A derivative based method for cost optimal area allocation in heat exchanger networks

Abstract

This paper presents a novel Cost Derivative Method (CDM) for finding the optimal area allocation for a defined Heat Exchanger Network (HEN) structure and stream data to achieve minimum total cost. Using the Pinch Design Method (PDM) to determine the HEN structure, the approach attempts to add, remove and shift area to exchangers where economic benefits are returned. From the derivation of the method, it is found that the slope of the ɛ-NTU relationship for the specific heat exchanger type, in combination with the difference in exchanger inlet temperatures and the overall heat transfer coefficient, are critical to calculating the extra overall duty each incremental area element returns. The approach is able to account for differences in film coefficients, heat exchanger types, flow arrangements, exchanger cost functions, and utility pricing. Incorporated into the method is the newly defined “heat duty flow-on” factor, θ, which evaluates downstream effects on utility use and cost that are caused by changing the area of one exchanger. To illustrate the method, the CDM is illustrated by application to a simple distillation process and a milk powder plant case study. After applying the new CDM, the total annual cost was reduced by 7.1% for the distillation problem and 5.8% for the milk powder plant. For the distillation process, the CDM solution was found to give a comparable minimum total area and cost to four recently published programming HEN synthesis solutions for the same problem without requiring the increased network complexity through multiple stream splits. The CDM has significant potential and is expected to improve with further development.