Description of Case

Nonboiling two-phase flow has many industrial applications, such as the flow of oil and natural gas in flow lines and wellbores, in which knowledge about nonboiling two-phase, two-component (liquid and permanent gas) heat transfer is required. During the production of two-phase hydrocarbon fluids from an oil reservoir to the surface, the temperature of the hydrocarbon fluids changes as a result of the difference in temperatures between the oil reservoir and the surface. The change in temperature results in heat transfer between the hydrocarbon fluids and the earth surrounding the oil well, and the ability to estimate the flowing temperature profile is necessary to address several design problems in petroleum production engineering.

Statement of Problem

In subsea oil and natural gas production, hydrocarbon fluids may leave the reservoir with a temperature of 75°C and flow in the subsea surrounding of 4°C.¹ As a result of the temperature gradient between the reservoir and the surrounding, knowledge about heat transfer is critical to prevent gas hydrate and wax deposition blockages.² Wax deposition can result in problems, including reduction of inner pipe diameter, causing blockage; increased surface roughness of pipes, leading to restricted flow line pressure; a decrease in production; and various mechanical problems.³ Some examples of the economic losses caused by wax deposition blockages are  as follows: The direct cost of removing the blockage from a subsea pipeline was $5 million, production downtime loss in 40 days was $25 million,⁴ and the cost of oil platform abandonment by Lasmo PLC (United Kingdom) was $100 million.⁵

One way of estimating heat transfer for nonboiling two-phase flow in pipes is to use empirical correlations. Numerous heat transfer correlations and experimental data for forced convective heat transfer during gas-liquid two-phase flow in vertical and horizontal pipes have been published over the last five decades. Through the use of a comprehensive literature search,⁶ it was concluded that there is no single correlation that is capable of predicting the heat transfer coefficient in two-phase flow involving different gas-liquid fluid combinations in various pipe orientations. Thus, a general heat transfer correlation for nonboiling two-phase flow in pipes is needed.

Description of Solution

In order to predict the heat transfer coefficient in two-phase flow regardless of flow pattern, gas-liquid combination, and pipe inclination angle, a general heat transfer correlation has been developed^7,8:

The flow pattern factor (F_p) and inclination factor (I ^*) are given as

where

subscripts l and g refer to the liquid phase and gas phase

D = tube diameter, m

g = gravitational acceleration, m/s²

h_l = liquid-phase heat transfer coefficient = , W/m²×K

h_tp = two-phase flow heat transfer coefficient, W/m²×K

k = thermal conductivity, W/m×K

= mass flow rate, kg/s

Pr = Prandtl number

Re_l = in situ liquid Reynolds number =

V = velocity, m/s

x = flow quality = /(+)

a = void fraction

r = density, kg/m³

m = dynamic viscosity (subscripts b and s refer to the bulk mean and surface temperatures for the evaluation of viscosity), kg/m×s

s = surface tension, N/m

q = inclination angle, rad

The values of the void fraction (α) used in Equation (2) is calculated on the basis of the correlation provided by Woldesemayat and Ghajar,⁹ which was developed in the context of the drift flux method:

where P_sys and P_atm are the system and atmosphere pressures in N/m², respectively, and V_sl and V_sg are the superficial liquid and gas velocities in m/s, respectively.

The heat transfer correlation [Equation. (1)] was developed from a database of experimental data points for different flow patterns, inclination angles, and gas-liquid combinations and is applicable over the following range of parameters: 750 £ Re_sl £ 127,000, 14 £ Re_sg £ 209,000, 9.99 ´ 10^-3 £ Pr_g / Pr_l £ 148 ´ 10^-3, and 3.64 ´ 10^-3 £ m_g/m_l £ 26.3 ´ 10^-3, where Re_sl and Re_sg are the superficial liquid and gas Reynolds numbers, respectively.

Description of Results

The general two-phase heat transfer correlation [Equation (1)] was validated with a total of 986 experimental data points (176 data points for horizontal flow, 555 data points for inclined flow, and 255 data points for upward vertical flow). The 986 experimental data points were compiled from various sources with different experimental facilities. Among all the 986 experimental data points, Equation (1) has successfully predicted 90% of the data points within ±25% and 94% of the measured data within an error band of ±30%, as shown in Figure 1. Overall, the prediction by the general two-phase heat transfer correlation has a root-mean-square deviation of 18.4% from the experimental data. For a detailed summary of this work, refer to references 7 and 8.

FIGURE 1

Comparison of the predictions by Equation (1) with all 986 experimental data points for different flow patterns, tube inclination angles, and gas-liquid combinations (from Ghajar and Tang⁸).

Wider Applicability of Results

The general two-phase heat transfer correlation [Equation (1)] is applicable to the estimation of heat transfer coefficients for nonboiling two-phase, two-component (liquid and permanent gas) flow in pipes. Intelligent oil wells that are equipped with downhole interval flow control devices allow optimization of productions for reservoirs with different complexity and flow conditions. It may be possible to incorporate the correlation presented in this article in models for the prediction of temperature distribution in intelligent wells.¹⁰

References

1. Trevisan, O. V., Franca, F. A., and Lisboa, A. C. Oil Production in Offshore Fields: An Overview of the Brazilian Technology Development Program Proceedings of the 1st World Heavy Oil Conference, Beijing, China. Paper No. 2006-437, Nov. 13–15, 2006.

2. Furuholt, E. M. Multiphase Technology: Is It of Interest for Future Field Developments? Society of Petroleum Engineers European Petroleum Conference, London, UK. Paper No. 18361, Oct. 17–19, 1988.

3. McClaflin, G. G., and Whitfill, D. L. Control of Paraffin Deposition in Production Operations. Journal of Petroleum Technology, vol. 36, no. 12, pp. 1965–1970, 1984.

4. Fogler, H. S. Paraffin Research. Porous Media Research Group, sitemaker.umich.edu/sfogler/paraffin_deposition.

5. Singh, P., Venkatesan, R., Fogler, H. S., and Nagarajan, N. Formation and Aging of Incipient Thin Film Wax-Oil Gels. AIChE Journal, vol. 46, no. 5, pp. 1059–1074, 2000.

6. Kim, D., Ghajar, A. J., Dougherty, R. L., and Ryali, V. K. Comparison of 20 Two-Phase Heat Transfer Correlations with Seven Sets of Experimental Data, Including Flow Pattern and Tube Inclination Effects. Heat Transfer Engineering, vol. 20, no. 1, pp. 15–40, 1999.

7. Ghajar, A. J., and Tang, C. C. Advances in Void Fraction, Flow Pattern Maps and Non-Boiling Heat Transfer Two-Phase Flow in Pipes with Various Inclinations, in Advances in Multiphase Flow and Heat Transfer, ed. L. Cheng and D. Mewes, vol. 1, pp. 1–52. Bentham Science Publishers, Bussum, Netherlands, 2009.

8. Ghajar, A. J., and Tang, C. C. Importance of Non-Boiling Two-Phase Flow Heat Transfer in Pipes for Industrial Applications. Heat Transfer Engineering, vol. 31, no. 9, 2010 (in press).

9. Woldesemayat, M. A., and Ghajar, A. J. Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes. International Journal of Multiphase Flow, vol. 33, pp. 347–370, 2007.

10. Muradov, K. M., and Davies, D. R. Prediction of Temperature Distribution in Intelligent Wells. SPE Russian Oil and Gas Technical Conference and Exhibition, Moscow, Russia. Paper No. 114772, October 28–30, 2008.