SOCIETY OF PETROLEUM ENGINEERS OF ATh1E 6300 North Central Expressway Dallas 6, Texas

THIS IS A PRE PRINT --- SUBJECT TO CORRECTION

DRILL COLLAR STRING DESIGN AND ITS EFFECT ON DRILLING M.E.R.

By

Fred K. Fox, Member ATh1E, and Nadim Nasir, Engineering Enterprises, Inc., Houston, Texas

The problem of obtaining a Maximum Economic Rate of drilling is the main task of engineers, tool pushers, superintendents, field drilling foremen and people involved in drilling research problems. A rig drilling at its Maximum Economic Rate will always make hole at a rate less than the maximum rate of penetration. However, in cases of extremely high rates of penetration, the conditions which give the Maximum Economic Rate will be very close to the conditions which give the maximum rate of penetration. In comparing the economic rate against the rate of penetration, the purpose for drilling the borehole must be considered. In drilling at the Maximum Economic Rate, geologic information of all types having practical interest to the oil company must be accumulated. The path which the drill takes in achieving its maximum depth should fall reason-ably within the prerequisites set up by the operating company. The borehole itself should be free of any characteristics which might prevent the running and cementing of casing, of a suit-able diameter, to the maximum depth drilled.

To drill this acceptable borehole, the drilling operating costs may be split into three general categories. First would be the "non-recurring costs" such as rig mOving, road build-ing, surface and protection casing, cementing of casing strings, primary wellhead equipment, and final logging of the borehole at total depth. The second group, "recurring costs", will include personnel salaries, rig insurance, depreciation of drilling equipment, supplies, drilling mud, con-sulting fees, bit costs, rig lubricants, rig repair, rig fuel, and transportation charges. The third group is a "special costs" and is an addition to the recurring and non-recurring charges. This would include loss of circulation, blow-out, fishing and sidetracking operations, and problems of borehole deviation control. Because of the recurring costs and exposure time to the "special costs" , it is important that the rate of penetration be as high as is practical.

In the early days of rotary drilling, a bit

References and illustrations at end of paper.

was screwed onto the bottom of the drill pipe and run in the borehole. The hole was drilled by rotating the bit under the compressive loading of the drill pipe. This type of drilling resulted in the questionable acceptability of the hole for running casing and in extremely high maintenance cost of the drill pipe. Special costs, resulting from fishing operations on drill pipe and casing stuck off bottom, multiplied rapidly as drilling depths increased.

Soon it was recognized that the amount of compression which could be transmitted through the drill pipe to the bit and thereby used to load the cones or the blades, was not directly proportional to the amount of weight which could be fed off the weight indicator. This is reason-able to assume when considering the limberness of the drill string, and the amount of torque which it was transmitting. The combination of compres-sion and torque resulted in the helical buckling of the drill pipe above the bit. It was observed that the increased indicated drill pipe weight used in loading the bit could result in a sub-stantial increase in rotary torque and a reduc-tion in the penetration rate.

As the number of drill pipe jOints in com-pression is increased, the amount of helical buckling increases. When the bending of the pipe against the side of the borehole exceeds l80 de-grees of arc, Fig. l, additional loading by com-pression will result in lateral forces being applied against the drill pipe by the wall of the borehole. These are frictional forces which in-crease drill pipe torque and decrease the effec-tive weight which may be transmitted to the drill bit. Fig. 2-A illustrates drill pipe run in com-pression. If the wall of the borehole does not have a constant radius similar to that of a cylinder through the area where the drill pipe is run in compression, then much of the indicated surface drilling weight may be lost by wall sup-port of the drill string. Under these conditions, increases in indicated bit weight will result in a decrease in effective bit weight.

2 DRILL COLLAR STRING DESIGN AND ITS EFFECT ON DRILLING M.E.R. SPE-501

In the early thirties a new member was added to the drilling string and this new member, the drill collar, was specifically designed to meet two of the general problems. One was to supply some of the compressive weight directly at the bit and thereby reduce the amount of drill pipe run in compression. Its other purpose was to help stiffen the drill string just above the bit and develop a resisting force to the forma-tion forces acting on the rotating bit. The use of the drill collar in the drill string soon be-came accepted as a standard member of the string. Until 1950, most drilling rigs used from six to 12 drill collars, which had diameters approxi-mately two-thirds that of the drill bit. With improved bit design, it was recognized in the hard rock area that large increases in penetra-tion rates could be obtained by additional drill collar weight. It was found, because of the high compression strength of some of the formations encountered, that to obtain a reasonable penetra-tion rate, the bit would require triple the collar weight which had been run in the past.

The introduction of long drill collar strings resulted in drill collar connection failure far out of proportion to the number of drill collars in the string. The introduction of additional drill collars resulted in a large in-crease in maintenance cost and "special cost" due to fishing; this also substantially increased the trip time necessary in changing the drill bit. The large increase in tool joint failures was caused by excessive fatigue occurring at the connection; the fatigue being accelerated by in-creased buckling due to higher compression loads run on the bit.

Investigation into drill collar string de-signs which would reduce tool jOint failure and result in higher rates of penetration along with a more acceptable borehole led directly to the tapered drill collar string design. A tapered column designed for compression loading with the diameter increasing with compression, can be made to have constant loading per unit area at all points up the column. To be suitable as a drill collar string, the tapered collars should provide the maximum recommended compressive load for the bit, allowing for both mud buoyancy and at least 15 per cent of the drill collar string to remain in tension. The most important collar of the tapered string is the bottom collar. The diameter of this collar, if cylindrical, must be less than the diameter of the bit to allow for formation of wall cake, circulating cuttings and vertical movement of the drill string without excessive surge and swabbing effects on the static pressure of the mud column.

In high bit weight drilling, the large in-crease in the number of tool joint failures on drill collars occurred as shown in Fig. 3 [this chart was based on general data obtained by Drilcc Oil Tools, Inc., from drill collar joint inspec-

tion and re~air records] when nine or more drill collars were run above the bit. The rapid change in slope of the curve, between an eight and nine collar load, may be due to the helical buckling of the collar string exceeding 180 degrees of con-tact arc, Fig. 2-B. In designing the tapered string, Fig. 2-C, the weight of the bottom collar was calculated to be approximately one-twelfth of the total required drill collar string weight, thereby imposing upon each drill collar in the tapered string a maximum of 11 times its own com-pressive load. The design requirements are based on a 12-1/4-in. borehole, approximately 5,000 Ibs/ in. of bit diameter to be applied to the drill bit after deducting a reasonable buoyance factor [10 to 13 Ibs/gal mud] and approximately 15 per cent of the collar string in tension. Calcula-tions resulted in a drill collar string having the bottom collar 10-1/2 in. in diameter, 2-13/16-in. LD . 30 ft long.

Seventeen additional collars were run above the bottom collar, each having a diameter of 1/4 in. less than the drill collar below. The diam-eter of the bottom collar, in addition to the weight consideration, was selected to be 10-1/2-in. O.D. in order that it would correspond to the coupling diameter of 9-5/8-in. casing which would normally be run and cemented in a 12-1/4-in. diameter borehole. It was felt that this one consideration would completely eliminate any changes in borehole angle or characteristic which would mechanically prevent the running to total depth of 9-5/8-in. casing. Each of the drill collars in the string were spiral grooved with helical flats. This type of spiral grooving, having negligible effect on the weight and rigid-ity, would allow the hydrostatic fluid pressure to act equally on the grooved surface of the drill collar and thereby greatly decrease the chances of sticking any of the drill collars against the side of the borehole due to differential pressure forces. The combination of the straight-hole characteristics of the tapered string used in con-junction with large bottom collar and the spiral grooving on the drill collar would effectively eliminate problems of dog-legs, key seats and dif-ferential pressure sticking. The most difficult problem confronted in the design of the tapered string was in the rig handling characteristics of the varying drill cOll.ar sizes. It was decided early that there would be very little practical benefit gained by tapering the diameter of each drill collar toward its upper end by approximately 1/4 in. Consequently,' all drill collars in the string were cylindrical in shape, and the tapering of the string developed by the reduction of drill collar O.D. of 1/4 in. of each drill collar up the string, Fig. 4.

To solve the handling and connection problems, it was decided to divide the string of 18 collars into three sections; the lower section being com-posed of 10-1/2 in., 10-1/4 in., 10 in., 9-3/4 in., 9-1/2 in., 9-1/4 in. drill collars, all having

SPE-501 FRED K. FOX and NADlM NASIR 3

7-5/8 in. API Regular connections and a slip recess. This slip recess around the collar was approximately 20 in. in length and varied from 9-3/4 in. on the 10-1/2-in. O.D. drill collar and decreasing by 1/4-in. increments to 8-1/2-in. di-ameter on the 9-1/4-in. O.D. drill collar. The slip recess on all of the lower six collars could be handled with one size of standard drill collar slip, covering the range from 9-3/4 in. to 8-1/2 in. This also allowed the drill collars of diameter of 10 in. and larger to be handled in a standard rotary slip bowl. The drill collar O.D. of the six lower collars also could be handled with one size of heavy rotary-tong jaw.

Above the 9-1/4-in. collar was run a short crossover sub, approximately 5 ft in length. This allowed the collars above to convert over to the 6-5/8-in. Regular tool joint connection. The middle six collars of the tapered string started at the bottom with a 9-in. drill collar, then 8-3/4 in., 8-1/2 in., 8-1/4 in., 8 in., and 7-3/4 in. at the top. Each collar was again machined with the same type of slip recess as the lower six collars with the exception of the diameter. The diameter of a slip groove of a 9-in. collar was 8-1/4 in., and reduced to 1/4-in. increments until it was 7 in. on the 7-3/4-in. collar at the top. The drill collar range for the second section of 9 in. to 7-3/4 in. would also be handled by one size rotary-tong jaw and drill collar slips.

Between the middle six collars and the top six collars, a second crossover sub was run which allowed the upper six collars to be threaded with a 4-1/2-in. I.F. Connection. The lower collar of the upper group was 7-1/2-in. O.D. and had a slip recess of 6-3/4-in. O.D. cut below the box. Each collar was cut with a slip recess similar to that of the middle and lower drill collar sections. The eighteenth drill collar, smallest in diameter -- 6-1/4 in. -- had a 5-1/2-in. diameter slip recess. The upper section of six drill collars could be handled with one size rotary-tong jaw and drill collar slips.

The rig tools to handle the tapered drill collar string amounted to three sizes of drill collar slips, one for the lower, one for the middle, and one for the upper section of collars. No safety clamp was needed because of the special slip recess cut in the drill collar. Three tong jaws were needed, one for each of the drill col-lar section; six lift nipples were used, two 7-5/8-in. API Regular, two 6-5/8-in. API Regular, and two 4-1/2-in. I.F. Because of the obvious difference in sizes of the lift subs, there was no confusion in their proper place when handling the tapered string of drill collars at the rotary. After several trips with the collars, the rig crews became very familiar with the necessary changes in tong jaws and rotary slips, thereby causing little delay in handling the"tapered drill collar string, as compared to the conventional

cylindrical drill collar string.

The use of large diameter drill collars is relatively common in areas of hard formation drilling. The primary aim in designing this drill collar string was to observe its use in areas of unconsolidated formations, sticky shales, and areas where borehole diameters are expected to deviate greatly from the bit size and thereby gain very little benefit from stabilizers or fully packed-hole techni~ues. The well selec-ted to be drilled with the tapered drill collar string was in the White Lake Field, Vermilion Parish, La. In drilling the surface hole, only the lower section of the tapered string was used, this being the 10-1/2-in. to 9-1/4-in. drill col-lars. upon drilling out below the 13-3/8-in. casing cemented at 2,000 ft three bit failures were encountered while using two-cone bits; two of these failures could not be accounted for by abnormal usage, and there was no explanation for their failure. Fig. 5 records the progress of the hole to a depth of 12,921 ft. The 9-5/8-in. casing string was run and could be reciprocated freely at total depth, which was extremely un-usual in this area. This was not the first well to be drilled to this depth in the field by this rig, but it was the best drilling time to this depth in the field.

The use of the tapered string on this hole led to several surprising conclusions. The pri-mary conclusion was that drill collars of the diameter range of 10-1/2 in., when protected from problems of differential pressure sticking, can be used effectively in soft formation drilling. The handling of the tapered string by the rig crews, which was expected to be a serious problem, was easily overcome after several round trips. The results of the borehole deviation surveys sub-stantiated the belief that tapering of drill col-lar sizes would reduce the buckling of the drill-ing string and reduce borehole deviation. The difficulty in obtaining general usage of a design such as the tapered string was its high initial cost and the difficulty in exchanging drill col-lars between rigs or rotating collars in the string for maintenance and repair. The excellent results in controlling the borehole path and pene-tration rates was believed to be attributed mostly to the larger drill collars in the lower section. Several wells have been drilled where the bit diameter was 9-7/8 in. and five or six collars of the tapered string were run below conventional diameter drill collars to have available the maxi-mum desired weight. It is impractical to attempt to design full tapered drill collar strings for use in small diameter boreholes. The combination of uniform O.D. collars with a suitable tapered section at the lower end of the collar string has resulted in substantial improvement in drilling performance.

In the past several years a great deal of interest has been developed in improving our fast-

4 DRILL COUJill STRING DESIGN AND ITS EFFECT ON DRILLING M.E.R. SPE-501

hole drilling technology. Fast-hole drilling programs such as those recently carried out in the Timbalier Bay Area have added greatly to our knowledge of drilling efficiency. One of the first improvements made was in the method of handling drill collars. Cylindrical drill col-lars of standard design using standard handling practices require six to seven minutes per stand as handling time in the derrick. A large portion of this time is used in the positioning and in-stalling of the conventional drill collar safety clamp and the making up of the drill collar lift sub, Fig. 6-A. Conversion from standard integral drill collars to the replaceable connection type was the first measure taken to reduce this wasted handling time. At the same time, the use of the drill collar safety clamp was abandoned. Drill collar slips were kept in first-class condition and set up on the cylindrical portion of the re-placeable connection collars, Fig. 6-B. By ex-changing elevators from the standard drill pipe elevator in the bales to a special elevator de-sic.:;cled to adapt to the replaceable connection coupling, the drill collars could now be handled on trips in approximately one-half the time pre-viously required. This method, which replaced thE use of lift subs, helped to eliminate potential drill collar connection failures by eliminating the necessity o~ making and breaking the lift subs on each stand on each trip. Many extremely fast holes were drilled with this type of hook-up, and no safety clamp was used above the drill collar slips. Later, however, it was thought advisable that a slip recess should be cut below the box end of each collar, Fig. 6-c. The use of this recess eliminated all fears concerning the handl-ing of long drill collar strings without the use of a drill collar safety clamp.

Because only a small percentage of the rigs presently operating in the United States are equipped with drill collars of the replaceable-end type, it was necessary for this method of handling drill collar stands to be adapted to the integral type of drill collar. This was first done by the introduction of a drill collar sub run between every third drill collar in order that this sub would be uppermost on each stand when racked in the derrick. The subs were essentially a short drill collar approximately 6 ft in length, cut with a long recess in the center section for about 4 ft, and extending within approximately one foot from each end. The diameter of the drill collar sub in the recessed area was approximately one inch less than the normal outside diameter of the sub. These short handling collars, as shown in Fig. 6-D, were used in several new areas where they contributed to the establishing of the new drilling records.

collar soon became very widely used throughout the Texas-Louisiana .Gulf Coast Area.

The "special handling recess", Fig. 6-E, was initially designed for use on relatively small O. D. drill collars, and was built to maintain the maximum drill collar rigidity along with adequate handling shoulder area. In places where stress concentrations might initiate fatigue cracks or failures, radii were specified and the cold working of these radii areas was recommended. In addition to the "special handling recess" incor-porated on the top of each drill collar, a speciaJ design of satellite elevator system was used which eliminated the time required to change from drill pipe elevators which had been bored specifi cally for the handling recess.

There have been no drill collar strings dropped in the borehole or failures while drill-ing as a result of the handling recess design or use of the satellite elevator system. The rig time and money saved by adapting to this type of drill collar handling system is so substantial that it is difficult for drilling management to accept this large unnecessary waste in its drill-ing costs, Fig. 7.

After several modifications, the most prac-tical system successful in minimizing the rig time lost in drill collar handling and improving straight-hole characteristics is shown in Fig. 8. The straight-hole hook-up incorporated two bottom collars, one having approximately the diameter of the casing coupling, the second having a diameter approximately that of the casing which will be rur: in the borehole at a total depth. A stabilizer is added to act both as a fulcrom and as a guide to eliminate possible dangers of pulling the two lower collars into borehole key seats. All drill collars in the string above the stabilizers are constructed with the standard ZIP groove. The outside diameter of these upper collars is the largest diameter which can be safely washed over with standard wash pipe.

Investigating the characteristics of the bottom stand of this straight-hole drilling string, the changes in moments of inertia of the individual drill collars and their centers of mass, effective weight, and diameters should allo~ the drill bit to obtain a lower borehole angle at its condition of drilling equilibrium as defined in several of the Woods and Lubinski publications on drill collar buckling. This increase in bit stability effectively reduces rapid changes in borehole angle and direction.

REFERENCES

At approximately the same time these drill l. collar subs were being used, a special design of drill collar handling recess was introducea on

Moore, Stanley: "CUrrent Trends in Controll-ing Hole Deviation", Drill Bit [May, 1962] p. 10.

many of the spiral grooved drill collars available 2. for rental in the Gulf Coast. This type of drill

Rollins, H. M. : "Studies of Straight Hole Drilling Practices, 1952-56", API Production

SPE-501 FRED K. FOX and NADIM NASIR

Division Southwest District Meeting, Fort Worth, Tex., March 21-25, 1956.

3. Hoch, R. S.: "A Review of the Crooked-Hole Problem and an Analysis of Packed Bottom-Hole Drill Collar Assemblies", API Southern and Mid-Continent District Meeting, April, 1962.

4. Bobo, R. A., Hoch, R. S.,Boudreaux, G. S. and Angel, R. R.: "Keys to Success:ful Competi-tive Drilling", Gulf Publishing Co.

5. Fox, Fred K.: "New Pipe Configuration Re-duces Wall Sticking", World Oil [Dec., 1960].

6. Brantly, J. E.: "Rotary Drilling Handbook", Palmer Publications.

7. Lubinski, Arthur: "A Study of the Buckling of Rotary Drilling String", Drill. and Frod. Frac., API [1950] p. 178.

8. Woods, H. B. and Lubinski, Arthur: "Use of Stabilizers in Controlling Hole Deviation", Drill. and Prod. Frac., API [1955] p. 165.

APPENDIX

It has been observed in the field that a tapered drilling string placed directly above the bit resulted in a hole close to being vertical and free of dog-legs. We propose in this appendix to set up and investigate the mathe-matics of this problem~ adopting the same nota-tion used by Lubinski. f

Assume the following physical model. The collar with the largest cross section is placed directly above the bit, with the second largest cross section above the first, and so on. We also assume the angle a to be the angle the hole makes with the vertical. Fig. 9 represents the elastic curve of this model, with the X-axis taken as the axis of the hole. W and H are the reactions at the bottom of the hole acting on the bit.

The Moment Equation

Since the area of the cross section is dif-ferent for different collars, the moment of inertia of the cross section would be different for different collars; therefore, if we consider the elastic curve of the system to be a super-position of the individual elastic curves, then we will have some means by which we can calculate the individual elastic curve, whence, the elastic curve of the system.

Let us consider the system to be made of regions, where the first region is occupied by the first collar, the second region by the second col-lar, and the nth region by the nth collar. We now can set up the moment equation about any cross section in any region, i.e., in the first region tge moment equation, following Woods and Lubinski is

d2Yl X EIl dX2 = HIX - WYl + J [(Yl - '1)Pl cos a

o

+ ex - t)Pl sin a] d ~. [1] wherein: E is Young's modulus for steel. I is the moment of inertia of the collar cross

section. p is the weight in mud per unit of length of the

drilling string. The subscript refers to the region under consid-eration. The moment equation about any cross section in the nth region is

d2

y f EIn dX2 n = HnX - WYn + 0 [(Yn - '1)Pn cos a + (X - ~)Pn sin a] d~ . [2]

If we introduce the follOwing dimensionless quantities

Yn = Yn/mu sin a . .

bn = W/Vn . . . . . . .

x = X/mn . . . . . .

hn = Hn/IDuPn sin a

wherein:

m -J E In n Pn

.

.

and if a is small, such that cos a 41, using Eqs. 3 - 7, Eq. 2, on differentiating becomes

[3]

[4] [5 ]

[6]

. [8]

Eq. 8 is in dimensionless units, and it repre-sents a set of n third order differential equa-tions. Consequently the general solution of each equation must contain three arbitrary constants, hence 3n arbitrary constants for the whole sys-tem. To determine these arbitrary constants, we refer to the boundary conditions. They are:

[i] The elastic curve is continuous at the boundary of any two regions.

[ii] The slope of the elastic curve is continu-ous at the boundary of any two regions.

[iii] The moment is the same at the boundary of any two regions.

Symbolically, the boundary conditions for the nth region, that is Xn_l ~ X:S xn , whereby Yn is a solution are:

at x = xn-l; Yn = dYn dYn-l. and Yn-lJ - = ~' dx

d2Yn d2Yn_l EIn -2- =

dx EIu-l dx2

The first region, that is 0 ~ x $:: Xl' however,

5

6 DRILL COLLAR STRING DESIGN AND ITS EFFECT ON DRILLING M.E.R. SPE-501

has entirely different boundary conditions, they are at x = 0, Yl = 0, where Yl is the solution in

d2n the first region and ------ 0

dx2

at x = xl; Yl = Y2, where Y2 is the solution in the second region. Also the uppermost region has different boundary conditions, that is, if the uppermost region was the kth region, with Yk as a solution, then the boundary conditions are:

at x = Yk = Yk- l dYk d2Yk dx W = 0,

The last two boundary conditions assume that the elastic curve at x = xk and beyond is parallel to the X-axis.

The Solution of The Differential Equation

Differential Eq. S permits an infinite series solution. To avoid confusion of sub-scripts, we omit them, and Eq. S becomes:

. [9]

""" Let Y = E ar xr be the solution for any region r"'O

dy ..,." 1 then - = E r ar xr - dx r::O

d3y "". . ;z; and ~ = E r(r-l)(r-2)ar xr --, dx-' r..:O

[10]

[ll]

Substitution of Eqs. 10 and 11 in Eq. 9 yields

~ r(r-1Xr-2)ar xr - 3 + b E r ar xr - l -~O =0

cP E r ar xr = x + h

r.:O . . . . . . . . [12]

For y = r ar xr to be a solution, Eq. 12 has to r~O become an identity, and the coefficients of the powers of x higher than the first should vanish. We have

".E r(r-J)Cr-2) ar xr - 3 + b ~ (r-2) ~-2 x r-3 r~O r=2 'E ( r-3) a ;z; x r-3 = x + h [13 ] r;:3 r--,

For r = 0, series 2 and 3 i~ Eq. 13 will not start yet, series 1 gives 0 x ao = 0 .'. aO is arbitrary.

For r = 1, series 2 and 3 in Eq. 13 will not start yet, series 1 gives 0 x al = 0 .'. al is arbitrary.

For r = 2, series 3 in Eq. 13 will not start yet, series 1 and 2 give 0 x ~ + b x 0 x aO = 0 .~ ~ is arbitrary.

For r = 3 3 x 2 x 1 a3 + b x 1 x al-O x ao=h

or a3 = (1/3!)(h-bal ). For r = 4

4 x 3 x 2 a4 + 2ba2-al = 1

or a4 = (1/40(1 + ar2b~). For r > 4 the recurrence relation is

(r-3 )ar _ 3 - b (r-2)ar _2 r(r-l)(r-2) [14]

It is observed from the previous work that all the a's could be determined in terms of aO' al, and a2, which in turn could be determined from boundary conditions. For example, the solu-tion in the first region is

at x d2y

0, Yl = 0, -- = 0 dx2

at x = xl' Yl = Y2' where Y2 is the solution in the second region.

These conditions will make aO = a2 = 0, and all the a's would become functions of al' al itself could be determined in terms of xl' hl' bl' Symbolically

ar = f ( al), where al = F (Xl' hl' bl ) The solution in any region assumes an infin-

ite series form also, with different coefficients in every region. At the boundary of two regions, the two infinite series, i.e., Yn-l and Yn, should become an identity. This requires match-ing of coefficients of two infinite series, which is very tedious and clumsy, especially if the two series are slowly convergent, and if our region exceeds 2 in number. The method of infinite series was attempted on the ground, that it might yield a rapidly convergent series, and could be applied to at least two regions without resorting to digital computers. This, however, was not the case, and if one has computer facilities, the infinite series method would not likely be the method of attack, as there are far better methods in numerical analysis for solving differential equation.

The inclusion of a stabilizer between the second and third collar, Fig. 10, will not in effect change the form of thesdifferential equa-tion, see Woods and Lubinski. It will, however, change the physical picture by introducing addi-tional lateral forces; consequently (hn ) and (bn)

SPE-50l FRED K. FOX and NADD1 NASIR

would be entirely different ~uantities, but they will retain their identity in the formulation of the differential e~uation for moments.

'" ... < c

'" ... < a t:l =

7/260117!~ 7/27 1 - Set 7/29 3 2 12~ 7/30 ~ 2 12 ~:.

7/31 5 II 12 It.. 8/ 1 6 5 12 l. 8/ 2 7 6 12 10\ 8/ 3 8 7 12 )I, 8/ 3 8 8 12 lit 8/ ~ 9 9 12 X. 8/ 5 10 10 12 )

A B c Fig. 1 Fig. 2

I ... ~ 1

, ~ ~ ~ " ~ ~

I 2 3 4 5 G 7 8 9 10 II 12 13 NUMBER OF DRILL COLLARS A B c D E

Fig. 3 Fig. 6

A W B Fig. 9 Fig. 10

6'1," .. 213/16" .. 30' - '189= 6',." II 2-13116" .. 30'- 3159::::

@ 7". 2-13/1ib" .. 30'-3429=

"

~ ,'., '''''''_-'_0 ~ ,,,,,,,,\3,.0",,0'-3999=

C, ... " b ~ 7',", '\3."0 .. , "-0'0=

@~ 7 '-." .. 2-1l/16" .. 30' _ 4299;:::-

8" II. 213/16" 30' - 4629= 8 'f." II. '.1]/16" .. 30' - 4959::

8'1>" II. 2-13/16" .lO'-S2.9=

8"1." .. 2-13/16" II: 30' _ 5649l:::

CD Coni., .f drill coilCIt' mOil

'" .. 2-13/16" II 30' - 5979=

4 ',," If bolt by 6 'f." API reg p.n

~

Cr ........ r tub "t." .. 213/16" II S' _1000::: 6'" "-II. box by 7%" API r " pin

",." II 2-13116" .. 30' - 6369::::

9"." II 21:1116" II. 30'-6729=

CD 10" .. 2i3"6" .. lO'-7509.tt

10'." II. 213/16" .. 30'-7929:

10'1, , ... ,13116" .. lO' _1319:

12':." roc" bir To'al wII'.ght

b.f.,. 'p"aling 96,147:-

Fig. 4

1 <

~ ..

)

1 ! double bo. collar

7~" API r.g_ fop 6 %" API r.,. bo"om

.. STRAIGHT HOLE" NWI - DRLL COLLAR HOOK UP

!tIT COLLAR'W' COLLM ..... COLLAR'\:" STABILIZER DIA. DlA, OIA, OIA BODY lLAIlt:

!!..!!!. ~ .,..-;. 1114" ," 12 VI" ~ ~ ," .....I.Ja: ...!..laZ ..!.J!. 1511" -.!..Jd.. _7_"_ . " III- I III"

2J!5 ...!J!!: -LU&: ," I" ~ .W ," 5114- ~ ~ ..Ult' '&iii- ""'i"ii4- "4"'W 4 III'

-'-'-43M' 41/8" 41/8" 3 liZ"

Fig. 8