Hydrodynamic Model for Intennittent Gas Lifting of Viscous Oil Zelimir Schmidt, SPE, U. of Tulsa Dale R. Doty, u. of Tulsa Peter B. Lukong,* SPE. U. of Tulsa Orlando F. Fernandez, INTEVEP S.A. James P. Brill, SPE. U. of Tulsa Summary A hydrodynamic model was developed for intermittent gas lift. Simulation results were verified by experimental tests conducted with a test facility 60 ft [18 m] high and 3 in. [7.6 cm] in diameter, that used air and an oil with viscosity of 108 cp [0. 11 Pa' s]. The simulation program was also successfully applied to data gathered on an in- strumented intermittent gas-lift well. Results of the study indicate that initially the liquid slug undergoes a rapid acceleration and then accelerates at a much lower rate until the surface is reached, at which time rapid slug acceleration again occurs. This study found that a significant portion of the liquid pro- duced at the surface, sometimes more than 50%, was contributed during the afterflow (i.e., liquid recovered in the form of entrained liquid in the gas core). In addition, the study has shown that by increasing the injection pressure, a higher recovery can be achieved more rapid- ly, but only at the expense of increased gas injection. The model is also capable of predicting the casing-to- tubing pressure ratio at which a minimum GOR will oc- cur. This minimum GOR pressure ratio was found to be sensitive to fluid viscosity. Introduction Intermittent gas lift is a common artificial-lift technique for producing oil from marginal wells. EOR developments in recent years have resulted in renewed interest in producing viscous oils. A major source of viscous oils is the Orinoco tar belt of Venezuela , which is estimated to contain 700 billion bbl [Ill X 10 9 m 3] of oil ranging in viscosity from 1,000 to 60,000 cp [1 to 60 Pa' s]. One technique being considered to lift this oil ar- tificially is intermittent gas lift. Intermittent gas lift is a cyclic production method in which a slug of liquid is first allowed to build up in the tubing string. When the slug reaches a given length, high-pressure gas stored in the casing-tubing annulus is injected under the slug through a gas-lift valve. The liq- uid slug is propelled upwards by the energy of the expanding and flowing gas beneath it. The faster-moving gas bubble constantly penetrates or overruns the bottom of the liquid slug, resulting in a continuously decreasing slug length. The gas-lift valve normally closes when the • Now with Sohio. 0149·2136/84/0031·0940$00.25 Copyright 1984 Society of Petroleum Engineers of AI ME MARCH 1984 top of the slug reaches the surface. Liquid is produced from both the slug and the annular film of liquid on the pipe wall in the form of liquid entrainment. Following production of the slug and part of the film, a portion of the remaining film falls back to join the liquid feeding in- to the tubing to form the next liquid slug and to begin a new cycle. Although intermittent gas lift has been used for ar- tificiallift in oil wells for many years, the unsteady-state nature of this technique has prevented developing a suc- cessful model that can predict all the important variables. Design methods and behavior predictions are as much an art as a science. There are very few published studies on two-phase flow in which a slug of liquid is driven by gas injected beneath the slug. Past publications on gas lift have dealt with efficiency, design, and predicting pro- duction rates. Brown and Jessen I conducted experiments on an 800-ft [244-m] experimental well equipped with 2-in. [5-cm] tubing. They attempted no analytical solution, but on the basis of experimental data developed an em- pirical foundation for intermittent gas-lift technology. A method of calculating the average bottomhole flowing pressure and pressure stabilization time for a lift cycle in a 2-in. [5-cm] tubing was presented to aid design considerations. White et al. 2 used dimensional analysis and dynamic similarity to model intermittent gas lift. The mathematical simulation was simplified by assuming that the liquid slug velocity rapidly reached a constant value and that the velocity of gas bubble penetration into the liquid slug was a constant. Experimental results con- firmed the conceptual model. Brill et al. 3 reported the results of a wide range of in- termittent gas-lift tests conducted in a 1,500-ft [457.2-m] experimental well. An empirical fallback correlation was developed in conjunction with a conceptual model that combined basic fluid-flow equations with the empirical liquid fallback correlation. The results compared favorably with the test data and verified the model. Doerr 4 conducted a study of liquid loss in an intermit- tent gas-lift system with 0.95-in. [2.4-cm] tubing. A theoretical approach for liquid loss was developed that related liquid and bubble velocities to film thickness . The results showed considerable discrepancy with the liquid fallback data of Brill. 475