Including detailed models of processing equipment in the process flowsheet model is required in the case of "non-standard" unit operations, including, e.g., intensified equipment and unconventional reactor designs. We provide a unified multiscale framework for including such models in equation-oriented process flowsheet modeling, simulation and optimization. Relying on the reaction/separation/recycle process prototype, we propose a multiresolution paradigm, whereby detailed, distributed-parameter representations of reacting systems and rigorous models of (intensified) separation units are embedded in process flowsheet models. We develop an equation-oriented modeling approach based on a pseudo-transient reformulation of the balance equations, enabling the reliable and robust simulation of the process flowsheet. We also describe a companion design optimization routine. We illustrate these concepts with an extensive case study on dimethyl ether production using an intensified process featuringa dividing-wall distillation column and an adiabatic packed bed reactor with intermediate quenching. (C) 2017 Elsevier Ltd. All rights reserved.