permeability is found to be highly sensitive to the magnitude of the bedding plane aperture. The bed-normal permeability is also found to be scale dependent, implying that a statistically homogeneous rock mass does not imply the existence of a representative elemental volume. The analytic solution was verified numerically using the computer program bnpflow, written expressly for this purpose. For fractures with constant spacing, the analytical prediction and the numerical solution agree with 0.6%. For fractures with negative exponential spacing, the analytical prediction and numerical solution agree within 25%. The larger difference for negative exponentially spaced fractures is assumed to be a result of the assumptions used in the analytical derivation. A potential application for the interlayer method is investigated, using rocks from the Cambrian-aged Conasauga Group in Eastern Tennessee. Only an upper and lower bound for bed-normal permeability is found, because current techniques for collecting fracture data overlook important parameters necessary to accurately employ the interlayer equation.

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