Fluid temperature enters into a variety of petroleum production–operations calculations, including well drilling and completions, production facility design, controlling solid deposition, and analyzing pressure-transient test data. In the past, these diverse situations were tackled independently, using empirical correlations with limited generality.
In this review paper, we discuss a unified approach for modeling heat transfer in various situations that result in physically sound solutions. This modeling approach depends on many common elements, such as temperature profiles surrounding the wellbore and any series of resistances for the various elements in the wellbore. We show diverse field examples illustrating this unified modeling approach in solving many routine production–operations problems.
The most prominent aspect of multiphase flow is the variation in the physical distribution of the phases in the flow conduit known as the flow pattern. Several different flow patterns can exist under different flow conditions which have significant effects on liquid holdup, pressure gradient and heat transfer. Gas–liquid two-phase flow in an annulus can be found in a variety of practical situations. In high rate oil and gas production, it may be beneficial to flow fluids vertically through the annulus configuration between well tubing and casing.
The flow patterns in annuli are different from pipe flow. There are both casing and tubing liquid films in slug flow and annular flow in the annulus. Multiphase heat transfer depends on the hydrodynamic behavior of the flow. There are very limited research results that can be found in the open literature for multiphase heat transfer in wellbore annuli.
A mechanistic model of multiphase heat transfer is developed for different flow patterns of upward gas–liquid flow in vertical annuli. The required local flow parameters are predicted by use of the hydraulic model of steady-state multiphase flow in wellbore annuli recently developed by Yin et al.
The modified heat-transfer model for single gas or liquid flow is verified by comparison with Manabe’s experimental results. For different flow patterns, it is compared with modified unified Zhang et al. Model based on representative diameters. IntroductionAs oil and gas development moves from land or shallow water to deep and ultradeep waters, multiphase flow occurs during production and transportation (Chen ). The flow normally occurs in horizontal, inclined, or vertical pipes and wells. Gas–liquid two-phase flow in an annulus can be found in a variety of practical situations.
In high rate oil and gas production, it may be beneficial to flow fluids vertically through the annulus configuration between well tubing and casing. For surface facilities, some large, under-utilized flow lines can be converted to dual-service by putting a second pipe through the large line (i.e., flowing produced water in the inner line and gas in the annulus). During gas production, liquids may accumulate at the bottom of the gas wells during their later life. In order to remove or “unload” the undesirable liquids, a siphon tube is often installed inside the tubing string, which would form a gas–liquid two-phase flow in the annulus. Flow-assurance problems, such as hydrate blocking (Jamaluddin et al.; Li et al.; Wang et al., ) and wax deposition (Zhang et al.; Bryan; Theyab and Diaz ), are strongly associated with both the hydraulic and thermal behavior. For example, they are related to the fluid velocity, liquid fraction, slug characteristics, pressure gradient and convective-heat-transfer coefficients of different phase and flow patterns in multiphase flow.
Heat Transfer Definition
Therefore, multiphase hydrodynamics and heat transfer in an annulus need to be modeled properly to guide the design and operation of flow systems.Compared to theoretical studies of multiphase hydrodynamics (Liu et al.; Wang and Sun ), and multiphase heat transfer in pipe flow (Zheng et al.; Gao et al.; Karimi and Boostani; Rushd and Sanders ), there are very limited research results in the open literature for multiphase heat transfer in wellbore annuli. obtained a model for calculating the local Nusselt numbers of stratified gas/liquid flow in turbulent liquid/turbulent gas conditions. The model was tested with heat-transfer experiments for air/water flow in a 63.5-mm inside diameter (ID) tube. established a mathematical model of heat transfer in a gas-drilling system, considering the flowing gas, formation fluid influx, Joule–Thomson cooling and entrained cuttings in the annular space. However, the multiphase flow effect on the heat transfer was not considered.Shoham, et al.
undertook experiments on heat-transfer for slug flow in a horizontal pipe. He found a substantial difference in heat-transfer coefficient existed between the top and bottom of the slug. Developing heat-transfer correlations of different flow patterns was the aim of most previous studies (Shah ). Twenty heat-transfer correlations were compared in Kim’s study (Kim et al. He collected the experimental data from the open literature and recommended the correlations for different flow patterns.
However, the errors with the experimental results by Matzain were large. Later, a comprehensive mechanistic model about heat transfer in gas–liquid pipe flow was obtained (Manabe ). It was compared with the experimental data, and the performance was better. However, there were some inconsistencies in annular and slug flow. It needed to be modified.Zhang et al. developed a unified model of multiphase heat transfer for different flow patterns of gas–liquid pipe flow at all inclinations – 90° to + 90° from the horizontal. The required local flow parameters were predicted by use of the unified hydrodynamic model for gas/liquid pipe flow developed by Zhang et al.
However, it is not fit for the gas–liquid flow in an annulus, because the flow patterns in annuli are different from pipe flow patterns, as seen in Fig. A new heat-transfer model for gas–liquid flow in vertical annuli needs to be established. Flow patterns for upward vertical flow in an annulus (Caetano )A hydraulic model was developed to predict flow patterns, liquid holdup and pressure gradients for steady-state gas–liquid flow in wellbore annuli (Yin et al. ).
The major advantage of this model compared with previous mechanistic models is that it is developed based on the dynamics of slug flow, and the liquid-film zone is used as the control volume. The effects of the tubing liquid film, casing liquid film and the droplets in the gas core area on the mass and momentum transfers are considered. Multiphase heat transfer depends on the hydrodynamic behavior of the flow.
The objective of this study is to develop a heat-transfer model for gas–liquid flow that is consistent with the hydrodynamic model in vertical wellbore annuli. 16where T ei is the temperature of formation at wellbore intake, °C; g e is the formation thermal gradient, °C/100 m; L is the depth, m.If Eq. is used for the riser of an offshore production well, then the surrounding sea temperature is not a linear function of depth. It will be calculated according to the actual environment (Wang and Sun ).If, for a certain segment of the wellbore, U a, c p, η l, g e, θ, v ld v l/d l and d p/d l can be approximately constants, combining Eqs. and and integrating, yields an explicit equation for the temperature.
Overall flowchart for present modelBased on flow patterns, further calculations are performed in different subroutines. If the flow pattern is single-phase flow, single-phase heat-transfer calculation will be performed; if the flow pattern is bubble or dispersed-bubble flow, the corresponding hydraulic model and heat-transfer model will be called for calculation.
For annular flow, corresponding hydraulic and heat-transfer calculations will be made. For slug flow, corresponding hydraulic and heat-transfer calculations will be made, as seen in Fig. Figure is the flowchart for the present annular flow heat-transfer model. Comparison of single-phase liquid flow model simulations and measured convective-heat-transfer coefficientsThere are few experimental research results in the open literature for multiphase heat transfer in annuli. The unified Zhang et al. Model (2006) is verified by comparison with Manabe’s experimental results for different flow patterns in a crude-oil/natural gas system, and good agreement has been observed in the comparison.
So, the unified Zhang et al. Model is modified to calculate the heat transfer of gas–liquid flow in annuli based on the “hydraulic diameter” of the annuli, Eq. , and the results are compared with the present mechanistic heat-transfer model for gas–liquid flow in annuli.Figures, and are comparisons of convective-heat-transfer coefficient for bubble flow, annular flow and slug flow predicted by the present model and the modified unified Zhang et al. For the bubble flow, the data points are located inside the 10% error band. The agreement is good. It shows that the influence of annulus geometry is small for the low gas volume fraction. For the annular and slug flow in annuli, most of the data points are located inside the 30% error band and all are overestimated. It may because there is a tubing liquid film and a casing liquid film in the wall and the geometry is different from the modified unified Zhang et al. model.
It may cause the hydraulic parameters and fluid physical properties to change a lot, leading to larger convective-heat-transfer coefficients. Conclusions and discussionA heat-transfer model for gas–liquid flow in vertical annuli is developed in conjunction with the mechanistic hydrodynamic model of Yin et al. , which can predict flow pattern transitions, liquid holdup, gas void fraction, pressure gradient, and slug characteristics in gas–liquid two-phase flow in vertical annuli. The heat-transfer modeling is based on energy-balance equations and analyses of the temperature differences and variations in the tubing liquid film, casing liquid film, gas core, Taylor bubble and slug body.The heat-transfer model for single gas or liquid flow is verified by comparison with Manabe’s experimental results. Good agreement has been observed in the comparison. For different flow patterns, it is compared with unified Zhang et al. Model modified based on “hydraulic diameter”.
For bubble or dispersed-bubble flow, the error is lower than 10%. With the gas void fraction and gas flow velocity increasing, the error will be larger but lower than 30%. In other words, the difference between the new model and modified unified Zhang et al. model will be small if the gas void fraction and velocity is small. The difference will be large when it changes. The modified method based on “hydraulic diameter” is no longer applicable for slug and annular flow in vertical annuli when the gas void fraction increases. It may be 1.3 times larger than the new model. Experimental investigations of heat transfer in vertical are required to improve the model performance.
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