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The planar shape of fractures has a profound effect on the connectivity of fractures and thus on the permeability of fractured reservoirs. It is important to know the planar shape of fractures when characterizing a fractured reservoir. However, the real planar shape of fractures at a site is rarely known since a rock mass is usually inaccessible in three dimensions. Information on the planar shape of rock fractures is limited and often open to more than one interpretation, making it difficult to correctly characterize fractured reservoirs. One simple way commonly used in oil reservoir characterization is to assume a circular disk fracture shape, which often leads to underestimated connection probability. Although extensive studies on the planar shape of rock fractures have been conducted, they are based on the macro-scale behavior of rocks and are empirical in nature. The goal of this project is to investigate the fundamental mechanism of fracture propagation in rock and the factors affecting the planar shape of rock factures, based on the numerical simulation with the three dimensional Particle Flow Code (PFC3D). The work includes (1) development and calibration of the numerical model using the experimental data including unconfined compressive strength, tensile strength and stress-strain curves; (2) validation of the calibrated numerical model by comparing the simulated fracturing pattern with the experimental fracturing results of the same rock; and (3) investigation of the planar shape of rock factures and the different factors affecting the fracturing of rocks using the validated numerical model.

During the 2010-2011 period of this project, we mainly worked on the development and calibration of the numerical model and the utilization of the model to simulate the experimental fracturing results. So far, we have achieved two main accomplishments: 1) modification of the PFC3D model to better simulate the mechanical behavior of rocks, and 2) development of an approach to simulate laboratory rock fracturing tests. Researchers have used the PFC3D model to simulate the mechanical behavior of rocks. Although the compressive strength is well simulated, the tensile strength, which is more related to rock fracturing, is over predicted. One major reason is that the porosity of the standard PFC3D model is significantly higher than that of a real rock. We developed a procedure to insert small balls within a standard PFC3D assembly of balls, by solving a 3D Apollonius problem. This procedure led to substantial decrease of the porosity and less over-prediction of the tensile strength. To further improve the prediction of the tensile strength, we considered releasing bond contacts at different levels and using a small normal to shear bond strength ratio, which simulates the pre-existent micro cracks in rock. Using the modified PFC3D model, we were able to better simulate the tensile strengths of two widely studied rocks, Lac du bonnet granite and Carrara marble.

Many researchers have conducted laboratory rock fracturing tests. So far, we have done an extensive literature review and have collected the laboratory fracturing test data for several types of rocks. To simulate the initial flaw (or pre-existing crack), a unique “excavation” procedure was developed to generate the corresponding hole. Because of the small particle size for some of the simulated rocks such as Carrara marble, the number of particles required for simulating the real laboratory fracturing test specimen is significantly large. To address this issue, we have developed a unique “zoned” particle assembly procedure. This procedure generates particle assembly in two (can be more if necessary) zones. The particles in each zone are placed randomly with a uniform distribution. In the inner zone which contains the initial flaw, the real particle size range of the rock is utilized. In the outer zone, the same maximum to minimum particle size ratio as in the inner zone is used and the minimum particle size is selected to be equal to the maximum particle size in the inner zone. Doing so not only ensures that the mechanical behavior of the real rock is captured in the inner zone but significantly reduces the total number of particles required in the simulation. 

Work is currently being carried out to apply the developed approach to simulate more laboratory rock fracture tests. After the developed approach is validated against the different experimental fracturing data, we will use to conduct systematic investigation of the planar shape of rock factures and the different factors affecting the fracturing of rocks.

So far, one journal paper has been completed and is currently in press in International Journal of Rock Mechanics and Mining Sciences and the other is about to be submitted. In addition, one conference paper has been presented in the 45th US Rock Mechanics/Geomechanics Symposium, San Francisco, California, June 26-29, 2011. We hope to write two to three more papers based on the results of this project.