In this article we address the design and optimization of chemical processes using Chemical Modular Process Simulators-that include state of the art models-including discontinuous cost and sizing equations. Equations are divided into "implicit" ones which include all the equations in the process simulators with an input-output black box structure, and other third party equations (i.e. sizing and costing correlations for any database) and "explicit" constraints in the form of equalities or inequalities like in any regular equation based optimization environment. Using this modular framework, the problem is formulated as a generalized disjunctive programming problem and reformulated and solved as a mixed-integer nonlinear programming problem. Different algorithms (branch and bound, outer approximation, and LP/NLP based branch and bound) have been adapted to deal with implicit equations and their capabilities have been studied. Several examples are presented in order to illustrate the performance of the algorithms. (C) 2007 American Institute of Chemical Engineers.