Evaluation of Critical Reynolds Number for Non-linear Crude Oil Flow through Rough-walled Fractures

One of the most important aspects of governing physical processes through rough-walled fractures is the non-linear behavior of flow. The onset of non-linear flow in rock fractures is characterized by critical Reynolds number, which is the main object of this paper. In this paper, the technical aspects of non-linear flow of crude oil through open rock fractures and critical Reynolds number were studied. These issues were studied based on the results of three-dimensional numerical simulation of the Navier-Stokes equations for crude oil flow through rough-walled fractures. The finite volume simulation of crude oil flow through three-dimensional space of rough-walled fractures was performed for a wide range of Reynolds numbers or flow rates. The results of crude oil flow simulations were analyzed based on the Forchheimer’s law. The coefficients of energy losses due to viscous and inertial dissipation mechanisms were derived from the Forchheimer’s law regression on the results. Then, the role of linear and nonlinear energy losses with viscous and inertial dissipation mechanisms was evaluated based on the relation between Reynolds and Forchheimer non-dimension numbers. Finally, the critical Reynolds number was determined for onset of non-linear flow through rough-walled fractures. The results of this study indicate that the Forchheimer’s law appropriately describes the non-linear crude oil flow through rough-walled fractures. By increasing the Reynolds number (or flow rate), the ratio of viscous energy lose from total energy losses decreases non-linearly and simultaneously, the inertial dissipation becomes the dominant mechanism of energy lose. The critical Reynolds number for crude oil is in the range of 30 to 46 for the open fractures of this study. The maximum and minimum of critical Reynolds number follow the minimum and maximum of inertial dissipation coefficient and also the gradient of Reynolds- Forchheimer curve, respectively.