Page 118 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap09 Final Proof page 112 21.12.2006 2:16pm

9/112 EQUIPMENT DESIGN AND SELECTION
ED o A pt(D t) ¼ p(0:217)(2:875 0:217) ¼ 1:812 in: 2
b ¼ , (9:20)
s ¼ E«
2R c
where F DL
¼ E
s b ¼ bending stress, psi A L
6
E ¼ Young’s modulus, psi F ¼ AE DL ¼ (1:812)(30 10 )(3:25) ¼ 17,667 lb f :
R c ¼ radius of hole curvature, in. L 10,000
D o ¼ OD of tubing, in.
Thus,anadditionaltensionof17,667 lb f atthesurfacemustbe
Because of the great variations in well operating condi- placed on the tubing string to counter the thermal expansion.
tions, it is difficult to adopt a universal tubing design It can be shown that turbulent flow will transfer
criterion for all well situations. Probably the best design heat efficiently to the steel wall and then to the completion
practice is to consider the worst loading cases for collapse, fluid and then to the casing and out to the formation. While
burst, and tension loads that are possible for the well to laminar flow will not transfer heat very efficiently to the
experience during the life of the well. It is vitally important steel then out to the formation. Thus, the laminar flow
to check the remaining strengths of tubing in a subject well situations are the most likely to have higher temperature
before any unexpected well treatment is carried out. Some oil at the exit. Therefore, it is most likely the tubing will be
special considerations in well operations that affect tubing hotter via simple conduction. This effect has been consid-
string integrity are addressed in the sections that follow. ered in the work of Hasan and Kabir (2002). Obviously, in
the case of laminar flow, landing tension beyond the buoy-
ancy weight of the tubing may not be required, but in the
9.3.2 Buckling Prevention during Production case of turbulent flow, the landing tension beyond the
A completion fluid is in place in the annular space between buoyancy weight of the tubing is usually required to prevent
the tubing and the casing before a well is put into buckling of tubing string. In general, it is good practice to
production. The temperature at depth is T ¼ T sf þ G T D, calculate the buoyant force of the tubing and add approxi-
where G T is geothermal gradient. When the oil is mately 4,000---5,000 lb f of additional tension when landing.
produced, the temperature in the tubing will rise. This
will expand (thermal) the tubing length, and if there is
9.3.3 Considerations for Well Treatment and Stimulation
not sufficient landing tension, the tubing will buckle. The
Tubing strings are designed to withstand the harsh
temperature distribution in the tubing can be predicted on
conditions during wellbore treatment and stimulation
the basis of the work of Ramey (1962), Hasan and Kabir
operations such as hole cleaning, cement squeezing, gravel
(2002), and Guo et al. (2005). The latter is described in
packing, frac-packing, acidizing, and hydraulic fracturing.
Chapter 11. A conservative approach to temperature
Precautionary measures to take depend on tubing–packer
calculations is to assume the maximum possible tempera- relation. If the tubing string is set through a non-restrain-
ture in the tubing string with no heat loss to formation ing packer, the tubing is free to move. Then string buckling
through annulus. and tubing–packer integrity will be major concerns. If the
tubing string is set on a restraining packer, the string is not
7
Example Problem 9.2 Consider a 2 ⁄ 8 in. API, 6.40 lb/ft free to move and it will apply force to the packer.
Grade P-105 non-upset tubing anchored with a packer set The factors to be considered in tubing design include the
at 10,000 ft. The crude oil production through the tubing following:
from the bottom of the hole is 1,000 stb/day (no gas or
water production). A completion fluid is in place in the . Tubing size, weight, and grade
annular space between the tubing and the casing (9.8 lb/ . Well conditions
gal KCl water). Assuming surface temperature is 60 8F and
geothermal gradient of 0.01 8F/ft, determine the landing - Pressure effect
tension to avoid buckling. - Temperature effect
. Completion method
Solution The temperature of the fluid at the bottom of
the hole is estimated to be - Cased hole
- Open hole

T 10,000 ¼ 60 þ 0:01(10,000) ¼ 160 F: - Multitubing
- Packer type (restraining, non-restraining)
The average temperature of the tubing before oil produc-
tion is
9.3.3.1 Temperature Effect
60 þ 160 As discussed in Example Problem 9.2, if the tubing string

T av1 ¼ ¼ 110 F:
2 is free to move, its thermal expansion is expressed as
The maximum possible average temperature of the tubing DL T ¼ bLDT avg : (9:21)
after oil production has started is
160 þ 160 If the tubing string is not free to move, its thermal expan-

T av2 ¼ ¼ 160 F: sion will generate force. Since Hook’s Law gives
2
This means that the approximate thermal expansion of the LDF
tubing in length will be DL T ¼ AE , (9:22)

DL T b DT avg L, substitution of Eq. (9.22) into Eq. (9.21) yields
where b is the coefficient of thermal expansion (for steel, (9:23)
DF ¼ AEbDT avg 207ADT avg
this is b s ¼ 0:0000065 per 8F). Thus,
for steel tubing.
DL T 0:0000065[160 110]10,000 ¼ 3:25 ft:
To counter the above thermal expansion, a landing tension 9.3.3.2 Pressure Effect
must be placed on the tubing string that is equivalent to the Pressures affect tubing string in different ways inclu-
above. Assumingthe tubingisasimpleuniaxialelement,then ding piston effect, ballooning effect, and buckling effect.