### Coefficient of Performance Calculations

Coefficient of Performance

COP    =    BTUH Output    /    kWh Input    x    3413    BTU/kWH
5.85994726        1000000        50

Heat Pump Performance (COP)

Open Cycle COPs The single most important measure of industrial heat pump performance is the Coefficient of Performance, or COP. COP is a dimensionless number defined as the ratio of the energy output and the energy input (all expressed in heat equivalents).

For electric-driven heat pumps, this translates to:

COP = Thermal Output (Btu/hr) / ((Power Input (kW) * 3413 Btu/kWh)

For example, a 50 kW heat pump delivering 1 million Btu/hr has a COP of 5.86.

It may be helpful to view COP like this:

Heat recovered = Heat delivered times the result of the formula coefficient of performance minus 1 divided by the coefficient of performance

And . . .
The heat delivered = The heat recovered times the result of the formula coefficient of performance divided by the coefficient of performance minus 1

The COP of any heat pump cycle can be estimated using the formula shown here:

COP ~ 0. 6 * (460 + Tcond)/(Tcond - Tevap)

where Tcond is the temperature at which the refrigerant used in the heat pump condenses and Tevap is the temperature at which this same refrigerant evaporates.

The factor 0.6 reflects typical industrial equipment efficiencies and is mostly a function of heat pump size. It can be less in smaller units and more in large units; using 0.6 is good enough for first approximations. This formula can be simplified in water heating applications:

If we assume the heat pump produces 120 degree hot water and cools a cooling tower water stream to 85 degrees, this formula predicts the heat pump COP to be 6.92:

COP ~ 0. 6 * (468 + 120)/(120 - 85 + 16) = 6.92.

Calculating the power required to drive the heat pump is simply:

kW = heating duty (Btu/hr) / (3,413 Btu/kWh * Coefficient Of Performance)

Carrying forward the 6.92 COP from before, one million Btu/hr would require

1,000,000 Btu / (3413 Btu/kWh * 6.92 COP) or 42.34 kWh.

This means that every million Btu of heating at 6.92 COP requires 42.34 kWh.

If we assume an industrial electric rate of \$0.06 per kWh, the cost of the heat recovered by the heat pump is \$2.54 per million Btu - much less than most industrial firms' cost of steam.

If the heat pump does not influence peak electrical demand (which may be possible by interrupting the heat pump during peak periods), the average price per kWh may be very low. This could improve the heat pump economics.