An Analytical Concept of the Static and Dynamic Parameters Of Intermittent Gas Lift
Authors: White Gerald W. , O&apos;Connell Bryan T. , Davis Roy C. , Berry Robert F. , Stacha Leon A. 
Published: December 2007

Abstract
An analytical method for describing the events of pressure, velocity and liquid fall-back in relation to time and other well variables from initial injection to completion of an intermittent gas-lift cycle is presented herein. Development of the method proceeded from mathematical postulates verified first by the construction of an electronically instrumented model, using the principles of dynamic similarity, and later by actual field data.Application of the method to intermittent gas-lift installation design is achieved by organizing well parameters into dimensionless ratios and applying the mathematical system to describe the results of gas injection. The method permits definition of optimum values of pressure, submergence, injection rate and volume, slug velocity, depth of injection, point of cut-off, production per cycle and gas-liquid ratio for a particular well setting and set of formation characteristics. To obtain this definition, the production of a slug of fluid has been divided into three successive intervals. Three systems of differential equations, each continuous over one of the intervals, were derived and subjected to verification. The discovery of a natural constant in the gas-liquid system has resulted in major simplification of the mathematical system for design work.Correlative data are presented from past recorded installations as well as from current field tests.

Introduction
Examination of the geometry of an oil well during the process of delivery of a slug of fluid by gas injection reveals some interesting and important relationships. It has long been recognized that more efficient gas lift occurs when the slug arrives at the surface intact, in advance of gas bubble breakthrough. This implies that the velocity with which the liquid slug travels to the surface is sufficient to surface with solid fluid before the gas bubble penetrates all of the slug. For a proper understanding of intermittent gas lift, the relationships of pressure, volume and velocity with respect to time at various points throughout the system must be defined. For this definition, the production of a slug of fluid will be divided into three successive intervals, and three systems of equations-each continuous over one of the intervals-will be derived. Much work has previously been done in relating these variables and others in the steady-state systems of constant flow, but the unsteady-state nature of intermittent flow has made analytical solutions very difficult to obtain.One of the most important tools in present-day fluid mechanics for the analysis of complex flow systems is a dynamically similar model. Reduction of a system to a dynamically similar model enables research to fill the gap between the theoretical calculation and the predicted results. An important item of experimental data in this paper is the evaluation of the velocity with which a gas bubble penetrates liquid above in vertical conduits. It has been necessary both to evaluate vb for various systems and to correlate it to other gas-lift dimensionless ratios. Two basic assumptions were made and verified by experimentation:the slug velocity v, reaches an essentially constant value very rapidly; andthe velocity at which the top of the gas bubble penetrates the liquid above is constant.

THEORY AND DEFINITIONS
Fig. 1 represents a very basic schematic drawing of an intermittent gas-lift well before, during and after an injection cycle.
JPT
P. 301^