Lenguaje y Comunicación, determinantes de nuestra Cultura

CÁPITULO II: MARCO TEÓRICO 2.1 La Comunicación

2.1.2 Lenguaje y Comunicación, determinantes de nuestra Cultura

Coiled tubing changes length every coiled tubing operation due to axial forces, temperatures, pressure differential across the CT wall, and helical buckling. Each of these can cause error between depth measured at the surface and the actual depth of the BHA downhole. Plastic length change can be recovered by subsequent plastic deformation in the surface equipment if the axial force is less than the transition force, Ft, from equation (2) above, or only partially recovered if the axial force exceeds F.

Figure 4.7 below illustrates this concept for a length of coiled tubing subjected to an axial force exceeding the transition force.

Fig. 4.7. Coiled Tubing Stretch Due to Axial Load

The amount of elastic stretch, ∆L, for a CT segment with the length L and the cross sectional area A, under the axial force F can be calculated as follows:

∆L = L σ / E = L F / A E (4.3)

The plastic stretch can be calculated with the following equations:

∆L =

Additional coiled tubing length change can occur due to thermal effects and to differential pressure across the wall due to Poisson effect (such length change being relatively small).

Helical buckling, discussed in section 4.3.2 below, always reduces the CT apparent length (depth in the well) because the axial force is compressive, but such reduction is typically small.

4.2

Coiled Tubing String Design

The length of coiled tubing on a reel varies depending on diameter. For comparison, a small reel may only be able to hold 4,000 ft. (1220 m) of 2⁷/8 in. (73.025 mm) tubing, but may have a 15,000 ft. (4570 m) capacity if 1¹/2 in. (38.1 mm) tubing is spooled on it.

A properly sized coiled tubing string must have the following attributes for the planned operation:

¾ enough mechanical strength to safely withstand the combination of forces imposed by the job;

¾ adequate stiffness to RIH (run into hole) to the required depth and/or push with the required force;

¾ light weight to reduce logistics problems and total cost;

¾ maximum possible working life.

Optimizing the design of a coiled tubing string to simultaneously meet the criteria listed above for a given coiled tubing operation requires a sophisticated CT numerical simulator and numerous iterations with proposed string designs. Coiled tubing strings designed in this manner usually will contain multiple sections with each one having a different wall thickness. Often called "tapered strings", the wall thickness does not necessarily taper smoothly from thick to thin (top to bottom). Instead, the wall thickness along the string will vary according to the position in the string. However, the OD of the string will remain constant and only the wall thickness changes with the position along the string. Likewise, CT strings are made from the same material from end to end.

The basic procedure consists of “running” the Ct operation on the computer simulation program for a given coiled tubing string and then modifying the string design

by changing the length and wall thickness of the sections to achieve the desired result.

Even though this technique can provide the best Ct string for a given job, the string may not be suitable for operations in other wells or even other applications in the original well. Usually a more generic string design is desirable.

The simplest method of designing a CT string considers only the wall thickness necessary at a given location for the required mechanical strength and the total weight of the string. This method assumes the open-ended CT string is hanging vertically in a fluid with the buoyed weight of the tubing being the only force acting on the string.

Starting at the bottom of the string and working up, the designer selects the wall thickness at the top of each section that provides sufficient tensile force at that location (e.g. the designer could limit the stress at the top of each section to 30% of the material yield strength).

4.3

Buckling of Coiled Tubing Strings

Coiled tubing under axial compression can buckle into a sinusoidal or helical shape if the compressive force exceeds a certain “critical” value for that particular mode of buckling. Such phenomenon is common for operations in deep and/or extended reach wells. Even though plastic deformation on the reel causes residual curvature in the coiled tubing (only when the axial force is quite low), this is not a buckling state.

However, such curvature may help promote buckling as axial compressive force on the coiled tubing increases.

Unlike drill pipe, casing or tubing, buckling of coiled tubing by itself is not a serious problem, being an elastic deformation that does not damage the CT (a buckled coil tubing can continue to slide and transmit axial force). However, CT buckling significantly increases the normal force (drag) between the coiled tubing and the wellbore. This may lead to lock-up, if the compressive force above the buckled section increases high enough.

A coiled tubing segment inside a wellbore buckles into different shapes (modes) when the axial compressive force acting on it exceeds values determined by the particular combination of geometry and physical properties of the segment. The segment remains unbuckled for lower axial compressive force. This threshold between buckling mode is normally called the critical compressive force. The buckling modes and limits are discussed in the following sections.

4.3.1 Sinusoidal buckling of coiled tubing strings:

When the axial compressive force increases to the critical sinusoidal buckling limit, the segment deforms into a sinusoidal (“snake-like”) shape in continuous contact with the wellbore. The buckled segment does not move away from the wellbore nor lie in a plane and continues to change shape as the axial force increases beyond the critical limit, but the normal force exerted by the segment on the wellbore is due mainly to the weight of the segment. Sinusoidal buckling does not present a limiting condition for CT operations, but is an intermediate condition on the path to helical buckling. A schematic of the CT sinusoidal buckling is shown in Figure 4.8 for a horizontal wellbore.

Fig. 4.8. CT Postbuckled Sinusoidal Configuration in a Horizontal Hole

The critical sinusoidal buckling limit, FCS, for a straight segment inclined at an angle, θ, greater than about 15^o (with respect to the vertical – it is the case of a highly inclined wellbore) can be calculated as follows:

FCS =

W EI sin

θ

2 ⋅ ⋅

, (4.6)

where rc = 0.5 (DH – OD) ,

in which OD is the outside diameter of the CT and DH is the hole (wellbore) diameter.

It can be seen that equation (4.6) contains only the bending stiffness of the CT segment, EI, its buoyed weight (per unit length), W, and geometrical terms. they are independent of the CT yield strength. Equation (4.6) includes also the case of a horizontal wellbore for which θ = 90^o and therefore sin θ = 1.

4.3.2 Helical buckling of coiled tubing strings:

If the axial compressive force continues to increase past the critical helical buckling limit, the segment assumes a helical shape in continuous contact with the wellbore. After the segment is buckled helically, the normal force exerted by the segment on the wellbore gains a component proportional to the square of the axial compressive force. Thus, drag on a helical buckled segment increases rapidly with increasing axial compressive force. In order to account properly for this additional drag in the force balance, we must know when the axial force on a segment exceeds the critical helical buckling limit. A schematic of the CT helical buckling is shown in Figure 4.9 for both a horizontal and a vertical wellbore.

The axial compressive force required to helically buckle an inclined CT segment is about 41% greater than FCS from equation (4.6). The critical helical buckling limit, FCH, for a straight inclined segment can be calculated as follows:

36 FCH =

W EI sin

θ

2 ⋅ ⋅

, (4.7)

The symbols from equation (4.7) are the one used in equation (4.6). The same observation applies, concerning the independence of the yield strength.

Fig. 4.9. CT Postbuckled Helical Configuration in a Horizontal / Vertical Hole

The critical helical buckling limit, FVH, for a straight vertical segment, i.e. inclined at angles less than about 15^o, can be calculated as follows:

FVH =

1 . 94

EI ⋅ W

² , (4.8)

It can be seen that equation (4.8) depends only on the stiffness and buoyed weigth of the segment, while the CT material yield strength is not a factor. For common coiled tubing sizes in vertical holes, FVH is typically less than 200 lbf (890 N) compression. This force may seem insignificant, but for many situations most of the coiled tubing in a vertical wellbore is in tension, and buckling is not an issue. If part of a CT string is in compression and the remainder is in tension, the location where axial force changes from tension to compression is called the neutral point (see fig. 4.9).

For common coiled tubing sizes, FCH for a segment can be 20-30 times greater than FVH. This partially explains why CT usually buckles first near the bottom of the vertical portion of a well during RIH. Another reason is that drag is much higher on curved and inclined segments leading to higher axial compressive force at the bottom of the vertical section. It can be also noted that FCH increases with decreasing radial clearance and increasing segment bending stiffness, weight and inclination.

This provides several options for reducing the tendency of a segment to buckle helically. If buckling could be a problem, larger diameter coiled tubing simultaneously

increases I and W while decreasing rc. Another alternative is to increase the CT wall thickness which simultaneously increases I and W.

It is very important to state that both alternatives increase the drag between the coiled tubing and the wellbore. Depending on the conditions, this can offset any benefit of greater stiffness. The only way to determine the effects of changing coiled tubing dimensions is by using a coiled tubing simulator program.

If the coiled tubing dimensions are fixed, the only way to increase the critical helical buckling limit is to lower mud weight (increase W) or conduct the CT operation inside a smaller casing or hole size (decrease rc).

4.3.3 Effects of wellbore curvature and of friction:

In general, wellbore curvature stabilizes a segment against buckling, I.e. Coiled tubing buckles more easily in straight sections of the wellbore than in dogleg or build sections. This does not necessarily means that tortuosity or curvature in the wellbore is beneficial for CT operations (reducing the buckled length would extend the CT reach into a well), because curvature also causes higher drag which may shift the location of buckling upwards.

Traditionally, equation (4.7) has been used in curved holes by considering θ as the average inclination of the curved segment. However this does not account for the stabilizing effect of curvature on buckling because equation (4.7) does not take into account the direction or rate of curvature. An improved procedure accounts for the effect of curvature by including the normal force due to curvature as additional resistance to buckling. Finally, a complex quadratic polynomial equation is obtained for the axial force requires for helical buckling in a curved hole, FH. Such force value is found to be greater than FCH in building, high dropping and purely azimuthal curvatures, while it is smaller for moderately dropping curvature.

Complex buckling experiments indicated that friction significantly affects buckling behaviour of tubing. In general, friction stabilizes a tubular under compression to delay the onset of buckling and also causes hysterezis in the post-buckling behaviour. Figure 4.10 below shows typical results from buckling experiments for a rod buckled inside a tube. It can be seen that hysterezis is significant and axial compressive force at unbuckling is always lower than the one at the onset of buckling.

The conclusion is that current theory actually predicts axial compressive force at unbuckling and therefore predicted critical buckling forces are conservative – equation (4.7) predicts FCH values significantly lower than determined experimentally.

Unfortunately, friction is very difficult to include in stability analyses (based on “energy”

methods) as it is not a conservative force.

Friction has a stabilizing effect on helical buckling by delaying the buckling onset.

An adjusted critical helical buckling limit for an inclined segment with friction can be obtained from equation (4.7) by adding the drag force (a frictional stabilizing force equal to Cf·W·sinθ where is Cf the drag coefficient). The following equation results:

F’CH =

( ) (

)

Fig. 4.10. Effects of Friction on Buckling (experimental results)

Equation (4.9) still seems to underestimate the measured critical helical buckling force. It implies that higher Cf values are beneficial as buckling is delayed, resulting in longer reach for RIH. However, once the coiled tubing buckles, higher Cf leads to a significantly higher post-buckling drag which will shift the buckling problem up to the wellbore by increasing the axial compressive force on the segments above.

4.3.4 Post-buckling lock-up:

Once the helical buckling occurs, the total length change, ∆L, in the coiled tubing by this phenomenon can be calculated using the following equations:

∆L = L·

⎥ ⎥

⎥

⎤

⎢ ⎢

⎢

⎡ ⎟ + −

⎠

⎜ ⎞

⎝

⎛ ⋅

1 2

1 λ π r

(4.10)

where

F 2EI 2

π

λ

= is the helix period

and F > FCH is the axial compressive force in the buckled CT segment.

By itself, helical buckling is neither a critical problem nor a limiting condition for coiled tubing. It does not damage or plastically deform the coiled tubing. However, post/buckling lock-up is the limiting condition for RIH. Lock-up can prevent the BHA from reaching the touch down point. In simple terms, lock-up is a local phenomenon that occurs during RIH when the local increase in drag exceeds the axial compressive force from the Ct segment above. When buckled coiled tubing reaches this condition, any further increase in axial compressive force at the top of the helix is lost completely to drag. Since normal force due to helical buckling increases as the square of axial compressive force, lock-up may occur almost immediately after a segment helically

buckles. Attempting to force more coiled tubing into a hole after lock-up can damage the tubing. Proper modelling of post-buckling drag effects with a CT computer simulator is required to determine whether lock-up occurs.

4.4

Coiled Tubing Limits. Burst and Collapse

When there is a large pressure differential across the coiled tubing wall, especially when combined with a large axial force, there is a risk of CT failure (burst or collapse). A positive differential pressure, i.e. an internal pressure greater than the external pressure, represents a burst condition, while a negative differential pressure, i.e. a grater external pressure, represents a collapse condition. Typically the greatest risk of burst or collapse occurs at the wellhead. These limits can be predicted by using a mathematical model, usually based on the von Mises combined stress and taking into account helical buckling, maximum expected pressures, torque and diameter growth.

Considering the coiled tubing geometry and the four applied loads (internal pressure - pi, external pressure - pe, axial force - F, applied torque - Mt), the principal stresses acting on a CT segment are determined (axial stress, including bending - σa, radial stress - σt, tangential / hoop stress - σh, shear stress - τ) and finally the total equivalent von Mises stress, σvM, is calculated. As the equations used for such calculation are widely known, they are not included in this module.

It has only to be mentioned that when calculating the axial stress, the real force, Fa, has to be considered and not the effective force, Fe. Fa is the actual axial force (as it would be measured by a strain gauge), while Fe, also called the “weight”, is the axial force if the effects of pressure are ignored (it is the force measured by the weight indicator on the CT unit and the load upon which buckling depends). The relationship between these two forces is (where Ai is the CT internal cross sectional area and Ae the CT external cross sectional area): Fa = Fe + Ai pi – Ae pe

Finally, the combined von Mises stress is compared with a given percentage (usually 80%, defined by the safety factor) of the yield strength of the given CT material.

Such approach, even if it is considered a good method for calculating the mechanical limits for steel CT (due to its conservative results), ignores the following conditions:

residual stress, work softening, perfectly plastic behaviour, ovality etc.

Above the injector, the dominant failure mode is fatigue. Below the injector chains and above the stripper, combined compression and burst pressure are the dominant loads but they are not usually a concern. Below the stripper, the most likely failure modes are collapse and tensile failure, while excessive compression is normally not a problem.

Coiled tubing mechanical limits curves can be drawn, showing the combination of the values of the axial force (real or effective) versus the ones differential pressure for which a limit condition is reached (the equivalent stress equals the yield limit) and therefore there is a risk of potential failure of the coiled tubing.

Collapse failure mode is difficult to predict by means of the von Mises criterion briefly described above because it depends on factors that are seldom known accurately (CT ovality and eccentricity, yield stress). To model CT collapse, apart the plastic hinge theory proposed by Newman, API RP 5C7 proposed a set of empirical equations to predict the collapse pressure differential.

5. Current Applications of Coiled Tubing Technology in Drilling and Workover

The final chapter of this module discusses the most important aspects of the drilling and workover applications of coiled tubing. The limitations of CT technology and a solution to overcome the limits of present CT drilling units are also discussed.

5.1

Coiled Tubing Drilling Applications

Coiled tubing drilling has been utilized on a commercial basis for many years, and can provide significant economic benefits when applied in the proper field setting.

Figure 5.1 shows a coiled tubing drilling unit detailing the subsurface standard equipment used for such operation.

In addition to potential cost advantages, CT drilling can provide the following additional benefits:

¾ Safe and efficient pressure control;

¾ Faster tripping time and speed (more than 150 ft./min – 45 m/min);

¾ Smaller footprint and weight;

¾ Faster rigup/rigdown;

¾ Reduced environment impact;

¾ Less personnel;

¾ High speed telemetry (optional feature).

However, the most significant disadvantage of coiled tubing drilling is the inability to rotate the CT in the borehole which implies that the energy required to rotate the drill bit must be supplied by the pressurised drilling mud driving a hydraulic motor. In addition, the lack of rotation causes increased friction between the CT and the walls of the wellbore which makes more difficult the translation of the CT string in the wellbore and may require more frequent tripping of the tubing. As a consequence, several attempts have been made to develop a CT unit capable also to rotate the coiled tubing (see figure 2.2 and 5.2). CT drilling applications have also other limitations that are commented in section 5.3, including the offshore drilling operations.

Table 5.2 below contains a coiled tubing drilling applications summary divided in four major categories. The first applications have been re-entry drilling.

Table 5.1. CT Drilling Applications Summary (Source: [10])

Vertical Drilling Deviated Drilling

Re-entry Drilling Depending on existing wells Lateral drainholes

New Well Drilling

Bit design and selection for coiled tubing drilling follows the same theory as is used in conventional rotary drilling. However, CT drilling generally uses higher bit

speeds at lower weight on bit as a result of the structural differences in coiled tubing versus jointed pipe.

Fig. 5.1. Typical CT Unit for Drilling Applications

5.1.1 Directional and non-directional wells:

In general, coiled tubing drilling can be divided into two main categories consisting of directional and non-directional wells, i.e. vertical and deviated drilling. Non-directional wells use a fairly conventional drilling assembly in conjunction with a downhole motor. Directional drilling requires the use of an orienting device to steer the well trajectory, per the well plan. CT drilling can then be further segmented into

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