A Lumped-Parameter Model for Transient Two-Phase Gas-Liquid Flow in a Wellbore
- Y.V. Fairuzov (Natl. Autonomous U. of Mexico) | J. Gonzalez Guevara (Mexican Petroleum Inst.) | G. Lobato Barradas (Pemex-Unam) | R. Camacho Velazquez (Pemex-Unam) | F. Fuentes Nucamendi (Pemex-Unam)
- Document ID
- Society of Petroleum Engineers
- SPE Production & Facilities
- Publication Date
- February 2002
- Document Type
- Journal Paper
- 36 - 41
- 2002. Society of Petroleum Engineers
- 1.10 Drilling Equipment, 5.1.1 Exploration, Development, Structural Geology, 4.1.5 Processing Equipment, 5.6.4 Drillstem/Well Testing, 5.2.2 Fluid Modeling, Equations of State, 5.2.1 Phase Behavior and PVT Measurements, 5.3.2 Multiphase Flow, 4.2 Pipelines, Flowlines and Risers, 4.1.2 Separation and Treating, 5.1.5 Geologic Modeling
- 2 in the last 30 days
- 369 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
In this study, a lumped-parameter model of transient two-phase gas/liquid flow in a wellbore is presented. The model is based on the assumption that the flow process is essentially one-dimensional so that an area's average properties can be represented as a function of one space variable and time. The wellbore is divided into a number of control volumes (nodes) that are connected by junctions (flow paths). A mass equation is formulated for each control volume, and an approximate momentum equation is used to calculate the flow rate at each junction. A numerical algorithm for coupling the wellbore model with a reservoir model is proposed. Calculations were carried out to determine the behavior of the wellbore flow during a pressure-buildup test. The results obtained from these calculations are compared to previously published theoretical results.
Most buildup tests are performed by shutting in the well at the surface. This complicates the interpretation of field data because of the effect of the wellbore on the pressure buildup at the sandface. When the shut-in is carried out at the surface, the fluid continues to flow from the reservoir into the wellbore for a period of time after the shut-in because of the compressibility of the wellbore fluid. This phenomenon is commonly called "afterflow" or "wellbore storage." The transient bottomhole pressure response during the wellbore-storage period is a result of a dynamic interaction between the reservoir and the wellbore. Furthermore, if the wellbore contains a two-phase mixture, the process of phase redistribution can cause anomalous pressure-buildup behavior (a pressure hump in the early portion of the buildup curve). Thus, understanding the physical processes that occur in the wellbore during the buildup test is important in well-test analysis.
Several mathematical models have been proposed for analyzing the pressure-buildup data. Van Everdingen and Hurst1 developed a simple, analytical model that assumes that the wellbore-storage coefficient is constant. This assumption is valid for single-phase liquid flow of constant compressibility. The use of a constant wellbore-storage concept for single-phase gas flow or two-phase flow in the wellbore may lead to great error in the evaluation of the sandface rate because of changes in the fluid compressibility and because of the phase-redistribution effects. Agarwal et al.2 presented an analytical solution for a constant wellbore-storage coefficient. Fair3 modified the equation proposed by van Everdingen and Hurst by adding a term to account for the pressure change caused by phase redistribution. Hegeman et al.4 extended the method of Fair with an error function representing field data. Based on the model proposed by Fair3 and Hegeman,4 Vasquez and Camacho5 developed a methodology to analyze transient buildup data obtained during short tests. All these models are analytical.
With progress in the development of two-phase flow models, a number of numerical models have been proposed to describe the fluid flow in wells. In contrast to analytical methods, these models are based on the basic conservation equations of two-phase flow. Winterfield6 presented a model that incorporates separate equations of continuity and momentum for each phase (the two-fluid model). Hasan and Kabir7 developed a mechanistic model for simulating phase segregation in the wellbore based on equations that describe the dynamics of a single bubble migrating upward through the liquid column in the tubing. Almenhaideb et al.8 used the Winterfield approach6 and showed that the two-fluid model of the wellbore fluid can reproduce a pressure hump at the buildup curve. They concluded that a model of two-phase flow that is simpler than the two-fluid model is unable to generate the pressure hump. However, Xiao et al.9 recently demonstrated the ability of the drift-flux model to describe the anomalous bottomhole pressure behavior caused by the phase-redistribution process.
As seen from the literature review, a correct description of multiphase flow in the wellbore needs a model that incorporates separate equations of continuum, momentum, and energy for each phase (the two-fluid model). To complete the formulation of such a model, additional relations must be supplied in the form of interfacial transfer closure laws; however, there is little information about these laws. Most existing models describing the interactions between the phases were developed for single-component systems (steam/water mixtures). The use of these relations for multicomponent hydrocarbon mixtures is not justified in most cases.
In this article, an attempt is made to describe the wellbore flow with a simplified two-phase flow model. This model assumes thermal equilibrium between the phases but allows for mechanical nonequilibrium.10 The basic flow equations are formulated with the lumped-parameter method. Example cases of calculations are presented to illustrate the capabilities of the model developed based on this approach.
Equations describing the flow in the wellbore are different from those that model reservoir flow. The Navier-Stokes equation of momentum is used in the wellbore model, while the Darcy type flow is usually assumed in the reservoir model. Hence, if both models are numerical, each set of equations should be solved separately to avoid an increase in the calculation time. In this article, an effective numerical procedure is proposed to couple the reservoir model with the wellbore model.
|File Size||1 MB||Number of Pages||6|