Underbalanced Drilling Dynamics: Two-Phase Flow Modeling and Experiments
- Antonio C.V.M. Lage (Petrobras) | Kjell K. Fjelde (RF-Rogaland Research) | Rune W. Time (Stavanger U. College and RF-Rogaland Research)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2003
- Document Type
- Journal Paper
- 61 - 70
- 2003. Society of Petroleum Engineers
- 1.6 Drilling Operations, 4.3.4 Scale, 3 Production and Well Operations, 4.1.2 Separation and Treating, 4.6 Natural Gas, 1.6.1 Drilling Operation Management, 5.4.2 Gas Injection Methods, 3.1.6 Gas Lift, 4.1.5 Processing Equipment, 5.3.2 Multiphase Flow, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 1.7.1 Underbalanced Drilling, 1.10 Drilling Equipment, 1.8 Formation Damage, 5.6.8 Well Performance Monitoring, Inflow Performance, 4.2 Pipelines, Flowlines and Risers, 1.11 Drilling Fluids and Materials
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A dynamic model based on the drift-flux formulation is presented for treating transient phenomena in underbalanced drilling (UBD) operations. A set of mechanistic steady-state procedures for dealing with the definition of flow patterns, pressure drops, gas volumetric fractions, and in-situ velocities completes the model. The iteration between those mechanistic laws and the conservation equations is discussed. The numerical solution uses a composite explicit scheme, which reduces false oscillations and numerical diffusion. In addition, details about the boundary treatment are also presented.
Model predictions are validated through comparison to fullscale experimental data in two distinct transient situations: first, a typical liquid unloading, and second, the injection of a high-velocity single pulse and a sequence of two pulses of a gas/liquid mixture. The comparisons address model limitations and improve the understanding of the physics involved.
The reduction of formation damage, which often greatly diminishes the productivity of oil and gas reservoirs, particularly in horizontal well applications, is the main target in UBD operations. This damage cutback is achieved by the elimination of drilling fluid invasion. However, damage caused by poorly designed or executed UBD operations can greatly exceed that which may occur with a well designed conventional overbalanced drilling program.1
A successful UBD operation hinges on the control of downhole pressures and the management of the fluids flowing out of the well2 which are affected by many variables, such as injection of fluids, reservoir inflow performance, and operational procedures. All of these parameters are inevitably subjected to fluctuations, bringing transient responses to the multiphase circulation system. In some cases, the changes in the variables are even necessary, as with, for instance, the injection interruption for pipe connection. Further, in most applications, the UB condition is artificially achieved through the injection of gas into the well. This gas-lift approach leads to a mixture in which the high-compressibility nature of the gaseous phase makes it more sensitive to fluctuations or changes in the operational parameters. As a consequence, UBD routinely deals with the dynamical behavior of a complex multiphase circulating system.3
In this scenario, dynamic computer simulations can contribute significantly to better engineering design and execution. Pressure variations at the bottom of the well, liquid and gas rates of return, and timing for flow stabilization are some of the computational outputs that are involved in determining the adequate injection flow rates, sizing of separation systems, and operational procedures. All of these variables can be more accurately determined with the help of a dynamic computer program, increasing the chances of operational success. However, besides this computer tool, the engineering team in charge of the drilling activity also should have a strong physical comprehension of the multiphase system, which includes a critical view of the assumptions and limitations behind computer codes.
This paper describes theoretically a dynamic model for calculating the two-phase flow parameters in an UBD operation. The model comprehends a system of conservation equations and a set of mechanistic closure laws that are solved by a composite explicit scheme. The model is evaluated through comparison to full-scale experimental data in two distinct dynamical scenarios. The comparison between the predictions and experimental data also attempts to address the model limitations and the influences of some assumptions, building an improved understanding of the physics involved.
The model is based on the numerical solution of a drift-flux formulation of the two-phase flow conservation equations.4 The numerical scheme solves a set of three conservation equations, one for the mass of each phase and the mixture momentum. The mixture energy equation is not taken into account by assuming a fixed known temperature gradient in the well. In addition, the steadystate mechanistic closure models restore the missing information about slip between phases, which depends on the knowledge of the flow pattern.
The drift-flux formulation of the conservation equations is given by
Equations 1 through 3
The first two equations represent the mass transport of gas and liquid. The third represents the total momentum balance, which states that the pressure gradient depends on friction, gravity, and acceleration. This transient drift-flux model is a system of nonlinear partial differential equations, which is hyperbolic in an ample region of physical parameters.5,6 It describes the fully transient behavior of both pressure pulse propagation and mass transport. In the standard drift-flux approach, the closure of the system is achieved by specifying density models for each phase and a slip relation between the phase velocities. Generally, the slip relation presents the following:
where C0 and v0 are flow-dependent parameters. In addition, it is necessary to provide an appropriate model for the source term in the momentum equation that corresponds to the frictional pressure losses.
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