Non-destructive testing of pipes
View Patent ↗To perform a non-destructive condition assessment of a pipe carrying a fluid, an actual value representative of the propagation velocity of an acoustic disturbance propagating between two longitudinally separated points on the pipe is determined. A corresponding predicted value for the propagation velocity is computed as a function of at least one wall thickness parameter of the pipe by using a theoretical model for the propagation of acoustic waves in the pipe that assumes said pipe has a finite wall thickness with a predetermined circumferential thickness profile. The wall thickness parameter is then computed by matching the actual value with the predicted value, for example, by substituting the actual value in a formula predicting the theoretical value.
1. A method for the non-destructive condition assessment of a pipe carrying a fluid, comprising:
detecting an acoustic disturbance propagating past two longitudinally separated points on said pipe;
determining an actual value representative of the propagation velocity of said acoustic disturbance;
computing a corresponding predicted value for the propagation velocity as a function of at least one wall thickness parameter of said pipe by using a theoretical model for the propagation of acoustic waves in said pipe that assumes said pipe has a finite wall thickness with a predetermined circumferential thickness profile; and
computing said wall thickness parameter by matching said actual value with said predicted value.
2. A method as claimed in claim 1 , wherein said actual value is determined by determining the time delays for said acoustic disturbance detected at said points, and computing said actual value by dividing the difference between the distances of said points from a source of said acoustic disturbance by said time delays.
3. A method as claimed in claim 2 , wherein said time delays are determined using a time-of-flight method or a cross-correlation method in the time or frequency domains.
4. A method as claimed in claim 1 , wherein said wall thickness parameter is computed by substituting the actual value of the propagation velocity in a formula giving the predicted value.
5. A method as claimed in claim 1 , wherein said wall thickness parameter is selected from the group consisting of the mean wall thickness, the maximum wall thickness, and the minimum wall thickness as a function of radial angle.
6. A method as claimed in claim 1 , further comprising measuring the actual propagation velocity of an acoustic disturbance along a reference pipe of known thickness profile and carrying said fluid, and computing at least one constant for use in said model.
7. A method as claimed in claim 6 , wherein said at least one constant includes the bulk modulus of elasticity of the fluid.
8. A method as claimed in claim 1 , wherein said actual value is the average propagation velocity of low-frequency acoustic disturbances in the pipe.
9. A method as claimed in claim 8 , wherein said average propagation velocity is computed from the time of detection of said acoustic disturbance by sensors located at said respective points.
10. A method as claimed in claim 1 , wherein said assumed predetermined circumferential thickness profile is linear.
11. A method as claimed in claim 10 , wherein the pipe is unconstrained in axial movement, and said predicted value is computed using the equation:
v
=
v
o
/
1
+
K
E
[
D
2
π
F
+
2
(
1
+
μ
)
]
where ν is the predicted value, ν 0 is the propagation velocity said fluid in an unbounded state, D is the internal diameter of the pipe, K is the bulk modulus of elasticity of the fluid, E is the elastic modulus of material forming the pipe, and t max and t min are respectively the maximum and minimum pipe wall thicknesses at respective angular locations θ=0 and θ=π, where θ is a polar coordinate, and F is given by the expression:
F
=
(
1
-
f
)
π
t
max
(
D
+
t
max
)
+
1
b
2
-
4
a
c
[
ln
(
2
π
fa
+
b
-
b
2
-
4
a
c
2
π
fa
+
b
+
b
2
-
4
a
c
)
-
ln
(
b
-
b
2
-
4
a
c
b
+
b
2
-
4
a
c
)
]
where
a
=
(
t
max
-
t
min
π
)
2
,
b
=
(
t
max
-
t
min
π
)
(
2
t
min
+
D
)
,
and
c
=
t
min
2
+
t
min
D
.
12. A method as claimed in claim 10 , wherein said pipe is constrained in axial movement, and said predicted value is computed using the equation:
v
=
v
o
/
1
+
K
E
[
D
2
π
F
(
1
-
μ
2
)
+
2
(
1
+
μ
)
]
where ν is the predicted value, ν 0 is the propagation velocity of said fluid in an unbounded state, D is the internal diameter of the pipe, E is the elastic modulus of material forming the pipe, and t max and t min are respectively the maximum and minimum pipe wall thicknesses at respective angular locations θ=0 and θ=π, where θ is a polar coordinate, and F is given by the expression:
F
=
(
1
-
f
)
π
t
max
(
D
+
t
max
)
+
1
b
2
-
4
a
c
[
ln
(
2
π
fa
+
b
-
b
2
-
4
a
c
2
π
fa
+
b
+
b
2
-
4
a
c
)
-
ln
(
b
-
b
2
-
4
a
c
b
+
b
2
-
4
a
c
)
]
where
a
=
(
t
max
-
t
min
π
)
2
,
b
=
(
t
max
-
t
min
π
)
(
2
t
min
+
D
)
,
and
c
=
t
min
2
+
t
min
D
.
13. A method as claimed in claim 1 , wherein said assumed predetermined circumferential thickness profile is non-linear.
14. A method as claimed in claim 1 , wherein said assumed predetermined circumferential thickness profile is uniform.
15. A method as claimed in claim 14 , wherein said pipe is unconstrained and said predicted value is computed using the equation:
v
=
v
o
/
1
+
D
t
K
E
(
2
t
D
(
1
+
μ
)
+
D
D
+
t
)
where ν is the predicted value, ν 0 is the propagation velocity of said fluid in an unbounded state, D is the internal diameter of the pipe, K is the bulk modulus of elasticity of the fluid, E is the elastic modulus of material forming the pipe, and t is the pipe wall thickness, and μ is the Poisson ratio.
16. A method as claimed in claim 14 , wherein said pipe is constrained and said predicted value is computed using the equation:
v
=
v
o
/
1
+
D
t
K
E
(
2
t
D
(
1
+
μ
)
+
D
D
+
t
(
1
-
μ
2
)
)
where ν is the predicted value, ν 0 is the propagation velocity of said fluid in an unbounded state, D is the internal diameter of the pipe, K is the bulk modulus of elasticity of the fluid, E is the elastic modulus of material forming the pipe, and t is the pipe wall thickness, and μ is the Poisson ratio.
17. A method as claimed in claim 1 , further comprising determining the damping capacity of said pipe, and deriving information about the tensile strength of said pipe from said damping capacity.
18. A method as claimed in claim 17 , wherein the attenuation of said acoustic disturbance propagating between said points is determined, and the damping capacity is derived from the attenuation.
19. A method as claimed in claim 17 , wherein the damping capacity is derived from the width of the frequency spectrum peak that corresponds to the fundamental ring frequency of the pipe or the logarithmic decrement of decaying ring vibration induced by a mechanical impact to the pipe.