Transient prediction of annular pressure between packers

Transient prediction of annular pressure between packersin high-pressure low-permeability wells during high-rate,staged acid jobsLiangliang Ding1,2, Jiyang Rao1, and Chengyu Xia3,*

1 College of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China2 State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation (Southwest Petroleum University), Chengdu 610500, China3College of Mechanical Engineering, Yangtze University, Jingzhou 434023, China

Received: 6 January 2019 / Accepted: 8 June 2020

Abstract. For high-pressure low-permeability wells, wellbore temperature drops drastically in high-rate andmultistage acid fracturing process. Under the combined action of the swelling of tubing string and the contrac-tion of annular fluid between packers, annular pressure between packers undergoes violent transient change instaged acid jobs, thereby deteriorating loading on the tubing string and packers. Based on the principle ofenergy conservation and wellbore heat conduction, the transient prediction of two-dimensional (2D) wellboretemperature field under pumping injection condition was established by considering the effects of heat gener-ated by friction and convection heat exchange. Moreover, the effects of wellbore temperature/pressure changeson the annular volume between packers were analyzed. Furthermore, in combination with the transient predic-tion model of wellbore temperature, PVT state equation of annular fluid, the calculation model of tubing stringradial deformation and the transient seepage equation of the formation, the transient prediction model ofannular pressure between packers in high-pressure low-permeability wells was established. Finally, by takinga high-pressure low-permeability well as an example, annular pressure between packers was calculated andthe forces on the packers and tubing string were analyzed. According to the prediction results, the tubing string,which was regarded to be safe using conventional design method, exhibited an extremely high risk of failureafter taking into account the decrease in annular pressure between packers. Therefore, the decrease in annularpressure should be fully considered in the design of tubing string for high-pressure low-permeability wells inmultistage acid fracturing process. In combination with sensitivity analysis results, it can be concluded thatformation permeability, injection rate and formation pressure all affected the change in annular pressurebetween packers.

1 Introduction

For some considerations in design and construction, one ormore enclosed fluid space may exist in oil-gas well structuressuch as annulus between tubing and casing with packerstrings and various casing annulus including free casing seg-ment. During well testing and production, fluid temperaturein various enclosed annulus within the wellbore increaseswith the rapid increase in wellbore temperature, which canlead to the increasing pressure in the annular enclosed spaceand may trigger a series of problems mainly including thefailures of tubing string and casing string as well as theelevation of wellhead (Hasan et al., 2010; Yang et al.,2013b). For example, in Marlin Oilfield owned by BP Cor-poration, the well was finally abandoned because of the

failure of production casing caused by pressure in casingannulus (Bradford et al., 2002; Gosch et al., 2004). At thePompano A-31 well in the Gulf of Mexico, the drilling toolwas jammed on account of casing deformation under annu-lar pressure alternation (Pattillo et al., 2006).

Since the 1980s, scholars all over the world have con-ducted a great deal of research on the annular pressure inwellbore enclosed space, examined the annular pressureinduced by the rise in wellbore temperature, establishedthe related theoretical calculation models (Halal et al.,1994; Hu et al., 2012; Oudeman and Kerem, 2006; Yin andGao, 2014) and raised some risk mitigation measures inaccordance with different well conditions and requirements(Ezell et al., 2010; Sathuvalli et al., 2005; Tahmourpouret al., 2010; Williamson et al., 2003).

Recently, scholars have mainly focused on the increasein annular increase induced by pressure/temperature* Corresponding author. [email protected]

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Oil & Gas Science and Technology – Rev. IFP Energies nouvelles 75, 49 (2020) Available online at:�L. Ding et al., published by IFP Energies nouvelles, 2020 ogst.ifpenergiesnouvelles.fr

https://doi.org/10.2516/ogst/2020046

REGULAR ARTICLEREGULAR ARTICLE

https://creativecommons.org/licenses/by/4.0/

https://www.ifpenergiesnouvelles.fr/

https://ogst.ifpenergiesnouvelles.fr

https://doi.org/10.2516/ogst/2020046

changes, while the induced decrease in annular pressure hasbeen poorly investigated (Bellarby et al., 2013). In recentyears, with gradual depletion of conventional gas/oilresources, more and more low-permeability and ultra-low-permeability oil/gas reservoirs have been exploited. A typ-ical technology in the development of low-permeabilityoil/gas reservoirs is high-pumping-pressure, high-rate andmultistage acid fracturing jobs, during which the wellboretemperature drops drastically. Under the combined actionof the swelling of tubing string and annular fluid contrac-tion between packers, the annular pressure drops, whichcan easily result in excessive inner and outer pressure differ-ence of the packer tubing and very large pressure differencebetween top and bottom of the packer. Accordingly, theloading conditions in the operating tubing strings and thepacker deteriorate, thereby easily causing the failures oftubing string and packers. At present, both tubing stringand packers are generally designed without consideringthe transient change in annular pressure between packers.It is generally assumed that the annular pressure is equiva-lent to the formation pressure, but the loading conditions ofthe tubing strings and downhole tools are more severe.

To overcome the shortcomings in traditional stringdesign, this study establishes a two-dimensional (2D) tran-sient prediction model of wellbore temperature field basedon the fundamental equation of energy conservation. Then,the model is calculated according to the variations in theannular volume between packers with wellbore tempera-ture/pressure, during which the transient annular volumechange, transient annular fluid volume change and theseepage characteristics of the connected strata outside theannulus are taken into full account. Moreover, the transientprediction model of annular pressure between packers isconstructed and the related prediction method is validatedby an application example.

2 Analysis of the failure of tubing string

It was reported that tubing string failures occurred in manylow-permeability oil wells of the Tarim Basin in westernChina during high-rate, staged acid jobs. The failure posi-tions were mainly located in the upper packers or the tubingstring between packers. Similar failure processes can also beobserved in other locations. A typical failure process isdescribed below. During the staged acid jobs in the lowerpacker, tubing-casing annular pressure increases suddenly,and simultaneously, tubing pressure drops. At thatmoment,tubing pressure and casing pressure connection can beobserved and the fracturing operation should be stoppedin advance. After the occurrence of accidents, the workershave found fractures in the central spindles of packers inmany wells during workover operation. Figures 1 and 2display tooth hole shrinkage and the fracture surface ofthe central spindle of upper 7-inch packer on top of a well.

Before the application in the well, these tubing stringsshould be fully verified in terms of tubing string mechanicsusing internationally accepted tubing string design methodsand software. When tubing string failures occurred,many experts from various fields were invited for analysis.

It was found that the loading on the packer was alwayswithin the designed envelope curves and the calculatedvalues of triaxial stress in the pipe, internal pressurestrength, collapse resistance and axial force safety coeffi-cient all exceeded the designed values, while all packersand tubing strings in the wells satisfied the designrequirements.

Based on the results of systematic analysis of variouskinds of wells, it is found that the annular pressure betweenthe packers in fracturing process is assumed to be equiva-lent to the pore pressure in the stratum outside the annuluswhen designing tubing strings using typical design methods.However, with regard to low-permeability wells representedby many of the failure wells in the Tarim Basin in westernChina, the annular pressure between packers undergoestransient change during high-rate, staged acid jobs. There-fore, it is unreasonable to assume that the annular pressurebetween packers equals to the pore pressure in the stratumoutside the annulus.

For the above representative wells (annulus betweenpackers shown in Fig. 3), wellbore temperature dropsrapidly when performing high-rate and multistage acid frac-turing on the lower strata. During the well operation, themaximum annular temperature between packers can reachup to 90 �C. The decrease in wellbore temperature caninduce fluid contraction in the packer annulus, thereby

Fig. 1. Photograph of recovered, diameter shrinkage at mandrelteeth.

Fig. 2. Photograph of recovered, mandrel fracture section ofupper 7-inch packer.

L. Ding et al.: Oil & Gas Science and Technology – Rev. IFP Energies nouvelles 75, 49 (2020)2

leading to the reduction in annular pressure. For low-permeability formation, the seepage velocity of pressurefrom the formation to the annulus is extremely small. Thiscan lead to significant decrease in annular pressure betweenpackers in multistage acid fracturing process and the dete-rioration of loading conditions on two packers and thetubing string between them. Therefore, based on the predic-tion of wellbore pressure/temperature field, the simulationof annular volume between packers and the seepagerules in the formation during fracturing process, this studyfirst realized the transient prediction of annular pressurebetween packers in multistage acid fracturing process andthen focused on mechanical analysis of tubing strings.

3 Prediction of wellbore temperature field

During high-rate, staged acid jobs in high-pressure low-permeability wells, the change in wellbore temperature fieldfollows the principle of energy conservation (Ding, 2011):

dQall þ dW all ¼ dEall; ð1Þwhere dQall denotes the heat flowing into the wellbore unitin unit time, with a unit of J/(s m); dWall denotes thework done by the surrounding on the wellbore unit, witha unit of J/(s m); and dQall denotes the energy variationof the wellbore unit in unit time, with a unit of J/(s m).

As shown in Figure 4, by selecting some units includingthe fluid in the oil pipe, the tubing string, the annular fluidbetween string and casing, the casing string, the cementsheath and the formation, the borehole system is divided intoa certain number of control units along both axial and radialdirections. Then, in combination with heat conduction andheat convection theories of various media in the boreholesystem, the control equations for transient prediction ofwellbore temperature field in 2D cylindrical coordinate sys-tem are established (Ai et al., 2015; Wang et al., 2018).

r Liquid unit in the oil pipeFigure 5 displays the established physical model of heat

convection of liquid in the tubing string. The quantity of

heat flowing from the external surroundings to the unitmainly includes the heat carried by the liquid during theflowing process in the oil pipe, axial heat conduction andradial heat convection along the tubing string wall. Fur-thermore, the viscous frictional work induced by the fluid’sviscous friction is taken into account. The energy-balanceequation can be written as (Hasan and Kabir, 1991; Yang,et al., 2013a):

kt@2T@z2

þ 2hti T t � Tlð Þrti

þQl

Al¼ ql cl

@T@t

þql clvl@T@z

; ð2Þ

where the subscript i represents the fluid in the oil pipe, thetubing string and the internal face of the string, respec-tively (i = l, t and ti); k denotes the coefficient of heatconduction, with a unit of W/(m K); T denotes the tem-perature, with a unit of K; z denotes the well depth, witha unit of m; h denotes the coefficient of interfacial heatconvection, with a unit of W/(m2 K); r denotes the unitradius, with a unit of m; Q denotes the friction-inducedheat, with a unit of J/s; A denotes the unit’s cross-sectional area, with a unit of m2; q denotes the fluid den-sity, with a unit of kg/m3; c denotes the specific heat, witha unit of J/(kg K); t denotes time, with a unit of s; and vdenotes the fluid’s flowing velocity, with a unit of m/s.

Fig. 4. Thermal transmission in radial direction in 2D wellbore.

Fig. 5. Fluid element inside the tubing.

Fig. 3. Annular space between packers.

L. Ding et al.: Oil & Gas Science and Technology – Rev. IFP Energies nouvelles 75, 49 (2020) 3

s Tubing string unitFigure 6 displays the established physical model of heat

conduction along the tubing string wall. The heat from theoutside world to the control unit includes axial heat conduc-tion in the tubing string and radial heat conduction alongthe tubing string wall. Since the fluid’s friction heating istaken into account, it can be assumed that the external sur-roundings did not apply work on the unit. The energy bal-ance equation in the tubing string can be written as:

kt@2T@z2

þ 4rtokcl Tcl � Ttð Þrci � rtoð Þ � r2to � r2ti

� �þ 2rtihti T l � Ttð Þr2to � r2ti

¼ qtct@T@t

;

ð3Þwhere the subscript i represents the external wall of thetubing string, annular fluid and annular internal diame-ter, respectively (i = to, cl and ci).

t Other unitsThe energy balance equation of the other units in the

wellbore can be written as:

kw@2T@z2

þ kw@2T@r2

þ kwr

@T@r

¼ qwcw@T@t

; ð4Þ

where the subscript i represents the annular fluid, the cas-ing string, the cement sheath and the formation unit,respectively (i = w).

By performing differential meshing discretization onequations (2)–(4), the solutions are acquired by means ofdifference method so as to derive the variation of tempera-ture field on 2D profile of the whole wellbore with timeduring the multistage acid fracturing process.

4 Transient prediction of annular pressurebetween packers

This study also assumes that the system is axially symmet-rical around the central line of the oil pipe, the oil pipes andcasing pipes are isotropic, and various physical parametersof the materials in the whole wellbore system remainconstant. The enclosed annulus between packers is full ofcompletion fluid, and the fluid pressure in the enclosed spacesatisfies the following function (Williamson et al., 2003):

P ¼ P T ;Vp; mð Þ; ð5Þwhere P denotes the annular pressure between packers,with a unit of MPa; Vp denotes the annular volumebetween packers, with a unit of m3; and m denotes theannular fluid mass between packers, with a unit of kg.

According to equation (5), annular pressure betweenpackers in multistage acid fracturing process is determinedby three factors, namely, fluid contraction induced by thedecrease in fluid temperature, change in annular volumeand change in annular fluid amount:

�P ¼ �Pt þ�Pv þ�Pm; ð6Þwhere DPt denotes the change in annular pressurebetween packers induced by thermal expansion/contrac-tion of annular fluid, with a unit of MPa; DPv denotesthe change in annular pressure between packers inducedby the change in annular volume, with a unit of MPa;and DPm denotes the change in annular pressure betweenpackers induced by the change in annular fluid mass, witha unit of MPa.

The change in annular pressure between packers causedby fluid contraction with decrease in temperature can becalculated as (Rizkiaputra et al., 2016):

�Pt ¼ aat

kT�T ; ð7Þ

where kT denotes the isothermal compressibility of thefluid between packers, with a unit of MPa�1; aat denotesthe thermal coefficient of annular fluid, with a unit of�C�1; DT denotes the decrease in annular temperaturebetween packers, with a unit of �C.

The change in annular pressure between packersinduced by fluid expansion or contraction with varyingtemperature, denoted as DPt, can be calculated based onthe prediction results of wellbore temperature as well ascompressibility coefficient and thermal coefficient ofannular fluid between packers.

4.1 Prediction of the change in annular volumebetween packers

The change in annular pressure between packers induced bythe change in annular volume can be calculated as:

�Pv ¼ � 1kTVa

�Va; ð8Þ

where DVa denotes the increment in annular volumebetween packers, with a unit of m3, and Va denotes theannular fluid volume between packers, with a unit of m3.

By taking into account the effects of wellbore pressure/temperature changes on annular fluid between tubing stringand the packer, the transient increment in annular volumebetween packers in multistage acid fracturing process,denoted as DVa, is then calculated.

r Radial contraction of the tubing stringDuring staged acid jobs, the tubing string shows radial

contraction with the decrease in wellbore temperature,thereby leading to the increase in enclosed annular volumebetween packers. The radial displacement of the tubing

Fig. 6. Tubing string element.


string induced by temperature change can be calculated as(Zhang. et al., 2010):

S1 ¼ 1þ l1� l

aagr

Z r

rti

�Trdr; ð9Þ

where S1 denotes the radial displacement at any point onthe string, with a unit of m; l denotes the steel pipe’sPoisson’s ratio, dimensionless; aag denotes the string steel’sthermal expansion coefficient, with a unit of 1/�C;r denotes the distance between any point on the stringand the axis of the string, with a unit of m; and rti denotesthe radius of the pipe, with a unit of m.

Under constant temperature difference, the change inexternal diameter of the pipe can be calculated as:

S1 ¼ aag�T1þ l1� l

r2to � r2ti2rto

; ð10Þ

where rt0 denotes the external diameter of the pipe, with aunit of m.

The change in annular volume induced by the pipe’sradial contraction can be calculated as (Yang et al., 2013b):

�V 1 ¼ p rt0 þ lrð Þ2 � r2t0� �

La; ð11Þ

where DV1 denotes the change in annular volume inducedby the pipe’s radial contraction, with a unit of m3, and Ladenotes the annular length between packers, with a unitof m.

s Contraction of the fluidWith the decrease in temperature, the fluid in the

enclosed annular space exhibits contraction, which can leadto the change in annular volume between packers. Thechange in annular volume can be calculated as:

�V 2 ¼ aatp�T r2c � r2t0� �

La; ð12Þ

where DV2 denotes the change in annular volume inducedby the fluid contraction, with a unit of m3.

t Radial expansion of oil pipeDue to the decrease in enclosed annular pressure, the oil

pipe is under pressure and exhibits radial expansion on theexternal surface. The change in the external diameter of theoil pipe induced by the decreasing annular pressure,denoted as S2 (with a unit of m), can be calculated as(Oudeman and Kerem, 2006):

S2 ¼ rt0�P1þ lð Þ r2ti þ 2 1� 2lð Þr2t0

� �Et r2to � r2ti

� � ; ð13Þ

where Et denotes the oil pipe’s elastic modulus, with a unitof MPa. Therefore, the reduction in annular volumeinduced by radial expansion, denoted as DV3 (with a unitof m3), can be calculated as:

�V 3 ¼ p r2to þ S1

� �2 � rt0 þ S1 � S2ð Þ2h i

La: ð14Þ

u Expansion effect of annular fluidThe decrease in annular pressure not only induces the

swelling of the tubing string but also the expansion of

annular fluid. The induced volume increment can be calcu-lated as (Azzola et al., 2007):

�V 4 ¼ pEt

r2c � r2t0� �

�PLa; ð15Þ

where DV4 denotes the change in annular volume inducedby the expansion of annular fluid, with a unit of m3, andEt denotes the bulk elastic modulus of the annular fluid,with a unit of MPa.

v Change in annular volumeAccording to equations (11)–(15), the change in the

enclosed annular volume can be calculated as:

�V a ¼ �V 1 þ�V 2 þ�V 3 þ�V 4: ð16Þ

4.2 Prediction of pressure transfer between annulusand formation

During the pumping-injection operation, annular pressurebetween packers drops steadily. Under the pressure differ-ence between formation and annulus, the pressure in theperforated formation outside the annulus may exhibit tran-sient seepage flow, which can result in the change in annularfluid mass between packers. Transient flowing behavior canbe described as (Kan et al., 2016):

Pi � Pwf ¼ Ql4pkh

Ei;lcrr2oh4kt

� �; ð17Þ

where P denotes the annular pressure between packers,with a unit of MPa; Pi denotes the pressure of the perme-able formation outside the annulus between packers,with a unit of MPa; Q denotes the production rate, witha unit of kg/m3; k denotes overall permeability, with aunit of D; h denotes the thickness of the permeable forma-tion, with a unit of m; U denotes the porosity of thepermeability formation, with a unit of %; l denotes theformation’s fluid viscosity, with a unit of MPa s; rohdenotes the drainage radius, with a unit of m; t denotesthe seepage time in the formation, with a unit of h; Crdenotes the total compression coefficient of the permeableformation, with a unit of MPa�1; and Ei is the exponentialintegral term.

According to equation (17), the seepage velocities fromformation to annulus under different pressures, denoted asQ, can be calculated. Therefore, the change in annularpressure induced by formation pressure transfer can becalculated as:

�Pm ¼ Q�t1

kTVa: ð18Þ

4.3 Solution to the theoretical model

During high-rate and multistage acid fracturing process inhigh-pressure low-permeability wells, annular fluid tempera-ture drops drastically. Due to the constraints of packers andpipe wall, annular fluid cannot be freely contracted, whichcan cause the decrease in annular pressure and thus inducethe swelling of tubing string and the reduction in annular


volume. The reduction in annular volume can enhanceannular pressure, which can also increase the annularvolume and generate additional pressure on the expansionof fluid. In turn, the pressure can react on the oil pipe andchange the annular volume again, while the change involume can also lead to the change in pressure. Further,after the decrease in annular pressure, pressure differencebetween annulus and the external formation is produced.Under this pressure difference, seepage may occur fromlow-permeability formation to annulus, thereby resultingin the rise in annular pressure. Therefore, the change inannular pressure between packers is determined by threefactors, namely, thermal fluid contraction, annular volumechange and annular fluid mass change. Moreover, thesefactors are coupled, and the change in annular pressure withthe pumping-injection time, denoted as DP, can also besolved via iterative computation. Figure 9 displays thedetailed calculation procedures.

As shown in Figure 7, the change in annular pressure canbe calculated as described below. Firstly, the time step isdetermined, and then, wellbore temperature distributionat different moments in multistage acid fracturing processis calculated. In the calculation, initial change in annularpressure, denoted as DPv, can be assumed. According toequations (11), (12), (14) and (15), the change in annularpressure induced by the change in annular volume, denotedas DPv, is calculated. The acquired results of DPv in two cal-culations are compared and the error is calculated. If theerror is within the allowable range, DPv is output and thecalculation continues; otherwise, the iterative calculationrestarts until the calculation results satisfy the requiredaccuracy. According to equation (7), the decrease in annularpressure, denoted as DPt, induced by the contraction ofannular fluid with decreasing temperature, is calculated.After DPt and DPv are obtained, the change in annularpressure induced by seepage between annulus and forma-tion, denoted as DPm, is calculated in accordance with thedifference between annular pressure and formationpressure. Given the total change in annular pressure (DP),the total change in annular pressure are recalculated afterthe recalculation of DPt and DPv. The values of DP in twocalculations are compared and the error is calculated.If the error is within the allowable range, DP is outputand the calculation continues; otherwise, the iterative calcu-lation restarts until the calculated results reach the requiredprecision. Subsequently, the total change in annular pres-sure at the next moment, denoted as DP, is calculatedaccording to the above steps. Finally, the calculation endswhen the calculation results at all moments are acquired.

5 Calculation in an example well

This study focused on a high-pressure low-permeability wellfor further analysis. The detailed parameters are listedbelow. The depth of the drilling well is 5000 m, the middlepressure in upper perforated formation is 90 MPa, the tem-perature on the bottom of wellbore is 136 �C, dual-packer isemployed for staged acid jobs, the depths of two packers are4510 m and 4850 m, the pumping pressure in construction

ranges from 80 to 90 MPa, and the displacement in theconstruction is 5–6 m3/min. Figure 8 displays the structuresof wellbore and the tubing string under construction.

5.1 Wellbore temperature distribution

Figure 9 displays the temperature distribution patterns ofthe fluids in tubing string and the annulus between tubingstring and casing string. It can be observed that the fullwellbore temperature drops significantly in high-rate,staged acid jobs, and the temperatures inside and outsidethe tubing string decrease more significantly in contrastwith original formation temperature.

5.2 Change in annular temperature between packers

According to the multistage acid fracturing operationconditions, wellbore temperature is predicted and thechange in annular temperature between packers with theinjection time is plotted, as shown in Figure 10. Apparently,with the increase in pumping-injection time, annular tem-perature between packers drops gradually, and it is reducedto 50 �C after pumping injection for 30 min. The tempera-ture drops gradually slow down with the pump injectiontime, and finally, the annular temperature between packersis stabilized at 32 �C.

Fig. 7. Calculation flow diagram for the mathematical model.


5.3 Change in annular pressure between packers

According to the change in annular temperature betweenpackers, annular pressure between packers is predicted,and the temporal variation is shown in Figure 11. It canbe observed that, at the beginning of injection, the wellboretemperature exhibits no drop. Under the pressure in thetubing string, annular pressure between packers rapidlyincreases to 98 MPa. Subsequently, with the continuousdecrease in wellbore temperature, annular pressure betweenpackers drops gradually, and it is reduced to approximately30 MPa after pumping injection for 40 min. As the drop offormation temperature slows down and with the supple-ment of formation pressure, annular pressure between pack-ers exhibits steady increase and finally stabilizes at a fixedvalue of 87 MPa.

5.4 Verification of tubing string and packers

The effect of multistage acid fracturing operation onannular pressure between packers is not taken into accountwhen using traditional design methods. As stated above,this study assumes that the annular pressure betweenpackers equals to the pore pressure in the formation. Based

on the prediction results of annular temperature and pres-sure between packers in multistage acid fracturing process,the intensities of tubing string and upper and lower packersare verified, and the verification results are shown inFigures 12–14. It can be observed that, using traditionaldesign method, the tubing string and upper and lower pack-ers all satisfy the requirements in terms of intensity andoperation safety. By taking into account the decrease inannular pressure between packers induced by productionincrease, tri-axial stress on the tubing string between pack-ers is smaller than the designed safety coefficient. Moreover,the loading conditions of both upper and lower packersexceed the envelope curves, while the tubing string andpackers are all at high risks of failure. It is necessary toredesign the tubing string or adopt some effective risk-mitigation measures.

6 Research on mitigation measures

6.1 Analysis on risk mitigation approach

String failure risk is because of decrease of the packer annu-lar pressure which is caused by wellbore temperaturedecrease. That is, three conditions for the risk are wellboretemperature drop, isolation state of the two packers andlack of strength for tubing and packers. If one of the three

Fig. 11. Annular pressure change vs. Injection time.

Fig. 9. The wellbore temperature field.

Fig. 8. Configuration and string diagram of the well.

Fig. 10. Annular temperature change vs. Injection time.


can be solved, string failure risk can be eliminated. Based onthe mechanisms of the risks, the following risk precaution-ary ideas have been drown:

1. String failures can be prevented by means of upliftingpacker pressure grade and tubing strength betweenthe packers. Due to the fact of the great pumpingpressure, after the packer annular pressure decreasesto 0 MPa, it is impossible to select required tubingand packers. Therefore, this measure is not feasible.

2. Decrease wellbore temperature and improve acid frac-turing fluid temperature and operation parameters toreduce wellbore temperature decrease, and then toprevent string failure by maintaining annular pressurebetween packers. However, Dibei gas field has com-mercial production only by means of large scale stim-ulation. Moreover, increasing temperature of acid maylead to the decrease of acid performance, increase ofthe corrosion on strings and cost for heating acid.Therefore, it is not feasible.

3. Break the isolation state between the two packers.Balance pressure between tubing-annulus and above-below packer, and then failure risks of string andpackers can be prevented. Based on mechanism andtechnique, this approach is feasible. However, poten-tial risks brought by perforated tubing still need tobe further investigated.

After tapping the tubing, pressure between tubing-annulus and packers will be the same. Stimulation stringand upper and lower packer calibration results are shownin Figures 15–17. As are shown in Figures 15, 16 and 17,pipe string and upper-lower packers can meet the need ofthe design.

6.2 Potential risk analysis of perforating tubing

After perforation for tubing, fluid in tubing and annularspace between packers can be connected with each other,therefore, can lead to the following risks:

1. When stimulating the lower interval, fluid diverters atperforations too much to realise staging stimulationaim. Diameter of equalizing orifice is 5 mm, 0.4% oftubing section. That is, when operation flow ratereaches to 4 m3/min, flow rate at equalizing orifice is0.016 m3/min, and influence of orifice throttle onlower interval fracture is small. Therefore, this riskcan be eliminated.

2. When stimulating the lower interval, great operationpressure will lead to the fracture of the productioncasing between two packers. Because inner compres-sive strength of the production casing between pack-ers in Dibei gas field, dual packer production casingis safe when stimulating lower interval.

According to the above analyses, perforating severalpressure release holes with diameter of 5 mm on tubingbetween two packers can effectively prevent failure risksof packers and strings during the staging stimulationtreatment.

Fig. 12. Triaxial-stress calibrated results for the stimulationstring for both methods.

Fig. 13. Calibrated results for both methods against the upperpacker operating envelope.

Fig. 14. Calibrated results for both methods against the lowerpacker operating envelope.


7 Discussion and sensitivity analysis

7.1 Formation permeability

Figure 18 displays the relationship between the change ruleof annular pressure between packers and the permeabilityof the formation outside the annulus between packers.Overall, annular pressure between packers shows a moresignificant drop in the formation with lower permeability.At a permeability of 0.001 md, annular pressure betweenpackers is reduced to 0 MPa in multistage acid fracturingprocess, and the retention time can even last over 1 h. Asthe formation permeability increases, the formation pres-sure supplement ability rises and annular pressure dropsless significantly. As the formation permeability increasesto 0.1 md, the reduction in annular pressure betweenpackers can reach a maximum of 12 MPa.

7.2 Displacement of pump

Figure 19 displays the relationship between the maximumreduction in annular pressure between packers and the dis-placement of pump. With the increase in displacement, themaximum reduction in annular pressure between packersincreases more significantly. As the displacement of pumpincreases to 2 m3/min, the maximum reduction in annularpressure between packers can reach up to 65 MPa.

7.3 Formation pore pressure between packers

Figure 20 displays the relationship between the maximumreduction in annular pressure between packers and theformation pore pressure. The maximum reduction in annu-lar pressure between packers increases more obviously asthe formation pore pressure rises. When the annular pore

Fig. 15. Triaxial stress calibration result for stimulation string.

-1200

-800

-400

0

400

800

-80 -40 0 40 80

Differential Pressure, MPa

Axi

al F

orce

, kN

Fig. 16. Strength calibration of upper packer.

-650

-250

150

550

950

-100 -60 -20 20 60 100

Differential Pressure, MPa

Axi

al F

orce

, kN

Fig. 17. Strength calibration of lower packer.

Fig. 18. Relation of annular pressure between packers andinjection time under different reservoir permeability.


pressure between packers equals to or is smaller than80 MPa, annular pressure between packers during stagedacid jobs can drop to 0 MPa. Therefore, the maximumreduction in annular pressure between packers equals toformation pore pressure. As the formation pore pressureincreases gradually, the formation supplement ability canbe steadily enhanced and the maximum reduction in annu-lar pressure between packers drops.

8 Conclusion

In this study, by taking into account the effects of heatgenerated by friction and convection heat transfer, the tran-sient prediction model of annular temperature field betweenpackers in a high-pressure low-permeability well duringhigh-rate, staged acid jobs under pumping injection condi-tion was established. Moreover, the effects of the changesin wellbore temperature and pressure on annular volumebetween packers were analyzed. Moreover, in combinationwith the transient wellbore temperature prediction model,PVT state equation of annular fluid, the calculation modelof tubing string radial deformation and the transient seep-age equation of the formation, the transient predictionmodel of annular pressure between packers in multistageacid fracturing process was established.

The established prediction model of annular pressurebetween packers was then applied to the annulus betweenpackers in a high-pressure low-permeability well duringmultistage acid fracturing period. In combination with themechanical analysis results of the tubing string, it wasfound that the designed tubing string using traditionalmethod is at a high risk of failure after considering thedecrease in annular pressure between packers. Accordingly,the reduction in annular pressure between packers shouldbe fully considered in the design of tubing string for high-pressure low-permeability wells in multistage acid fractur-ing period.

For string failure risks of multilayer stimulation forhigh-pressure gas well, risk prevention measure study hasbeen developed in terms of mechanism of decrease of annu-lar pressure between packers resulted from wellbore temper-ature decrease. Based on the comparative analyses, safetyperformance of string and packers can be improved bymeans of perforating several holes on tubing betweenpackers.

Acknowledgments. The authors are grateful for the support ofNational Natural Science Foundation of China (Grant no.51704034), Open Fund (PLN201707) of State Key Laboratoryof Oil and Gas Reservoir Geology and Exploitation (SouthwestPetroleum University).

References

Ai S, Cheng L., Huang S., Liu H., Zhang J. (2015) A criticalproduction model for deep HT/HP gas wells, J. Natural GasSci. Eng. 22, 132–140.

Azzola J.H., Tselepidakis D.P., Pattillo P.D., Richey J.F. (2007)Application of vacuum-insulated tubing to mitigate annularpressure buildup, SPE Drill. Complet. 22, 1, 46–51.

Bellarby J., Kofoed S.S., Marketz F. (2013) Annular pressurebuild-up analysis and methodology with examples frommultifrac horizontal wells and HPHT reservoirs, in: PaperSPE 163557 Presented at the SPE/IADC Drilling Conferenceand Exhibition, Amsterdam, The Netherlands, 5–7 March.

Bradford D.W., Gibson D.H., Gosch S.W., Pattillo P.D., SharpJ.W., Taylor C.E. (2002) Marlin failure analysis and redesign:part 1 description of failure, in: IADC/SPE Drilling Confer-ence, Dallas, USA, February 26–28.

Ding L. (2011) Mechanical study of testing string and itsapplication in deep gas well with high pressure and highproduction, Doctoral Dissertation of Southwest PetroleumUniversity, pp. 18–21.

Ezell R., Fontenot E.S., Robinson E.F., Cunningham L.E.,Patrickis A. (2010) High performance aqueous insulating packerfluid improved flow assurance and reduced annular pressurebuildup in ultra deepwater wells, in: SPE Deepwater Drillingand Completions Conference, Galveston, USA, October 5–6.

Gosch S.W., Horne D.J., Pattillo P.D., Sharp J.W., Shah P.C.(2004) Marlin failure analysis and redesign: part 3 – VITcompletion with real-time monitoring, SPE Drill. Complet.19, 02, 120–128.

Halal S., Mitchell R.F. (1994) Casing design for trapped annularpressure buildup, SPE 25694, Society of Petroleum Engineers,pp. 107–114. doi: 10.2118/25694-PA.

Fig. 19. Relation of displacement of pump and annularpressure drop between packers.

Fig. 20. Relation of formation pressure and annular pressuredrop between packers.


https://doi.org/10.2118/25694-PA

Hasan R., Izgec B., Kabir S. (2010) Sustaining production bymanaging annularpressure buildup, SPE Prod. Oper. 25, 02,195–203.

Hasan A.R., Kabir C.S. (1991) Heat transfer during two-phaseflow in wellbores: part I – formation temperaturein: SPEAnnual Technical Conference and Exhibition, Dallas, USA,October 6–9.

Hu W., Wang J., Zhang W. (2012) Confined annular pressuretrap pressure prediction and release technology for deepwaterdrilling, Sino-glob, Energy 17, 08, 41–45.

Kan C., Yan J., Yu X., MengW., Hu N., Zhou B., Zhang B., Hu Z.(2016) Numerical simulation of thermal stress on entrappedpressure of deepwater and further research on anti-thermal-stresscasing tools, in: SPE/AAPG Africa Energy and TechnologyConference, Society of Petroleum Engineers.

Oudeman P., Kerem M. (2006) Transient behavior of annularpressure buildup in HP/HT wells, SPE Drill. Complet. 21, 4,234–241. SPE-88735-PA

Pattillo P.D., Cocales B.W., Morey S.C. (2006) Analysis of anannular pressure buildup failure during drill ahead, SPE Drill.Complet. 21, 04, 242–247.

Rizkiaputra R., Siregar R., Wibowo T., Mabunga S. (2016) Anew method to mitigate annular pressure buildup by usingsacrificial casing, case study: a deepwater well in Indonesia,Society of Petroleum Engineers.

Sathuvalli U.B., Payne M.L., Pattillo P.D., Rahman S.,Suryanarayana P.V. (2005) Development of a screeningsystem to identify deepwater wells at risk for annular pressure

build-up, in: SPE/IADC Drilling Conference, Amsterdam,Netherlands, February 23–25.

Tahmourpour F., Hashki K., Hassan H.I.E.l. (2010) Differentmethods to avoid annular pressure buildup by appropriateengineered sealant and applying best practices (cementing anddrilling), SPE Drill. Complet. 25, 02, 248–252.

Wang L., Gao B., Gao L., Tianxiang H. (2018) Prediction ofannular pressure caused by thermal expansion by considering thevariability of fluid properties, Appl. Therm. Eng. 141, 234–244.

Williamson R., Sanders W., Jakabosky T., Serio M., Grith J.E.(2003) Control of contained-annulus fluid pressure buildup, in:SPE/IADC Drilling Conference, Amsterdam, Netherlands,February 19–21.

Yang M., Meng Y., Li G., Deng J. (2013a) Effects of the radialtemperature gradient and axial conduction of drilling fluid onthe wellbore temperature distribution, Acta Phys. Sin. 62, 7,79–84.

Yang J., Tang H., Liu Z., Yang L., Huang X., Yan D., Tian R.(2013b) Prediction model of casing annulus pressure fordeepwater well drilling and completion operation, Petrol.Explor. Dev. 40, 5, 661–664.

Yin F., Gao D. (2014) Improved calculation of multiple annulipressure buildup in subsea HPHT Wells, in: Paper SPE170553 Presented at the IADC/SPE Asia Pacific DrillingTechnology Conference and Exhibition, Bangkok, Thailand,25e27 August.

Zhang Y., Li Z., Zhang L. (2010) Study on the casing strength ofvacuum insulated shaft, Eng. Mech. 27, 05, 179–183.


Documents

Transient prediction of annular pressure between packers