The drilling fluid, more commonly called by professionals in the area by mud or drilling mud, is an essential component in the oil and gas exploration process. This material is used for a number of purposes, such as cooling the drill bit, loading the gravels to the platform, maintaining the desired pressure in the well, transferring the hydraulic force to the drill bit, preventing sedimentation of the gravels during the operation of the platform, keeping the well in a state of mechanical stability, and other utilities of lesser interest. In the industry, parafin-based drilling fluids were used, or paraffinic, but there was a change to oil-based olefin drilling fluids. In the present work, an extensive rheological study of the characterization of an olefin drilling fluid is performed to obtain the relation between the sedimentation process and the rheological properties of this kind of fluid. This study was performed during the required period of 90 days. After creating a reservoir for the fluid and the initial characterization of the fluid through the stress sweep and time sweep tests to distinguish the parameters that would be used in the rheometer, tests were started. At the end of the period, we could see that the sedimentation of the fluid stagnated in a different period of time than expected. The visible results of the sedimentation process in the reservoir also revealed interesting features.