A new numerical model for simulation of flow on rough fracture

Abstract

Hydraulic fracturing is an important means to develop unconventional oil and gas. The fractures produced by hydraulic fracturing have the characteristics of a rough surface, high tortuosity, and strong randomness. The fluid migration law in rough fractures is more complicated, which leads to the change of the law of conductivity in fractures becoming more complex. Meanwhile, it is difficult to get certain regularity for the fracture surface obtained by direct fracturing. As a result, it is an arduous task to explore the influence of fracture roughness on conductivity by experimental means. Therefore, it is a feasible idea to use simulation to study the flow conductivity in rough fractures, which can be calculated by Darcy's seepage equation. In previous studies, quantitative characterization of rough fractures was rarely studied, and the three-dimensional Darcy seepage model of rough fractures was lacking too. In this paper, the rough surface profile and waveform are analyzed by analogy, and the height of the rough fracture surface, as well as the phase and wavelength of the waveform, were taken as the control parameters to generate the rough fracture surface. Then, the fractal dimension was used to characterize the roughness of the fracture surface. Coupled with the rough fracture model and the Darcy flow model, a three-dimensional Darcy flow model of rough fracture was established. Next, a new parameter, equivalent permeability, was defined to quantify and characterize the fracture permeability affected by roughness. Subsequently, the simulation results were verified by the experimental data. Finally, the effects of fracture surface fractal dimension, fracture width, proppant distribution, shear slip, and tortuous angle on the flow field were studied. This study provides a new model for the simulation of a rough fracture flow field, which provides important insight for understanding the properties of rough fracture flow fields.