Variable Speed Pump Operation Can Cut Energy Costs but System Static Head Reduces Savings
Determining pump speed using the affinity rules is not as easy as it appears.
By Jeffrey L. Sines, Engineering Training Lead, Engineered Software, Inc.
As printed in Pumps & Systems, June 2011
The days of inexpensive electricity are gone, and with environmental pressures on the oil, coal, and
nuclear industries, electricity prices will only go up. In today’s economy, many companies are looking at
options to reduce energy consumption as a way to add to the bottom line or just stay in business. For
companies that use centrifugal pumps in their processes, one method to reduce energy consumption is
to install a variable speed drive to reduce the motor and pump speed. For some piping systems this is a
great solution, but is it always the best solution?
To answer that question, it’s important to understand how a pump and piping system interact, and
to understand the affect static head has on the pump’s operating point. The pump affinity rules describe
how a pump’s performance will change with a change in pump speed, but the actual operating speed of
the pump, and the energy savings, will depend on the amount of static and dynamic head in the system.
Systems with Differing Dynamic and Static Heads
Consider the three piping systems in Figure 1. Each system consists of a Supply and Product Tank, a
variable speed pump, valves and the interconnecting pipelines. The working fluid is water at 60 F with a
density of 62.37 pounds per cubic feet. Each system has the same pump selected to meet an operating
point of 1,000 gallons per minute and 98 feet of total head at 1735 rpm, but each has a different
amount of static and dynamic head, achieved by varying the total pipe length and Product Tank
elevations.
Figure 1. Systems with varying amounts of static and dynamic head.
It’s important to note that the pump does not know how much of its total head is allocated to static
and dynamic head in the system. Static Head is the sum of the difference in elevations of the liquid
levels and surface pressures in both tanks. The dynamic head is the sum of the head losses in the
pipelines, valves, fittings, and other components in the system. For pipelines, head loss can be
calculated using the Darcy method shown in Equation 1, taken from the Crane Technical Paper No. 410 –
Flow of Fluids Through Valves, Fittings, and Pipe.
Equation 1. Darcy Head Loss Equation
Although it appears that the head loss is a second order function of the flow rate, the Darcy friction
factor ( f ) is also a function of the flow rate, which makes the head loss not quite a second order
relationship. The pump and system resistance curves for these piping systems are shown in Figure 2.
Figure 2. Pump and system resistance curves for three piping systems with various amounts of static and
dynamic head.
How a System’s Static Head Affects Pump Speed in Variable Speed Applications
The pump affinity rules in Equation 2 describe how a centrifugal pump’s flow rate (Q), Total Head (H),
and power consumption (P) change with a change of impeller speed (N).
(
)
(
)
Equation 2. Pump Affinity Rules
Since the flow rate changes in direct proportion to speed, and head changes proportional to the
speed squared, a second order relationship exists between flow rate and head in pump performance as
the speed changes. Mathematically, the affinity rules are easy calculations. However, although the rules
describe how the pump’s performance will change with a change in speed, they do not show how a
pump will perform in any particular piping system. It is the piping system that determines what speed
the pump has to run at to overcome the static head and dynamic head at any given flow rate.
What is the pump speed needed to reduce the flow rate in each system in Figure 1 to 500 gallons
per minute with the variable speed pump? Using just the affinity rules, to reduce the flow rate by 50
percent the speed has to be reduced by 50 percent to 867.5 rpm:
( )
The affinity rules can then be used to determine the pump head at this speed:
(
) (
)
However, does the pump produce the amount of head required by the system at 500 gallons per
minute? The total head needed by the system can be determined by calculating the pressures at the
pump suction and discharge based on the Supply and Product Tank levels and pressures, the piping and
valve losses, and the system flow rates. The required differential pressure across the pump can then be
converted to head using Equation 3.
Equation 3. Converting differential pressure (in psi) to head (in feet of fluid). Fluid density () is in units
of lb/ft3.
Figure 3 shows this for the three systems.
Figure 3. Calculating the suction and discharge pressures and the pump Total Head required for each
system.
Using Equation 3, the Total Head required by System 1 is:
⁄
The pump head calculated using the affinity rules was 24.64 feet, which is not enough to meet what
the system requires at 500 gallons per minute, so the speed must be slightly higher to meet the needs of
the system. Figure 4 shows the required pump speed needed to meet the head requirements of all three
systems.
Figure 4. Systems with pump speeds calculated to match the head requirements of each system.
In order to meet the total head requirements of System 1 for a 50 percent flow reduction, the pump
speed must be 895 rpm, compared to 867.5 rpm calculated using the affinity rule. This underestimation
in pump speed is due to the fact that the system resistance is not quite a second order relationship to
the flow rate.
Underestimating the pump speed with the affinity rules is exacerbated by increasing the static head
in the system. For Systems 2 and 3 in Figure 4, the total head requirements and the calculated pump
speeds needed to meet them are even higher. Only the dynamic head is affected by a reduction in the
flow rate. The static head stays the same as long as the difference between liquid levels and pressures
between the two tanks stays the same.
The pump in System 2 requires a speed of 1140 rpm to obtain a total head of 44.6 feet at 500
gallons per minute, whereas the pump in System 3 must run at 1530 rpm because it requires 81.3 feet of
total head. Using just the pump affinity rules in these cases would grossly underestimate the pump
speed needed to reduce the flow to 500 gallons per minute. Figure 5 shows how the pump curve shifts
down as the pump speed is reduced.
Figure 5. The pump curve shifts down as speed is reduced. The system requirements determine the
operating speed of the pump.
Effect of Static Head on Pump Efficiency and Energy Savings
The determination of pump speed for systems with static head also explains why the use of variable
speed pumps in a system with a large amount of static head does not save as much money compared to
a system with just dynamic head. The affinity rules show that the power consumption is reduced by the
cube of the change in pump speed, so the completely dynamic head system will consume much less
power at the reduced flow rate because of the greater change in pump speed compared to the high
static head system. For the same 50 percent reduction in flow rate, System 1 saw a reduction in pump
speed from 1735 rpm to 895 rpm (840 rpm change), System 2 went from 1735 rpm to 1140 rpm (a 595
rpm change), and System 3 went from 1735 rpm to 1530 rpm (205 rpm change).
The pump efficiency at the operating point is also affected by the amount of static head. Figure 6
shows the pump and system resistance curves, as well as the ISO-efficiency lines to show how pump
efficiency changes with a change in pump speed. Figure 6 also shows the operating points for each
system at the original and reduced flow rate. At 1,000 gallons per minute, all three pumps operate at
about 88.6 percent efficiency. When the flow rate is reduced, the pumps in System 1, 2, and 3 operate
at an efficiency of 88.3 percent, 83.1 percent and 72.4 percent, respectively.
Figure 6. Constant efficiency lines follow a second order relationship as pump speed is reduced. Pump
efficiency decreases with increased static head in the system.
To put all of this into perspective, assume each system is operated for half the year at 1,000 gallons
per minute and half the year at 500 gallons per minute with an energy cost of $0.10 per kilowatt hour
and motor efficiency of 93 percent. Table 1 summarizes the energy costs and annual savings for each
system as compared to operating the systems with a fixed speed pump at 1,750 rpm and using a throttle
valve to control the flow rate.
Table 1. Operating costs and energy savings for systems with various amounts of static head
Fixed Speed Pump with
Throttle Valve
Variable Speed Pump Annual
Savings
System 1
(100% Dynamic Head)
$17,200 $11,400 $5,800
System 2
(75% Dynamic Head)
$17,200 $12,500 $4,700
System 3
(25% Dynamic Head)
$17,200 $15,200 $2,000
Conclusion
Static head in a system reduces energy savings when using a variable speed pump. The pump affinity
rules describe how the pump performance will change with a change in pump speed, but the actual
operating speed of the pump will depend on the head requirements of the system.
The more static head the system has, the higher the pump speed needed to overcome this head. In
addition, the pump will operate farther back on its pump curve, resulting in lower pump efficiency at
reduced flow rates. The net effect of higher operating speeds and lower pump efficiency in systems with
static head is a reduction in the energy savings when using variable speed pumps.
Jeff Sines has over 20 years of plant operations experience in the US Navy nuclear power program and
pulp and paper industry. He is currently the Engineering Training Lead for Engineered Software, Inc. and
provides technical support for their PIPE-FLO Professional and Flow of Fluids programs. He is also an
instructor for ESI’s Piping System Fundamentals and Piping System Assessment and Optimization
courses. For more information, go to www.eng-software.com. He can be contacted at Jeff.sines@eng-
software.com.