Intermediate Casing (13|-in. pipe)
Intermediate casing is set to depth of 11,100 ft and partially cemented at the casing seat. Design of this string is similar to the surface-string except that
|
Section |
Depth |
Grade and Weight |
Length |
|
(ft) |
(lb/ft) |
(ft) |
|
|
1 |
0 — 3.550 |
L-80. 84 |
3.550 |
|
2 |
3.550 — 5.000 |
K-55. 109 |
1.450 |
some of the design loading conditions are extremely severe. Problems of lost circulation, abnormal formation pressure, or differential pipe sticking determine the loading conditions and hence the design requirements. Similarly, with only partial cementing of the string it is now important to include the effect of buckling in the design calculations. Meeting all these requirements makes implementing the intermediate casing design very expensive.
Below the intermediate casing, a liner is set to a depth of 14.000 ft and as a result. the intermediate casing is also exposed to the drilling conditions below the liner. In determining the collapse and burst loads for this pipe, the liner is considered to be the integral part of the intermediate casing as shown in Fig. 3.8.
As in the case of surface casing, the collapse load for intermediate casing is imposed by the fluid in the annular space, which is assumed to be the heaviest drilling fluid encountered by the pipe when it is run in the hole. As discussed previously, maximal collapse load occurs if lost circulation is anticipated in the next drilling interval of the hole and the fluid level falls below the casing seat. This assumption can only be satisfied for pipes set at shallow depths.
In deeper sections of the well, lost circulation causes the drilling fluid level to drop to a point where the hydrostatic pressure of the drilling fluid column is balanced by the pore pressure of the lost circulation zone, which is assumed to be a saturated salt water gradient of 0.465 psi/ft. Lost circulation is most likely to occur below the casing seat because the fracture resistance pressure at this depth is a minimum.
For collapse load design, the following assumptions are made (Fig. 3.8):
1. A lost circulation zone is encountered below the liner seat (14,000 ft).
2. Drilling fluid level falls by ha, to a depth of hm2.
3. Pore pressure gradient in the lost circulation zone is 0.465 psi/ft (equivalent mud weight = 8.94 ppg).
|
Fig. 3.8: Collapse and burst loads on intermediate casing and liner. Thus, the design load for collapse can be calculated as follows: |
Collapse pressure at surface = 0 psi
Collapse pressure at casing seat = external pressure — internal pressure
External pressure = GPm x 11.100
= 12 x 0.052 x 11.100
= 6,926.4 psi
where:
hmi = the height of the drilling fluid level above the casing seat.
The top of the fluid column from the liner seat can be calculated as follows:
GPf x 14,000 0.465 x 14,000
m2 ~ x 0.052 “ 17.9 x 0.052
= 6,994 ft,
The distance between the top of the fluid column and the surface. ha, is equal to:
ha = 14,000 — 6,994 = 7,006 ft
Height of the drilling fluid column above the casing seat, hmi, is equal to:
Ami = 11,100 — 7,006 = 4,094 ft
Hence, the internal pressure at the casing seat is:
Internal pressure = GPm x hmi
= 17.9 x 0.052 x 4,094
= 3,810.7 psi
Collapse pressure at 11,100 ft = 6,926.4 — 3,810.7
= 3,115.7 psi
Collapse pressure at 7,006 ft = external pressure — internal pressure
= 12 x 0.052 x 7.006 — 0
= 4,371.74 psi
In Fig. 3.9, the collapse line is constructed between 0 psi at the surface, 4,371.74 psi at a depth of 7,006 ft and 3,115.7 psi at 11,100 ft. The collapse resistances of suitable steel grades from Table 3.2 are given in Table 3.11 and it is evident that all the steel grades satisfy the requirement for the conditions of maximal design load (4,371.74 psi at 7,006 ft).
The design load for intermediate casing is based on loading assumed to occur during a gas-kick. The maximal acceptable loss of drilling fluid from the casing is limited to an amount which will cause the internal pressure of the casing to rise to the operating condition of the surface equipment (blowout preventers, choke manifolds, etc.). One should not design a string which has a higher working pressure than the surface equipment, because the surface equipment must be able to withstand any potential blowout. Thus, the surface burst pressure is generally set
|
Collapse load line |
|
Fig. 3.9 : Selection of casing grades and weights based on collapse and burst loads for intermediate casing. |
|
———————- gurst |oacj ||Пе |
PRESSURE
Fig. 3.10: Burst load with respect to the relative position of the drilling fluid and the influx gas.
|
Table 3.11: Collapse resistance of grades suitable for intermediate casing.
|
to the working pressure rating of the surface equipment used. Typical operating pressures of surface equipment are 5.000. 10.000. 15.000 and 20.000 psi.
The relative positions of the influx gas and the drilling fluid in the casing are also important (Fig. 3.10). If the influx gas is on the top of the drilling fluid, the load line is represented by a dashed line. If instead the mud is on the top. the load line is represented by the solid line. From the plot, it is evident that the assumption of mud on top of gas yields a greater burst load than for gas on top of mud.
The following assumptions are made in calculating the burst load:
1. Casing is partially filled with gas.
2. During a gas-kick. the gas occupies the bottom part of the hole and the remaining drilling fluid the top.
3. Operating pressure of the surface equipment is 5.000 psi.
Thus, the burst pressure at the surface is 5.000 psi.
Burst pressure at the casing seat = internal pressure — external pressure.
The internal pressure is equal to the injection pressure at the casing seat. The intermediate casing, however, will also be subjected to the kick-imposed pressure assumed to occur during the drilling of the final section of the hole. Thus, determination of the internal pressure at the seat of the intermediate casing should be based on the injection pressure at the liner seat.
Injection pressure at the liner seat (1 1.000 ft)
= fracture gradient x depth = (18.4 + 0.5) x 0.052 x 14.000
= 13,762 psi.
The relative positions of the gas and the fluid can be determined as follows (Fig.
14.0 = hg + hm (3.5) Surface pressure = injection pressure — (GPghg + GPmhm)
5. = 13,762 — (0.1 x hg + 17.9 x 0.052 x hm) (3.6)
Solving Eqs. 3.5 and 3.6 simultaneously, one obtains hg and hm:
hg = 5,141 ft hm = 8,859 ft
The length of the gas column from the intermediate casing seat. hgl. is:
hgi = 11,100 — 8,859 = 2,241 ft Burst pressure at the bottom of the drilling fluid column
= internal pressure — external pressure
Internal pressure at 8,859 ft = 5.000 + 17.9 x 0.052 x 8.859
= 13.246 psi
External pressure at 8859 ft = 0.465 x 8.859
= 4.119 psi
Burst pressure at 8,859 ft = 13,246 — 4.119
= 9.127 psi
Burst pressure at casing seat — internal pressure — external pressure
Internal pressure at 11,100 ft = pressure at 8.859 ft + [Gpg x hgl)
= 13.246 + 224.1
= 13,470 psi
Burst pressure at 11,100 ft = 13,470 — 11.100 x 0.45
= 8.475 psi
In Fig. 3.9, the burst pressure line is constructed between 5.000 psi at the surface. 9,127 psi at. 8,859 ft and 8,475 psi at 11.100 ft. The burst resistances of the suitable grades from Table 3.2 are given in Table 3.12.
The grades that satisfy both burst and collapse requirements and the intervals for which they are valid are listed in Table 3.13.
|
Grade |
Weight (lb/ft) |
Coupling |
Burst resistance (psi) SF — 1 SF =1.1 |
|
L-80 |
98 |
BTC |
7.530 6.845 |
|
P-110 |
85 |
PTC |
8.750 7.954 |
|
P-110 |
98 |
PTC |
10.350 9.409 |
|
Table 3.13: Most economical intermediate casing based on collapse and burst loading.
|
The suitability of the selected grades for tension are checked by considering cumulative buoyant weight, buckling force, shock load and pressure testing. A maximal dogleg of 3°/100 ft is considered when calculating the tension load due to bending. Hence, starting from the bottom. Table 3.14 is produced.
It is evident from Table 3.14 that grade L-80 (98 lb/ft) is not suitable for the top section. Before changing the top section of the string the effect of pressure testing can be considered.
Pressure Testing and Shock Loading
Axial tension due to pressure testing:
= Grade L-80 burst pressure resistance x 0.6 x.4S = 7,530 x 0.6 x 28.56 = 129.034 lbf
Top joint tension = (4) + (6) + 129.034 = 1,240,007 lbf
|
(1) |
(2) |
(3) |
(4) |
|
Depth |
Grade and |
Buoyant weight |
Cumulative buovant |
|
interval |
Weight |
of section |
weight carried |
|
(ft) |
(lb/ft) |
joint (1.000 lbf) |
by the top joint |
|
(1) x Wn x BF |
(1.000 lbf) |
||
|
BF = 0.817 |
|||
|
11,100 — 6,400 |
P-110, 98 |
376.310 |
376.310 |
|
6,400 — 4,000 |
P-110, 85 |
166.668 |
542.978 |
|
4,000 — 0 |
L-80. 98 |
320.264 |
863.242 |
|
(8) Total tension |
(5)
Shock load
carried by each joint (1,000 lbf) (3, ‘200 Нд) (6)
Bending load in each section (1.000 lbf) (63 d0WnQ)
Total tension (1.000 lbf) (4) + (5) + (6)
|
313.60 272.00 313.60 |
247.731 TOC o "1-5" h z 937.641 2.800/937.64 = 2.98
214.869 1.029.847 2.290/1.029 = 2.22
247.731 1,424.573 2.286/1.424 = 1.61
SF _ Yp _ 2.286,000
Total tension 1.240.007 = 1.84
The pressure testing calculations indicate that the upper section is suitable. However, it is the worst case that one is designing for and in this case, as Column (5) in Table 3.14 attests, it is the shock load.
Tension load is calculated by considering the cumulative buoyant weight at the top joint (4), shock load (5), and bending load (6). The length of Section 1. ,r. that satisfies the requirement for tensional load can be calculated as follows:
|
ension |
Minimum safety factor (= 1.8) = — r, i / J v ‘ lotal tp
Total tension load = (98a: + 2, 400 x 85 + 4, 700 x 98) x 0.817 + 313,600
+ 24,7731 = 80.07.Г + 1,104.309.2 lbf
Hence,
2,286,000
298,243.44 „ .
х = —————- = 2,069 ft or 52 joints.
144.118
Thus, the part of Section 1 to be replaced by a higher grade casing is (4.000 — 2.000) 2,000 ft or 50 joints. If this length is replaced by P-110 (98 lb/ft), the safetv factor for tension will be:
2,800,000
1,424,573
In summary, the selection based on collapse, burst, and tension is given in Table 3.15. Table 3.16 shows the reworked tension results based on the revised string.
|
Table 3.15: Intermediate casing selection based on collapse, burst and tensile loads.
|
The weakest grade among the four sections is P-110 (85 lb/ft). It is. therefore, important to check for the collapse resistance of this grade under axial tension.
(1) Axial stress, era, carried by P-110 (85 lb/ft) is:
376, ЗЮ,
^ = 14^T = 10,431 PS1-
(2) Pipe yield stress:
2.682,0 . "«= 24.39 —
|
(1) |
(2) |
(3) |
(4) |
|
Depth |
Grade and |
Buoyant weight |
Cumulative buoyant |
|
interval |
Weight |
of section |
weight carried |
|
(ft) |
(lb/ft) |
joint (1.000 lbf) |
by the top joint |
|
(1) x |
: И’,, x BF (= 0.81 |
7) (1.000 lbf) |
|
|
11,100 — 6,400 |
P-110, 98 |
376.310 |
376.310 |
|
6,400 — 4,000 |
P-110, 85 |
166.668 |
542.978 |
|
4,000 — ‘2,000 |
L-80, 98 |
160.132 |
703.110 |
|
2,000 — 0 |
P-110, 98 |
160.132 |
863.242 |
|
(5) |
(6) |
(7) |
(S) |
|
Shock load |
Bending load |
Total tension |
|
|
carried by each in each section |
(1.000 lbf) |
у 8’F — p » Total tension |
|
|
joint (1000 lbf) (1,000 lbf) |
(4) + (5) + (6) |
||
|
(3,200W„) |
(63 d0WnQ) |
||
|
313.60 |
‘247.731 |
937.641 |
2,800/937.64 = 2.98 |
|
‘272.00 |
‘214.869 |
1.029.847 |
2.290/1.029 = 2.22 |
|
313.60 |
‘247.731 |
1.264.441 |
‘2.286/1.264.44 = 1.81 |
|
313.60 |
‘247.731 |
1.424.573 |
2.800/1.424.57 = 1.97 |
(3) From Eq. ‘2.163, the effective yield stress is given by:
|
1 -0.75 |
— 0.5 I —
|
15.431 109.981 |
|
15.831 109.981 |
|
— 0.5 |
|
= 109,981 = 101, 450 psi |
|
1 — 0.75 |
(4) d0/t = 13.375/0.608 = ‘21.998.
(5) The values of A to G are calculated using the equations in Table 2.1 and the value of <re above:
A = 3.1483
В = 0.0776
С = 2,596.26
F = 2.0441
G = 0.0504
(6) Collapse failure mode ranges are:
|
= 12.661 = 20.913 = 27.389 |
[(A — 2)2 + 8(B + C/cre)]o s + (Л — 2) 2 (B + CK)
<Te(A — F)
C + <re{B-G) 2 + B/A
(7) Inasmuch as da/t — 21.99, the failure mode is in the elasto-plastic region.
(8) Hence, the reduced collapse resistance of P-110 (85 lb/ft) is 4,317 psi.
(9) Thus, the safety factor for collapse at 6,400 ft is:
Reduced collapse resistance
SFC =
Collapse load at 6,400 ft
4,317 ля
’ 1.07
4,023
which satisfies the design criterion SFC > 0.85
Table 3.17: Intermediate casing properties and mud weights during landing operation.
TOC o "1-5" h z Depth Grade and A, A0 As 7, 7s
Weight
(ft)_______ (lb/ft) (in.2) (in.2) (in.2) (lb/gal) (lb/gal)
0 — 2,000 P-110, 98 111.91 140.5 28.59 12 12
2.0 — 4,000 L-80, 98 111.91 140.5 28.59 12 12
4.0 — 6,400 P-110, 85 116.11 140.5 24.39 12 12
6,400 — 10,000 P-110, 98 111.91 140.5 28.59 12 12
10,0 — 11,100 P-110, 98 111.91 140.5 28.59 12 14 (cement)
Buckling
As discussed in Chapter 2, casing buckling will occur when the axial stress is less than the average of the radial and tangential stresses. Thus, the buckling condition for the above casing grades can be found by determining the neutral point along the casing length. Casing sections above this point are stable and those below are liable to buckle.
It is assumed that the pipe is cemented to 10,000 ft from the surface and the specific weight of the slurry is 14 ppg. Thus, the pipe will be subjected to buckling
due to the change in the specific weight of the fluid between the outside and the inside of the casing and the change in the average temperature during the drilling of the next interval. Lengths and properties of the different pipe sections and the mud weight during the landing operation are shown in Table 3.17.
For the conditions summarized in Table 3-17, the values of axial stresses are given in Table 3.18. Note that the two top strings of L-80. 98 lb/ft and P-110. 98 lb/ft have been grouped together in one 4,000-ft string as their ID’s. OD’s and casing weights are the same.
|
Table 3.18: Axial stresses on intermediate casing string during landing operation.
|
Examples of Calculations in Preparing Table 3.18:
Axial stress, <raWi (item 3), due to pipe weight and pressure differences at 6.400 and 4,000 ft, can be calculated as follows:
craw at 6,400 ft on pipe section P-110 (98 lb/ft)
_ Wn{D — x) — (Aop0 — A, pt)
TOC o "1-5" h z ~ As
98(11,100 — 6,400) — [140.5 x 0.052(12 x 10.000 + 14 x 1,100)
~ 28.59 ^
— (111.91 x 12 x 0.052 x 11,100)]
28.59
460,600 — 214,099 , .
= ———- 2M9——— =—- 8’622ps’
aaw at 6,400 ft on pipe section P-110 (85 lb/ft):
460,600 — 214,099 in ,n7 .
= ——— 2M9——— = ‘M07ps,
_ [98 (11,100 — 6,400) + 85(6.400 — 4.000) ] — 214.099
TOC o "1-5" h z “ 28.59
664,600 — 214.099 . .
uap (item 4) at 4,600 ft on pipe section P-110 (85 lb/ft)
Pi (^upi )
~ A,
12 x 0.052 x 6,400(116.11 — 111.91)
“ 24.39
= 688 psi
crap at 4,000 ft on pipe section L-80 (98 lb/ft)
0.624 x 6,400 (116.11 — 111.91)+ 0.624 x 4,000(111.91 — 116.11)
“ ‘ 28L59
= 321 psi
The effective axial stresses and the average of the radial and tangential stresses are presented in Table 3.19.
|
Table 3.19: Effective axial and the average of radial and tangential stresses in the intermediate casing during landing operations.
|
An Example of Calculations in Preparing Table 3.19:
Average of radial and tangential stresses (item 6) at any depth x is given by:
f°r + сгЛ _ A, Gp> x — A0 GPo x V 2 / x Asx
(111.91 х 12 — 140.5 х 12) х 0.052 х 4,000 “ 28.59
= -2,496 psi
The values of axial and average of radial and tangential stresses are plotted in Fig. 3.11 (page 159). From the plot it is evident that the line of axial stress and the average of radial and tangential stresses intersect at the casing shoe, indicating that the casing is not liable to buckle during landing and cementing operations.
Equally important is to check whether the pipe is liable to buckle during the drilling of the next interval. The specific weight of the fluid used to drill the next interval is 17.9 ppg and the annular fluid is again assumed to be saturated salt water (8.94 ppg). Consider also that the pipe is subjected to an average increase in temperature of 90°F and that in calculating the values of axial stress due to the change in fluid densities, the effect of surface pressure is ignored. Table 3.20 summarises the results.
<7r + at
|
Table 3.20: Stresses in the intermediate casing during the drilling of the next section of borehole.
|
Examples of Calculations in Preparing Table 3.20:
Change in pipe weight (item 1). Дсгаа.. due to the change in fluid densities, at
6.400 ft (P-110, 85) is as follows:
w — .
■^sx
0. 28 x 6,400 x 0.052 [116.11 x 5.9 — (-3.05) x 140.5]
~ 2T39
= 4,260 psi
Change in piston effect (item 2). A(Tap, due to the change in fluid densities, at
6.400 ft (P-110, 85) is:
(Aupi Alowi,
|
Лег„„ = |
ap A,
6,400 x 0.052 x 5.9 x 4.2
“ 2T37
= 338 psi
In Table 3.21, the values of the total axial stress and the average of radial and tangential stresses are presented.
|
Table 3.21: Stresses in intermediate casing during drilling of next section of borehole.
|
Examples of Calculations in Preparing Table 3.21:
Change in axial stress (item 5), cr^j. due to the increase in average temperature (90°F), is given by:
(jaT = -ЕГАТ
= -30 x 106 x 6.9 x 10“6 x 90 = —18,630 psi
Average of radial and tangential stresses (item 9). at 10,000 ft (P-110. 98) is:
{°т + о-Л _ (AjGPi — A0GPo) x
(111.91 x 17.9 — 140.5 x 8.94) x 0.052 x 10,000
“ 28.59
= 13,590 psi
Values of axial, radial, and tangential stresses are plotted in Fig. 3.11. From the plot it is evident that the lines of axial stress and the average of radial and tangential stresses intersect at a depth of 2.650 ft. This means that below this
|
Fig. 3.11: Axial and average of radial and tangential stresses along the length of the pipe. |
depth the pipe is liable to buckle and it should, therefore, be cemented up to a depth of ‘2,650 ft from the surface.
The presence of buckling force does not necessarily mean that the casing will buckle. For buckling to occur, the existing buckling force must exceed the critical buckling force for the casing string. The existing buckling force is:
= A. [(^
= 28.59 [13,590 -(-16, 795)]
= 868,637 lbf
According to Lubinski (1951), the critical buckling force on the intermediate casing can be determined as follows:
FbuCcr = 3.5 [EI(WnBF)2}F3
where:
|
Pressure in psi 2000 4000 6000 8000 10000 |
Selection based on |
||
|
Collopse |
Burst |
Collapse Burst |
|
|
> i i i i — 2000 — 4000 — 6000 -8000 -10000 UNER T0P 10500 ft |
10500 ft |
10500 ft |
10500 ft |
|
/ f Pn0 — 12000 j ] 47i^ /ГТ80—- ! I / / !58i4 # |
P110 47# — L80 — 58.4 # |
PI 10 47# 12500 L80 58.4 § |
P110 47# 12500_П L80 58.4 # |
|
LINER SHOE 14000 ft |
Collapse load line Burst load line
Fig. 3.12: Selection of casing grades and weight based on the collapse and burst loads for liner.
= ~ 7Г (13.3754 — 11.9374)
64
= 573.97 in.4
WnBF is the buoyant weight/ft and can be calculated as follows:
Wa — (paA0 — ptA,)x
x
94,880 — 10,000 x 0.052(140.5 x 8.94 — 111.91 x 17.9)
= 134.7 lb/ft
Hence,
Fbuccr = 3.5 [30 x 106 x 573.97 x (134.7)2 ]1/3 = 237,482 lbf
or,
237,482 = -25^- = S,307ps.
Thus, the pipe experiences a buckling force which is 3.7 times greater than its critical value.
Figure 3.11 shows that the critical buckling force occurs at about 5,000 ft from the surface and, therefore, the pipe should be cemented to this depth to prevent any permanent deformation that may result due to the buckling.