Effect of mid-surface undulations on flow behavior in rock fractures: A comparison between three-dimensional and two-dimensional fracture models

In recent years, fracture network modeling has been extensively used in studying the flow and transport processes in fractured rocks. The fractures in existing fracture network models are usually represented by planar fractures, by ignoring the mid-surface undulation. This simplification may lead to an inaccurate description of the physical process with large mid-surface undulation. In this study, the effect of mid-surface undulation is examined by comparing the hydraulic properties of three-dimensional (3D) rough rock fractures, two-dimensional (2D) rock fractures with rough mid-surfaces, and 2D planar mid-surface rock fractures. The geometric properties of the fracture mid-surface are also assessed to infer the significance of mid-surface undulation on the fluid flow behaviors. The results show that rock fractures with rougher mid-surfaces demonstrate more tortuous flow paths, and the conductivities of the 2D planar mid-surface fractures and 2D fractures with rough mid-surfaces are generally 20% higher than those of 3D rock fractures. For mid-surface undulation to have an insignificant impact on the general flow properties, the two mid-surface undulation parameters Tor and Z2 are found to be less than 1.08 and 0.32, respectively. These results can provide an important reference for assessing the uncertainties in replacing the actual 3D rock fractures with 2D planar mid-surface ones, as routinely performed in fracture network modeling.