Effect of non-Darcy Flow on induced stresses around a wellbore in an anisotropic in-situ stress Field

After drilling a well, the  stresses will be altered and the induced stresses present the new state of stress. These induced stresses which result in geomechanical problems. The studies indicate that the flow of hydrocarbon into the wellbore influences the induced stresses. Darcy equation has been used in the past; however, the laminar flow assumption embedded in this equation cannot correctly model the flow of fluid when a non-Darcy flow dominates near a wellbore. Example of such situation includes the gas wells. In this study, analytical equations are developed to incorporate the effect of non-Darcy flow on the induced stresses around a wellbore. These equations developed based on Forchheimer flow equation. Then the simplified solutions were presented by considering the second term of Forchheimer flow equation. It was found that the difference between the results from Darcy and non-Darcy flow models is proportional to the drawdown pressure. Further studies included numerical simulation of non-Darcy fluid flow in a typical reservoir. Comparison of the results with the analytical models indicated that the magnitude of stresses in non-Darcy flow is larger than of Darcy flow. Finally, sensitivity of the reservoir properties on the induced stresses in the non-Darcy flow regime was investigated.