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Collapse Resistance for Composite Casing

Although the improvement of collapse resistance in composite casing has been rec­ognized by several investigators (Evans and Harriman, 1972; Pattillo and Rankin. 1981; and Burkowsky et al., 1981), it was Marx and El-Sayed (1984) who first provided theoretical and experimental results. The authors showed that for a composite pipe (Fig. 4.17), the contact pressure at the interface and the re­sulting tangential stresses could be expressed in terms of internal and external pressures, modulus of elasticity of the individual pipes and the cement, and the physical dimensions of the casing. Collapse behavior of the composite pipe can be distinguished in two principal ranges: elastic collapse and yield collapse.

CEMENT

Fig. 4.17: Cross-sectional view of composite casing.

4.2.1 Elastic Range

Using Lame’s equation for thick-walled pipe and Eqs. ‘2.114 and 2.115. pres­sures and resulting stresses for homogeneous and isotropic composite pipe can be expressed as follows:

For the interface between the outer pipe and the cement sheath, (r = r,2):

(4.81)

Tangential stress, <r, = « + 1 ~ P” <

(4.82)

(r2C2 — rf.)

Radial stress, oy = —pv

Radial deformation;

(4.83)

A rt2 =

E

(l-Fy.,(t»+r-)-2p, r;, F +

(го2-П2)

2 Po, p,2 (rf2 — -2

{rf

For the cylindrical cement sheath (r = r,2):

at = И°1 , и’2—————————————————————————— v 12 (4.84)

r-2

(4.85)

(4.86)

~Ph

2 Pci Г1 — Ph {r j — rp (rl-rl)

(1 — vim)

A r =

12 Em

+ (iScm + ^cm) Pi2

For the interface between the cement sheath and the inner pipe (r = r0l):

Po j (rf, +<) — 2pn r

(4.87)

(4.88)

(4.89)

(rl — roJ2

Po!

Ar# = —

Л/л —

/1 . .2 ^<>i(r£ +г»1)-2р*Г? , / , 2 ч

i1 “ Vcm) —————— ТА ————————— +- ("cm + I’cmlPo

(rl-rl)

For the inner pipe (r = r0i):

„ _ 2Рч rl ~ Pox (ro, — rl :

(4.90)

(4.91)

(4.92)

(V2 — r2

V oi ‘ u,

&T Poi

2Phrl — Рог (rl ~ rl)

u-*’2)

+ (v + V2)Pol

Ar — —

01 E

fr2 — Г2 ‘ V 01 M >

where:

Modulus of elasticity for the cement sheath.

vCm = Poisson’s ratio for cement sheath.

From the continuity of radial deformation at the interface one obtains:

Ar j. Ar

*-J’ о

A rt2 Ar).

Finally, substituting Eq. 4.83 into Eq. 4.86 and Eq. 4.89 into Eq. 4.92, one obtains the following expressions for collapse resistance of the composite pipe:

r2 — f r2

02 1 32

Г2 — 7’2 02 »2

l-v<

Vcm "Ь Vcm

r2 _ r2

h о l

l-v,

V + V1

E

+

Er.

2<

2 r2

1 — vl

(4.93)

Poi

г 2 — r 2

rt2 ri

1zA

Erm

From the above equations, values of p,2, p01 and cr< can be determined from the physical dimensions of the pipes, internal and external pressures, and the modulus of elasticity of steel and cement.

Fig. 4.18: Tangential stress in 13| — 91-in. composite casing as a function of modulus of elasticity and Poisson’s ratio of cement sheath. (After El-Sayed, 1985; courtesy of ITE-TU Clausthal.)

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