A Mechanistic Heat Transfer Model for Vertical Two-Phase Flow
Authors: Manabe Ryo , Wang Qian , Zhang Hong-Quan , Sarica Cem , Brill James P. 
Published: December 2007

Abstract
Convective heat transfer for vertical gas-liquid two-phase flow was investigated experimentally and theoretically.
Experimental data on convective two-phase heat transfer were acquired with a crude oil-natural gas system at cooling conditions using a large diameter (2.067-in I.D.), high pressure (450 psia) test facility. Flow pattern dependencies of convective heat transfer with changing liquid and gas velocities were revealed.
A comprehensive mechanistic heat transfer model was developed by flow pattern dependent approach for bubbly, intermittent and annular flow in vertical pipes. The model is capable of predicting flow pattern first and then predicting hydrodynamics and heat transfer based on the predicted flow-pattern.
Comparing with experimental data, the model is found to predict two-phase flow heat transfer coefficient within ±26% error for all flow patterns showing a better overall performance than existing correlations.

Introduction
As oil and gas production moves to deepwater environments, production systems with subsea completions and tiebacks to existing platforms have become common occurrences. In such systems, long-distance transportation of unprocessed reservoir fluids, which are normally multiphase systems, from the reservoir to downstream process facilities, must be assured. In order to optimize the design and operation of such systems, engineers must understand how petroleum fluids behave, both hydrodynamically and thermally, during transportation. In particular, wax deposition during transportation of waxy crudes is found to be sensitive to convective heat transfer1.
Experimental data2–5 on two-phase heat transfer were reported for a variety of fluids, gas and liquid flow rates, pipe diameter, inclination, and flow patterns. There are a number of single-phase heat transfer correlations6 and prediction methods2,3,6–9 available in the literature for two-phase heat transfer. Convective heat transfer in gas-liquid two-phase flow clearly depends on the resulting flow patterns under given operating conditions. Therefore, the prediction models must be able to predict the resulting flow pattern first, and predict the hydrodynamics and heat transfer for the specific flow pattern.
The Tulsa University Paraffin Deposition Project (TUPDP) developed a prediction method for two-phase heat transfer that combined two-phase flow pattern and hydrodynamics mechanistic models and flow-pattern-dependent heat transfer correlations1. Based on a comparison with a set of published experimental data, Aggour3 correlation for bubbly flow; Rezkallah-Sims5 correlation for intermittent flow and Ravipudi-Godbold7 correlation for annular flow were recommended by Kim et al.10.
Multiphase flow modeling moved from correlation approach to mechanistic approach. Although comprehensive flow pattern and hydrodynamics models are available11–13, no adequate heat transfer models exist. Moreover, no available experimental data on two-phase heat transfer in crude oil - natural gas systems with cooling conditions under high pressure conditions were found. Mechanistic models for improved prediction of two-phase convective heat transfer are needed.
In this paper, a comprehensive mechanistic model for vertical upward two-phase flow convective heat transfer is proposed. The following sections present a summary of the experimental and modeling studies.

Experimental Study

Test Facility and Heat Transfer Measurement Method
South Pelto crude oil (35° API gravity) was used as the liquid phase. Natural gas supplied by Oklahoma Natural Gas Company was used as the gas phase. The Prandtl numbers of the liquid and gas phases were 32&lt;PrL&lt;42, and Prg~0.74, respectively.