The analysis of the composite curves guided by the so-called Plus / Minus Principle is a crucial and innovative phase of the study where we identify judicious process modifications that could improve significantly the energy saving potential at a better overall cost. Among others, the current operation's factor that creates the Heat Recovery Pinch (the bottleneck to energy recovery) can be pinpointed and challenged with the client. At this stage, very innovative and surprising ways to change the process can often be discovered even if we usually have to restrict the findings to more conventional ideas in order to limit the inherent risk behind any "first-of-its-kind" solution. Changes of flowrates by some recycling, temperatures and pressures increases or reductions, and others, are among the options that are examined to achieve additional energy efficiency improvements  at a minimal cost. Thus, Pinch Analysis is MUCH MORE THAN JUST OPTIMUM HEAT EXCHANGER NETWORK DESIGN !!

For the hot water tank example, the Pinch point is created by the economizer outlet water temperature. We can observe on the composite curves of figure 5 that we can reduce the heating load if we increase the slope of the cold composite curve located above the pinch. This slope increase corresponds to a reduction in flowrates. This can be done if we decrease the economizer water flowrate sent in the hot water tank until its overflow in the warm water side equals zero. 

Another option would be to reduce the economizer outlet water temperature. If this temperature is lowered, it will be possible to move the cold composite curve further on the left for the same DT_min value, thus leading to a smaller minimum heat load target. This option corresponds to reduce the hot water overflow and to heat the warm water side only with the economizer.

4. Capital cost targeting and DT_min selection for a global optimal solution

In addition to its energy targeting capabilities, Pinch Analysis uses a set of rules to establish targets for the minimum heat exchangers' area and the minimum number of installations or projects for a given DT_min value. In brief, these informations come from the composite curves and the streams population met in the part of the graph where heat is exchanged from the upper hot composite curve to the lower cold composite curve.

The temperature differences between the curves and the individual streams' heat transfer coefficicients allow the estimation of the total minimum heat exchangers area. This value is a minimum area target because it is calculated assuming a perfectly vertical heat transfer between the hot and the cold composite curves. Vertical heat transfer is synonym of global pure counter-current heat transfer. This is usually the most efficient possible way to transfer heat while minimizing the exchangers' size.

The streams population met in both composite curves serves to target the minimum number of unit (or heat exchangers or projects) Umin. Following the Euler rules for nodes, Umin equals the streams count minus 1. This calculation is done for both regions above and below the Pinch, since both regions are considered independant. Since the Pinch location moves with DTmin, the streams count in each zone will change accordingly. Hence, Umin is also a function of DTmin.

These area and number of unit targets (and other informations specific to each stream like piping cost for example) are the primary information used to estimate the capital cost and the profitability associated to a chosen DTmin. Costing equations for different types of heat exchangers, metallurgy, pressure, etc, are developped and used with these figures for capital cost estimations.

Theses capital cost targets can be used for prediction purposes ahead of any design because appropriate and consistent design rules support them. Once the design is completed, the final solutions obtained will be closed to the targeted values. In other words, for any DTmin value, the predicted energy savings and heat exchangers' minimum area and number are compatible targets.

It is then possible to explore the economic space of the problem to find the global optimum DTmin value that meets the management profitability criteria, thereafter to proceed to the final design of projects. Thus, each project will be a piece of a global strategic set of well integrated actions to be taken to achieve the management objectives in energy efficiency.

For our hot water tank example, the path presented in figure 6 is followed to find the optimum DTmin = 7 deg. C.