A new method for finding the optimum gas injection rates for a group of continuous gas lift wells to maximize the total oil production rate is established. The new method uses a quasi-Newton non-linear optimization technique which is incorporated with the gradient projection method. The method is capable of accommodating restrictions to the gas injection rates. The only requirement for fast convergence is that a reasonable estimate of the gas injection rates must be supplied as an initial point to the optimization method. A method of estimating the gas injection rates is developed for that purpose.
A computer program is developed capable of implementing the new optimization method as well as generating the initial estimate of the gas injection rates. This program is then successfully tested on field data under both unlimited and limited gas supply. The new optimization technique demonstrates superior performance, faster convergence, and greater application than the standard â??equal slope allocationâ?¿ procedure.
Continuous flow gas lift is one of the most common artificial lift methods employed throughout the world. Ideally, sufficient gas should be injected into each individual well so that it would yield maximum revenues. However, in most cases the total amount of gas available is insufficient to achieve this objective simultaneously for every well in the field. Thus, it is often necessary to allocate a restricted amount of gas to each well in some optimal way to achieve maximum oil production from the field.
Fig. 1 is a schematic diagram of a typical gas lift system. The most efficient gas lift system can be obtained by analyzing four main components:
Flow through a porous media
Flow through a production string
Flow through a flowline and trunkline, and
Total injection gas volume available for the system.
Usually, the total injection gas volume available for the system is limited to a certain amount so that a proper allocation of injection gas is critical when designing a gas lift system.
The objective of gas allocation optimization as it relates to this study, is to maximize the total oil production rate from the gas lift system under the amount of gas volume available to support the system. This objective can be considered as a problem of maximizing a non-linear function which gives the total oil production rate from the system. The variables or unknowns for this function are the gas injection rates for each well and these are subjected to physical restrictions which are referred to as constraints. For example, the gas injection rate for each well must not be negative, and the sum of the gas injection rates should be less than or equal to the total gas volume available for the system.
In this study, a non-linear optimization technique is introduced into the problem of finding the optimum gas injection rates. This paper concentrates on presenting a general description of the quasi-Newton optimization technique along with the results of numerical experimentation and a comparison with the equal slope allocation method. A detailed analysis of the theory surrounding this method can be found in Ref. 1.
Historically, several studies have been conducted to determine the optimum gas injection rates.