The Effect of Liquid Viscosity in Two-Phase Vertical Flow
Authors: Hagedorn Alton R. , Brown Kermit E. 
Published: December 2007

Abstract
Continuous, two phase flow tests have been conducted during which four liquids of widely differing viscosities were produced by means of air-lift through 1 1/4 -in. tubing in a 1,500-ft. experimental well. The purpose of these tests was to determine the effect of liquid viscosity on two-phase flowing pressure gradients. The experimental test well was equipped with two gas-lift valves and four Maihak electronic pressure transmitters as well as instruments to accurately measure the liquid production. air injection rate, temperatures, and surface pressures. The tests were conducted for liquid flow rates ranging from 30 to 1,680 B/D at gas-liquid ratios from 0 to 3,270 scf/bbl. From these data, accurate pressure-depth traverses have been constructed for a wide range of test conditions. As a result of these tests, it is concluded that viscous effects are negligible for liquid viscosities less than 12 cp, but must be taken into account when the liquid viscosity is greater than this value. A correlation based on the method proposed by Poettmann and Carpenter and extended by Fancher and Brown has been developed for 1 1/4 -in. tubing, which accounts for the effects of liquid viscosity where these effects are important.

Introduction
Numerous attempts have been made to determine the effect of viscosity in two-phase vertical flow. Previous attempts have all utilized laboratory experimental models of relatively short length. One of the initial investigators of viscous effects was Uren with later work being done by Moore et al. and more recently by Ros. However, the present investigation represents the first attempt to study the influence of liquid viscosity on the pressure gradients occurring in two-phase vertical flow through a 114-in., 1,500 ft vertical tube. The approach of some authors has been to assume that all vertical two-phase flow occurs in a highly turbulent manner with the result that viscous effects are negligible. This has been a logical approach since most practical oil-well flow problems have liquid flow rates and gas-liquid ratios of such magnitudes that both phases will be in turbulent flow. It has also been noted, however, that in cases where this assumption has been made, serious discrepancies occur when the resulting correlation is applied to low production wells or wells producing very viscous crudes. Both conditions suggest that perhaps viscous effects may be the cause of these discrepancies. Ia the first case, the increased energy losses may he due to increased slippage between the gas and liquid phases as the liquid viscosity increases. This is contrary to what one might expect from Stokes law of friction, but the same observations were made by Ros who attributed this behavior to the velocity distribution in the liquid as affected by the presence of the pipe wall. In the second case, the increased energy losses may be due to increased friction within the liquid itself as a result of the higher viscosities. The problem of determining the liquid viscosity at which viscous effects becomes significant is a difficult one. Ros' has indicated that liquid viscosity has no noticeable effect on the pressure gradient so long as it remains less than 6 cstk. Our tests have shown that viscous effects are practically negligible for liquid viscosities less than approximately 12 cp. Actually there is no single viscosity at which these effects become important. These effects are not only a function of the viscosities of the liquids and of the gas hut are also a function of the velocities of the two phases. The velocities in turn are a function of the in situ gas-liquid ratio and liquid flow rate. Furthermore, the role of fluid viscosities in either slippage or friction losses will depend on the mechanism of flow of the gas and liquid, i.e., whether the flow is annular, as a mist, or as bubbles of gas through the liquid. These mechanisms are also a function of the in situ gas-liquid ratios and the flow rates. It would thus seem that the best one could hope for is to determine a transition region wherein the viscous effects may become significant for gas-liquid ratios and liquid production rates normally encountered in the field. The viscous effects might then be neglected for liquid viscosities less than those in the transition region but would have to be taken into account when higher viscosities are encountered. There are numerous instances where crude oils of high viscosity must be produced. The purpose of this study has been to evaluate the effects of liquid viscosities on two-phase vertical flow by producing four liquids of widely differing viscosities through a 1 1/4 -in. tube by means of air-lift.
JPT
P. 203ˆ