Single-and Two-Phase Fluid Flow in Small Vertical Conduits Including Annular Configurations
Authors: Gaither Orville D. , Winkler Herald W. , Kirkpatrick C.V. 
Published: December 2007

Abstract
This paper is an analytical study of the flow of fluids through small vertical conduits. Small conduits are defined as 1 1/4-in. nominal diameter tubing size and smaller, and approximately twice this area for annular conduits (i.e., 1- × 2 1/2-in. annulus and smaller). Experimental data are presented for the 1- × 2-in. and 1 1/4- × 2 1/2-in. annuli, and the 1-in. and 1 1/4-in. tubing, since these represent the small conduit sizes and configurations generally encountered in oilfield applications. Data have been gathered for these conduits for single-phase water, single-phase gas and two-phase water-gas mixtures, with particular emphasis on high gas-liquid ratios. Water rates in excess of 2,000 B/D and gas rates in excess of 2.5 MMcf/D, and two-phase flow ratios in between these two, represent the scope of the data gathered. Existing equations have been applied to predict flowing pressures and compared with experimental data. New correlations have been developed.

Introduction
The increased economic pressure on the domestic oil industry in the United States has constantly required the use of new techniques and equipment designed to reduce the cost of finding and producing oil and gas. Since tangible items are most readily apparent in economic analysis, the advent of lower-cost well completions was inevitable. One of the methods used to reduce costs which has received widespread attention is the slim-hole completion technique where tubing is used as the well casing and in which small conduits are used for tubing if necessary. Small conduits, defined by Kirkpatrick as "1 1/4-in. diameter nominal tubing and smaller for tubing flow and less than twice the 1 1/4-in. diameter nominal tubing internal flow area for annulus flow", have also found widespread usage as siphon strings for dewatering gas wells and as "kill" strings in deep high-pressure oil and gas wells.The growing use of small-diameter tubing has resulted in an increased need for development of improved methods to measure or predict flowing bottom-hole pressures since the physical dimensions generally preclude the use of subsurface-recording pressure gauges. Even in the cases where small bombs are available, the relatively high velocities encountered at nominal flow rates make it necessary to use excessive weight bars or special hold-down devices.Attempts to use recognized correlations to accurately predict flowing or gas-lift performance in wells equipped with small conduits have been generally unsuccessful. Insufficient field data were available to allow the development of a correlation on this basis, and an experimental approach was applied in an attempt to obtain a workable relation. The experimental approach used to obtain the data presented in this paper was actually a compromise between a field installation and a laboratory study. A test well 1,000 ft in length was used to obtain flow data on single-phase liquid, single-phase gas and two-phase water/gas flowing mixtures. Liquid rates up to 2,200 B/D and gas rates up to 3 MMcf/D were used in the single-phase flow studies. Two-phase flow rates from 100 to 600 B/D with gas-liquid ratios from 500 to 8,000 cu ft/bbl were recorded. Experimental data were obtained for single- and two-phase flow through 1-in and 1 1/4-in. nominal tubing, and through the annuli between 1- and 2-in. and 1 1/4- and 2 1/2-in. nominal tubing strings.Experimental results for the two-phase flow are compared to the Poettmann-Carpenter correlation which is widely used as a comparative standard for development of multiphase flow predictions in flowing and gas-lift wells. Correlations developed by Tek, Baxendell and Thomas were also investigated. The experimental data recorded herein fell in between the two flow regimes as defined by Ros, and this correlation also failed to yield satisfactory results. The fact that existing correlations failed to confirm the experimental data led to the need for development of a new correlation.Although a two-phase flow study was the primary objective of this investigation, data were also recorded for single-phase flow of water and gas, and constants were developed relating to pipe roughness and equivalent diameters for annular flow. These single-phase studies assisted materially in the development of certain of the two-phase flow results.Considerable previous work has been published which presented relationship of surface measurements to bottomhole condition. The works of Buthod and Whiteley, Jones, Poettmann and the Texas Railroad Commission are classic examples of the successful use of mathematical relationships which allow acceptable predictions of subsurface pressures, when gas is the flowing fluid. Darcy and others have derived relationships which may be used with minor modifications to predict subsurface flowing conditions in injection and water-supply wells.
JPT
P. 309^