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Casing/Tubing Design Manual 13-7

October 2005

The optimum size of tubing is clearly the size which will be most cost effective

over a number of years, typically 5 to 8 years. Where high costs workovers are

involved such as on subsea wells, the selection may be for an even longer period

of time, incurring early loss of potential production.

The following sub-sections describe the various factors and their effect on TPC.

Figure 13-2. Example Tubing Sizes on Well Deliverability

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October 2005

Figure 13-3. Effect of Reservoir Pressure on TPC

13.4.3 Reservoir Pressure

As reservoir pressure declines over time, it collapses towards the origin as

illustrated in Figure 13-3, leading to decreasing natural flow rates. Unstable flow

conditions and eventually cessation will occur unless some other change in the

system is made. In reservoirs where significant reductions in reservoir pressure

are anticipated, the effect on productivity must be considered during the

completion design stage to find the most cost effective method of maximizing

productivity, e.g., where workover costs are high to complete with smaller size

tubing to ensure stability through the economic life of the well.

13.4.4 Flowing Wellhead Pressure

Any flowing wellhead pressure is actually back-pressure transmitted down hole to

the bottom-hole flowing pressure, therefore reducing the potential drawdown.

Additionally, high wellhead pressures reduce the amount of free gas and

compress the remaining free gas, of both which increase hydrostatic head. All of

these reduce the natural flow rate of the well.

Larger tubing sizes are more sensitive to changes in flowing wellhead pressure

as the density factor dominates more than in smaller tubing. Again, this means

that smaller tuning may need to be selected instead of the ideal larger tubing to

cater for anticipated changes in wellhead pressure.

Changes in wellhead pressure can be attributed to slugging in the flowline, wells

being produced or closed in which use the same flowline, facility malfunctions,

build-up of wax, etc. This clearly shows how important the assumed wellhead

pressure accuracy is in the well deliverability forecast and economics.

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October 2005

13.4.5 Gas-Liquid Ratio

Increasing gas-liquid ratios cause a decrease in hydrostatic head and increase in

frictional pressure drop, which in the early stages may actually result in increased

flow rates. However, above a critical point there will be a net increase in the

overall pressure drop, hence, flow rates. In these circumstances, the frictional

effects near surface become very dominant and can be alleviated by the use of a

tapered tubing string. Figure 13-4 shows the effect of increasing GLR.

Figure 13-4. Effect of Increasing GLR

13.4.6 Artificial Lift

The intention of installing artificial lift is to reduce the hydrostatic head and,

therefore, bottom hole pressure. This effectively shifts the TPC downwards

bringing the intersection point further towards stable flowing conditions. An

example of rates, which can be obtained by different artificial lift methods, is

illustrated in Figure 13-5. Refer to Section 10 for the applications and

comparisons of the various methods of artificial lift.

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October 2005

Figure 13-5. Examples of Artificial Lift Performance

13.5 Tubing Stress Analysis

13.5.1 Load Considerations

Profiles of the well’s temperature and pressure should be modeled based on the

expected well’s future. The following operations should be considered:

• Long-term well production

• Full tubing evacuation

• Immediate shut-in of the well

• Long-term shut-in of the well

• Fracture stimulation treatment

• Fracture sand screen-out or ball out

Landmark’s thermal simulation software program (WELLCAT

™

) is recommended

to model the well and to generate the temperature (and pressure) profiles. The

temperature and pressure profiles are then used to calculate the stresses in the

tubing string.

13.5.2 Triaxial Stresses

Other than collapse, the tubing design can be based on a triaxial design analysis

for stresses. Triaxial equations assume the failure will occur due to yielding of the

material.

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October 2005

13.5.2.1 Von Mises Triaxial Design Equations

v2 = 1/2 [(

r -

a)2 + [(

a -

t)2 + [(

t -

r)2] (13-1)

= Triaxial stresses

= Radial Stresses

= Axial Stresses

= Hoop stresses (tangential)

The Von Mises triaxial equation is only to be used when:

• Taking into account different stresses in three dimension.

• The yield strength of the material in three dimensions are the same

(isotropic)

13.5.2.2 Hill’s Modification to Von Mises Triaxial Design

Equations

Hill’s modification to the Von Mises equation is used to take into account

materials with different yield points under different directions for non-isotropic

materials such as CRAs).

v2 = 1/2 [C1(

r -

a)2 + C2(

a -

t)2 + C3(

t -

r)2] (13-2)

The constants are:

C1 = (1/RR2 ) + (1/RA2 ) - (1/RT2 )

C2 = (1/RA2 ) + (1/RT2 ) - (1/RR2 )

C3 = (1/RT2 ) + (1/RR2 ) - (1/RA2 )

Where:

RR = (σYR/σYH)

RA = (σYA/σYH)

RT = (σYT/σYH)

And:

σR = The calculated radial stress

σA = The calculated axial stress

σT = The calculated tangential stress

σYR = The maximum radial stress

σYA =The maximum axial stress

σYT =The maximum tangential stress

σYH= The highest of the three stresses above (σYR, σYA, σYT)

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October 2005

When a radial load is ignored (as it is always much smaller than the hoop stress),

it yields the following familiar ellipse from the Design Limit Plot (that we are used

to seeing).

Figure 13-6. 2D Triaxial Ellipse

The plot in Figure 13-6 is a two dimensional triaxial ellipse. It represents the

triaxial solution taken through a plane where the radial stress is set to zero. The

plot also shows the uniaxial API equation boundaries for a specific design factor.

The tubing should be designed to stay within the boundary of the triaxial stress

ellipse but above the lower API collapse boundary.

13.6 Collapse Design

For collapse, the standard four region API formulas should be used. The mode of

failure in collapse can be geometric instability and thus a material yield failure

design (such as the triaxial design) cannot be used. The API formulas were

based on actual test data that takes into account the geometric instability in the

failure mode (see API RP 5c2).

13.7 Tubing Load Cases

The load conditions of the tubing string during the well’s life causes stresses

through the pressure, temperature, and mechanical loads for each condition

imposed. Therefore, it is obvious why, when selecting the type of tubing for a

completion, it is essential to identify exactly what operations will be carried out in

future to determine the consequent loads and thus the associated load

conditions. A manual or computer program is used to calculate and then

ascertain whether the given tubing is able to withstand the maximum load with an

acceptable safety level.

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October 2005

The operations normally carried out on a well for which the string control is

necessary are illustrated below. These should be seen only as an example of

load conditions as each case must be addressed individually as planned

operations may vary. It is important, in any case, to analyze the characteristics of

each operation in order to be able to identify the heavier loads which may be

imposed.

13.8 Pressure Testing

The very first load condition experienced during and after the installation of the

completion string is pressure testing. This involves applying predetermined test

pressures to both the tubing and annulus. These pressures may be applied more

than once during the installation operation.

During the time taken to install the tubing, the completion will have warmed up to

ambient well conditions; therefore, the only load applied is the pressure-induced

forces of piston-effect buckling and ballooning. However, the designed test

pressures should be equal to or greater than any other subsequent pressures

applied to the completion so the magnitude is high. This may be of particular

concern when using large bore tubing movement devices as the forces

generated by the test pressure are greater than packer tubing seal

arrangements.

13.9 Acid Stimulation

Acid jobs are carried out to remove formation damage caused during drilling by

the invasion of fluids and cuttings or to stimulate the formation by improving

permeability. This operation is carried out by pumping a predetermined quantity

of acid down the tubing to the formation at set pressures and flow rates.

From the point of view of the stresses exerted on the tubing string, the maximum

pressure able to be applied at the wellhead must be considered to determine the

rate of acid which can be applied, together with the temperature variations

caused by the injection of colder fluid. It may be necessary, in some cases, to

reduce the loads on the tubing by preheating the acid to limit the thermal

expansion and pressurizing the annulus to reduce the tubing ballooning effect.

Friction reducers may also be used to increase flow at the same wellhead

pressure, and decreasing the bottomhole pressure thus reducing the load.

It is important to monitor the pressure and temperature trends during the

operation as the acid rate will probably increase because of the effect of the acid

on the formation. This may lead to greater cooling down of the tubing with

reduced pressures.

13.10 Fracturing

Fracturing involves the propagation of fractures in the formation for the

improvement of productivity of hydrocarbons. These fractures reach from the

wellbore deep into reservoir and they allow better drainage.

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October 2005

To carry out fracturing, the formation must be pressurized until one or more

fractures are created. This entails obtaining in advance the injection parameters

from various injectivity tests with increasing flow rates. The calculated flow rate is

applied during the operation and the pressure trend (which usually decreases

when the fracture is created due to the reduction of load losses in the formation)

is monitored.

With regard to the stresses on the string similar to acid stimulations, it is

important to assess the drop in temperature caused by the injection of colder

fluid, which is carried out at high flow rates even though in short duration.

The pressures attained, especially during the early injection stage, are higher

than that during acid jobs. At times during these early stages, in order to exceed

the fracturing gradient, the maximum allowable pressure for some wellhead

equipment may be reached. This equipment must, therefore, be protected using

special isolating tools or protection sleeves.

13.11 Flowing

In this case, it is not an operation carried out on the well but the normal flowing

load conditions to which the string is being subjected. It is, therefore, very

important to establish or at least approximate the pressure and temperature

profiles during the life of the well.

Different production situations occur that cause changing load conditions, e.g.,

temperature differences between the beginning and end of the productive life or

the need to increase or decrease the flow rate for reasons external to the well.

Compared to the initial condition, the string undergoes temperature increases,

which cause elongation in it. The resulting compressive forces may lead to the

buckling phenomena and even cause the tubing to exceed its elastic limit.

13.12 Shut-In

After a well is in production, it is necessary to interrupt production for

maintenance or in order to take some data measurements. This shut-in operation

involves closing the well during which the wellhead pressure increases because

the reservoir pressure rises to static condition, pressuring up the fluids in the

tubing.

This load condition is considered critical as, at the moment of shut-in, the

temperature of the string does not vary greatly because of the thermal inertia of

the well. The situation is now similar to that during production but with wellhead

pressures which are greater and, hence, an increase in the stresses on the

string.

13.13 Tubing Movement

When a well is completed, either with a tubing seal unit in a packer bore or a

tubing movement device, it will have completion fluid in both the tubing and the

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October 2005

annulus referred to as the “initial condition.” All subsequent conditions are

calculated from this initial condition.

The pressure-induced effects produce forces that move the tubing. These effects

are the:

• Piston effect.

• Buckling effect.

• Ballooning effect.

• Temperature effect

Each effect is addressed in this section.

13.13.1 Piston Effect

Then run in a well, tubing must first be able to withstand the load of its own

weight, which may be a significant factor especially in deep wells. This tensile

load is greatest in the joint immediately below the tubing hanger. The tubing is

run into a completion fluid with equivalent fluid density inside and outside the

tubing, which results in a reduction of the load due to buoyancy.

If there is an alteration from this initial condition causing a change in pressure

forces across the packer seal unit, then a piston effect is caused. This will alter

the tensile load on the top and bottom of the tubing.

The change in length from these alterations is calculated from Hooks Law.

Where E is the modulus of elasticity (sometimes referred to as a Young’s

modulus formula)

The force (F) change is caused by the change in piston force from the initial

conditions created by a change in pressure in the annulus or tubing at the

packer. Equation 13-3 and Figure 13-7 illustrate this piston force for two cases:

tubing larger than the packer bore and tubing smaller than the packer bore. The

formula in each case is the same:

−=Λ (13-3)

Substituting for F, the equation becomes:

(

)

(

)

[

]

oopip

PAAPAA

L Λ−−Λ−−=Λ

(13-4)

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October 2005

where:

L = Length of the tubing string to the packer depth (ins)

E = Young’s Modulus of Elasticity (psi)

As = Cross-sectional area of tubing (ins 2 )

Ap = Area of the packer bore (ins 2 )

Ai = Area of the tubing ID (ins 2 )

Ao = Area of the tubing OD (ins 2 )

∆Pi = Change in tubing pressure at the packer (psi)

∆Po = Change in annulus pressure at the packer (psi)

Figure 13-7. Packer Bore Larger or Smaller than Tubing OD