Mathematical Foundation of Pinch Analysis

Techniques of Process Integration can be applied to conserve resources such as energy, freshwater, cooling water, hydrogen, solvent, etc. Process Integration methodologies are broadly classified into two categories: methodologies based on the numerical optimization techniques and methodologies based on the conceptual approaches of Pinch Analysis. In this paper, a generalized problem definition for Pinch Analysis problems is mathematically analyzed and a rigorous methodology to solve this problem is discussed. There are three important graphical methodologies also proposed in the literature: Limiting Composite Curve, Material Recovery Pinch Diagram, and Source Composite Curve. In this paper, fundamental derivation of these graphical representations and interrelation between them are established mathematically.