Pump performance assessment
The following will provide you with a simple guidance to assess and trend the performance of a pump and how it has been practically used by an operator to improve asset availability.
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The purpose of the exercise is to compare the actual pump performance with the pump performance as new and to normalize this value so you are able to trend it and visualize the degradation of pump performance.
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A typical plotted result is shown below:
Field of application
This can be applied to any pump but will particularly useful for critical services where:

Pump duty is a matter of safety such as for fire water pumps

Pump performance has a direct impact on asset production (Export pumps, injection pumps)

Pump operated in erosive services (Produce water) and is subject to more regular maintenance.
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Theoretical background:
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The pump hydraulic power (in W) is expressed by:
Ph = ro . g . dH . Qv
Where ro is the density (in kg/m3)
g is the gravitational acceleration or 9.81m/s2
dH is the differential head generated by the pump (in m)
Qv is the volume flow (in m3/s)
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or Ph= dP . Qv eq1
Where dP is the differential pressure generated by the pump (in Pa)
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The actual electrical active power (in W) is expressed by:
Pelec=Ph . Eff eq2
Where Eff is the pump efficiency
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Inputs required:
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Theoritical inputs:

Pump curves (head vs. flow) and (efficiency vs. flow)
Site data:

Suction pressure

Discharge pressure

Pump flow

Absorbed power

Process fluid properties (specific gravity)
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Calculations
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Input your pressure and flow values into the calculation tool. Record the hydraulic power (ref to eq1). To perform a spot check, you can use the pump calculation tool available on this website.
Case study
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A good example of this approach was partly presented by BP in the 2014 during the European Sand management forum in Aberdeen.
The presentation is available here.
ETAP is a north sea platform operated by BP. It was designed in the late 90s for sand free production. However the sand content in the oil stream has prove over the years to be a significant source of loss production (1 MMbbl/yr) and has been putting a huge stretch on the POB (additional 600 POB per year to deal with sand consequences).
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Divide the hydraulic power by the absorbed power. This gives the actual pump efficiency (ref to eq2)

For your given flow, read the theoretical efficiency from the vendor pump curve.

Divide the actual efficiency by the theoretical efficiency to obtain the relative pump efficiency

Plot the relative pump efficiency against running hours
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Outcome
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The outcome is a graph where the relative efficiency is plotted vs. the pump running hours. This can be done by performing spot checks or by calculating averages over a large number of points.
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The trend can be extrapolated to estimate when a critically low efficiency will be met and allowing to predict the time for maintenance.
If previous data are available, the calculation of loss of relative efficiency can be performed retrospectively between 2 pump overhauls and mapped with observed damages or other data indicating a degradation of the condition such as high axial thrust / high bearing temperature, higher radial vibrations. You might for example observe that your axial bearing temperature gets close to trip value when your efficiency has dropped by x%.
If no previous data are available The rule of thumb is that at 10 to 15% of efficiency loss, several modes of failure will start to materialize.
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The relative head can also be plotted. It can offer an interesting alternative in case the pump absorbed power is not measured.
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Assumptions and limitations:
Significance of theoretical efficiency in excessive wear condition: Loss of efficiency, especially when due to erosive wear, means that significant recirculation are happening inside the pump. The pump measured flow " at flange" can therefore be significantly different from the actual flow going through the pump and the determination of a theoretical efficiency from the measured flow becomes quite inaccurate.
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Location of pressure measurements: the above calculation assumes that the suction and discharge pressure readings have the same datum elevation. If this is not the case, it introduces a offset on the dP used for the power calculation. On high energy pump, this value will usually be negligible. On smaller head (fire water pump in particular), the contribution can be more significant and should be corrected in the calculation.
Specific gravity of the fluid: The pump flow retrieved from the control system and calculated from a pressure difference across an orifice plate usually assume a constant SG. If the pump operates at a different SG, the flow can be corrected as follow
Qv corr = Qv ref . (SGref / SGact)^(0.5)
where Qv ref is the flow measurement retrieved from the control system
SGref is the SG used in the control system calculation
SGact is the actual SG of the fluid
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Pump efficiency: most of the time, the efficiency and power curve are provided for the pump and motor, however this may differ from one vendor to another. It is advise to cross check the values from the pump curve and the datasheetâ€‹ to make sure that the motor efficiency is already factored.
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If the few points above may introduce some inaccuracy in the calculation and in the absolute numbers, keep in mind that the trend remain however valid.
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A huge fraction of the sand end up in the produced water system and his handled by the produced water reinjection pumps (PWRI). These pumps are integrally geared pumps with 2 stages running at very high speed and therefore very limited tolerance to sand which has been driving the requirement for frequent pump overhaul.
Effect of sand erosion can be seen on the picture below.
Over the years, the asset has integrated the pump performance assessment to schedule their pump overhauls and optimize the time between maintenance.
The pump performance had also be mapped with the asset operation to understand what where the well bringing more sand and if some operating modes were detrimental to the pump performance.
The graph below shows for example a case where a decline in pump performance is observed even if no sand producing well was online but due to the sand being recirculated in the system.