Advanced Two-Phase Well Control Analysis (November)
Authors: Choe J. 
Published: March 2010

Abstract
Pressure responses during well control operations can be analysed using the coupling solution of the conservation of mass equations, the conservation of linear momentum equation, and the equation of state. For a realistic well control simulation, a computer model should include the effects of well geometry, well control methods, formation parameters, bubble rise velocity, and mud compressibility on well stabilization. Typical numerical problems encountered in two-phase well control modelling are numerical dissipation, difficulty of selecting appropriate time step and grid sizes, negative liquid velocity, and divergence due to distinct two-phase flow maps. Among these numerical problems, the numerical dissipation is the most prominent and it should be handles properly for an accurate two-phase well control simulation.
An unsteady state two-phase well control model is developed and compared successfully with the Nickens model, the Santos model, and a single-phase model. However, an exact match is very difficult because of different two-phase correlation models used and complexity of two-phase flow. Wellbore geometry, gas velocity, formation permeability, and handled of numerical dissipation are found to be important factors in the prediction of the pressure behaviour of the kick fluids.

Introduction
As proven petroleum reserves decline through continued production, exploration for new oil and gas resources will extend into environments which present significant economic risks and technical hurdles. A detailed study using multi-company data disclosed about 8 to 10 billion bbls of oil equivalent in place for the deep water area of the Gulf of Mexico outer continental shelf(1). There are more than 15 known discoveries in water depths between 910 m and 2,300 m in the Gulf of Mexico(2) and there is great interest in accelerating the development of the known deep water discoveries.
Since safety is one of the biggest concerns in drilling operations, the oil industry routinely trains its personnel in areas which are critical for safe and economical drilling procedures. One of these major areas is well control. Well control includes not only kick prevention and kick detection but also the process of removing kick fluids from the kicking well and circulating heavy drilling mud under controlled conditions.
Well control simulation has received attention in recent years because of its applicability and flexibility, and many computer models(3-10) have been developed to analyse the behaviour of a kick. The main objective of a kick simulator is to predict pressure and volume behaviour of kick fluids as a function of time. One of the earliest mathematical models was published by LeBlanc et al. assuming a known volume of gas kick as a single-phase(3). They ignored effects of frictional pressure loss (FPL), gas-mud mixture, gas slip velocity, and reservoir parameters.
Nickens presented a dynamic two-phase computer model of a kicking well(4). He set up finite difference equations (FDEs) for uniform wellbore geometry. Nickens also applied those equations for variable wellbore geometries by changing the gas and liquid velocities at the locations of changes in area. He did not modify the conservation of momentum equation for uneven wellbore geometries.