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An analytical solution for transient flow of Bingham viscoplastic materials in rock fractures

International Journal of Rock Mechanics and Mining Sciences

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DOI: 10.1016/S1365-1609(00)00080-0

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Abstract

We present below an analytical solution to model the one-dimensional transient flow of a Bingham viscoplastic material in a fracture with parallel walls (smooth or rough) that is subjected to an applied pressure gradient. The solution models the acceleration and the deceleration of the material as the pressure gradient changes with time. Two cases are considered: A pressure gradient applied over a finite time interval and an applied pressure gradient that is constant over time. The solution is expressed in dimensionless form and can therefore be used for a wide range of Bingham viscoplastic materials. The solution is also capable of capturing the transition that takes place in a fracture between viscoplastic flow and rigid plug flow. Also, it shows the development of a rigid central layer in fractures, the extent of which depends on the fluid properties (viscosity and yield stress), the magnitude of the pressure gradient, and the fracture aperture and surface roughness. Finally, it is shown that when a pressure gradient is applied and kept constant, the solution for the fracture flow rate converges over time to a steady-state solution that can be defined as a modified cubic law. In this case, the fracture transmissivity is found to be a non-linear function of the head gradient. This solution provides a tool for a better understanding of the flow of Bingham materials in rock fractures, interfaces, and cracks. ?? 2001 Elsevier Science Ltd. All rights reserved.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
An analytical solution for transient flow of Bingham viscoplastic materials in rock fractures
Series title:
International Journal of Rock Mechanics and Mining Sciences
DOI:
10.1016/S1365-1609(00)00080-0
Volume
38
Issue:
2
Year Published:
2001
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
International Journal of Rock Mechanics and Mining Sciences
First page:
285
Last page:
296
Number of Pages:
12