# Tubing design

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### Tubing design

In the previous chapter, selection procedure of tubing diameter was based on well performance analysis. In this section, the procedure for selecting tubing material properties is presented. Selection of material is carried out by considering different forces that act on the tubing during production and workover operations and then a graphical method is used to present the tubing load against material properties.

### 1.1 Forces on tubing

During the life of the well, tubing is subjected to various forces from production and workover operations which include:

* production of hydrocarbon,

* killing of the well,

* squeeze cementing,

* hydraulic fracturing etc.

The activities result in change in temperature and pressure inside the tubing and casing-tubing annulus, which can cause a change in tubing length (shortening or lengthening).

The change in length often leads to increase in compression or tension in tubing and in extreme situation unseating of packer or failure of tubing (Hammerlindl, 1977 and Lubinski et.al, 1962).

### According to the authors the change in pressure inside and outside of tuning and temperature can have various effects on tubing:

* piston effect(According to Hooke's Law),

* helical buckling,

* ballooning and

* thermal effect.

### HOOKE'S LAW EFFECT'S

Changes in pressure inside and outside the tubing can cause tubing movement due to piston effect. According to Hooke's law, change in length of tubing caused by this effect can be calculated using the Equation 4.1.

Where is the change in forces due to the change in pressures inside ( ) and outside () tubing and can be expressed as:

Where, (see Fig. 4.2)

DL1= change in length due to Hooke's Law effect, inch,

L = length of tubing, inch,

F = force acting on bottom of tubing, lb.,

E= modulus of elasticity,

As = cross-sectional area of tubing, inch2,

Ai = area based on inside diameter of tubing, inch2 and

Ao = area based on outside diameter of tubing, inch2,

Ap= area based on diameter of packer seal, inch2,

= change in pressure inside annulus at packer (Final - Initial), psi and

= change in pressure inside tubing at packer (Final - Initial), psi.

Notes: DL, DF, DPi or DPo indicates change from initial packer setting conditions. It is assumed Pi = Po when packer is initially set.

### HELICAL BUCKLING

The difference in pressure inside tubing and casing-tubing annulus acts on the cross sectional area of packer bore at tubing seal and leads to a decrease in the length of tubing due to buckling. This effect is known as helical buckling. When the tubing is restricted from movement, a tensile load is developed. This effect is increased with increase in inside tubing pressure.

The change in length caused by helical buckling can be calculated by the Equation 4.3.

where

Force causing buckling: Ff = Ap (Pi - Po)

If Ff (a fictitious force) is zero or negative, there is no buckling.

Length of tubing buckled: n = Ff / w

Where,

DL2= change in length due to buckling, inch,

r= radial clearance between tubing and casing, inch,

w = ws + wi - wo,

ws = weight of tubing, lb/incn,

wi =weight of fluid contained inside tubing, lb/in. (density multiplied by area based on ID of tubing),

wo= weight of annulus fluid displaced by bulk volume of tubing, lb/in. (density multiplied by area based on OD of tubing),

=tubing outside diameter, inch and

=tubing inside diameter, inch.

Buckling can be avoided by applying surface annular pressure.

### BALLOONING EFFECT'S

The radial pressure inside the tubing causes tubing to increase or decrease in length. When the pressure inside the tubing is greater compared to the pressure inside the casing-tubing annulus, it tends to inflate the tubing, thus shortening the tubing. If the pressure inside the casing-tubing annulus is greater compared to pressure inside the tubing, then the tubing length is increased. This effect is known as ballooning and the change in length caused due to this effect is given by Equation 4.4.

Where,

DL3=change in length due to ballooning, in.

m= Poisson's ratio (0.3 for steel)

R= tubing OD/tubing ID

Dri=change in density of fluid inside tubing, lb/in3

Dro=change in density of fluid outside tubing, lb/ in3

Dpi=change in surface pressure inside tubing, psi

Dpo=change in surface pressure outside tubing, psi

d=pressure drop in tubing due to flow, psi/in. (usually considered as d= 0)

### THERMAL EFFECT'S

Due to the earth's geothermal gradient, the temperature of the produced fluids can be high enough to change the tubing length. The effect is opposite (decrease in length) when a cold fluid is injected inside the tubing. It is ideal to take the change in average string temperature. The change in length due to temperature can be calculated using the Equation 4.5.

Where,

DL4=change in length, in.

L=length of tubing string, in.

C=coefficient of expansion of steel per oF

DT=temperature change, oF

PACKER SETTING FORCE

The setting of packer requires forces which may lead to change in length of tubing.

This change in length can be calculated using the Equation 4.6., which is derived based on Equations 4.1 and 4.3.

The force on packer should not exceed critical values whereby it can cause permanent damage to the tubing. The initial weight on packer may cause "slack off" and to check if this situation might exist, one could use Equation 4.7.

Where, F = set-down force.

The tubing can suffer permanent damage if the stress in the tubing exceeds the yield strength of the tubing material. It is therefore advised to determine the safe tubing stresses for a given production or workover operation. The safe tubing stress can be calculated by using the following Equations (Allen and Roberts, 1989):

The critical values can be calculated using Equations 4.8 and 4.9.

Where,

Si=stress at inner wall of the tubing

So=stress at outer wall of the tubing

### For free-motion packer:

When the packer exerts some force on the tubing, an additional term Ff should be added to Fa and the sign in Equations 4.8 and 4.9 varies in way to maximize the stresses.

### Example 4.1: An example of Tubing Movement calculation:

The following operations are to be performed on a well completed with 9,000 ft of 2-7/8" OD (2.441" ID), 6.5 lb/ft tubing. The tubing is sealed with a packer which permits free motion. The packer bore is 3.25". The casing is 32 lb/ft, 7" OD (6.049" ID). Calculate the total movement of the tubing (note: " notation is used for inch).

Conditions |
Production |
Frac |
Cement |

Initial Fluid |
12 lb/gal mud |
13 lb/gal saltwater |
8.5 lb/gal oil |

Final Fluid |
|||

Tubing |
10 lb/gal oil |
11 lb/gal frac fluid |
15 lb/gal cement |

Annulus |
12 lb/gal mud |
13 lb/gal saltwater |
8.5 lb/gal oil |

Final Pressure |
|||

Tubing |
1500 psi |
3500 psi |
5000 psi |

Annulus |
0 |
1000 psi |
1000 psi |

Temp Change |
+25oF |
-55oF |
-25oF |

### SOLUTION

### Production:

### Hooke's Law Effect

At bottom hole conditions

DPi = Final pressure inside tubing - Initial pressure inside tubing

DPo = Final pressure inside annulus - initial pressure inside annulus

Using Eq. (4.2)

Using Eq. (4.1)

### Helical Buckling Effect

Using Eq. (4.3)

### Ballooning Effect

Using Eq. (4.4)

### Temperature Effect

Using Eq. (4.5)

Total Tubing Movement

(Tubing lengthens)

Fracturing:

### Hooke's Law Effect

At bottom hole conditions

DPi = Final pressure inside tubing - Initial pressure inside tubing

DPo = Final pressure inside annulus - initial pressure inside annulus

Using Eq. (4.2)

Using Eq. (4.1)

### Helical Buckling Effect

Using Eq. (4.3)

### Ballooning Effect

Using Eq. (4.4)

### Temperature Effect

Using Eq. (4.5)

Total Tubing Movement

(Tubing shortens)

### Cement:

### Hooke's Law Effect

At bottom hole conditions

DPi = Final pressure inside tubing - Initial pressure inside tubing

DPo = Final pressure inside annulus - initial pressure inside annulus

Using Eq. (4.2)

Using Eq. (4.1)

### Helical Buckling Effect

Using Eq. (4.3)

### Ballooning Effect

Using Eq. (4.4)

### Temperature Effect

Using Eq. (4.5)

### Total Tubing Movement

(Tubing shortens)

### 1.2 Selection of Tubing Material

Tubing selection should be based on whether or not the tubing can withstand various forces which are caused due to the variations in temperature and pressure. The API has specified tubing based on the steel grade. Most common grades are: H40, J55, K55, C75, L80, N80, C95, P105 and P110. The number following the letter indicates the maximum yield strength of the material in thousands of psi. The failure of the tubing can be attributed to the loading conditions. There are three modes of tubing failure which include:

* burst (pressure due to fluid inside tubing),

* collapse (pressure due to fluid outside tubing) and

* tension (due to weight of tubing and tension if restricted from movement).

The graphical design of the tubing can be achieved by creating a plot of depth vs pressure. This design is carried out by calculating pressures inside the tubing and casing-tubing annulus at the bottom hole and tubing head. The maximum differential pressures at surface and bottom hole are examined using the plot. This maximum condition usually occurs during stimulation.

When the maximum allowable annular pressure is maintained during stimulation, a considerable amount of reduction in the tubing load can be achieved. The burst pressure load (difference between the pressure inside the tubing and annulus) is mostly experienced in greater magnitude close to the surface but may not necessarily be always true. The burst load lines are plotted followed by plotting collapse load lines.

The collapse loads are calculated with an assumption that a slow leak at the bottom hole has depressurized the tubing. This scenario is sometimes expereinced after the fracturing treatment when operators commence kickoff before bleeding off the annular pressure.

If the data for pressure testing conditions (usually most critical load) is available, it should be included in the plot.

Along with the collapse and burst loads, the burst and collapse resistance for different tubing grades (available) are plotted. By observing the plot we can determine which tubing grade to be selected that can withstand the calculated loads.

An example of selecting tubing based on graphical design is presented below.

Example 4.2: Graphical tubing design

Based on the data given below, select a tubing string that will satisfy burst, collapse and tension with safety factors of 1.1, 1.0 and 1.8 respectively.

### Planning Data:

D =9000 ft true depth,

f = 2.875 inches, tubing OD,

CIBHP = 6280psi, closed-in bottom hole pressure,

FBP = 12550psi, formation breakdown pressure,

FPP = 9100psi, fracture propagation pressure,

Gpf = 0.4 psi / ft packer fluid gradient,

Gf = .48 psi /ft fracturing fluid gradient,

g = 0.75 gas gravity at reservoir,

Pann = 1000 psi, maximum allowable annulus pressure,

SFB =1.1, safety Factor, Burst Condition,

SFC =1.0, safety Factor, Collapse Condition,

SFT =1.8, safety Factor, Tensile Load,

Burst and Collapse rating of available tubing's:

B_L80 =9395 psi,

C_L80 =9920 psi,

B_J55 =6453 psi,

C_J55 =6826 psi,

B_H40 =4693 psi and

C_H40 =4960psi.

### Solution:

### Step 1: Calculate the ratio of bottomhole pressure to surface pressure.

Referring table 4.1 in the manual, determine the ratio of surface and BHP at the given reservoir gas gravity,

At a gas gravity = 0.8 and Depth 9000 ft, the ratio is 0.779

At a gas gravity = 0.7 and Depth 9000 ft, the ratio is 0.804

At gas gravity 0.75 the ratio of surface pressure to BHP is

### Table 4.1 - Ratio of surface pressure and BHP in gas wells for a range of gas gravities.

Depth of Hole |
Gas Gravity |
||||

(ft) |
(m) |
0.60 |
0.65 |
0.70 |
0.80 |

1000 |
305 |
0.979 |
0.978 |
0.976 |
0.973 |

2000 |
610 |
0.959 |
0.956 |
0.953 |
0.946 |

3000 |
915 |
0.939 |
0.935 |
0.93 |
0.92 |

4000 |
1219 |
0.92 |
0.914 |
0.907 |
0.895 |

5000 |
1524 |
0.901 |
0.893 |
0.885 |
0.87 |

6000 |
1830 |
0.883 |
0.873 |
0.854 |
0.847 |

7000 |
2133 |
0.864 |
0.854 |
0.844 |
0.823 |

8000 |
2438 |
0.847 |
0.835 |
0.823 |
0.801 |

9000 |
2743 |
0.829 |
0.816 |
0.804 |
0.779 |

10000 |
3048 |
0.812 |
0.798 |
0.764 |
0.758 |

11000 |
3353 |
0.795 |
0.78 |
0.766 |
0.737 |

12000 |
3660 |
0.779 |
0.763 |
0.747 |
0.717 |

13000 |
3962 |
0.763 |
0.746 |
0.729 |
0.697 |

14000 |
4267 |
0.747 |
0.729 |
0.712 |
0.678 |

15000 |
4572 |
0.732 |
0.713 |
0.695 |
0.659 |

16000 |
4876 |
0.717 |
0.697 |
0.67 |
0.641 |

17000 |
5181 |
0.702 |
0.682 |
0.652 |
0.624 |

18000 |
5486 |
0.687 |
0.656 |
0.645 |
0.607 |

19000 |
5791 |
0.673 |
0.652 |
0.631 |
0.59 |

20000 |
6097 |
0.659 |
0.637 |
0.615 |
0.574 |

### Step 2: Calculate the pertinent pressures for different operating conditions.

a) Pressures inside casing-tubing annulus

Assuming during the production and killing of well, packer fluid is present inside the casing tubing annulus.

### For producing situation:

Pressure inside annulus at surface = packer fluid gradient * Depth

Pkill_prod_surface= = 0.4* 0 = 0 psi

Pressure inside annulus at bottom hole = packer fluid gradient * Depth

Pkill_prod = Gpf *D = 0.4* 9000 = 3600 psi

### For Stimulation:

Pressure inside annulus at surface= Pstim_surf = 1000 psi

Pressure inside annulus at bottomhole = packer fluid gradient * Depth + (Max

Allowable pressure inside annulus)

Pstim_bh= Gpf *D + Pann = 0.4*9000 + 1000 = 4600 psi

### b) Pressures inside tubing

At bottom hole, pressure = CIBHP

At surface, pressure = CITHP (closed in tubing head pressure)

CITHP = ratio * CIBHP

CITHP = 0.792 * 6280 = 4973 psi

### KILL SITUATION:

When a well is killed, the bottom hole pressure is given as sum of CIBHP and maximum allowable annulus pressure.

At bottom hole, pressure inside tubing during kill situation (BHIP) = CIBHP+Pann

BHIP =6280 +1000 = 7280psi

Tubing head pressure during kill situation is calculated by multiplying BHIP with gas gravity.

At tubing head kill pressure (THIP) = ratio * BHIP = 0.792*7280 = 5765 psi

### FORMATION BREAKDOWN SITUATION:

During stimulation the bottomhole pressure is the formation break down pressure and can be calculated by the density of the fracture fluid .In this problem the break down pressure is specified.

At bottomhole, pressure inside tubing during formation breakdown (BHFBP) = FBP

BHFBP = 12550 psi

The tubing head pressure can be calculated by subtracting the hydrostatic head generated by the fracturing fluid from the bottomhole pressure.

At tubing head, pressure (THFBP) = FBP -Gf* D

=12550- 0.48* 9000 = 8230psi

### FRACTURE PROPAGATION

During stimulation (propagation), we experience some pressure drop due to friction. Based on the pumping rates and properties of proppants we can determine the drop in pressure. Assuming a pressure drop of 0.35 psi / ft (usually calculated through properties of fracturing fluid and pumping rate), the bottomhole pressure at fracture propagation (BHFP) can be calculated as:

DPfr = 0.35 psi/ ft

At bottomhole, BHFP = FPP

BHFP =9100 psi

### At tubing head, the pressure inside tubing can be calculated as:

Tubing head fracture propagation pressure (THFP) = BHFP + DPfr* D - Gf*D

= 9100 + 0.35*9000 -0.48*9000 =7930 psi

### Step 3: Calculate the burst load for different operating conditions:

### Defining the burst loads:

Burst Load pressure = pressure inside tubing - pressure in the casing- tubing annulus

### Burst Load at tubing head for producing conditions:

BL _surface_prod = CITHP - Pkill_prod_surface = 4973 - 0 = 4973 psi

### Burst Load at bottomhole for producing conditions:

BL _bh_prod = CIBHP - Pkill_prod = 6280-3600 = 2680 psi

### Burst Load at tubing head for killing operation:

BL _surface_kill = THIP - Pkill_prod_surface = 5765 -0 = 5765 psi

### Burst Load at bottomhole for killing operation:

BL _bh_kill = BHIP - Pkill_prod = 7280-3600 = 3680 psi

### Burst Load at tubing head for formation breakdown:

BL _surface_fbp = THFBP - Pstim_surf = 8230 -1000 = 7230 psi

### Burst Load at bottomhole for formation breakdown:

BL _bh_fbp = BHFBP - Pstim_bh = 12550 -4600 = 7950 psi

### Burst Load at tubing head for fracture propagation:

BL _surface_fbp = THFP - Pstim_surf = 7930 -1000 = 6930 psi

### Burst Load at bottomhole for fracture propagation:

BL _bh_fbp = BHFP - Pstim_bh = 9100 -4600 = 4500 psi

### Step 4: Calculation of collapse Load

### Defining the collapse loads:

Collapse load pressure = pressure in casing-tubing annulus- pressure inside tubing

In order to plot critical collapse load conditions (CLL) normally, we assume that a slow leak in tubing has changed the pressure inside casing-tubing annulus to CITHP and that tubing is empty and depressurized.

### Step 5: Plot the Load lines.

Plot the burst load and collapse load lines for various completion operations, burst and collapse resistance lines for the available tubing grades. The obtained plot is illustrated in Fig. 4.4.

It can be observed from plot that formation breakdown situation has the maximum burst pressures. The maximum burst pressure line and collapse line are plotted with the available ratings of tubing. The resulting plot will look like Fig. 4.5.

Then by inspecting the graph we can come to a conclusion that L-80 grade is the best grade available that can withstand the collapse and burst pressures during various operations. But in other situations we have an option to select multiple grades on tubing which are guided by the estimated loading conditions.

### Estimation of Tensile Load:

Most of the tubing failures are caused due to coupling leakage and failure. The failure of coupling can be attributed to inadequate design for tension of the tubing.

This load being one of the significant and causes most failures compared to failures due to burst and collapse pressures.

A higher safety factor is used while designing tubing. The design can be initiated by considering only the weight of tubing on packer. Some companies even ignore buoyancy effects while calculating weight to have a better design.

So ideally a tubing design for tension is carried out by calculating the weight of the tubing in air. Then the buoyant weight of the tubing is calculated using the densities of steel and mud. Selecting a grade of casing which can handle the tensile load generated due to the weight of the tubing. An example below illustrates the design of tubing for tension.

### Example 4.3

Tension Design

Tubing weight: 7.2 lb/ft

Tubing length: 12,500 ft

Packer fluid: 0.38 psi/ft = 54.72 lb/ft3

Density of steel: 490 lb/ft3

Win_air = 7.2 x 12,500 = 90,000 lb

Wbuoyant = = 0.89 x 73,600 = 80,100 lb

### Joint Specifications

J55 |
L80 |
||||

EUE |
HYD CS |
EUE |
HYD A95 |
||

API joint strength (Klb) Design factor Design capacity (Klb) |
99.7 1.8 55.4 |
100 1.8 55.6 |
135.9 1.8 75.5 |
150 1.8 83.3 |

Tubing Tension Design Considerations

1. Requires L80 tubing at surface

2. Requires joint strength capability of HYD A95 or equivalent

### Review questions

1. When would buckling of tubing above a packer likely to occur?

2. A 10,000-ft, high-rate oil well is completed with 5Â½" 15.5 lb/ft tubing (wall thickness 0.275"). Under producing conditions the flowing temperature gradient is 0.40F/100 ft, and under static conditions the geothermal gradient is 1.8oF/100ft from a mean surface temperature of 40oF. When the well is killed with a large volume of 40oF seawater, the bottom-hole temperature drops to 70oF. If free to move, what tubing movement can be expected from the landing condition to the hot producing and to the cold injection conditions? If a hydraulic packer were to be used and set in 30,000 lb tension, what would be the tension loading on the packer after killing the well? (Ignore piston, ballooning and buckling effects).

3. A 7000-ft well that is to be produced with a target of 15,000 STB/D using 5Â½" tubing encounters 170 ft of oil-bearing formation with a pressure of 3000 psi. What rating of wellhead should be used? If a single grade and weight tubing is to be used, what is the cheapest string that can probably be run, assuming that

Grade |
Weight (lb/ft) |
Collapse Strength (psi) |
Burst Strength (psi) |
Tensional Strength (1000 lb) |
Cost Comparison |

J-55 C-75 N-80 |
15.5 17.0 17.0 17.0 20.0 |
4040 4910 6070 6280 8830 |
4810 5320 7250 7740 8990 |
300 329 423 446 524 |
Cheapest Most expensive Moderately expensive |

### REFERENCES

1. Allen, TO and Roberts, AP, Well Completion Design- Production Operations-1, 3rd edition, 1989, pp 182-187.

1. Hammerlindl, DT, Movement, Forces and Stress Associated with Combination Tubing Strings Sealed with Packers, JPT, February 1977.

2. Lubinski, A, Althouse, WS, Logan, TL, Helical Buckling of Tubing Sealed in Packers, JPT, June 1962.

3. Well completion design and practices PE 301-IHRDC E&P Manual Series, Boston, MA 02116, USA.

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