7
SPE/lADC 29342 Gas Migration: Fast, Slow or Stopped Ashley Johnson and Ian Rezmer-Cooper, Schlumberger Cambridge Researeh; Tim Bailey, Sedco Forex; and Dominic McCann, Anadrill SPE/lAOC Membsrs Co@aht 1S6 SPEMIDC Drilling Conference. TIIis paper was pm$nred for presentation at fhe 1SS5 SPEflAOC Orllllng Caferense held in Amatwdam, 28 FelNwy-2 March 1SS5. TM papar was 9abco3d for preearmbn by an SPE/lAOC Prugmn COmmHtOetollowlng revbw G+Infomrafbm cdatned ~~ti,hmtitin~ man 8bafracI aubmlffad by lb aufhotls). Curfenm of the paper, by Ihe lnf6mafic+rd AaacciMbn of Drflllng Curtractaa w the Society of Pefmleum Englnmm and are wb+oct to oxradkm by the MirOr@). The mtwid, - PWWntd, doM not mxesswiiy tafbct anY podfkn of the SPEorWC, fh.komm w mm-. PSWMm~ ~ s~~ MOOWS IVO s@PaffOw~~bn ravbwbyEdMwlal Commfttaas of the SPE and lADC. PermksJmI to copy b msffwdto anabsfmof ofnofmomtkwti. MtmbmmaymfbcoW.~~swW contain conspicw uaacimdsdgmror WIIOIVEI. *J . .. .... . _ .. . . . . . .. . . . . . ....--.A ,A.... qu IUIWWi. nr~ad. Write t.ibrukn, SPE, P.0, S4X ~, Rk_fh n 79XMS26, U.S.A. Tef% 1SS24S SPEUT. Abstract We review the conflicting literature on gas migration ve- hxities during kicks. We consider the laboratory and large scale test data that shows that for any locat gas void frac- tion of more than 10%, the influx migrates at approximately 100 fthnin. We atso review the evidence from field expe- rience that shows that gas can migrate much more sIowly (the typicat rule of thumb suggests that gas bubbles move at approximately 15 fthnin) and in some cases remain sta- tionary. We show that the yield stress of the drilling mud which holds cuttings in suspension whilst mrddngconnections,can also hold gas bubbles in suspension, and report an expef- imentst study of these gas suspension effects. Significant volumes of gas can be held in suspensionduring a gas kick this trapped gas remaining Statkriiar-y uiitii tiie find k ~li- culated out of the well. We consider the implications of this for well control oper- ations, and present field data where gas was injected into a marine riser, it dispersed and remained stationary until cir- culated out. We show that a single bubble migration model, which neglects gas suspension, predicts that as the gas rises and eXptUNIS it unloads the risa. By simulating the gas suspension characteristics we model the field data. We conclude that gas in moderate concrxmations(more than 10%)migrates quicldy, typicatly at 100 ft/min. This migrat- ing influx leaves a trait of suspended gas in the mud that remains stationary. For small kicks in deep wells the entire influx can be distributed, at a low concentration, and remain in suspension until the gas-cut mud is circulated out of the well. Referencesandillustrationsat the cod of paper Gas Migration Velocity - Literature Con- troversy There is a major controversy in the published literature ova gas migrationrates during kicks while drMng. Experimen- tal tests in small flow loops and in teat wells ahow the gas migration velocity is around 100 ft/min, while field esti- mates suggest that gas rises at around 15 fthin or more slowly. We consider this dqancy. Johnson and White [1] showed rha~ in typicat drilling g~ ometries, in reatistic tilting fluids, for gas concentrations larger than 10%, gas migration velocities were around 100 Mnin, significantly larger than the equivalent migration rates in water. The viscosity of dritting mud hinders the bubble break-up proms allowing gas to migrate as bigg= bubbles (which travel faster). They also observed that the yield stress of the drilting mud woutd hold low concentra- tions of gas in suspensionwith no migration. Radef et al. [2] reported similar resutts for gas migration in a 3.7 m, (12 ft) flow loop and a 1800 m (6,000 ft) well. The gas veloeity in the well was measured using the time of flight principle. Hovkmd and Rommetveit [3] reported large state tests in a 1500 m (5000 ft) deep test well, which had a maximum deviation of 63°. They used the time of flight between pressure transducersmounted at different depths in the well to measure a gas slip velocity of 0.55 xn/s(110 Mnin). A widely accepted“rute of thumb” used in the field says that L u---- —, gSS DUDDKS IN@te ti 0.0% WJS,(15 fttftiifi). Iii@Xtt[4] claimed that he had evidence of gas migration rates of around 0.014 rnk (3 fthnin), sKhough he did not specify how these were derived. In field situations an accurate estimation of gas migration during a well control incident is very difficult. Velocities 93

SPE-29342 Gas Migration Rates

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Page 1: SPE-29342 Gas Migration Rates

SPE/lADC 29342

Gas Migration: Fast, Slow or StoppedAshley Johnson and Ian Rezmer-Cooper, Schlumberger Cambridge Researeh; Tim Bailey, SedcoForex; and Dominic McCann, Anadrill

SPE/lAOC Membsrs

Co@aht 1S6 SPEMIDC Drilling Conference.

TIIis paper was pm$nred for presentation at fhe 1SS5 SPEflAOC Orllllng Caferense held in Amatwdam, 28 FelNwy-2 March 1SS5.

TM papar was 9abco3dforpreearmbn byan SPE/lAOC Prugmn COmmHtOetollowlng revbw G+Infomrafbm cdatned~~ti,hmtitin~

man 8bafracI aubmlffad by lb aufhotls). Curfenm of the paper,

by Ihe lnf6mafic+rd AaacciMbn of Drflllng Curtractaa w the Society of Pefmleum Englnmm and are wb+oct to oxradkm by the MirOr@). Themtwid, - PWWntd, doM not mxesswiiy tafbct anY podfkn of the SPEorWC, fh.komm w mm-. PSWMm~ ~ s~~ MOOWSIVOs@PaffOw~~bnravbwbyEdMwlal Commfttaas of the SPE and lADC. PermksJmI to copy b msffwdto anabsfmof ofnofmomtkwti. MtmbmmaymfbcoW.~~swW

contain conspicw uaacimdsdgmror WIIOIVEI. *J . .. ... . . _ .. . . . . . . . . .. . . ....--.A , A.... qu IUIWWi. nr~ad. Write t.ibrukn, SPE, P.0, S4X ~, Rk_fh n 79XMS26, U.S.A. Tef% 1SS24S SPEUT.

Abstract

We review the conflicting literature on gas migration ve-hxities during kicks. We consider the laboratory and largescale test data that shows that for any locat gas void frac-tion of more than 10%, the influxmigrates at approximately100 fthnin. We atso review the evidence from field expe-rience that shows that gas can migrate much more sIowly(the typicat rule of thumb suggests that gas bubbles moveat approximately 15 fthnin) and in some cases remain sta-tionary.

We show that the yield stress of the drilling mud whichholds cuttings in suspensionwhilst mrddngconnections,canalso hold gas bubbles in suspension, and report an expef-imentst study of these gas suspension effects. Significantvolumes of gas can be held in suspensionduring a gas kickthis trapped gas remaining Statkriiar-yuiitii tiie find k ~li-

culated out of the well.

We consider the implications of this for well control oper-ations, and present field data where gas was injected into amarine riser, it dispersed and remained stationary until cir-culated out. We show that a single bubble migration model,which neglects gas suspension,predicts that as the gas risesand eXptUNISit unloads the risa. By simulating the gassuspension characteristics we model the field data.

We conclude that gas in moderateconcrxmations(more than10%)migratesquicldy, typicatly at 100 ft/min. This migrat-ing influx leaves a trait of suspended gas in the mud thatremains stationary. For small kicks in deep wells the entireinfluxcan be distributed, at a low concentration, and remainin suspension until the gas-cut mud is circulated out of thewell.

Referencesandillustrationsat the cod of paper

Gas Migration Velocity - Literature Con-

troversy

There is a major controversyin the published literature ovagas migrationrates during kicks while drMng. Experimen-tal tests in small flow loops and in teat wells ahow the gasmigration velocity is around 100 ft/min, while field esti-mates suggest that gas rises at around 15 fthin or moreslowly. We consider this dqancy.

Johnson and White [1] showed rha~ in typicat drilling g~ometries, in reatistic tilting fluids, for gas concentrationslarger than 10%, gas migration velocities were around 100Mnin, significantly larger than the equivalent migrationrates in water. The viscosity of dritting mud hinders thebubble break-up proms allowing gas to migrate as bigg=bubbles (which travel faster). They also observed that theyield stress of the drilting mud woutd hold low concentra-tions of gas in suspensionwith no migration.

Radef et al. [2] reported similar resutts for gas migration ina 3.7 m, (12 ft) flow loop and a 1800 m (6,000 ft) well.The gas veloeity in the well was measured using the timeof flight principle.

Hovkmd and Rommetveit [3] reported large state tests ina 1500 m (5000 ft) deep test well, which had a maximumdeviation of 63°. They used the time of flight betweenpressure transducersmounted at different depths in the wellto measure a gas slip velocity of 0.55 xn/s(110 Mnin).

A widelyaccepted“rute of thumb”used in the field says thatL u---- —,gSSDUDDKS IN@te ti 0.0% WJS,(15 fttftiifi). Iii@Xtt[4]

claimed that he had evidence of gas migration rates ofaround 0.014 rnk (3 fthnin), sKhough he did not specifyhow these were derived.

In field situations an accurate estimation of gas migrationduring a well control incident is very difficult. Velocities

93

Page 2: SPE-29342 Gas Migration Rates

2 GAS MIGIUTION: FAST, SLOW, OR STOPPED

are sometimesderived from casingpressurerise rates duringshut-in, using a simple correlation which assumes that thewellboreis a rigid leaktight vessel filledwith incompressiblemud. However, Johnson and Tarvin [5] showed that Udsprocedure could underestimatethe actual migration velocityby more than 10 times.

A time of flightmeasure of gas velocityis more reliablethansurface pressure interpretation. However, in a well controlincident, it may be difficult to identify when the gas firstentered the well. In terms of the gas arrival time, there aremany well control incidents where EARLYGAShas arrivedat surface indicating a larger velocity than expected, butthere are also cases where the gas has taken many days toappear, often only arriving at the top of the well when themud is being circulated out. Although the precise time ofgas entry into the well may not be known, tlds evidenceshows that in some cases the gas migrates very quicklywhile elsewhere it moves extremely slowly or, more likely,not at all.

Gas Migration - Bimodal Bubble Distri-~ti$;~~,

Many authors, notably Johnson and White [1] and Phillipset al [6] have reported that visual observations of gas -drilling mud flows show a bimodal distribution of bubblesizes. For gas void fractions larger than 10% the flow isdominated by large bubbles which almost fill the pipe andmigrate up the well at a high velocity. In addition to thisthe liquid phase holds a suspension of very small bubbleswhich remain stationary relative to the fluid. These bubblesme typically smaller than 2 mm in diameter and are held insuspensionby the effective yield stress of the mud.

Initially, the bulk of the gas is carried in the large bubbles.However, in shedding a trail of small gas bubbles (whichcan become significant in total volume) the gas cloud be-comes smaller. If a well is deep enough, all of the migratinginflux WKI‘becomesuspended and gas migration Wli ceasecompletely (for a large influx the well would have to bevery deep).

The suspended gas void fraction will be dependent on thetheological characteristics of the drilling mud so we mustconsider these characteristicsand how they can vary duringa well control oneration.–=_-–..-–

Mud Rheology

Drilling mud has a yield stress to prevent sedimentationofcuttings when pumping is suspended. The small bubblesare held in suspension in a similar manner.

The magnitudeof the yield stress is dependentupon not onlythe mud type and consistency,but for a bentonitebased mudit is also dependent on the shear history. If a Bentonite mudremains unsheared then the yield stress will increase. Fig-ure 1 shows the evolution of yield stress for a 6% bentonitemud. We see that over a period of 1 hour the yield stressof the mud increases considerably. In terms of a well con-trol operation when tbe well is shut–in and the influx hasceased, the yield stress of the mud column increases. Thishas implications for the volumes of gas which can be heldin suspension.

In the field it is conventional pracdce to measure the 10second and 10 minute gel strengths. These give some in-formation on the short time characteristics of the mud, butthey give no information on the long time (i.e. shut-in timescale) characteristics. For typical field fluids the 1 hour gelstrengthcan be in the range 10 to 100lbs/100sq.ft, althoughtypical values would be below 50 lbs/100sqft.

Experimental Tests

W- m.,+- am .aw-i-ant.l .h,t+.rtfl 4m.met;oatr=the hllhhle7. w ,,,a”w au “*p ,1.,”.1- ..UWJ .“ . . ..- U5CAW b..” “..””.”

break-up and suspension processes and to evaluate the ef-fects of mud properties on the gas void fractions which canbe held in suspensionby the mud.

The experimental programme was executed in the muiti-phase flow loop test facility at Schlumberger CambridgeResearch, Figure 2, which forms a universal multiphaseflow test centre. The present test configuration, describedin detail by Johnson and White [1], is used for gas-liquidflows, although solid-liquid and liquid-liquid flows can alsobe evaluated. The facility offers a straight flow length ofalmost 15 m [49 ft], 13.5 m [45 ft] of which is perspex topermit visualevaluationof the flows. The piping is mountedon a table which can be pivoted, enabling tests to be carriedout in all orientations from horizontal to verticti, althoughthe teats reported here were made with deviations horn ver-ticat to 60°. It has been designed to permit tests in New-tonian and non-Newtonian fluids. Shear degradable liquidscan also be used without damage to either the fluid or thefacility. ‘fhe facility is designed to operate at pressures upto 10 bar [145 psi]. lle working section used for the ex-periments reported here comprises 5 perspex pipe sectionsof 200 mm [7.8”1 internal dhmeter with a removable 89mm [3.5’~centrebody.

The tests were made by suspending a column of gas-fkeemud in the loop, and then injecting a single bubble at thebouom. After the bubble had risen up through the column●l.a --.:-:”- . ....-a..AA. . . ..,.:A &,.,.*:,... .... . . ..a .....dLUG 1GUlalllulg NqJGuusal go v Ulu u abuuu w aa Jluiasu w

using differential pressure transducers.

We used two Xantham Gum solutions as the liquid phasefor the tests. These fluids have a yield stress, so they simu-late the low shear behaviour of conventional drilling muds.

94

Page 3: SPE-29342 Gas Migration Rates

A. B. JOHNSON & I. REZMER-COOPER&T. BAILEY &D. MCCANN 3

However, they offer some significant advantages over con-ventional Bentonite fluids. Primarily, this yield stress isindependentof shear history, making the experimentalanal-ysis much more simple. Also the fluids are transparent al-lowing visual observations of the fluids before during andafter the large bubbles have risen through the column. Arheogram of the fluids is shown in F@ure 3.

We made a comprehensive experimental study of the gas—------: --- -La --.4 .,:O= ffi. I141W mnm!ar and tool jointSuspcllslull Ularavb=! 10U** AU. y.~-, -------

geometries, for single bubbles, trains of bubbles, and forbubbles of different sizes. Figure 4 shows the suspendedgas fraction from a large number of tests with the two mudsin an annular drilling geomety. The results are presentedas the mean gas fraction (averaged over many tests) and thelimits of scatter in this data, plotted against the yield stressof the mud. The scatter in the measurements was random,with large variations in the measurementsat different pointsin the column, even for the same test. This scatter did notcorrelate with any of the experimentalvariables, or locationalong the column.

We apply a quadratic fit to the data. If we consider that in awell control operation the yield stress can vary in the range10 to 50 lb/100sq f~ then we can expect the suspendedgasfraction to vary in tbe range 0.5 to 5%.

Suspended Gas - Well Control Implka-tions

There are two effects that the suspended gas fraction willhave during a well control operation. (1) As the gas mig-rates up the well it will leave a trail of gas behind,reducingthe volume of gas migrating. (2) Also the gas left in suspen-sion will act to increase the compressibility of the mud inthe well and therefore reduce the rate of the shut-in surfacepressure rise. We consider these two effects separately.

(1) To calculate the volume of an influx which can be sus-pended in a well we must consider how the intlux volumechanges as it migrates. We consider a case where fluid isbeing bled off through the choke to maintain bottom holepressure. As the intlux rises up the wellbore its pressurefalls, and volume increases. We need a calculation of theinflux volume which can be suspended, in terms of the ini-tial volume at bottom hole conditions. This is derived inAppendix A. The suspended gas volume under bottom holeconditions, v, is:

V*= +8Ad . . . . . . . . . . . . . . ...(1)

cr$is the suspendedgas fraction, A the annularcross sectionaod d the well depth.

For a 10,000 ft weil with 8.5” hole and 5“ drill pipe, ifthe mud could sustain a suspended gas fraction of 2%, 4.7

bbls of influx could remain in suspension before the influxmigratedup to the top of the well. This is in additionto anyinflux which dlssolvea into the mud. For a 5% suspendedgas fractionthe suspendedinflux volumecould be 1I.8 bbls.Once this gas is held in suspension,it will remain there untilthe mud rheology breaks down, not arriving at the surfaceuntil the gas cut mud is circulated out of the well.

(2) llte effect of the suspended gas on the wellbore pres-sure rise rate is more difficult to calculate. Johnson et al [51showed that the system compressibWy (mud compressfDii-ity + wellbore elasticity) and fluid loss were all-importantin determining the wellbore pressure rise rate. They didnot separate the effects of a suspended and migrating gasfraction in their model. Neglecting the effects of wellboreelasticity and fluid 10SSwe extend their model to show thatthe shut-in pressure rise rate, P,, can be written as:

Xg Vg~/2gV,lipP. =

Xmudvm.d + Xgvgt.... . . . ...(2)

X and V are the volumetric compressibilityand volume re-spectively of the mud and gas identifiedby subscripts mudand g. The denominator of thk model is the total systemcompressibility, so Xgt V’gtis the compressibility of M ofthe gas in the wellbore. The numerator is the growth rate ofthe migrating gas, so Vgm is the volume of migrating gas.As the migrating gas cloud becomes smaller, as it leavesa trail of suspended gas, the system compressibility will

. ...11 Ua -not change, but V$~ WUI IX iediiced & -... . . . . . . . . -.c will the wellh(ye

pressure rise rate.

We have calculated (see Appendix B) the effect of Udsgason the wellbore pressure evolution as an influx migrates upthe well. For simplicity we neglect the effects of wellboreelasticity and fluid loss. For a 10 Bbl irdhtx, migrating at100 ft/min, in a 10,000 ft well we calculate the pressureincrease as the gas migrates. In figure 5 we show 3 traces,assuming no suspension, 2% and 5% gas suspension. Theeffect of gas suspension on the wellbore pressure rise rateis very significant. If there is nq gas going into suspensionthe surface pressure would rise by nearly 5,000 psi. With2% gas suspension the surface pressure will rise by only3:000 psi, before the influx reaches the top of the well. Butfor the 5% suspended gas fraction the maximum pressureincrease is less than 1000 psi, with all of the gas goinginto suspension. For the cases of a trail of suspended gasremainingin the well the rate of surfacepressure rise wouldgive an inaccurate(low) estimate of the actual gas migrationrate.

Suspended Gas - Field Evidence

An analysis was made of data horn Amoco teats [7] con-ducted on a deep water riser to examine the effect of gasrelease from a BOP. Various gas volumes were injectedinto

95

Page 4: SPE-29342 Gas Migration Rates

4 GAS MIGRATION FAST, SLOW, OR STOPPED

a 3118 ft, 183 x 17*” marine riser. The influx was injectedinto 13.2 ppg water based mud.

When 10 Bbl of gas were injected no gas appeared at thesurface during the test period of 3.6 hrs. 200 Bbls of mudwere then circulated through the riser, and gas finally ap-peared at the surface as small bubbles boiling out of themud.

A simulation of this test with a single bubble model showsthat the intlux would migrate up the well until the top ofthe bubble was at 335 ft from the top. It would then expandvery rapidly, unloading the top 670 ft of the riser.

There was no measurement of the long time scale yieldstress, so an accurate prediction of the suspendedgas frac-tion is not possible. Figure 6 showsthe influxvolumewhichcan be suspendedin the riser as a function of the suspendedgas fraction. This is calculated from equation 1. If the mudcan sustain a suspended gas fkaction of 2.5% then all ofthe injected gas would be suspended in the well with nonereaching the surface.

When 20 Bbls of gas were injected into the riser, the mudat surface started to bubble after 9 minutes, but it did notunload the riser and the riser woutd not flow during thenext 3.6 hours. When the influx was circulated out the mudcontinued to bubble. Later, after pumping more than 500Bbls of mud, an estimated 6 Bbls of gas came out of thewell in a slug.

Clearly all 20 Bbls of gas were not behg held in suspension,so (from figure 6) the suspended gas tiaction was less than5%. The gas cloud rose up the riser at a very high speed.From the injection time and the surface arrival time wefind a gas velocity of 1.7 rnh (330 fthnin). This is notsurprising for such a large annular geometry. As the gascloud migrates it leaves a tail of gas in suspension in thewell and tfds comes out more S1OW1y as the mud is circulatedout. ‘he rapid slugging, later in the circulation, occurs asgas from close to the bottom of the riser, which had beenheld in suspension,expands, to form a large gas cloud whichrises rapidly through the riser.

Implications

If an influx is taken and a well shut–in, the maximum sur-facepressure occurs if the gas cloud is allowed to rise to thesurface. If the effects of gas suspension and system corrl-preasibility are neglected the influx will carry the bottomhole pressure to the BOP. Gas suspension has a dramaticeffect (a huge reduction) on these maximum wellbore prea-surea. With a knowledge of the mud gel strength, and thegas suspensioncharacteristics(discussedhere) we show thatthe maximum wellbore pressures can be much smaller.

In a modelling study conducted as part of a co-ordinatedproject on deep water drilling for the Norwegian Petroleum

Directorate, Bailey et al [8] reinforced some of the aboveideas. Using a kick simulator it was shown that when aSxtidi~OUnt Ofg= trapped ‘iUidei ~i =imi~- pieiK5ii’b3i(5bbl) is released into a risw containing water-base mud, invery deep water (> 1000 m) the gas will become d@ersedin the riser.

In certain cases, where some gas migrates into the riser onopening ‘he UIIIIUIiUPIWGUW1, ~L w- Ueluvllou — & ,11

---..1 ..- . . . . . . . . . . :. . . ...” A . . ..- . . ..t..l+aA * .* ;“

deep water the gas becomes dispersed to such a degree thatit represents less of a threat than possibly supposed.

Conclusion

Gas migration through drilling muds is complex and cannotbe described by a single slip velocity or “rule of thumb”.

. At large gas concentrations (> 10%) the gas wilt riseFAST, at around 0.5 m/s (100 ft/min) in a typicatdrilling geometry.

. This rapidly moving gas cloud will leave a trail ofbubbles suspended in the well by the yield stress ofthe mud. llese small gas bubbles will be STOPPED.

● MIs – interpretationof surface pressures during shut-in will indicate that gas migration is SLOW.

The suspendedgas has a huge effect on the shut-in surfacepressure rise rate, reducing the terminal wellbore pressureand the rate of pressure rise significantly.

In deep wells, or wells with large annular geometries thevolume of gas suspended can become very significant inrelation to the totat influx volume. In some cases the entireinflux can become suspended and remain stationary indefi-nitely, not aniving at surface until the gas cut mud is circu-lated out of the well. ~is is particularly important in deepwater well control operations when gas is released from theBOP.

The size of the suspended gas fraction is dependent on theyield stress of the mud. To make an accurate prediction ofthk level we need a measure of the gel strength of mud leftat rest for a similar period to the shut-in time.

References

[1]

[2]

96

A.B. Johnson and D.Et.White. Gas rise velocity duringgas kicks. SPEDriUing Engineering, December(20431),1991.

D.W. Rader, A.T. Bourgoyne Jr, and R.H. Ward. Fac-tors affecting bubble-rise velocity of gas kicks. J. ofPetroleum Technology, May 1975.

Page 5: SPE-29342 Gas Migration Rates

A. B. JOHNSON & I. REZMER-COOPER&T. BAJLEY &D. MCCANN 5

[3]

[4]

[5]

[6]

[7]

F. Hovland and R. Rommetveit. Analysis of gas - risevelocities from full scale kick experiments. SPE Tech-nical Con., Washington, (SPE24580E331 – 340, 1992.

E. Blount. Editorial comment. SPE Drifling Engineer-ing, page 236, 1991.

A.B. Johnson and J.A. Tarvin. Field calculations un-derestimate gas migration velocities. IADC EtqooeunWell Control Con&, 1993.

J. Philip, J. M. proctor, K. Niranjan, and J. F. David-son. Gas holdup and liquid circulation in inter@loop reactors containing highly viscous newtonian and- ---”-.,.*-”; O“1in..iri. ~ham+nl J7n oinn~n”no Ginnrv.tu.,-.i~w LU.S.CUI ..yusuo. wr=rr.m--e ur.~ -w-, .,.s u-.--.. -,

45(3):651-664, 1990.

J.M. Shaughnessy. Test of the effect of gas in a deep-water risa-. Technical repofi Amoco Internal Memo-randum, 1986.

[8] T. Bailey et al. NPD Voring Plateau Deep WaterDrilling Project, Well Control, Final Report. Techni-cal Report NPD/REP/Final 1, Sedco Forex, 1994.

Appendix A: Suspended Gas Volume

If we consider a worst case, where the wellbore pressureremains constant as the gas migrates then for a well ofdepth d with bottom hole pressure p, then the pressure atdepth dd (iOcdj is:

Pd=p+.................(3)

For the gas we assume that pv = const, then the volumeof an influx under bottom hole conditions, W,which has avolume Vdat depth dfj is:

V=V~;=Vd+..............(4)

In a section of the well of cross sectional area A, of lengthdl at depth dd, the suspended gas fraction v,l is

v,l=a,Adl . . . . . . . . . . . . . . ...(5)

a, is the suspended gas fraction. Substituting U,I for Udin4 and integrating over the length of the wellbore we findthe suspendedgas volume under bouom hole conditions, u,is:

Summing over each section of the wellbore(where nu andd are the upper and lower limits of the element n) with adifferent cross section. Assuming a constant annular crosssection, tlds can be simplified to

1t), = -an Ad

2. . . . . . . . . . . . . . . . .(7)

Appendix B: Wellbore Pressure Rise

We consider a case where the influx has risen from thebottom of the well d to depth d~. The wellbore pressurehasincreasedby AP, so the bottom hole pressure is ~~h+ fi~and the gas pressure P~ is:

Pg()

spbh + +Ap.., . . . . . . . ..(q

We consider conservation of gas in terms of the gas underinitirdbottom hole conditions, i.e. volume at pressure Pbh,identifiedby subscript M. So we wriw

vbh= v,bh+v~bh . . . . . . . . . . . ...(9)

Vbh is the initial influx volume, and subscripts s and mindicate suspendedand migrating gas respectively. We alsoconsider conservation of wellbore volume

.,. . —., -1-., AY .1/ A DUoh — .S T .tn T JNmaufx.tntla”--. . . . . . . .(!!!)

X~.~ and Vm.d are the mud compressibility and volumerespectively. (For simplicity we neglect wellbore elasticityand fluid 10sS here).

We can also write

v, =~tA(d-dg)............(ll)

V,bh = CY.A[ 1~(d’-d;)+~(d-ds) ..(12)

v~ ()Pbh= Vmbh — . . . . . . . . . . . ..(13)

P9

Solving the above for AP we can calculate the wellborepressure rise rate as the gas bubble migrates.

11“ ‘3a’2zA’’(d~’-d~~) ““”””””””(6)

97

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6 GAS MIGWITION FAST, SLOW, OR STOPPED

o0 50 100 150

Time (rnins)

Figure 1: Evolution with time of yield stress for a 6% ben-tonite mud.

o~o 500 1000

shearRate(1/s)

Figure 3: Rheogram of Xanthum solutions used for exper-imental tests.

5.0

4.0 “

3.0 “

12.0

/ I

jAK--Jo 10 m 30 40 50

Yield Stress (lb/l(M)ftA2)

F@ure4: Suspended gas fraction from a large numbtx oftests with the two muds in an annular drilling geometry.

fa-

98

Page 7: SPE-29342 Gas Migration Rates

A. B. JOJ-LNSON& I. REZMER-COOPER&T. BAILEY & D. MCCANN 7

5000

n‘O 20 40 60 80 100 120

Tme (reins)

Figure 5: Shut-in wellbore pressure rise rate for casea of nosuspension,2% and 5% gas suspension.

\

20 -

10 -

0‘o 2 4 6“.–-———J-J-.– - ––..– /.-,,.iiuspenoeuwas rmcuon IYOJ

Figure 6: Influx volume which can be suspended in themarine riser used for field test. Volume calculated fromequation 1.

99