Nonlinear model predictive control (NMPC) has become an appealing control concept for chemical processes because it can directly take into account the multivariable character, nonlinearities and constraints on inputs and states. While linear MPC is frequently applied in the process industries, practical applications of NMPC are rare. One reason is the relatively large computation time still needed to solve the nonlinear constrained optimization problems inherent to NMPC schemes. For faster controller response, the use of an extended partially reduced SQP method within the direct multiple shooting framework is proposed. This method is implemented in the code MSOPT which allows for an accelerated calculation of the directional derivatives and thereby saves computation time. Furthermore, this method is adapted to the real-time iteration scheme, which leads to a tremendous reduction of the time needed to provide new controls. The new NMPC variant is compared with a previously introduced scheme based on the optimization code MUSCOD-II, where the extended reduction is not in use. Numerical results are presented for both NMPC schemes and a decentralized PI controller in closed loop with a simulation model of a highly nonlinear thermally coupled distillation column which separates a ternary mixture.