Intermittent gas lift is commonly known as one of artificial lift technique that is implemented into wells with low bottom-hole pressure. The injection process will be in cycles with spesisified period. Previously, intermittent gas lift is modeled using nodal analysis method, which is intersection between inflow performance relationship (IPR) and tubing performance relationship (TPR) and mechanistic method. Both solutions required a hard-working numerical approach to solve the model. In this paper, a new-simple-effective analytical approach is introduced to solve a set of equations that was derived from Transport Reynolds Theorem. The work is slightly different from the Liao and Bordalo model. A complex equation that represents movement of the gas-column, the slug, and the film from surface to sub-surface is presented. Gas column is formed during the injection time and the injected gas will push the oil to the surface. The dynamics of the gas column greatly affect the success of the process of oil production with gas injection method intermittently. The gas-column pressure, surface injection pressure and rate, gas column density, and surface gas injection density are successfully obtained using this approach. The gas-column pressure in the tubing is strongly influenced by the surface gas injection rate. By controlling the surface gas injection rate then the column-gas pressure in the tubing will be stable. The stable gas-column pressure leads to the stable oil production. This research is genuinely believed to be the first analytical approach of determining intermittent gas lift parameters. The results are give huge advantageous and applicable either for the educational as well as industrial purposes.

Abstract. In this study, a transmission model of the Avian influenza disease was developed and analyzed in view of optimization of vaccination and medical treatment. The model is a host-vector model. We focussed on control of Avian influenza, where a vaccination is given to susceptible poultry, while medical treatment is given to infected humans. In the model, the human population is divided into four compartments: susceptible humans, infected humans, recovered humans, and treated humans. Meanwhile, the poultry population is divided into three compartments: susceptible poultry, infected poultry, and vaccinated poultry. To analyze the dynamical behavior of the model, we obtained the disease-free equilibrium, the endemic equilibrium, and the basic reproduction ratio. Furthermore, a model of the optimal vaccination and medical treatment schedule was constructed to know the optimal strategy for controlling Avian influenza. The model can be used to determine the minimal cost of controlling the disease. The model is solved by a genetic algorithm method. Numerical simulations showed that effective control of Avian influenza can be achieved with a combination of vaccination and medical treatment. Likewise, the optimal schedule and strategy for controlling Avian influenza are shown.

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