Akademik Veri Yönetim Sistemi
Applicable Analysis, 2025 (SCI-Expanded, Scopus)
A specific variational approach has been developed in this article to model the steady flow process of a non-mixing viscous mass obeying non-slip boundary regime system in a perfectly circular pipe. Through consistent mathematical reasoning, concrete analytical results have been obtained for the principal physical quantities of the aforementioned non-mixing viscoussystem, such as the velocity profile (along the pipe radius) in vertical (or non-vertical) pipes, pressure drop, the flow rate of the pipe (Hagen–Poiseuille formula) and the shear stress on the pipe surface. Such issues may be relevant in the operation of oil wells using the gas lift method, in water-cut and sand-producing oil wells, as well as in two-phase and multiphase flow processes. Additionally, it is known that in deep oil and hydrocarbon wells, the temperature increases by 1 degree per 10 meters of depth. Considering that such wells can be extended to several kilometers deep, it becomes evident that, the temperature in the well and the reservoir is an essential actor in all prepossess. As the mixed fluid moves upward from the bottom of the well, the extracted mass begins to cool, but this cooling is not uniform. Therefore, even a homogeneous fluid exiting the well behaves like a non-mixing fluid system, as the viscosity and density of the non-uniformly cooled volume will be unevenly distributed depending on temperature likely to the immiscible system For this reason, it can be considered as the motion of a non-mixing viscous mass. These considerations, along with other practical issues, are the subject of discussion in this article.