188
W. Li et al.
The frictional resistance loss of the bubble flow can be calculated by the Shaw - Sean
– Brill [3] method,
−
dp
dx
=
2f m ρ m v 2
m
D
(5)
Where, ρ m —The average density of a gas-liquid mixture, kg/m3; fm—Fanning friction
coefficient of gas-liquid mixture;
(3) The corner in the pipe
Due to the presence of air, liquid have not freely between gravitational potential
energy and kinetic energy transformation, according to the principle of conservation of
momentum, after a V-shaped (or ) bent under additional pressure loss can be obtained
from,
P 0 = ρa[v 2 − v 1 cos(θ 1 + θ 2 )]
(6)
Where, v 1 —The velocity of the liquid in the first half, m/s; v 2 —The velocity of the
liquid in the second half, m/s; a—Wave velocity in liquid, m/s; θ 1 —The Angle between
the first half of the pipe and the horizontal line, rad; θ 2 —The Angle between the second
half of the pipe and the horizontal line, rad;
The Eq. (6) is considered in the most serious case. In fact, the accumulated gas in
the pipeline may not be enough to generate such a large pressure loss. Therefore, the
actual additional pressure loss is,
P a = kP 0
(7)
The actual commissioning is a cycle of the above three conditions, in which the
pressure loss includes two aspects: frictional resistance loss and additional pressure loss
at the corner.
As for the frictional resistance loss, according to the analysis in (2) Air bubble
section, we believe that the whole pipe segment is in the bubble flow state, which can
be calculated. It must be pointed out that the liquid phase in the bubble flow should be
the emulsion formed by the mixture of oil and water. It is the presence of the emulsion
that intensifies the process of air mass breaking and carrying. However, in the analysis
and calculation, there is a lack of relevant data of on-site oil and water emulsion.
For the additional pressure loss at the turning point, the momentum equation (Eq. 6)
can be used first to calculate the maximum momentum loss, and then the appropriate gas
accumulation coefficient can be selected to obtain the final pressure loss in combination
with the gas-holding condition of the pipe section.
When there is only liquid in the pipe, According to the Dancy formula, the pressure
difference of the pipe before inflation can be obtained, and the pressure difference after
inflation in the pipe is the pressure difference measured on the spot. The value of can
refer to the detection value of the day, while the value of a is about 1100 m/s.
V = v ×
L
a
(9)
W. Li et al.
The frictional resistance loss of the bubble flow can be calculated by the Shaw - Sean
– Brill [3] method,
−
dp
dx
=
2f m ρ m v 2
m
D
(5)
Where, ρ m —The average density of a gas-liquid mixture, kg/m3; fm—Fanning friction
coefficient of gas-liquid mixture;
(3) The corner in the pipe
Due to the presence of air, liquid have not freely between gravitational potential
energy and kinetic energy transformation, according to the principle of conservation of
momentum, after a V-shaped (or ) bent under additional pressure loss can be obtained
from,
P 0 = ρa[v 2 − v 1 cos(θ 1 + θ 2 )]
(6)
Where, v 1 —The velocity of the liquid in the first half, m/s; v 2 —The velocity of the
liquid in the second half, m/s; a—Wave velocity in liquid, m/s; θ 1 —The Angle between
the first half of the pipe and the horizontal line, rad; θ 2 —The Angle between the second
half of the pipe and the horizontal line, rad;
The Eq. (6) is considered in the most serious case. In fact, the accumulated gas in
the pipeline may not be enough to generate such a large pressure loss. Therefore, the
actual additional pressure loss is,
P a = kP 0
(7)
The actual commissioning is a cycle of the above three conditions, in which the
pressure loss includes two aspects: frictional resistance loss and additional pressure loss
at the corner.
As for the frictional resistance loss, according to the analysis in (2) Air bubble
section, we believe that the whole pipe segment is in the bubble flow state, which can
be calculated. It must be pointed out that the liquid phase in the bubble flow should be
the emulsion formed by the mixture of oil and water. It is the presence of the emulsion
that intensifies the process of air mass breaking and carrying. However, in the analysis
and calculation, there is a lack of relevant data of on-site oil and water emulsion.
For the additional pressure loss at the turning point, the momentum equation (Eq. 6)
can be used first to calculate the maximum momentum loss, and then the appropriate gas
accumulation coefficient can be selected to obtain the final pressure loss in combination
with the gas-holding condition of the pipe section.
When there is only liquid in the pipe, According to the Dancy formula, the pressure
difference of the pipe before inflation can be obtained, and the pressure difference after
inflation in the pipe is the pressure difference measured on the spot. The value of can
refer to the detection value of the day, while the value of a is about 1100 m/s.
V = v ×
L
a
(9)