Calculation analysis of sustained casing pressure in gas wells Calculation analysis of sustained casing pressure in gas wells

Calculation analysis of sustained casing pressure in gas wells

  • 期刊名字:石油科学(英文版)
  • 文件大小:262kb
  • 论文作者:Zhu Hongjun,Lin Yuanhua,Zeng D
  • 作者单位:State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation,Jilin Field Company
  • 更新时间:2020-09-13
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论文简介

DOI0.1007/s12182-0120184yCalculation analysis of sustained casing pressurein gas wellsZhu Hongjun, Lin Yuanhua", Zeng Dezhi, Zhang Deping 2 and Wang Fengd State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu,Sichuan 610500. China2 Jilin Field Company, PetroChina, Songyuan, Jilin 138000, Chinao China University of Petroleum( Beijing) and Springer- Verlag Berlin Heidelberg 2012Abstract: Sustained casing pressure(SCP)in gas wells brings a serious threat to worker safety andenvironmental protection. According to geological conditions, wellbore structure and cement data of gaswells in the Sichuan-Chongqing region, China, the position, time, environmental condition and the valueof SCP have been analyzed. On this basis, the shape of the pressure bleed-down plot and pressure buildupplot were diagnosed and the mechanism of SCP has been clarified. Based on generalized annular Darcypercolation theory and gas-liquid two-phase fluid dynamics theory, a coupled mathematical model of gasmigration in a cemented annulus with a mud column above the cement has been developed. The volumeof gas migrated in the annulus and the value of SCP changing with time in a gas well in Sichuan havebeen calculated by this model. Calculation results coincided well with the actual field data, which providesome reference for the following security evaluation and solution measures of SCP.Key words: Sustained casing pressure, gas migration, coupled mathematic model gas wellI Introductionfrequently tested in order to monitor and control the severityAfter well completion, pressure in all of the casing strings buildupof SCP. These tests include pressure bleed-down and pressureshould be zero if the well is filowing at steady state conditions, The diagnostic test calls for bleeding the pressure tobut due to initial thermal expansion effects a small volume of zero through a 0.5- in needle valve and recording the casingfluids has to be bled through a needle valve in order for theThen the value of initialed down duringcasing pressure to fall to atmospheric pressure(Bourgoyne the test can be obtained from the recorded data. Recordedet al, 1999). If the casing pressure builds up when the needle pressures from other annuli would indicate whether therevalve is closed, the casing is said to exhibit sustained casing is communication between different casings in the wellpressure(SCP)However, no analytical method has been developed forWell cement problems such as small cracks or channels quantitatively analyzing these tests. The needle valve iscan result in gas migration and lead to SCP at casing heads closed to initiate pressure buildup and the pressure recorded( Dusseault et al, 2000; Kinik and Wojtanowicz, 2011). In for 24 hours. The rate of pressure buildup could providesome cases, the casing pressure can reach dangerously high additional information about the size and possibly the locationalues. SCP in acid gas wells brings a serious threat to worker of the leak. But there is still no method for interpreting thesafety and environmental protection. Therefore, we need test. Furthermore, testing of Scp is mostly qualitative andto better understand the reason for gas migration and the limited to arbitrary criteria. Such information is insufficientmechanism of SCPfor operators to quantitatively analyze SCP problems. Thus11,498 casing strings in 8, 122 wells in the Gulf of there is a need for improved analysis that could provide moreMexico(GOM) have been reported with SCP(Bourgoyne informationet al, 1998). Studies funded by the MMS (US MineralsThe work presented here focuses on the mechanism ofManagement Service)have been done by some investigators SCP and a coupled mathematical model of gas migration in(Wojtanowicz et al, 2001; Xu, 2002; Xu and Wojtanowicz, a cemented annulus with a mud column in a gas well, which2001; 2003). Based on previous research, MMS regulations provide somela inn security evaluation(30 CFR 250.517)require elimination of SCP and grant and solution中国煤化工departures permitting operation of wells with small SCPCNMHGproblems. However, wells with approved departure must be 2 Field data andlySis*Correspondingauthoremailyhlin28(@163.comSCP is a universal problem occurred in gas wells inReceived May 6. 2011China. The field data are casing pressure records providedPet. Sci.(2012)9:66-74y various operators from 13 gas wells, which mainly comefrom the Longgang, Luojiazhai, Puguang, Zhongba and Moxi1gas fields in Sichuan-Chongqing region in China2.1 Statistical analysis of SCP dataOf the 13 gas wells, 12 show SCP problems(shown inTable 1)and all the production casing strings exhibit Scp 80The percentage of SCP presenting in intermediate casing 2strings, surface casing strings and conductor casing stringsare 90%0, 83.3%and 7. 7%, respectivelyFig. 1 shows the frequency of SCP for different casingsProduction casings and intermediate casings present more<10 MPaserious SCP. Fifty percent of the production casings and 56<10 MPapercent of the intermediate casings have SCP of less than 10MPa. And 80 percent of the surface casings have SCP of lessthan 5 MPa. The SCP magnitude in conductor strings is theProduction casing Intermediate casing Surface casinglowest, all have SCP of less than 5 MPaFor instance, the productive reservoir of A gas field isFig. 1 Frequency of SCP for different casingsin the Feixianguan Formation. After well completion, thegas production rate of the Al well reached 114x10" m/d. 2.2 SCP typical patternsHowever, the casing pressure in the prouns migration in the Smith, 2005) could be concluded from the field data of 13 gasFive typical response patterns(Xu, 2002; Milanovic andis 43.5 MPa, which indicates seriousannulus. The location of the mud surface in the annulus is at wells, which include two SCp bleed-down patterns and threea depth about 200 m. The possible reasons leading to SCP SCP buildup patternsare a poor cementing job, pressure fluctuation, and tubing Instant bleed-down patternleak. In some cases, the tubing leak even presents above the Long bleed-down pattemmud surface. The production casing pressure in the A2 well Normal buildup patternis 23 MPa, and the intermediate casing pressure is 8.4 MPa. S-shape buildup patternIntermediate casing pressure in the A3 well is 12 MPa. A Incomplete buildup patternmajor cause of the SCP problem in the two wells, besides The bleed-down pattern depends on the opening of thepoor quality of cement, is casing leakageneedle valve controlled by operators and the amount of fluibled from the casing annulus. If the needle valve is openedTable 1 SCP occurrence in various casing stringswide to bleed a small amount of gas and liquid from thecasing annulus, the casing pressure would drop to 0 in a veryshort time, named as instant bleed-down pattern. On the other129389783 20 the removal of fluids, the duration of bleed-down would behand, if operators manipulate the needle valve to minimizeprolonged by the operation, so the casing pressure may notdecrease to 0 over the duration of the bleed-down test. ItA3NAthe other pattern, the long bleed-down patterm. The two bleed-down patterns are shown in Figs. 2 and 3.YNNNNNYNNNNNRemoved 0.15 m31.21 g/cm fluidN中国煤化工CNMHGTotal8337.7Notes: Y-SCP problem; N-no SCP problem: NA-data not availableFig. 2 Instant bleed-down pattermPet. Sci(2012)9:66-74田Transition time0早25Time. hFig. 3 Long bleed-dowFig. 5 S-shape buildup patternAs shown in Figs. 4, 5 and 6, we can see three buildupatterns, which depend on operating conditions such as themagnitude of gas migration, the duration of bleed-downand the mud weight. After the bleed-down, a normal builduppattern is observed when a quick initial pressure increaseis followed with a transition period of gradual increaseTransition timeuntil it comes to pressure stabilization. The stabilizeddepends on the mud weight and gasformation pressure. The transition period is determined by the 5magnitude of gas migration in the cement and mud column. 86If there is almost no gas left in the mud column after bleeddown, there would be no obvious increase in the casingpressure until the first pulse of gas reaches the casing headThen the casing pressure will increase gradually and finallystabilize. This is the S-shape buildup patten. An incompleteTime. hbuildup pattern is noted where no late-time stabilization isapparent in the testing interval (usually 24 hours) and theFig. 6 Incomplete buildup patteminitial casing pressure increase in the early time is relatively3 Mechanism of sCPGas wells are composed of many layers of casing strings,which constitute several annuli. According to the location, theannulus from inside to outside can be named"A"annulus. "Bannulus, " C""annulus, and so forth(Anders et al, 2006).Asshown in Fig. 7, "A"annulus represents the annulus betweeng61the tube and production casing. " B"annulus represents theannulus between production casing and adjacent intermediateTransition timecasing. The rest can be obtained by analogyAs shown in Fig 8, two possible configurations of theement column in the annulus are common: cemented to thesurface or a mud column above the cement. A gas cap maybe present above the mud column In wells cemented to thesurfac中国煤化工 as a one-dimensionalflow thTime, h1999). AfterCNMH Ghavior is controlledby cement properties, such as permeability and porosity, andFig. 4 Normal buildup patternby the gas formation pressure. While in wells with a mudPet. Sci.(2012)966-74column above the cement, gas migration occurs in two stages. From Fig. 9, we can see that there are several reasons forFirstly, gas flow follows Darcy's Law in the cement column. casing pressure buildups such as thermal expansion, tubularThen gas rises as bubbles through stagnant non-Newtonian mechanical failures, and gas migration(Nishikawa anddrilling fluids, in which the gas migration is affected by the Wojtanowicz, 2001; Duan and Wojtanowicz, 2005). The SCPharacteristics of mud and the status of the top gas capcaused by thermal expansion can be eliminated after bleed-down. And disabled tubing or casing strings can be replacedby the new ones. While SCP resulting from gas migrationTubing hangerwould rebuild after bleed-downTubing headAn SCP problem in different annuli may have differentA annulus monitorreasons For A annulus, a possible reason for SCP can be seenheadfrom Fig. 10. For the external annulus such as B or C annulus,B annulus monitorthe possible way leading to SCP is shown in Fig. IIC annulus monitor4 Coupled mathematical modelAlthough there are two possible configurations of theannulus monitorcement column in the annulus we focus our attention on acoupled mathematical model of gas migration in a cementedannulus with a mud column, which includes gas migrationin the cement column As shown in Fig. 12, gas sequentiallyflows through cement and mud. Finally it either accumulatesat the gas chamber when the needle valve is closed,orSafety valveD annulusevacuates from the chamber when the needle valve is open. InC annulusfollowing sections, the mathematical model for this situationwill be builtB annulProduction4.1 Gas migration in cementA annulusGas migration in a cement column can be consideredas a one-dimensional flow through a medium having someconductivity, which related with the cement properties,D Surface casinginterface pressure, interface flow rate, gas formation pressure,Intermediate casingand elapsed time. The following assumptions were madefor developing the mathematical model. Firstly, the gasIntermediate casingformation pressure is constant because the permeability of theA Production casinggas zone is much higher than that of the cement. Secondly,the pseudopressure is used. Finally, gas is vented out fromFig. 7 Annulus schematic drawingthe well at a small constant rate at the end of bleed-downThen with a constant flow rate g, during the n-th period, theMudGasbubbleGasFormationFormation中国煤化工(a) Annulus cemented(b)Annulus with a mudCNMHGabove mud columnFig. 8 Configurations of the cement column in the annulusPet. Sci.(2012)9:66-74PWell-head leakGasMicro-annulusbetweencement andCement leakMudcasingCementTubingGasmigration∠ Packer failurep=constFormatioFormationFig. 12 Gas migration in a cement and mud columnFig. 9 Possible reasons leading to SCPpressure in the cement can be obtained asA annulusifp15MPa and zsLCementeakwithTubekCorrosionPackerAgpefailurewhere p is the pressure in the cement, MPa; z is the distancefrom the gas-source formation, m; t is time, s; k is the cementConnectorCorrosion ConnectorValvepermeability, m: Le is the length of the cement column,failure m;u, is the gas viscosity, Pa s; is the cement porosityFig. 10 Possible causes of SCP in the A annuldimensionless; and cg is the gas compressibility; PaThe boundary and initial conditions may be stated asfollowsB. C annulusa) p=pe at t0 for z(0<0CementWellheadCementwhere P is the pressure on the top of the cement, MPa; Pr isleakthe reservoir pressure, MPa; as is the gas flow rate, m/s; andHangeA is the wellbore area, m2Corrosionfailure4.2 Gas mV凵中国煤化工udGas migCNMH Gcan be modeled asConnectorheadCoonnecailureeakdispersed two-phase flow that can be described by a drift-flux model (Xu and Wojtanowicz, 2003). Basic assumptionsFig. 11 Possible faults leading to SCP in the B or C annulusare a concentric annulus, equal phase pressure, uniform phasePet. sci.(2012)9:66-74densities normal to the flow direction, constant temperatureprofile, and thermodynamic equilibrium. Due to slow phase=1.53-Pl80segregation after the bleed-down, it is assumed that therelative velocity term is negligible. Under the assumptions,the one-dimensional two-equation drift-flux model is where o is the surface tension of liquid, N/msummarized in the following(Santos and Azar, 1997; Xu,And for slug flow in the vertical annulus, it is described as2002)( Hasan and Kabir, 1992)Continuity equations for the continuous(mud) and thedispersed phase(gas)are.=0.345+01d4gd(A-2)a(d-a)Pl o[d-a)PiViI-oUsing the apparent Newtonian concept, equations for(3) flow in Newtonian fluid can be used to calculate the Fanningazfriction factor. For laminar flow, the friction factor is(ap2),O(aP2y)=0(4)tRwithwhere a is the void fraction; P, and p are the gas and liquiddensity, kg/m; and vs and vi are the gas and liquid velocity, RePm dm/sAnd mixture momentum equation is:where um is the mixture viscosity, m/s; and Rem is the(),2(),中+g+p=0Reynolds number of two-phase flowThe mixture viscosity for two-phase flow is:azA21+2(-4withvg=vs +Com(6)=4Vm=(qg+qL )/A=vse +sA+ Awhere u, is the mud viscosity, PaS; A, is the liquid holdup,dh=do -d(8) dimensionless; and Ag and At are the flow areas occupied bygas and liquid respectively, mpn=02a+n1(-a)(9) For turbulent flow(Reynolds number is usually less tha10 due to the high viscosity of mud), the friction factor iswhere Pm and vm are the mixture density (kg/m)and0.3164velocity(m/s), respectively; f is the friction factor; Co is the(17distribution factor; d, is the hydraulic diameter of the annulusm;d, and do are the diameter of the inner string and the outer Obtaining an analytical solution is generally not possiblestring, respectively, m; vs is the gas slip velocity, m/s; vs and for most practical problems in two-phase flow. NumericalVsL are the superficial velocity of gas and liquid, respectively, methods based on finite-difference concepts providem/s;and g, is the liquid flow rate, m/san alternate and powerful solution approach. The threeIn order to complete the model, the slip velocity(vs)and equations, 3),(4)and(5)have been solved using the finitethe fluid fraction factor ( must be algebraically specified. difference method with computational cells shown in Fig. 13Based on analysis of the SCP field data, it can be safely the semi-implicit pattern of which is as follows(Xu, 2002)assumed that the flow pattern in annulus is either bubble orslug flow. According to the Hasan and Kabir method(Hasan1-a)PLnand Kabir, 1993), the value of the distribution factor Co for(18)bubble flow can be described as:[(l-a)p2V:1-(-a)2(=2C-12 if d, <0. 1 m or va>0.02m/s(10)12=02.0ifd>0.12ml3a<0.02m/s中国煤化工While for slug flow, Co is equal to 1. 2.YHCNMHGFor bubble flow, the slip velocity can be calculated(19)Caetano et al, 1992)(ap2)m2()2-(a)m2(。)=0Pet. Sci(2012)966-74△zFig. 13 Computational cells for finite difference solutionwhere y is the ratio of specific heats, dimensionlessPm"mm+1/2ye.d) Repeat step b)to c)until there is no change in the flow(20) conditionPi+ln2-Pi-inL+(Pm\\X Om'm)"=0The gas chamber in the wellhead is treated separatelyfrom all other cells, which are completely filled with gas4.3 Gas unloading and accumulation at the wellhead when the needle valve is closed, it does not lose gas to anyAt the wellhead, gas is released from the top when the it. The volume of this gas chamber changes with time, at n+Ineedle valve is open. While in SCP buildup, gas accumulates time step, which is related to the n-th step volume(Xu, 2002),at the top with the closed needle valve. Thus, two different in the following manner:upper boundary conditions are consideredGas or gas-liquid flowing through the needle valve to=v+the atmosphere can be considered as single-phase gas or(24)multiphase flow through a choke(Perkins, 1993). During∑()-△∑()-(9,X4△+(qm)△rbleed-down, gas usually flows at choked velocity and its flowrate is easy to record. If the gas flow rate cannot be measureddirectly, it can be computed from the following iterative where N is the number of equal-size cells in the well; wh isocedurethe volume of gas chamber, m; g and VL are the volumes ofa)Initial guess that the critical pressure ratio ye=0.5, gas and liquid respectively, m; and qgm is the gas flow ratethen calculate the pressure ratio y=papi, where p2 is the from the choke, m/sdownstream pressure(atmospheric pressure), and P, is theThe second term on the right side of the equation is theupstream pressure.volume of gas accumulated in the remaining mud columnb)If ysye, critical ftow exists. Calculate the gas flow rate The following term is the volume increase caused byusing the following equation(Gilbert, 1954)increased liquid column pressure during this time step. Thesecond to last term is the volume reduction due to gas flowm=7389×/d)from the cement below the liquid column. The last term(21) indicates the increased volume caused by gas flow out fromthe annulus during the bleed-down, which is zero duringcasing pressure buildupwhere dch is the diameter of the choke, m; and gum is the The wellhead pressure at n+I time step isliquid flow rate(m/s) which can be calculated by the volumepwnn"/wZof liquid collected and the bleed-down time recorded in SCP(25)diagnostic testsIf not, sub-critical flow exists. The gas flow rate iswhere Pwh is the wellhead pressure, MPa; Z is gas-lawdeviation factor, and n' is the moles of gasOnce the volume of the gas chamber is estimated by Eqm=02×2an,B-9(22)(24), the wellhead pressure can be calculated from Eq(25)This step, in turn, allows calculation of interface pressurefrom the wellhead pressure from Eq (20)where Pmi is the mixture density at Pr, kg/mc)Calculate the gas/liquid ratio R, (Ashford and Pierce, 4.4 Coupled gas flows in cement and mud1975)and ye, which is obtained from the following equationThe most important problem for coupling gas flow inthe cement and the mud is calculating the interface pressure7(+/aThe calculati-1y+2R(y+1)中国煤化工 which involves asimultaneous(23) for pressureCNMmentum equationsmud column except2R,-2R2for the gas chamber.The coupling procedure is shown in Fig. 14(Xu andPet. Sci(2012)96674Wojtanowicz, 2003), which begins with the pressure bleed- condition at the instant of shut-in is known. The buildup justdown because the SCP diagnostic test begins with it. At initial. right begins with the variable distribution at the end of bleed-time, the wellhead pressure, size of the gas chamber and the down. Assuming zero flow-rate at the interface, the pressuregas concentration in the mud column are known. a constant distribution in mud and cement can be calculated If there ispressure gradient throughout the entire mud column and a pressure difference across the interface, a force will drivezero flow-rate at the interface between cement and mud were gas flowing through the interface. Therefore, the pressureassumed. Then the pressure and gas distribution in the mud as distribution should be recalculated using a assumed flow rateell as pressure at the interface can be calculated. Assuming The computation is repeated until pressure at each side of thethe cement is filled with gas, the pressure is uniform and interface is equal. Time is then incremented, the boundaryequal to the interface pressure in the entire cement, except at conditions defined again, and the process is repeated until thethe point of the gas-source formationdesired time is reached5 Illustrationefine initial conditionsAssume 9=0The mathematic model was verified with selected datafrom one gas well in Xinjiang Uygur Autonomous RegionDetermine pressure above interface(PJChina. The geological conditions, wellbore structureand below (Pa)and cement data of this well are shown in Fig. 15.Andinformation about gas, mud, cement and formation are listedPin Table 2YAssume q,Table 2 Information of the illustration wellAssume the interface pressure, pCategoryvalueViscosity, Pa'sAssume a pressure, pta1.112×10pressure, pand the gas and liquid densities, p,PSolve Eqs.(18).(19).(20)for a and vViscosity, Pas0.056Calculate mixture density, pand solve Eq (20)for p. uaMudInterface tension. n/m0.068Density, kg/22701pnapn1<10Np,ni'050n+pn2Solve Eq (24)for V and Eq(25)for pFormatiPressure MPaP|<103d508 mmxJ55B*88 mCalculate paTaxihe groupCemented to the surfaceGuess aPaP|<103d3397mmxP110×1318mShawan groupCemented to the surfacett△tt△n?1568mN244.5mm×P110×2380mStopAnjihaihe arouCement top locates at 1320 mFig. 14 Solution procedure for gas flow in mud and cement中139.7mmxP110×2680mCement top locates at 1458 mThe gas flow rate at each recorded time interval wasdetermined from the bleed-down pressure history. With initialZiniquanzi group Packera73 mm external upset tubingcondition and two boundary conditions(known flow rate atthe wellhead and constant formation pressure), the pressure 2=0distribution in the mud can be calculated by the iterativeH中国煤化工procedure. The pressure distribution in the cement can beCNMHGcalculated by Eq (1). Iteration stops when the flow rate andThe casing pressure of the b annulus in the illustrationpressure at either side of the interface are equalwell has been calculated from the coupled model.TheWhen a good match for bleed-down is obtained, the initial annulus between the 139.7 mm production casing and theet. Sci.(2012)9:66-74244.5 mm intermediate casing was bled for 12 minutes before LSU/MMS Well Control Workshop held on 1 April, 1998the needle valve was closed and the following casing buildup Bourgoyne A T Jr, Scott S L and Regg J B Sustained casing pressure inmeasurement lasted 24 hours. As shown from Fig. 16, theoffshore producing wells. Paper OTC 11029 presented at Offshorecalculation result coincides well with the actual data, whichTechnology Conference, 3-6 May, 1999, Houston, Texaspresents a long bleed-down and normal buildup patternCaetano E F, Shoham O and Brill J P. Upward vertical two-phase flowthrough an annulus, Part 1: Single-phase friction factor, Taylorbubble rise velocity and flow pattern prediction. Journal of Energy9Resources Technology. 1992. 114(1): 1-13Duan S and Wojtanowicz A K. Risk analysis method of continuous airemissions from wells with sustained casinghead pressure. Paper SPE94455-STU presented at the 2005 SPE/EPA/DOE Exploration andProduction Environmental Conference, 7-9 March, 2005, Galveston,Dusseault M B, Gray M N and Nawrocki P A. Why oilwells leakCement behavior and long-term consequences. Paper SPE 64733presented at SPE International Oil and Gas Conference andCalculation resultField dataExhibition, 7-10 November, 2000, Beijing, ChinGilbert W E. Flowing and gas-lift well performance. API Drilling andProduction Practice. 1954: 126-157(Paper API 54-126)Hasan A R and Kabir C S. Two-phase flow in vertical and inclinedannuli. Intermational Journal of Multiphase Flow. 1992. 18(2):279.10010030900110013001500Hasan AR and Kabir C S. A mechanistic approach to understandingTime, minwellbore phase redistribution. Paper SPE 26483 presented at theFig. 16 Calculation result of the casing pressure68th Annual Technical Conference and Exhibition of the Society ofPetroleum Engineers, 3-6 October. 1993. Houston. TexasKinik K and Wojtanowicz A K. Identifying environmental risk of6 Conclusionssustained casing pressure. Paper SPE 143713 presented at theSPE Americas E&P Health, Safety, Security and EnvironmentalFive patterns of scp bleed-down and buildup were Conference, 21-23 March,2011,Houston, Texassummarized from the field data. The possible mechanisms Milanovic D and Smith L. A case history of sustainable annulus pressureleading to SCP have been analyzed, which include thermal in sour wells: Prevention, evaluation and remediation. Paperexpansion, tubular mechanical failures, and gas migration.SPE 97597 presented at the SPE ATw HPHT Sour Well DesignThen possible reasons for SCP in different annulus have alsoConference, 17-19 May, 2005, Woodlands, Texasbeen indicated. On this basis, a coupled mathematical moNishikawa S. Mechanism of gas migration after cement placement andof gas migration in a cemented annulus with a mud columncontrol of sustained casing pressure. Master Thesis. Louisiana StatenIversity. 1999has been developed based on annular percolation and gas- Nishikawa S and Wojtanowicz A K Experimental assessment of theliquid two-phase flow theories. Finally, the mathematicalbleed-and- lube method for removal of sustained casing pressuremodel was verified with selected data from one actual gas Paper SPE 2001-041 presented at Petroleum Society's CanadiwellInternational Petroleum Conference, 12-14 June, 2001, CalgaryAcknowledgmentsPerkins T K. Critical and subcritical flow of multiphase mixtures throughResearch work was co-financed by the China Nationalchokes. SPE Drilling Completion. 1993. 8(4): 271-276(Paper SPE20633)Natural Science Foundation and Shanghai Baosteel Group Santos O L A and Azar JJ. a study on gas migration in stagnant non-Corporation(No. 51074135), Program for New CenturyNewtonian fluids. Paper SPE 39019 presented at Latin American andExcellent Talents in University (No. NCET-08-0907)and Caribbean Petroleum Engineering Conference and Exhibition, 30Jilin Oilfield Company Project(No. JS10-W-14-JZ-32-51). August-3 September, 1997, Rio de Janeiro, BrazilWithout their support, this work would not have been Wojtanowicz A K, Nishikawa S and Xu r Diagnosis and remediationpossibleof sustained casing pressure in wells. Final report submitted to USDepartment of Interior Minerals Management Service, 31 July,ReferencesR. Analysis of diagnostic testing of sustained casing pressure inells. Doctoral Thesis. Louisiana State University. 2002Anders J, Rossberg S, Dube H, et al. Well integrity operations at Prudhoe Xu R and Wojtanowicz A K. Diagnosis of sustained casing pressureBay, Alaska. Paper SPE 102524 presented at the 2006 SPE Annual from bleed-off/buildup testing patterns. Paper SPE 67194 presentedTechnical Conference and Exhibition, 24-27 September, 2006, San at SPE Production and Operations Symposium, 24-27 March, 2001Antonio. TexasOklahoma City. OklahomaAshford F E and Pierce P E. Determining multiphase pressure drops Xu R and wojtar中国煤化工 of wells with sustainednd flow capacities in downhole safety valves. Journal of Petroleumcasing pressTechnology.1975.27(9:1145-1152CNMHGnternational petrolBourgoyne A T Jr, Scott S L and Manowski w A review of sustained Conference, 10-12 June, 2003, Calgary, Albertacasing pressure(SCP)occurring on the OSC. Paper presented at the(Edited by Sun Yanhua

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