A derivative method for minimising total cost in heat exchanger networks through optimal area allocation

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, without any stream splits 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 ε-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 “utility cost savings 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 applied to the distillation example of Gundersen (2000). After applying the new CDM, the total annual cost was reduced by 7.1 % mainly due to 24 % less HEN area for similar heat recovery. Area reduction resulted from one exchanger having a minimum approach temperature (ΔTmin) of 7.7 °C while the other recovery exchangers had larger ΔTmin values. The optimum ΔTmin for the PDM was 12.5 °C. The CDM solution was found to give a comparable minimum total area and cost to two recently published programming HEN synthesis solutions for the same problem without requiring the increased network complexity through multiple stream splits