by: Joseph Nasal, General Physics
Boiler feed pumps (BFPs) play a major role in the capacity and heat rate of a powergenerating unit. As such, they merit routine performance testing to assess their condition and trend deficiencies to predict the optimum time before overhaul. Since most large power plants use mechanical drive turbines (MDTs) as the prime mover for the BFPs, determining pump shaft input power is prone to large errors that result in an unacceptably high degree of test uncertainty. Measurement inaccuracies associated with the various MDT steam flows, pressures, temperatures, and exhaust steam quality can lead to test uncertainties so high that the information is of no value.
Because of the high uncertainty associated with calculating MDT shaft horsepower using conventional methods, this article presents an alternative method that eliminates reliance on shaft horsepower measurement, and instead uses the pump affinity laws. The concept of using the affinity laws for BFP testing was initially derived from an article written by Ronald J. Ragains with Northern Indiana Public Service Company in Power Engineering in April 1989. Measurement of pump suction pressure and temperature, discharge pressure and temperature, RPM, and flow is required using this method, but no measurements associated with the MDT are needed. By eliminating the uncertainties associated with MDT power, reliable and consistent performance information can be calculated.

The general concept behind this method is that if a pump is operating at design performance, field test data for pump speed, head, and flow will match the design curves provided by the manufacturer (Figure 1). As pump performance degrades, it becomes necessary to rotate the pump at a higher RPM to attain the needed head and flow; this additional speed is indicative of pump inefficiency and can be quantified using pump affinity laws.
The basis of this method follows. When considering pump performance, test results must be corrected to a standard condition for comparison. The affinity laws state that test flow, head, and water horsepower can be extrapolated from fieldtest speed values to design speed values by multiplying each parameter by a correction factor. For flow, the correction factor is the ratio of design speed to test speed (Equation 1). For total head, the correction factor is the ratio squared (Equation 2). For power, it is the ratio cubed (Equation 3).

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where:
Q = Pump capacity, gpm
n = Pump speed, rpm
H = Pump head, ft
P = Pump power input, bhp
To use these relationships in determining pump performance, accurate measurement of pump speed and flow is required during the test. Most BFPs are monitored with highly accurate digital speed instrumentation; alternatively a handheld stroboscope can be used. For flow measurement, an ultrasonic flow measurement on the pump suction or discharge pipe provides consistent and accurate data — this data can be also be compared to installed flow metering to increase measurement confidence.
Using fieldtest data obtained for flow, total developed head, and RPM, the test flow and head values are corrected to corresponding values at design speed using the ratio of test to design RPM with the affinity laws. The corrected test flow and head values are then compared to the design flow and head curve at rated RPM. The percent of design flow (pdf) is then calculated. The pdf multiplied times the design efficiency (at the corrected test head) results in the astested efficiency for the pump. This approach is presented below mathematically.
whp_{d} = Q_{d} x H_{d} x (dimensional conversion factor) Equation 4
whp_{f} = Q_{f} x H_{f} x (dimensional conversion factor) Equation 5
Since testing is conducted at design head or corrected using the affinity laws, pump efficiency (h) can be determined from:

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where:
whp = Useful pump power output, water horsepower
bhp = Pump power input, brake horsepower
d = Design data
f = Field data
Based on the premise that brake horsepower is constant between the two curves for a given head value, bhpd design can be mathematically substituted for bhpf and the following relationship can be obtained:

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where pdf, or percentage of design flow, can be calculated from:

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An example using this method is provided below. For this particular test, the pump being tested was placed in “manual” (with the minimum flow recirculation valve and the superheater and reheater attemperation stop valves isolated) while the other pump was placed in “automatic” to maintain drum level during the testing period (20 minutes). Table 1 lists the relevant pump design and test data.
Pump suction head calculation:
Velocity at Pump Suction, Vs Water velocity at the pump suction was computed as follows:

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where:
H_{s} = Pump suction head, ft H_{2}O
144 = Conversion factor, in^{2}/ft^{2}
P_{s} = Pump suction pressure, psia [163.5]
ρ_{s} = Water density at suction conditions, lb/ft^{3} [56.37]
Z_{s} = Vertical distance between gauge and horizontal centerline of pump discharge flange, ft [negligible]
V_{s} = Average water velocity at suction, ft/sec [12.7]
g = Gravitational acceleration, 32.174 ft/sec^{2}
Water density at suction conditions, ρ_{s}(lb/ft^{3})
Water density was determined from the ASME properties of water and steam at the BFP suction absolute pressure (gauge + barometer) and temperature.
Suction Water Leg Correction, Zd (ft)
Since the BFP suction pressure gauge was located at approximately the same elevation as the centerline of the BFP discharge flange, this negligible correction was ignored. To verify the calibration of the gauge, deaerator pressure (crosschecked with deaerator condensate temperature to assure saturated conditions) was added to the elevation head between the condensate level in the deaerator storage tank and the gauge.
Pump discharge head calculation:
H_{d}= (144 P_{d} / ρ_{d}) + Z_{d} + (V_{d}^{2} / 2g)
H_{d} = (144 * 2996.5 / 56.97) + 0 + (12.7^{2} / 64.348) = 7,577 ft
where:
H_{d} = Pump discharge head, ft H_{2}O
144= Conversion factor, in^{2}/ft^{2}
P_{d} = Pump discharge pressure, psia [2996.5]
ρ_{d} = Water density at discharge conditions, lb/ft^{3} [56.97]
Z_{d} = Vertical distance between gauge and horizontal centerline of pump discharge flange, ft [negligible]
V_{d} = Average water velocity at discharge, ft/sec^{2} [12.7]
g = Gravitational acceleration, 32.174 ft/sec^{2}
Water density at discharge conditions, ρ_{d} (lb/ft^{3})
The water density was determined from the ASME properties of water and steam, by adding the atmospheric pressure (barometer) to the astested discharge gauge pressure and temperature.
Discharge Water Leg Correction, Z_{d} (ft)
Since the discharge pressure gauge elevation was close to the pump’s centerline, this negligible correction was not considered. In the event that the gauge elevation was significantly different (higher elevation) from the pump’s centerline, this correction (in ft) would be added to the measured discharge pressure at the gauge.
Velocity at Pump Discharge, Vd
Since the suction and discharge pipes are the same diameter, the discharge velocity is essentially the same as the suction velocity (12.7 ft/sec). As seen from the results of the velocity head calculations, it can be reasonably argued that these calculations be ignored when testing a highhead boiler feed pump. Furthermore, if the suction pipe and discharge pipe have the same inside diameter (as is the case here), the velocity pressures cancel out.
Total Dynamic Head Developed Calculation:
The test total dynamic (developed) head (TDH) is the difference between the discharge and suction heads.
TDH = h_{d} – h_{s}Equation 13
TDH = 7577 – 420 = 7157 ft
where:
h_{d} = Pump discharge head, ft [7577]
h_{s} = Pump suction head, ft [420]
BFP Efficiency Calculation:
Calculate the corrected test flow to pump design speed (5600 rpm):
Q_{d} = Q_{t} * (n_{d} / n_{t}) Equation 1
Q_{d} = 4340 * (5600 / 5497) = 4421 gpm
Calculate the corrected test head to pump design speed (5600 rpm):
H_{d} = H_{t} * (n_{d} / n_{t})^{2}Equation 2
H_{d} = 7157 * (5600 / 5497)^{2} = 7428 ft

Determine design test flow at the corrected test head from manufacturer’s curves (Figure 2) by entering the ordinate axis at the corrected test head [7428 ft] and reading the design flow from the abscissa = 4785 gpm.
Calculate the percent of design flow expected at the corrected test head if pump were operating at design:
(pdf) = 4421 / 4785 = 92.4% – Equation 9
Determine design point efficiency at the corrected test head if pump were operating at design, from manufacturer’s curves (Figure 2) = 82%
Calculate the pump’s test efficiency by multiplying pdf * design efficiency:
η_{t} = 0.924 * 0.82 = 75.8%
Author –
Joseph R. Nasal, P.E., has 32 years of experience in the operation and performance testing of fossil power plants. As Vice President of Energy Services at General Physics, he is responsible for two business units that provide a wide array of workforce and equipment performance improvement products and services for power plants. Nasal holds a BSME from RIT, an MBA from Canisius College, and is a registered PE in New York State.