Non-linear Behavior of Crude Oil Flow through Rough-walled Fractures by Three-Dimensional Nevier-Stokes Numerical Simulation

One of the most important aspects of governing physical processes through rough-walled fractures is the non-linear behavior of flow. The main aim of this paper is to investigate the effect of non-linear flow on the hydraulic parameters and deviation from Darcy’s law. To reach this goal, the three-dimensional simulation of crude oil flow inside rough-walled fractures was performed by numerical solving the Navier-Stokes equations supplemented by the continuity equation through application of finite volume technique. The crude oil flow through three-dimensional space of rough-walled fractures was numerically simulated for a wide range of inlet velocity of flow rates. Then, the regime of flow, the deviation of crude oil flow through rough-walled open fractures from Darcy’s law, nonlinear relationship between hydraulic gradient and flow rate, and the effect of non-linear flow on the hydraulic aperture and permeability of fractures were investigated by analysis of crude oil flow simulation. The results of this study indicate that the crude oil flow through rough-walled fractures is non-linear; therefore the hydraulic parameters such as hydraulic aperture and permeability are not constant and highly depend on the flow rate of crude oil. In fact, hydraulic aperture and permeability of fractures decrease non-linearly by increment of flow rate, where these parameters show 10% and 20% of relative decrement, respectively. In addition, the results of regression analysis show that the Forchheimer’s law appropriately describes the behavior of crude oil flow through rough-walled fractures than Darcy’s law. Moreover, the accuracy of Forchheimer’s law is much more than 98%, but the relative error of Darcy’s law reaches to 27%.