Casing Cost Optimization in Directional Wells
Directional Well Formulation
The minimum-cost casing procedure for vertical wells can be expanded to directional wells because the flexible structure of the model allows for independent calculations of casing loads and cost minimization. For this procedure, the following assumptions are made:
1. The well is planed in a vertical plane; therefore, its trajectory is confined to two dimensions.
2. Only elastic properties of casing are considered in bending calculations.
3. The bending contribution to the axial stress is expressed as an equivalent axial force.
4. The bending contribution to the normal force is neglected because its impact on the final design is very small.
5. The effect of inclination on axial loads is considered by using the axial component of casing weight.
6. The favorable effect of mechanical friction on axial load during downward pipe movement is not considered.
7. The unfavorable effect of mechanical friction on axial load during upward pipe movement is considered.
8. Axial load is calculated as the maximum pulling load.
9. Burst and collapse corrections for biaxial state of stress are calculated using the axial static load at the time the casing is set.
The general flow chart of the program is shown in Fig. 5.8. The input of the program contains the following data:
• Casing Data: Size, mechanical properties and price data of all available casings.
• Drilling Data: Vertical depths for the casing to be designed and the next casing setting depth; fracture gradient at the casing seat; minimum pore pressure anticipated; density of the mud in which the casing is run and the heaviest mud density planned for use in subsequent drilling operations.
• Directional Data: Measured depths (Dkop that is equal to (-kop, (eob, (dop, (eod, where KOP stands for kickoff point, EOB for end-of-build, DOP for dropoff point, EOD for end-of-drop); well inclination data (buildup rate and dropoff rate).
• Design Data: Type of casing load (surface, intermediate, or production); design factors for burst, collapse, tension, and borehole friction factor: minimum allowable length for each section of the casing string, and; the maximum surface pressure allowed.
Program Description for Directional Wells
In the calculations, the computer program considers four basic directional well profiles:
1. The build and hold type well.
2. The ‘S’ shape well.
3. The modified ‘S’ shape well.
4. The double-build shape well.
Collapse and burst loads are calculated assuming the casing is placed in its final position and, therefore, vertical depths are used to calculate the pressure load profiles. Calculations of axial loads in directional wells, however, is much more complex than in vertical wells because the effect of the borehole friction must be considered.
To determine frictional loads the program simulates the casing being pulled out from the well. In addition to the frictional loads all other axial loads, including the bending effects, are calculated at each measured depth the casing’s section would pass through on its way up the hole. The largest value of axial stress withstood by an individual pipe on its way up must be greater than the minimum yield value of this pipe selected from the casing data base file. In addition, the minimum pipe length requirement must also be satisfied. Thus, the number of iterations performed before a solution is found can be very large; and for a large data base file (more than 100 casing entries), the program may take some time to run (several hours on a regular 286-based PC, for example).
When editing the CSGLOAD. DAT file, it is necessary to ensure that all measured depths are multiples of the individual pipe length, e. g., a multiple of 40 ft if 40 ft pipe lengths are chosen.
Vertical Depths (D) and Inclination Angles (a):
The conversion from measured depth to true vertical depth is made by projecting the actual well profile onto a vertical axis. In the program, vertical depths and inclinations are calculated for all casing unit sections and. as a result, the complete directional well profile is generated from the directional well data. The profile is shown in Fig. 4.8 (page 188). By considering the well to be comprised of sect ions of constant build and drop between known measured dept hs, the program simplifies the actual well for the purpose of casing design. This approach requires little input data relative to an analysis based on a detailed directional survey.
The five formulas used in the depth conversion procedure are given below.
1. From the surface to the buildup point:
A = ii (5.26)
a, = 0 (5.27)
2. From the buildup point to the end of build:
= Ш {i‘ “ (kop) (5/28)
n n 180 x 100 . , ,
A = DKop~ :————— sin a,- (5.29)
where a = rate of change of inclination with depth, deg/100 ft.
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Note: the term ————- converts — the units of d from degrees per 100 ft 180 x 100 ь у |
Note: the teri to radians/ft.
3. For the slant portion (also known as the sailing portion):
<*i = (5.30)
A = A+i + (A — Ah) cos o,+1 (5.31)
Note: г decreases with increasing depth (Fig. 5.9).
4. From the dropoff point to the end of drop:
a’ = ai ~ 100 ~~ ^Dop) (5.32)
„ 180 x 100 , .
A = Ddop- :————— (sin at — sin аЛ (5.33)
тг a2
where:
ai ~ loo ^EOB ~ ^A’op) (5.34)
5. From the end of the dropoff point to the final depth:
ai — ai ~ (^eod — (dop) (5.35)
A = A+1 + Hi — f,+i) cos Q,+1 (5.36)
Using the vertical depth equations shown above, it is possible to associate the resulting burst and collapse pressure loads to each ith position in the well:
Apb((i) = Apb (Di) = (&pb)n (5.37)
and
Д pc(ti) = Apc(D,) = {Apc)n (5.38)
As mentioned earlier the calculation of the axial load is the most difficult part of directional-well casing design. Using the maximum load principle, the concept of the maximum pulling load is applied.
The maximum pulling load is obtained by placing the casing (each unit section) in its final position and calculating the axial load it would be subjected to while
being pulled out of the well. This is achieved in a stepwise manner for every casing
section’s position above its final resting position, until reaching the surface. This process is depicted in Fig. 5.9
Fig. 5.9: Instantaneous ith position of the nth unit section of casing in a directional well. (After Wojtanowicz and Maidla, 1987; courtesy of SPE.)
The calculations for axial pulling loads are shown in Chapter 4, Eqs. 4.1 through 4.41. These equations are the analytical solutions to the above problem and are very easy to use for hand calculations. They can also be simplified for numerical calculations in the form of recurrent formulas. The recurrent calculation is actually a numerical integration technique with results within 0.25% of the largest error possible (compared to the analytical solution). The simplification follows.
The value of the axial pulling load supported by the n section at position i is calculated as:
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(5.39) |
(Fa)’n = FBn + {Fl)u
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0.847194 Al a, d0 y/(FL)n (d* — df) |
where the equivalent axial force caused by bending, Fbn. is:
(5.40)
The axial force, Fl, is calculated with the recurrent formula (Fl)u = (F[y)s for s = n, where:
A( Ws cos (a,_n+s) + Fid + Fbd (5-41)
where:
s — 1,2 ,n.
7 = specific mud weight, Ib/gal (3.42)
The linear friction drag, Fld, is:
SHAPE * MERGEFORMAT
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Fld = (1 — |
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5.43) |
MW, sin (a, x fh
The belt friction drag, Твд, is:
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is M 200 |
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F, |
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(5.44) |
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BD |
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(-1)“ 2 fb (Fl)s_1 sin — |
a = 1 for buildup portion a = 2 for dropoff portion
The position at which the maximum value of the axial load is achieved is selected for the maximum axial pulling load of unit section n:
(Fa)n = max (Fa)’n (5.45)
Applications of Optimized Casing Design in Directional Wells
The casing optimization computer program was developed on the basis of the casing design model for directional wells. Preliminary application of the program revealed that the computing time is largely dependent on the iterations associated with the calculations of maximum axial loads. Moreover, it was found that in most cases, the highest axial pulling loads were at the surface and at a point one casing joint below the KOP. As a result of these observations, the program was modified to consider only three borehole points: the surface, the KOP. and the top of the dropoff portion.
EXAMPLE 5-5: Casing Design in Directional Wells
Given the following information for a planned directional well, use the casing optimization program to design an intermediate combination casing string based on the minimum price criteria. With the exception of the directional data, the well data is the same as the earlier vertical wells.
9|-in. intermediate casing set at 10.000 ft
Smallest casing section allowed: 1,000 ft
Design factor for burst: 1.1
Design factor for collapse: 1.125
Design factor for pipe body yield: 1.8
Production casing depth (next casing): 15.000 ft
Mud density while running casing: just below 12 lb/gal
Equivalent circulating density to fracture the casing shoe: 15 lb/gal
Heaviest mud density to drill to final depth: 15 lb/gal
Blow Out Preventer (BOP) working pressure: 5.000 psi
Kickoff point depth: 2,520 ft
Measured depth at the end of the buildup section: 4.520 ft
Total measured depth: 10,000 ft
Buildup rate (BUR): 2°/100 ft
Design factor for running loads: 1.7
Borehole friction factor: 0.4
Buoyancy should be considered.
As in the earlier examples, an ASCII file named CSGLOAD. DAT is created from CASING3D using the CASING. BAT file (CASING3D is the modified version of the original CSG3DAPI program: see page 284). The first entry informs the program that the well is directional.
Upon running CASING3D. an output file DESIGN. OUT (Table 5.10.) is printed out. The table contains the following information:
• The underlined title specifies the type of casing string designed. (In this case an intermediate casing string.)
• The first text block contains the input data used to run the program.
• The last line of the first block gives the design criteria. (In this example the minimum cost.)
• The second block gives names of the price file and the main program used in the design computations. (In this example. PRICE. DAT and CASING 3D. respectively.)
• The third block gives the design output. The first section of casing from bottom covers the interval from 10.000 ft to 7.320 ft, a length of 2,680 ft. The casing suggested is an S-80. 40.0 lb/ft. short thread that costs $2,215/100 ft. For this interval, the lowest actual safety factors for burst
(thread or body, whichever is the smallest), collapse and pipe body yield (or joint strength, whichever is the smallest) are 1.15, 1.13 and 9.0. respectively.
Table 5.10: Intermediate casing design example for a directional well (Example 5-5).
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 LN = 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 .DESIGN FACTOR FOR RUNNING LOADS= 1.800 .KICK OFF POINT= 2520. FT
.MEASURED DEPTH AT END OF BUILD UP= 4520. FT. MEASURED DEPTH AT DROP OFF POINT=10000. FT .MEASURED DEPTH AT END OF DROP OFF =10000. FT. TOTAL MEASURED DEPTH = 10000. FT .BUILD UP RATE= 2.0 DEG/100FT. DROP OFF RATE= 2.0 DEG/100FT. PSEUDO FRICTION FACTOR= .400 DIMENSIONLESS. BUOYANCY CONSIDERED ON STATIC LOADS DESIGN METHOD: MINIMUM COST
9 5/8" CASING PRICE LIST. FILE REF.:PRICE958.CPR MAIN PROGRAM: CASING3D
TOTAL PRICE=257813. U. S.DOLLARS TOTAL STRING BUOYANT WEIGHT=281792. LB PULLING OUT LOAD = 381976. LB
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2215.20 3007.88 2783.29 2743.75 2565.56 |
TOC o "1-5" h z DI=10000- 7320 L= 2680 NN = 16 W = 40.0 M = 1 MB=1.15 MC = 1.13 MY= 9.0 P: DI= 7.320- 6320 L= 1000 NN=13 W = 43.5 M = 2 MB=2.02 MC= 1.47 MY= 10.2 P:
DI= 6320- 4280 L= 2040 NN = 13 W = 40.0 M = 2 MB=1.59 MC = 1 .14 MY= 5.9 P
DI= 4280- 3280 L= 1000 NN= 6 W = 40.0 M = 3 MB= 1.25 MC = 1.1 ‘3 MY= 5.2 P:
DI= 3280- 0 L= 3280 NN= 6 W = 40.0 M =2 MB = 1.07 MC= 1.42 MY= 2.6 P:
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= …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 NN17= ..SS95 NN18= .LSI 10
NN19= .LS125
• The two text blocks at the bottom define symbols and codes used in the output file.
In this example the design string consists of five sections with a total casing combination string cost of $257,813. Changing the minimum section length to
2.500 ft and rerunning the program produces a new design file DESIGN. OUT (Table 5.11) with only three-sections. The cost of the string increases by $10,951
(4.2%); however, as mentioned earlier, this may be offset by cost savings in other areas, e. g., string running and pipe storage costs.
Table 5.11: Intermediate casing design example for a directional well — 3 sections (Example 5-5).
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 = !2.0 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
.DESIGN FACTOR FOR RUNNING LOADS = 1.800
.KICK OFF POINT= 2520. FT
.MEASURED DEPTH AT END OF BUILD UP= 4520. FT MEASURED DEPTH AT DROP OFF POINT = 10000. FT .MEASURED DEPTH AT END OF DROP OFF =10000. FT. TOTAL MEASURED DEPTH= 10000. FT .BUILD UP RATE= 2.0 DEG/100FT. DROP OFF RATE= 2.0 DEG/100FT. PSEUDO FRICTION FACTOR= .400 DIMEN SION LESS. BUOYANCY CONSIDERED ON STATIC LOADS. DESIGN METHOD: MINIMUM COST
9 5/8" CASING PRICE LIST. FILE REF.:PRICE9S8.CPR MAIN PROGRAM: CASING3D
TOTAL PRICE=268764. U. S.DOLLARS TOTAL STRING BUOYANT WEIGHT=285120. LB PULLING OUT LOAD = 387688. LB
DI= 10000- 7320 L= 2680 NN = 16 W = 40.0 M = 1 MB=1.15 MC = 1.13 MY= 9.0 P=2215.20
DI= 7.320- 4800 L= 2520 NN = 13 W=43.5 M = 2 MB=1.81 MC = 1.47 MY= 7.1 P=3007.88
DI= 4800- 0 L= 4800 NN = 1.3 W=40.0 M = 2 MB=1.27 MC’ = 1.41 MY= 3.0 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= ..PI 10 NN 9= ..V150 NN13= …SOS
NN14= .CYS95 NN15= ..S105 NN16= …S80 NN17= ..SS95 NN18= .LSI 10
NN19= .LS125
When a non-API casing is included for use in the design it is a good practice to use the minimum weight, criteria and rerun the program to examine the convergence between the minimum cost method and the minimum weight method.
Effect of the Borehole Friction Factor
The borehole friction factor affects the drag between the pipe and the wall of the borehole. This drag depends on a number of factors including: drilling mud and its properties (solids content, oil content and filtration cake quality), borehole conditions (type of rock, roughness, cuttings bed, keyseats, washouts, etc.) and centralizer type and spacing. Thus, unlike the true friction coefficient recognized in other engineering sciences, the borehole friction factor is more accurately described as a pseudo-friction factor. Its value is generally obtained from the field and not from laboratory experiments. Good field values are better than those obtained from the API Lubricity Tester.
Typical values of the pseudo-friction factor measured while running casing are found to be in the range of 0.25 to 0.4. The uncertainty in this value has led some designers to suggest using the oversimplified model of the equivalent vertical well where I = D. This is not only a conservative approach, but also overdesigns casing tremendously and could result in extremely high costs. This point is further illustrated in the following example.
Table 5.12: The effect of the pseudo-friction factor (0.5 in this case) on the final cost (Example 5-6).
INTERMEDIATE CASING DESIGN THE WELL DATA USED IN THIS PROGRAM WAS
•EQUIVALENT FRACTURE GRADIENT AT CASING SEAT=17.4 PPG
.BLOW OUT PREVENTER RESISTANCE= 5000. PSI
.DENSITY OF THE MUD THE CASING IS SET LN=13.0 PPG
■ DENSITY OF HEAVIEST MUD IN CONTACT WITH THIS CASING = 16.9 PPG
.TRUE VERTICAL DEPTH OF THE NEXT CASING SEAT=15000. FT
.PORE PRES. AT NEXT CASING SEAT DEPTH = 16.4 PPG
.MINIMUM CASING STRING LENGTH= 1000. FT
.DESIGN FACTOR: BUR=1.100: COL=1.125. YIELD=1.800
.DESIGN FACTOR FOR RUNNING LOADS=1.500
.KICK OFF POINT= ‘2800. FT
.MEASURED DEPTH AT END OF BUILD UP= 5600. FT. MEASURED DEPTH AT DROP OFF POL’T= 9200. FT. MEASURED DEPTH AT END OF DROP OFF =12000. FT TOTAL MEASURED DEPTH= 16000. FT BUILD UP RATE= 3.0 DEG/100FT. DROP OFF RATE= ‘2.0 DEG/100FT. PSEUDO FRICTION FACTOR= .500 DIMENSIO. NLESS. BUOYANCY CONSIDERED ON STATIC LOADS. DESIGN METHOD: MINIMUM COST
7" CASING PRICE LIST. FILE REF.: PRICE7.CPR MAIN PROGRAM: CASING3D
TOTAL PRICE=173269. U. S.DOLLARS TOTAL STRING BUOYANT WEIGHT= 188662. LB PULLING OUT LOAD = 399961. LB
DI= 16000- .3800 L=12200 NN=10 W=23.0 M=3 MB=1.15 MC=1.67 MY= 5.4 P=1006.56
DI= .’3800- ‘2800 L= 1000 NN= 8 W = 26.0 M= 3 MB = 1.52 MC=2.38 MY= 6.1 P=22’28.50
DI= 2800- 0 L= 2800 NN=10 W=23.0 M=3 MB=1.22 MC=2.79 MY= 3.3 P=1006.56
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= …K55 NN 4= …C75 NN 5= …L80
NN 6= …N80 NN 7= …C95 NN 8= ..P110 NN 9= ..V’150 N’N’10= …S95
NN11= .CYS95 NN12= ..S105 N’N’13= …S80 N’N’14= ..SS95 N’N15= .LS110
NN16= .LS125 NN17= .LS140 NN’18= N’N’19= . .. NN20=
EXAMPLE 5-6: Drag vs Equivalent Vertical Depth, for Axial Loads Calculations in Directional Wells
Given a 7-in., 38 lb/ft casing in a horizontal section, what is the percentage error introduced to the design load by using the equivalent vertical depth (evd) method rather than the drag model? Assume a pseudo-friction factor of 0.36. Also, consider directional well data specified in Table 5.12 and make a plot of casing cost vs. pseudo-friction factor.
Solution:
Wdrag = fbxWN = 0.36 x 38 x sin 90° = 13.68 lb/ft Wevd = 38 lb/ft
„ . . 38 — 13.68
(Jverestimation = ————- = 1.(8
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Fig. 5.10: Effect of the pseudo-friction factor on casing cost.. |
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Borehole Friction Factor (Dimensionless) |
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Note that for horizontal wells, the equivalent vertical depth approach is equivalent to the drag model only if the pseudo-friction factor is 1. a totally unrealistic proposition. In continuing Example 5-6 the minimum cost casing program has been used to estimate the effect of the borehole friction factor on the optimum casing design. As an example, the calculations for the 7-in. intermediate casing string set at 16,000ft with the borehole friction factor value of 0.5 are shown in Table 5.12. Also, a plot of the 7-in. casing cost vs. the borehole friction factor is shown in |
13.68
Fig. 5.10. Note that for values of the borehole friction factor smaller than 0.4, the effect of friction is small. Above this value, however, the optimum casing design is considerably affected by the frictional drag.
The main advantage of using the drag model for the design of casing is that it enables the calculation of the axial stress distribution along the casing string with respect to well deviation and curvature; hence, it correlates casing axial load with directional well parameters.
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Fig. 5.11: Well trajectories for Example 5-7. |
Also, cost analysis provides the most convincing argument for using the drag concept. In Example 5-6, if a borehole friction factor of 1 (evd method) is used, cost is $303,837. However, if a borehole friction factor of 0.5 (drag method) is used, the cost is reduced by 75% to $173,269.