Pressure Dynamics in Wells During Gas Kicks: Part 2 - Component Models and Results
Authors: Hoberock L.L. , Stanbery S.R. 
Published: December 2007

Summary
This is the second part of a theoretical study of the dynamic pressure and flow behavior of an onshore well containing a gas kick controlled by the driller's method. The main results from this study show that (1) casing pressure profiles under assumed constant bottomhole pressure can be very sensitive to both pump stroke variations and standpipe pressure pump stroke variations and standpipe pressure variations, (2) the pressure time delay from casing choke to standpipe is extremely variable, (3) pressure changes rapidly as the gas begins to exit the choke, and (4) the effects of a sudden adjustment at the choke can be magnified at bottomhole, with the largest magnification occurring after the gas begins to exit the choke.

Introduction
In this paper, the proposed well model described in Part 1 is developed employing the transmission line Part 1 is developed employing the transmission line solution techniques of Part 1. The final model is operated as a real-time, manually controlled simulator, whose outputs are compared with actual test well data.In Part 1, the development of the digital and analog solution techniques were based on the flow of a Newtonian fluid in a line of constant cross section and length. Thus, to use either of these techniques to represent the drillpipe and annular lines, it is necessary to account for the facts that the drilling mud is actually non-Newtonian and that the annular liquid lines are of time-varying lengths and annular cross section. In addition, to represent the two-phase fluid line, the fact that the fluid within this region is a gas/mud mixture with the gas rising at a velocity relative to the mud must be taken into account. Accordingly, the necessary modification to the basic solution techniques to model these effects and suitable models for the mud pump, casing choke, and drill bit are discussed.

Drillpipe Transmission Line
To account for the change in inner diameter between drillpipe and collars, it is necessary to model the drillpipe as two coupled fluid-line sections. However, in the specific test well installation that is modeled, there are no collar sections in the drillstring. Thus, it can be assumed that the drillstring is a single constant-length section of constant circular cross- sectional area.Within the range of drillpipe velocities encountered in practice, the most commonly used drilling muds frequently are modeled as non- Newtonian Bingham plastics. Accordingly, to use the solution techniques of Part 1 to predict pressure and flow propagation in the drillpipe, it is necessary to make suitable modifications to reflect the non- Newtonian nature of the drilling mud. It can be shown that the steady-state frictional pressure drop per unit length dp/dz for the flow of a Bingham per unit length dp/dz for the flow of a Bingham plastic in a smooth circular pipe is given by plastic in a smooth circular pipe is given by(1)
where
p = fluid density, D = pipe diameter, U = mean fluid velocity, andf = Fanning friction factor.
Unlike the Newtonian case, however, the Fanning friction factor in Eq. 1 for a Bingham plastic is a function of the Bingham Reynolds number N ReB 1 and the Headstrom number NHe .
JPT
P. 1367