Process operability emerged in the last decades as a powerful tool for the design and control of complex chemical processes. The design of such processes is a challenging task as they are represented by nonlinear models with large numbers of differential and algebraic equations that demand high computational effort for their solution. In particular, process operability was proposed as a method for verifying the ability of a process design, defined by the available input set, to reach an achievable output set that considers production targets. However, existing operability methods for nonlinear systems are limited by the problem size that they can address.;In this thesis, a novel operability framework for process design and intensification of high-dimensional nonlinear chemical and energy processes is developed. This proposed framework bridges the gap in the literature by addressing the challenges of process nonlinearity and model size. This framework also broadens the scope of the traditional path of operability approaches for design and control, mainly oriented to obtain the achievable output set from the available input set, and compare the computed achievable output set to a desired output set. In particular, an optimization algorithm based on nonlinear programming tools is formulated for the high-dimensional calculations of the desired input set that is feasible considering process constraints, performance levels, and intensification targets. The high computational effort required for the high-dimensional calculations is addressed by the incorporation of bilevel and parallel programming approaches into the classical process operability concepts.;To illustrate the effectiveness of the developed methods, two natural gas utilization processes of different dimensionalities are addressed: i) a catalytic membrane reactor for the direct methane aromatization conversion to benzene and hydrogen, for which an intensified reactor design footprint reduction up to 90% when compared to the base case is obtained; and ii) a natural gas combined cycle system for power generation, for which a dramatic reduction in size, from 400 to 0.11 [MW], is produced by specifying conditions of the gas and steam turbine cycles, while still keeping the high net plant efficiency between 55 and 56.5 [%]. These results indicate that this novel operability framework can be a powerful tool for enabling process intensification and modularity. Moreover, results on the implementation of the bilevel and parallel computing methods show a reduction in computational time up to 2 orders of magnitude, when compared to the original results. The results in this thesis have culminated in four peer reviewed publications and four delivered presentations by the time of the defense