Fracture aperture is usually estimated by cubic law, which assumes flow between two smooth parallel plates. However, many researchers have proved that the fracture aperture is not a smooth surface but rather has tortuous paths and roughness, and hence the flow behavior is different. Previous research showed that fracture aperture follows lognormal distribution. Nevertheless, there has not been any research conducted to validate the fracture aperture distribution with the change in stress conditions, which is common in fractured reservoirs. With the advent of X-ray CT scanner in the field of petroleum engineering, fracture apertures can be visualized and measured. Since there is no direct calculation for fracture aperture measurement from CT scanner data, a calibration curve needs to be established. We developed a calibration curve based on existing calibration techniques, which involves area integration of the fracture region to obtain a correlation between integrated CT numbers and the calibrated fracture aperture. Using this calibration curve, we obtained distribution patterns for fracture apertures along the length of the core for various stress conditions, from about six thousand fracture aperture measurements for each stress condition. The results show that aperture distributions still follow lognormal distribution under various stress conditions.
Naturally fractured reservoirs have millions of barrels of oil left unrecovered due to the poor knowledge of the fluid flow through these reservoirs. Several approaches had been taken to model the fluid flow through a single fracture. Early researchers1,2 assumed the fracture model as a set of parallel plates separated by a constant fracture aperture. However the actual fracture surface in the reservoirs is very rough due to mineralization. Hence, the fluid flow in these tortuous paths tends to follow a preferred path. Pyrak et al.3 (1985) performed laboratory experiments wherein they injected molten wood's metal into single fractures at different applied stress conditions. The direct evidence of tortuous paths was observed upon opening the cooled metal in the fracture. The fluid flow in these paths will be through the larger apertures which offer least resistance to the fluid flow. However, the effect of tortuosity becomes less when the distribution is sharply peaked at large apertures with a long tail in the small apertures4. This brought many researchers to think about fracture aperture distribution. They thought that fracture aperture distribution should follow a particular pattern.
When the parallel plate approach is no longer valid, Tsang and Witherspoon5 accounted for the variation of apertures in a rough fracture. Later, Tsang4 modeled the variation of fracture apertures by electrical resistors with different resistance values placed on a two-dimensional grid. The results indicated that small apertures play a key role in restricting fluid flow. When the fracture contact area increases, tortuosity and connectivity of fractures become important. The flow in a single fracture took place in a limited number of channels which was evident from the field experiment carried out in a single fracture6. Upon drilling five holes in the fracture plane and pressurizing each to atmospheric pressure, the results showed that the channels occupied a total area of only about 10% of the fracture plane.
