Quantitative evaluation of fracture geometry influence on nonlinear flow in a single rock fracture

Abstract

The nonlinear flow behavior in a single rock fracture (SRF) has been studied for decades. However, the existing models to link fracture geometries and nonlinear flow behavior are less accurate due to insufficient characterization of fracture geometries. The primary goal of this study is to propose new parameters to characterize the geometric characteristics of a SRF, and then to evaluate the nonlinear flow behavior in a SRF. A series of high precision hydraulic tests are conducted on 50 mated and unmated artificial fractured samples. The results show that Forchheimer equation adequately describes the nonlinear fluid flow through a SRF with rough walls and variable apertures, and its nonlinear coefficients can be determined by quantifying the fracture geometries. By introducing the concept of a threshold aperture, meaning that only those zones with greater apertures than a threshold value are involved in the flow process, the heterogeneity of aperture distribution is quantified based on the cumulative distribution of individual apertures of sampling points. In addition, the influence of surface roughness on the nonlinear flow in a SRF is quantified with the standard deviation of secondary roughness. Lastly, an equation that relates the nonlinear coefficient to the newly proposed geometrical parameters is arrived, which is further used to link the friction factor, nonlinear flow model, and critical Reynolds number with the fracture geometric characteristics. The newly proposed equations in this study predict and characterize the nonlinear flow characteristics in a SRF very well.