The “two-thirds” Rule for Locating Sensors to Control Variable Flow Systems – Part 2

In my previous post, I looked at what happens to differential pressures at different points in this variable flow pumping system as the flow rates drop off.

In the example, when one of the AHUs shut down while the other remained in operation at full load, the differential pressure required at the pump dropped by about 40% relative to what was required at full load while the flow dropped by by 50%. In the energy conservation game, our goal is to exploit this potential for reduced power consumption while still meeting the requirements of the load.

Let’s revisit the pump power equation.

Both head and flow appear in the numerator. Clearly, if we could control the pump in a way that reflected the reduction in both of these operating parameters, we would optimize its energy consumption.

Let’s take a minute to think through what would happen in our example on a design day when one of the AHUs shuts down. For the purposes of discussion, I’m going to make a pump selection for our example using Bell and Gossett’s ESP software.

Entering our design flow and head (800 gpm at 44.2 ft.w.c.) generates a number of selections. I chose the one with the best efficiency, which comes at a cost premium of approximately 17% relative to the lowest cost option. The 17% price premium buys a 2 % increase in pump efficiency. In economic terms, this may or may not be justified based on the load profile.

Holistically, one might argue that the price for improved efficiency is justified no matter what the load profile is since the improvement likely represents a reduction in the use of non-renewable energy with a corresponding reduction in emissions. (Of course, I’m from Oregon and grew up in the 60’s, so when I’m not busy hugging trees, I’m probably out trying to save salmon; so you have to take all of that with a grain of salt).

If AHU1 shuts down while AHU2 remains in operation at full load, AHU1’s control valve closes.  Eliminating one of two parallel paths by closing AHU1’s control valve forces all of P1’sflow through AHU2. Increasing the flow through AHU2requires more head that was being produced by P1 with both units online.  As a result, the flow through AHU2 will not double;  rather the system will shift towards a new operating point/system curve with a higher pump head than previously existed but at a reduced flow relative to what was provided with both units in operation.

Initially, the reduced system flow is still in excess of what AHU2requires at design conditions.  As a result, the control valve serving AHU2 will throttle in response to the excess capacity. Ultimately, interactions between the flow supplied by P1and the capacity the flow produces in AHU2 will cause the control valve to throttle the flow through AHU2 to the design value of400 gpm.  The figure below illustrates our pump curve along with the design system curve associated with two units in operation and the new system curve associated with AHU2 operating alone at its design capacity.

Reducing Pump Power by Pushing the Pump Up Its Curve via a Throttling Process

Back in “the olden days”, before variable speed drive technology had been perfected and made affordable we often allowed the pumps to be pushed around on their performance curves by two way valves. While crude by today’s standards, this approach was relatively simple and could save some energy as can be seen below.

By way of explanation and to provide some perspective, the “olden days is an expression my son Aaron would use when he was younger to preface a question about something in my past. Back in the “olden days”, when I first priced a VFD, it was for a 40 hp motor; the price was about $50,000 and the package as about the size of 2 motor control center sections.

On the plus side, when the pump was throttled:

  • The brake horsepower required at part load is reduced by about 2 bhp.
  • No special technology is required.
  • The theory of operation is simple and easy to understand.

On the minus side:

  • Pushing the pump up its curve moves it away from peak efficiency as can be seen by comparing the two operating points on the pump curve above.
  • The head produced by the pump at part load is significantly above what is required , as illustrated in the calculation below.  Specifically, pushing the pump up its curve results in an operating point that produces 400 gpm at about 54 ft.w.c. as can be seen from the pump curve above.   But, as can be seen from the calculation with AHU1 off and AHU2 at full load, you only need 26.5 ft.w.c. of head at the pump to deliver 400 gpm to the load and provide 20 ft.w.c. of head at the load.  Initially, the extra head drives more than the required flow through the load.  This causes the temperature leaving the coil to drop below set point.  In turn, the control system closes the valve until the extra head is simply “chewed up” by the control valve and the design 400 gpm flow rate is again achieved through the load.

  • The above design pumping head could lift valve plugs off of their seat if care is not exercised in selecting the actuators.  As a result, we may not achieve the desired reduction in flow and associated energy savings.
  • Plugging the desired flow and the head it would take to produce it into the pump power equation reveals that in theory, we should be able to serve the reduced load condition with about 3.3 bhp.

The bottom line is that while pushing the pump up its curve provided a simple way to reduce pumping capacity and save energy, the potential exists to save even more if:

  • We can find a way to reduce pump flow and pump head at the same time.
  • We can make this shift in operating conditions while preserving the pump’s efficiency.
  • We can control the pump head and flow in a manner that provides exactly what the loads require, no more and no less.

Variable speed drives and the 2/3 rule provide a mechanism to achieve these goals.  In my next post, we’ll take a look at what happens if we apply this combination of technology and technique to our example.


David Sellers
Senior Engineer – Facility Dynamics Engineering

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