This paper studies different decomposition approaches for real-time optimization of process systems with a decentralized structure where the idea is to improve computational efficiency and transparency of a solution. The contribution lies in the application and assessment of the Dantzig-Wolfe method which allows us to efficiently decompose a real-time optimization problem into parts. Furthermore, the nonlinear system is modeled by piecewise linear models with the added benefit that error bounds on the solution can be computed. The merits of the method are studied by applying it to a semi-realistic model of the Troll west oil rim, a petroleum asset with severe production optimization challenges due to rate dependent gas-coning wells. This study indicates that the Dantzig-Wolfe approach offers an interesting and robust option for complex production systems. Moreover, the method compares favourable with earlier results using Lagrangian relaxation which again was favourable compared to a global approach.