Page 193 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap13 Final Proof page 189 3.1.2007 9:07pm Compositor Name: SJoearun

GAS LIFT 13/189
rotary compressors (vane or impeller type) are generally The theoretical formula for volumetric efficiency is
driven by electric motors. Large-volume positive compres- 1=k
sors operate at lower speeds and are usually driven by E v ¼ 1 (r 1) C l , (13:21)
steam or gas engines. They may be driven through reduc- where
tion gearing by steam turbines or an electric motor. Re-
ciprocation compressors driven by steam turbines or E v ¼ volumetric efficiency, fraction
electric motors are most widely used in the petroleum r ¼ cylinder compression ratio
industry as the conventional high-speed compression ma- C l ¼ clearance, fraction.
chine. Selection of compressors requires considerations of In practice, adjustments are made to the theoretical
volumetric gas deliverability, pressure, compression ratio, formula in computing compressor performance:
and horsepower.
z s 1=k
E v ¼ 0:97 r 1 C l e v , (13:22)
13.4.3.1 Reciprocating Compressors z d
Two basic approaches are used to calculate the horse- where
power theoretically required to compress natural gas. One
is to use analytical expressions. In the case of adiabatic z s ¼ gas deviation factor at suction of the cylinder
compression, the relationships are complicated and are z d ¼ gas deviation factor at discharge of the cylinder
e v ¼ correction factor.
usually based on the ideal-gas equation. When used for
real gases where deviation from ideal-gas law is appre- In this equation, the constant 0.97 is a reduction of 1 to
ciable, they are empirically modified to take into consid- correct for minor inefficiencies such as incomplete filling
eration the gas deviation factor. The second approach is of the cylinder during the intake stroke. The correction
the enthalpy-entropy or Mollier diagram for real gases. factor e v is to correct for the conditions in a particular
This diagram provides a simple, direct, and rigorous pro- application that affect the volumetric efficiency and for
cedure for determining the horsepower theoretically neces- which the theoretical formula is inadequate.
sary to compress the gas.
Even though in practice the cylinders in the reciprocating 13.4.3.1.2 Stage Compression The ratio of the dis-
compressors may be water-cooled, it is customary to con- charge pressure to the inlet pressure is called the pressure
sider the compression process as fundamentally adiabatic— ratio.Thevolumetricefficiencybecomesless,andmechanical
that is, to idealize the compression as one in which there is stress limitation becomes more, pronounced as pressure
no cooling of the gas. Furthermore, the process is usually ratio increases. Natural gas is usually compressed in stages,
considered to be essentially a perfectly reversible adiabatic, with the pressure ratio per stage being less than 6. In field
that is, an isentropic process. Thus, in analyzing the practice, the pressure ratio seldom exceeds 4 when boosting
performance of a typical reciprocating compressor, one gas from low pressure for processing or sale. When the total
may look upon the compression path following the compression ratio is greater than this, more stages of
general law
compression are used to reach high pressures.
k
pV ¼ a constant: (13:19) The total power requirement is a minimum when the
pressure ratio in each stage is the same. This may be
For real natural gases in the gravity range 0:55 < g g < 1, expressed in equation form as
the following relationship can be used at approximately 1=N s
150 8F: r ¼ p d , (13:23)
p s

k 150 F 2:738 log g g (13:20)
2:328 where
When a real gas is compressed in a single-stage compres- p d ¼ final discharge pressure, absolute
sion, the compression is polytropic tending to approach p s ¼ suction pressure, absolute
adiabatic or constant-entropy conditions. Adiabatic com- N s ¼ number of stages required.
pression calculations give the maximum theoretical work
As large compression ratios result in gas being heated to
or horsepower necessary to compress a gas between any
undesirably high temperatures, it is common practice to
two pressure limits, whereas isothermal compression cal-
cool the gas between stages and, if possible, after the final
culations give the minimum theoretical work or horse-
stage of compression.
power necessary to compress a gas. Adiabatic and
isothermal work of compression, thus, give the upper
and lower limits, respectively, of work or horsepower 13.4.3.1.3 Isentropic Horsepower The computation is
requirements to compress a gas. One purpose of intercool- basedontheassumptionthattheprocessisidealisentropicor
ers between multistage compressors is to reduce the horse- perfectly reversible adiabatic. The total ideal horsepower for
power necessary to compress the gas. The more a given compression is the sum of the ideal work computed
intercoolers and stages, the closer the horsepower require- for each stage of compression. The ideal isentropic work can
ment approaches the isothermal value. be determined for each stage of compression in a number of
ways.Onewaytosolveacompressionproblemisbyusingthe
Mollier diagram. This method is not used in this book
13.4.3.1.1 Volumetric Efficiency The volumetric effi-
ciency represents the efficiency of a compressor cylinder because it is not easily computerized. Another approach
to compress gas. It may be defined as the ratio of the commonly used is to calculate the horsepower for each
volume of gas actually delivered to the piston displacement, stage from the isentropic work formula:
#
"
corrected to suction temperature and pressure. The principal k (k 1)=k
reasons that the cylinder will not deliver the piston w ¼ k 1 53:241T 1 p 2 1 , (13:24)
displacement capacity are wire-drawing, a throttling effect g g p 1
on the valves; heating of the gas during admission to the where
cylinder; leakage past valves and piston rings; and re-
expansion of the gas trapped in the clearance-volume space w ¼ theoretical shaft work required to compress the
from the previous stroke. Re-expansion has by far the gas, ft-lb f =lb m
greatest effect on volumetric efficiency. T 1 ¼ suction temperature of the gas, 8R