Model predictive control (MPC) has been widely used in the chemical process industry; however, the industrial applications use a simplified model to describe the time evolution of the system in order to make the dynamic optimization problem easier to solve. Models based on fundamental principles describe in detail the dynamics of the system, but they define a problem of differential-algebraic equations (DAE) that can present high-index difficulties related to the definition of consistent initial conditions. Index reduction techniques have been applied to solve this kind of problem. This study presents an alternative to using high-index DAE models in MPC. The problem is discretized using orthogonal collocation on finite elements, and the original high-index model is used in the numerical integration, but its equivalent reduced index one model is used to define efficiently consistent initial conditions. The set point tracking problem and the disturbance rejection problem for a flash separation drum using nonlinear model predictive control are considered. It is shown that the proposed model does not present a practical difference with respect to the index one reduced model and that it is more efficient in computational terms.