MATHEMATICAL MODELING OF FLUID FLOW AND TOTAL HEAT TRANSFER PROCESS IN WELLBORE
Mathematical modelling of fluid flow and total heat transfer process in the wellbore is very important for predicting the actual situation in the realm. The wellbore consists of cement, tubing, casing, and for the total heat transfer, the effect of their respective temperatures on the flowing fluid and the surrounding earth must be investigated. The hot fluid from the reservoir moving up the wellbore had to pass through the tubing which is surrounded by casing and the cement and the surrounding earth formation and subsequently causes loss to the fluid temperature. Many studies about the wellbore consider that fluid temperature from bottom to top of the wellbore remain constant during the process and that heat transfer between the fluid and the surrounding earth temperature does not change resulting to inadequate optimization of wellbore function. This scenario if not properly studied will lead to inefficiency of optimising the wellbore or even premature closure of the wellbore. In this paper, a one-dimensional transient compressible model in the radial direction comprising the conservation of mass and momentum has been presented to investigate the behavior of the heat exchange between fluid temperature and the surrounding earth. Heat transfer equation was also developed to account for radii of tubing, casing and cement. The model was solved by flux vector splitting method of Steger Warming. The method allows the application of gas state equation which is best used in fluid temperature calculation and also account for heat exchange between fluid temperature and surrounding earth. It also allows investigation of the effect of wellbore temperature which is surrounded by casing and cement on the fluid temperature and can be extended to oil reservoir modelling especially in permafrost regions where geothermal gradient is significant. The result obtained shows that flowing fluid temperature drop toward the wellhead due to earth temperature effect on the flowing fluid. It can help gas production engineers in selecting types of pipes, casing and cement used in the wellbore construction.