Modelagem matemática da transmissão de pressão em fluidos newtonianos generalizados confinados em geometrias cilíndricas com transferência de calor

Abstract

With the advance of the technologies related to oil and gas exploration, it is possible to drill ever deeper wells in larger ocean depths. That made necessary the development of more precise pressure prediction models, once the well must work within an operating window. This dissertation proposes a mathematical model to compute pressure and temperature inside wells and auxiliary lines during the drilling phase. Based on pressure propagation models, the equation system considers the rheological and thermal properties of the drilling fluid. It is also imposed a heat transfer condition with the external environment, being either convection with the seawater of diffusion to the rock formation. The numerical solution of the equation system is done through the method of characteristics. Results using field data showed good agreement with the measured pressure during the kill line leak-off test, implying that the model is adequate for these situations. Dimensionless parameters were defined to generalize the leak-off test cases, making the comparison between simulations easier and, potentially, to aid field operators in their decision making. Comparisons show that, in general, there is a quick pressure drop after the fluid confinement due to the pressure propagation throughout the well, related to the fluid’s rheological parameters. There is also another, slower, pressure change, related to the thermal parameters and heat exchange with the external environment. The main parameter associated with this second pressure change is the ratio between the fluid’s thermal expansion coefficient and isothermal compressibility. It is concluded that small changes in temperature are enough to cause significant pressure changes during leak-off tests where leaks are not observed. However, although the model is capable of predicting these variations, it cannot differ them from pressure drops caused from actual leaks.