Duct rod system for installing an elongated element in a conduit

Abstract

A duct rod system to be pushed in a conduit of a defined configuration for installing an elongated element in the conduit and comprising at least one rod having a flexible main body, the flexible main body having a bending stiffness arrangement defined in relation to the defined configuration of the conduit to permit a friction reduction of the flexible main body in the conduit.

Claims

1. A method of optimizing a bending stiffness of a duct rod with regard to a specific configuration of a conduit, the method comprising: determining a defined configuration of a conduit, wherein the defined configuration comprises at least the number and/or kinds of bends and/or junctions of the conduit; determining a bending stiffness of at least one rod having a flexible main body, wherein the flexible main body has a bending stiffness arrangement defined in relation to the number and/or kinds of bends and/or junctions of the conduit according to the formula: $B\ge \frac{14{\left(D_d-D_c+\frac{{\alpha }^2}{8}{R}_b\right)}^2}{{\alpha }^2}{P}_F;$ wherein B is the bending stiffness, D.sub.d is the inner diameter of the conduit, D.sub.c is the diameter of the rod, R.sub.b is the bend radius of the bend and a is the angle of the bend and P.sub.F is the local pushing force applied to the rod; and feeding the at least one rod with a bending stiffness substantially equal to the determined bending stiffness into said conduit.

2. The method of claim 1, wherein the conduit has a length and the defined configuration of the conduit comprises at least its length to define the bending stiffness arrangement of the flexible main body.

3. The method of claim 1, wherein the flexible main body comprises at least a first and a second elongated part being disconnectable, with the first elongated part to be first introduced into the conduit, the bending stiffness of the second elongated part being greater than the bending stiffness of the first elongated part.

4. The method of claim 1, wherein the at least one rod comprises a sleeve configured to be introduced into the conduit and cover at least one portion of the flexible main body.

5. The method of claim 4, wherein a friction factor between the sleeve and the flexible main body is lower than 0.1.

6. The method of claim 1, wherein when bent, the flexible main body has a reaction moment in a portion where the flexible main body is bent, wherein the reaction moment of the flexible main body is lowered in the portion where the flexible main body is bent.

7. The method of claim 6, wherein the flexible main body has a cross section with an area moment of inertia, wherein the bending stiffness is lowered by a reduction of the area moment of inertia in the portion where the main body is bent.

8. The method of claim 6, wherein the flexible main body has a cross sectional shape and wherein the cross sectional shape is concavo-convex.

9. The method of claim 8, wherein the sides of the flexible main body are equipped with circular rods.

10. The method of claim 1, wherein the flexible main body comprises an attachment device located at a first end to be first introduced into the conduit.

11. The method of claim 10, wherein the attachment device is detachable from the main body.

12. The method of claim 1, wherein the at least one rod comprises pigs to be installed along the length of the flexible main body, to apply on the rod a pulling force from a fluid flow created in the conduit.

13. The method of claim 1, wherein the length of the flexible main body is greater than 20 meters.

14. The method of claim 1, wherein the flexible main body has a first end to be first introduced into the conduit, wherein there is at least one first point located on the flexible main body at a first distance from the first end and in that there is at least one second point located on the flexible main body at a second distance from the first end, the second distance being greater than said first distance and the bending stiffness of the flexible main body at the second point being greater than the bending stiffness at the first point.

15. A duct rod system having a duct rod with a bending stiffness optimized according to the method of claim 1.

16. A method of optimizing a bending stiffness of a duct rod with regard to a specific configuration of a conduit, the method comprising: determining a defined configuration of a conduit, wherein the defined configuration comprises at least the number and/or kinds of bends and/or junctions, and undulations with amplitude A and period P of the conduit; determining a bending stiffness of at least one rod having a flexible main body, wherein the flexible main body has a bending stiffness arrangement defined in relation to the number and/or kinds of bends and/or junctions, and undulations with amplitude A and period P of the conduit according to the formulas: $B\ge \frac{14{\left(D_d-D_c+\frac{{\alpha }^2}{8}{R}_b\right)}^2}{{\alpha }^2}{P}_F;$ $R_b=\frac{\left(\pi -2\right)P^2}{4{\pi }^{2}A};$ $\alpha =\frac{4\pi A}{P};$ wherein B is the bending stiffness, A is the amplitude of the undulations, P is the period of the undulations, D.sub.d is the inner diameter of the conduit, D.sub.c is the diameter of the rod, R.sub.b is the bend radius of the bend and a is the angle of the bend and P.sub.F is the local pushing force applied to the rod; and feeding the at least one duct rod with a bending stiffness substantially equal to the determined bending stiffness into said conduit.

17. The method of claim 16, wherein the conduit has a length and the defined configuration of the conduit comprises at least its length to define the bending stiffness arrangement of the flexible main body.

18. The method of claim 16, wherein the flexible main body comprises at least a first and a second elongated part being disconnectable, with the first elongated part to be first introduced into the conduit, the bending stiffness of the second elongated part being greater than the bending stiffness of the first elongated part.

19. The method of claim 16, wherein the at least one rod comprises a sleeve configured to be introduced into the conduit and cover at least one portion of the flexible main body.

20. The method of claim 19, wherein a friction factor between the sleeve and the flexible main body is lower than 0.1.

21. The method of claim 16, wherein when bent, the flexible main body has a reaction moment in a portion where the flexible main body is bent, wherein the reaction moment of the flexible main body is lowered in the portion where the flexible main body is bent.

22. The method of claim 21, wherein the flexible main body has a cross section with an area moment of inertia, wherein the bending stiffness is lowered by a reduction of the area moment of inertia in the portion where the main body is bent.

23. The method of claim 21, wherein the flexible main body has a cross sectional shape and wherein the cross sectional shape is concavo-convex.

24. The method of claim 23, wherein the sides of the flexible main body are equipped with circular rods.

25. The method of claim 16, wherein the flexible main body comprises an attachment device located at a first end to be first introduced into the conduit.

26. The method of claim 25, wherein the attachment device is detachable from the main body.

27. The method of claim 16, wherein the at least one rod comprises pigs to be installed along the length of the flexible main body, to apply on the rod a pulling force from a fluid flow created in the conduit.

28. The method of claim 16, wherein the length of the flexible main body is greater than 20 meters.

29. The method of claim 16, wherein the flexible main body has a first end to be first introduced into the conduit, wherein there is at least one first point located on the flexible main body at a first distance from the first end and in that there is at least one second point located on the flexible main body at a second distance from the first end, the second distance being greater than said first distance and the bending stiffness of the flexible main body at the second point being greater than the bending stiffness at the first point.

30. A duct rod system having a duct rod with a bending stiffness optimized according to the method of claim 16.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other characteristics and advantages of the present invention will appear more clearly from the following detailed description of particular non-limitative examples of the invention, illustrated by the appended drawings where:

(2) FIG. 1 represents a conventional duct rod pushed in a conduit, according to the state of the art;

(3) FIG. 2 represents typical undulations in a rod described at FIG. 1;

(4) FIG. 3 represents a duct rod according to an embodiment of the present invention pushed in a duct;

(5) FIG. 4 represents duct rod according to an alternative embodiment of the invention pushed in a duct;

(6) FIG. 5 illustrates different rods passing a bend or a junction in a conduit;

(7) FIG. 6 illustrates a duct rod system to be inserted in a conduit;

(8) FIG. 7 illustrates the duct rod system of FIG. 6 inserted in a conduit; and

(9) FIG. 8 represents a duct rod according to an embodiment of the present invention with a specific cross section.

DETAILED DESCRIPTION

(10) FIG. 1 presents the common situation when a rod is pushed into a duct. A Pushing force Pf is applied to the rod 2 at the entry of the conduit 12. Depending on the weight W of the rod 2, a friction force Ff acts against the movement of the rod 2 and is characterized the formula Ff=f.Math.W, where f stands for the coefficient of friction. It should be understood that the friction force increases with the inserted length of the rod. When a rod of length l is subjected to a pushing force Pf it will buckle (Euler's criterion) when this force reaches the value Pf=(AEI)/l.sup.2, where A is a constant, E is the Young's modulus and I the area moment of inertia. In what follows, B=EI will be called the bending stiffness B (units N.Math.m.sup.2). When buckling occurs, the rod 2 will contact the conduit 12 and will not further collapse because of the confined space. Therefore it is better to speak about undulation than about buckling.

(11) FIG. 2 represents typical undulations of a portion of a conventional long rod 2 inserted in a conduit 12. At each undulation, an extra friction force between the conduit 12 and the rod 2 is generated so that the represented portion of the rod 2 is pushed with a pushing force Pf to enter the conduit 12 and at the opposite, the sum Ff of the friction forces acts against the movement of the rod 2. The undulation period is typically much shorter than the rod length, so the rod 2 will form a “train” of undulations in the duct 12. When pushing a rod 2 over a length L, with a force Pf at the insertion end, a “train” of undulations is formed with decreasing period when going backwards, where the forces are higher. The higher the pushing force, the shorter the induced undulation periods of the rod inside the conduit, leading to increased friction forces, and above a certain critical limit even rendering impossible any further movement of the rod inside the duct. At this limit the increase in friction force becomes higher than the increase in pushing force.

(12) FIG. 3 represents a duct rod according to an embodiment of the invention. As explained here-above, the undulation period depends on the bending stiffness. The duct rod portion 2a is inserted into the duct 12 with a pushing force Pf such that the induced undulation period of the rod 2a will not be too short, limiting the friction, and then duct rod portion 2a is connected to a duct rod portion 2b which has a greater bending stiffness than duct rod portion 2a and which is at its turn inserted into the conduit. As a result, any risk of too short an undulation period is avoided, reducing the friction. Duct rod portion 2b may have a greater bending stiffness either if its Young's modulus is increased by changing its material, or if its area moment of inertia is increased by changing its cross section for example. The use of this bending stiffness arrangement helps to avoid too short of undulation periods of the duct rod portion 2a inside the conduit 12 so that the friction force is reduced to the lowest limit.

(13) The FIG. 4 represents an improvement of the duct rod system presented at FIG. 3. It consists in covering a portion of the duct rod 2a, 2b by a sleeve 15. The sleeve 15 is introduced simultaneously with a first end 3 of the rod 2a, 2b so as to be first introduced into the conduit 12. At this step, there is no relative movement between the rod portion 2a, rod portion 2b and the sleeve 15, as it is only the sleeve 15 which is rubbing against the conduit 12 during the sliding. Once the sleeve 15 is completely inserted into the conduit 12, it is stopped and maintained in place, and the rod portion 2a, rod portion 2b are still pushed so that a relative movement between the rod portion 2a, rod portion 2b and sleeve 15 starts. The interest of using this sleeve 15 is that the material of sleeve can be chosen to offer a lower friction ratio between sleeve 15 and rod portion 2a, rod portion 2b than the friction ratio between conduit 12 and rod portion 2a, rod portion 2b. It is understood that in such a case, the friction force is lowered so that the undulation period is increased. The improvement by using the sleeve 15 is even more striking when a duct rod is inserted into a conduit that is occupied with (a) resident cable(s). Once the sleeve is inserted, the duct rod will no longer suffer from further increased friction caused by the wedge between the resident cable(s) and the conduit wall.

(14) FIG. 5 represents different cases of a rod 2 passing a bend or a junction of the conduit 12.

(15) In case a), the rod 2 inserted in the conduit 12 with a pushing force Pf has a close to optimized bending stiffness and then contacts the conduit 12 at two places 20 in the bending area. Since the rod 2 is in flexion, its bending stiffness creates normal forces normal to the conduit walls at the contact points 20 and friction forces Ff are created at each contact point 20, acting against the movement of the rod 2 into the conduit 12. Here the friction force is solely resulting from the direct reaction of the pushing force.

(16) In case b), the rod 2 inserted into the conduit 12 with a pushing force Pf has a bending stiffness usually too high and as a result contacts the conduit 12 at three contact points 20 in the bending area. At each contact point 20, the bending stiffness makes the rod apply a normal reaction force to the conduit 12 and friction forces Ff appear and act against the movement of the rod in the conduit. The sum of these three resulting friction forces is of course greater than the sum of the two friction forces acting in case a). Here, besides the reaction from the pushing force, also a force resulting from the bending stiffness is adding to the friction.

(17) In case c), the pushed rod 2 has a bending stiffness too low and has not enough rigidity to correctly pass the bend. Its bending stiffness is not sufficient to prevent the rod from being pushed onto the wall of the conduit 12. In this situation, the rod 2 will buttress onto the wall and the associated friction force will inhibit any further movement of the rod 2 into the conduit 12, or at least increasing the friction forces further.

(18) From those cases a), b) and c), it is understood that an appropriate bending stiffness will ensure that passing bends is done with reduced and optimized friction forces. The preferred situation is the transition from situation b) to situation a), when the rod 2 has just not become loose from the inner wall of the bend. In situation a) there is no contribution from the bending stiffness to the friction. So, as long as this situation applies, the straight section benefits from increasing bending stiffness, without a penalty for extra friction in the bend. When, in case of increasing the bending stiffness, the rod starts to touch the inner wall of the bend, the penalty in the bend starts to count, but the benefit in the straight section is at first still dominating. When increasing the bending stiffness further the penalty in the bends will prevail. The best bending stiffness is a balance between the effects in the straight and bent parts of the conduit and depends on the trajectory.

(19) FIG. 6 presents a duct rod system according to an embodiment of the invention to be inserted into a conduit 12. The rod 2a has a first end 3 to be first introduced into the conduit 12 with the help of a pushing device 6 which can be caterpillars for example. In view of the length of the conduit 12, it is determined that the rod 2a should be connected to a rod 2b having a greater bending stiffness and further connected to a rod 2c having a further greater bending stiffness. For an easy installation of the rods 2a, 2b, 2c, they are coiled onto a coil device 4.

(20) FIG. 7 represents the duct rod system presented at FIG. 6 once the rods 2a, 2b, 2c have been pushed through the entire conduit 12. The first end 3 of the rod 2a has reached the exit of the conduit 12. When the pushing force gets higher and risks causing undulations of rod 2a, the latter is connected, using a connection device 10, to a more rigid rod 2b, having a greater bending stiffness, in order to limit excessive undulations of the rod that would result in excessive friction. Considering the rod 2b, once again when the pushing force gets higher and risks causing undulations of rod 2b, it is connected to an again more rigid rod 2c, which has an increased bending stiffness. The points were the rods are connected to more rigid rods are also ruled by the stiffness effects of the rod in bends and junctions in the trajectory, such that the best compromise for the friction is obtained. With this invention, the maximum length of the conduit in which a rod can be pushed is increased compared to a rod having the same stiffness all along its main body.

(21) FIG. 8 represents a duct rod 2 inserted in a conduit 12, having a concavo-convex cross sectional shape, to minimize the friction force in the bends of the conduit. This particular cross sectional shape has the property of being deformed in a bend so that its area moment of inertia is significantly reduced, resulting in a reduced flexion moment of reaction. The reaction forces of the rod 2 on the conduit walls will be severely reduced and the induced friction forces will consequently be proportionally decreased. It is assumed that the area moment of inertia is decreased by 30% minimum in the bends of a conduit with such an embodiment.

(22) Coming back to the formula that gives the pushing force in relation to the characteristics of the rod (bending stiffness and diameter) and the characteristics of the conduit (diameter and bends), some calculations may be shown:

(23) $B\ge \frac{14{\left(D_d-D_c+\frac{{\alpha }^2}{8}{R}_b\right)}^2}{{\alpha }^2}{P}_F;$
wherein B is the bending stiffness (in Nm.sup.2), D.sub.d is the inner diameter of the conduit (in m), D.sub.c is the diameter of the rod (in m), R.sub.b is the bend radius of the bend (in m) and α is the angle (in radians) of the local bend and P.sub.F is the local pushing force applied to the rod (in N).

(24) Firstly, the following system is considered: a conduit having an inner diameter of 26 mm, bends of 90° (π/2), and a rod having a diameter of 9 mm is pushed with a force of 34N (determined either experimentally or with a simulation software), then the optimum bending stiffness of the rod, found with the formula, is:
B≈5.7 Nm.sup.2
This value (i.e. this value or just little higher by 5%-10%) guaranties that the local stiffness of the rod is such that it just gets loose from the inner curve of the bends in the duct (situation between FIG. 5a and FIG. 5b).

(25) Alternatively, the same conduit is considered, but three rods are successively inserted, with the following characteristics:

(26) Rod 1: diameter 6.5 mm, stiffness 1.0 Nm.sup.2

(27) Rod 2: diameter 9 mm, stiffness 5.7 Nm.sup.2

(28) Rod 3: diameter 11 mm, stiffness 10.1 Nm.sup.2

(29) The formula that gives the pushing force in relation with the bending stiffness is used:

(30) $P_F\le \frac{{\alpha }^2}{14{\left(D_d-D_c+\frac{{\alpha }^2}{8}{R}_b\right)}^2}B$

(31) It is found that first Rod 1 can be pushed inside until a force of 6 N, then rod 2 is pushed, until a force of 34 N, and finally rod 3 is pushed, it is still in its optimum until a pushing force of 62 N (i.e. these values or just a little less by 5%-10%). It could be replaced then by an even stiffer rod.

(32) The last case could be that instead of bends the duct only shows windings, with amplitude A of 20 cm and period P of 4 m.

(33) The hereunder formulas are used to determine the maximum pushing force of each rod as defined above:

(34) $P_F\le \frac{{\alpha }^2}{14{\left(D_d-D_c+\frac{{\alpha }^2}{8}{R}_b\right)}^2}B$
With:

(35) $R_b=\frac{\left(\pi -2\right)P^2}{4{\pi }^{2}A}$$\alpha =\frac{4\pi A}{P}$
wherein B is the bending stiffness (in Nm.sup.2), A is the amplitude of the undulations (in m), P is the period of the undulations (in m), D.sub.d is the inner diameter of the conduit (in m), D.sub.c is the diameter of the rod (in m), R.sub.b is the bend radius of the bend (in m) and α is the angle of the local bend (in radians) and P.sub.F is the local pushing force applied to the rod (in N).

(36) It is found that the undulations are equivalent to bends with bend radius of 2.31 m and angle of 36°.

(37) Then, first rod 1 may be pushed inside until a force of 2 N, then rod 2 is pushed, until a force of 9 N, and finally rod 3 is pushed, it is still in its optimum until a pushing force of 17 N (i.e. these values or just a little less). It could be replaced then by an even stiffer rod.

(38) It is understood that obvious improvements and/or modifications for one skilled in the art maybe implemented and being under the scope of the invention as it is defined by the appended claims.