Control-oriented modeling of gas-lift system and analysis of casing-heading instability

Gas-lift is widely used in mature oil field to boost the production rate. However, a well-recognized severe problem associated with the gas-lift system is the casing-heading problem, which results not only in production loss, but also in a negative impact on downstream equipment. Active control is preferable to handle this problem, where a control-oriented model is required for proper design of controller/observer. Such a model must be given by ordinary differential equations (ODE), and a subsequent linearization of the model may be required too. Although a number of simplified models for the gas lift system can capture the main feature of the casing-heading phenomenon, most of them assume that the substances in the tubing are homogeneous, which ignores the propagation phenomenon. In this paper, a novel high-order model is proposed to address this problem by virtually dividing the tubing into adjacent segments, which are connected by virtual channels. In addition, a reference model, which involves a solution of the partial differential equations (PDE), is developed for validation purposes. Extensive investigations of the high-order model are conducted by simulation and comparison with the results of the PDE model simulations. The results show that the proposed high-order ODE model can more accurately describe the dynamics of the gas-lift system for control objective and casing-heading phenomenon analysis.