Modelagem da propagação de pressão em fluidos de perfuração durante kick de gás

Abstract

In the process of drilling oil and gas wells the pressure control is an important task. If the pressure inside the well is smaller than the formation pressure, an influx of the formation may occur, phenomenon denominated as kick. If the influx is not controlled there may be an uncontrolled flux from the formation to the surface (blowout). The closing pressures are used to calculate the formation pressure, however, the viscoplastic character of the drilling fluid reduces the pressures measured on the surface. This current work presents a mathematical and numerical modeling to predict the pressure propagation along the well during a gas influx (kick). The compressibility and the viscoplastic behavior of the drilling fluid were considered, modeling it as a Bingham Plastic. The flow is considered as one-dimensional, laminar, transient, isothermal and homogeneous. The solubility of the gas in the drilling fluid is disregarded and the gas is modeled as a real gas. The flux of the formation into the wellbore is treated by Darcy’s law. The balance equations of mass and momentum for the mixture result in a system of hyperbolic partial differential equations, having as unknowns the pressure and the velocity, which are solved by the method of characteristics. Two study cases were considered: the dynamic kick and the static kick. The pressure and velocity fields along the well are obtained by a computer program developed in FORTRAN language. Afterwards, the results obtained from the model developed were assessed by comparing to analytic solution and experimental data. The results present that the bigger the yield stress is, the smaller is the pressure transmission and that if the formation pressure is not high enough, there is no pit-gain in the mud tanks.