Page 150 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap11 Final Proof page 145 3.1.2007 8:54pm Compositor Name: SJoearun

TRANSPORTATION SYSTEMS 11/145

dp 32mu relative to the inside diameter of the pipe. Relative rough-
¼ : (11:83)
dL f g c D 2 ness, e D , is defined as the ratio of the absolute roughness to
the pipe internal diameter:
Equating the frictional pressure gradients given by Eqs. «
(11.78) and (11.83) gives e D ¼ D , (11:90)
f M ru 2 32mu where « and D have the same unit.
¼ , (11:84)
2g c D g c D 2 The absolute roughness is not a directly measurable
property for a pipe, which makes the selection of value of
which yields pipe wall roughness difficult. The way to evaluate the
absolute roughness is to compare the pressure gradients
64m 64
f M ¼ ¼ : (11:85) obtained from the pipe of interest with a pipe that is sand-
dur N Re roughened. If measured pressure gradients are available,
the friction factor and Reynolds number can be calculated
In the turbulent flow region, a number of empirical cor- and an effective e D obtained from the Moody diagram.
relations for friction factors are available. Only the most This value of e D should then be used for future predictions
accurate ones are presented in this section. until updated. If no information is available on roughness,
For smooth wall pipes in the turbulent flow region, a value of « ¼ 0:0006 in. is recommended for tubing and
Drew et al. (1930) presented the most commonly used line pipes.
correlation:
0:5
f M ¼ 0:0056 þ , (11:86) 11.4.1.1 Oil Flow
N 0:32
Re This section addresses flow of crude oil in pipelines. Flow
of multiphase fluids is discussed in other literatures such as
which is valid over a wide range of Reynolds numbers, that of Guo et al. (2005).
3
6
3 10 < N Re < 3 10 . Crude oil can be treated as an incompressible fluid. The
For rough wall pipes in the turbulent flow region, the relation between flow velocity and driving pressure differ-
effect of wall roughness on friction factor depends on ential for a given pipeline geometry and fluid properties is
the relative roughness and Reynolds number. The Nikur- readily obtained by integration of Eq. (11.78) when the
adse (1933) friction factor correlation is still the best kinetic energy term is neglected:
one available for fully developed turbulent flow in rough
pipes: g f M ru 2
P 1 P 2 ¼ r sin u þ L, (11:91)
1 g c 2g c D
p ffiffiffiffiffiffi ¼ 1:74 2 log (2e D ) (11:87)
f M which can be written in flow rate as

g f M rq 2
This equation is valid for large values of the Reynolds P 1 P 2 ¼ r sin u þ 2 L, (11:92)
g c 2g c DA
number where the effect of relative roughness is dominant.
The correlation that is used as the basis for modern where
3
friction factor charts was proposed by Colebrook (1938): q ¼ liquid flow rate, ft =sec
! A ¼ inner cross-sectional area, ft 2
1 18:7
p ffiffiffiffiffiffi ¼ 1:74 2 log 2e D þ p ffiffiffiffiffiffi , (11:88) When changed to U.S. field units, Eq. (11.92) becomes
f M N Re f M
p 1 p 2 ¼ 0:433g o L sin u þ 1:15 10 5
which is applicable to smooth pipes and to flow in
2
transition and fully rough zones of turbulent flow. It f M g o Q L
degenerates to the Nikuradse correlation at large values d 5 , (11:93)
of the Reynolds number. Equation (11.88) is not explicit where
in f M . However, values of f M can be obtained by a numer-
ical procedure such as Newton–Raphson iteration. An p 1 ¼ inlet pressure, psi
explicit correlation for friction factor was presented by p 2 ¼ outlet pressure, psi
Jain (1976): g o ¼ oil specific gravity, water ¼ 1.0

1 21:25 Q ¼ oil flow rate, bbl/day
p ffiffiffiffiffiffi ¼ 1:14 2 log e D þ : (11:89) d ¼ pipe inner diameter, in.
N 0:9
f M Re
Example Problem 11.4 A 35 API gravity, 5 cp, oil is
This correlation is comparable to the Colebrook correlation.
For relative roughness between 10 6 and 10 2 and the transported through a 6-in. (I.D.) pipeline with an uphill
3
8
Reynolds number between 5 10 and 10 , the errors were angle of 15 degrees across a distance of 5 miles at a flow
reported to be within + 1% when compared with the Cole- rate of 5,000 bbl/day. Estimate the minimum required
brookcorrelation.Therefore,Eq.(11.89)isrecommendedfor pump pressure to deliver oil at 50 psi pressure at the
all calculations requiring friction factor determination of outlet. Assume e ¼ 0.0006 in.
turbulent flow.
The wall roughness is a function of pipe material, Solution
method of manufacturing, and the environment to which
it has been exposed. From a microscopic sense, wall Pipe inner area:
roughness is not uniform, and thus, the distance from the
2
peaks to valleys on the wall surface will vary greatly. The p 6 2
absolute roughness, «, of a pipe wall is defined as the mean A ¼ 4 12 ¼ 0:1963 ft
protruding height of relatively uniformly distributed
and sized, tightly packed sand grains that would give the The average oil velocity in pipe:
same pressure gradient behavior as the actual pipe wall.
(5,000)(5:615)
Analysis has suggested that the effect of roughness is u ¼ ¼ 1:66 ft=sec
not due to its absolute dimensions, but to its dimensions (24)(60)(60)(0:1963)