Buckling of Tubing in Pumping Wells, Its Effects and

Means for Controlling It Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021

ARTHUR LUBINSKI MEMBER AIME PAN AMERICAN PETROLEUM CORP. K. A. BLENKARN TULSA, OKLA. JUNIOR MEMBER AIME

T. P. 4482

ABSTRACT INTRODUCTION ancy.":; It was shown that the com­ monly used concept of a neutral It is explained why the bottom It is well known that a column point, as being a point in the string portion of freely suspended tubing must be subjected to some compres­ with neither compression nor tension, in a pumping well buckles and sion in order to buckle; and also that is inadequate, and a more relevant straightens in succession during the a structural member does not buckle definition of the neutral point was in­ pumping cycle. Field evidence of re­ if subjected to a tension. When con­ troduced. The findings were also gen­ sulting rod-on-tubing wear, excessive sideration is given to a tubular col­ eralized to cases of different pres­ polished rod load, and excessive umn, the question may be asked, sures inside and outside a pipe."" horsepower are given. The possibility "How is the buckling phenomenon Later, in a further generalization, al­ that buckling hastens pump wear is affected by inside or outside pres­ lowance was made for variations of strongly suggested. Means for either sure?" At first, it seemingly should stress and pressure with depth.' The prevention of buckling or for mini­ not be affected. However, this is not findings were applied to the new tech­ mizing its effects are explained, their so. In order to arrive at a correct de­ nique of hydrostatic high pressure relative merits compared, and field duction one should first understand testing of lengths of pipe in the results of their use given. These the basic reasons for buckling of a mill.s means are: tension anchors, tail pipe, column under loading*. Then he sucker rod guides, and corrosion in­ should add to the effect of that load­ In 1952 it was observed that pre­ hibitors. Charts and formulas for best ing the effect of pressure. Follow­ vious theoretical findings apply to use of tension anchors, tail pipe, and ing this procedure, one may discover tubing in pumping wells. The lower guides are given. Use of tension an­ quite unexpected phenomena. In part of freely suspended tubing chors, or compression anchors with some cases, when subjected to more buckles during the upstroke portion a heavy tail pipe, prevents both buck­ pressure inside than outside, a pipe of the pumping cycle. Later, it was ling and breathing, thus improving may buckle under tension. In other ascertained that this phenomenon is volumetric efficiency. Without tail cases, a pipe may remain straight, responsible for wear and malfunc­ pipe, buckling above compression an­ although subjected to a very large tioning of the equipment. Various chors precludes such improvement. compression. remedial measures were devised and successful field trials conducted. Original manuscript received in Sodety of In 1950 and 1951 it was explained Petroleum Engineers office on Sept. 15, 1956. why the bottom portion of a string Only brief mentions on the subject Revised manuscript received Jan. 24, 1957. Paper presented at Petroleum Branch Fall of pipe freely suspended in a well have been published:" Meeting in Los Angeles, Oct. 14-17, 1956. Discussion of this and all following tech­ does not buckle even when SUbjected In this paper, the phenomenon of nical papers is invited. Discussion in writing (3 copies) may be sent to the offices of the to a large compression due to buoy- tubing buckling is explained, field Journal of Petroleum Technology. Any dis­ cussion offered after Dec. 31. 1957, should be in the form of a new paper. :·'Using, for instance. Ref. 1. ZReferences given at end of paper.

VOL. 210, 1957 SPE 672-0 7.1 evidence is reported, various preven­ tive measures are analyzed and their respective merits compared. The au­ thors believe that presentation of this '-b':::::::::~::: ::::::::1- , paper will be useful to the industry FIG. 2-BUCKLING EFFECT OF INTERNAL for the following reasons: PRESSURE. 1. Perhaps few people are aware ling effect of internal pressure. For today that tubing buckles in pumping this reason, this column load will be wells. The use of adequate preven­ referred to as "fictitious." As shown tive means is rare. in the Appendix, its magnitude is 2. Frequently preventive means equal to pressure times piston area. are used improperly. The correct If the pressure is large enough, the amount of tubing pickup for tension pipe will buckle. It is interesting to anchor installation is not known and note that it buckles, although sub­ spacing for sucker rod guides is gen­ jected to actual tension due to pres­ erally guessed. Information for bet­ sure acting on the annular area ter use of anchors and rod guides is marked AB in Fig. 1. given in this paper. Consider now a pumping well as 3. The choice of preventive means shown diagrammatically in Figs. 3U may often be made without full Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 and 3D. During pump upstroke (Fig. knowledge of their respective merits. FIG. 4---BUCKLING EFFECT OF PRESSURE 3U), the standing valve is open and IN TUBING. the traveling valve is closed. This PROCEDURE means that the plunger acts in the if subjected to a fictitious column Through analytical means, the same way as the pistons of Fig. 1. load, a drilling string buckles under phenomenon of tubing buckling in Therefore, if the pressure is large the influence of an actual upward pumping wells has been investigated enough, the tubing will buckle as if column loading, commonly called and quantitative relationships have subjected to an upward fictitious col­ "weight on bit." Both strings are been developed to permit design of umn load or buckling force, t. shown buckled below the neutral point and corrective means. in Fig. 4 and equal to: essentially straight above it. * But the t = a f':..P . (1) Through field observations both neutral point should not be con­ the detrimental effects of buckling in which a is plunger cross-section strued as the point where there is and the improvements due to use of area, and f':..p is the pressure differ­ neither longitudinal compression nor corrective means have been estab­ ential across the plunger. tension. This confusing subject has lished. Results are included in each During pump downstroke (Fig. been largely covered in the liter­ item as discussed. 3D), the traveling valve opens and ature.""" For the purpose pursued in the standing valve closes. Thus the this paper, the neutral point may be DISCUSSION AND RESULTS tubing no longer acts as if terminated considered as that point in the string by a piston, and straightens. below which it buckles. In a drilling BUCKLING OF FREELY SUSPENDED It is evident that there is a simi­ string, the location of the neutral TUBING IN A PUMPING WELL larity between a drilling string and point is obtained from the fact that Consider a pipe lying on the the tubing string of Fig. 3U. Just the weight in fluid of the portion of the string below the neutral point is ground terminated by pistons, as as the tubing of Fig. 3 U buckles as shown in Fig. 1. Pressure is applied equal to the weight on bit.' inside the pipe. Pistons are connected In other words, by a rod in order to prevent their W being expelled by pressure. 11 = -. (2) q It is proven in the Appendix that in which 11 is the distance to the neu­ pressure inside the pipe terminated tral point, w is the weight on bit, by pistons exerts a buckling effect and q is the weight per foot in fluid on the pipe. Furthermore, this buck­ of drill collars. Eq. 2 holds true only ling is the same as if the pipe, in­ if a sufficient length of drill collars stead of being subjected to internal is carried, i.e., if the neutral point is pressure, were subjected to a column in the drill collars. load t, as shown in Fig. 2. Although If w is replaced by the fictitious this column load actually does not force, and if q is taken as tubing exist, it is introduced as a device to t, permit easy calculation of the buck- weight per foot in fluid, Eq. 2 may be applied to a tubing string. How­ ever, for tubing, the equation holds true only if the working fluid level IS sufficiently high, i.e., if the neutral

';'Actually a string of drill collars buckle, helically up to the neutral point in a vertical hole and does not in a slightly inclined hole. FIG. 3U (U:FT)-HELlCAL BGCKLl"i; uF The criterion which led to this conclusion i~ TeBING DURING PU~IP UPSTROKl:. given in Ref. 8. Application of this criterion to buckling of tubing leads, however, to th. FIG. l-PIPE WITH PISTON CLOSED, ENDS FIG. 3D (RIGHT)-TuBING STRAIGHTENS conclusion that tubing buckles helically even SUBJECT TO INTERNAL PRESSURE. DURING PUMP DOWNSTROKE. in inclined wells.

.. I PETROLEI'M TR'\,'''ACTIO'''~. AIME point is below the working level. The is subjected only to a small pressure tributed the trouble to crooked hole tubing weight per foot in fluid may differential. In low working fluid conditions. The then common belief also be written as follows: level wells, where the pressure dif­ that hole deviation from vertical could q = q. + Wi - W , (3) ferential in the pump is large, the cause severe wear is not correct. This in which q. is the tubing weight per fictitious force, j, is much greater is borne out by surveys conducted in foot in air, Wi is the weight per foot than the critical force, and thus a large number of highly inclined Cal­ of fluid inside, and w, is the weight buckling is of a high order. There­ ifornia wells' which indicated that the of outside fluid displaced, per foot. fore, the tubing buckles into a helix production cost in these wells was Eq. 2 may easily be modified to ap­ which contacts the rod string over its either equivalent to that in so-called ply to another simple case; namely, entire length below the neutral point. straight holes or, at most, 10 per cent where the working fluid level is at It is to be remembered that buck­ higher. Thus the inclination of 5 to 0 the pump. In this case, there is no ling occurs during pump upstroke, 10 in the above four wells should not have affected pumping problems at fluid outside, so that W 0 is zero, and while the weight of the column of liq­ Eq. 3 may be written : uid in the tubing rests on the plunger; all. In addition, directional surveys run in these wells showed that there q = q. + 0 a; . (4) therefore, the rod string is under were no dog-legs which would explain in which 0 is the fluid gradient in­ great tension and remains essentially the difficulties. In one of the weIls the side in psi/ ft, and a i is the ID cross­ straight in spite of the forces exerted section area of the tubing in sq in. upon it by the helically buckled tub­ pump was moved a few hundred feet, after which the zone of fast wear The situation is more complicated ing. As the sucker rods move upward, when the fluid level is between the there is friction between them and moved by the same amount. This con­ Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 pump and neutral point. However, the helically buckled tubing. More­ firms that the trouble was not due to for practical purposes, it is sufficient over, since, on upstroke, the tubing is crooked hole conditions. to choose some average value of q. buckled while the rod string is straight, there is a tendency to cock Consider the following example : the plunger in the pump barrel, as a = 2.4 sq in. (134 in. plunger) shown in Fig. 3U. Based upon the /':. p 2,500 psi (working fluid = foregoing, the following speculations level 5,000 ft, gradient 0.5 have been put forth regarding the psi/ft, i.e., fluid specific detrimental effects of buckling: gravity 1.154) pump depth = 6,000 ft 1. Friction between the rod string and the tubing could result in sucker­ Assuming, tentatively, that the fluid rod-on-tubing wear below the neutral level is above the neutral point, point. q = 5.545 lb/ft (wt/ft in air of 2Y2-in. tubing, i.e. 6.5 lb/ft 2. This friction could also increase multiplied by 0.853, which is polished rod load and horsepower. the buoyancy factor for 1.154 3. Cocking of the plunger in the specific gravity) barrel could hasten pump wear. Substitution of these values into Fig. 5 is a photograph of a mode! Eqs. 1 and 2 gives which was built to demonstrate the Fictitious force . j = 6,000 lb sLlccessive buckling and straightening Distance pump to in freely suspended tubing in a pump­ neutral point . 11 = 1,082 ft ing well. The operation of the model From the conditions of the example clearly illustrates the manner in which the distance of pump to fluid level = the tubing coils around the sucker 6,000-5,000 = 1,000 ft . rods. This means that the working fluid It is probable that during pump level is between the pump and the downstroke, while the tubing is neutral point, but is close enough to straight, the lower portion of the rod the neutral point for the above de­ string buckles. The effects of such termination of distance to the neu­ buckling are negligible compared to tral point to be sufficiently close. the effects of tubing buckling. This The fictitious buckling force must will become apparent further in this exceed some critical value in order paper from the fact that means which to buckle the tubing. This critical prevent the tubing from buckling, but value may be determined by exactly still permit the sucker rods to buckle, the same means as the critical value entirely remove the detrimental effect of the weight on bit in a drilling of buckling. string. * Comparison of actual values of critical force, thus obtained, with FIELD EVIDENCE OF THE the fictitious force as given by Eq. 1, DETRIMENTAL EFFECTS 01' has shown that the force is large TUBING BUCKLING enough to buckle the tubing in all Some years ago, fou r wells, lo­ wells except those with a very high cated in widely scattered areas, were working fluid level , where the pump plagued by rod-an-tubing wear which necessitated tubing pulling jobs eve ry ·"R.ef. 2. p. 179. replacing t he string weig ht other week. These wells were inclined P wIth the corrected tubing weight 'I. a s given by Eq. 3. 5 to ]00 and field personnel first at- FIG. 5-TuBING BUCKLING M ODEL.

YOLo :! 10 . IY,')j' 7:> That wear occurred only near the TABLE 1 pump suggested that tubing buckling location Wyoming louisiana Gulf Coast .. _... _. ------.~.- - -- caused the trouble. Data and calcu­ Pump Setting Depth Peet 2694 230B 1650 4020 lated distances to the neutral point for Liquid Specific Gravity (Estimated) 0.88 0 .8 0 .8 1.0 2500 the four wells are summarized in Pumping level in Casing (Estimated) At Pump At pump At pump feet from Table 1. The correlation between the surface Calculated Distance from Pump Setting Feet distance from pump to neutral point Depth to Neutral Point and the zone of fast wear is very satis­ Assuming 13/.·in. Plunger 414 354 23. 637 factory. A more perfect correlation Assuming l'j,·in. Plunger 304 260 172 467 {Actual plunger size was not known} could hardly be expected, not only Feet Portion of Tubing Reported os because several factors were only esti­ Above the 524 283 350 320 Subiected to a Fast Wear mated, but also because the calcula­ ~ tions pertain to static conditions. As a matter of fact, the satisfactory corre­ There is also some field evidence in On the other hand, during upstroke, lation indicates that the phenomenon support of the second speculation, part of this load is transferred to the of static buckling investigated here is pump plunger and the rod string, and not substantially disturbed by the namely, that friction due to buckling increases polished rod load and horse­ therefore the tubing shortens. This re­ motion. power. Use of a means for preventing peated shortening and lengthening is Later, a survey was made in a buckling (tension anchors, discussed commonly called "tubing breathing." North Louisiana field. In a two-year further in this paper) has resulted in It is proven in the Appendix that in Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 period, 122 tubing leaks were de­ both a decrease of load, which com­ order to prevent buckling during up­ tected. Almost all of them were due pletely eliminated weekly rod failures, stroke, the tubing must be permitted to rod-on-tubing wear and the great and a decrease of power for the same to elongate freely on downstroke, but majority of them (83 per cent) oc­ stroke, but an even greater number of prevented from shortening during up­ curred in the bottom 400 ft of the strokes per minute. stroke. In other words, the tubing string. On the other hand, very limited must be caught by anchoring it at its Eastman' reports a similar conclu­ field evidence has been gathered, so most elongated position. This can be sion reached from the above men­ far, regarding the speculation that seen clearly in experiments made with tioned survey of several hundred di­ cocking of the plunger hastens pump the model shown in Fig. 5. Buckling is rectionally drilled wells in California. wear. One pump manufacturing and stopped by catching in a clamp the His wording is as follows: "Most of servicing company estimates that 70 lower end of the tubing at the lower­ the wear on tubing and sucker rods per cent of all pump failures are due most position reached during the has been found to occur between the to plunger or barrel wear which could breathing cycle. pump and about 20 joints up from the be mainly due to tubing buckling. A tubing anchor which permits the pump." Fig. 6, taken from the East­ Other observers report no such wear. tubing to elongate, but prevents short­ man paper, shows a typical example Field observations concerning the na­ ening, is called a tension anchor, in of sucker rod wear. Eastman wrote ture of pump wear are conflicting. opposition to a compression or hook· that this wear probably occurred in a which might be due to differences in wall anchor, which permits shorten­ dog-leg. It is thought that it was due, pumping conditions in various fields. ing but not elongation. rather, to buckling of tUbing. Tn view of this, the significance of the Any tubing catcher, run upside Freely suspended tubing buckles in speculation concerning pump wear down, could perform as a tension an­ the great majority of pumping wells. cannot be evaluated without further chor. The actual tool, however, must One might wonder, therefore, why re­ field evidence. be provided with one or more safe sulting failures are not equaIly fre­ and reliable retrieving devices. A few quent in tubings subjected to about TENSION ANCHORS Among the means which either pre­ hundred of such tools are presently in the same buckling conditions. That operation. failures are not equally frequent is vent buckling or minimize its detri­ most likely due to different friction mental effects, there are anchors, tail Since a tension anchor permits and corrosion conditions. In the pres­ pipe, sucker rod guides, and corrosion elongation, one method of installation ence of good lubrication, wear is min­ inhibitors. Discussion of the respec­ could be to set the anchor as soon as imized. And in presence of corrosion, tive merits of these means and tech­ the tubing has been run. After pump­ sand, etc., wear is fast. Friction, more­ niques for proper use of some of them ing starts and as the tubing fills up, over, continuously removes scale and will be presented later in this paper. the anchor would, on downstroke, other corrosion products, thus accel­ During pump downstroke, the en­ permit progressive elongation, due to erating the corrosion process. The tire fluid load is carried by the tubing. progressively increasing fluid load authors do not know of any case of and temperature; but it would prevent serious mechanical trouble due to shortening on each upstroke. Thus. buckling in wells where corrosion is the anchor would eventually work its controlled with inhibitors'·, most way down and fix the tubing in its likely because, in the presence of an most elongated position. inhibitor, the coefficient of friction Objections have been raised to per­ is small. mitting an anchor to "walk" down as Thus, the first speculation men­ described above. These are: (a) dur­ tioned in the preceding section, and ing the slow progressive descent of the which pertained to rod-on-tubing anchor, rust and scale might fill the wear due to tubing buckling, has been teeth of the slips, thus making them definitely confirmed by field evidence. FIG. 6-SUCKER ROD WEAR. inoperative; (b) in present designs,

76 PETROLEUM TRA:'I'SACTIONS, AIME upward motion of the anchor is not In addition, some people claim that made by a member that is essentially entirely eliminated in that a slight up­ the occurrence of leaks in tubing cou­ a friction member. Friction anchors ward travel is necessary for the teeth plings is greatly reduced by use of now on the market are hydraulically of the slips to engage the casing. Re­ tension anchors. While tension an­ operated. Pressure inside the tubing peated upward motion of the slips on chors have the advantages discussed acts on a few horizontal cylinders upstroke might eventually damage the above, their use involves the hazard which actuate members that contact casing. of difficulty in retrieving. In order to the casing. Instead of permitting the anchor to avoid these difficulties, some manu­ work progressively downward, an­ A manufacturer of friction anchors facturers build anchors with a double other manner of installation is to set says the friction, while it stops breath­ the anchor and then pick up the tub­ retrieving mechanism. If the primary ing, is not strong enough to com­ ing at the surface. Formulas and retrieving mechanism fails, then a pletely prevent the progressive down­ charts for determination of the re­ feature, such as shearing of a member ward motion; thus the tool jerks quired amount of pickup are pre­ of a predetermined strength, still per­ somewhat downward after pumping is sented further in this paper. mits pulling the anchor out of the started and the temperature increases. The necessity for determining the hole. To the best knowledge of the This means that this anchor does not correct amount of pickup and for authors, it has always been possible keep the tubing at its most extended to retrieve such anchors. performing the pickup operation is an position, but at some level interme­ Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 inconvenience. In view of the obvious In some cases, the added tension, diate between the upper and lower advantages of installation without due to the amount of pickup given by breathing positions. In spite of this, it resorting to the pickup operation, the chart, could endanger the string. is to be expected that such an anchor anchors have recently been developed should tend to minimize the effects of which are designed to avoid the diffi­ It might seem that the difficulty could buckling. Beneficial results from the culties of both scale accumulation in be avoided by picking up by some the slips and casing damage, and lesser amount and then letting the use of friction anchors have been re­ which seek the lowest level auto­ anchor "walk" down to make the ported. In each of three wells in a matically. remaining adjustment. However, if North Louisiana field, rod-on-tubing wear failures occurred about twice a The useful effects of using tension the well is later shut down with the anchors, as opposed to freely suspend­ tubing anchored in the most extended year. One year after installation of ing the tubing, were strikingly dem­ position, added tension will result friction-type anchors in these wells, onstrated by experiments carried out when fluid drains from the tubing and no failures have occurred. While these in two Oklahoma wells. In those the string cools. This added tension anchors seem to operate successfully, wells, prior to the installation of an­ subjects the tubing to the same tension use of the tension anchors previously chors, the problems of tubing leaks which would have occurred had the described might bring further im­ provement by an amount difficult to and of rod and tubing failures were tubing been originally picked up by evaluate. constantly encountered. After the an­ the amount indicated in the charts. chors had been in service for a year, This means that if the charts indicate It has been further reported that the conclusion was reached that ten­ a pickup which might endanger the the effectiveness of friction anchors sion anchors successfully overcame tubing, a tension anchor should not has been improved by lowering the these difficulties. In addition, their use he used. weight of the rods on the pump and resulted, for the same pumping condi­ The above limitation of tension an­ thus forcing the anchor down farther. tions, in greater production for less chors suggests the need for develop­ Perhaps operation of friction anchors horsepower spent. ment of a different type of anchor, could also, in some cases, be improved by picking up the tubing at the surface. This increase in production can be which could be designated as a "posi­ attributed to the two following effects: tive-action anchor." After setting, TUBING PICKUP FOR First, prevention of breathing in­ such an anchor would be definitely TENSION ANCHORS attached to the casing and would pre­ creases the volumetric efficiency of The amount of necessary tubing vent both upward and downward the pump. And second, elimination of pickup is given by the two following motion. With a positive action anchor buckling reduces rod-on-tubing fric­ expressions, which are derived in the it would be possible, if necessary, to tion. Thus increase in production and Appendix: pumping efficiency are further defi­ pick up the tubing by a lesser amount than indicated by the charts. Although nite advantages of tension anchors. In /'-..7 , = aoo.. { X, [ vI:X, + (1 - 2v) J the past, attempts have been made to picking up by less than the indicated amount would not eliminate buck­ D' - d' [ X ]} improve pump volumetric efficiency -- D' X, V L' + (1 - 2v) by preventing breathing with com­ ling, it would lessen its detrimental effects. /'-..t pression anchors, but expected bene­ ao(l - 2v)p, + Ea -a., (5) ficial results did not materialize for There is another class of anchor 2 reasons which will be explained fur­ which is not provided with slips, and L' £0.1 /'-..L = -- (6) ther in this paper. in which contact with the casing is Ea, .

VOL. 210, 1957 77 111 which to a fluid of specific predicted by the charts. Pumping vi­ gravity 1.154) D T is the pickup in pound, 0.5 psi/It brations decrease friction and thm Tubing temperature at also any extra tension due to friction. DL is the pickup in feet the surface when Therefore, if the pickup is made by E is Young's modulus of steel; pumping inches, the desired condition will be E = 30 X 10· psi reached. Mean yearly tempera­ It might be thought that the extra v' is Poisson's ratio of steel; v = ture (Mid-Continent) tension due to friction could result in 0.3 Dt = 100 - 60 = too much load on the tubing and on Anchor depth 3 is the fluid gradient in psi/ft the anchor. Actually, the extra ten­ To solve the problem, proceed as sion is not applied to the anchor. It ao is the tubing cross-sectional area corresponding to the follows on Chart 2: is, however, added to the tubing load at the surface and might therefore OD; ao is in sq in. Locate point A (pump depth 6,000 ft, working fluid level 5,000 ft) decrease the amount of pickup which a, is the tubing wall cross-sec- can be used. tional area in sq in. Locate line BB (fluid level at the time anchor is set 4,000 ft) TAIL PIPE D is the tubing OD in inches Vertical line through A intersects It has been explained previously d is the tubing ID in inches Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 line BB at C that freely suspended tubing buckles L is the depth of the pump m Slanting line through C intersects on upstroke as if it were subjected to feet reference line at D a fictitious column load, t, given by Eq. 1. Therefore, the buckling effect L' is the depth of the anchor in Vertical line through D intersects of pressure during upstroke might be feet line for a gradient of 0.50 psi/ft at E counterbalanced by the straightening X, is the fluid level in feet at the effect of the weight of tail pipe below Horizontal line through E inter­ time the anchor is set the pump. It is proven in the Appen­ sects reference line at F dix that it is the weight of tail pipe in X, is the working fluid level in Vertical line through F intersects fluid which must be equal to f. feet the line Dt = 40°F at G Consider, for instance, the numer­ Pc is the gas pressure in casing Draw horizontal line GH ical example given in this paper below when pumping; pc is in psi Locate line II (anchor depth 6,500 Eq. 4. The fictitious force was t = 0: is the coefficient of thermal ft) 6,000 Ib, and the weight of tubing in expansion of steel; Eo: = Line II intersects line GH at J fluid was q = 5.545 lb/ft. Thus the 207 psi/1°F necessary length of tail pipe is 6,000/ Read at H: pickup equal 16,100 Ih 5.545 = 1,082 ft. Dt is the temperature of the Read at J: pickup equal 23 in. pumped fluid at the surface However, if the hole were not deep The pickup in inches given by Eq. 6 minus the mean yearly tem­ enough to accommodate a tail pipe of or by the charts is the effective pick­ perature. The mean yearly sufficient length to control buckling, up. One should add to it the pickup temperature is about 60°F or if for any other reason a long tail needed for the expansion of the an­ in the Mid-Continent and pipe were not deemed desirable, then chor, which varies from make to 70°F in the Gulf Coast. one could suspend below the pump a make. short string of heavy-walled pipe sim­ Chart 1 (2-in. tubing) and Chart 2 The fluid level in the well at the ilar to drill collars. The high quality (2 1h -in. tubing) are graphical repre­ time the anchor is set is generally not steel used for drill collars would, how­ sentations of Eqs. 5 and 6. The charts known exactly. In such an event, this ever, not be needed for tubing heavy make no allowance for casing gas level should be estimated, assuming it tail pipe. On the other hand, old and pressure, the effect of which is small. too high rather than too low, so as to worn drill collars, if available, could In other words, the term containing obtain a value of calculated pickup be used. In the above example, one pc in Eq. 5 is disregarded. somewhat too large rather than too could, for instance, use 120 ft of 5V4 The construction of the charts is small. in. OD, 2 114 in. ID drill collars. explained in the Appendix. The use of The working fluid level goes down The advantage of tail pipe, com­ the charts is illustrated in Chart 3, with the life of the well. It might pared to the use of tension anchors, is which shows the solutions of the fol­ therefore be best to use in calculations the safety in retrieving the string. On lowing numerical example. not the present but some future work­ the other hand, the disadvantage is ing fluid level. This leads to some­ that breathing, which decreases pump Tubing size 21/2 in. what larger values of pickup. efficiency, is not prevented. Pump depth 6,000 ft Working fluid level 5,000 ft As tubing is picked up, friction be­ One could also use a string of Fluid level at the time the tween the tubing and the casing may heavy, drill-collar-like pipe suspended anchor is set 4,000 ft develop. Thus actual pickup in pounds not below the pump, but located required for a given pickup in inches above the pump. This would not en­ Gradient (corresponding may exceed the pickup in pounds as tirely stop the buckling, but would

78 PETROLEUM TRANSACTIONS, AIME minimize it and would confine it to a If a tension anchor is placed on a which is more than necessary to pre­ short zone above the pump. Gen­ string with no tail pipe, then picking vent buckling. One might therefore erally, however, suspending a tail pipe up the tubing by the amount given think that picking up by a smaller below the pump seems to be more by the charts results in a tension which amount could be advisable. However, attractive. is just that needed to prevent buck­ this is not so; as already explained, in If the weight of the tail pipe is not ling. On the other hand, if the tension presence of a tension anchor, the ten­ enough to prevent buckling, its use anchor is placed on a string with tail sion which the tubing will carry does will nevertheless minimize the detri­ pipe, then picking up the tubing by not depend upon pickup. This is be­ mental effects of buckling. the same amount results in a tension cause the tension anchor automat-

ANCHOR DEPTH- THOUSAND FEET 12 II 10 9 8 7 6 5 4 3 2 Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021

FLUID GRADIENT

MINUS MEAN YEARLY TEMPERATURE.

APPROXIMATE MEAN YEARLY TEMPERATURES: MID-CONTINENT -60 of GULF COAST - 70 of

CHART TENSION ANCHOR PICKUP FOR 2" TUB I NG

VOJ~< 210, 19~7 79 ically will "walk" down by an amount tail pipe. By doing so, the weight of the conditions of Fig. 7 A and 7 B. equal to the difference between the the tail pipe would be suspended the tubing shortens due to decrease amount given by charts and the actual from the anchor. of outside pressure and increase of amount. pressure inside. COMPRESSION ANCHORS The above statement would not, A compression or hookwall anchor however, hold true for a positive­ Fig. 7 A represents diagrammati­ is understood to be one which permits action anchor, for which the pickup cally freely suspended tubing before the tubing to move upward freely but given by charts could safely be de­ the pump is set. Fig. 7B shows the prevents downward motion. In Fig. creased by the weight in fluid of the same tubing during upstroke. Between 7B the downstroke position is shown Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021

10

Q. :::> (.)'" 0..

30

40 12 II 10 9 8 7 6 5 4 3 2 I 0 ( f-:-I---t--t---t--t---t--t---t--t---t--t-+-f-/,j--\--1' I ANCHOR DEPTH - THOUSAND FEET a: ~~r-~-r-~-r-~-r-~-r-~-~~~\~~~2 *.6.t IS FLUID TEMPERATURE AT SURFACE ~ ~+--+-_+--+-_+--+-_+--+-_ ",,'" of I \ \ 3 MINUS MEAN YEARLY TEMPERATURE. ~o '<~ l7 \ \ l;j APPROXIMATE MEAN YEARLY TEMPERATURES ~ ~ ~~~'-+'::"rt\~\~\-H-+1f-H--l4 ~ MID-CONTINENT-60 OF !;[ ~ "'~o~~ ..t 1\ \ ~ GULF COAST -70"F g~ .,,-v / ~ \ \ \ \ 5 i ~ ~v 6 ~ ~ l:l ~ "~j \ \ \ \ \ 'I ~~ ~~ ,

80 PETROLEUM TRANSACTIONS. AI ME by dashed lines. It is apparent from of the tubing buckles helically, but its under great tension, buckling is lim­ this figure that if a compression an­ deflection is stopped by the sucker rod ited by the casing and not by the chor is set before pumping starts string, which, being under great ten­ straightened sucker rods. This situa­ (Fig. 7A), the anchor will never per­ sion, remains essentially straight. tion is drawn in Fig. 80, which also mit the tubing to reach its lowermost On the other hand, during the shows that the sucker rod string is breathing position, as would a tension bent by the buckled tubing. anchor. Thus, during pump upstroke, downstroke, the tubing cannot elon­ the situation with a compression an­ gate as would a freely suspended The fact that the tubing may be chor, shown in Fig. 8U, is similar to string, and the tubing remains buck­ bent more during pump downstroke that for freely suspended tubing, led. Moreover, since, on the down­ (Fig. 80) than during upstroke (Fig. shown in Fig. 3U. The lower portion stroke, the sucker rods are no longer 8U) may result in fatigue and cause Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021

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v 0 I", 2 10. 195 7 8~ equation which is discussed In the pression anchor without any tail pipe Appendix: is shown in Figs. 9U and 9D, in /:::.t which the anchor is located in the W, = f + EaTa, (7) string high above the pump. Unless in which f is defined by Eq. 1, and the distance between the pump and other symbols are defined with re­ the anchor is large enough, the tubing spect to Eq. 5. will still buckle above the anchor, both during upstroke and downstroke, as Consider the following example: in the case of Figs. SU and SD. How­ tubing size, 2112 in.; plunger size, 1% ever, if the anchor were high enough, in.; fluid gradient, 0.500 psi/ft; work­ the tubing above the anchor would be ing fluid level, 5,000 ft; /:::.t previously straight. It would nevertheless stilI defined, 40°F. Substitution of the buckle below the anchor as would above conditions into Eq. 7 leads to: illl_.= --~~~~NSTROKE freely suspended tubing. The advan­ W, = 13,520Ib FIG. 7A (LEFT)-TUBING BEFORE tage of this compression anchor in­ PUMP IS SET. . W, 13,520 stallation over freely suspending the Length of tall pipe = q = 5.545 FIG. 7B (RIGHT)-TUBING DURING tubing is that breathing is due only to PUMPING. Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 = 2,450 ft. the length of tubing below the anchor. In the case where plunger diameter Shown in Fig. lOA is the case of a frequent tubing bending failures in is much smaller than tubing ID (in­ compression anchor at the pump with the first engaged thread, as reported sert pumps), tubing may elongate sufficient tail pipe. Shown in Fig. lOB further in this paper in a letter re­ rather than shorten between the con­ is the case without tail pipe but with ceived from Cities Service Oil Co. The ditions of Figs. 7 A and 7B. For the the anchor sufficiently high above the situation may be aggravated by a sake of brevity, the analysis of this pump. Now Fig. tOC shows an inter­ large size casing and/or corrosive case is omitted here. Because of this, mediate case which minimizes breath­ conditions and/or excessive setting the actual weight of required tail pipe ing and avoids buckling above the slack-off. is somewhat greater than calculated anchor. Furthermore, the fact that sucker with Eq. 7, and it is recommended In the first approximation, buckling rods move inside a helically buckled that for insert pumps, the results from above the anchor will be avoided in tubing, both upward and downward, Eq. 7 be increased by 10 per cent. all three cases if the length of tubing must result in a decrease of pumping Thus, for the above example, the below the anchor is equal the length efficiency. This decrease might very length of tail pipe should be 2,700 ft of tail pipe as given by Eq. 7. Thus, well overshadow the expected bene­ instead of 2,450 ft. in the case of the example, the anchor ficial effect of the compression anchor A common installation of a com- as a means for prevention of tubing breathing. This is undoubtedly the reason why the beneficial effect rarely materialized. It has been explained that sufficient tail pipe will prevent buckling but not breathing. On the other hand, without tail pipe, a compression anchor will prevent breathing but not buckling. By using both tail pipe and a com­ pression anchor, both buckling and breathing may be avoided. With a compression anchor at the pump, the required weight of tail pipe is greater than that for freely sus­ pended tubing. This arises from the need for subjecting the tubing to more tension at anchor setting time to avoid future thermal buckling when the tubing is heated by hot formation FIG.8U (LEFT)-SITUATION DURING PUMP FIG. 9U (LEFT)-SITUATION DURING Up­ UPSTROKE WITH A COMPRESSION STROKE WITH A COMPRESSION ANCHOR crude. ANCHOR AT PUMP. HIGH ABOVE PUMP. The required weight in fluid W, of FIG. 8D (RIGHT) - SITUATION DURING FIG. 9D (RIGHT) - SITUATION DUR!],;C PUMP DOWNSTROKE WITH COMPRESSION. DOWNSTROKE WITH A COMPRESSIO;\ the tail pipe is given by the following ANCHOR AT PUMP. ANCHOR HIGH ABOVE Pr;MP.

82 PErROLEl'M TRA"ISACTIONS, AIME occurred in the first 15 joints above resulted in reducing the average oc­ the anchor. During this period, rod currence of failures due to rod-on­ failures of the body break variety hap­ tubing wear from one in 6.3 months pened almost weekly. to one in 11.2 months. It is interest­ W, "Now, 10 months after the installa­ ing to note that in the same field even tion of the tension anchor, there have better results have been obtained with W, been no tubing failures; only three friction-type anchors. This is to be ex­ I rod failures; and with the same pol­ pected, in view of the fact that rod , B" I ished rod stroke, speed and pump guides cannot prevent buckling but L size, the well is pumping a greater only minimize its detrimental effects. W, 'c" amount of fluid. Frankly, the results Eq. 8 below, derived in the Appen­ we have obtained from this installa­ dix, gives the required sucker rod I tion have far exceeded our expecta­ guide spacing. Although the deriva­ L tions." tion concerns an idealized system, the 'A" It is believed that the situation was authors nevertheless feel the spacing FIG. lO-UsE OF COMPRESSION ANCHOR. as shown in Figs. 9U and 9D. For the thus obtained is adequate. should be 2,700 ft above the pump, conditions prevailing in this well, Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 G = 254 _I D' - tf (8) which is much higher than commonly however, the small deflection buck­ f'::, "qG' believed necessary. A rigorous and ling was not particularly harmful. On in which the other hand, large deflection buck­ complete determination of this length D and d have the same meaning ling in the 9% -in. casing caused fail­ must account for the working fluid as in Eq. 5 level, and the fact that the thermal ures. The situation was aggravated by f'::, G is the required distance be­ effect is somewhat different from the the presence of salt water and prob­ tween two successive guides in case where the anchor is at the pump. ably by excessive setting slack-off. In feet Since these considerations would re­ view of the explanation given in this sult in considerable complication, they study, it may be understood why re­ G is the distance in feet from the are not included in this paper. placement of the compression anchor lower of the two guides to the neutral point The following field case, encoun­ with a tension anchor avoided such tered in Oklahoma by Cities Service, failures. Since there was no room for q is as follows: For guides below shows an example of troubles which tail pipe below the pump, the only the working fluid level q is the resulted from the use of a compres­ other means for avoiding the above wtlft of tubing in fluid. For sion anchor and how these troubles mentioned troubles would have been guides above the working fluid disappeared after a tension anchor to place the compression anchor much level q is given by Eq. 4. higher in the string or to do without was installed. Chart 4 is a graphical representa­ any anchor. Neither of these means " ... we installed a ... Tension tion of Eq. 8. Guide spacing f'::,G is would have resulted in the increase of Type tubing anchor in one of our plotted vs distance G below the neu­ efficiency which was realized from use wells. The anchor was installed in an tral point for 2-in. and 21/z -in. tubing. of a tension anchor. attempt to eliminate tubing failures For simplicity, q is taken constant and that were occurring monthly. The fail­ SUCKER ROD GUIDES equal to the largest possible value, i.e. ures were perpendicular to the axis of Sucker rod guides were devised to given by Eq. 4 assuming 8 equal 0.50 the tubing at the first non-engaged minimize the detrimental effects of psi/ft. thread. The breaks extended approxi­ friction in crooked holes. They could The chart shows that the guide mately 180° around the plane at the also be used to minimize the effects of spacing must be the closest in the base of the first non-engaged thread. tubing buckling. vicinity of the pump. This spacing The failures had been caused appar­ In order to be effective in minimiz­ may be progressively decreased as the ently by the working of the 2112 -in. ing buckling effects, the guides must neutral point is approached. No guides tubing in the 9% -in. casing. The be properly spaced on the string be­ are needed above the neutral point to tubing was anchored with the con­ tween the pump and the neutral point control buckling effects, although they ventional type tubing anchor [com­ and must not move on the rods while might be useful in severe dog-legs. At pression anchor]. The anchor was the well is being pumped. The nega­ the pump the guides must be very installed at 5,119 ft, i.e., 1,116 ft tive results encountered in the past closely spaced in wells with a low above the pump [bottom of the cas­ with sucker rod guides do not justify working fluid level. ing]. The pumped fluid temperature condemnation of the technique, be­ The way the distance from the arriving at the surface was 125°F; 84 cause the guide spacing used was too pump to the neutral point is calcu­ per cent of the fluid was heavily sat­ large. lated, and the sucker rod guide spac­ urated salt water of specific gravity Field trials with sucker rod guides ing is determined, will be shown with equal to 1.15. All the tubing failures conducted in a North Louisiana field the following example:

VOJ~. 210, 1951 83 Pressure differential across the 358,375,392,410,428,446,464. 2. In presence of a large coefficient plunger t::,.p = 2,500 psi (work­ 482, 500, 520, 540, 560, 580, 600, of friction due to sand or corrosion, ing fluid level 5,000 ft, gradient 622, 644, 666, 688, 710, 734, 758, buckling results in frequent tubing 0.5 psi/ft) 782, 806, 834, 862, 890, 918, 953, leaks caused by rod-on-tubing wear. 3 988, 1,038. Plunger area 2.4 sq in. (1 ,4 -in. 3. Probably friction due to buck­ plunger) CORROSION INHIBITORS ling increases both polished rod load Fictitious force f = 2,500 X 2.4 It has already been said in this and horsepower. = 6,0001b paper that the authors do not know of 4. Possibly buckling of tubing has­ Weight per unit length in fluid: any case of serious mechanical trou­ tens pump wear. q 5.545 lb/ft (21h-in. tubing, = ble due to buckling in presence of 5. For a freely suspended tubing, 1.154 specific gravity fluid) corrosion inhibitors. Thus, use of in­ the pumping efficiency is adversely Distance to the neutral point: hibitors might possibly be a means to affected by both the known effect of 6,000 control wear due to buckling. This is, tubing breathing and the newly n = 5.545 = 1,082 ft however, not definitely established, discovered phenomenon of tubing Then the following guide spacing since generally inhibitors have not buckling. is obtained from Chart 4: been used when wear has seemed to 6. Tubing buckling and its harmful Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 be primarily mechanical rather than Dist,]nce Distance Below Guide effects may be entirely prevented by Ab,)ve Neutral Spacing, chemical. It should be kept in mind Pump, Feet Point, Feet Feet anyone of the following means: (a) in evaluating the merits of inhibitors 0 1,082 15 tension anchors, i.e. anchors which leO 982 15 that prevention of corrosion cannot 200 882 16 can move only downward, (b) a suf­ 30~ 782 17 stop breathing. Use of inhibitors is ficient weight of tail pipe below the 40' 682 18 outside the scope of this paper. Tech­ 5011 582 20 pump. 600 482 22 niques pertaining to their use are de­ 70(1 382 24 800 282 28 scribed in the literature, in Refs. 11 7. Harmful effect of tubing buck­ 900 182 35 1,000 82 50 through 15. ling may be minimized by anyone of the following means: (a) friction an­ One could, for instance, use 52 CONCLUSIONS chors, (b) less tail pipe than neces­ guides and locate them at the follow­ sary to eliminate buckling, (c) sucker ing distances from the pump in feet: I. The lower portion of freely sus­ rod guides spaced as described in this 15, 30, 45, 60, 75, 90, 105, 120, pended tubing buckles in a pumping paper, and (d) corrosion inhibitors. 135, 150, 165, 180, 195,211,227, well during pump upstroke and wraps 243,259,275,291,307, 324, 341, itself around the sucker rod. 8. Among the techniques men­ tioned above, only tension anchors SUCKER ROD GUIDES SPACING, FEET may entirely prevent both buckling o 10 20 30 40 50 and breathing. o 9. With a compression, i.e. a hook­ wall anchor, both buckling and breathing could be avoided only by I- 500 UJ placing the anchor at the pump and UJ suspending an extremely heavy tail IJ.. 2"-.... pipe below. I- II Z 10. With a compression anchor at 0 1,000 11. 2 ~' TUBING the pump and no tail pipe below. ...J ~ buckling is much more harmful than 0:: I- for a non-anchored tubing, and may ::> UJ 1,500 result in: (a) frequent first engaged z thread bending failures, (b) frequent UJ J: I- rod tensile failures resulting from ad­ ditional load due to friction, and (c) ~ 2,000 ...J decrease of pumping efficiency due to UJ m friction, which cancels the expected UJ increase of efficiency due to pre­ <.:> z 2,500 vention of breathing. ~ ~ 1 I. Buckling of tubing above a 0 compression anchor cannot be pre­ 3,000 vented by placing the anchor high CHART 4--SUCKER ROD GUIDE SPACING FOR PREVENTION OF BUCKLlNC. above the pump, unless the distance

·1-1 PETROLEIJllf TRA'iSACTIO'iS, AIME from the pump to the anchor is ex­ 6. Lubinski, Arthur: '"Crooked Holes," that the deflected shape is as shown in tremely large. presented at Twelfth Annual Meet­ Fig. 11. Consider an arbitrary cross­ ing, AAODC, Oklahoma City (Sept., section MN, the center of which is 12. Means for determining the 1952). Published in Pet. Engr. (Jan., proper amount of pickup when using 1953), and Drill. Contractor (Dec., marked O. The bending moment at tension anchors are given in this 1952). this cross-section is equal to the sum paper. 7. Texter, H. G.: "Oil-Well Casing and of the moments about 0 of all exter­ 13. In the choice of a tension an­ Tubing Troubles," Presented at API nal forces acting on the portion of the Division of Production Meeting, New chor, consideration should be given to pipe to the left of MN. The weight Orleans (1955). Published in Oil and features of the tool which insure safe having no effect on moments about Gas Jour. (Aug. 29, 1955). 0, these forces are pressure forces retrieval. 8. Lubinski, Arthur, and Woods, H. B.: and the reaction of the piston on the 14. Use of a tension anchor, or of "Factors Affecting the Angle of In­ pipe. a compression anchor with a suffi­ clination and Dog-Legging in Rotary Because the arc BC is longer than ciently heavy tail pipe below, results Bore Holes," API, Drill. and Prod. Prac. (1953), New York. arc DE, there is a net pressure force in increased production for less horse­ h (Fig. 12) acting on the walls of the power. A similar improvement ex­ 9. Eastman, H. John: "Producing Di­ rectionally Drilled Wells," Published pipe in addition to force i acting on pected in the past from use of

by Eastman Oil Well Survey Co., the shoulder AB (Fig. 12). For clar­ Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 compression anchors did not occur Denver, Colo. ity, force i is represented by two vec­ because of buckling, which was not 10. lones, Loyd W., and Barrett, Jack tors in Fig. 12. then known. P.: "Laboratory Development of Cor­ The force h cannot readily be cal­ rosion Inhibitors," Gorrison, NACE, culated, since it depends upon the ACKNOWLEDGMENT (May, 1955), II, No.5. shape of the elastic line. Therefore, 11. Elliott, D. J.: "Mechanical Aspects Use of a short length of heavy of Corrosion Inhibitor Injection," the resultant of j and h is best calcu­ tubing has been proposed by l. A. World Oil (Nov., 1952). lated by the following means: Stinson, Pan American Petroleum 12. Gross, W. F., and Andrews, H. W.: Consider an entirely closed cavity Corp. "Prevention of Corrosion in Sour BCED (Fig. 13), of the same shape The authors wish to express their Wells with Organic Inhibitors," Oil as the inside of the pipe BCED (Fig. and Gas JOllr. (Oct. 28, 1948). appreciation to all those who submit­ 12), and containing fluid under pres­ ted constructive criticism or field in­ 13. Villagrana, R. J., and Musick, W. F.: sure equal to that applied inside the "Economics of Oil Well Corrosion formation, particularly B. C. Frihart pipe. The horizontal pressure forces Control," API, Drill. and Prod. Prar. and T. R. Moore. Cities Service (1949), New York. which the fluid exerts on the walls of Oil Co. the cavity are as follows: hand j prc- H. Frisius, E. N.: "Oil Field Scale and Corrosion," World Oil (June, 1953). ]{EFERENCES M 15. Clements, F., and Barrett, J. P.: I. Timoshenko, S.: Theory of Elastic "Corrosion Cost Cut is Promised in Stability, First Edition, McGraw·HilI San Andres Field," W orid Oil (Oct.. I Book Co., New York (1936). 1952) . c 2. Lubinski, Arthur: "A Study of the 16. TimoE'henko, S., and Goodier, J. N.: h Buckling of Rotary Drilling Strings," Theory of Elasticity, Second Edition, API Drill. and Prod. Prac. (1950). McGraw-Hill Book Co., Inc., New o New York. York (1951). :{. Klinkenberg, A.: "The Neutral Zone,. E in Drill Pipe and Casing and Their APPENDIX Significance in Relation to Buckling and Collapse," API Drill. and Prod. EXPLANATION OF BUCKLING Prac. (1951), New York. :)a. Woods, H. B.: Discussion to th" Consider that the length of pipe of N paper, Ref. 3 above. FIG. 12. Fig. 1 has been deflected by applica­ ,I. Lubinski, Arthur: "Influence of Ten­ tion of horizontal lateral forces so sion and Compression on Straight­ ness and Buckling of Tubular GooEis M in Oil Wells," Proc. 31st Annual ,,-reeting, Prod. Bu!. 237, API, New York, (Nov. 1951).

;>. Texter, H. G.: "Variolls Methods of High Pressure Testing Oil Country Tubular Material," paper presented at ASME, Petroleum Division Con­ \~ ference, Kansas City, Mo. (Sept., 1952) . FIG. 1 \. FIG. 13.

'"OL. 210. 1957 viously defined, i equal to pressure of "( i), which is the same as f in the of Hooke's law. Eq. 5 is derived In times piston area, and k equal to pres­ body of the paper. the following manner. sure times ID cross-section area of the pipe. Then written as vectors, the hor­ PREVENTION OF BUCKLING PICKUP WITH NO izontal forces acting on the fluid are TEMPERATURE CHANGE It is explained in the body of the (-h), (-I), (-7), and (-i0. The paper that on upstroke, freely sus­ Consider tubing in a well as shown liquid being in equilibrium, the fol­ pended tubing buckles as if subjected in Figs. 16A and 16B. The axial lowing vector equation must be sat­ to an upward fictitious force f· strain ex in the tubing, due to pres­ isfied: Therefore, buckling will not occur sure acting on the walls of the tubing, (-h) + (-/) + (-7) + if the buckling effect of f is counter­ is: (-k) = 0 (9) balanced by the straightening effect V Ic, = -- E (ITT + IT,) . (12) From this, obtained by increasing the tension (or compression) in the tubing by where ITT and IT, are radial and tan­ adding at the level of the pump a gential stresses given by thick wall In order to determine the reaction tension equal to f. Therefore, the cylinder formulas*. Substitution for of the piston on the pipe, consider tension in the tubing at the pump IT, and IT, leads to: equilibrium of the piston. The piston level during downstroke is just that 2v Pi d' - po D' Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 is subjected to the following forces needed to prevent buckling during I, = - If D' _ d' (13) (Fig. 14): pressure force i, pull T upstroke. And if the tubing is caught III which alI the symbols were pre­ of the rod, and the resultant r of all in its most extended position during viously defined except Pi and Po, the reactions of the pipe upon the downstroke, then this tension will which are pressures inside and out­ piston. The piston is assumed to be also be present during upstroke and side of the tubing. frictionless so that the vector (;) will prevent buckling. This is a state­ The axial strain E ~ due to pres­ ment made, but not proved, in the must be perpendicular to (t). The sure acting on the bottom of the body of the paper. equilibrium of vectors (t), (1), and tubing is: (;) is shown in Fig. 15. 1 'd' - 'D' DERIVATION OF PICKUP E'=-P, Po (14) The external forces acting on the rED' - d' FORMULAS FOR TUBING portion of the pipe to the left of MN SET ON A POSITIVE-ACTION III which P: and p:' are inside and are pressure forces (h) and (D and TENSION ANCHOR outside pressures respectively, acting the reaction (-;) of the piston on on the bottom of the tubing. It is to the pipe. In view of Eq. 10, the No proof is deemed necessary for above forces may be replaced by Eq. 6, which is a direct application '·"See, for instance, Ref. 16. Eq. 4;:), ( - l), (-k), and (-;). From Fig. 15: GAS PRESSURE P ( - t) + (-;) = (I). ( 11 ) c Thus the resultant of external forces acting on the portion of the pipe to the left of MN is the resultant of ( - k) and ('1). Therefore, the bend­ ing moment at MN is the moment of force (r) about 0, the moment of ( - k) being zero. As far as elastic stability is concerned, the pipe acts L as if it were subjected to a column load (T). Since stability is decided on the basis of small deflections, the magnitude of (T) is essentially that

r----;===:::z L __ -,

)~,~~T FIG. 16A. FIG. 16B. ~ ~ __L -=- -=-.:1 ELONGATION OF FREELY SUSPENDED TUBING BETWEEN STAT\(: A:\D FIG. 14. FIG. 15. PUMPING CONDITIONS. lit. PETROLEt:'" TRA,\"ACfIO',. ..\1:\11-: be noted that ex varies with depth. Section .6.p, .6.p, (16) while < does not. AB /lx p, The changes .6.c.. and .6.< in the /lX, p, - /l(x - X,) in which .6.p" .6.p" .6.P: and .6.P ~ BC strains [; x and < respectively, be­ CD /lX, P, - /l(X, - X,) tween the condition of Figs. 16A are changes in these pressures. From in which x is the distance from the and 16B are: Figs. 16A and 16B, one finds that surface . .6.p', equals /lX, .6.P~ equals P, - 2v 6.p,d' -- 6.p,D' The total elongation of the tubing .6.e. = -~ E D' - d' /l (X, - X,) and that the other between the conditions of Figs. 16A (15) changes are as summarized: and 16B is: Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021

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MEAN l'fMLl' H:"JPfRATURfS,;' 11litI'H-E>O of xf FIG. 18 CHART 2.

ING

VOL. 210, 1957 87 ,. 6t _I ted to elongate, then its elongation e TUBING IS: o A2. A AI C TEMPERATURE e = L" ex~ 2 From Hooke's law, the compres­ -M sive stress c, which is needed to re­ store to the pipe its original length, is: c = E _e_= Eo::~ :I 11I L" 2 I wal I I which explains the term containing I I I I 6.t in Eq. 5. L-l Lfl PICKUP CHARTS i/N~I ANCHOR DEPTH The pickup charts are a graphical FIG. 19/\. FIG. 19i1. :J: B l­ ll. representation of Eqs. 5 and 6. For 1&1 as shown by dotted lines in Fig. 19B. o convenience, the following designa­ When the tail pipe is attached to tions are made: FIG. 17-EFFECT OF TEMPERATURE. the tubing, the buoyancy force M Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 Y, = a" X, v y+Xl (I - 2v)]D'D-'" d' no longer exists. This is equivalent 6.L' = J~ (6. 10 • + 6. E)dx. (17) [ to adding to the tubing a force, - M, 6.L' is also the pickup in inches (19) shown in Fig. 19B. On the other hand, suspending the tail pipe from which would be required if there X, ] Y2 = a" X, v + (1 - 2V) the tubing adds two vertical forces: were no temperature change. [ L (20) The weight in air, W a , of the tail The corresponding pickup 6.T' in pipe, and the upward pressure force, pounds IS obtained from Hooke's Eq. 5 is rewritten, neglecting the N, with which the fluid acts on the law: term with p,., bottom of the tail pipe. 6.L' 6.t I\T' = Ea-- 6.T = .'l(Y, - Y,) + E ex Ta, Thus, the forces added to the tub­ L'. 'L ing by suspending tail pipe are W,,, in which a., is the wall cross-sectional For any value of Xl> the function Y, N, and - M. Their resultant is area of tubing. Replacing a, with is largest for L equal X, and, for the equal to the weight of tail pipe in D' - d' range of L covered by the Charts, is fluid. (/"=({ .. ~ smallest for L equal 12,000 ft. The In order to counteract the bend­ Charts are simplified by assigning to ing effect of fictitious force f with one obtains: Y, the average value for each X" It added tension by hanging tail pipe, has been determined that doing this the weight of the tail pipe in fluid 7·' E D- - d- 6.L' (18) 6. ~ -(/ D' L results in a maximum error in 6. T must be equal to f. This proves the Substituting the expression of 6.L' of 400 lb, which is negligible. statement made, but not proved, in into Eq. 18 and proceeding through The graphical representation is the body of the paper. a few transformations, an expression made in five sections, as shown in No proof is deemed necessary for for 6.T' is ohtained, which is the Fig. 18. Each section represents a Eq. 7, pertaining to use of tail pipe same as Eq. 5 without the term con­ functional relationship among three in conjunction with a compression taining 6.t. variables: two of the variables are anchor. the coordinate axes, and curves are PICKUP DUE TO drawn for constant values of the SUCKER ROD GUIDE SPACING TEMPERATURE CHANGE third variable. The variables for each Consider the tubing between two It is assumed that at the time the section are shown in the table be­ successive rod guides as a column anchor is set, the tubing is in ther­ low. The ordinate of Section 3 and subjected to a load qG. If this col­ mal equilibrium with the surround­ the abscissa of Section 4 are the umn is considered to have hinged ing formations and that its tempera­ same. The slanting reference line is ends, the critical length 6.G,., ob­ ture varies with depth as shown by used for transfer between them: tained from Euler's formula, express­ BA (Fig. 17), OA being the mean ing the moment of inertia in terms of yearly temperature. Seasonal changes, sectio~__ 1 Ordinate Abscissa I V:r~~gle D and d, is: 1 I y. X .. - _ I (;r/64) (D' - d')E BA, or BA" affect only a negligible y, y, Y2 - Y I 6. G ,-" qG length of tubing. It is further as­ o(Y, - Yd Y:.! -- YI ~ sumed that, during pumping, tem­ ,I(Y, -Y,) " (21) perature varies with depth, as shown ". ECX~o., ,I(Y.,· y,) L I - If we make the length of the col­ by BC. Then AC, designated 6.t, is ,"(Y' Yd I umn, i.e. the distance 6.G between I .It, the temperature change of the tubing ;" ECXT"'! L' guides, equal 0.8 6. G" the tubing near the surface between the time --.-._.... _----'--- will certainly not buckle. Eq. 8 in the anchor is set and a later time TAIL PIPE the body of the paper is obtained by when the well is being pumped. This multiplying 6.G, by 0.8 and making means that 6.t/2 is the average tem­ Consider the lower end of a tubing allowance for customary units. Ac­ perature change of the tubing. string as shown in Fig. 19A. There tually, the tubing between rod guides If the average temperature of a is acting on the bottom of the string is somewhat stiffer than a hinged end pipe of length L" is increased by a buoyancy force M. Now consider column which brings an additional 6.t/2 and the pipe is freely permit- that more tubing (tail pipe) is added, factor of safety into Eq. 8. ***

83 I'ETHOI.EFC\'! THA:\,SACflOXS, \IME Note on Buckling of Tubing In Pumping Wells

T. SELDENRATH COMPANIA SHELL de VENEZUELA JUNIOR MEMBER AIME MARACAIBO, VENEZUELA A. W. WRIGHT' Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021

ABSTRACT In the case of a loaded column, this may be written: This paper is written as a dillcussion oj the paper, tfy I dx' = - PI EI (y + e). For the pressurized tube it "Buckling oj Tubing in Pumping Wells, Its EfJects and was shown, by analogy with the loaded column, that Means for Controlling It" by Arthur Lubinski and K. tfyldx' = - P';EI (y + e), where p. = A.p. This equa­ A. Blenkarn, which was published in the March, 1957, tion has a solution that, for p. = 71" Ellf', any deflec­ tion is stable (a criterion for buckling). An attempt issue of JOURNAL OF PETROLEUM TECHNOLOGY. An analogy iJ drawn between the buckling of tubing in will be made to describe more precisely, the forces pumping wells and a tube, fitted with frictionless pis­ acting on the tube, and to analyze the buckling' con­ tons, linked by an inelastic rod, and which is subject ditions. to an internal pressure. A simple derivation shows that the critical internal pressure exerts a hydrostatic force DISCUSSION on the piston which is close to the Euler load for com­ If the tube assumed a deflected position, the volume pression buckling of the same tube. While the results between the pistons would increase so that in deflecting, agree with those of Ref. 1, the basis of calculations the energy of the fluid would decrease. When the in­ has been changed and clarified. crease in elastic energy of the tube (due to bending) The presence of internal upsets at the pistons is is equal to the decrease of fluid pressure energy, buckl­ discussed. ing conditions exist. INTRODUCTION Analyzing the forces on the tube (Fig. 3), two trans­ verse forces, T" T" exerted by the pistons, are balanced In the Appendix" Lubinski and Blenkarn state that by a resultant of the pressure elements which are a tube with ends closed by frictionless pistons connected linearly dependent on the local curvature of the elastic by an inelastic rod (Fig. 1) will behave as a column line (Fig. 4). loaded with a force equal to the tension force in the rod. They note that, while the fluid may not resist a 1', + 1'2 = R, shear force, the moment in every cross section is piston R, + R, = 0 force multiplied by the elastic line deflection (c.f., the Unlike most buckling cases, the forces depend on the loaded column). Since the equations of the elastic lines shape of the elastic line, a condition that makes a are similar in the two cases, the solution is carried rigorous mathematical treatment difficult. Several ap­ over from the loaded column. proximations may be used to clarify the problem. On the contrary it is suggested that while the method of solution remains unchanged from the column case, the actual stress distribution is different, a fact which is taken into account in this note. A simple method of approximating the buckling pres­ sure is given, and their reasoning in our mathematical language is continued. FIG. I-SCHEMATIC DIAGRAM OF TUBE.

GENERAL EQUATIONS The equation of an elastic line, initially straight in the x direction (Fig. 2), is given by cI'y At, dx' E1

Original manuscript received in Society of Petroleum Engineers office Feb. 24. 1958. Revised manuscript received April 30. 1958. "Deceased. Dec.. 1957. ]References given at end of paper. SPE 1053-G FIG. 2-SCHEMATTC DIAGRA)l.

AIlGVST. 19fiR (9) According to Euler theory, buckling occurs in a ~TP, EI column when P (an 'end load) = .. '7 (Ref. 2), c. which is indeed between the two cases. FIG. 3-FoRCES ACTli\"G O!'i THE TCDE. In the loaded column case, the com~ression forces are axial and do not vary due to the buckling, while the moment at any section depends linearly on the de­ flection. On the contrary, in the pressurized tube case, the forces act normally to the elastic line, and vary linearly with the deflection. In the latter case, the moment arm of every force is almost independent of the de­ flection. If the ends of the tube are internally upset (Fig. 6), a new condition prevails. The force on a shoulder due to the fluid pressure has a small tranverse component (dependent on the end slope of the clastic line) and a large axial component, almost independent of the end Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 slope, but whose moment varies linearly with the deflec­ tion (Fig. 7). A = A, + A,

Pk = p.At P, = p.A, = PkA,IA,

p." = P k ' A,IAt Tan x p,. ~ P, ~ P,AjA,. Resultant tranv'erse component of shoulder and pis­ ton forces, PkA,IA z Tan a + Pic Tan a = P" AlA, Tan a.

Resultant axial component of shoulder force, Pk

AjA, Cos a ~ P k A 2IA,. It is noted that the resultant tranverse component is

T R2

FIG. 4--FORCES EXERTED DY PISTOi\"S AND FLCID 0'( THE TUDE.

Since a is small, the axial components of both the pressure elements acting on the tube, and T" T, are of FIG. 5-DISTRlBCTIO!'i OF FORCES ACTING ON A BEAM. second order. To simplify calculations, the force dis­ tribution (due to the fluid pressure) is approximated ~\\\\\\\\\\\\\, by two separate cases: (1) a uniformly loaded beam, having a lower moment in every cross section (Fig. 5a), and (2) a beam with a point load at mid-span, having a higher moment in every cross section (Fig. 5b). B======:J CASE 1 ~\\\\\\\\\\\\~ T = P k Tan a (Fig. 3c) , (1) 10 T l' a b e = -----m- 384 (Fig. 5a) , (2) FIG. 6-TuBE WITH INTERNAL UPSET ENDS. and a = Tan a~ 3.2 ell (Ref. 2) (3)

From Eqs. 1 and 3, T ~ 3.2 P k ell (4) When the system buckles, deflection e may take any value. Thus, eliminating e from Eqs. 2 and 4, nE! P = -.- (5) k t- CASE 2 2Tl" e = 48EI (Fig. 50) , (6) 3e a = Tan a ~ -1- (7) Thus,

T ~ 3Pk ell (8) FIG. 7-DIAGRAM OF FORCES ON A TUBE WITH INTERNAL UPSET Eliminating e from Eqs. 6 and 8, • ENDS.

50 JOURNAL OF PETROLEUM TECHNOLOGY independent of the ratio in which the area A is divided NOMENCLATURE between piston and shoulder. Fig. 7 demonstrated that the equivalent end load is I = I'cngth of undeflected tube equal in magnitude to the hydrostatic force on the pis­ x = distance from origin along undeflected clastic ton only. line Buckling involves a shortening of the distance be­ y "" deflection of elastic line tween the 'ends of the tube, but no net axial stresses E = Young's modulus for tube material are introduced by internal pressure. However, the pres­ I = moment of inertia of tube section ence of shoulders causes an axial tension which delays M x = moment of tube section at x buckling. P = axial load on a column It is also inter,esting to note that tube dilation causes e = infinitely small initial deflection of the elastic an increase in the moment of inertia, which in turn line delays buckling. This last effect is paramount in the P k = force on pistons due to fluid pressure Bourdon tube. P t = tension in rod CONCLUSIONS p = fluid pressure 1. Buckling may occur in a pressurized tube with A = cross-sectional area of tube hole ends closed by two frictionless pistons connected by an A, = piston area when internal upsets are introduced inelastic rod. A, = shoulder area 2. The critical hydrostatic force on the pistons ap­ T = transverse force exerted by piston on tube Downloaded from http://onepetro.org/trans/article-pdf/210/01/73/2176282/spe-672-g.pdf by guest on 01 October 2021 proximates or equals the buckling end load: 12EI/1" B = resultant cf forces exerted by pistons on tube > P k > 8EI/I'. B, = resultant of hydrostatic force elements on the 3. If the tube ends are internally upset, the critical tube internal pressure is increased, and a net axial stress is IX = ead slope of the elastic line introduced into the tube. e = deflection at mid-span 4. Many more practical applications than mentioned in Ref. 1 can be found, especially if similar cases, in­ P, = hydrostatic force on shoulder volving different pressures inside and outside a tube are P" = c::mponent of P, transverse to undeflected elas­ included. Using the Lubinski theory as discussed in this tic line (y direction) note, interesting observations can be made in the follow­ p,. = cJmponent of P, parallel to undeflected elastic ing cases: (a) free hanging strings at greater depths, line (x direction) (b) lubricated rod pumping, and (c) sandfracing and producing of PTWC wells with two fixed tubing points, REFERENCES e.g., Baker Model D production packer and Otis-SOB 1. Lubinski, A. and Blenkarn, K. A.: "Buckling of Tubing in packer. Pumping Wells, Its Effect and Means for Controlling It", 5. Temperature effects and reduced collapse resistance Trans. AIME (1957) 210, 73. might make it less attractive to use tension anchors 2. Theoretische Gmndlagen: H~tte. W. Ernst und Sohn, Ber- in deep wells. lin, Germany. ***

AUGUST, 1958 51