Distribution and control of the available lift gas is crucial for maximizing total oil production in a cluster of gas lifted wells in an oil field. This paper describes an improved dynamical model for a continuous gas lifted oil field with two oil wells. It is assumed that the fluid that comes out of the reservoir is not just pure oil, but it is a mixture of oil, water, and gas. A global sensitivity analysis using the variance-based method is performed to classify the parameters, which are both highly sensitive and uncertain simultaneously. The improved model is further used to design a model based predictive controller to optimally distribute a limited supply of lift gas being shared to the oil wells. Several simulation cases are performed to study the performance of the optimal controller under varying operational scenarios. An increase in the total oil production from the field was observed when the deterministic nonlinear model predictive control was applied to the nominal model of the gas lifted oil field. At the same time, all the constraints were fully satisfied when the perfect prediction was assumed. To study the effect of parametric uncertainty, the deterministic MPC based on the nominal model of the plant is applied to the plant model containing the uncertain parameters. It has been shown that some of the constraints were not satisfied leading to unachievable and unrealistic distribution of the lift gas supply to the two oil wells.