Investigations of a drilling operation by using a simplified gas-liquid mathematical model

Investigations of a drilling operation by using a simplified gas-liquid mathematical model ABSTRACT There was a strong wish to investigate the physics of fluid flow involved in drilling operations where nitrogen injection is used to lower the hydrostatic pressure. This work is based on a reduced version of the full drift-flux model first presented to the academic community by Zuber and Findlay [1] that Dr. Steinar Evje developed and programmed numerically in MATLAB. The mathematical model implemented to predict the behavior of the system is a simplification of the full “transient gas-liquid drift flux model” [2], where a system of two strongly coupled “advection-diffusion” equations is obtained [2]. The model allows exploring relevant phenomena for drilling operations including the effect of liquid and gas expansion on pressure distribution along the wellbore. Two methods of gas injection are studied: 1) Direct nitrogen injection: Nitrogen is injected directly through the drill string from the surface to the bottom of the well and out through the annulus, see figure 1.1. This process will create a reduction in pressure at the bottom of the well and hence a reduction of the equivalent circulating density (ECD), the method is particularly used in depleted reservoirs and underbalanced drilling, however the disadvantages of this method relay on tools functionality due to excessive gas flowing through the drill string affecting mainly positive displacement drilling motors (PDM) and measurement while drilling tools (MWD) [3, 4] and some issues related to transmission of surveying parameters such as inclination and azimuth (maximum 20% gas cut to allow proper communication of such parameters [5]). 2) Concentric nitrogen injection: In this method nitrogen is injected through the annulus space between casings, (e.g. 9 5/8” and 7 5/8”) using a complement perforated at the bottom and connected to the top of a liner, see figure 1.2. We will demonstrate in this work that the injection point (top of the liner) along with wellbore inclination and liquid-gas injection rate play an important role on pressure distribution; we also want to gain insight into the understanding of forces intervening in this operations (e.g. friction and gravity). The main advantage of this method relays on the existence of proper communication of surveying parameters (inclination and azimuth) because the pressure pulses are not disturbed by gas and they can travel along a continuous liquid phase since the drill string is filled with mud. Two different scenarios with concentric nitrogen injection are investigated: 1) The first set up, models the injection of nitrogen in a vertical well, where the natural phenomena of slippage between phases liquid-gas coexists due to the natural tendency of gas to flow faster than liquid in vertical pipes because of buoyancy and lower frictional effects in the gas phase [2, 6], gas expansion is observed close to the surface due to pressure reduction [2, 5] as well as downward liquid flow once the gas injection has been stopped or the mixture velocity is sufficiently small [2, 7], followed by a transition from multiphase system to a state where single phase of liquid and gas is archived [2]. 2) The second set up simulates a more realistic scenario for our purposes, where a horizontal well flow is studied and nitrogen is introduced in the system at different positions given by the injection point, the phenomena explored include different phase flow velocities of liquid and gas and friction effects [2], strong gas expansion close to surface is observed [2, 5] and a reduction of gravitational effects due to the inclination of the well. 2