Newtonian fluid flow from an arbitrarily-oriented fracture into a single sink

Abstract

A model of fluid flow from an arbitrarily-oriented compressible fracture into a sink has been developed. Effects of fracture inclination, fracture dimensions, in-plane aspect ratio, fracture compressibility, sink location, sink pressure, initial equilibrium pressure inside the fracture and fracture wall roughness on fluid flow into the sink have been investigated. It has been found that the effect of fracture inclination decreases with decreasing fracture compressibility. Sink location (in the middle of the fracture, at the edge, or in the corner) has a significant effect on the fluid flow into the sink. Fluid flow into the sink is shown to be controlled mainly by the difference between the initial fluid pressure in the fracture and the sink pressure, but not by the absolute values of these parameters. The effect of the fracture wall roughness was investigated using fractures with artificial surfaces having Hurst exponent of 0.5. In case of a widely-opened fracture, the effect of roughness is negligible, and the fracture can be approximated with a smooth-walled fracture of the same mean aperture. In case of a partially-closed rough-walled fracture, the roughness was found to affect the flow rate significantly by extending the discharge time. This has an important implication for oil production from certain types of naturally-fractured reservoirs. The roughness of partially-closed fractures did not, however, affect the results of the comparative parametric study, which justified the use of a simplified smooth-wall model in such studies. Modeling results have implications for the simulation and analysis of some drilling situations in fractured rocks as well as for well testing analysis and oil production simulation.