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Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap11 Final Proof page 146 3.1.2007 8:54pm Compositor Name: SJoearun

11/146 EQUIPMENT DESIGN AND SELECTION
Oil-specific gravity: equations that are noniterative or explicit. This has in-
volved substitutions for the friction factor f M . The specific
141:5 substitution used may be diameter-dependent only
g o ¼ ¼ 0:85
131:5 þ 35 (Weymouth equation) or Reynolds number–dependent
only (Panhandle equations).
Reynolds number:

6 (1:66)(0:85)(62:4) 11.4.1.2.1 Weymouth Equation for Horizontal Flow
N Re ¼ 1,488 12 ¼ 13,101 Equation (11.97) takes the following form when the unit of
5
scfh for gas flow rate is used:
> 2,100 turbulent flow s ﬃﬃﬃﬃﬃﬃs ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2
2
3:23T b 1 ( p p )d 5
Equation (11.89) gives q h ¼ 1 2 , (11:98)

p b f M g g T zzL
T
1 0:0006 21:25 q ﬃﬃﬃﬃ
p ﬃﬃﬃﬃﬃﬃ ¼ 1:14 2 log þ 0:9 ¼ 5:8759, 1
f M 6 (13,101) where f M is called the ‘‘transmission factor.’’ The friction
factor may be a function of flow rate and pipe roughness.
which gives If flow conditions are in the fully turbulent region, Eq.
f M ¼ 0:02896: (11.89) degenerates to
1
Equation (11.93) gives f M ¼ 2 , (11:99)

p 1 ¼ 50 þ 0:433(0:85)(5)(5,280) sin (15 ) þ 1:15 10 5 [1:14 2 log (e D )]
where f M depends only on the relative roughness, e D .
2
(0:02896)(0:85)(5,000) (5)(5,280)
When flow conditions are not completely turbulent, f M
(6) 5 depends on the Reynolds number also.
Therefore, use of Eq. (11.98) requires a trial-and-error
¼ 2,590 psi:
procedure to calculate q h . To eliminate the trial-and-error
procedure, Weymouth proposed that f vary as a function
of diameter as follows:
11.4.1.2 Gas Flow
Consider steady-state flow of dry gas in a constant-diam- f M ¼ 0:032 (11:100)
eter, horizontal pipeline. The mechanical energy equation, d 1=3
Eq. (11.78), becomes With this simplification, Eq. (11.98) reduces to
dp f M ru 2 p(MW) a fu 2 s ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2
2
¼ ¼ , (11:94) 18:062T b ( p p )D 16=3
dL 2g c D zRT 2g c D q h ¼ 1 2 , (11:101)
TzzL
p b g g T
which serves as a base for development of many pipeline
equations. The difference in these equations originated which is the form of the Weymouth equation commonly
from the methods used in handling the z-factor and fric- used in the natural gas industry.
tion factor. Integrating Eq. (11.94) gives The use of the Weymouth equation for an existing
ð ð transmission line or for the design of a new transmission
(MW) a f M u 2 p line involves a few assumptions including no mechanical
dp ¼ dL: (11:95)
2Rg c D zT work, steady flow, isothermal flow, constant compressibil-
ity factor, horizontal flow, and no kinetic energy change.
If temperature is assumed constant at average value in a
pipeline, T ¯ , and gas deviation factor, z ¯, is evaluated at These assumptions can affect accuracy of calculation
average temperature and average pressure, p ¯, Eq. (11.95) results.
In the study of an existing pipeline, the pressure-mea-
can be evaluated over a distance L between upstream
suring stations should be placed so that no mechanical
pressure, p 1 , and downstream pressure, p 2 :
energy is added to the system between stations. No me-
2
25g g Q T zzf M L chanical work is done on the fluid between the points at
T
2
2
p p ¼ , (11:96)
1 2 d 5 which the pressures are measured. Thus, the condition of
no mechanical work can be fulfilled.
where
Steady flow in pipeline operation seldom, if ever, exists
g g ¼ gas gravity (air ¼ 1) in actual practice because pulsations, liquid in the pipeline,
Q ¼ gas flow rate, MMscfd (at 14.7 psia, 60 8F) and variations in input or output gas volumes cause devi-
T ¯ ¼ average temperature, 8R ations from steady-state conditions. Deviations from
z ¯ ¼ gas deviation factor at T ¯ and p ¯ steady-state flow are the major cause of difficulties experi-
p ¯ ¼ (p 1 þ p 2 )/2 enced in pipeline flow studies.
L ¼ pipe length, ft The heat of compression is usually dissipated into the
d ¼ pipe internal diameter, in. ground along a pipeline within a few miles downstream
F ¼ Moody friction factor from the compressor station. Otherwise, the temperature
of the gas is very near that of the containing pipe, and
Equation (11.96) may be written in terms of flow rate
measured at arbitrary base conditions (T b and p b ): because pipelines usually are buried, the temperature of
s ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ the flowing gas is not influenced appreciably by rapid
2
2
( p p )d 5 changes in atmospheric temperature. Therefore, the gas
CT b
q ¼ 1 2 , (11:97) flow can be considered isothermal at an average effective

T
p b g g T zzf M L
temperature without causing significant error in long-
where C is a constant with a numerical value that depends pipeline calculations.
on the units used in the pipeline equation. If L is in miles The compressibility of the fluid can be considered con-
and q is in scfd, C ¼ 77:54. stant and an average effective gas deviation factor may be
The use of Eq. (11.97) involves an iterative procedure. used. When the two pressures p 1 and p 2 lie in a region
The gas deviation factor depends on pressure and the where z is essentially linear with pressure, it is accurate
friction factor depends on flow rate. This problem enough to evaluate z ¯ at the average pressure
prompted several investigators to develop pipeline flow p p ¼ ( p 1 þ p 2 )=2. One can also use the arithmetic average

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