Cox Buckling and Wellhead Load Paper

7/29/2019 Cox Buckling and Wellhead Load Paper

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Key Factors Affecting Landing of Casing?W. R. Cox*

ABSTRACTIn 1955, the API Southwestern District Study Com-

mittee on Casing Landing Practices recommended thatspecial consideratioil be given to landing of casing inwells where design fac tors ar e low, where extrem e pres-sur es are encountered, where escessive mud weights arenecessary or where other unusual circumstances exist.In this paper equations and nomographs are provided

for use in arriving at sound landing procedures forthese unusual wells, and for evaluating landing pro-cedures now in effect for other wells. It is concludedthat landing methods should reflect proper considerationof both the buckling and the wellhead-load cha ract er-istics of the string. An example problem is included toillustr ate application of t he equations and nomographs.

INTRODUCTIONIn March 1955, the API Southwestern District Study

Committee on Casing Landing Practices reported ontheir review of approximately 3,700 wells drilled in 1952by 21 operators in the Southwestern District.l Thesewells ranged in depth from 2,000 f t t o 14,000 f t wi th a naverage depth of 8,000 ft. The casings in these wellswere landed by one of fo ur methods: 1 , a s cemented; 2, intension a t the freeze point; 3, neutral a t the freeze point;o r 4 , in compression a t the freeze point. I n view of th ewide difference in methods of landing casing undersimilar conditions, the study committee recommendeda landing practice which they believed ". . . hould affordthe greate st amou nt of protection for and service fro mAP I casing in a ver y high percentage of wells drilled inthe Southwestern United States."

The study committee recommended that casing belanded as cemented in all wells where mud weights donot exceed 12.5 lb per gal, where standard design factorsar e used, and where t he wellhead equipment and o utercasing strin g are of sufficient s trengt h to withstand t helandin g loads. The term "as cemented" means th at thecasing is landed in approximately the same position inwhich i t was hangin g when the cement set. The onlymovement of the casing would be that necessary totransfe r the weight to the casing hanger.

In wells where design fact ors ar e low, where ex tremepressu res ar e encountered, where excessive mud w eightsare necessary, or where other unusual circumstancesexist, the stu dy committee recommended th e land ingpractice be based on theoretical considerations developedby L ~ b i n s k i . ~ubinski's theoretical analysis yieldsmeans fo r determinin g if casing is buckled or ha s atendency to buckle under down-the-hole conditions. Byprop er selection of l andin g procedure, Lubinski showedthat buckling could be prevented.

I t has been recognized th at a landin g procedure basedonly on buckling considerations ma y resu lt in undesirableaxial loading. For example, if the hanging method callsfor casing to be picked up a considerable amount from*Shell Oil Co.. Cornus Christi. Texas.t~ re se nt ed t.the spring meeting of the Southern District, Division ofProduction. Shreveport, La.. March 1957.IReferences are a t the end of the paper.

the as-cemented position, then large temperature dropsin the free casing subsequent to hanging could produceadditional tensile loading sufficient to cause tensilefailure. In addition to temperature, pressure and fluid-weight changes influence the hanging load and thesealso should be considered before selecting a hangingprocedure.

In order to conform to the study committee's recom-mendation f or determ ining special landing proceduresin wells where u nusual circumstances exist, it is believedtha t convenient means should be available for calculatinglanding loads t ha t preclude buckling. I t is also believedth at means must be available for evaluating the landingmethod in term s of wellhead loads tha t may occur in the'life of the well. It is the purpose of th is pap er to providea single equation to use in selecting the optimum pickupor slack-off to preclude buckling and to provide a singleequation for computing the wellhead load. The para-meters in the equations are believed sufficient for con-sideration of most down-the-hole environments. Nomo-graphs, o r alignment charts, ar e provided t o aid in th esolution of the equations.

BUCKLING PHENOMENONThe phenomenon of buckling of oil-well tubular mem-

bers has received increased attention in the last six orseven years. This is the result of several ~ t u d i e s ~ ! " ~nthe subject which concluded that, fo r certai n conditions,buckling occurs to tubular members subjected to axialtension; and f or oth er conditions, buckling will not occurunder axial compression. These findings introduced aparadox.

Fo r a number of y ears arior to these buckling studiesit wa s believed th at a small amoun t of axial compressionwould cause buckling in lo ng and slend er oil-well tub ula rmembers. F or this reason many operators adopted land-ing practices which placed axial tension a t and above thefreeze point. New concepts indicate that casing didbuckle in some of the wells completed with these oldlanding practices. This has been difficult to reconcilebecause in most cases the operator had no evidence offailure and experienced no difficulty in completing andproducing wells with buckled casings. The apparent con-tradiction of buckling theory with field experience lies


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22 6 W. R. Cox

in a misunderstanding of buckling phenomenon and notin a n incorrect buckling theory.There are three types of buckling th at ar e familiar tomost of us. The first type occurs in a beam which hasbeen overloaded to the point of yielding. It is often saidthat the beam has buckled; however, this is perhaps in-correct nomenclature. It would be more proper 'to saythat the beam h as failed by yielding.The second type of buckling occurs when a thin-wallcylinder or tank is subjected t o high end loading. Undera critical load the sides of the vessel distort i nt 0. a cor-rugated surface and the height of the vessel decreasesappreciably. This is the classic case of symmetricalbuckling.The third type of buckling occurs when a colunln issubjected to its critical load. The column deflects fromits vertical alignment and, depending on the intensityof the load and the properties of 'the column, it may notretu rn to i ts original alignment when the load is removed.

This is the classic case of asymmetrical buckling.I t is the third type of buckling t hat h as been investi-gated as a criterion for landing casing. This type buck-11ng is mos t famil iar because i t occurs in cer tain sizesof clrill pipe and tubin g th at ar e racked in t he derrick.The clrill pipe and tubing may bow from a stra ight align-ment but they have not failed. They will return to theiroriginal alignment if laid on a flat surfa ce or picked upin the derrick.Casing that has buckled down the hole will return, oits original ali g~nn ent fter t he buckling forces are re-moved, if the yield stress of the casing is not exceeded.Parting or pemn~anentdefonnation probably seldom oc-

curs i n buckled casing. If a larg e cavity is, opposite thebuckled section, the casing will tend to bow into theenlargement. In such an event the casing could be per-manently distorted. Trouble would probably first beexperienced in passing other st ring s or tools through thebuckled section.Test er5 reports on one failure of 5;h-in. casing tha twas evidently the result of wear caused by rotation ofthe tubi ng st ii ng which had drilled out the cement plug.

, Investigation indicated th at t he casing had buckled in to acavity, permitting the drilling tubing to r ub harcl again stth e convex side of t he buckle.There may be many casing failures that have beenaggr avat ed by buckled casing. It is understandable that

there is a lack of information on this subject inasmuchas in past years i t was not suspected that the casing wasbuckled, and in recent years the tools for examiningbuckling tendencies have been difficult to understand andapply.BUCKLING-CRITERION EQUATION

Equations which have been d e~ iv ed n Appendix Aare given in Table 1 fo r determining th e required pickupto preclude buckling of t he casing af te r the cement sets.The pickup is given in the first equation in the unit ofpounds. By sub stituti ng the value found in pounds in t hesecond equation, th e can be expressed in inches.


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wI W = wellhead load, Ib.? AS = pickup when hanging casing, Ib (-AS = slack-off).,r r y - - t - - ~ ;D L r 1 AL = pickup when hanging casing, in. (-AL = slack-off).

Pe = surface pressure outside casing when cement sets, psi.AP, = change in surface pressure outside cas ing after cement sets, psi.

P, = surface pressure inside casing when cement sets, psi.AP, = change in surface pressure inside casing af ter cement sets, psi.

L, '

.. m = fluid-leve l drop outside casing after cement sets, ft.

n = fluid-leve l drop inside casing after cement sets, ft.At = average change in casing temperature above cement top after

cement sets, deg F.

d, = fluid weight outside casing when cement sets, Ib per.gal.Adc = change in fluid weight outside casing after cement sets, Ib per

gal.- d, = flu id weight inside casing when cement sets, Ib per gal.

Ad, = change in fluid weight inside casing after cement sets, lb ' per Igal.

De = outside diameter of casing, in. (A c = 0.785 D: s q in.).D, = inside diameter of casing above cement top, in.

For term B 4 use inside diameter below cement top.For term W, use average inside diameter in string

(A , = 0.785 DI" s q in.).w = weight of casing in cemented zone, Ib per ft.wr = weight o f casing above cement top, Ib per ft.w" = average weight of casing in string, Ib per ft.dc = cement slurry weight, Ib per gal. 'L =.distance from cement top to casing hanger, ft.h = distance from casing shoe to cement top, ft.

Note: All A or change quantities plus when increase and minus whkndecrease.

' Fig. 1-Parameters o f the Buckling-criterion an d Wellhead -load Equations


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Two sets of equations are given, one for fluid weightsexpressed in pounds per gallon and a second for fluidweig hts expressed. in pounds p er cubic foot. Symbolsused in the equations are defined in Fig. 1. Negative'values of the buckling-criterion expression indicate thatslack-off i n the anlo unt indicated c an 11e permitte d with-out causing buckling of the casing.In using the equation, an estimate is first made ofth e down-the-hole conditions which exist o r will exi st a tthe time the cement sets sufficiently to fis the casingshoe. Second, a n estima te is made of the change in thoseconditions which will occur during the drilling or pro-ducing history of the well. These estimated initial andchanged conditions give ralues for the parameters inthe buckling-criterion equation. Solution of the equationyields the required pickup or allo\ilable slack-off whichshould be applied a t the ti me the casing is hung.I n the actual case, several solutions of th e equationwill be necessary to evaluate the optimum hanging loaclsfor precluding buckling during the several drilling, pro-ducing, or workover conditions. For example, duringdrilling below the shoe of the casing string, a changein the inter nal mud weight ancl th e average t emperatureabove the cement toll may occur. This will require acertain hanging load to preclude buckling. When thewell is on production the same casing string will besubjected to an environment different from the as-cemented or drilling-ahead environment. This productionenvironment will also dictate an optimum hanging loadfor precluding buckling. The same holds true for work-over conditions. A selection of the largest of the severaloptimum hanging loads will insure that no buckling ofthe casing will occur under any of the conditions in-\-estigatecl.In Appendis C the buckling espression from Table 1ha s been expressed a s the sun1 of 10 terms. Each tern1represents the effect on buckling of a down-the-holevariable. Nomographs are supplied in Appendix C forevaluating the 10 terms. The amount of pickup or slack-off required to preve nt buckling is enual to t he s um ofthose term s ,which apply to the condition investigated.

The nomographs express the 10 terms in the units ofljounds. A conversion nomograph is supplied in AppendisC for converting the pickup or slack-off in pounds toinches.

The buckling equation has been derived for single-weight casing strings. A stud y of equations for combina-tion-weight strings indicates that no significant erroris introduced in using the single-weight equations foreval uati ng buckling tendencies of comlnon d esigns ofcombination weight strings.

Certain considerations tnay be given to combinationstri ngs in the equations of Table 1. In the term hzu, w isdefined a s the weight per foot of casi ng below the cementtop. In combination weight strings zu nlay have two ormore values below the cement top. I n th is case the t enn ,Rzu, should be take n a s equal to th e weight in ai r of pipebelow the cement top. I n a similar manner t he factor w'i n the temperature-effect term may be taken a s the aver-

age weight of casing above the cement top: The valueof D,,nside diameter, may be selected to correspond to,t he weight of pipe of t he longest section above the cementtop. 11;general the accur acy of t he buckling theory doesn o t justify a more esa ct solution.It will be noticed th at t he-equat ions assume th e freezepoint to be at the ce~ nentop. Freeze points determinedby stretch curves and strai n instivmen ts are frequentlyfound to be considerably above the cement top. In gen-eral, after setting casing, the freeze point moves very.rapidly from t he cement top t o the 'shoe of t he nex tlarg est size of casing. This high freeze point i s believedto be of a temporary nature, and the effect of a pro-longed change in the environment of the casing willeventually be felt a t the permanent freeze point, the topof cement. Oberg and Masters6 determined by strainmeasurements on the top joint of casing in two wellsthat the freeze ~ o i n t t the shoe of the surface s tr ingwas indeed of a temporary nature. They concluded

tha t ". . . freeze points above the top of the cementnlay not hold th e casing in a fixed position. I n choosinga landing tension in such wells, all of the casing to thetop of t he cement should be considered a s possibly beingfree to move."If it is concluded that a permanent freeze point hasbeen established above the top of the cement, the buckli ngequations are still valid provided th e value of IL s takenequal t o th e distance fro111 the casl ng shoe to t he pe r-#man ent reeze point, th e value of L is taken equal to thedistance from the pernlanent freeze point to the casinghanger, and the value of dc IS taken equal to the averageweight per gallon of the fluicl and cement-slurry colunmbelow the permanent freeze point.

WELLHEAD-LOBD EQUATIONThe selected hanging load for the casing should becompatible not only with buckling requirements, but alsowith the stren gth of the casing itself, the str ength of t heouter casing strings, and the load-cariying capacity ofthe casing-hanging assembly. Several manufacturersar e providing casing-hanging assen~bli eswhich can re-sist loads larg er than th e joint st reng th of casing. There-fore the load on the assembly is not as critical now a s i nthe past. Equations f or use in determining the wellheadload a re given in Table 2 fo r fluid weights expressed i npounds p er gallon and pounds per cubic foot. The pa ra-meters i n the equation,ar e identical to those used in th e

buckling-criterion equations.The wellheacl-load equation can be used to evaluatethe load a t any time in the history of the drilling orproducing well. It, therefore, becomes a valuable aid inthe design of the casing string a s well a s in the studyof buckling.In Appendis D the wellhead-load equation fr om Ta ble2 has been espressed a s,th e sum of 12 terms. The firstterm represen ts the effect of t he casing-landing practice;i.e., so much pickup, slack-off, or no weight adju stme nta t all. Each of the ot her 11 ter ms represents th e effect onwellhead load of a down-the-hole variable. Nomographsar e supplied in Appendix D for evaluating the 11 terms.


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The.amount of wellhead load is equal to t he sum of thosetemnls which apply to the condition investigated.

The wellhead-load equation ha s been' derived fo r sin-gle-weight strings, but it can be used'sat isfacto r~ly orcombination-weight string s by procedures s ~m ll ar othose outlined fo r th e buckling equation. I t will be seenth at the suln of ternls FVs through TV6 in Appendix D isequal to the hanging w eight of the s tring while waitin gfo r the cement to set. If the casing or casing annulusis shut-in under pressure P I or P, , respectively, whilewaiting fo r the cement to set, then pa rt of terms TVs andFVlo can also be included in t he initial ha ngin g load. Bysubstituting the initial hangi ng load fo r the sum of theseterms, t he wellhead-load equation becomes quite accura tefo r combination strings.

When the plug hmnps, caution should be exercised inaccepting the load on the rig's weight in d~c ato r s thehang ing load tha t will esi st when the cement sets. Initialdr ag of t he casing, centralizers, and scratchers map beappreciable. After several hours the casing may have ,slipped fur th er down the hole and increase t he wellheadload t o th at value whicli will exist when th e cement sets.It sl~ou ld e recognized tha t a considerable amount of th e

~dr ag may still be in the casing when the cement sets. Inthis case the wellhead-load equation developed in thispaper should be adjusted by subtracting the amount of"locked-in" drag.

EXAMPLE PROBLEMA 10,000-ft combination-weight string of 7-in. OD

casing has been selected for illustrating the applicationof the buckling and wellhead-load equations. Weight perfoot, grade, and length of sections in this string areshown in Fig. 2. Terms given in Appendixes C and Dwill be usecl to arriv e a t values fo r the buckling and well-head loads inasmuch as t his will serve to point out in- ,fluence of th e various parameters . Nomographs i n Ap-pendixes C an d D can be used fo r the solution. However,in the follovling example the ter ms will be evaluated bysubstitution in order to presen t the method in detail. Thecasing will be ex amined fo r fou r down-the-hole con-ditions.1. Condition when C ement Sets(L. Bzickliny Criterion

By referring to Fig. 1 and Appendix C it will be seentha t only terms B:. BJ, and BJ apply when the cementsets. There ar e two weights of casi ng below the cementtop in th e example problem, I~ enc ehe tenn B:.1s equal toth e weight in a ir of ca sing below the cement top.

The factor D L ppears ~n er m Bq and, according toFig. 1, the value of D , or this term 1s equal to insidediameter of casing below the celllent top. Sufficientaccuracy wlll be obtained by using inside diameter of29-lb pipe even though a small am oun t of 26-lb pipe i sbelow the cement top.

Evalu ation of th e terms yields:PoundsB2-= -(30O) (26)- 2,700) (29) - -86,100B3 = +o.o4os ( r )? (3,000) (15) = +9o,ooo


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230 W: R. Cox


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. ..Bq = -0.0408 (G.lS4)"5,000) ( 1 3 ) = ,GOSOO-.56,900Thus, when th e ceinent sets, the casing can be slec$ecl off56,900 lb without causing buckling.

b. 1~T;elllrcc~docrdTerins T V j through T'V6 in Appendix D shoulcl he usedto cleternline the h ang ing load of th e casin g when t heceinent sets. If the casing or casing annulus is shut inunder a pressure PI or P,.,espectively, when waitingfor cement to set, then ternis IVy and W I Omust also beinclucled to determine t he h ang ing load when the ceinentsets.Term IVs for coinhination-weight strings is equalto the weight in ai r of the entire string. Tern1 T176 in-cludes a factor DL hich for combination strings shouldbe taken approsiinately equal to the average insidediameter in the str ing. For this tern1 the inside cl ~ a ~ n e t e ~for 26-lh pipe will be used.Evaluation of the te nn s yields:

, ~Po~lmdsm73 = (23 ) (5,500) +(26) (1,500)

+ 29) (2,700;) = + i s i , s o oW q = -0.0408 (7)' (5, 000 ) ( 15 ) = - 0,000Ws = -0.0498 (7)' (7,000) (1 3) = -1S1,900l v f i = +0.040S ( 6 . 2 7 6 ) ~ 1 0 , 0 0 0 ) 1 3 ) = +20S,900

+1SS,600Thus, the h angin g load when t he cement s ets is 188,600 lb.2. Co~~di t ionhen ~ e e ~ e n i n gAfter setting the 7-in. OD casing at 10,000 ft, it isassu~necl ha t the hole is deepened and the inud ~v e ig l~ tsincreased from 13 to 18 lb per gal. Also, the circulatedmud will be considerably hotter from th e grea ter depths.In this esample i t is assumed th at the average tenipera-tu re of the c asing above the cement top increases 35 deg ,from the average temper ature esistln g when the cementset. These changes in environnlent introduce th e follow-ing changes i n buckling and wellhead loads.a. B ~ i c k l i n g PoundsBI = +59.8 (2 3) (5 5) = +4S,lOOBfi = +0.0286 (6.366)' (7,00 0) ( 5 ) = +40,600

+SY,700In order to offset the effect on buckling of a 35-(legincrease in average teniperature above the cement topand a n increase of 5 lb per ga l of intern al inud weight,the cas mg must he picked up 88,700 lb. When coinbinedw i t h the 56,900 Ib t ha t th e casin g corlld be slackecl offwhen cemented, the casing must be picked up a net of31,800 lh from the as-cemented position if buckling is tobe prevented when drilling ahead.b. I.T;ellheod Load PoundsWo = -59.8 (2 3) (3 5) - -48,100W s = +0.0122 (6.366)? (7 ,0 00 ) ( 5 ) = +17,300

When drilling ahead the wellhead load decreases30,800 lb. If th e cas ing wa s hu ng a s cenlented, th e well-head load when drilllng ahea d would be 188,600 -30,800= 157,800 lb.3. Condition when Test ing a LinerIf a l iner is set and i t is desired to test the l iner bypressuring the 7-in. OD casing to 2,000 psi with 18 lbper g al inud in the hole, anoth er cha nge will occur in th eas-cemented buckling and wellhead-load characteristics.It is assunled a t the tinle of testing the liner that -th eavera ge tem per atu re of t he 7-in. casing above its celllenttop ret urns to th e as-cemented value; hence A t is zero.a. Bztcliling PoundsB6 = +O.O2SC (6.566)' (7 ,0 00) ( 5 ) = +40,600Bs = +0.5'14 (G.366)".2,000) = +25,500

+66,100Thus, when t he casing is hung, the net required pickupto prevent buckling when the liner is tested is 66,100- 6,900 = 9,200 lb.If the well had been shu t in with 1,000 psi when wait-ing fo r the cement to set behind the 7-in. casing, thenthe value of AP , in term B e would be 2,000 - ,000 =+ 1,000 psi.b. TVellheacl Loc~d Pounds

= +0.0122 (6.36/;)* (7,000) ( 5 ) z +17,300TVlo = +0.!+71 (6.366)"2,000) = +.3S,200

+55,500When testing the liner, the wellhead load increases55,500 lb above the load t ha t wa s ha ngi ng oil th e eleva-tors when the cement set. If the casing was hung ascemented, the wellhead load when testin g th e line r wouldbe 188,600 + 55,500 = 244,100 lb.4. Condi t io~~hen Prod~ici i ~gn Gas LiftFor this condition the fluid weight in the casing istaken as 8.7 lb per gal and the fluid-level drop in thecasing is assumed to be 5,000 ft . No tempe rat ure cl~angeis assuinecl froi n the 'as-celnented temp era ture . Th esupply ga s is i~ljectecl n th e casing a t 900 psi.n. Bzcekling PoundsBfi = +0.02SG (6.366)' (7 ,000) (-J.5) = -34,900B y = +0..314 (6.36 6)P (9 00 ) = +11,500B lo = -0.0163 (6.366)"8.7) (7 ,689 ) - -44,100

-67,500Thus, when t he casing i s hung, t he masirnuin slack-offth at can be allowed i n order not to cause buckling a t thetime the well i s on gas l ~ f ts - 6,900 - 7,500 =- 24,400 lb. %b. Wel lhenc l Load 6 PounclsTi's = +0.0122 (h'.SGG)"(7,00 ) (-4.5) = -14,900W I O= +0.471 ( G . S G G ) ~ ~ O O ) = +is ,aoow12 = -0.0245 (6.366)"S.7) (3 ,210) = -27,700


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When the well is producing on gas lift the wellheadload decrease s 25,400 lb fronm the ha ng ing load when thecement sets. If the caslng was hung as cemented, thewellhead load when on gas l ift would be 188,600- 5,400= 163,200 lb.5. Summary of Esa mple ProblemI n t he f o~w onditions esanmined, the required masi-mum pickup occurs for the condition of deepening thewell. The \vellheacl loads a re shown in Fig. 2 fo r the fo urconditions if this maximum pickup of 31,800 lb is applied.The minimum clesign factor against joint pullout is 1.45.This occurs when th e liner is tested.In order to hang the casing with 31,800 lb additionalload it is required to pick up the casing 13.4 in. fromthe as-cemented position. This can be detelnlined on theconversion nonlograph i n Appendix C. If a t the timeof hanging casing a temporary freeze point should esista t the shoe of th e surf ace strlng, a t say 2,000 ft, then apickup of 13.4 in. will requ ire 112,000 lb aclditional pullinstead of 31,800 lb. This 118,000 Ib can be determinedfrom the conversion nomograph by entering with. zu'= 23, L = 2,000, AL.= 13.4, and solving for AS . (In theactual solution the nomograph w as entered with AL =1.34 and th e value of AS wa s found to be 11,200 Ib, or t heeq u~ va len t f 112,000 Ib for AL = 13.4.) A pickup of112,000 lb will increase the hanging load to 112,000 +188,600 = 300,600 111 and th e design fac tor aga ins t pull-out would be 400/300.6 = 1.33.If th e freeze point at the shoe of the sui-face strin gis temporary, the large hanging load of 300,600 lb willdecrease to 220,400 lb a s th e casing adjusts down to t hepermanent freeze point a t the cement top. If th e shoeof t he surface str ing is the permanent freeze point, thena pickup of 112,000 lb would mean th at 244,100 f - 112,000= 356,100 lb would be on the casing hanger when theliner is tested. The design factor against pull-out wouldbe 4001356.1 = 1.12. This would be a very undesirabledesign facto r fo r tension.A pickup of 31,800 lb with a temporary freeze pointa t 2,000 f t will require (13.4) (217) = 3.8 in. pickup.When t he c asing ad justs dowim to t he cement top a t 7,000ft , the ne t pickup in pounds will be (31,800) (21.7) =9,100 lb. This would mean that the casing mould stillbuckle when drilling aheacl with 1 8 lb pe r gal mud andwould be on th e verge of buckling when t he line r is tested.Buckling may not occur when the liner is tested if thesho rt interval of time required for testin g is not sufficientfo r the freeze point a t 2,000 f t o move hack down to th ecement top.

BUCKLING O F TUBING ON PACKER, The buckling ancl wellhead-load equat ions can b e usedto examine tubing set on a packer. For tubing theparameter h. is equivalent to the length of packer an dniay be taken as zero. The value of L is then the dis-tance fro m packer t o tuh,ing ha nger.Fo r studies of buckling of t ubi ng in pumping wellsthe pap er by Lubinski ,dnd Blenkani' will serve a s a nexcellent reference. lt'is of inte res t to note th at theLubinski and Blenkarn general equation (5) fo r bucklingof tubing can be determined from th e buckling expression

Coxpresented in Table 1 of this paper by exchange of equiv-alent symbols and by correcting for a fluid-level dropth at exis ts when the packer is set. Th e fluid-level correc-tion is made by evaluating buckling terms. B,?ancl Blofo r the condition when the packer is set and s ubtrac tingthe ir sun1 from the buckllng conclltion when the well ison pump.

SUMMARY AND CONCLUSIONS1. The key factors that affect landing of casing areth e buckling tendencies of th e casing and th e intensityof wellhead load that will occur in the life of the well.2. Equati ons and nomographs presented in this pap erar e adequate fo r use in examining buckling and wellhead-load characteristics under most down-the-hole conditionsth at will occur in th e life of th e well.3. Location of t he pemnmanent free ze point is a n im-portant consideration in the casing-landing problem.Limited field infoinlation indicates the p ermane nt free zeljoint t o be a t the cement top. However, temporary andpermanent freeze points may esi st above the cement top

and these require attention when adjusting the casingpickup or slack-off prior to landing.4. High teinperar y freeze points may preclude land-in g with adequate pickup to prevent buckling under cer-tain down-the-hole conditions.5. Equations in this paper can be used for selecting,landing procedures in wells where a permanent freezepoint exis ts above th e cement top.6. La rge changes i n wvellheacl loacl ma y occur a ft erthe casing is hung. These are caused by temperature,pressure, and fluid-weight variations subsequent t o land-in g casing. Fluctuations in wellhead load should be con-sidered in the design of the string a s well a s in selectinga landing procedure.REFERENCESlAPZ Bu l 07 : Casi?lg Landing Reco?iz?)ze7zdatio?zs,Re-port of the AP I southwestern District Stu dy Committee

on Casing Landing Practice, American Petroleum Insti-tute, Dallas, Texas, 1955. Also published in The Mono-yrn))?,15, Spm~ng-S ummer 1955).2Lubinski, A: Influence of Tension and Compressionon Stra ightnes s and Buckllng of Tubula r Goods in OilFields, Proc. Ant. Pet. Ilzst. Sect. IT (Prod. BLLZ.37), 31(1951).3Bo un~ an, . A: Buckling of Oil Well Piping, Petro-lezen Engineer, 28 [61 B-60, June (1956)."linkenberg, A: The Neu tral Zones in Drill Pip e andCasing and Their Significance in Relation to Bucklingand Collapse, Drilling and Prodzcction Practice, 64(1951).

5Texter, H. G: Oil-well C asing a nd T ubi ng Troubles,Drilliwg C I ~ Z ~roclz~ctio?~ractce, 7 (1955) ; also Oil GusJ., Ju ly 4, Aug. 1, and Aug. 29 (1955).

60b erg, C. H. and Masters, R. W : The Deternlinationof Stre sses in Oil-well Cas ing in Place, Drilling a nd Pro -cl~~ct ionractice, 257 (1947).'Lubinski, Ar th ur and Blenkarn, K. A: Buckling ofTubing in Pumping Wells, Its Effects and Means forControlling it, 3. 6f Petr. Tech., March (1957).


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APPENDIX ABUCKLING-CRITERION EQUATION

In this section a single equation will be developed fordetermining the buckling tendency of cemented casing.The buckling expressions developed by Lubinski2 and byBouman3 will be examined to show th at they can be madeidentical for certain conditions.

In this p aper th e permanent freeze point of the casingstr ing is assumed to be a t the cement top. Fo r this reasonall calculations ar e based on a n assumed point of fixity atthe cement top.Lubinski's Buckling Criterion

Lubinski2 has developed his equation (13) as thecriterion fo r buckling of a cemented st rin g of casing orof tub ing set on packer. He fu rth er shows tha t the right-hand part of this equation (13) may be neglected forcommon sizes of casing an d tub ing and common fluidweights. This results in the following expression:

wherein, according to Lubinski's notation:V = ver tica l reaction of th e frozen portio n of pipe

or, the free portion (V positive when a down-ward force).

Pn = external pressure a t the freeze point.pr = internal pressure a t the freeze point.S z cross-section a re a based on outside diameter.s = cross-section ar ea based on inside diamete r.Usina the notation system as shown in Fig. 1 of this

paper, and considering conditions existing when thecement sets sufficiently to fix the casing i n the cementedzone, the following substitutions can be made in equa-tion (1) .V = hw + [Pi + di ( h + L) ] Ai - Pe + dcL + dchl AePIS = ( P , + d,L) A,P I S = (Pi +diL) AiThese substitution s yield:

h ( w + diAi- Ae) > 0 (2 )If equation ( 2 ) is satisfied, the n no buckling exists a t

th e time the cement sets.Changes in environment of the casing afte r th e cement

sets will introduce changes in the buckling tendencyabove th e cement top. In line with Lubinski's theory,these changes can be considered by adding to equation(2) three t erms to yield:h (w + diA;- A,) + AV + A P ~ S- pp > 0 (3 )wherein: AV, Apt, and Apf are the changes after thecement sets that occur in the vertical reaction, externalpressure, an d internal pressure a t the cement top, re-spectively.

I n computing the effect of the three delta or chang eterm s in th e buckling expression, equation ( 3 ) ' it is con-venient to assume tha t the casing is cut a t the cement topso as to result in a section of c asing of length L hanging

free from the casing hanger; and fu rth er to assumeth at th e end of t hi s free section of casin g is closed. Th isimaginary closed-end section of casing will change inlengt h when subjected to changes of i nternal an d ex-ternal pressures occurring after the cement sets. If avertical force F is applied to the bottom of th e imagin aryclosed-end section of casing so as to re tu rn th e bottomof th at section to the exact position it occupied when thecement sets, then i t will be seen tha t:

F = AV + PIS- ~ I S (4 )an d the buckling expression, equation (3) , becomes :

h (w + d,Ai- A,) + F > 0 (5)The value of F is positive when it acts downward on

th e section of casing above th e cement top.Bouman's Buckling Criterion

Bouman3 has developed his equation (11) as thecriterion f or buckling of a cemented str in g of casing.This equation is valid fo r examining the buckling ten-dency a t an y cross section above the cement top. By sub-sti tuting 1 = 0 n Bouman's equation (11) a n expressionresults fo r examining the buckling tendency a t only thecement top. If the expression is satisfied, then no buck-ling tendency exists a t the cement top or a t any crosssection above th e cement top. T o confol-m wit h no tation sused in this paper, ?u is substituted for d, ( A , - i)used in Bouman's pap er. These subs titutio ns yield:

Bouman defines C a s the force acting on the bottom ofan imaginary section of length L hanging free andwith closed end a t the cement top. Bouman defines V a sth e vertical reaction force which occurs a t the cementton a s the re sult of chana es in environment above thecement top after the cement sets. Therefore, C + V i sequivalent to F used in this paper, and Bouman's buck-ling expression can fur th er be reduced to:

h (nu + diAi- Ae) + F > 0 (7 )Equations (5) and (7) developed from Lubinski's and

Bouman's criteria, respectively, are identical.Evaluation of the Force F

The force F in equation ( 7 ) consists of various com-ponents which relate the effect on buckling tendencycaused by environment changes after the cement sets,such a s hangin g procedure and changes of fluid weight,fluid level, temperatu re, a nd p ressure. These componentsF1, Fz, . .Fs ar e evaluated in the subsequent p arag rap hsby procedures similar to those used by B ~ u m a n . ~1 . Change in Weight per Unit Volume and Drop ofLevel of Fluids Inside Casing

If after the cement sets, the internal fluid weightchanges an amount Adi and the fluid level drops anamount n in casing which is assumed Lo be free and


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with closed end a t the cement top, a n elongation wouldoccur a s a consequence of axial, stres ses c au se d by a nas ia l force a t the closed end of t he casing. Thi s force is:A , L a d,- , n ( d + Ad,)

The component of F required to balance this elongationis : - , LAdr + Atn ( d + Ad,)

Furtherm ore, an elongation of the ca sing would occura s a consequence of tangent ial an d radi al st resse s causedby th e change jn int ernal fluid weig ht an d fluid-level drop.In computing this elongation z will represent verticaldistance measured fro m top of t he casing.a. Elongation from z = 0 o z = n.The radial pressure change in this region is --d,z. A ta distance z from t he top of t he casing, considered a s athick-walled cylinder, th e suin of the additional ta ngen -tial stress ut and radial stress ur is:

~t + UT = - 2A i~ l z z / ( Ae - , )The unit elongation a t dep th z is:

[z =- p / E ) ( ~ t ~ r ) ( 4 p / E ) C A T / ( A e - , ) ] d zWll . ere in:

p = Poisson's ratio for steel.The tota l elongation AL1 from z = 0 to z = n is:

?1A L I = j Z dz = ( p / E ) C A I / (A c- , ) ] n 2 d ,0b. Elongation from z = n to z = L.

The radial pressure change in this region is zAd, -n ( d l + Adl) .ut + u , = C 2. 4 , / ( Ae - , ) ] [ Z Ad , - L ( d l + A&)]& = - ( p /E ) [A1 / ( . 4e - t ) ] [Z A il,- L (d l + Adz)]L /A L , = ( [ r : (7, = ( p / E ) [ . 4 , / ( A e- , ) ] [ 2 n ( L- )

n ( d l + ~ c l , )- d , ( L e- v]c. Total Elongation o = 0 to o = L.

AL = ~ L I AL e = ( p / E ) [ - 4 t / ( A e- t ) ][? L ( L- ) el,- ( L- ) e Ad,]

The conlponent of F required to balance this elonga-tion is :-AL ( A ,- , ) E / L = ( - p /L ) A, [n ( 2 L - ) dl- L- )%cll]

The total component of F required to balance thechanges in fluid weight and fluid level inside casing is:F I = -0.7L A, Ad, + A, ( d , + Ad,) r0.41~+ ( O . SnP/L ) ]

(8)W h e r e i n : p, for steel, has been taken a s 0.3.

The effect of n on the buckling tendency of casingabove the cement top is such t ha t ?L should never be sub-stituted in equation (8) with a value greater than L,even though the casing may be completely evacuated.2. C I ~ c ~ n g en T*i'eigltt pe r h i t Volztm e ctnd Dr op of L eve lo f F l~ i i e l sO u t s i d e C a s i n gBy a procedure sim ~l aro th at used fo r deterinining F I

the total component of F requirecl to balance changes influid weight and fluid level outside casing after thecement sets can be shown to be:F Z= +O.7L Ae Ade- e ( d ef de) [0.4?1tf O. ~ W Z ' /L ) ]

(9)3. C l ~ a n g e n S r ~ r f a c ePress lwe I l l s ide and Ozi ts ide .C a s i n g ,If, a fte r the ceine~lt ets, the surface internal pressurechanges an ainount A P, and the surface external pres-sur e changes an amount A p e 011 casing which is assumedto be fre e and with closecl end a t the cement top, a nelongation would occur as a consequence of a si al s tre ssescaused by an a si al force a t the closecl end of the casing.This force is AP , 4 ,- P,. A,..The coml>onent of F recluired to res ist this el ongationis- P , A l + AP, A, .The elongation A L caused by radial and tangentialstres ses may be computed a s follows:ut + u, = 2 (AP, ,- p t. 4 , ) / ( A e - I )[z = - P I E ) ( ut + ur)LA L = J Ez d z = - 2 p L / E ) ( u t + a,)

0The coniponent of F required to balance -thi s elonga-

t101l S - A L E ( A e- I ) / L = + 2 p ( A P , A ,- pe Ae )The total component of F required to balance thechange in internal and external surface pressure is:4. C11an.ge o f Avercrge Te~ ~p er cc t cw ef C as ingIf, after the cenient sets, the average temperature 01the ca sing above the celllent top changes a n amount At incasing assunlecl f re e a t the cement top, a n elongationwill occur of the amount:

A L = ALAtT Vl~ e re in

A = coefficient of therm al exp ansion of steel.The co~nponent f F required to balance this elonga-tion is:

-A L ( A , - , ) E / L = - E ( A e - l ) AtW h e r e z n :

? E = 30 X 106 x 6.9 x = 207 psi per deg F.A, - , = A (cross-sectional ar ea of c asing body).Fo r normal sizes and weights of casing used 111 inter-~necllate nd production strings, the cross-sectional areaof t he casing bocly, A, nlay be taken a s equal to 0.289w1,where 20' is the nominal weight per foot of the casingabove the cement top. The component of F for tempera-ture change At is then:It should be noted t ha t th e symbol 7u was usecl in thefirst section of this appendi x to designate the nominalweight per foot of casing below the cement top. Whenconsidering buckling causecl by a temperature change,only th at p ar t of th e casing above the cement is effective.For this reason r c~ ' has been used here to differentiatefroin .lo. For single-weight strings tu' is equal to 2u.


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5. Pick~cp .r Slack-off b e f o ~ e [c.?lcliny - . . . .The amount of pickup' or slack-off before landing

caslng can be taken into account 111 the value of F by thetern1 :

F j = AS (12)TVh e~ ei ?z

AS = the anlount of pickup in weight units (nega-tive values of AS incl ~cat e lack-off.. .

' Expansion of the Buckling Criterion, Equation (7 )Ecluatlon (7) was developed to deternline the buckling

tendency of cemented caslng. This equatioq contains atern1 F which has been evaluated in te rms of conlponentsF1, Fc, . .F s. An espressi on will be rleveloped ,here whichincludes the components F1 , Fa , . . Fs and which can beusecl in exanlin ing the gene ral case of buckling tendencyof cemented casing.

S u b s t ~ t u t ~ n ghe value of F , , F I ', . . F j for F equa-tlon ( 7 ) yields:11, (10 t: c At-clc Ae)-0.7 L A , ~ c l ,+ A , ( d l + ad, ) [0 .4n + (0.31r"/L)]+0.7LAe Ade- e ( d , f el,) [0.4,)11.+ (0.311~"L)]+0.4 (Ae Ape - , Apt)-59.8 ru' At+ a s > 0By r earrangin g .and inaking the substitutionsA , = !1.;85 DF2,A, = 0.785 Dt2 he espression hecomes:

AS =j ,5,9.S iO' At - rtc3+0. ;85 D,Vhd, - .7LAclF- 0.4AP,

+ (d e + Ade) (0.41 )~+ O..??n"L)]-0.785 D1Vltdi - .7LAdI- .4APt

+ ( d , + ad , ) (0.411+ 0 . 3 n 2 / L ) ](13)

This means th at no buckling tendency mill es is t a s longas the p ~ck up f the casing, AS, in force u n ~ t s eforehanging is g reat er th an the valde indicatecl on the right-hand pa rt of t he espression. A negative value inclicatesthe c asmg m ay be slacked off a n amou nt not to esceeclth e absolute value of t he espresslon.

The slack-off or pickup inay be conlputecl in lengthunits a L by multiplying the espresslon by L / A E or byv".46L/ZUfE.

Ecluation (13) is not dimensionally correct f or fluiclweights espressecl in pouncls pe r ga llon or pounds pe rcubic foot. If the fluid we ~g ht s re expressed In pounds,per gallon, they may be converted to p o ~ ~ n d ser squareinch per foot by mult ~ply ing y the factor 0.05195. Thisconverslon fact or is included i n th e first two expressionsgiven in Table 1. Hence, fluid \veights expressed inpounds per gallon may be substituted d~rectw ~ t h o u tchange.

If the fluid weights are espressed in pounds percubic foot, they may be converted to pounds per squareinch per foot by d~v ~cl ingy 144. This converslon fact or isincluded in the second two espressions in Table 1, andno further conversion of units of fluid weights is neces-sary before substituting in the espression.

, A P P E N D I X BWELLHEAD-LOAD EQUATION

The development of the equation f or use in determin-ing the wellhead load at any time in the history of thewell is given following.Wellhead Load a t Time Cenlent Se ts

By referring to Fig. 1 it can be deterlnined that thewellhead load a t the time t he cement sets is equal tothe weight of the entire string in air plus the weightof the internal fluid and the internal pr essure a t the toptiines the area based 011 ihside diameter, and minus theweight of the clisplacecl fluid and the esternal pressurea t the top times the a rea based on o uts ~de iameter. Asmall er ro r is introduced i n computing the \\.ellhead loadfo r combination string s by this method but the e rror i s,negligihle in most cases. The algebraic espression forth e ~vellheacl oad, W c ,a t the time t he cement sets is:,TVc = 7 ~ " 11 + L ) f .785 D,' (h d l + Ltlr + Pl)

-0.785 Dc2 (llcl, f cZ, + P C )In this expression the symbol ru" has been used to

differentiate from Z L J , the nominal weig ht of cas ing belowthe cement top, and .to', the noniinal we ~g ht f caslngabove the ceinent top. For combination-weight stringsthe sylnbol zu" designates the average nominal weightof casing in the string. For this reason the termzu" (IL+ L ) 1s equal to the total we~ghtn ai r of theca s~ ng tring. F or single-weight strings, w", rut an d ruar e equal.Changes in Wellhead Load aft er ceme nt Sets

Changes in the load a t the cement top af te r the cementset s hav e been computed in A.ppenc11s A,. assu ming theend of t he ca sing a t th e cement top i s closecl. Thechange 111 the wellhead load is identical to the changeIn the load a t the cement top esc ept caslng must heconsiclerecl open-elided. T he correct ion for open-enclconditions is made hy sul ~tr act lnghe effect of closecl-endcond ~tio ns ro111 th e value of F determined in Appendis .A. This yields:


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236 W. R. Cox

AW = -0.7L A i Adi + Ai (di 4- Adi) [0.4n 4- (0 .3n 2/ L) ] +0 .7L A , Ad ,- , ( d , + ad,) [0.4?n -!- (0 .3?n2/ L) ]-59.8 w' t + 0.4 (AP, A , - Pi Ai) + AS - [ n Ai di- L- ) Ai Adi - A , d u+ ( L- ) A , a d ,-

Ai APi + A , AP,]Wellhead Load for Any Condition in the History

of the WellBy combining the equation for wellhead load W c fo r

the condition when the cement sets and the equation forthe change in wellhead load AJV after the cement sets,th e equation fo r wellhead load, JV, for a ny condition inthe hi story of th e well is obtained.

Equation (14) is not dimensionally correct for fiuidweights expressed in pounds per gallon or pounds per

cubic foot. The wellhead-load equati ons in Tab le2 includeconversion factors such that fluid weights may be sub-stitute d in units of pounds per gallon in the first equationand pounds per cubic foot in the second equation.

Similar to the buckling-criterion expressions, the well-head-load equations in Table 2 are for single-weightstrings. However, the err or involved in usin g these equa-tions to determine wellhead loads for combination strin gsis small.

W = W , + AW= AS - 9.8 w' t 4- w" 114- L )- .785D,2 [hde 4- Ldc + 0.3 Lad e+ P e + O.6APe- d e + Ad,) (0.6m- . 3 m 2 / L ) ]+ 0.785D,2 [hd, + Ld, + 0.3LAd, 4- P , 4- 0.6AP1- d , -!- Ad,) (O.(in- ..?n"L]

APPENDIX CNOMOGRAPHS FOR SOLUTION OF THE BUCKLING-CRITERION EQUATION

The buckling criterion equation for pickup in poundsand fo r fluid weights in pounds per gallon may beexpressed as:

Term ValueB I = +59.8 W' AtB,o = -hwB3 = 4-0.0408 DL2 hdcBq = -0.0408 D,Vld,Bs = -0.0286 DL2 LAdeBg = 4-0.0286 Dr2 LAdtB: = -0.314 Dp2 APpBs = +0.314 DL2 APzBg = 4-0.0163 D ev d e + Adr) (?n 4- 0.7.5?n"L)Blo = -0.0163 DZ 2 d , 4- Ad,) ( n + (0.75n"L)

AS > B , + Bz + B3 + . . . . . . . . B I Owhere the 10 terms ar e a s defined following.

Physical Description of Factor Influencing BucklingTemperature effectWeight of casing hanging below cement topCement-slurry weightMud weight inside casingChange in mud weight outside casingChange in mud weight inside casingChange in surface pressure outside casingChange in surface pressure inside casingDrop of fluid level outside casingDrop of fluid level inside casing ( n Z L )

Nomographs have been developed for solving the I term B6 an increase of mud weight inside the casing

- .th at th e proper sign of the term is used. F or example, in value for Adi and the sign of BF s negative.

several terms of t he buckling-criterion equation. Th esenomographs ar e given in Fig. 3 through 9 (p. 238 to 244).caremust be taken in use of the nomoaraDhs to assure

gives a positive value Adi and the sign of B6 POSi-tive. A decrease of mud weight inside gives a negative


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APPENDIX DNOMOGRAPHS FOR SOLUTION OF THE WELLHEAD-LOAD EQUATION

The wellhead-load equation f or fluid weights in pounds W = W I + W Z+ Ws + . . . . . . . W I Sper gallon may be expressed a s: / where the 12 terms a re as defined below.

Term ValueWl = + A SW2 = -59.8 W' 4 tWs = +w" ( h + L )TVr, = -0.0408 De2 l~ d eTVs = -0.0408 D,"deW 6 = $0.0408 D,"lz + L ) d lW7 = -0.0122 DL2 LAdrWe = $0 .01 22 DL2 LAdtWg = -0.471 Dp2 ( 4 P e + 1.G7 Pe)Wlo = $0.471 DL2 Apt + 1.67 PL)Wll = $0.0245 De2 (de + 4 4 ) ( m- . .5m2/L)W 1 2= -0.0245 DL2 d , + 4 d , ) ( n- .5n91L)

Physical Description of Factor InfluencingWellhead Load

Pickup when hanging casingTemperature effectWeight of entire string in a irCement-slurry weightMud weight outside casingMud weight inside casingChange in mud weight outside casingChange in mud weight inside casingSurface pressure outside casingSurface pressure inside casingDrop of fluid level outside casingDrop of fluid level inside casing ( n 7 L )

Nomographs have been developed for solving the I in term We an increase in mud weight inside casingseveral te rms of t he wellhead-load equation. These nomo-gr aph s ar e given in Fig. 10 through 15 (p. 245 to 250).Care must be taken in use of the nornographs to assure

gives a positive value for Adi and t he sign of W8 is posi-tive. A decrease of mud weight inside gives a nega tive

- .th at the proper sign of the te rm is used. For example, I value for Adi and th e sign of We is negative.

DISCUSSIONH. M. Krause, Jr. (Humble Oil & Refining Co., Hous-

ton, Texas) (written ): I n 1955 the AP I SouthwesternDistrict Stud y Committee on Casing-land ing Practiceconcluded their work with the recommendation thatcasing be landed in th e casing head a t exactly the posi-tion in which i t was hangi ng on th e hook when the cementplug hi t bottom. This recommendation applie s to all wellswhere mud weights do not exceed 12.5 lb per gal; wherestandard design factors a re used in tension and collapse;wellhead equipment is available to permit hangingweight equal to the tensile stren gth of t he casing on thehanger without damage to the casing; and where thejoint s tr eng th, in compression, of t he top section of t hesurface casing is sufficient to withstand the loads im-posed by landing t he casing a s cemented, plus the weightof the tubing, plus induced loads that may be broughtabout by futu re operations.

I t was concluded afte r much st udy th at t his practiceshould afford the gr eate st amount of protection for a ndservice from API casing in a very high percentage ofwells drilled in the Southwestern District, and th at con-clusion is still valid. However, i t was recognized a t t ha t

time th at a number of wells ar e drilled and operated tha trequire special consideration in land ing casing and refer-ences were made to th e work of Lubinski and others inarriving a t casing-landing programs for wells wheredesign factors are low, where extreme pressures areencountered, where excessive mud weight s a r e necessary,or where abnormal ope rating conditions exist.

Mr. Cox is to be complimented on the fine work thathas been presented in this paper. He ha s presented a toolthat should prove to be a significant contribution tocasing-landing procedure, particularly for the deepabnormal-pressure wells that are becoming more fre-quent in the API Southern District. We who are con-cerned with thi s problem ca n thank Mr. Cox fo r the com-pleteness of his paper and particularly for the nomo-grap hs which greatly simplify a rather lengthy and time-consuming calculation procedure.

As pas t chairman of the Study Committee on Casing-landing Practice, it is most gratifying to acknowledgethe work th at is being done to furnish th e missing linksin the fast-gr owing chain of understanding and practicesfo r the landing of casing in order to gain t he maximumutility from that casing throughout th e life of t he well.


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EFFECT OF TEMP ERATU RECHANGE ON BUCKLING.0 , - 49.8 ' A ~

EXAMPLE :w' = 23 l bs / f t .

Fig. 3


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EFF,ECT OF WE IGH T OFCASING ON BUC KLIN GEXAMPLE:h = woo t.

I 250 7= 29 1 bs. / f t

Fig. 4


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240 W. R. CoxEFFECT OF F L U I DWEIGH TS. ON BUCK LING8,' *0.0408 D hdc8,' -0.0408 D i2hdi

EXAMPLE:4' 7 n.h = 3,000 t .dc= 15 1 bs./gal.Bs= +90,000 s.

Fig. 5


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E FFE C T O F FL U I D . W E I G H TCHANGE ' O N ~ ~ U C K L IGB5' -0.0286 0:Lbde

- B6' +0.0286 D ~ ' L A ~ IEXAMPLE :Di' 6.366 in.L = 7,000 f 1.

ad i ' '5 Ibs./gal.&= +40,600 bs. 400

3003

-L IO L- 0In- 2E XI 1

I I lFig. 6


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24 2 W. R. CosEFFE CT OF SURFACE PRESSURECHANGE ON BUCKLINGB,= -0.314 ~ e ? pe88: 40.314 D API

, EXAMPLE:

Fig. 7


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EFFECT OF F LU ID L E V E L .CHANGE ON U C KLIN G

- 4; 10.0163 D +dQl lm+0.75$)6,f -0.0163 Di' (d l dJ ( n 0.75 f2 1

EXAMPLE: iI = 6.3661n.d i t ~ d i 13- 4.3 = 8 Ibs./qol.- n - 5,000 f 1.

I - 2Fig.' 8


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244 W. R. Cox

Fig. 9


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100 EFFECT OF TEMPERATURECHANGE ON WE LL HE AD LOAD

90 w*= -59.8w'atEXAMPLE 8w' = 23 bs./ tt.

Fig. 10


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, ,246 W. R. CoxEFFECT OF WEIGHT O FCASING ON WE LLH EADWS = twn(h+L)

EXAMPLE: 1,500' w,": 26Ibs./ft.

h = 3,000 f t.L = 7,000ft.W3=+260,000 bs. IQOO

800700600

LOAD

Fig. 11


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Idc l d e I d , IEFFECT OF FLUIDWEIGHTS ON WELLHEAD LOADWI= -0.0408 02 hdcWs= -0.0408 0c'~drWd= +0.0408 Di2( +L)di

Fig. 12

EXAMPLE:Di ' 6.276 in .

h+L = 3,000t 7,000d l = 13 lbs./gol.W, = +209,000 b r

10,000 ft .3,000 ---=--2,000 4-----

--4-2k+ \

\C \ii?Q)0a3 -'2 -0u'C.- -5 4rC %O -CrC -0 0C CQ) .=-I +

V)- IC.t 0

-. 2 0 0 \ q \Y3 \-L -0 -

100903 80C.- 70Eu 60r" ""0 -7


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24 8 W. R. COXEFFECT OF FLUID WEIGHTCHANGE ON WEL L H EAD L OADW,= -0.0122 DL rideWs' t0.0122 D?La dEXAMPLE 300

-, = 6.366 in. -L = 7,00011 -ad1 = + 5 bs./gol. 2007-WB' t I 7 , 3 0 0 1 b $ ' -150----I 0 090807060,//---I. I

Fig. 13


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EFFECT OF SURFACE -OIV WELLHEAD LOAD%= -0.471 D : ( A ~ + 1.67W$ t0.471 D~ '( AR +I .~ ? R)EXAMPLE:D = 6.366in.

AP i = + 2,00O~.i .4 = 0W I ~ 38300 lbs.

Fig.


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EFFECT O F F L L l lD L E V E LCHANGE Old W ELL HEA D LOADWIF +0.0245 D43(de & d c ) ( m - 0 . 5 ~ ~ )Wn= -0.0245 D z ( d i +adi)(n-0 .5 f )

EXAMPLE: . .D I= ,6.366in.di t ~ d i ' 13-4.3-8.7 1 bs./~Ol.n = 5,000 ft.L = 7,000 ft. I 000 -

n-o.sf= 3,210 t. oWit= -27,700 Ibs. ?-u

500400 -

Cox Buckling and Wellhead Load Paper

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