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Summary This paper presents an analytic model for computing the wellbore-fluid-temperature profile for steady fluid flow. Although wells with a constant-deviation angle can be handled with existing analytic models, complex well architectures demand rigorous treatment. For example, changing geothermal-temperature-gradient and deepwater wells present significant challenges. Additionally, available analytic models rarely provide calculation methods for various required thermal parameters, such as the Joule-Thompson (J-T) coefficient and fluid expansivity. The approach taken in this study entails dividing the wellbore into many sections of uniform thermal properties and deviation angle. The governing differential equation is solved for each section, with fluid temperature from the prior section as the boundary condition. This piecewise approach makes the model versatile, allowing step-by-step calculation of fluid temperature for the entire wellbore. We present simple, thermodynamically sound approaches for estimating thermal parameters. Success is indicated when performance of the proposed model is compared with data from three wells, producing two-phase gas/oil mixture, single-phase oil, and single-phase gas. Sensitivity of the estimated fluid temperatures to various thermal properties is also examined with our model. Overall, the effects of the J-T coefficient and liquid expansivity are found to be significant. Introduction Modeling fluid-temperature and density profiles in wellbores is crucial for the design of production tubulars and artificial-lift systems, gathering pressure data for real-time reservoir management, and estimating flow rates from multiple producing horizons with distributed-temperature sensors. Significant advances have occurred in wellbore-fluid-temperature modeling since the pioneering work of Ramey (1962). Ramey's work addressed single-phase flowing-fluid temperature in a line-source well. In this regard, models of Alves et al. (1992), Sagar et al. (1991), and Hasan and Kabir (1994) are worthy of note. In particular, these models extended application to two-phase flows. Yet, the available analytic models are inadequate for direct application to modern directional wells that traverse formation with significantly varying thermal properties with multiple changes in deviation angles. In such cases, even the simple task of estimating geothermal temperature as a function of measured depth (MD) becomes nontrivial. Obviously, geothermal gradient strongly influences heat loss of wellbore fluids, requiring careful piecewise computation. The solution presented in this paper addresses these issues and lends itself to user-friendly spreadsheet computations, if one so chooses.
A Simple Model for Annular Two-Phase Flow in Wellbores
Hasan, A. Rashid (U. of Minnesota) | Kabir, C. Shah (Chevron Corp.)
Summary Annular flow is associated with production from both gas-condensate and geothermal wells. Oil wells also experience it during high-gas-to-oil-ratio (high-GOR) production. The current semimechanistic modeling approach requires estimation of film thickness before computing frictional pressure drop as gas flows past the wavy-liquid film surrounding the pipe wall. This study intends to investigate this film thickness and its impact on pressure-drop computation in wellbores producing steam-water, gas-condensate, and gas-oil mixtures. Computational results show that this dimensionless liquid-film thickness is most likely less than 0.06 in annular flow. For such values of thin-film thickness, the computed friction factor is only slightly higher than that estimated with a smooth-channel assumption. When the homogeneous model is used to compute pressure gradient by ignoring the wavy-liquid film on frictional pressure drop, good agreement is achieved with field data and with the predictions of a semimechanistic model. Introduction Annular flow is dominant in gas-condensate and geothermal wells. Oil wells also experience annular flow when high-GOR production occurs after gas breakthrough or when gas lift is installed. In general, the annular-flow pattern consists of a gas core in the middle of the flow string with a thin liquid film flowing up the pipe wall. Two issues appear to dominate the modeling needs. One needs to estimate, first, the liquid entrainment in the gas core, and second, the frictional resistance that the gas core experiences when flowing past the wavy-liquid film. Note that the frictional gradient is a very large contributor to the total pressure loss in annular flow and therefore has obvious importance. In the past, a few models treated this flow pattern assuming zero slip between the two phases in the gas core. For instance, the models of Duns and Ros (1963) and Aziz et al. (1972), who essentially adopted the Duns and Ros approach, fall into this category. Subsequently, the method of Hasan and Kabir (1988), based on the approach of Wallis (1969), estimates both the entrainment and the film-friction factors. However, the rigorous method of Ansari et al. (1994) is rooted in sound modeling of film thickness followed by accurate estimation of frictional and hydrostatic heads. The same approach was adopted by Kaya et al. (2001). At approximately the same time, Gomez et al. (2000) proposed a method based on a two-fluid approach. The intent of this study is to present an alternative approach to modeling annular flow. We show that the liquid-film thickness is generally too small to be of any consequence when computed with the model of Ansari et al. (1994). The main objective is to demonstrate the application of a much simpler model with accuracy comparable to a semimechanistic model. In fact, the authors' recent study (Kabir and Hasan 2006) on gas-condensate wells has shed some light on the possibility of simplified modeling of annular flow.
- Research Report > New Finding (0.48)
- Research Report > Experimental Study (0.34)
- North America > United States > Texas > Permian Basin > Midland Basin > Steen Field (0.89)
- North America > Canada > Northwest Territories > Wallis Field (0.89)
- Well Drilling > Drilling Operations (1.00)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Gas-condensate reservoirs (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics (1.00)
- Reservoir Description and Dynamics > Fluid Characterization > Phase behavior and PVT measurements (1.00)
Summary Predicting long-term reservoir performance with realistic wellbore models is fraught with uncertainty owing to the complexity of two-phase flow. That is because even a calibrated two-phase-flow model departs from its expected performance trend when changes in flow conditions occur. These inevitable changes include gas/liquid ratio, wellhead pressure, and flowline pressure with time, among others. Influx of water further exacerbates the prediction problem. This study explores the possibility of using simplified approaches to compute bottomhole pressure (BHP) from wellhead pressure (WHP), measured rates, gravity of producing fluids, and tubular dimensions. BHP computations on three independent data sets comprising 167 gas/condensate-well tests suggest that the no-slip homogeneous model applies quite well. Statistical results show the homogeneous model compares quite favorably with mechanistic two-phase-flow models. However, the main advantage of the simplified model is that its recalibration with field data is not required because the gas/oil ratio increases with time, thereby making the model increasingly reliable. Most field data sets suggest random error in BHP calculations; uncertainty in rate measurements appears to be the most probable cause. High-gas-liquid-ratio (GLR) systems can tolerate large errors in rate measurements, but low-GLR wells demand greater accuracy because of increasing importance of the hydrostatic head. Introduction Two-phase-flow modeling for gas/condensate wells has not received as much attention as that for oil wells. Recent SPE books (Brill and Mukherjee 1999; Hasan and Kabir 2002) on this topic make very little mention of this flow condition, presumably because modeling is supposed to conform to that offered for oil wells. This study probes this premise, among other issues. The popular Gray correlation (User's Manual for API 14B 1978) appears to do a good job in most gas/condensate wells. However, applicability of this correlation outside the bounds of its specified parameters remains unclear. Take the upper limits of condensate/gas ratio (CGR) of 50 STB/MMscf, or flow-string diameters of 3.5 in., for instance. Questions arise whether one should use a different model when one of these criteria, as set by Gray, is not met. Boundaries of applicability often get violated beyond a correlation's original intent; Gray's correlation is no exception in this regard. Practicality demands that a user specifies one computational approach for flow in pipes when long-term integrated reservoir/wellbore/flowline performance is sought over a field's producing life. Declining CGR and increasing water production with time have the potential to complicate any modeling effort. What also remains unclear is how to treat the multicomponent fluid mixture entering the wellbore/flowline system after undergoing compositional calculations in the reservoir. Besides the two-component gas/liquid Gray correlation (User's Manual for API 14B 1978) other approaches have emerged for modeling gas/condensate flow. The semimechanistic model of Govier and Fogarasi (1975) represents the multicomponent approach with flash calculations. In contrast, the wet-gas concept offered by Peffer et al. (1988) suggests extreme pseudoization with single-component gas. Nonetheless, the simplified approach of Peffer et al. with good accuracy is appealing. A minor drawback of both methods is exclusion of the accelerational term, which may be significant in wells producing fluids at high GLR. This paper advocates the use of a two-component homogeneous model to circumvent issues with any rigorous two-phase-flow modeling, such as delineating flow-pattern boundaries, estimating slip between phases, and doing flash calculations. We show that Gray's correlation is essentially a homogeneous model, and the model of Ansari et al. (1994) also simplifies to a homogeneous model when mist flow is assumed in gas/condensate wells. The steady-state version of the transient simulator OLGA (Bendiksen et al. 1991) also lends support to the notion of homogeneous modeling.
- Research Report > New Finding (0.34)
- Research Report > Experimental Study (0.34)