Review pubs.acs.org/EF
Review of High-Viscosity Oil Multiphase Pipe Flow Hong-Quan Zhang,* Cem Sarica, and Eduardo Pereyra McDougall School of Petroleum Engineering, The University of Tulsa, Tulsa, Oklahoma 74104, United States ABSTRACT: Heavy oil makes up a major portion of the world’s total oil resources. The high viscosity of heavy oil poses great challenges for its production and transportation through wells and pipelines. Experimental results show that the high-viscosity oil multiphase flow behaviors are very different from the low-viscosity oils. Significant discrepancies are displayed when the highviscosity oil data are compared to the available mechanistic multiphase flow models, which were developed on the basis of lowviscosity oil experimental results. In this paper, the recent experimental findings on high-viscosity oil multiphase pipe flows are reviewed in contrast to low-viscosity oil multiphase flows. These include flow pattern, pressure gradient, holdups, slug characteristics, oil/water mixing, core-annular flow, gas-lift effect, and phase distributions. Individual closure relationships in the mechanistic models are discussed in light of experimental measurements and observations with high-viscosity oils. Future experimental and modeling needs are suggested. slug (or intermittent) flow region expands significantly compared to low-viscosity liquid/gas flow. In Figure 1, the
1. INTRODUCTION Heavy oil, extra heavy oil, and bitumen make up about 70% of the world’s total oil resources of 9−13 trillion barrels. Many large development projects have been targeting heavy oil.1 The viscosity of heavy oil is significantly higher than that of light oil. Low temperature at deep water or in the arctic region also causes the viscosity of relatively light oil to increase exponentially. As the dominant transport fluid property, high oil viscosity poses great challenges for oil production and transportation through wells and pipelines. The required pressure drop is much higher compared to low-viscosity oils. When gas and/or water are involved, the multiphase flow behavior becomes more complicated and difficult to predict. Experimental results show that the high-viscosity oil multiphase flow behavior is significantly different from that of the lowviscosity oils. Most of the available mechanistic multiphase flow models were developed on the basis of low-viscosity oil experimental results. When these models were compared to high-viscosity oil data, they displayed significant differences. There have been numerous theoretical and experimental studies on low-viscosity multiphase pipe flow, with the majority focused on liquid/gas two-phase pipe flow. Many predictive tools have been developed from the early empirical correlations to the mechanistic models and to the latest unified approach.2 Comparably, much fewer studies can be found on oil/water and oil/water/gas flows. No comprehensive model has been developed for pressure gradient and holdup calculations of heavy oil multiphase flow corresponding to different flow regimes. This review will focus on the recent experimental findings on high-viscosity oil multiphase pipe flow behaviors. The individual closure relationships in the mechanistic models are discussed on the basis of experimental measurements and observations.
Figure 1. Flow pattern map and experimental observations of oil/air flow in a horizontal 2 in. pipe (μO = 0.181 Pa s).3
discrete symbols represent the flow pattern observations for oil/air flow in a horizontal 0.0508 m (2 in.) inner diameter (ID) pipe corresponding to oil viscosity μO = 0.181 Pa s. The area bounded by the continuous lines is the prediction of the unified model for slug flow by Zhang et al.2 It is seen that the predicted transition boundary between slug and annular flows is at a much higher superficial gas velocity. Assuming turbulent liquid flow, the Zhang et al.2 unified model predicts transition between slug and dispersed-bubble flows based on the balance between the total surface free energy of the gas bubbles and the total turbulent energy of
2. OIL/GAS FLOW 2.1. Flow Pattern Transitions. Using a viscous synthetic oil and air, Gokcal3 observed that oil flows slower and the average oil holdup increases with increasing oil viscosity. Because of the slower oil velocity and higher oil holdup, the © 2012 American Chemical Society
Special Issue: Upstream Engineering and Flow Assurance (UEFA) Received: January 30, 2012 Revised: April 14, 2012 Published: April 19, 2012 3979
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liquid. The turbulent energy of liquid is estimated on the basis of the shear stress at the pipe wall. At high oil viscosity, the shear stress is high but the Reynolds number of the flow is low and mostly corresponds to a laminar flow. Therefore, the turbulent dispersion is not a proper mechanism for the transition to dispersed-bubble flow. A similar problem also exists in the criteria by Taitel and Dukler4 and Barnea et al.5 for the same transition. Foletti et al.6 conducted a experimental study of viscous oil (μO = 0.896 Pa s) and air flow in a 0.022 mm ID horizontal pipe. A strong influence of fluid properties was shown from the comparison between air−water and air−oil flow pattern maps. They also compared the experimental flow pattern maps to several empirical and theoretical models and found poor agreement. Colmenares7 conducted experiments with high-viscosity liquid around the transition between slug and dispersed-bubble flows in a horizontal pipe. He did not observe any pressure fluctuation, which is typical for slug flow. However, he observed large bubbles traveling at the top of the pipe without coalescing and small bubbles traveling at the bottom of the pipe as a homogeneous mixture. Once the gas bubbles are dispersed in liquid, they can stay dispersed even if the turbulent fluctuations are low because of high viscosity. There are no systematic experimental data that demonstrate the effect of liquid viscosity on the transition to dispersed-bubble flow. Figure 2 shows a high-speed video snapshot of the film region of high-viscosity oil/gas slug flow in a 0.0525 m ID
Figure 3. High-viscosity oil/gas stratified flow in a horizontal pipe (μO, 0.15 Pa s; d, 52.5 mm; vSO, 0.2 m/s; and vSG, 5 m/s).8
shows a stratified flow, in which the bottom gas−liquid interface is very unstable. High intermittent waves are generated and broken by the gas flow. The shear stress between gas and oil is probably much higher than that in lowviscosity oil/gas flow because of the higher slippage and rougher interfacial wave structures. The interfacial friction factor correlations developed on the basis of low-viscosity oil data may not be applicable for high-viscosity oil multiphase flow. This may be the reason that the Zhang et al.2 unified model overpredicts the expansion of the slug flow area on the lower and right sides. For horizontal flow, Mata et al.9 and Gokcal3 observed that the transition boundary between slug and annular flows shifted to the left (lower superficial gas velocity) as the oil viscosity increased. This is probably also related to the interfacial phenomena. Because of possibly higher interfacial shear and liquid entrainment caused by the larger interfacial waves, a less gas flow rate (superficial velocity) is required for the transition to annular flow. The interfacial friction factor and liquid entrainment fraction are the two closure relationships intrinsically dependent upon the interfacial flow structures. Future studies need to be conducted to examine the validity of the available interfacial friction factor and entrainment fraction correlations against high-viscosity oil multiphase flow data. Model improvements or new model developments are required. 2.2. Slug Characteristics. Gokcal’s10 experiments show that the dependence of drift velocity on liquid viscosity is significant. The drift velocity decreases with an increasing liquid film height and liquid viscosity. A new drift velocity model for high viscosity oil slug flow was developed by extending the analysis by Benjamin.11 A comparison of measured translational velocities to the model by Nicklin12 shows that the performance of the model is significantly improved after the newly developed drift velocity model is implemented. Through computational fluid dynamics (CFD) simulations and dimension analysis, Ben-Mansour et al.13 suggested that the drift velocity (vD) in a horizontal pipe can be correlated using Froude, viscosity, and Eötvös numbers v Fr = D gd
Figure 2. Film region of high-viscosity oil/gas horizontal slug flow (μO, 0.15 Pa s; d, 52.5 mm; vSO, 0.2 m/s; and vSG, 1 m/s).8
horizontal pipe by Wang.8 ND 50 Lubsoil oil with viscosities between 0.15 and 0.57 Pa s (corresponding to a temperature range from 100 to 60 °F) and natural gas at 2.59 MPa (375 psig) pressure were used as the two phases. In comparison to low-viscosity oil/gas slug flow, the film height is much higher because of the low film velocity. The high liquid holdup corresponds to a high velocity difference between gas and liquid. This is the main reason that the slug flow region on a flow pattern map expands significantly for high-viscosity oil/gas flow. After a liquid slug passed, oil drains to the bottom slowly. At the same time, irregular wave structures are created on the draining oil film. The wavelength looks shorter at the top than that toward the bottom oil stream with the film thickness increase. At the interface between the gas core and the bottom oil stream, the wave amplitude appears to be much larger than that for low-viscosity oil under similar flow conditions.3,8 This becomes more prominent at higher gas velocities. Figure 3
Nμ = Eo ̈ = 3980
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through the flow loop, live oil viscosity became as low as 60% of the dead oil viscosity measured with a pipe viscometer. In comparison to experimental data, the unified model by Zhang et al.2 gives the best overall predictions for the pressure gradient and oil holdup. The flow pattern in all of the tests is predicted and assessed as intermittent flow. Akhiyarov22 also observed an interesting phenomenon in high-viscosity oil/gas upward vertical flow: the frictional pressure gradient may become positive at low oil flow rates (slug flow) (as shown in Figure 4). When this happens, the
where d is the pipe ID, μ is the liquid viscosity, ρ is the liquid density, g is the gravitational acceleration, and σ is the interfacial tension between gas and liquid. With the same oil used by Gokcal,3,10 Jeyachandra14 carried out an experimental investigation on the effect of the liquid viscosity and inclination angle (θ) on drift velocity. A total of 60 tests were conducted at different viscosities and pipe inclination angles from 0° to 90°. A closure relationship for horizontal drift velocity was developed. FrH = 0.53e−13.7Nμ
0.46
Eo 0.1 ̈
(1)
15
Joseph considered the liquid viscosity effect on the drift velocity in vertical slug flow and developed a model FrV = −
1 gd
⎛ μ ⎜4 ⎜ 3 ρr + C ⎝
4 16 μ2 grC + 9 9 (ρrC)2
⎞ ⎟ ⎟ ⎠
(2)
where rC is the radius of the cap bubble. Using the combination approach proposed by Bendiksen,16 the drift velocity in inclined pipes can be predicted by Fr = FrH cos θ + FrV sin θ
(3)
14
Jeyachandra compared this correlation to experimental measurements at different liquid viscosities and inclination angles from 0° to 90°, and good agreement was observed. Gokcal3 also observed that slug length is much shorter at high oil viscosity and decreases with increasing oil viscosity. The slug lengths are in the range of 8−13d at μO = 0.589 Pa s in a horizontal 2 in. pipe. At low oil viscosity, the range is 30−40d. A new slug length model needs to be developed that reflects the dependency upon liquid viscosity. Similar for the transition boundary between slug and dispersed-bubble flows, most of the previous models (such as those from Barnea and Brauner17 and Zhang et al.18) for the slug liquid holdup are also based on turbulent dispersion. The performances of these models are unsatisfactory when applied to high-viscosity oil slug flow, where the slug body is laminar. Nuland,19 Kora,20 and Jeyachandra14 reported an insignificant effect of the oil viscosity on slug liquid holdup once the flow in the slug body became laminar. Kora proposed a two-step correlation for the high-viscosity oil slug liquid holdup, which is strongly dependent upon the Froude number based on the mixture velocity. This reflects that the gas entrapment is probably dominated by the slug propagation and mixing with the liquid film. In an actual production system, gas bubbles dispersed in liquid may also be attributed to gas supersaturation. When pressure is reduced from saturation, gas evolves from the liquid phase and forms small bubbles, which grow as the gas continues to come out of the solution. The equilibrium is achieved when all of the gas evolves and separates completely from the liquid. Memon et al.21 pointed out that this process might take hours or days in heavy oil flow, while in a typical production system, the residence time of the heavy oil at a constant pressure is on the order of seconds to minutes. Thus, the heavy oil can be supersaturated with small bubbles. 2.3. Upward Vertical Flow. Akhiyarov22 investigated highviscosity oil/gas flow in a 0.0525 m ID upward vertical pipe. ND 50 Lubsoil oil with a viscosity of 0.1−0.5 Pa s and natural gas at a gauge pressure of 2.515 MPa were used as the two phases. He observed a significant effect of dissolved gas on the oil viscosity. After sufficient circulations of the oil and gas
Figure 4. Positive frictional pressure gradient.22
upward shear force in the film region (because of downward flow) is greater than the downward shear force in the slug body region. The pressure drop to maintain the flow is lower than the hydrostatic pressure drop after the flow is stopped with the same oil holdup. The unified model by Zhang et al.2 captures this phenomenon, although the predicted region is larger than that observed. In comparison to previous literature, the positive frictional pressure gradient behavior was also observed by Sakharov and Mokhov.23 2.4. Liquid Holdup, Pressure Gradient, and Model Predictions. In comparison to low-viscosity liquid/gas flow, the liquid holdup in high-viscosity oil/gas flow is significantly higher because of the slowdown of the oil phase. At the same time, gas flows much faster than oil. The pressure gradient increases dramatically. Foletti et al.6 compared their pressure gradient measurements to several early two-phase flow models and found the model performances unsatisfactory. Gokcal3 compared his experimental results to the recent mechanistic models, including the model by Xiao24 and the unified model by Zhang et al.2 He found considerable discrepancies in the model predictions for liquid holdup and pressure gradient. The performance of the mechanistic models is related to the adequacies of the closure relationships for highviscosity oil/gas flow, such as slug length, slug liquid holdup, interfacial friction factor, etc. Akhiyarov22 found that mechanistic model predictions are generally better when used for vertical flow than for horizontal flow. In vertical flow, the gravitational pressure gradient is the main part of the total pressure gradient. The pressure gradient prediction relies largely on the liquid holdup prediction. The mechanistic models (such as the unified model by Zhang et al.2 and the OLGA steady-state model) perform consistently better than the early empirical models. 3981
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Figure 5. Oil/water interfaces at low and high oil viscosities.
3. OIL/WATER FLOW Oil/water flow is a common occurrence in heavy oil production and transportation. Water may be naturally present in the formation or introduced by enhanced oil recovery (EOR) operations, such as steam injection. With favorable phase distribution, such as core-annular flow, water lubrication can dramatically reduce the frictional pressure gradient.25,26 In coreannular flow, oil occupies the center of the tube surrounded by a thin water annulus. The corresponding pressure drop is comparable to the flow of water only at the same total flow rate. On the basis of experimental results, Bannwart27,28 proposed criteria for the existence of stable core-annular flow and the oil volumetric fraction assuming a slip velocity ratio of 1.39 between oil and water. He also suggested using a modified mixture viscosity (μM) to represent the annulus water viscosity (HO is the oil holdup). H 1 − HO 1 − HO 1 = O + ≅ μM μO μW μW
Figure 6. Core-annular flow with oil film at μO = 0.4 Pa s.31
At a lower flow rate, the oil core becomes in contact with the top of the pipe. The flow becomes partially stratified and partially core-annular (as shown in Figure 7). Zhang and
(4)
In modeling oil/water pipe flow, the key considerations include the oil/water mixing status, interface shape, and interfacial shear, among others. In most of the existent mechanistic models, the stratified oil/water interface is simplified as flat. However, in reality, the oil/water interface is rarely flat. Figure 5 shows typical images of oil/water interfaces from the highspeed video recordings by Atmaca29 for low-viscosity oil and by Vuong30 for high-viscosity oil. It is seen that there is no distinct interface between the oil and water layers. Because of the small density difference and relatively low interfacial tension compared to gas/liquid flow, droplets are easy to be formed when the interface becomes unstable. The interface is actually corresponding to the phase inversion point. Above the inversion point, oil is continuous with dispersed water droplets. Below the inversion point, water is continuous and oil droplets are dispersed in it. Sridhar31 conducted an experimental study on high-viscosity oil/water flows in horizontal and inclined 0.0525 m ID pipes. He observed that, corresponding to a relatively high flow rate, an oil film formed on the pipe wall and extended from the top of the pipe to almost the bottom (as shown in Figure 6). Inside the oil film is a water layer that surrounds the majority of the oil in the core area. The oil core is deviated to the upper part of the pipe in horizontal flow. The formation of the oil film on the pipe wall is probably due to the wettability of the pipe inner surface.
Figure 7. Phase distribution in horizontal oil/water pipe flow (brown, oil; blue, water).
Sarica32 developed a mechanistic model to predict the wetted wall fraction and gravity center of the liquid film in gas/liquid stratified pipe flow. Similarly, the water-wetted wall fraction in oil/water flow can be modeled through the water film gravity center, which is correlated to the oil/water flow Froude number and the water film Reynolds number. In a vertical core-annular flow (as shown in Figure 8), most oil flows at the center of the pipe surrounded by a water film. The pressure gradient is much lower because of the lubrication effect of the water film. On the other hand, the viscous (laminar) oil in the core area also has a dampening effect on the turbulence in the water film. 3982
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Figure 10. Low-viscosity oil/water/air slug flow at μO = 0.02 Pa s.35
Figure 8. Phase distribution in vertical oil/water pipe flow (brown, oil; blue, water).
shows the pickup of the liquid film by the slug front of a lowviscosity oil/water/air three-phase flow.35 It is seen that the interface is smoother and the pipe surface in the gas core region is clean. At high flow rates, oil and water become fully mixed and the void fraction in the slug body becomes very high (as shown in Figure 11). Oil and water can be treated as a pseudo-single-
4. OIL/WATER/GAS FLOW Very few studies have been conducted on high-viscosity oil/ water/gas three-phase flow until very recently. Bannwart et al.33 investigated heavy oil/water/air flows in horizontal, upward vertical, and inclined 0.0284 m ID pipes. The oil has a viscosity of 34.95 Pa s. Flow patterns were identified from analogies with gas/liquid flow. In horizontal flow, the presence of gas would considerably increase the pressure loss compared to oil/water two-phase flow. On the other hand, the pressure loss would be reduced with the injection of water because of lubrication and keeping oil from touching the pipe wall. In upward vertical pipes, where the gravitational term plays an important role, the three-phase pressure drop can be reduced to as low as 5% of the single-phase oil pressure drop. Poesio et al.34 examined the effect of air on horizontal oil/water intermittent flow in a 0.021 m ID pipe. Two oils with viscosities of 0.9 and 1.2 Pa s were used. It was found that, with the increase of air superficial velocity, the total pressure drop would increase. A hybrid model for pressure drop prediction based on the Lockhart−Martinelli method was proposed and compared to experimental data. Wang8 conducted experiments of high-viscosity oil/water/ gas flows in horizontal and upward vertical 0.0525 m ID pipes. Oil with viscosities between 0.15 and 0.57 Pa s, filtered tap water, and natural gas at 2.59 MPa (375 psig) gauge pressure were used as the three phases. Figure 9 shows the film region of
Figure 11. Three-phase slug flow (μO, 0.28 Pa s; vSO, 0.3 m/s; vSW, 0.3 m/s; and vSG, 5 m/s).8
phase liquid with proper estimations of the fluid properties. Because of the high oil viscosity, the flow still demonstrates significant liquid film on the upper part of the pipe wall and large amplitude wave structures on the bottom gas−liquid interface. Figure 12 shows the measured frictional three-phase pressure gradients by Wang et al.36 versus water cut at 0.5 m/s superficial oil velocity and different superficial gas velocities. The water cut is increased by increasing superficial water velocity only. It is shown that, with the increase of superficial gas velocity, the frictional pressure gradient increases. There is a clear trend that, with the increase of water cut, the pressure gradient increases in the oil continuous region, peaks around the inversion point (at ∼20% water cut), and then decreases. At 40−50% water cut, the pressure gradient reaches the minimum
Figure 9. Film region of three-phase slug flow (μO, 0.28 Pa s; vSO , 0.1 m/s; vSW, 0.1 m/s; and vSG, 1 m/s).8
a three-phase slug flow, where oil and water are stratified. Similar to high-viscosity oil/gas two-phase slug flow, an oil film drains slowly around the gas core after the passing of a liquid slug. However, the liquid film height is lower than that in the oil/gas two-phase flow shown in Figure 2. This is mainly due to the lubrication effect of the water film at the bottom. Figure 10 3983
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gradient is significantly overpredicted because of the high oil viscosity.
5. CONCLUDING REMARKS High-viscosity oil multiphase pipe flow is significantly different from low-viscosity oils with respect to interfacial wave structures, entrainment and deposition, phase distribution, slug characteristics, oil−water dispersion, and rheology. Future experimental and theoretical studies should focus on the individual closure relationships, such as interfacial friction factor, entrainment fraction, wall contact fraction by each phase, slug length and translational velocity, gas entrapment in liquid, oil−water dispersion inversion, and effective viscosity.
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AUTHOR INFORMATION
Corresponding Author
Figure 12. Three-phase frictional pressure gradient measurements in horizontal flow at μO = 0.15 Pa s.36
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
value and then increases again. There is an optimum water cut that gives the minimum pressure gradient. The water cut increase in the oil continuous region does not reduce the pressure gradient. The minimum pressure gradient seems to move to a lower water cut with the increase of the superficial oil velocity. Probably with more oil in the pipe, core-annular-type flow can be formed and the water lubrication effect is more significant. Significant waviness is also observed in upward vertical highviscosity oil/water/gas three-phase flows. The slug length in vertical flow is much shorter (about half) than that in horizontal flow. Figure 13 shows the film regions of slug
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ACKNOWLEDGMENTS The authors thank the Tulsa University High-Viscosity Oil Projects (TUHOP) and Tulsa University Fluid Flow Projects (TUFFP) members for their financial and technical support.
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REFERENCES
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Figure 13. Film regions of three-phase upward vertical flows at μO = 0.28 Pa s.8
flows corresponding to different flow rates.8 The liquid film is thicker than that in low-viscosity liquid slug flow. It is seen that the liquid films are not uniformly distributed around the pipe. Behind a liquid slug, the liquid film falls back downward because of gravity until being picked up by the following liquid slug. The fall back velocity in the thick film area is much higher than that in the thin film area. Corresponding to the flow conditions of Figure 13, oil is dispersed in water as relatively big oil droplets. When the measured pressure gradients are compared to predictions of the mechanistic model, such as the unified model by Zhang and Sarica,37 the largest errors are normally corresponding to horizontal and near-horizontal stratified flows. The model tends to overpredict the contact area between the oil and pipe wall, and as a result, the pressure 3984
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