Utility targeting in heat exchanger network with parametric uncertainties

For almost a half-decade, the methodology of Pinch Analysis (PA) and heat integration (HI) has been used to optimize the requirements of external utilities. Though much has been done, optimizations under uncertain conditions still need more work, discussion, and practical implementation. In most of the HI problems, it has been observed that variation in the minimum driving force affects the shape of the source and sink profile eventually the heat exchanger network (HEN) design. Due to changing operating conditions, human errors, and sometimes poor maintenance, it has been experienced that the process plants along with their equipment and vessels do not operate at the desired value upon which they are expected to run. The parameters with variations and uncertainties due to disturbances in the process plants need to be addressed for the desired product output. In this work, the concept of PA has been unified with robust optimization (RO) to target the utility requirements in HEN optimization where the uncertainties in the heat capacity flow rate $F$ and supply temperatures $T_{in}$ of the source streams are considered. The developed nominal forms of mathematical programming are converted into the deterministic robust counterpart equivalents to incorporate the uncertainties whose set of variations is known. RO is an optimization technique where the information of accurate probability distribution needs not be known; rather, it works in a defined set of uncertainty ensuring the feasibility of the solution. Using two examples from the literature, the developed models have been solved and results for the solutions against the range of uncertainties in parameters have been established. The produced data demonstrates, in the case of uncertain inlet temperature the rise in total utilities is 115% and 225% in examples 1 and 2 for worst case is calculated. Plots of budget parameter Γ vs the utility requirement have also been compared with results. Application of this model will further assist the plant engineers/managers in deciding the requirements of hot utilities and cold utilities under the parametric uncertainties as needed.