The effects of tortuosity on flow through a natural fracture

Fractures can play a dominant role in the movement of fluid through rock media. As a result, much work has been done, both theoretically and experimentally, on laminar fluid flow through open fractures consisting of parallel plates of varying degrees of surface roughness. In many cases the behavior of the fluid can be described using the expression developed by Lomize (1951) and used by others such as Witherspoon et al. (1980). This equation has become generally known as the cubic law equation because flow rate is proportional to the cube of the aperture. Although the relation of fracture aperture to flow is obvious, tortuosity of the flow paths in a fracture may also have a significant effect on flow. In this paper the results of a series of flow tests performed on a naturally fractured siltstone sample taken at depth from an oil reservoir are presented. The results of flow measurements over a wide range of apertures showed that tortuosity was a primary factor in explaining the difference between the measured flow rates and those predicted by the cubic law equation.