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Y. Xu et al.
sources represent the outlet pressure node of the unit. They have one node. The other
units represent by two nodes.
After expanding Eq. (16), three equations can be obtained:
Y 11 P 1 + Y 12 P 2 + K 1 F = −q 1
(16)
Y 21 P 1 + Y 22 P 2 + K 2 F = −q 2
(17)
C 1 P 1 + C 2 P 2 + C 3 F = d
(18)
Expressing P 1 in Eqs. (16)–(18) with P 2 and F, then:
P 1 = Y
−1
11 (−q 1 − Y 12 P 2 − K 1 F)
(19)
Substituting Eq. (19) into Eqs. (16) and (17). Then the equation can be written as
(20):
D 11 D 12
D 21 D 22
P 2
F
=
R 1
R 2
(20)
Solving the Eq. (20) can get the outlet node pressures P 2 and the flow F through
units. Then the pressure of other nodes can be solved by Eq. (19). The system equations
are solved by linear approximation method.
2.2 Thermal Calculation
The hydraulic calculation ignores the influence of the temperature of natural gas, but the
influence of temperature must be considered at the medium or high pressures pipeline
network. The thermal calculation is based on the steady-state hydraulic analysis. The
temperature drop of the pipe is calculated by Eq. (21), and the average temperature is
calculated by Eq. (22). The outlet temperature of all connecting nodes must be equal.
For a single node, it can be expressed as Eq. (23).
Pipe temperature drop equation:
T R = T 0 + (T L − T 0 )e
−al
− D i
P L − P R
aL
1 − e
−al
(21)
Pipe average temperature equation:
T cp = T 0 + (T L − T 0 )
1 − e −al
aL
− D i
P L − P R
aL
1 −
1
aL
1 − e
−al
(22)
Thermal model of connecting nodes:
T out,1 = · · · = T out,N out =
N in
i=1
c p GT
in,i
N out
j=1
c p G
in,j
(23)
Y. Xu et al.
sources represent the outlet pressure node of the unit. They have one node. The other
units represent by two nodes.
After expanding Eq. (16), three equations can be obtained:
Y 11 P 1 + Y 12 P 2 + K 1 F = −q 1
(16)
Y 21 P 1 + Y 22 P 2 + K 2 F = −q 2
(17)
C 1 P 1 + C 2 P 2 + C 3 F = d
(18)
Expressing P 1 in Eqs. (16)–(18) with P 2 and F, then:
P 1 = Y
−1
11 (−q 1 − Y 12 P 2 − K 1 F)
(19)
Substituting Eq. (19) into Eqs. (16) and (17). Then the equation can be written as
(20):
D 11 D 12
D 21 D 22
P 2
F
=
R 1
R 2
(20)
Solving the Eq. (20) can get the outlet node pressures P 2 and the flow F through
units. Then the pressure of other nodes can be solved by Eq. (19). The system equations
are solved by linear approximation method.
2.2 Thermal Calculation
The hydraulic calculation ignores the influence of the temperature of natural gas, but the
influence of temperature must be considered at the medium or high pressures pipeline
network. The thermal calculation is based on the steady-state hydraulic analysis. The
temperature drop of the pipe is calculated by Eq. (21), and the average temperature is
calculated by Eq. (22). The outlet temperature of all connecting nodes must be equal.
For a single node, it can be expressed as Eq. (23).
Pipe temperature drop equation:
T R = T 0 + (T L − T 0 )e
−al
− D i
P L − P R
aL
1 − e
−al
(21)
Pipe average temperature equation:
T cp = T 0 + (T L − T 0 )
1 − e −al
aL
− D i
P L − P R
aL
1 −
1
aL
1 − e
−al
(22)
Thermal model of connecting nodes:
T out,1 = · · · = T out,N out =
N in
i=1
c p GT
in,i
N out
j=1
c p G
in,j
(23)