Application of the fractal geometry theory on fracture network simulation

In this paper, we introduce an L-system based on the fractal geometry to study complex fracture networks. Comparing with other simulation models, the fractal fracture could not only maintain the bifurcation of the fracture geometry but also represent the multi-level feature of the complex fracture networks according to its fractal characteristics. Since the fractal geometry is always connected with several controlling parameters, the factors affecting on the fracture propagation can be quantized. With the fractal fractures, further studies on the fracture geometry and the multi-leveled branches are carried out, and the results can be concluded as: (1) when the complex fracture geometry is considered, the influence of the connectivity and complexity of the fracture network on the well performance is hard to ignore, and enhancing the connectivity and complexity of the fracture network will perform better than making a long but disconnected fracture on the shale gas development; (2) of a multi-leveled fracture network, the main fractures near the horizontal well contributes to the initial production, but the conductivity ratio (conductivity of the secondary fractures versus the conductivity of the main fractures) influences the decline rate, so a high production rate cannot be maintained without an efficient contributing area covered with conductive secondary fractures.