Experimental Study and the Development of a Mechanistic Model for Two-Phase Flow Through Vertical Tubing
Authors: Chokshi Rajan N. , Schmidt Zelimir , Doty Dale R. 
Published: December 2007

Abstract
Ah extensive experimental investigation has been carried out to measure pressure drop in a test well. Measured data was gathered from 324 tests for widely varying flow rates. The tests were conducted on a air-water system in a 3 1/2 in. diameter, 1348 ft long, vertical test section. Each data set consists of flow rate measurements, pressure and temperature measurements at eight locations along the test section, and non-intrusive holdup measurement at 490 ft below the surface using a custom-made gamma-ray densitometer. A comprehensive, mechanistic model considers three flow patterns: bubble, slug and annular. Drift flux modeling approach provides bubble to slug transition, as well as holdup and pressure gradients for bubble flow. The transition from annular to slug flow is governed by a two fluid approach based on a coaxial-cylinders model that also yields the holdup and pressure gradients for annular flow. The pressure drop prediction for slug flow is based on a mechanistic cellular model. Pressure drop predictions of the new model are compared to eight correlation/ mechanistic models using measured data and an independent data bank of 1712 data-sets. The new model performs better than the other methods yielding the smallest average error and the least scatter.

Introduction
Upward co-current flow of multiphase fluids through tubing has been a topic of significant interest in the petroleum industry. A production engineer must predict downhole flow conditions to design well tubing, well completions, surface processing facilities, surface and sub-surface control measures, and artificial lift equipment. Reservoir exploitation plans for a particular field or reservoir are also formulated based on the expected flow performance of the planned well completions in that field or reservoir.
Traditionally downhole flow predictions, involving determination of flow pattern and pressure-profile over the length of tubing are made by dividing the tubing into short sections with constant geometric characteristics. Inside each section, the pressure gradient is calculated by a hydrodynamic method after assuming a constant pressure and temperature over the section. The correlations or models used for the hydrodynamic calculations are known to be accurate at best to within 20% of the measured values. Having known about the low accuracy of these methods, the designer relies heavily on judgment when sizing facilities based on results of these methods. This practice has often resulted in overly conservative designs or a finished facility with an unplanned restriction in the production capacity.
Low accuracy of these correlations and models has been attributed to the use of either (incomplete) field data or experimental data taken from small scale laboratory setups. An alternative approach that fulfills both the issues of data quality and scaling- requires that experiments be conducted in field-scale facilities operating near to field conditions while ensuring data acquisition of the highest quality. While emphasizing quality data-acquisition in a full scale test facility, effective modeling can not be ignored. This paper presents results of such an experimental and theoretical investigation.

Experimental Program
Fig. 1 shows a schematic for a 2360 ft deep well that houses the test section. The well is cased with 10 3/4 in., J-55, 40 lb/ft, casing, and is dually completed with 2 7/8 in., EUE, 6.5 lb/ft, injection, and 3 1/2 in. 9.3 lb/ft, production tubings. There is a packer downhole at 2300 ft to create an isolated casing-tubing annulus. The test section is 1348 ft long, 3 1/2 in. nominal diameter (2.992 in. ID) tubing string through which a two-phase mixture of air-water flows in the upward direction. The test liquid, water, flows down the 2 7/8 in. tubing into the space below the packer, and then it ascends through the 3 1/2 in. tubing. P. 255