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15.08.2018 Солнце в сеть




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Axial Force Due to Changes in Drilling Fluid spe­cific weight and Surface Pressure

The specific weight of drilling fluid is often increased prior to drilling through the next hole section below the existing casing shoe. The specific weight may also change due to several other reasons: (1) solids often settle down reducing the drilling fluid specific weight outside the casing; (2) invasion of lighter formation fluids, e. g., salt water or gas, reduces the drilling fluid specific weight both inside and outside the casing; (3) lost circulation may lead to partial or complete evac­uation of the casing and hence a change in internal pressure of the casing. In the event of complete evacuation internal pressure may be reduced to zero.

Pressure testing is often carried out prior to drilling the float collar and float shoe. This results in an increase in surface pressure inside the casing. Surface pressure

Depth

(ft)

Fa

(lbf)

Fbu

(lbf)

FP

(lbf)

= [Fa — Fhu + Ftp)/A, (psi)

(a, + ar)/2 (psi)

10,000

0

123.605

0

-7.323

-7.322

9,100

52,560

123,605

0

-4.209

-6,388

7,500

146.000

123,605

0

1.327

-5.265

7,500

146,000

123,605

17.427

2.935

-5.265

2,000

404,500

123,605

17,427

21.984

-1,404

2,000

404,500

123 605

12.780

17.398

-1.404

0

521,300

123,605

12.780

24,318

0

inside and/or outside of the casing may also increase if a gas or salt water kick is experienced. Pressure changes also occur in a production or injection well if the flow rate changes.

Any change in surface pressure causes the casing to contract or expand radially and results in shortening or lengthening of the pipe. As the movement of the casing is restrained, contraction or lengthening causes an axial stress in the casing. Thus, using Hooke’s Law, the strain due to a change in fluid densities and surface pressures can be expressed as follows:

[Avaw — vA(crr + at)] (2.182)

А/ = [Aaaw — i/A(ar + crt)} (2.183)

where:

Aaaw = Acrahux + Acrabu2 (2.184)

AcTabu-i = change in axial stress arising from a change in buoyant

weight due to the change in mud specific weight.

Acabu2 = change in axial stress arising from a change in buoyant

weight due to the change in surface pressure. v — Poisson’s ratio.

and

<7r + M (Or+<Tt _ (°г+°Л (2185)

2 / final 2 / initial

where:

‘сгт + at

A, pi — A0 pa ASX

x {Ai Gp> — A0 GPo)

JZ

initial

(2.186)

(2.187)

o> + (?t _ Aj(pi + A — Ай (po A Др0)

Hence:

oy + °t

2 / final

(2.188)

oy + _ .4, Ар, — A0 Ap0

2 / initial Asx

where:

А, Дрг — А0Др0 = AGPl = ДСВ„ =

Др31 and Др A,

Hence:

AiAGPtx + AjApSi A0AGPox — j — A0ApS0

change in fluid pressure gradient inside the pipe, change in fluid pressure gradient outside the pipe, change in surface pressure inside and outside the pipe, cross-sectional area of the pipe at depth, r.

д | o> A ^7^ A{{AGPt x — f — ДPsi] A0(AGPo i A Aps0) ^ 189)

Substituting Eq. 2.189 in Eq. 2.182 and expressing in integral form yields:

A,(AGp, x + A p„)

/ dl — J Acraw — 2v |

dx (2.190)

A0(AGPox + Aps

A sx

Integrating both sides over the length x one obtains:

Al =

As

A0(AGPox[2]/2 A x Apso) Asx

But Д/ = 0, so:

Aj(AGPl x + 2 Дpst) — A0(AGPo x + 2 Дpso) А. т

Thus, the axial stress due to the pipe weight and change in fluid densities and surface pressures can be expressed as:

j A,(GPi J" + 2 Дpsl) A0(AGPo x + 2 ДpSo) (

Oau,, = <?aw + V ^^f (2.1У4)

&awi — ~t" A(7aw (2.193)

Changes in fluid densities and surface pressures also result in a change in piston effect which can be expressed as:

д = (AGP, Daa, + Apst)(Aupi — .4,^.) (2 ig5)

As

Total change in axial stress due to piston effect is given by:

_ , (Д Gp, Da а, + Apsl)(A

upi Alou.4 ) 1 лу^

®api — 0-ap + ————————————————————————————————————————————————————————————— (Z. iy/——————————————————————————————————— ■

®ap — &ap A(7ap (2.196)

2.5.2 Axial Force due to Temperature Change

Drilling of the next section below the casing shoe and subsequent production operations cause the casing temperature to change from the casing shoe to the surface. During the drilling operation circulating drilling fluid is heated as it moves down the string to the bottom of the hole and is cooled by the surrounding casing on its way back to the surface. According to Raymond (1969), during drilling fluid circulation, the maximal temperature occurs at a quarter to a third of the way up the annulus. The actual location of the temperature maximum depends upon the ciculating velocity: it moves further up the hole as the velocity
increases. This means that during circulation the drilling fluid cools the lower part and heats the upper part of the hole and as a result, casing in the top part of the hole is subjected to a higher temperature than the ambient temperature.

In a freely suspended casing, an increase or decrease in ambient temperature results in expansion or shortening of the casing. If the casing is held in place, a change in ambient temperature results in an additional compressive or tensile stress. According to Hooke’s Law, change in axial stress, аат, due to the change in temperature can be expressed as:

<jaT = Ее (2.198)

where:

l-jl + lTAT)

I + IT AT v

IT AT = change in length.

T = coefficient of thermal expansion.

AT — change in temperature (7j — Tj).

T = initial temperature.

X2 = final temperature.

IT AT is very small in comparison with I. so Eq. 2.199 can be simplified to: e = — TAT (-2.200)

aat = —E T AT (2.201)

Change in axial force, FaT, due to the change in temperature is given by:

FaT = —ASET AT (2.202)

According to Rabia (1987), change in casing temperature can be computed as the average initial temperature minus the average final temperature:

(Tb)initial + initial (Tb)final T (Ts)jtna[ ^ 203)

where:

Tf, = bottomhole temperature. Ts = surface temperature.

Fig. 2.29: Modulus of elasticity of steel grades as a function of temperature. (After Shryock and Smith, 1980.)

Temperature — ’F

It is important to note that the modulus of elasticity varies between different steel grades. At the same time, high temperature has the effect of reducing the modulus of elasticity as shown in Fig. ‘2.29 (Shryock and Smith. 1980). Figure 2.29 shows that the modulus of elasticity of N-80 steel is greatly affected by the increasing temperature and, therefore, temperature effects should be taken into consideration when computing changes in axial stress.

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