Method for estimating the location of a leak in a pipeline
A method for estimating a location of a leak (x) in a pipe ( 1 ). A liquid of a known density is fed into the pipe at a first inlet pressure (P 1 ). When the liquid achieves a substantially steady flow rate, the flow rate passing into the pipeline is recorded. This step is repeated at a second, different, inlet pressure (P 2 ). Using this data, an estimate of the leak location (x) and the area of the leak is calculated by simultaneously solving an expression which is based on relating the frictional energy losses of the liquid travelling through the pipeline ( 1 ) to the pressure in the pipeline at the leak (P leak ) and the flow rate of liquid from the leak.
1. A method for estimating a location of a leak in a pipeline, the method comprising the steps of:
A) feeding a liquid of a known density into said pipeline at a first inlet pressure and shutting said pipeline downstream of said leak, such that, once said liquid achieves a substantially steady flow rate, the flow rate of liquid passing into the pipeline can be assumed to be equal to the flow of liquid from the leak;
B) when said liquid achieves a substantially steady flow rate at said first pressure, recording the flow rate of the liquid passing into the pipeline;
C) repeating steps A and B at a second, different, inlet pressure; and
D) calculating, using a computer, an estimate of the leak location and the area of the leak by simultaneously solving a first and a second expression of the leak location relative to the flow rate recorded for each of said first and second inlet pressures, wherein at least one of said first and second expressions is represented by:
Q
L
=
C
d
A
L
2
g
[
P
1
ρ
m
g
+
(
ρ
m
-
ρ
w
ρ
m
)
D
-
λ
(
x
d
)
(
V
2
2
g
)
]
where
Q L is the flow of liquid through the pipeline measured at the inlet;
C d is the coefficient of discharge;
A L is the area of the leak;
g is gravitational acceleration;
P 1 is the pressure at the pipeline inlet;
ρ m is the liquid density in pipeline;
ρ w is the density of seawater;
D is the depth beneath the sea at the leak location;
λ is the friction factor along the line;
x is the leak location;
d is the pipeline diameter;
V is the liquid velocity, and
wherein said first and second expressions comprise estimating the leak location and the area of the leak based on frictional energy losses of said liquid travelling through the pipeline to the leak location and relating this to the pressure in the pipeline at the leak and the flow rate of liquid from said leak.
2. A method according to claim 1 wherein at least one of said expressions applies the D'Arcy Weisbach relationship for estimating said frictional energy losses.
3. A method according to claim 1 wherein at least one of said expressions applies Bernoulli's Equation for relating frictional energy losses to the pressure in the pipeline at the leak.
4. A method according to claim 1 wherein at least one of said expressions applies the Orifice Flow Equation for relating the pressure in the pipeline at the leak to the flow rate.
5. A method according to claim 1 wherein at least one of said expressions further comprises accounting for external pressure at the leak location on the flow rate of liquid from said leak.
6. A method according to claim 1 wherein in said steps B and C, said liquid achieves a substantially steady flow rate when there is less than a +/−20% change in flow rate.
7. A method according to claim 1 wherein in said steps B and C, said pressure and flow rate are sampled over a period of 30 to 60 minutes and an average pressure and flow rate value is recorded.
8. A method according to claim 1 further comprising:
repeating step C at further, different, inlet pressures;
calculating, said computer, further estimates of the leak location using the flow rates recorded for said further inlet pressures; and
averaging said estimates.
9. A method according to claim 1 , wherein step B further comprises recording the pressure and flow rate of the liquid at a location downstream of the leak; and
wherein at least one of said expressions accounts for the flow of liquid downstream of the leak in calculating an estimate of the leak location by deducting the effect of frictional energy losses and pressure in the pipeline of the liquid travelling from the leak location to the downstream location.
10. A method for estimating a location of a leak in a pipeline, the method comprising the steps of:
A) feeding a liquid of a known density into said pipeline at a first inlet pressure;
B) when said liquid achieves a substantially steady flow rate at said first pressure, recording the flow rate of the liquid passing into the pipeline and recording the pressure and flow rate of the liquid at a location downstream of the leak;
C) repeating steps A and B at a second, different, inlet pressure; and
D) calculating, using a computer, an estimate of the leak location and the area of the leak by simultaneously solving a first and a second expression of the leak location relative to the flow rate recorded for each of said first and second inlet pressures, wherein at least one of said expressions is represented by:
A
L
=
1
M
·
(
V
1
∓
N
)
where
N
=
2
·
g
[
P
1
ρ
·
g
-
P
out
ρ
·
g
+
z
1
-
z
out
+
V
1
2
2
·
g
-
Δ
H
1
→
out
]
M
=
C
d
·
1
A
2
ρ
·
(
P
1
+
g
·
ρ
·
(
z
1
-
z
*
)
-
g
·
ρ
·
Δ
H
1
→
*
-
P
ext
)
Δ
H
1
→
*
=
λ
(
x
d
)
(
V
1
2
2
·
g
)
Δ
H
1
→
out
=
λ
(
x
d
)
(
V
1
2
2
·
g
)
+
λ
(
(
L
-
x
)
d
)
(
V
out
2
2
·
g
)
A L is the area of the leak;
V 1 is the inlet liquid velocity;
V out is the liquid velocity at the downstream location;
g is gravitational acceleration;
P 1 is the pressure at the pipeline inlet;
P out is the pressure at the downstream location;
ρ is the liquid density in pipeline;
Z 1 is the static head at the inlet;
Z out is the static head at the downstream location;
Z * is the static head at the leak location;
ΔH 1-* is liquid energy loss between the inlet and the leak location;
ΔH 1-out is liquid energy loss between the inlet and the outlet;
C d is the coefficient of discharge;
A is the cross sectional area of the pipeline;
P ext is the external pressure at the leak location;
x is the leak location;
L is the length of the pipeline between the inlet and the downstream location;
d is the pipeline diameter; and
λ is the friction factor along the line, and
wherein at least one of said expressions accounts for the flow of liquid downstream of the leak in calculating an estimate of the leak location by deducting the effect of frictional energy losses and pressure in the pipeline of the liquid travelling from the leak location to the downstream location.