Tight integration through material and energy recycling is essential to the energy efficiency and economic viability of process and energy systems. Equation-oriented (EO) steady-state process simulation and optimization are key enablers in the optimal design of integrated processes. A new process modeling and simulation concept based on pseudo-transient continuation is introduced. An algorithm for reformulating the steady-state models of process unit operations as differential-algebraic equation systems that are statically equivalent with the original model is presented. These pseudo-transient models improve the convergence of EO process flowsheet simulations by expanding the convergence basin. This concept is used to build a library of pseudo-transient models for common process unit operations, and this modeling concept seamlessly integrates with a previously developed time-relaxation optimization algorithm. Two design case studies are presented to validate the proposed framework. (c) 2014 American Institute of Chemical Engineers AIChE J 60: 4104-4123, 2014