Mathematical Modelling of Thermal Profile of Well Drilling Thermal Profile in One of the Iran Southern Vertical Wells to Optimize the Rheological Characteristics of the Drilling Fluid

The present work deals with finding the thermal profile of fluid in a vertical well to determine the temperature distribution in different depths and parts of a well during digging. since drilling fluid plays an important role in a well drilling process, it is important to study the effect of several parameters on it. moreover, one of the main purposes of using fluid is to cool down the drill and the process. this study aims to investigate the role of fluid as a heat exchanger from the bottom to the surface of the well and the surrounding area. in addition, on this base, the heat can affect the fluid characteristics such as rheology, density, and pressure variation. moreover, knowledge about the thermal distribution of drilling fluid plays an important role in designing the fluid, estimating drop pressure, cementing and fencing, and drop of thermal energy in the well. in addition, this thermal profile is made by using mathematical modeling based on energy conservation and heat transfer auxiliary equations in the form of displacement, delivery, and fluid movement in the well. furthermore, the equations in the model are solved by coding in matlab, and thermal profiles show the results obtained for every part of the well. moreover, the temperature distribution of fluid in the digging pipe, lining pipe, lining, and surface lining is specified. furthermore, the thermal profile is obtained for both the water and oil base fluids. ultimately, in this research, it is proved that the thermal gradient of the earth, well depth, rate of fluid flow in the well, density, and thermal capacity of the fluid affect the thermal profile of the fluid, and also, there is a large difference between the thermal profile of the fluid in a digging well.