Nearly all of us have designed heat exchangers. We use standard temperatures dictated to us by our seniors. The standard at Jake’s company was 10°F. The approach temperature for the column to cooling fluid was 10°F. The delta T for the cooling fluid was 10°F. The approach of the refrigeration evaporator to the cooling fluid was 10°F and the delta T for the cooling fluid was 10°F. The approach of the cooling tower water to the refrigeration condenser was 10°F. The delta T of the cooling tower water was 10°F. The cooling tower operated with a range of 10°F and the approach to ambient wet bulb was 10°F. Oh, and the design fluid velocities were all 7 ft/s.
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Jake eventually moved from the design job to a plant. There, he discovered a completely different world. He constantly found operators violating his strict upbringing on design temperatures. When he asked why, they responded, “We found a sweet spot and the process runs better there!” Also, “If we could just get more flow we could improve the process yield.”
As he gained more experience in the field, Jake realized the operators were settling on about 70% of the design delta T that he had used. They also were operating the cooling fluids at about 10 ft/s instead of 7 ft/s. This seemed to be pretty universal whether it was the process area or the HVAC systems. He coined Jake’s law: operations will run the heat exchangers at 70% of design delta T.
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So what are the implications of Jake’s law? Are there extra costs? Does the increased yield pay for the added expense?
The first thing to note is the flow rate increased by nearly 50%, so naturally, pumping costs went up. But by how much? The increased flow raises pump energy proportionally. However, there may be an increase in pressure. Because the velocity increased by 50%, the incremental pressure drop went up by the square of 1.5 or 2.25. Flow × head (or pressure) = pump energy, so it rose by a factor of 3.37. Obviously, there’s a base pump head, so this would cause a smaller overall pumping cost increase. Depending on where the online pumps fall on their pump curves, another pump may be needed. Also note that this additional energy is passed on through the system as increased energy load and will eventually be dumped to the cooling tower.
Next, Jake reviewed the resultant log mean temperature differences (LMTD) and their effects through the system. The change in process temperature results in a lower LMTD in the evaporator, which in turn reduces the evaporator pressure, raising the lift and the power required. The slight rise in pumping power is extracted through the evaporator, also increasing power needs. Finally, if the process load is raised as a result of the process improvements, this also will require more power.
So, with all the generalizations — potentially with negative results, Jake was perplexed. To solve his dilemma, Jake developed a model to determine what would actually happen. He modeled each heat exchanger in the system. He added a decision box to use actual fouling factors. He used pump curves and a selection process for pumps on line. He modeled the compressors in the refrigeration machines. He also added a selection box for each refrigeration machine in the plant.
The result? Jake concluded you should never use generalizations when dealing with a complex system. The height of the columns added a static load to the overall pump pressure that masked the increased pressure across the heat exchangers. The slight increase in pressure moved the pumps to a better efficiency point on the curve. Jake also found that operations had one more pump online than needed. First savings achieved. The process heat exchangers were a lot cleaner than expected; actual LMTDs were better and resulted in improved performance compared to the conservative design points.
The refrigeration machines were being operated in a partially unloaded mode; reducing the number of machines to only those necessary to handle the load cut the energy consumption. In the end, Jake was able to show a 10% reduction in energy while production increased by about 5%.
So, be careful using generalizations. They can lead you astray. Develop models for complex interacting systems and test your assumptions — and the generalizations! Happy energy hunting!
