Fluid Flow In Rough Fractures
Authors: Parrish David R. 
Published: December 2007

Parrish, David R., Member AIME, Pan American Petroleum Corp., Tulsa, Oklahoma
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This paper was presented at the University of Oklahoma-SPE Production Research Symposium in Norman, Okla., April 29–30, 1963, and is considered the property of the Society of Petroleum Engineers. Permission to published is hereby restricted to an abstract of not more than 300 words, with no Illustrations, unless the paper is specifically released to the press by the Editor of the Journal of Petroleum Technology or the Executive Secretary. Such abstract should contain conspicuous acknowledgement of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request providing proper credit is given that publication and the original presentation of the paper.
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Abstract
The single-phase flow characteristics of several rough fractures were determined. The rough fractures were constructed by cementing uniform diameter glass beads to flat glass plates. The absolute roughness was varied by changing the bead diameter and the relative roughness was varied both by changing the bead diameter and by changing the fracture clearance.
During truly viscous or laminar flow, friction factors are little, if any, higher for rough fractures than for smooth fractures.
The Reynolds number at which transition from laminar to turbulent flow occurs remains constant at 1500–2000 until the relative roughness exceeds 1/4. For greater roughness, the critical Reynolds number decreases rapidly as roughness increases.
Strictly turbulent flow is achieved when the Reynolds number exceeds about 4000. Flow is then independent of viscosity and friction factors do not change with Reynolds number.

Introduction
Many petroleum reservoirs are fractured, either naturally, artificially or both. Such fractures can be of the utmost importance in petroleum production. Yet, fluid flow in fractures has received little attention compared to the study of fluid flow in the rock matrix.
To put it strictly in the terms of the reservoir engineer, our knowledge of the permeability characteristics of fractures simply is inadequate.
The purpose of this paper is to attempt to contribute to the understanding of fluid flow in fractures.

History
The two studies perhaps most directly related to the present wok are those of Nikuradse and Huitt. The latter gives an excellent literature survey that need not be repeated in detail here.
Fluid flow in smooth pipes can be described by the well-known Fanning friction factor - Reynolds number correlations. For laminar flow in such conduits (symbols are defined at the end of the paper)
Nikuradse cemented sand grains to the inner surface of pipes and showed that this relation also held for laminar flow in rough pipes, at least for certain degrees of roughness.