Reciprocating Compressors – Capacity and Power Calculations

The power required by a reciprocating compressor is normally calculated using adiabatic (isentropic) relationships. The common industry practice is to state power in units of “brake horsepower per million cubic feet per day” (Bhp/MMCFD).

It is important to differentiate between:

• Bhp/MMCFD – brake horsepower per million cubic feet per day (14.4 psia and actual suction temperature)
• Bhp/MMSCFD – brake horsepower per million standard cubic feet per day (14.7 psia and 60°F)

When the capacity is given in MMSCFD, it may be converted to MMCFD as follows:

where:
Ts = Actual suction temperature, °R
Zrc = Compressibility at reference conditions of 14.4 psia and actual suction temperature
Zo = Compressibility at 14.7 psia and 60°F

Note Zrc/Zo can usually be taken as 1.0 with negligible error

If the capacity is given in SCFM, or pounds per minute, MMCFD can be calculated as follows:

where:
w = weight flow in lbs/minute
M = molecular weight

When the flow rate in MMCFD, and Bhp/MMCFD are known, brake horsepower can be calculated from:

MMCFD can be converted to ICFM (inlet cubic feet per minute), or Q as follows (bearing in mind that MMCFD is equal to 10^6 cubic feet/day):

where:
Ps = Suction pressure in psia

(Notice that division of 14.4 by 1440 results in 1/100 which simplifies the arithmetic, and it is for this reason that 14.4 psia is used as a convenient reference pressure for MMCFD.)

Combining Equations 300-4, 300-8 and 300-9:

where:
Vd = displacement rate, CFM
Ev = volumetric efficiency as a decimal
Note Zrc is often taken as 1.0 in Equations 300-9 and 300-10 as a simplifying assumption. The error is usually small.

A number of formulas and charts have been developed over the years for determining Bhp/MMCFD. (Note that Bhp/MMCFD is often shortened to Bhp/MM.) Most of the recently published charts and equations have been for large motordriven, low-speed, heavy-duty machines for critical refinery and chemical plant services covered by API 618. These relationships are also generally applied to large low-speed integral gas-engine compressors.

The Bhp/MM curves are used along with several correction factors to account for specific gravity, low-inlet pressure, etc. Additional correcting factors are often applied for smaller frames with higher speeds.

Computer programs have also been developed to calculate the theoretical horsepower and power losses associated with specific types of valves, and mechanical friction. The resulting power predictions are much more accurate than the Bhp/MM curves and the correction factors, and the computer methods continue to be improved. By the mid-1980’s, the major manufacturers were using computer methods on most applications.

The manufacturers consider their valve designs and loss factors to be proprietary, and they are, therefore, not available. However, fairly good estimates can be made using updated Bhp/MM curves or formulas with some corrections.

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