Formation Fracture Resistance
Drill-String DesignThe drill-string consists of:Drill BitBottom
Hole Assembly BHA The primary component of the BHA is the drill
collar.Drill pipes
The design process shall address the following items:1.
Selection of drill collar diameter2. Selection of BHA connections3.
Determination of drill collar and or HWDP length4. Tool joint
torsional capacity check5. Tension design limitations6. Burst
pressure determination7. Collapse pressure determination8. Slip
crushing load9. Fatigue limits10. Combined tension and torsional
load limits4Drill Pipe PropertiesEach joint of drill pipe includes
the tube body and the tool joint, which connects the sections of
drill pipe. Drill pipe is available in several sizes and weights.
The grade of drill pipe describes the minimum yield strength of the
pipe. This value is important because it is used in burst,
collapse, and tension calculations. Common grades are as
follows:
Tool Joints
Eng.M.Salah
Drill CollarsDrill collars are the predominant components of the
bottom-hole assembly. Some of the functions of the drill collars
are as follows:Provide weight for the bitProvide strength needed to
run in compressionMinimize bit stability problems from vibrations,
wobbling, and jumpingMinimize directional control problems by
providing stiffness to the BHA
Eng.M.Salah10Proper selection of drill collars (and BHA ) can
prevent many drilling problems. Drill collars are available in many
sizes and shapes, such as round, square, triangular, and spiral
grooved. The most common types are round (slick) and spiral
grooved. Spiral-grooved collars reduce the surface contact area
between the pipe and well bore. The lower contact area reduces the
probability of differential pressure sticking.
The API dimensions for collars of various outer diameters are as
follows
D/C Size CriteriaSelection of drill collar diameter for a slick
or pendulum assembly is based on the required effective minimum
hole diameter. That is, the size of the bottom drill collar would
be the limiting factor for lateral movement of the bit.
More commonly drill collar size is selected based on stresses.
Components subject to bending have both tensile and compressive
forces induced in them. When rotated under bending, individual
metal fibers are subject to rapidly alternating tension and
compression, which may induce fatigue failureBHAs are subject to
both bending and rotation. Fatigue failures commonly occur where
stresses are concentrated. Stresses are concentrated at connections
and changes in pipe size. Stress concentration is restricted by
ensuring that changes in bending resistance are within tolerable
ranges. The bending resistance of a BHA component is dependent upon
its section modulus, which is definedas follows:
Generally, the change in bending resistance is expressed in
terms of a bending resistance ratio (BRR), which may be calculated
as follows:
The bending resistance ratio should be checked at changes in
pipe size. BRRs are calculated using the pipe body dimensions and
should generally be below 5.5
EXAMPLE: Bending Resistance Ratios BRRA proposed BHA consists of
9 x 3 drill collars. Is it acceptable to make this up directly to 5
x 3 HWDP?BRR = ([ 9.04 - 3.04 ] * 5.0) / ([ 5.04 - 3.04 ] * 9.0) =
6.62 which is unacceptable (greater than 5.5)Is it acceptable to
make this up directly to 8 X 3 drill collars?BRR = ([ 9.04 - 3.04 ]
* 8.0) / ([ 8.04 - 3.04 ] * 9.0)= 1.44 which is acceptable (less
than 5.5)
Is it acceptable to make the 8 collars to the 5 X 3 HWDP?BRR =
([ 8.04 - 3.04 ] * 5.0) / ([ 5.04 - 3.04 ] * 8.0) = 4.61 which is
acceptable (less than 5.5)Therefore, if 9 X 3 drill collars are
required on bottom, one acceptable BHA would include both 8 X
3drill collars and 5 X 3 HWDP above them.Drill Collar
ConnectionsThe bending resistance ratio of drill collar connections
is defined as the section modulus of the box (measured 4 from the
end) divided by the section modulus of the pin (measured 3 from the
end).The inside diameter of the box and outside diameter of the pin
are determined by the type of connection; therefore, only the
outside diameter of the box and inside diameter of the pin need to
be measured.Allowable Weight on Bit (vertical holes)An important
function of the bottom hole assembly (BHA) is to protect the drill
pipe from buckling. In straight holes, buckling of the pipe is
prevented by using a BHA of sufficient weight to ensure that the
neutral point of bending is kept within the BHA. A common
misconception is that the neutral point of tension and compression
is relevant in BHA designWhen a drill string is run into a straight
hole, the forces acting on the string are self-weight and
hydrostatic pressure of the drilling fluid. This hydrostatic
effect, commonly called buoyancy, results from the pressure exerted
vertically on the cross-sectional area of the drill string. For a
drill string of constant cross section, the resulting hook load can
be calculated as followsHL = (WTstring x D) - (CSAstring x 0.052 x
MW x D) HL = Hook load lbfWT string = Weight of drill string lb ft
D = Depth of well ftCSAstring = Cross sectional area of drill
string wall in MW = Mud weight ppgBuoyancy acting at the bottom of
the drill string places the lower portion of the drill string in
compression and reduces the hook load.Buckling occurs only below
the neutral point of bending, which is defined as the pointwhere
the average of the radial and tangential stress in the string equal
the axialstress.The neutral point of bending occurs where the
effective hydrostatic force equals thecompressive force in the
drill string. With no WOB, this point is at the bottom of the
string; therefore, the drill string is not buckled.
Stress conditions within the drillstring in a vertical hole are
shown at right.If weight is placed on the bit, there is additional
compression in the bottom of the drillstring, and theneutral point
of tension and compression moves up the drillstring. The neutral
point of bending also moves up the drillstring to the point where
the equivalent mud hydrostatic force is again equal to the
compressive force in the drillstring.The height of the neutral
point of bending above the bottom of the drillstring can be
calculated as follows:-Fhyd = (D H) x 0.052 x MW x CSAstring Fcomp
= WOB + (D x 0.052 x MW x CSAstring) (H x WTstring)At the neutral
point of bending Fhyd = Fcomp and the calculation is H x 0.052 x MW
x CSAstring = WOB + (H x WTstring)
H = WOB WTstring - (0.052 x MW x CSAstring H = WOB / Bouyed
WTstring Where H = height of neutral point of bending, ft Fcomp =
compressive force in drilling string lbf WOB = weight on bit
lbfBuoyed WTstring = buoyed weight of drill string lbf = WTstring x
( 1 0.015 x MW)
The height of the neutral point of bending above the bottom of
the string is thus the weight on bit divided by the buoyed weight
per foot of the drillstring. The forces in the drillstring in this
situation are shown below:-To prevent the neutral point of bending
from being in the drill pipe, the buoyed weight of the BHA must
exceed the applied WOB. In practice, field applications commonly
allow for asafety factor. It is recommended that the applied WOB
should be limited to 85% of the buoyed weight of the BHA (provided
the HWDP is not buckled)
Heavy-weight drill pipe is generally run as transition pipe
between the drill collars and the drill pipe.it is not acceptable
to run heavyweight drill pipe for WOB in vertical holes.
Discussion Inclined HolesIn inclined holes, two additional
factors must be considered when calculating the maximum weight on
bit that can be run without buckling the drill pipe Weight on bit
is applied at the inclination of the well, but the weight of the
BHA continues to act vertically.To allow for the reduction in
available BHA weight, the buoyed weight must be reduced by a factor
equal to the cosine of the well inclination.The drillstring
generally lies on the low side of the hole and obtains some lateral
support from the bore hole wall. In these circumstances, pipe above
the neutral point of bending buckles only when the compressive
forces in the drillstring exceeds a critical load, calculated as
follows:
Fcrit = 1617
------------------------------------------------------------ODpipe4
IDpipe4) x BF x (ODpipe2 IDpipe2) x Sin Dhole - ODtjWhere: Fcrit =
Critical buckling force, lbfODpippe = Outside diameter of pipe,
inOdtj = Max OD of pipe (tool joint), inIDpipe = Inside diameter of
pipe, inBF = Buoyancy factor = (1 0.o15 MW)Dhole = diameter hole,
in = Hole inclination, degrees
1- Vertical Hole Calculation ProcedureAvailable weight on bit
can be calculated as follows: WOBmax = 0.85 x Ldc xWTdc (1 - 0.015x
MW) Where WOBMAX = Available weight on bit, lbLdc = Length of drill
collars, ftWTdc = Air weight of drill collars, lb/ftMW = Mud
weight, ppg0.85 = 85% safety factor2- Inclined Hole Calculation
Procedure Calculate the available WOB provided by the drill
collars. WOBdc = 0.85 [ Ldc x WTdc(1 0.015 x MW) x Cos ]Calculate
the maximum available WOB provided by the HWDP WOBHWDP = 0.85 [
LHWDP x WTHWDP (1 -0.015MW) x Cos]Calculate the critical force to
buckle the HWDP Fcrit. As for drill pipe
4. Calculate the critical force to buckle the drill pipe. If
WOBhwdp + Fdp > Fhwdp then the maximum allowable weight on bit
is given by the followingWOBmax = 0.85 [ WOBdc + Fhwdp ]If WOBhwdp
+ Fdp < Fhwdp then the maximum allowable weight on bit is given
by the followingWOBmax = 0.85 [WOBdc +WOBhwdp + Fdp ]
3. Weight of BHA RequiredWeight of DCs required is estimated
from the bit specs and formation classification.
4. Tension1 Static LoadThe design of the drill string for static
tension loads requires sufficient strength in the topmost joint of
each size, weight, grade and classification of drill pipe to
support the submerged weight of all the drill pipe plus the
submerged weight of the collars, stabilizers, and bit. This load
may be calculated as shown in the following equation. The bit and
stabilizer weights are either neglected or are included with the
drill collar weight. FTEN = [(Ldp x WTdp ) + ( Ldc x WTdc )]
BFWhere Ften = submerged load hanging below this section of drill
pipeThe tensile strength can be calculated from the equation
4-1. Margin of Over Pull (M.O.P.)If the pipe is loaded to the
extent shown in the API formula above it is likely that some
permanent stretch will occur and difficulty may be experienced in
keeping the pipe straightTo prevent this condition a design factor
of approximately 90% of the tabulated tension value is
recommended
Fdesign = Fyield x 0.9Where Fdesign = minimum tensile strength,
lb Fyield = minimum tensile strength, lb 0.9 = a constant relating
proportional limit yield to strengthThe difference between the
calculated load FTEN and the maximum allowable tension load
represents the Margin of Over Pull (M.O.P.).M.O. P. = Fdesign
FTENThe same values expressed as a ratio may be called the Safety
Factor S. F. = Fdesign / FTEN By combining the above equations to
determine the maximum length of a specific size, grade,
andinspection class of drill pipe which can be used to drill a
certain well the following equation results:
5. BurstThe drill pipe internal yield pressure can be calculated
as follows wherePi = burst pressure, psiYm = specified minimum
yield strength, psiWt = pipe wall thickness, in.D = outside pipe
diameter, in.
6. CollapseAPI specifications for collapse resistance of drill
pipe is calculated assuming either plastic, transition, or plastic
failure based on the pipes D/t (diameter / wall thickness
ratio).Effect of tensile load on collapseThe effect of tensile load
applies only to greater than transition load on normally elastic
item, and to any load on plastic collapse items. The collapse
resistance of drill pipe corrected for the effect of tension
loading may be calculated with the following equation
7. Slip crushingThe maximum allowable tension load must be
determined to prevent slip crushing. In an analysis of the slip
crushing problem, Reinhold, Spini, and Vreeland, proposed an
equation to calculate the relation between the hoop stress (SH)
caused by the action of the slips and tensile stress in the
pipe(ST) resulting from the load on the pipe hanging in the slips.
If the dimensions for the cross-sectional area of the pipe (A) and
the cylindrical surface are of the pipe under the slips (As) are
used, the equation can be presented as:
Slips are typical 12 or 16 long. The friction coefficient ranges
from 0.06 0.14 inasmuch as tool joint lubricants are usually
applied to the back of rotary slips, a coefficient of friction of
0.08 should be used for most calculation. The equivalent tension
load from slip crushing can be calculated as follows
Critical Rotary SpeedTransverse Vibration:The approximate
critical rotary speeds which induce nodal (transverse) vibration
can be calculated using the following
Axial Vibration:The approximate critical rotary speeds which
induce pendulum or spring (axial) vibration can be calculated using
the following equation
Where L(ft) = total length of string
ReferenceSchlumberger Drill String Design Manual
