**BHA Weight & Weight-On-Bit: **One important consideration in designing the BHA is determining the number of drill collars and heavy-weight pipe required to provide the desired weight-on-bit. When drilling vertical wells, standard practice is to avoid putting ordinary drill pipe into compression (recommended by Lubinski in 1950). This is achieved by making sure that the “buoyed weight” of the drill collars and heavy-weight pipe exceed the maximum weight-on-bit. This practice has also been adopted on low inclination, directionally drilled wells. In other types of directional wells, it must be remembered that since gravity acts vertically, only the weight of the “along-hole” component of the BHA elements will contribute to the weight-on-bit. The problem this creates is that if high WOB is required when drilling a high inclination borehole, a long (and expensive) BHA would be needed to prevent putting the drillpipe into compression. However, for these high inclination wells, it is common practice to use about the same BHA weight as used on low inclination wells. On highly deviated wells, operators have been running drillpipe in compression for years. Analysis of drillpipe buckling in inclined wells, by a number of researchers (most notably Dawson and Paslay), has shown that drillpipe can tolerate significant levels of compression in small diameter, high inclination boreholes. This is because of the support provided by the “low-side” of the borehole. Drillpipe is always run in compression in horizontal wells, without apparently causing damage to the drillpipe.

**Required BHA Weight For Rotary Assemblies: **When two contacting surfaces (i.e drillpipe and the borehole wall) are in relative motion, the direction of the frictional sliding force on each surface will act along a line of relative motion and in the opposite direction to its motion. Therefore, when a BHA is rotated, most of the frictional forces will act circumferentially to oppose rotation (torque), with only a small component acting along the borehole (drag). Measurements of downhole WOB by MWD tools has confirmed that when the BHA is rotated there is only a small reduction in WOB due to drag. This reduction is usually compensated for by using a “safety factor”.

**Buoyancy & Hookload: **Drillstrings weigh less in weighted fluids than in air due to a fluid property known as buoyancy. Therefore, what is seen as the hookload is actually the buoyed weight of the drillstring. Archimedes’s principle states that the buoy force is equal to the weight of the fluid displaced. Another way of saying this is that a buoy force is equal to the pressure at the bottom of the string multiplied by the cross sectional area of the tubular. This is due to the fact that the force of buoyancy is not a body force such as gravity, but a surface force.

For example, the buoy force exerted on 7.5-inch x 2-inch drill collars in a 700 ft vertical hole with 12 ppg mud would be 17,925 pounds.

**Buoy Force = Pressure x Area**

### Hydrostatic Pressure

= 0.0519 x MW x TVD = 0.0519 x (12) x (700) = 436.8 psi

**Cross Sectional Area **= /4 x (OD2 – ID2) = /4 x (7.52 – 22) = /4 x (56.25 – 4) = 41.04 in2

**Buoy Force **= 436.8 x 41.04 = 17,924.99 pounds

By looking at the API RP 7G it can be determined that the air weight of these 7.5-inch drill collars is 139 pounds per foot. If we have 700 feet of collars, the total air weight would be 97,300 pounds.

**Total Air Weight = weight per foot x length **= 139 x 700 = 97,300 pounds

The buoyed weight of the collars, or the **Hookload**, is equal to the air weight minus the buoy force.

**Hookload = Air Weight – Buoy Force **= 97,300- 17,925 = 79,375 pounds

This method for determining the buoyed weight is not normally used. Instead, the following formula, which incorporates a buoyancy factor, is used and recommended by the API.

Buoyancy Factor = 1 – (MV/65.5) = 1 – (12/65.5) = 0.817

MW=Mud Density (ppg)

**Hookload = Air Weight x Buoyancy Factor **= 97,300 x 0.817 = 79,494 pounds

Buoyancy Factors rounded off to three places can also be found in the API RP 7G (Table 2.13).

**Note: ***The formula above for hookload does not take into account axial drag. Hookload, as determined in the formula above is the approximate static surface hookload that would be displayed by the weight indicator in a vertical hole with no drag, excluding the weight of the traveling block, drill line etc.*

In practice, hookload will vary due to motion and hole drag. Pick-Up Load refers to the hookload when pulling the drillstring upwards. The highest hookload normally encountered will be when attempting to pick up the string. Slack-Off Load refers to the hookload when lowering the drillstring. Drag Load refers to the hookload when drilling in the oriented mode. Other references to hookload are Rotating Off-Bottom Load and (rotary) Drilling Load.

**Maximum Hookload When Two Grades Of Drill Pipe Are Used: **When two grades of drill pipe are used, the higher grade (i.e. the pipe with the higher load capacity) is placed above the lower grade pipe. The maximum tension to which the top joint can be subjected is based on the yield strength of the higher grade of pipe. Calculations similar to those already dealt with may be used to determine the maximum length of both grades of pipe. Another consideration is the maximum hookload which can be applied when only a few stands of the higher grade pipe have been added. Provided the higher grade pipe is in the vertical section, maximum hookload (pickup load) is calculated as the yield strength of the lower grade of pipe PLUS the “air weight” of the higher grade pipe. This is because the surface hookload includes the weight of the higher grade pipe; but that weight (since it is supported from the surface) does not act on the top joint of lower grade pipe.

**Maximum Hookload** = Yield Strength + Weight Of Lower Grade Pipe Of Higher Grade Pipe

When a sufficient length of higher grade pipe has been added, the limiting condition will become the yield strength of the higher grade pipe. The air weight of the higher grade pipe is used because the buoy force acting on the drillstring is acting on the bit and components of the BHA. The hydrostatic pressure which the mud exerts on the drill pipe in the upper (vertical) section of the hole does not create a resultant force acting upwards.

**Neutral Point: **The neutral point is usually defined as the point in the drillstring where the axial stress changes from compression to tension. The location of this neutral point depends on the weight-on-bit and the buoyancy factor of the drilling fluid. In practice, since the WOB fluctuates, the position of the neutral point changes. It is therefore quite common to refer to a “transition zone” as the section where axial stress changes from compression to tension. Drillstring components located in this “transition zone” may, therefore, alternately experience compression and tension. These cyclic oscillation can damage downhole tools. A prime example is drilling jars, whose life may be drastically shortened if the jars are located in the transition zone. It is also important, as previously explained, to know if any drill pipe is being run in compression. Therefore it is important to know the location of the neutral point.

**Overpull: **In tight holes or stuck pipe situations, the operator must know how much additional tension, or pull, can be applied to the string before exceeding the yield strength of the drill pipe. This is known as **Overpull***, *since it is the pull force over the weight of the string. For example, in a vertical hole with 12 ppg mud, a drillstring consists of 600 feet of 7.25-inch x 2.25-inch drill collars and 6,000 ft of 5-inch, New Grade E drill pipe with a nominal weight of 19.5 lbs/ft and an approximate weight of 20.89 lbs/ft. First, the hookload is determined

**Hookload = Air Weight x Buoyancy Factor**

= [(6,000 x 20.89) + (600 x 127)] 0.817 = 164,658 pounds

Referring to the API RP 7G, the yield strength in pounds for this grade, class, size and nominal weight of drill pipe is 395,595 pounds. Therefore: Maximum Overpull = Yield Strength In Pounds – Hookload

= 395,595 – 164,658 = 230,937 pounds

The operator can pull 230,937 pounds over the hookload before reaching the limit of elastic deformation (yield strength). Obviously, as depth increases, hookload increases, at a certain depth the hookload will equal the yield strength (in pounds) for the drill pipe in use. This depth can be thought of as the maximum depth that can be reached without causing permanent elongation of the drill pipe (disregarding hole drag as a consideration). Practically, an operator would never intend to reach this limit. A considerable safety factor is always included to allow for overpull caused by expected hole drag, tight hole conditions or a stuck drillstring. In practice, selection of the drill pipe grade is based upon predicted values of pick-up load. For a directional well, the prediction of pick-up load is best obtained using a Torque and Drag program, as well as including the capacity for overpull. Some operators include an additional safety factor by basing their calculations on 90% of the yield strength values quoted in API RP7G.

**Torque & Drag: **Several factors affect hole drag, including hole inclination, dogleg severity, hole condition, mud properties, hole size, and drillstring component types, sizes and placement. However, as mentioned earlier, in drilling situations where the drillstring is not rotated (as when a steerable system is used in the oriented mode) axial drag can become very significant and should be evaluated using a Torque and Drag computer program. Torque and Drag programs can be found in ** EC*Track **and

**.**

*DrillByte***Along Hole Components of Force**

Consider a short element of a BHA which has a weight W.

Effective weight in drilling mud = W(BF)

**Component of weight acting along borehole **= W(BF)cosq

If the BHA is not rotated, *the force of friction, *FFR acting up the borehole on the BHA element is given by:

FFR = mN

…where m is the coefficient of friction,

N is the normal reaction force between the BHA element and the borehole wall. If this normal reaction is due only to the weight of the BHA element itself, then:

N = W(BF)sinq and hence

FFR = mW(BF)sinq

The net contribution to the WOB from this BHA element is therefore

WBIT = W (BF) (cosq – msinq)

**Computer Models of Drillstring Friction: **Proper evaluation of drillstring friction requires the use of a computer program. These programs analyze drillstring friction for rotary drilling as well as drilling with no drillstring rotation. These mathematical models make a number of simplifying assumptions and consider the drillstring as composed of discrete elements. Using these models, it is possible to solve equations for the normal force of drillstring/ well bore contact at the bottom drillstring element, the friction force deriving from that normal contact force, and the load condition at the upper end of the drillstring element. Such methods, repeated for each Drillstring element over the length of the drillstring, yield the following information:

• Surface hookload and rotary torque

• Normal forces of drillstring/well bore contact at each Drillstring element

• Average torsional and tensile load acting upon each Drillstring element

**The E*C TRAK Torque and Drag Module: **This program, developed at the Drilling Research Center in Celle, Germany, is used to calculate torque and drag when a friction factor (coefficient of sliding friction) is known or estimated. It will calculate the friction factor when either torque or hookload is known. Software accuracy has been verified against actual field data, with inputs and outputs handled in user selected units.

**General Uses: **The program may be used to: • Optimize well path design for minimum torque and drag • Analyze problems either current or post-well • Determine drillstring design limitations • Determine rig size requirements

**Inputs Required: **• Drillstring component data (OD, ID, tool joint, and material composition) • Survey data (actual or planned) • Friction factor(s) or actual hookload or torque values (for friction factor calculation)

**Outputs: **Information concerning loads, torques and stresses are calculated for discrete points in the drillstring from rotary table to the bit. These values are output in both tabular (summary or detailed) and graphical formats:

• Drag load (pick-up or slack-off) **• **Pick up load • Slack off load • Rotating off bottom load • Drilling load • Rotating off bottom torque • Rotary torque (drilling and off-bottom) • Maximum allowable hook load (at minimum yield) • Drillstring weight (in air) • Bit to neutral point distance drillstring twist • Drillstring twist • Axial stress • Torsional stress • Bending stress • Total equivalent stress

**Use Of Torque & Drag Programs For BHA Weight Evaluation: **These programs have a wide range of applications, but have mainly been used to evaluate drillstring design integrity and alternative well plans for horizontal wells or complex**, **unusual directional wells. However, the program can be used to check BHA weight calculations for normal directional wells. The program will calculate axial drag for a non-rotated assembly and also calculates the position of the neutral point in the drillstring. In addition, the program calculates the forces on the drill pipe and will “flag” any values of compressive load which exceed the critical buckling force for the drill pipe.