Abstract
Gas lift is the process of injecting gas into the tubing at a predetermined depth in order to lift the crude oil to the surface. Gas lift is applied to a well when the reservoir pressure falls to such a level that it does not produce without application of external energy. There are mainly two types of gas lift which are Continuous and Intermittent gas lift. This paper deals with the theoretical determination of relationship between liquid accumulation and gas injection duration in an intermittent gas lift well and how this knowledge can be combined with the experience of Engineers to maximize the production of a well. In order to find the relationship between the given durations, a simple mathematical approach with the assumption that the gas injection time is independent of liquid accumulation time is followed. We, then apply various tools of mathematics such as the principles of maxima and minima, Leibnitz theorem, definition of the slope of a line etc. to finally prove the interdependence of liquid accumulation and gas injection time at which the well can produce at its maximum capacity. This interdependence is plotted on a separate graph with the given times on two axis. This curve represents the values at which the reservoir inflow is maximised and hence another curve representing the tubing outflow is drawn on the same graph to intersect the former curve at the optimum value of liquid accumulation and gas injection time. The paper also discusses the physical significance of the cases in which the two curves do not intersect and its possible solutions which vary in accordance with the experience of engineers and conditions of well. Our mathematical calculation led to an astonishing result that the interdependence between the two given durations is elegant and can be easily found without the use of computer in a very short interval of time. The result indicated that if a tangent is drawn from a point representing gas injection time to the graph of accumulation height versus time, it touches the graph at the value of liquid accumulation time at which the production of well is maximized. This novel approach to determine the value of time in an intermitter or time cycle controller in an intermittent well can be proved to be a boon for gas lift optimizers who would otherwise spend a large part of the time in setting the value on hit and trial basis. The graphical method can determine the optimum value in a shorter interval of time and with greater accuracy saving companies from extra man-hours and unscientific approach to optimizing any intermittent gas lift well.
