# A New Way to Skin a Cat-Part 1

Written by:
Robert X. Perez

A Simplified Method for Monitoring Pump Performance

Pump users should regularly monitor the condition of their critical centrifugal pumps to keep them operating efficiently. Otherwise, lost production, product releases, or fires could occur.

However, monitoring performance in the field has always been a challenge due to an absence of field-mounted instrumentation, the time required for testing, and imprecision from the cumulative uncertainty of all performance variables involved.

A practical, cost-effective, and environmentally-friendly method can determine the pump’s health and whether repairs are economically justified. The simplified pump performance assessment method described here, as researched by D. Budhram, M. Russek, and myself, is based upon comparing expected horsepower consumption with actual horsepower consumed at a given pump flowrate.1 Process pressure measurements are not required.

## Background

Traditionally, machinery engineers have used the following equation to assess centrifugal pump efficiency:

η  =  pump efficiency  =

flow  x  head  x

(specific gravity  ÷  brake hp)  x  3,960

(Equation 1)

This method is often used for pumps with electric motor drives, since the brake horsepower can readily be determined using the following equation2:

bhpmotor  =  (V  x  I  x  PF  x  √3  x  ηFL)  ÷  746

where: V = voltage

I = current

PF = power factor

ηFL = motor full-load efficiency

(Equation 2)

This method can be quite challenging due to the numerous variables involved and the difficulties surrounding flow and pressure measurements. Flow presents problems because flowmeters are not always found in the field, or those available are hampered by uncertainties of 5 percent or more. Pressure is a challenge because the analyst must verify gauge accuracy before each usage, locate a pressure connection close to the pump, and deal with process leakage associated with installing and removing the pressure gauge.

You must measure six variables (flow, suction and discharge pressures, specific gravity, voltage and amperage) in the field and know the motor efficiency and motor power factor variables to calculate pump efficiency with reasonable confidence. This collection of uncertainties can lead to an efficiency uncertainty greater than the efficiency loss in question.

An alternate method of assessing pump performance evolved from ideas suggested by Bloch3 and Lightle and Hohman4. For specific speeds (Ns = N x Q1/2 / H3/4) from 200 to 3,000, they suggested that pump horsepower requirement increases as wear ring clearances increase (see Figure 1).

Figure 1. Horsepower losses and consumption increases as wear ring clearances increase.

This is intuitive, since pumps with low specific speeds tend to generate more pressure per stage and experience more leakage between stages than similar-size pumps with higher specific speeds.

This internal leakage is very sensitive to actual wear ring clearance, which can change with time due to wear. We can model this by depicting internal leakage as a spillback line from discharge to suction (see Figure 2).

Figure 2. Internal leakage can be modeled as a spillback line from discharge to suction.

As the internal seals wear, internal leakage increases, as depicted here by opening a valve in a spillback line. This recirculation flow, QL, leads to lost horsepower. As Figure 3 shows, for an overall measured flow, QM, how internal leakage, which is depicted as spillback line flow, QL, leads to a lower differential head across the pump and an increased horsepower requirement. The process “sees” QM  as the net flow, but the pump “senses” that it is pumping QM +QL, thus requiring more horsepower than expected.

Figure 3. Internal leakage increases horsepower requirements.

If you rewrite Equation 1 in terms of horsepower you get:

bhpexpected   =  (flow  x  head  x  specific gravity)  ÷  (3,960  x  pump efficiency)

(Equation 3)

If we select a certified performance curve for a given pump and specific gravity, we can say that head, H, and efficiency are functions of flow. Therefore, we can write:

bhp  =  (flow  x  H(flow)  x  specific gravity (constant))  ÷  (3,960  x  η (flow))

(Equation 4)

For a given certified performance curve with a set fluid, brake horsepower is strictly a function of flow – assuming that the pump is in “new” or ideal condition. To assess a pump’s condition at a given flowrate, you must compare actual horsepower consumed with ideal horsepower predicted for a given pump. Only flow is required, but an elimination of variables causes a loss in some performance insight. To understand the method’s limitation, we will examine what conditions are required, what assumptions are made and what is being lost along the way.