Process units may operate different time scales (for example, reactors with different volumes) thus requiring plantwide control systems with multiple sampling rates to avoid over or under sampling. Moreover, it may be preferable to sample critical variables at a higher rate than non-critical ones to decrease capital. Motivated by the above considerations, this paper addresses the issue of distributed multirate model predictive control design for chemical process networks. In order to ensure the closed-loop stability and achieve a minimum performance, dissipativity-based constraints are included in the design of the individual local controllers.