In the first part of this work, we present two different architectures for distributed model predictive control (DMPC) of nonlinear process systems: sequential distributed model predictive control and iterative distributed model predictive control. In the present work, we focus on the application of the theoretical results developed in to a catalytic alkylation of benzene process example, which consists of four continuous stirred tank reactors and a flash separator. In order to carry out the simulations, a first principle model is developed via mass and energy balances. Based on the process model, three distributed Lyapunov-based model predictive controllers are designed to control the process in a coordinative fashion. Extensive simulations are carried out to compare the DMPC architectures proposed in with an existing centralized Lyapunov-based model predictive control design from computational time and closed-loop performance points of view.