Page 271 - Compression Machinery for Oil and Gas

256 SECTION II Types of Equipment

and as gas molecular weight decreases. All compressor sizing and performance
calculations take slippage into account; therefore, it is critical to have accurate
gas data and clearance information in order to get accurate data with respect to
volumetric efficiency and discharge temperature.
Please note that the working process description given above is idealized
because the real compression phase is not isentropic but polytropic. The work
W needed for the compression is indicated by the area limited by the suction,
compression, and discharge line and is mathematically given by.

ð
W ¼ Vdp (4)
It must be noted that the beginning of the discharge is only determined by the
position of the outlet ports in the casing and is independent from the actual pres-
sure in the discharge line. Therefore, the internal pressure p 2i may deviate from
the discharge line pressure p 2 . This may occur if the suction or discharge line
pressures change or if the isentropic exponent k of the gas changes.

Undercompression

A case where the internal pressure p 2i is lower than the discharge line pressure
p 2 is called undercompression (Fig. 6.3). In this case the compression chamber
opens before the inner pressure p 2i has reached the line pressure p 2 and gas is
flowing back rapidly from the discharge line into the compression chamber until
the pressures have equalized. By further rotation of the rotors the volume is
finally reduced to zero and the gas is expelled into the discharge line at the pres-
sure p 2 . Fig. 6.3 shows that the area between the lines is larger than the ideal
process in Fig. 6.2 thus indicating that for undercompression a larger compres-
sion work W is needed. This is equivalent to a lower efficiency and higher

FIG. 6.3 Undercompression.