Page 212 - Compression Machinery for Oil and Gas

Reciprocating Compressors Chapter 5 201

l A higher number for VE does not mean it is “better” as might be the case for
energy efficiency. VE simply represents capacity. The influence of VE on
energy efficiency is through the relationship of VE to average piston veloc-
ity (average velocity of gas through valves).
The equation for VE as derived from thermodynamics (or from the P-V dia-
gram) is:

1
Z S P D
VE ¼ 100 CL K 1
Z D P S
where
VE¼volumetric efficiency, %
CL¼fixed clearance, %
Z S ¼compressibility factor at P S and T S
Z D ¼compressibility factor at P D and T D
P D ¼discharge pressure, absolute
P S ¼suction pressure, absolute
K ¼adiabatic exponent, “K-value”
A VE equation that might be used in compressor selection software might
look like this:

Z S 1
VE ¼ 100 R C CL R K 1
C
Z D
Note the term “ R C ” that has been added. Instead of subtracting from
100%, this equation subtracts from 100 R C . This term is intended to account
for the fact a real-running compressor does not conform to pure thermodynamic
theory. For example, the seals surrounding the compression chamber, specifi-
cally the compressor valves, piston rings, and packing, are not perfect. There is
always some internal gas leakage. This means real VE will never agree with VE
from theory. So a “fudge factor” must be used, and “ R C ” is just such a factor.
Every compressor manufacturer has a unique method for adjusting the VE equa-
tion and “ R C ” is just one simple method. Compression ratio (R C ) typically
varies from 1.3 to 3.5 so the R C term reduces VE (capacity) by 1.3%–3.5%.
There can be a concern with VE being too low. Fig. 5.23 shows a P-V dia-
gram (in red) that has low VE. The P-V diagram is very narrow and the dis-
charge event is very short. This raises the possibility that the discharge
valves may not have enough time to open and close properly and can cause
the discharge valves to fail prematurely.

Power
The power required to drive a reciprocating compressor can be divided into
three pieces: adiabatic, valve loss, and friction and each will be discussed
separately.