## Drill String Design

One of the initial planning steps for a rotary drilling operation is the design of the drill string. The drill string must have the strength to drill to the intended target depth and be light enough so that the hoisting system can extract the string from the well when the target depth has been reached. Described below is the API procedure for drill string design [1].

The axial tension force (or load), F (lb), at the top of the drill string in a vertical well is where Lp is the length of the drill pipe (ft),

Wp is the weight per unit length of drill pipe (lb/ft), Lc is the length of the drill collars (ft), wc is the weight per unit length of drill collars (lb/ft), Kb is the buoyancy factor. The buoyancy factor is

where jm is the specific weight of the drill fluid (lb/ft3), Ys is the specific weight of steel (lb/ft3).

The maximum allowable design axial tension force, Fa (lb), is

where Fy is the drill pipe tension force to produce material (steel) yield (incipient failure of the drill pipe) (lb). These tension failure values can be obtained from the tables in Appendix B or Tables 3-3, 3-6, and 3-7.

For most drill string designs a factor of safety is used to insure there is a margin-of-overpull (MOP) to allow for a stuck drill string. The drill string design factor of safety, FS, is given by

The MOP is determined by the rotary drilling rig hoisting capacity. Thus, MOP is

where Fc is the hoisting capacity of the rotary drill rig (lb). But the total hoisting axial force cannot exceed Fa.

Illustrative Example 3.1 A section of a vertical well is to be rotary air drilled from 7,000 ft to 10,000 ft with a 7 7/8 inch tri-cone roller cutter drill bit. This is to be a direct circulation drilling operation. Above the drill bit the BHA is made up of 500 ft of 6 3/4 inch by 2 13/16 inch drill collars and similar diameter survey subs and nonmagnetic drill collars. The drill pipe available from the drilling contractor is API 4 1/2 inch, 16.60 lb/ft nominal, EU-S135, NC50(IF). Determine the FS and the MOP associated with using this drill string to drill this section of the well.

From Appendix B, Table B-1 gives 100 lb/ft for the 6 3/4 inch by 2 13/16 inch drill collar. Table B-5 gives 18.62 lb/ft for the drill pipe actual weight per unit length (includes tool joints). Since the drilling fluid is air, then ym = 0, and Kb = 1.0. The maximum axial tension force in the top drill pipe element of the drill string is when the depth is 10,000 ft and when the drill bit is lifted off the bottom of the well (after the target depth has been reached). The maximum axial tension force is determined from Equation 3-1. This is

Table B-5 gives the tension force to produce yield in the drill pipe (in this case the pipe body). This tension force to yield is 595,004 lb. Equation 3-3 can be used to determine the maximum allowable axial tension force for the drill pipe. Thus, Equation 3-3 is

The factor of safety is determined from Equation 3-4. Equation 3-4 gives 535,504

Most land double and triple rotary drilling rigs do not have lifting capacities as high as 535,504 lb. Assuming a rotary drilling rig is selected with a maximum hoisting capacity of 300,000 lb, then Equation 3-5 can be used to determine the MOP. Equation 3-5 gives

From the calculations above, the additional 73,110 lb (above the weight of the drill string) or, a total axial tension force of 300,000 lb can be safely pulled by the rig hoisting system with the assurance that the drill string will not structurally fail.

Illustrative Example 3.2 The George E. Failing Company Star 30K self-propelled drilling rig (shown in Figure 1-3) is to be used to air drill a shallow well with dual wall pipe (reverse circulation). The well is to be vertical with a depth of 820 ft and will use 5.50 inch concealed inner-tube pipe (see Table 3.6). The drilling operation will drill a borehole having a 6 1/4 inch diameter. The hoisting capacity of this drill rig is 30,000 lb. Determine the factor of safety for this drill string and the MOP for this drilling operation.

The 5.50 inch dual wall pipe has a weight per unit length of 27.4 lb/ft (see Table 3-6). Since the drilling fluid is air, then ym = 0, and Kb = 1.0. The maximum axial tension force in the top dual wall pipe element of the drill string is when the depth is 820 ft and when the drill bit is lifted off the bottom of the well (after the target depth has been reached). The maximum axial tension force is determined from Equation 3-1. This is

Table 3-6 gives the axial tension force to produce yield in this dual wall pipe. This tension force to yield is 206,900 lb. Equation 3-3 can be used to determine the maximum allowable axial tension force for the drill pipe. Thus, Equation 3-3 is

The factor of safety is determined from Equation 3-4. Equation 3-4 gives 186,210

22,468

The MOP for this drilling example is obtained from Equation 3-5. Equation 3-5 gives

This example demonstrates that the dual wall pipe has very high strength in resisting structural failure. However, most shallow drilling rigs do not have the hoisting capacity to lift these dual wall drill strings when deep drilling operations are considered. This example shows that the Factor of Safety for the drill string is quite high illustrating this structural strength. But this low MOP value illustrates the inadequate capacity of most single rotary drill rigs that might be used for a typical shallow drilling operation.