Casing Design Optimization in Vertical Wells
Cost Optimization Criteria for Casing Design
The development of the model was based on both the casing design theory presented in the previous chapters and the theory of optimization (Roberts, 1964: and Phillips, 1976). The following design elements were used in the development of the computer model:
1. For casing loading patterns, the Maximum Load Method (Prentice. 1971) for surface, intermediate, and production casing is considered. An example detailing all of the calculations is provided in this chapter. At each depth, the maximum external and internal pressure values can be predetermined on the basis of the casing run. the specific weight of the drilling fluid (subsequently referred to as mud weight), the maximum anticipated mud weight that will be in contact with the casing, the fracture gradient at the casing seat, and the pore pressure at the bottom of the next casing depth.
2. For tension calculations the maximum surface running loads are considered. This is because the compression force acting at the lower end of the casing is at a minimum and, therefore, axial tension load is at a maximum. As depth increases, the hydrostatic pressure increases, as does the compressional force acting on the lower end of the casing.
3. Buoyancy and bending (see Lubinski’s Eq. 2.39) are considered.
4. Shock and pressure test loadings are not considered.
The calculations for string design in directional wells have already been covered in Chapter 4 but will be addressed again later in this chapter because the computer program allows for some formula simplifications.
As mentioned above, the program in its present form does not consider the effects of shock or pressure test loading. However, the program code is provided to allow for further modification, if required.
Bending effects are considered using Lubinski’s formula which considers the pipe to be supported at two points rather than in continuous contact with the borehole. This somewhat more complex approach to bending is easily implemented in a computer program, though not in manual calculations.
Finally, buckling effects have to be considered separately, as demonstrated in the examples in Chapter 3.
Casing Design Optimization Theory
The optimization model for the absolute minimum cost is first formulated in a general way and is then simplified.
The casing string is arbitrarily divided into. V unit sections of equal length. Д/. In the computer program, this is done by dividing the measured depth by the casing length (a necessary input to the program). The casing design procedure starts at the bottom of the casing string and proceeds, in a stepwise manner, to
|
И I I r*tn±jj |
|
d |
. Pn _
CASING LOADS*
лк
n -1
| П-1 j
! [
[ [
Ш
OUTPUT (RETURN) COST C(s) MINIMUM TOTAL COST Cmin„
i = 1tornx Ns„.,
|
и ] I |—»|n+l| |
|
rf |
|
n-1 |
|
CASING TYPES. Pn . CASING LOADS* F. |
|
INPUT COST Cp П — 1 |
|
OUTPUT (RETURN) _ COSTC(s) ‘MINIMUM TOTAL COST Cmin_ |
|
NEW VARIANTS Cjn j = 1 to г x Ns, ‘ n n -1 |
|
i i Ш |
Fig. 5.3 : Recurrent calculation procedure for optimum casing design, the top (Fig. 5.3). The absolute minimum cost problem is formulated as follows:
|
Ct |
|
(5-1) |
min C(s)
|
where: С = CT = о = |
cost of a particular combination casing string, USS. minimum cost of combination casing string, USS. total number of combination casing strings possible, index of casing string combinations (1 < s < .Yco)
TOC o "1-5" h z (Pcc)n > Rc (APc)n (5.2)
(.Pcb)n > Rb (Арь)п (5.3)
{F,)n > RtFAn (5.4)
where:
Apc — differential collapse load. psi.
Арь = differential burst load. psi.
FAn = axial load at the top of the casing considered, lbf.
Rc, Rb, Rt = design factor0 for collapse, burst and tension,
respectively, d-less6. pcc — collapse pressure rating corrected for biaxial
stress (API Bui. 5C3, 1989). psi. pcb = either burst pressure rating corrected for biaxial or triaxial stress0, psi Ft = casing axial load rating (either pipe body yield or joint strength, whichever is smaller), lbf.
and
Fa„ = FAn_t + Al Wn cos (on) + Rj
j=i
where:
n = 1,2-•• A’
Ад = number of axial forces considered
Note that only the nomenclature for the variables introduced in this chapter will be provided. Refer to Appendix 1 at the end of the book for the others.
The summation term in Eq. 5.5 represents all axial forces other than casing weight. These axial forces include, but are not limited to. buoyant force, linear
belt friction (axial friction force generated to pull and move a belt around a
curved surface), bending force, viscous drag (a result of the fluid viscosity effect), and stabbing effect (stabbing the casing into the formation while running it into the well). In vertical wells, the axial load is:
Fa„ = FAn_, + AtWn — 0.052 7m /„ (Asn — Л5„_,) (5.6)
“The design factor (R) is selected by the engineer, whereas the safety factor (SF) is the value obtained after selecting the casing: this way SF > R.
^Dimensionless
°Normally triaxial stress is not corrected for. Triaxial stress correction, which is appropriate for designing casing for deep wells is left up to the engineer to introduce into the program.
where:
As — pipe cross-sectional area, in2.
7m = specific weight of the well fluid, lb/gal.
For the force calculation, n varies from 0 to, V because its effect is considered at both ends of the casing; therefore, for. V pipes in a combination casing string, the program calculates Л’ + 1 forces.
Thus for vertical wells, where externally generated forces are not significant (friction forces), the initial conditions are:
Fa0 = 0.052 7m Dj — As0, the hydrostatic forces acting on the first pipe.
A s0 = As,, the initial condition for the cross-sectional area.
Referring again to Eq. 5.6, it can be seen that F4] refers to the force acting on the top of the first casing. For directional wells, the conditions are changed because the hydraulic force acting on the casing end does not induce normal forces that would, in turn, generate friction forces.
At each unit section n. the set of the best casing is selected from the available casing supply. The best casing includes the cheapest and the lightest ones. The best casing choice for any unit section depends on all previous decisions, i. e., n — l, rc — 2,■ ■ •, 1 due to the additive nature of axial loads. Such a problem, from the standpoint of the optimization theory, is classified as the multistage decision process and is solved using a computer and the recurrent technique of dynamic programming. The definitions and recurrent formulas are covered in General Theory of Casing Optimization.
The general solution described above is impractical. It requires a relatively large amount of computer memory and time-consuming calculations. Also, large number of variants may be generated as the recursions progress. Therefore, the only practical solution to this problem is to reduce the number of casing variants.
Major Conflict in Casing Design: Weight vs Price
The analysis of the iterative procedure for casing design shows that the only source of the multitude of casing variants is the dilemma between casing weight and casing price. This dilemma has been observed by many casing designers, and is known as the “Weight/Price Conflict". The conflict arises from the observation that the decision made in favor of the cheapest casing for any bottom section of casing string may eventually yield a more expensive combination casing string. On the other hand, the combination casing string with a lighter (yet more expensive) lower part may be cheaper overall due to the reduction in axial load supported by the upper casing strings. The concept of the weight/price conflict is illustrated in Fig. 5.4. Insofar as the conflict cannot be resolved before the casing
|
WEIGHT |
|
о. ш о |
|
PRICE |
|
Fig. 5.4: Hypothetical conflict between minimum weight and minimum price design methods. (After Wojtanowicz and Maidla. 1987; courtesy of the SPE.) |
|
min. weight min. price |
design is completed, every casing that is lighter than the cheapest one has to be memorized at each step of the casing design, thereby generating new variants.
Over the course of a large number of calculations, however, it was noticed that the weight/price conflict depends on the price structure of each steel mill. Two examples will be solved to illustrate this observation. The first will be solved for a particular case where the conflict was present when using API grades only. Another will be solved for a case which shows no conflict of design methods when API grades were considered together with commercial grades from a particular steel mill.
Theory for the Minimum Weight Casing Design Method
The minimum weight casing design method is based on selecting the cheapest casing from among the lightest available. Priority is given to the weight over the price. Mathematically, this can be written as:
Ct = (5.7)
П= 1
pn = rain Pr (5.8)
|
Pn = min VP’1 m€(c, d) |
|
where: |
r€{a, b)
а = the lowest value of r within a given weight m.
b = the highest value of r within a given weight m.
с — the lowest value of m that satisfies load requirements.
С = cost, USS.
d = the highest value of m that satisfies load requirements.
m = index of casing weight that satisfies load requirements.
n — number of the casing section being designed.
n — 3 means the third pipe from lower end.
P = distributed price, USS/100ft.
r = index of casing that satisfies load requirements.
W = distributed weight, lb/ft.
EXAMPLE 5-2: Understanding the Notation
For a particular well, the design factors for burst, collapse, and pipe body yield are 1.1, 1.125 and 1.5, respectively. The loads at the point of interest are 5.020 psi for burst, 6,000 psi for collapse and 881.333 lbf for tension. The casings available are listed in Table B. l (Appendix B) (For this example only, the table values do not need to be corrected for axial loads.). The measured depth of the well is 10,000 ft, and the individual pipe length is 40 ft. Using this information, answer the following:
1. Define. Vp, Nw and N. and determine their values.
2. What are the possible values for r and for m?
3. What are the values of r when m = 3. 5. 7 and 9 ?
4. Why are the values of r — 53 and 79 not considered to be viable alternatives? Solution:
1. Лр is the number of all casings to be considered in the design. From Table B. l this number is 98. Aw is the number of casing weights within the casing file. The following weights are in the file: 36, 40. 43.5. 47. 53.5. 58.4.
61.0 lb/ft; thus, ,V = 7. N is the number of pipes of casing (or unit sections) in the combination casing string: therefore. A ss 10.000 — f — 40 = 250. (N is only approximately equal to 250 because casing lengths are not always 40 ft even for the common case of API length range 3 (see page 12 ), and certainly this is not the case for API ranges 1 and 2. Throughout this chapter the casing length is assumed to be 40ft.
2. The design loads are:
(a) For burst, 5,020 x 1.1 = 5,522 psi.
(b) For collapse, 6,000 x 1.125 = 6,750 psi.
(c) For tension, 881,333 x 1.5 = 1,322,000 lbf.
Selecting from Table B. l (Appendix B), the values for r and m that exceed these requirements are found:
(a) r = 61, 62, 63, 64, 70, 71. 72, 73, 74, 75, 76. 77. 78. 80. 81. 82, 83, 84. 85, 86, 87, 88, 89, 90. 91, 92, 93, 94. 95. 96, 97. 98.
(b) rn = 4, 5, 6, 7.
In the case of m, the lightest casing weight that meets load requirements is 47 lb/ft; the 3 weights below this 36, 40 and 43.5 lb/ft, do not.
3. From the previous answer, m = 3 is not a viable option because it fails to meet the load constraints and, therefore, no /■’s within this weight range will either. For m = 5, the corresponding r values are 61, 62. 63, 64, 70, 71, 72, 73, 76, 77, and 78 . Finally, for m — 7. the r values are 80. 82, 87, 89, 90, 92, 94, 95, 97, and 98.
4. Neither r = 53 nor r — 9 meets the design requirements. Specifically, г = 53 does not meet the collapse constraint and r — 79 does not meet the pipe body yield constraint due to the thread strength limitations.
Program Description and Procedure for Minimum Weight Design
Within a given set of load constraints, the lightest casing is chosen. In the computer program provided, this is achieved through a routine that sorts the casing PRICE. DAT table first by weight, and then within the same weight category by price.
This particular computer program was developed and written in FORTRAN 77 and can be run on any personal computer. The source code is provided with the disk so that it can be modified if required; however, it is suggested that rather than using the master disk, a backup should be used.
EXAMPLE 5-3: Minimum Weight Design Method
Using the computer program, rework Example 5-1 to design a casing string based on the minimum weight design method.
Solution:
The program CSG3DAPI. EXE uses the API criteria for collapse correction calculations (API Bui. 5C3, 1989). First, create an ASCII file named CSGLOAD. DAT
INTERMEDIATE CASING DESIGN THE WELL DATA USED IN THIS PROGRAM WAS:
.EQUIVALENT FRACTURE GRADIENT AT CASING SEAT = 15.0 PPG
.BLOW OUT PREVENTER RESISTANCE= 5000. PSI
DENSITY OF THE MUD THE CASING IS SET IN = 12.0 PPG
.DENSITY OF HEAVIEST MUD IN CONTACT WITH THIS CASING = 15.0 PPG
.TRUE VERTICAL DEPTH OF THE NEXT CASING SEAT = 15000. FT
PORE PRES. AT NEXT CASING SEAT DEPTH= 9.0 PPG
.MINIMUM CASING STRING LENGTH= 1000. FT
.DESIGN FACTOR: BUR= 1.000: COL=1.125: YIELD = 1.800
.TRUE VERTICAL DEPTH OF THE CASING SEAT=10000. FT
.DESIGN METHOD: MINIMUM WEIGHT
9 5/8” CASING PRICE LIST. FILE REF..PRICE958.CPR MAIN PROGRAM: CSG3DAPI
TOTAL PRICE=299031. U. S.DOLLARS TOTAL STRING BUOYANT WEIGHT = 344841. LB
DI=10000- 8520 L= 1480 NN= 6 W=43.5 M = 3 MB = 1.73 MC’ = 1.13 MY=19.1 P = 2983.77
DI= 8520- 7080 L= 1440 NN=13 W=43.5 M=3 MB=1.80 MC=1.13 MY=11.5 P=3216.91
DI= 7080- 5640 L= 1440 NN = 18 W=43.5 M=3 MB = 1.86 MC = 1.15 MY= 8.9 P=3488.41
DI= 5640- 4840 L= 1000 NN=13 W=43.5 M=3 MB=1.49 MC=1.13 MY= 6.3 P=3216.91
DI= 4640- 3640 L= 1000 NN= 6 W=43.5 M = 2 MB = 1.18 MC = 1.14 MY= 3.7 P = 2879.99
DI= 3640- 2640 L= 1000 NN= 6 W=40.0 M=3 MB=1.00 MC = 1.25 MY= 3.5 P=2743.75
DI= 2640- 1640 L= 1000 NN=13 W=40.0 M = 2 MB=1.18 MC = 1.62 MY= 2.9 P=2783.29
DI= 1640- 0 L= 1640 NN= 6 W=40.0 M=2 MB = 1.04 MC = 2.37 MY= 2.1 P=2565.56
THE MEANING OF SYMBOLS:
.DI, DEPTH INTERVAL, (FT)
.L, LENGTH, (FT)
•NN, TYPE OF GRADE (SEE THE GRADE CODE BELOW)
•W. UNIT WEIGHT, (LB/FT)
.M IS THE TYPE OF THREAD: 1…SHORT: 2…LONG: 3…BUTTRESS
..MB. MC. MY, MINIMUM SAFETY FACTORS FOR BURST. COLLAPSE. AND YIELD
.P. UNIT CASING PRICE S/100FT
GRADE CODE:
NN 1= …H40 NN 2= …J55 NN 3= …K55 NN 4= …C75 NN 5= …L80
NN 6= …N80 NN 7= …C95 NN 8= ..P110 NN 9= ..VI50 NN13= …S95
NN14= CYS9S NN15= ..S105 NN16= …S80 NN17= ..SS95 NN18= .LSI 10 NN19= .LS125
that contains the data for the design. The instructions for how to do this are shown in the program listing itself under CSG3DAPI. FOR. However, the CSGAPI. BAT file is a batch hie formulated to help edit the necessary data and then to run the program. For this example only, a step-by-step walk through the program will be made.
Again, following the instructions in CSGAPI. BAT, a price hie named PRICE. DAT must be created. The price hie used in this example is shown in Table B. l (Appendix B). In addition to the price, the hie PRICE. DAT contains the casing properties necessary to undertake the design.
To proceed to this point:
1. Insert the program disk.
2. Type "CSGAPI”. A screen will appear titled “PROGRAM PRICE.”
3. Choose [1] to read a hie. Hit enter.
INTERMEDIATE CASING DESIGN THE WELL DATA USED IN THIS PROGRAM WAS:
.EQUIVALENT FRACTURE GRADIENT AT CASING SEAT = 1S 0 PPG
BLOW OUT PREVENTER RESISTANC’E= 5000. PSI
.DENSITY OF THE MUD THE CASING IS SET IN = 12.0 PPG
.DENSITY OF HEAVIEST MUD IN CONTACT WITH THIS CASING = 15 0 PPG
TRUE VERTICAL DEPTH OF THE NEXT CASING SEAT = 15000. FT
PORE PRES. AT NEXT CASING SEAT DEPTH= 9.0 PPG
.MINIMUM CASING STRING LENGTH= 2500. FT
.DESIGN FACTOR: BUR=1.000: COL=1.12S: YIELD = 1.800
•TRUE VERTICAL DEPTH OF THE CASING SEAT= 10000. FT
.DESIGN METHOD: MINIMUM WEIGHT
9 5/8" CASING PRICE LIST. FILE REF.:PRICE958.CPR MAIN PROGRAM: CSG3DAPI
TOTAL PRICE=313169. U. S.DOLLARS
TOTAL STRING BUOYANT WEIGHT=3S5246. LB
DI=10000- 7080 L= 2920 NN = 13 W=43.5 M=3 MB=1.80 MC= 1.13 MY= 11.5 P=3216.91
DI= 7080- 4560 L= 2520 NN = 18 W = 43.5 M=3 MB=1.72 MC = 1.15 MY= 7.1 P = 3488.41
DI= 4560- 0 L= 4560 NN= 6 W=43.5 M = 2 MB=1.09 MC=l. lti MY= 2.3 P=2879.99
THE MEANING OF SYMBOLS:
• Dl, DEPTH INTERVAL, (FT)
• L, LENGTH, (FT)
• NN, TYPE OF GRADE (SEE THE GRADE CODE BELOW)
• W, UNIT WEIGHT, (LB/FT)
.M IS THE TYPE OF THREAD: 1…SHORT; 2…LONG: 3…BUTTRESS
• MB, MC, MY, MINIMUM SAFETY FACTORS FOR BURST, COLLAPSE. AND YIELD
• P. UNIT CASING PRICE S/100FT
GRADE CODE:
NN 1= …H40 NN 2= …J55 NN 3= …K-55 NN 4= …C’75 NN.5= …LSO
NN 6= …N80 NN 7= …C95 NN 8= ..PllO NN 9= ..V150 NN13= …S95
NN14= CYS95 NN15= ..S105 NN16= …SSO NN17= ..SS95 NN18= .LSI 10
NN19= .LS125
4. Choose PRICE958.CPR. Hit enter.
5. Choose [4] to Exit. Hit enter.
6. A screen will appear titled "PROGRAM CSGLOAD."
7. Choose [3] to initialize the data. Input the requested information. Note that even if the well is vertical, the current version of the program will ask for deviated hole data; just answer with a zero. If unsure of the data to enter for this example, check with Table 5.4.
8. When the data input is complete, an input file will be created and the “PROGRAM CSGLOAD’1 screen will reappear. When creating the data files, try to develop a logical system of naming them.
9. Choose [4]. Hit enter.
10. The program will run provided the input data is correct.
11. The result will be outputted to the screen and to a file DESIGN. OUT. If there are likely to be multiple runs, this file needs to be renamed after each run to avoid overwriting it in the subsequent run.
As a result of running the program CSG3DAPI, (using the CSGAPI. BAT file) a file named DESIGN. OUT. as shown in Table 5.3, is generated. This file contains the following information:
• The casing string being designed. In this case, an intermediate casing string.
• A summary of the inputted well data used to run the program.
• The design criteria. Here, it is the minimum weight criteria.
• The name of the price file used and the main program name. In this example, PRICE958.DAT and CSG3DAPI were used, respectively.
• The casing string’s total price of 8299.031 and buoyant weight of 344.841 lbf. are also listed.
• At this point, the sectional breakdown of the string is given. The first section for depth interval (Dl), 10.000 ft to 8,520 ft with a length of 1,480 ft. is an N-80 43.5 lb/ft Buttress thread that costs 82,983.77/100 ft. In this interval, the lowest actual safety factors for burst (thread or body, whichever is the smallest), collapse and yield (thread or body, whichever is the smallest) are 1.73, 1.13 and 19.1. respectively.
• The remainder of the output is an explanation of the nomenclature used in the file.
For the lower part of the casing string, the limiting constraint is collapse. The lowest of the three safety factors, the value for collapse, equals the collapse design factor given earlier, whereas both the burst and yield constraint values are higher than their design safety factors. Near the surface. howrever. the limiting constraint is now burst loading.
Another point to observe is that the design suggests a tapered string (combination casing string) with eight main sections, all of which have lengths above the required minimum of 1,000 ft. As in the previous example using the Quick Design Charts, it is reasonable to try to keep the number of sections down to three. In this particular program, the desired number of sections is obtained by altering the minimum length and observing the output. Of course, this requirement can be built into the main program to avoid the trial and error procedure suggested above. However, the decision of whether or not to do so is left up to the engineer, as the source code is included on the disk package. In this example, by altering the minimum length requirement to 2.500 ft, the desired result is achieved as shown in Table 5.4.
Prior to comparing the above results to the Quick Design Chart method, several program refinements will be illustrated with further examples. Finally, comparison and cost analysis of all the methods are made.
Theory on the Minimum Cost Casing Design Method
The minimum cost casing design method always selects the cheapest casing that meets the load requirements. Mathematically, this can be written as:
|
CT |
N = 71 — 1 |
|
Pn where: |
= min PTn r£(a, i>) |
a — the lowest value of r that satisfies load requirements. b — the highest value of r that satisfies load requirements.
Program Description and Procedure for the Minimum Cost Design
Within a given set of load constraints, the selection is made such that the cheapest pipe is chosen. In the computer program, this is achieved by sorting the casing PRICE. DAT table by price.
EXAMPLE 5-4: Minimum Price Design Method
Again using the computer program, this time rework Example 5-1 to design a casing string based on the minimum price design method.
The program CSG3DAPI uses the API approved method for collapse correction calculations (API Bui. 5C3, 1989). First create an ASCII file named CSGLOAD. DAT, which contains the required design data. The batch file created to help edit the necessary data and then run the program is called CSGAPI. BAT, but the method is the same as detailed in Example 5-3.
After running the program CSG3DAPI, a file named DESIGN. OUT, as shown in Table 5.5, is generated.
The format of the output (Table 5.5) is the same as previously described in Example 5-3, except that this time the design is different from the earlier minimum weight design. The reason for this is that the design criteria was changed to include minimum cost.
In this example, seven intervals of grades N-80 (NN6) and S-95 (NN13) are suggested. Consider the design output for the depth interval from 8,520 to 5,440 ft; the only difference between the two casing sections is thread type: long thread and buttress, respectively. To analyze why the change in thread type occurred, refer to Table B. l (Appendix B). First identify the line that contains casing N-80.
INTERMEDIATE CASING DESIGN THE WELL DATA USED IN THIS PROGRAM WAS:
.EQUIVALENT FRACTURE GRADIENT AT CASING SEAT=15.0 PPG
BLOW OUT PREVENTER RESISTANCE= 5000. PSI
DENSITY OF THE MUD THE CASING IS SET IN = 12.0 PPG
DENSITY OF HEAVIEST MUD IN CONTACT WITH THIS C’ASING = 15.0 PPG
TRUE VERTICAL DEPTH OF THE NEXT CASING SEAT = I5000. FT
.PORE PRES. AT NEXT CASING SEAT DEPTH= 9.0 PPG
.MINIMUM CASING STRING LENGTH= 1000. FT
.DESIGN FACTOR: BUR= 1.000: COL=1.125: YIELD= 1.800
.TRUE VERTICAL DEPTH OF THE CASING SEAT = 10000. FT
.DESIGN METHOD: MINIMUM COST
9 5/8" CASING PRICE LIST. FILE REF.:PRICE958.CPR MAIN PROGRAM: CSG3DAPI
TOTAL PRICE=288651. U. S.DOLLARS TOTAL STRING BUOYANT WEIGHT=35707S. LB
DI=10000- 8520 L= 1480 NN= 6 W = 43.5 M=3 MB=1.73 MC = 1.13 MY=19.1 P = 2983.77
DI= 8520- 6440 L= 2080 NN= 6 W=47.0 M=2 MB=1.56 MC = 1.13 MY= 6.8 P=3014.47
DI= 6440- 5440 L= 1000 NN= 6 W = 47.0 M=3 MB=1.45 MC = 1.22 MY= 6.4 P = 3223.84
DI= 5440- 4440 L= 1000 NN= 6 W = 47.0 M=2 MB=1.35 MC=1.20 MY= 4.3 P=3014.47
DI= 4440- 3440 L= 1000 NN= 6 W=43.5 M=2 MB=1.16 MC = 1.18 MY= 3.4 P = 2879.99
DI= 3440- 2360 L= 1080 NN = 13 W’=40.0 M=2 MB=1.18 MC = 1.25 MY= 3.1 P = 2783.29
DI= 2360- 0 L= 2360 NN= 6 W = 40.0 M = 2 MB=1.00 MC = 1.66 MY= 2.1 P = 2565.56
THE MEANING OF SYMBOLS:
,DI. DEPTH INTERVAL (FT)
.L, LENGTH (FT)
.NN, TYPE OF GRADE (SEE THE GRADE CODE BELOW)
,W, UNIT WEIGHT (LB/FT)
.M IS THE TYPE OF THREAD: 1…SHORT: 2…LONG: 3…BUTTRESS
MB, MC. MY, MINIMUM SAFETY FACTORS FOR BURST. COLLAPSE. AND YIELD
P. UNIT CASING PRICE S/100FT
GRADE CODE: NN 1= …H40 NN 6= …N80 NN14= .CYS95 NN19= .LS125
NN 2= …J55 NN 7= …C95 NN15= ..S105
NN 3= …K55 NN 8= ..P110 NN16= …S80
NN 4 = …C75 NN 9= ..VI50 NN17= ..SS95
NN 5= …L80 NN13= …S95 NN18= .LSI 10
47.0 lb/ft long thread (M=2), at a cost of S3,014.47/100 ft; then identify the line containing casing N-80, 47.00 lb/ft Buttress (M=3), at a cost of 83,223.84/100 ft. Notice that, both casings have the same collapse and burst resistances. Returning to the computer output again (Table 5.5). it is apparent that the collapse rating is the limiting restriction that determined the change from long threads to buttress threads. Given that the collapse ratings for both casings is the same, why is there a change from long thread to more expensive Buttress thread?
The answer lies in the program’s use of API Bui. 5C3 (1989) formulas to calculate the collapse resistance. Instead of using the tabular value for collapse resistance shown in manufacturer’s specifications. API Bui. 5C3 (1989) calculates the collapse resistance based on the yield strength value. The algorithm used in the program will be explained later; suffice to say that, in this example, the pipe body yield in Table B. l (Appendix B) was chosen as the smaller of the pipe body and the joint strength.
As in the previous examples, the solutions for a three-section string were inves-
INTERMEDIATE CASING DESIGN’
THE WELL DATA USED IN THIS PROGRAM WAS:
• EQUIVALENT FRACTURE GRADIENT AT CASING SEAT=15.0 PPG. BLOW OUT PREVENTER RESISTA.’CE= 5000. PSI
.DENSITY OF THE MUD THE CASING IS SET L’ = 12.0 PPG
• DENSITY OF HEAVIEST MUD IN CONTACT WITH THIS C’ASING = 15.0 PPG. TRUE VERTICAL DEPTH OF THE NEXT CASING SEAT= 15000. FT
• PORE PRES. AT NEXT CASING SEAT DEPTH= 9.0 PPG. MINIMUM CASING STRING LENGTH= 2500. FT. DESIGN FACTOR: BUR=I.000: COL=1.125; YIELD=1.800 •TRUE VERTICAL DEPTH OF THE CASING SEAT=10000. FT. DESIGN METHOD: MINIMUM COST
9 5/8” CASING PRICE LIST. FILE REF.:PRICE958.CPR MAIN PROGRAM: CSG3DAPI
TOTAL PRICE=301398. U. S.DOLLARS TOTAL STRING BUOYANT WEIGHT=372510. LB
DI=10000- 6480 L= 3520 NN= 6 W=47.0 M = 2 MB=I.57 MC = 1.13 MY= 6.7 P = 3014.47
DI= 6480- 3960 L= 2520 NN= 6 W=47.0 M=3 MB=1.31 MC = 1.22 MY= 4.7 P = 3223.84
DI= 3960- 0 L= 3960 NN= 6 W = 43.5 M = 2 MB = 1.09 MC = 1.31 MY= 2.2 P = 2879.99
THE MEANING OF SYMBOLS:
.DI, DEPTH INTERVAL (FT)
.L, LENGTH (FT)
NN. TYPE OF GRADE (SEE THE GRADE CODE BELOW)
,W, UNIT WEIGHT (LB/FT)
,M IS THE TYPE OF THREAD: 1…SHORT: 2…LONG: 3…BUTTRESS
.MB. MC, MY. MINIMUM SAFETY FACTORS FOR BURST. COLLAPSE. AND YIELD
.P, UNIT CASING PRICE S/100FT
GRADE CODE:
NN 1= …H40 NN 2= …J55 NN 3= …K55 NN 4 = …C75 NN 5= …L80
NN 6= …N80 NN 7= …C95 NN 8= ..P110 NN 9= ..V1S0 NN13= …S95
NN14= .CYS95 NN15= ..S105 NN16= …S80 NN17= ..SS95 NN18= .LS110
NN19= .LS125
tigated; the results are shown in Table.5.6. The only difference between the two bottom sections is in the thread type. The change of the thread type indicates that the yield strength rather than body yield was considered in the calculations. Thus, the limiting constraint is again the collapse resistance. Whether or not to consider the joint strength in the collapse calculations is debatable because it will depend oil the manner in which the joint fails. Insofar as this information is not available in the tables, the result is somewhat conservative.
The results of the three-section combination string calculated in the last three examples will be compared and explained. In this particular example only, the casing load plots for collapse and burst are calculated to aid in the analysis. The results are shown in Figs. 5.5 and 5.6.
Casing Loads for Collapse
The load line is given by connecting points Л, B. and С with a straight line.
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Fig. 5.5: Casing load study for collapse. |
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5000 10000 Fig. 5.6: С’ asing load study for burst. |
1. Depth (D) and pressure (p) at point A:
Da = 0 pA = 0.
2. Depth and pressure at point В:
(a) To determine the depth at B. calculate the height (H) of the hydrostatic column of the heaviest mud used to drill to the next casing setting depth that equals the formation pore pressure at that depth:
0. 052 x 15 x Я = 0.052 x 9.0 x 15.000
H = 9,000 ft
DB = 15,000 — 9,000 — 6.000 ft
(b) Pressure: pB — 0.052 x 6.000 x 12 x 1.125 = 4.212 psi.
3. Depth and pressure at point С:
pc = (0.052 x 10,000 x 12 — 0.052 x 4.000 x 15) x 1.125 = 3.510 psi.
4. Point D lies at the intersection of the straight line that passes through
points A and В and the straight line that passes through point C, parallel
to the collapse pressure axis.
The load line is determined by using a straight line to connect the points E. F. and G in Fig. 5.6.
1. Depth and pressure at point E:
De — 0
The surface burst pressure is either the lowest value of the BOP working pressure or the surface pressure of gas column inside the casing with fracturing pressure at the casing seat.
(a) Pressure at the casing seat {pei)
Pei = 0.052 x 15 x 10.000 = 7.800 psi.
(b) Pressure at the surface (pE-2)
Consider a static column of methane gas (M=16) at the surface, a bottomhole temperature calculated by assuming an average surface temperature of 70°F, and a temperature gradient of 1.2°F/100 ft. Using the equation of state for ideal gas behavior, the following formula can be derived:
71____ (n I i < v 51.182 + 1.159 x D I ii-? ■
PE2 — [Pei + 14./) x e / — 14./ psi where the pressures are in psig and the depth is in feet. Therefore:
/7 sjnn i i i " 51.182 + 1.159 x 10.000 / , . ~ ..,,, •
Pei — (c800 + 14л)хе V x —14./ = 6.649 psi
The BOP working pressure is given as (рез):
Pei = 5,000 psi.
The smallest value, corrected by the design factor, is selected:
Pe = 5,000 x DFB = 5.000 x 1.0 = 5.000 psi. where DFB is the design factor for burst.
‘2. Depth and pressure at point F:
At point F, pressure equilibrium is achieved with the gas column, the BOP maximum working pressure and the heaviest mud gradient in contact with the internal casing wall.
Using a stright line to approximate the pressure curve between pE and p£2 gives:
jj _ Рез ~ Pei______________________________
f“^- 0.052 x-;2 Dg
where (ppg) is the specific weight (“density") of the heaviest mud in
contact with the internal casing wall and Dg is the total depth. In the
following example. Dg is 10.000 ft. Thus:
n 5,000 — 6.649
7.800 — 6.649
— 0.052 x 15.0
Assuming that a backup pressure gradient of 0.465 psi/ft is acting on the external casing wall, the pressure at point F is equal to
pF = (5,000 + 0.052 x 15 x 2.480 — 0.465 x 2.480) x 1.0 = 5.781 psi.
3. Depth and pressure at point G:
Dc = 10.000 ft
Pa = (Pei ~ 0.465 x Dg) x DFB
pa = (7,800 — 0.465 x 10,000) x 1.0 = 3.150 psi.
These values and the casing properties (Table B. l. Appendix B) are plotted in Figs. 5.5 and 5.6.
The results of the different design methods are shown in Table 5.7°. Notice that in none of the designs has the load constraints been violated (In doing this analysis.
3The data above was purposely chosen to emphasize the strength of the Quick Design Chart. Exercises 6, 7, 8, and 9, are formulated more realistically for cases in which the data does not readily fit the Quick Design Chart scenario.
|
Description |
|
Burst (psi) |
|
Collapse (psi) |
|
Length, ft Bottom to Top |
Quick Design Charts — S 297.471
|
2,243 2,150 5,607 |
|
8.150 7.510 6.820 |
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7.100 5,600 4.230 |
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S-95. 47.0 lb/ft LTC S-95. 43.5 lb/ft LTC S-95, 40.0 lb/ft LTC |
Note: Collapse was not corrected according to API Bui. 5C3 (1989).
|
Minimum Weight Design — API — S 313.169
|
|
Note: Collapse according to API Bui. 5C3 (1989). |
Minimum Cost Design — API — 8 301.398
|
3.520 2.520 3,960 |
|
6.870 6.870 6,330 |
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4.750 4.750 3.810 |
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N-80, 47.0 lb/ft LTC N-80. 47.0 lb/ft BUT N-80, 43.5 lb/ft LTC |
Note: Collapse according to API Bui. 5C3 (1989).
|
Cheapest Solution Min. Cost and Min. Weight Design — 8 283.989
|
|
Note: Collapse based on a modification to API Bui. 5C3 (1989). |
care must be taken to account for collapse reduction due to the axial loading.). This being the case, why is the quick design chart design less expensive than the two computer designs? Furthermore, not only is it less expensive, but the mechanical properties for burst and collapse are, in most instances, superior to the computer-generated designs.
The reason for this difference is that until now the API Bui. 5C3 (1989) has been used to calculate the corrected collapse properties of casing that were developed according to API tubular specifications. In these calculations, the corrected collapse rating (considering axial loads) was found by using the yield stress of the pipe and by disregarding manufacturing processes or other factors that might increase the total collapse rating. For example, compare the API casing collapse rating for C-95, 40 lb/ft of 3.330 psi against a non-A PI casing collapse rating for
Ш
ОС
D
СО
со
ш
ОС
0_
ш
со
CL
3
—I
о
о
р = collapse rating for API casing ^ listed in the tables
Pa2 = collapse rating for casing
listed in manufacturer’s tables
Fig. 5.7: Diagram of non-API casing collapse pressure correction.
S-95, 40 lb/ft of 4,230 psi. The difference is significant and. moreover, the cost of the S-95 is less than that of the C-95. Thus, by following the API Bui. 5C3 (1989) method for calculating collapse resistance, the design results will be as demonstrated in the above examples.
For a non-API casing, an alternative to this procedure is to consider a reduction of the manufacturer’s collapse rating proportional to that which occurs in the API procedure. According to the API formulas for corrected collapse rating due to axial loading, the collapse pressure predictions follow path abc in Fig. 5.7. Non-API casings have better collapse resistance and. therefore, higher values are reported for these casings in the tables for zero axial stress (pcr2 or point d). Assuming pcr2 is correct, it is unlikely that the actual casing pressure failure behavior would follow path dabc. As an alternative to this practice, path dec is suggested for these cases. The question now becomes how to find point e?
The only point known so far is pcr2■ which is obtained directly from the man-
Table 5.8: Minimum cost design for non-API casing using the modified API collapse calculations.
INTERMEDIATE CASING DESIGN THE WELL DATA USED IN THIS PROGRAM WAS:
.EQUIVALENT FRACTURE GRADIENT AT CASING SEAT=1S.0 PPG
.BLOW OUT PREVENTER RESISTAN’CE= 5000. PSI
.DENSITY OF THE MUD THE CASING IS SET IN = 12.0 PPG
.DENSITY OF HEAVIEST MUD IN CONTACT WITH THIS CASING = 15.0 PPG
.TRUE VERTICAL DEPTH OF THE NEXT CASING SEAT= 15000. FT
.PORE PRES. AT NEXT CASING SEAT DEPTH= 9.0 PPG
.MINIMUM CASING STRING LENGTH = 2500. FT
.DESIGN FACTOR: BUR=1.000: COL=1.125: YIELD = 1.800
.TRUE VERTICAL DEPTH OF THE CASING SEAT=10000. FT
.DESIGN METHOD: MINIMUM COST
9 5/8’’ CASING PRICE LIST. FILE REF.:PRICE958.CPR MAIN PROGRAM: CASING3D
TOTAL PRICE=283989. U. S.DOLLARS TOTAL STRING BUOYANT WEIGHT=333864. LB
DI=10000-6800 L= 3200 NN = 13 W=40.0 M = 2 MB=1.60 MC=1.13 MY= 8.2 P = 2783.29
DI= 6800- 4280 L= 2520 NN = 13 W=43.5 M = 2 MB=1.46 MC=1.45 MY= 4.9 P=3007.88
DI= 4280- 0 L= 4280 NN=13 W=40.0 M = 2 MB=1.18 MC=1.47 MY= 2.6 P=2783.29
THE MEANING OF SYMBOLS:
• DL DEPTH INTERVAL (FT)
.L, LENGTH (FT)
.NN, TYPE OF GRADE (SEE THE GRADE CODE BELOW)
,W, UNIT WEIGHT (LB/FT)
,M IS THE TYPE OF THREAD: 1…SHORT: 2…LONG; 3…BUTTRESS
.MB, MC, MY, MINIMUM SAFETY FACTORS FOR BURST. COLLAPSE. AND YIELD
.P, UNIT CASING PRICE $/100FT
GRADE CODE:
NN 1= …H40 NN 2= …J55 NN 3= …K55 NN 4= …C75 NN 5= …L80
NN 6= …N80 NN 7= …C95 NN 8= ..PU0 NN 9= ..V150 NN13= …S95
NN14= .CYS95 NN15= ..S105 NN16= …S80 NN’17= ..SS95 NN18= .LSI 10
NN19= .LS125
ufacturer’s pipe specification tables. The pressure at point a can be calculated using the API collapse formula for axial loads (flowchart shown in Table 2.1) for zero axial stress. Similarly, the pressure at point b can be calculated using the API formula for the appropriate value of axial stress. (This would be the value of corrected collapse pressure only if the API correction criteria is used.)
The collapse pressure, pe, can be obtained by assuming the following relationship between these pressures:
^ ^ (5.12)
Pa Pb
Rearranging Eq. 5.12 results in:
Pd / ,
Pe = — X рь (0.1.3)
Pa
The computer program for minimum price design with a minimum section length of 2,500 ft, was rerun after modifying the manufacturer’s collapse ratings in the manner shown in Fig. 5.7 and Eq. 5.13.
Table 5.9: Minimum weight design for non-API casing using the modified API collapse calculations.
INTERMEDIATE CASING DESIGN THE WELL DATA USED IN THIS PROGRAM WAS:
• EQUIVALENT FRACTURE GRADIENT AT CASING SEAT = 15.0 PPG. BLOW OUT PREVENTER RESISTANCE= 5000. PSI
.DENSITY OF THE MUD THE CASING IS SET IN = 12.0 PPG
DENSITY OF HEAVIEST MUD IN CONTACT WITH THIS C’ASING=1S.0 PPG
.TRUE VERTICAL DEPTH OF THE NEXT CASING SEAT=15000. FT
PORE PRES. AT NEXT CASING SEAT DEPTH= 9.0 PPG
•MINIMUM CASING STRING LENGTH= 2500. FT
■ DESIGN FACTOR: BUR= 1.000; COL=1.12S: YIELD= 1.800
.TRUE VERTICAL DEPTH OF THE CASING SEAT=10000. FT
.DESIGN METHOD: MINIMUM WEIGHT
9 5/8” CASING PRICE LIST. FILE REF.:PRICE958.CPR MAIN PROGRAM: CASING3D
TOTAL PRICE=28.3989. U. S.DOLLARS TOTAL STRING BUOYANT WEIGHT=333864. LB
DI= 10000- 6800 L= 3200 NN = 13 W=40.0 M = 2 MB=1.60 MC = 1.13 MY= 8.2 P=2783.29
DI= 6800- 4280 L= 2520 NN=13 W=43.5 M = 2 MB=1.46 MC = 1.45 MY= 4.9 P=3007.88
DI= 4280- 0 L= 4280 NN=13 W=40.0 M = 2 MB = 1.18 MC=1.47 MY= 2.6 P=2783.29
THE MEANING OF SYMBOLS:
•DI, DEPTH INTERVAL (FT)
• L, LENGTH (FT)
•NN, TYPE OF GRADE (SEE THE GRADE CODE BELOW)
• W, UNIT WEIGHT (LB/FT)
,M IS THE TYPE OF THREAD: 1…SHORT; 2…LONG: 3…BUTTRESS
■MB. MC, MY, MINIMUM SAFETY FACTORS FOR BURST. COLLAPSE. AND YIELD
• P, UNIT CASING PRICE S/100FT
GRADE CODE:
NN 1= …H40 NN 2= …J55 NN 3= …K55 NN 4= …C75 NN 5= …L80
NN 6= …N80 NN 7= …C95 NN 8= ..P110 NN 9= ..VI50 NN13= …S95
NN14= .CYS95 NN15= ..S105 NN16= …S80 NN’17= ..SS95 N’N’18= .LSI 10
NN19= .LS125
As an exercise, the engineer should make the suggested program modifications as detailed in the following steps:
1. The subroutine to be modified in CSG3DAPI. FOR is SUBROUTINE POOR.
2. Delete line 68, IF(CFNAPI. GT. l.)THEN.
3. Delete line 69, CFNAPI=1.0.
4. Delete line 70, ENDIF.
5. Recompile to produce an updated. EXE file.
After recompiling and rerunning the program, the output should appear as it is in Table 5.8. If it does not, compare the modified file with CASING3D. FOR on the disk. The revised string shows a significant decrease in price. 813.482. from the earlier cheapest alternative, the Quick Design Chart. These casing loads were added to Figs. 5.5 and 5.6 for comparison with the earlier results.
|
Fig. 5.8 : Flow diagram of the minimum-cost casing design program for directional wells. (After Wojtanowicz and Maidla, 1987: courtesy of SPE.) |
All subsequent examples are based on this modification. The modified program is named CASING3D. EXE and the batch file provided to help run it is named CASING. BAT.
Comparison between the minimum cost and minimum weight methods using the API collapse calculations shown in Tables 5.4 and 5.6 show a Si 1.771 cost increase when a lighter string of casing was selected. However, if the same example is rerun after implementing the changes in the program for the use of non-API casing in designs, the results using the minimum weight and the minimum price criteria are the same as shown in Tables 5.8 and 5.9. Provided the design criteria for non-API casing is agreed upon, this design represents the most economical alternative in Table 5.5.