How does the theoretical framework underpinning chemical engineering facilitate the optimization of processes and the development of innovative solutions? Expound on the foundational principles, such as thermodynamics, transport phenomena, and kinetics, and their integration into modeling and simulation techniques. Discuss the role of theoretical constructs in understanding complex reactions, phase equilibria, and mass transfer phenomena, thereby enabling the design of efficient separation processes, reactor systems, and product purification methods. Explore the significance of theoretical frameworks in addressing sustainability challenges, such as energy efficiency, resource conservation, and waste minimization, through process intensification and green chemistry principles. Additionally, investigate the interdisciplinary nature of theoretical approaches in chemical engineering, encompassing fields like mathematics, physics, and materials science, to elucidate phenomena at various scales and develop robust methodologies for process optimization and product innovation.