Cement Sheath Stress Failure K .... Goodwin, SPE, Mobil E&P Services Inc., and R .... Crook, SPE, Halliburton Services Research Center

Summary. Observation of the sudden appearance of annular pressure in wells exposed to high temperature changes or excessive internal casing pressure prompted a laboratory investigation to simulate conditions under which cement sheath failure could occur and thereby define the causes, characteristics, and limits of the problem. Cement sheath failure is manifested by interzonal annular-fluid movement and abnormally high annular pressure at some point behind the casing up to and at the surface. Cement sheath failure can be observed in any producing area where excessive flowing temperatures exist at the surface or where excessive internal casing test pressures are used. The detrimental effects of cement sheath failure are numerous and may include lost revenue from lost production, potentially hazardous rig operations (especially when annular isolation loss creates shallow-water sands supercharged with gas), and potentially hazardous producing operations. Exposure of steel casing to excessive temperature increases or internal test pressures causes diametrical and circumferential casing expansion. This circumferential force creates a shearing force at the cement/casing interface, causing failure at the cement/casing interface or radial fracturing of the cement sheath from the inner casing surface to the outer casing (or borehole) surface.

Introduction In several operating areas, annular-flow problems not attributable to common annular-flow-after-cementing definitions are experi­enced. This paper is not intended to discuss short-term annular­influx problems. Long-term annular-influx problems usually ex­perienced after a well begins producing represent a completely different set of circumstances. Long-term annular influx generally occurs after excessive casing test pressures once the cement sheath has set and attained some compressive strength, or following ex­cessive temperature changes resulting from excessively high produc­ing temperatures or steam-injection temperatures. Long-term annular influx has long been believed to be caused by either ce­ment sheath failure or hydrostatic pressure loss in a channeled (bypassed) mud column after the weighting material has settled out of the drilling mud.

An extensive investigation was begun to determine the reasons for these long-term annular-flow phenomena. Analysis of cement­ing systems and well cementing techniques concentrated on the use of "good cementing practices" (i.e., pipe movement; effective casing centralization; sufficient circulation times and rates before cementing for mud and hole conditioning; and sufficient volumes of water, washes, or spacers for hole cleaning). Such current ce­ment sheath evaluation devices as fluid-compensated bond logs or ultrasonic-type logging devices were used to determine the pres­ence of primary cement channels. After analyzing only a relative­ly few problem wells, it became evident that something drastic had happened to the cement sheath in each well. In all the wells inves­tigated, clean cement was circulated to surface with no indication of lost circulation or fallback; however, the presence of a cement sheath was not evident.

The only evidence of cement in the annulus visible on the bond logs was an approximate 50% decrease in amplitude; no evidence of casing or formation signal was visible on the microseismogram of the bond log. The presence of a cement sheath was extremely difficult to prove on the ultrasonic logs as well. Without evidence of a viable cement sheath on any of the logging devices, the exis­tence of a mud channel in the primary cement sheath was difficult to ascertain. With the understanding that full circulation was at­tained during primary cement placement, gas-cut cement is readi­ly identifiable on ultrasonic logging devices, cement particles cannot enter formation-matrix permeability, and cement (once it has set) does not magically disappear from the annulus, it was readily ap­parent that something had destroyed the cement sheath. Further in­vestigations indicated that all these production casing strings had been exposed to either high internal test pressures or high surface flowing (or injection) temperatures.

Typically, oil- or gas-well casing strings are pressure tested to some value after the string has been cemented, or before drilling out in the case of intermediate casings, and after the cement has attained some compressive strength. These pressure tests are in-

Copyright 1992 Society cif Petroleum Engineers

SPE Drilling Engineering, December 1992

tended to ensure the mechanical integrity of the casing string. The maximum internal test pressure generally will equal some percent­age of rated casing burst pressure, assuming an equivalent annular pressure equal to a gradient of water, which decreases the assumed differential pressure created across the casing-wall thickness.

Cooke et al. 1 demonstrated that a cement column in the annu­lus exhibits full hydrostatic pressure as long as the cement is in the liquid state but that, as the cement passes through the gel state and sets, the cement-column pressure can vary from 2 Ibm/gal to the equivalent formation pore pressure covered by the cement column. Carter2 and Burkowsky et al. 3 showed that the cement­column hydrostatic pressure can be as low as 0 psi. These low pres­sure values generally occur when the cement sets in casing/casing annuli, nonpermeable laboratory-test models, or openhole sections, with no pore pressure and no water available for the cement hydra­tion/hydrolysis reaction. Carter2 demonstrated cement sheath failure in unsupported cases created by excessive internal casing pressures causing diametrical, and subsequently circumferential, expansion.

Assuming that the cement column represents a physical force (not a hydraulic pressure) against the outer casing surface, the total in­ternal casing pressure (and the differential pressure across the casing­wall thickness) becomes the sum of the surface pressure plus the hydrostatic pressure of the casing fluid. Depending on the casing­fluid density and depth, these differential pressures can range from equal to the surface test pressure to as high as 20,000 psi at the bottom of the hole. This implies that cement sheath failure caused by excessive casing test pressures generally should occur some­where in the bottom one-halfto three-quarters of the casing string, creating zonal isolation loss over those intervals. Postcementing annular flow caused by this type of cement sheath failure generally is not evident at the surface, unless the differential test pressure is sufficient to create sheath failure to the surface. If excessive casing test pressures are conducted while the cement is gelled but not set, casing expansion frequently will create a large microannulus be­tween the casing and cement sheath, creating a flOW path to the surface.

The magnitude of unsupported casing expansion5 (Fig. 1) may be calculated as

Me=(tlpd~)/(Ehc)' ............................... (1)

where tlde=change in OD, tlp=change in pressure, E=Young's modulus for steel, and hc=casing-wall thickness.

The casing ID also increases concurrent with casing expansion. The casing ID, d j , may be calculated after internal pressurization as

d j =( {[7 , 854(tlde +de)2] -A tl/0.7854)O.5, ............. (2)

where A 1 =original cross-sectional area, in. 2 . Eqs. 1 and 2 were derived by Zinkham and Goodwin. 4

In some subject wells, annular surface pressure became evident only after a well had begun producing. This phenomenon was ob-

291

a; 0-

<I

12000

1000

"I /, I(j

V!J /

~ ~ v I#) v

800

600

400

200

0 0.00 0.02

Il v /

/ V / V

v /"

v

v V i-e--+-

13.375" (85 6 )

9625" (53.5") .... 7" (29") ... 7" (38 6 )

.... 55" (155#) -e- 5S (23.5 6 )

0.04 006 008 0.10

l>. 00 .in ..

Fig. 1-Unsupported casing expansion vs. pressure.

served where surface flowing temperatures were excessively high or in steamflood injection wells. In cases where annular flow (gas or liquid) was measured and sampled at the surface, we determined that the flow did not originate in the producing zone of interest, but in other zones considerable distances above the primary produc­ing zone. This implies that cement sheath failure occurs in the up­per one-fourth to two-thirds of the casing string when failure is caused by excessive temperature changes. In the case of shallow steamfiood injection wells, however, cement sheath failure appears to occur over the entire cemented interval.

This type of cement sheath failure was believed to result from sheath stress cracking caused by diametrical and circumferential casing expansion from excessive temperature increases. Labora­tory measurements of the cementing systems in these cases dem­onstrated that compressive-strength retrogression accompanied by matrix-permeability increases caused by high temperatures (320 to 500 0 P) was. not occurring.

T.st Mod.1 Fig. 2 is a schematic of the test model devised for laboratory meas­urements to determine the effects of excessive pressure or temper­ature changes on cement sheaths in casing/casing annuli. A test model was built for each test as it was taken to cement sheath failure, then was cut into four sections for visual observation and to photo­graph the sheath. The model consisted of a 5lh-in., 23-lbm!ft in­ner casing and a 7%-in., 29.7-lbm/ft outer casing with mounting plates welded at the top and bottom of the 7%-in. casing, leaving 5lh ft of annulus for the cement. A pad of steel wool was placed in the bottom of the annulus for even distribution of water to the annular cement sheath to test permeability. The cement system was mixed and pumped into the annulus. then cured at temperature by circulating hot (350 0 P) oil through the 5lh-in. casing. The annu­lus was maintained at 500 psi during the curing phase. Typically, the temperature on the outside of the 7%-in. casing dropped by 35 to 40o P.

Testing procedures after compressive-strength development within the cement sheath follow.

0.03 -r---.--.---.-.----.-...,--,r-.----,-,---,r--, 23,s so

!' 0.02

g

I 0.01

......... v / Sys m No 1

0 0

2000 4000 6000 8000 10000 '2000

Internal Casing Pressure, psi

Fig. 3-Supported and unsupported casing-diameter ex­pansion.

292

~5 112" Inner Casing

,-""~'" ~

75/8" Outer Casing ~

1== Inlet For Permeability

--:::--_~--1 Measurement

Hot Oil CirculatIOn ~ ----.l I Fig. 2-Schematlc of the pressure-/temperature-change test model.

1. At 0 psi in the 5lh-in. casing, measure the base permeability of the annular cement sheath to water.

2. Increase the inner (5lh-in.) casing pressure to 2,000 psi, record any pressure increase in the annulus, and then measure the perme­ability of the annulus to water.

3. Decrease the pressure on the inner casing to 0 psi, then meas­ure the permeability of the annulus to water.

4. Repeat Steps 2 and 3 in 2,000-psi increments to a maximum of 1O,000-psi inner casing pressure.

Cement Systems The cementing systems tested and their measured physical proper­ties are as follows.

1. System 1 contained a cement/siliceous material mixture, 30% latex by weight of water (BWOW), 1.25% synthetic fluid:-Ioss ad­ditive, and 0.5% gelling agent mixed at 12.1Ibm!gal with 10.81 gal mix water/sack. The yield was 2.49 ft3/sack. The compres­sive strength of the system at the time of testing was 1,000 psi, E=0.69 x 106 , and Poisson's ratio was 0.42.

2. System 2 contained a cement/pozzolan mixture, 10 Ibm silica flour/sack, 30% latex BWOW, 2 gal/sack synthetic fluid-loss ad­ditive, and 0.25% gelling agent mixed at 13.1 Ibm/gal with 6.48 gal mix water/sack with a yield of 1.76 ft3/sack. The compres­sive strength of the system at the time of testing was 2,500 psi, E=0.8 x 106 , and Poisson's ratio was 0.32.

3. System 3 was the same as System 2 without the latex at 13.1 Ibm/gal. The compressive strength of the system at the time oftest­ing was 2,000 psi, E=0.9 x 106 , and Poisson's ratio was 0.30.

4. System 4 contained Class H cement and 35% silica flour mixed at 18 Ibm! gal. The compressive strength of the system at the time of testing was 9,600 psi, E=2.4x 106 , and Poisson's ratio was 0.11.

Test Results Figs. 3 through 5 show the test results. The first test, using Ce­ment System 1, reflects the presence of a siliceous, highly porous, reactive filler material. As internal casing pressure was increased incrementally, the cement matrix permeability decreased incremen­tally to 0 md at 8,OOO-psi inner casing pressure (Pig. 4). After sec­tioning the test cell, we found that the cement had failed and was in a liquid state with the consistency of putty. Subsequent labora­tory testing indicated that the putty-like material consisted of fully hydrated cement, evidence that the cement system had been com­pressed to total crystalline (structural) collapse during the test. The remaining cement systems tested (Systems 2 through 4) show no appreciable change in matrix permeability with increasing inner casing pressure (Fig. 3).

Fig. 5 illustrates changes in the integrity of the cement sheath, representing measurements of the annular permeability to water after the inner casing pressure had been bled to 0 psi following each in­cremental pressure increase. Because only System 1 exhibited a change in matrix permeability, increases in annular permeability

SPE Drilling Engineering, December 1992

., E

o

S .. tem <0. I

\ ~ --r--....... yste No 2

'\/ f.-- "-.,.,... ..... _r--..J. "'" -., Syst m No.

~ ~ - - ---+--+--+syst m No

r-~I'--2000 4000 6000 8000 10000

Internal Casing Pressure, psi

Fig. 4-Annular permeability chart with Internal casing pres­sure Indicated.

must reflect creation of flow channels (stress cracks) within the ce­ment sheath structure. All the cement systems tested withstood the 2,OOO-psi inner casing pressure cycle with minor stress fracture for­mation. Major stress fractures were observed after the 4,000-psi pressure cycle, and catastrophic stress fractures developed after the 6,000-psi pressure cycle.

During the inner casing pressure cycling as the cement sheath in the tests began to fail, annular pressure changes could be meas­ured to determine the supported casing diametrical changes for com­parison with unsupported diametrical changes. Combining the definition of bulk modulus of elasticity with the volumetric change in the annulus created by the internal casing pressure provides a solution for the resulting supported diameter of the inner casing.

ds = ({[(.:1pIEb )O. 7854(d~ -dr)] +(0. 7854d~) -[0.7854(d~ -dr)]}/0.7854)O.5, ..................... (3)

where d2 =outer casing ID (hole diameter), d l =original inner casing 00, .:1p=change in internal casing pressure, V=original annular volume, and Eb=bulk Young's modulus. Eq. 3 was de­rived by Zinkham and Goodwin. 4

Fig. 3 illustrates the calculated inner-casing expansion resulting from the support provided by each of the cement systems tested. The 5~-in. casing line represents calculated expansion of nons up-

Before Pressure Test

After Pressure Test - -

_ ...

Fig. 6-Cross section of Cement System 1 failure.

SPE Drilling Engineering, December 1992

80

0.3

., 60 / E / N . I

g ~ ~ 40

~ / ..... ./ / N .2

a. / j / 20 ~/ ....... ..-' N 4

--- -0 0 2000 4000 6000 8000 10000 12000

Internal Casing Pressure, psI

Fig. 5-Annular permeability chart at O-psl Internal casing pressure.

ported casing. Fig. 3 also illustrates a rnicroannulus that occurred in the test of Cement System 2 with no subsequent change in casing support up through 6,000-psi pressure cycling. System 2 is more ductile than the other cements, although it started to develop minute stress cracks during this portion of the test. System I, another duc­tile cement, also exhibited elastic behavior and provided full casing support until its catastrophic failure at 6,OOO-psi internal casing pres­sure. Systems 3 and 4, the more brittle cements, exhibited failure at the first test pressure (2,000 psi), although the total change in inner casing diameter was not as severe as that of the elastic mate­rials after catastrophic failure.

From these tests, it appears that the higher-compressive-strength material (i.e., the more brittle cements) provided better casing support but lost the ability to seal the annulus at a much lower in­ternal casing test pressure. After these cement systems fail catas­trophically, the slope of the line of diameter change should equal that of the unsupported casing. These magnitudes of casing expan­sion become even more significant when considering the size of the rnicroannulus created, M/2, and during attempts to evaluate a cement sheath with bond logging tools.

Permeability measurements were made in the annulus while pres­sure testing the internal casing and after release of the internal casing pressure to determine when the cement sheath failed. The permea-

Before Pressure Test

--- - After Pressure Test

Fig. 7-Cross section of Cement System 2 failure.

293

bility measurements were made with water at a loo-psi !J.p. This procedure measures the total annular permeability and the cement sheath matrix permeability. Figs. 4 and 5 show these measurements; Fig. 4 illustrates cement matrix permeability measurements dur­ing application of internal casing pressure, and Fig. 5 illustrates total annular permeability with no internal casing pressure. In Fig. 4, the complete loss of matrix permeability in System 1 illustrates internal collapse of the cement system to a plastic material (total compressive failure to O-psi compressive strength). Subsequent tests indicated that System 1 was totally amorphous (hydrated cement). Fig. 5 dramatically illustrates when excessive stress cracking be­gan in the systems. Although System 4 did not fail as catastrophi­cally as the other systems, it still began to fail at the first internal pressure test at 2, ()()() psi.

Figs. 6 through 9 illustrate the types of stress cracks observed in the test models sectioned after each test. The crack direction ap­parently may be determined by the greater value of tensile strength or shear-bond strength. In higher-tensile-strength cements, the cracks generally tended to generate either within the cement sys­tem or at the casing/cement interface and parallel to the inner casing surface until internal test pressures also exceeded the tensile strength. The cracks then radiated toward the outer casing surface. In higher­shear-bond cements, the cracks radiated directly from the inner to the outer casing surface.

Temperature Temperature changes in a flowing well also can create significant casing-diameter increases. This expansion is cubical (volumetric). The coefficient of cubic expansion of a solid is approximately three times the linear coefficient. 5 The axial stresses created by the in­creasing casing OD create stress cracks in the cement sheath much as the previously described excessive inner casing pressure does.

Fig. 10-Expanslon of 51/z-ln. casing. temperature vs. pres­sure.

294

These stress cracks result from the cement failure in tension, not in compression. These changes in temperature do not occur near a producing zone but toward the surface, where significant differ­ential temperatures can occur (e.g., surface flowing temperature less the normal geothermal temperature or steamflood inlet tem­perature less the normal geothermal temperature). Generally, the presence of the stress cracks in the cement sheath is not a problem while the casing is expanded (e.g., while the well is flowing or during steam injection) as long as the cracks do not extend into the formation at a well-bonded interface. When the casing relaxes during cooling, the cracks open sufficiently to permit annular flow. The differential temperature, !J.T, required to create casing expansion equal to internal test pressure expansion may be defined as

!J.T=(hw1 -hw2)/(Ohwl)' ............................ (4)

where hwl =original casing-wall thickness, hw2 = pressurized casing-wall thickness, and O=volumetric (cubical) expansion of steel, 2.07xlO-5 in.lin.-oF.

Eq. 4 was derived by Zinkham and Goodwin. 4 This method was used to generate Figs. 5 and Figs. 10 through 13.

Field Trials Field testing was conducted with the same casing sizes and cements previously used in the laboratory test model. Following placement and curing of the cement in a well, the quality and quantity of the cement sheath were measured with an ultrasonic cement-evaluation

Fig. l1-Expanslon of 7·ln. casing. temperature vs. pressure.

SPE Drilling Engineering, December 1992

500'---~~---r----~--~-----r--~

400~--~r----+----+---~--~~--~

300i---~r----+----+-~~~--~--~

200i---~r----+~~~~~-----r----;

o 2000 4000 6000 8000 10000 1 2000

6 P, PSi

Fig. 12-Expanslon of 9%-ln. casing, temperature vs. pres­sure.

device. One well was cemented with Cement Systems 3 and 4, and the other well was cemented with Cement System 2. In response to the results of the laboratory tests and to meet the necessities of field operation, the casing was pressure tested with tubing and a retrievable packer to isolate the lowest test pressure to the bottom end of the casing, subsequently increasing test pressures toward the top of the well. An upper section of the first well contained Cement System 3, which had developed compressive strength in the range of 2,000 psi, and Cement System 4, which had devel­oped compressive strength in the range of 3,000 psi.

Comparison of the evaluation logs of Systems 3 and 4 (Figs. 14 and 15) before and after being subjected to 12,150-psi internal casing pressure (surface pressure plus casing-fluid hydrostatic pres­sure) demonstrates that the more brittle system (System 4) failed, while the more ductile system (System 3) remained intact.

Another casing string was cemented with commercial lightweight cement containing silica flour and 20 vol % latex. To date, the well has been pressure tested, but no evaluation logs have been run for definitive effects of the pressure tests on the more ductile cement sheath.

Conclusions 1. Casing expansions created by excessive internal casing pres­

sures can create radial stress cracks in the set cement in the annu­lus. These cracks, which cause loss of annular zonal isolation, generally are created in the lower one-quarter to one-third of the well.

2. Typical causes of such cracks include pressure testing the casing after the cement has attained high compressive strength. The

500

400

300

<l 200

100

o

9 5/S"' Casing

./

/ /' ~ V

~ V P. 43. .# 1ft

~ 53 . .#/ft

V V'

o 2000 4000 6000 8000 10000 1 2000

6 P, psi

Fig. 14-Acoustlc Impedance log showing Transducer 2 track before and after pressure testing casing, Cement System 3.

SPE Drilling Engineering, December 1992

<l

500~--~-----r----~--~----~--~

400~----+-----~--~-----+~~~----~

3004---~----~----~~-t~~4---~

100~---'~~~-----r----+-~~~#~/f~t~

o

..It 1ft

2000 4000 6000 8000 10000 12000

6 P, psi

Fig. 13-Expanslon of 13%-ln. casing, temperatul'e vs. pres­sure.

same type of failure has been observed on wells that used expend­able perforating guns to shoot high-density (8- to 12-shot/ft) pat­terns with large holes (0.45 to 0.5 in.).

3. Generally, low-compressive-strength (500- to 1,000-psi) ce­ments are more ductile than other cements and can withstand the stress cycling. Also, ultrahigh-compressive-strength (> 12,OOO-psi) cement can withstand stress cycling without cracking. One sugges­tion for circumventing the cracking problem is to use a low-density cement slurry to cement the entire well (deleting the high-strength tail slurry).

4. Loss of annular control of gas or water also has been observed in cases of excessively high surface flowing temperatures or steam­flood injection. Where pumping low-density, low-compressive­strength cements was possible, the cracking problem practically was eliminated.

5. Cement sheath stress cracking as a result of excessive tem­perature changes generally occurs in the upper one-third to one­half of the well.

Methodology Eq. 2 solves for the new casing ID following expansion. The method involves subtracting the cross-sectional area of the steel (which does not change) from the expanded-OD cross-sectional area, which de­fines the new ID cross-sectional area of the expanded casing.

Eq. 3 combines the classic definition of the E b equation with the annular-volume change caused by increased casing OD measured during testing. An average bulk modulus of elasticity for cement is 1.51x105 .

Eq. 4 assumes that the casing expansion caused by increased tem­perature is equal to casing expansion caused by internal pressure

<l

13 3/S"' Casing

600~---4-----r----~--~-----r--~

5004---~ __ ---+----+---~--~~--~

400;---~r----+----;---~~7'~--~

100~--~~~~-----+----~--~+-~~

2000 4000 6000 8000 10000 1 2000

6 P, psi

Fig. 15-Acoustlc Impedance log showing Transducer 2 track before and after pressure testing casing, Cement System 4.

295

Authors

K.... Goodwin Is an associate drill­Ing engineering ad­viser with Mobil E&P Services Inc. In Dallas. Before joining Mobil In 1985, he was em­ployed by Dowell and Western Co. of North America.

Goodwin Crook During his career, he has worked In

the laboratory and field In stimulation, cementing, and lost circulation. His Interests Include remedial cementing and ce­ment sheath evaluation, and he currently teaches cement­Ing courses, conducts remedial cementing and cement sheath evaluation seminars, and provides technical assistance In these areas worldwide. He holds a BS degree In chemistry from Northwestern State U. Goodwin, a 25-year SPE mem­ber, served on the 1990-91 Forum Series Committee and cur­rently Is a Short Course Instructor. Ronald ... Crook is a research engineer and technical team leader for the Appli­cations Research Group at Halliburton Services Research Center in Duncan, OK. His research Interests are In squeeze cementing, the use of spacers and flushes, new cementing materials, large-scale displacement of drilling fluids, and prac­tices related to devlated-wellbore cementing. He also has con­ducted field studies associated with downhole temperature measurements and geothermal cementing. He holds a BS degree In chemical engineering from Oklahoma State U. Crook served on the program committees for the 1989-91 SPElIADC Drilling Conferences and on a Technical Program Commit­tee for the 1990 Annual Meeting.

increases. All that remains is setting the casing-pressure expansion method equal to the temperature expansion method and solving for the change in temperature required to produce an equivalent ex­pansion value.

Nomenclature

296

Al = original cross-sectional area, L2, in. de = OD, L, in. di = ID, L, in. ds = supported OD, L, in. d l = original inner casing OD, L, in.

d2 = outer casing OD (hole diameter), L, in. E = Young's modulus for steel, mlU2

Eb = bulk Young's modulus, m/U2, psi he = casing-wall thickness, L, in.

hwl = original casing-wall thickness, L, in. hw2 = pressurized casing-wall thickness, L, in.

p = internal casing pressure, m/U2, psi T = differential temperature, T V = original annular volume, L3, in. 3

o = volumetric (cubical) expansion of steel, 2.07 x 10-5

in.lin.-oF

Acknowledgments We thank the managements of Mobil E&P Services Inc. and Hal­liburton Services for permission to publish this paper. The help of all persons concerned with the project is deeply appreciated.

References 1. Cooke, C.E., Kluck, M.P., and Medrano, R.: "Field Measurements

of Annular Pressure and Temperature During Primary Cementing," JPT (Aug. 1983) 1429-38.

2. Carter, L.G.: "Effect of Bore-Hole Stresses on Set Cement," MS the­sis, U. of Oklahoma, Norman, OK (1968).

3. Burkowsky, M., Ott, H., and Schillinger, H.: "Cemented Pipe-in-Pipe Casing Strings Solved Field Problems," World Oil (Oct. 1981) 143-47.

4. Zinkham, R.E. and Goodwin, R.J.: "Burst Resistance of Pipe Cement­ed Into the Earth," JPT (Sept. 1962) 1033-40.

5. Handbook of Chemistry and Physics, 36th edition, Chemical Rubber Pub­lishing Co. (1954-55) 2066.

51 Metric Conversion Factors ft x 3.048* E-Ol m

ft3 x 2.831685 E-02 m3 OF (OF - 32/1.8) °C gal x 3.785412 E-03 m3

in. x 2.54* E+OO cm in. 3 x 1.638706 E+Ol cm3

Ibm x 4.535924 E-Ol kg md x 9.869233 E-04 Ilm2

psi x 6.894757 E+OO kPa

• Conversion factor is exact. SPEDE Original SPE manuscript received for review Sept. 2, 1990. Revised manuscript received June 15, 1992. Paper accepted for publication April 30, 1992. Paper (SPE 20453) first presented at the 1990 SPE Annual Technical Conference and Exhibition held in New Orleans, Sept. 23-26.

SPE Drilling Engineering, December 1992