Research Article

Hao Huang, Qiao Deng*, and Hui Zhang

Study of dynamic pressure on the packer fordeep-water perforationhttps://doi.org/10.1515/phys-2021-0025received September 09, 2019; accepted March 11, 2021

Abstract: The packer is one of the most important tools indeep-water perforation combined well testing, and itssafety directly determines the success of perforation testoperations. The study of dynamic perforating pressure onthe packer is one of the key technical problems in theproduction of deep-water wells. However, there are fewstudies on the safety of packers with shock loads. In thisarticle, the three-dimensional finite element models ofdownhole perforation have been established, and a seriesof numerical simulations are carried out by using ortho-gonal design. The relationship between the perforatingpeak pressure on the packer with the factors such as per-forating charge quantity, wellbore pressure, perforatingexplosion volume, formation pressure, and elastic mod-ulus is established. Meanwhile, the database is establishedbased on the results of numerical simulation, and the cal-culation model of peak pressure on the packer during per-forating is obtained by considering the reflection andtransmission of shock waves on the packer. The resultsof this study have been applied in the field case of deep-water well, and the safety optimization program for deep-water downhole perforation safety has been put forward.This study provides important theoretical guidance for thesafety of the packer during deep-water perforating.

Keywords: deep-water perforation, downhole packer, numer-ical simulation, prediction model, optimization program

1 Introduction

With the rapid development of oil and gas industry inrecent years, the exploration of offshore oil and gasresources has gradually become the focus, especially indeep water [1]. The perforation combined well testing isone of the most important links in the development ofdeep-water well operations. The researchers focus on thesafety of downhole perforation, which is an importanttechnical problem in deep-water well completion [2].The study of dynamic pressure on the downhole packerin the wellbore during perforation is a key step for thesafety analysis of deep-water perforation jobs. Tubing-conveyed perforating (TCP) combined well testing is anadvanced technology, which has been widely used in off-shore completion operations, especially in deep-waterwells [3]. A series connection of the perforating gun,the operation tubing or perforated string, the packers,and other tools are put into the downhole casing of thewellbore during TCP, as shown in Figure 1. The packer isone key tool connected to the perforated string, and thefailure of the packer will lead to huge economic damageand seriously threaten the safety of field operators. Since2011, the safety of the packers has been seriously threa-tened during deep-water well perforating in the Gulf ofMexico, with sealing failure and central pipe fracture [4].Therefore, it is necessary to study the safety of packerduring deep-water perforating. However, there is a lackof safety analysis for the packer during deep-water wellperforating at present. The relevant research in detail hasbeen carried in this study.

As we know, perforation is an intensely violent explo-sion process. In a few microseconds, the shaped chargesinside the perforating gun explode and form a high-speedjet to penetrate the casing to the reservoir. Meanwhile, partof the perforating explosion energy will be released intothe downhole wellbore, and the downhole space is longand narrowwith the packer completely set. The wellbore isfilled with perforation fluid, and the interaction betweenperforating explosion products with wellbore fluid is thebeginning of the hydrodynamics effects with shock loads

Hao Huang: School of Petroleum Engineering, Yangtze University,Wuhan, China, e-mail: 18772645696@163.com

* Corresponding author: Qiao Deng, School of PetroleumEngineering, Yangtze University, Wuhan, China,e-mail: dengqiao2008@163.com

Hui Zhang: College of Petroleum Engineering, China University ofPetroleum, Fuxue Road 18 Changping, Beijing 102249, China,e-mail: zhanghuicup2018@163.com

Open Physics 2021; 19: 215–223

Open Access. © 2021 Hao Huang et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0International License.

during perforating. The dynamic perforating pressure inthe wellbore has been formed, and the packer has beenimpacted [5]. In recent years, in order to maximize theproductivity and reduce the costs, larger perforating gunswith higher-shot densities and propellants have beenrapidly developed, which are widely adopted in deep-wateroil and gas wells, resulting in a large increase in shock loadsin the wellbore by using such perforating systems [6]. Allthe tools in the TCP system exposed to perforation fluid willbe subjected to the pulsating pressure during perforating,and the safety of the TCP system will be seriously threa-tened, especially for the packer. As the perforation processof deep-water well is more complex and difficult with theincrease in water depth, to predict downhole perforationpressure on the packer is the key to ensure the safety ofdownhole perforation.

Researchers have come to realize the importance ofstudying the dynamic pressure of perforation in recentyears. Some research work has been carried out in theory,experiment, and simulation of perforating pressure.Combining theory with experiment, the characteristicsof perforation pressure fluctuation during composite per-forating have been studied [7]. Based on the empiricalformula, the dynamic load of downhole perforation hasbeen analyzed [8]. It is concluded that the dynamic pres-sure from perforation will increase the damage risk ofdownhole equipment of deep-water wells [9]. The per-foration process is simulated by using the finite elementsoftware, and a prediction model is obtained based on

the simulation data [10]. These studies have promotedthe research progress of downhole perforation pressure.However, the dynamic perforation pressure on the packerunder actual deep-water conditions is not clear.

The load output of perforating explosion in wellboreis very complex, including detonation wave, shock wave,interaction between detonation gas and perforation fluid,fluid solid coupling, etc. Moreover, the reflection andtransmission of shock waves at the interfaces of thepackers are almost impossible to be calculated with the-oretical formula. Therefore, it is difficult to analyze suchdynamic problems by theoretical or experimental means.Due to the development of modern science and tech-nology, numerical simulations on the computer provideconvenience for the study of downhole perforation, whichcan show the dynamic process of perforation. Meanwhile,it is very convenient and flexible to obtain dynamic data atdifferent positions in the wellbore after the simulation,which provides a basis for in-depth study of the packersafety under different perforating conditions.

In this article, the numerical simulation of actualdeep-water conditions has been carried out by the soft-ware LS-DYNA to simulate the physical process of perfora-tion, the peak pressure on the packer during perforating isobtained, and the safety analysis of the packer is proposedand the measures of shock absorption are put forward.

2 Numerical model

Some previous studies have focused on the numericalsimulation for downhole perforation. A 2D Euler codingwas used to simulate the process of jet formation andpenetration into the casing during perforating [11]. Theprocess of perforation has been studied by the softwareLS-DYNA, and the results have been verified by the fieldcase [12]. The process of perforation to cement damage hasbeen studied by the software LS-DYNA [13]. A pressure fieldmodel of shaped charge was set up to study the downholeperforation, which can simulate the changing process ofshell, charge, and liner during perforating by the softwareLS-DYNA [14]. A model for estimating perforating depthhas been obtained by considering the factors such as thenumber of bullets, the charge, the wellbore pressure, andthe formation pressure. A prediction model based on simu-lated data has been fitted under different perforating con-ditions [15]. These studies promote the numerical simulationprocess of modern perforation completion.

However, due to the complexity of deep-water per-foration model, previous studies mostly focused on a

Figure 1: Downhole TCP system.

216 Hao Huang et al.

single or a small number of perforation bullets, withoutconsidering the influence of various factors in the per-foration process of deep-water wells, while the study ofperforation pressure on the packer has not been reported.The process of perforation is composed of complex phy-sical and chemical changes, and some simplifications canbe applied for the simulation. As the string system consistsof different rods, the components of the string are regardedas isotropic, and the physical model of deep-water perfora-tion can be established, as shown in Figure 2.

Some perforating bullets are distributed in the perfor-ating gun at a certain phase. The string system involves theperforating gun (177.80/152.53mm), tubing (73.02/62.00mm),and casing (244.40/220.50mm). The air fills inside theremaining space of the gun, and the perforation fluidfills the annulus space of tubing and casing. The packerrestrains the upper end of the string radially, and the cir-cumference of the string is restrained by the casing withreservoir surrounding. The parameters of the perforationmodel for the deep-water wells are shown in Table 1.

Since the physical process of perforation includescomplex fluid–structure interaction with high strain rate,the Arbitrary Lagrange–Euler (ALE) algorithm in LS-DYNAcan be used for the calculation. The ALE algorithm canaccurately simulate the formation and penetration ofa shaped charge jet with high strain rate and large defor-mation, which can be used in RDX (Royal DemolitionExplosive) explosives, air, fluid, and the space positionof the ALE grid remain unchanged with the material flowsamong the grids. The Lagrange algorithm is used in the

perforated string. The Lagrange algorithm can be first exe-cuted by the ALE algorithm at each time step.

The hexahedral meshing is used in the perforationmodel. In order to capture the deformation and move-ment process of the material structure effectively, allparts of the material needs have common nodes on thecontact interfaces, which can ensure the effective transferof energy between the parts of the mesh. Figure 5 showsthe local mesh of the cross perforated string and perfor-ating gun. The grid size is an important factor affectingthe speed and accuracy of simulation calculation. Thelarger size cannot guarantee the accuracy of calculation.The smaller size will greatly increase the amount of cal-culation. The appropriate mesh size is the prerequisite forthe success of numerical simulation. After many times oftest calculations, the average mesh spacing is set to4–5 mm, and the total number of meshes is about 1 mil-lion (Figure 3).

The material model of HIGH_EXPLOSIVE_BURN isused for the charge, and its characteristics such as pres-sure, volume, and energy can be accurately described bythe state equation of EOS_JWL during perforating, asshown in ref. [16]:

= − + − +

− −

P A ω

R Ve B ω

R Ve ωE

V1 1 ,R V R V

1 2

01 2 (1)

where V is the relative volume of explosives; E0 is theinitial internal energy value per unit volume of explo-sives; and A, B, R1, R2, and ω are the physical propertiesof explosives.

The material model of MAT_NULL can be used for thefluid, which can be described by the state equation ofEOS_GRUNEISEN, as shown in ref. [15]:

( )

=

+ − −

− ( − ) − −

+ ( + )

+ ( + )

Pρ C α α α

S α S S

γ δ α E

1 1

1 1

,

γ δ

αα

αα

J J2

J 2 J 2 J2

1 J 22

1 3 1

0 J J J

0 J

J2

J2

J3

J 2(2)

where ρJ is the initial density of medium; CJ is the curveintercept of shock wave velocity; αJ is the compressibilityof medium; and δJ are the constant coefficients andcorrections of state equation; and S S S, , and1 2 3 are theconstant coefficients of stress wave velocity curve inmaterials.

The material model of EOS can be used for the mate-rial air, as shown in ref. [17]:

= ( + + + ) + ( + + )P C C μ C μ C μ C C μ C μ E,0 1 22

33

4 5 62 (3)

where C C C C C C C, , , , , ,0 1 2 3 4 5 6 is the equation of statecoefficients.Figure 2: Numerical model.

Study of dynamic pressure on the packer for deep-water perforation 217

3 Numerical analysis

According to the aforementioned modeling methods,the numerical simulations have been carried out on alarge computer, and the simulation result data can beextracted by the post-processing.

3.1 Simulation results

The dynamic response process of perforated gun underperforating pressure from 50 to 350 µs with an interval of100 µs can be obtained, as shown in Figure 4. The unitsystem is cm–g–µs, and the unit of the fringe level is105 MPa.

As shown in Figure 4, when the perforator begins todetonate, the equivalent stress changes appear in theperforating gun under the action of perforating dynamicpressure. With the dynamic pressure of perforation pro-duced by subsequent explosion of perforating bullets,the equivalent stress changes at different positions ofperforating gun body begin to appear. The dynamic pres-sure of downhole perforation is formed in this way. Thephenomenon of equivalent stress concentration betweenthe adjacent blind holes occurs, which is the weak part ofperforating gun.

In order to obtain the perforating pressure, somemain methods are used by researchers: empirical formulacalculation, experimental test, downhole actual measure-ment by high-speed P–T testing instruments, or special

perforation software simulation. The results from theempirical formulas often refer to underwater explosiontheory, which is inaccurate. The experimental test is lim-ited by the various conditions, which cannot reflect theactual working conditions of perforation. The field mea-sured data are often one-time, and the data obtained byspecial perforation software are relatively single, butboth are very accurate, which can be used as the impor-tant reference of the verification of numerical simulationcalculation results. Therefore, the pressure–time curvecan be drawn by extracting the simulated data, whichcan be verified by the result calculated by the perforationsoftware.

The simulated perforating pressure–time curve in thisarticle (blue solid line) and that calculated by the perforationsoftware (red dashed line) are shown in Figure 5. The time ofnumerical simulation is 0–5,000 µs.

As shown in Figure 5, as the perforation bulletsexplode, the perforating pressure rises sharply, reachinga peak value of 106.54 MPa in 800 µs. After the explosion,the pressure decreases instantaneously and tends to bestable after showing a trend of oscillation attenuation,which truly reflects the law of the perforating pressurechanging with time in deep-water wells. The time curveof perforation pressure calculated by the perforation soft-ware is relatively smooth because the dynamic theoretical

Table 1: Model parameters

Perforation gun length 10 m Tubing length 20mRathole length 6m Tubing yield limit 536MPaNumber of perforating bullets 270 Single charge 40 gCharge type RDX Perforation phase 45°Wellbore pressure 50MPa Formation pressure 45 MPaPerforation fluid density 1.13 g/cm3 Formation elastic modulus 5 GPa

Figure 3: Local mesh of perforating gun and perforated string.

Figure 4: Equivalent stress of perforated gun (unit: 1011 Pa).

218 Hao Huang et al.

calculation model adopted by it is calculated on the basisof many assumptions. Although the above differencesexist, there are similarities between the two trends withrising rapidly at first and then decreasing sharply. More-over, the peak pressures of the two are very close.The peak pressure of the perforation software result is102.36 MPa. The error between both peak values can becalculated by:

=

−

× =δ 106.54 102.23102.23

100% 4.22%. (4)

The comparative analysis of the aforementioned for-mulas shows that the simulated result is accurate, whichshows that the numerical simulation method proposedin this study is reasonable. Therefore, a large numberof numerical simulation calculations can be carried outto analyze perforation dynamic pressure on packers bychanging model parameters.

3.2 Prediction model

The perforating pressure on the packer can be got fromthe perforation fluid under the lower end of packer in the

wellbore according to the unit. In order to obtain thedownhole perforation pressure on the packer under dif-ferent perforation conditions, the method of orthogonaltest is applied to carry out a series of numerical simula-tion calculations on a large computer. Five influence fac-tors are considered: perforating charge quantity, wellborepressure, perforating explosion volume, formation pres-sure, and elastic modulus. In this orthogonal design,there are five factor variables and four-level values. Theorthogonal table design is shown in Table 2.

A database can be established based on the afore-mentioned simulation results. In order to obtain a modelthat can be used to predict the perforating peak pressureon the packer, the database can be fitted. The function byconsidering multi-factor changes can be expressed as:

= ( )p f M P V F G, , , , , (5)

where p is the perforation peak pressure on the packer;M is the perforating charge quantity; P is the wellborepressure; V is the perforating explosion volume; F isthe formation pressure; and G is the formation elasticmodulus.

The modified multivariate nonlinear regression modelcan be established by using the least square method, andthe peak perforating pressure on the lower end of thepacker can be obtained [18–21]. The dimensionless formcan be written as follows:

= × + ×

( ) ×

×

+

⋅

p a P a Ln M FG e

a ,a

a a V1 2 63

4 5(6)

where a a a a a a, , , , ,1 2 3 4 5 6 are the undetermined values ofthe coefficients, which can be fitted by the simulateddatabase.

The perforating charge quantity can be calculated by:

= ×M n m, (7)

where n is the number of the perforating bullets and m isthe single charge per hole.

The downhole volume for perforation can be obtainedby:

= + +V V V V ,1 2 3 (8)

Table 2: Model parameters

Orthogonal level Perforatingcharge (kg)

Wellborepressure (MPa)

Explosionvolume (m3)

Formationpressure (MPa)

Elasticmodulus (GPa)

Level 1 5 10 1 5 5Level 2 10 50 2 45 10Level 3 15 90 3 85 15Level 4 20 130 4 125 20

Figure 5: Perforating pressure–time curves.

Study of dynamic pressure on the packer for deep-water perforation 219

where V V V, ,1 2 3 is the volume of the perforated string sec-tion, perforation section, and rathole section, respec-tively, which can be calculated as follows:

= × ( − ) ×

= × ( − ) ×

= × ×

V π φ ϕ L

V π φ ϕ L

V π φ L

4,

4,

4,

1 c2

t2

1

2 c2

g2

2

3 c2

3

(9)

where φ ϕ ϕ, ,c t g is the inner diameter of casing, the outerdiameter of tubing, and the outer diameter of perforatinggun, respectively.

With the combination of equations (6–9), the modelto predict the peak perforation pressure on the lower endof the packer can be obtained as:

= × +

×

( ⋅ ) ×

× ⋅

+

{ ( + + )− × − × }

p A P ALn n m F

G A eA ,

A

A φ L L L ϕ L ϕ L

1 2

56

3

4 c2

1 2 3 t2

1 g2

2

(10)

where A A A A A A, , , , ,1 2 3 4 5 6 are the fitting coefficients bythe simulated result.

The upper and lower interfaces of the packer areplaced in the perforation fluid, as shown in Figure 6.

When the dynamic pressure of perforation acts on thelower interface of the packer, the reflection and transmis-sion will occur. According to the principle of reflectionand transmission, the perforating pressure acting on thepacker will increase, and the pressure on the packer is thedifference between the overpressure and transmissionpressure, as shown in:

= + − = ×

( ) [( ) − ( ) ]

[( ) + ( ) ]

P p P P p ρc ρc ρcρc ρc

2 ,p f t2 2 1

1 22 (11)

where Pp is the perforating peak pressure on the packer;p is the pressure on the lower end of the packer; Pf isthe reflected pressure; Pt is the transmitted pressure;and ( ) /( ) = /ρc ρc 1 51 2 .

Combining equation (10) with equation (11), the finalprediction model of the perforating dynamic peak pres-sure acting on the packer can be expressed as follows:

= × + ×

( ⋅ ) ×

×

+

{ ( + + )− × − × }

p k P k Ln n m FG e

k .k

k φ L L L ϕ L ϕ L1 2 53

4 c2

1 2 3 t2

1 g2

2(12)

3.3 Factor analysis

Under the condition that the material of deep-water per-forated string and downhole formation conditions remainunchanged, the influencing factors such as wellborepressure, number of perforating bullets, single chargeper hole, inner diameter of casing, and length of tubingare analyzed, respectively. Figure 7 shows the relation-ship between the wellbore pressure and the peak perfora-tion pressure on the packer.

As shown in Figure 7, the peak perforation pressureon the packer increases linearly with the increase in well-bore pressure. The higher the initial wellbore pressure is,the greater the load in the environment of the packer is.With the explosion of the perforating charge, the impactpressure on the packer will be greater, which is consis-tent with the actual operation. The reason is that thewellbore pressure provides the basis for the dynamicpressure of perforation. It is necessary to control the well-bore pressure effectively during perforating.

Figure 6: Interfaces of the packer in the perforation fluid.Figure 7: Influence of wellbore pressure on peak pressure of thepacker.

220 Hao Huang et al.

The relationship between the number of bullets andthe peak perforation pressure on the packer is shown inFigure 8, and the relationship between the charge perhole and the peak perforation pressure on the packer isshown in Figure 9. As shown in the aforementioned fig-ures, it can be seen that the perforating peak pressureon the packer and the number of perforation bulletsshow a logarithm function. The perforating peak pressureon the packer increases with the increase of the numberof perforating bullets, and it also has a logarithmic rela-tionship with the charge per hole. With the increase of thecharge per hole, the perforating peak pressure on packerincreases. The reason is that the dynamic pressure ofdownhole perforation mainly comes from the explosiveenergy of perforation bullets with the shaped charge.

The perforating peak pressure on the packer increaseswith the increase of the number of perforating bullets andsingle charge. It is necessary to design perforation densityand charge quantity reasonably to ensure the safety ofpacker during deep-water perforating.

Figure 10 illustrates the relationship between the per-forating peak pressure on the packer and the inner dia-meter of the casing.

As shown in Figure 10, the relationship between theperforating peak pressure on the packer and the innerdiameter of the casing shows an exponential function.The value of the peak pressure gradually becomes smallerwith the increase in the inner diameter of the casing.The reason is that with the packer seated, the downholewellbore is in a closed space. With the increase in theinner diameter of the casing, the energy generated by per-foration explosion has more space to release, and the per-forating peak pressure on the packer becomes smaller.Therefore, increasing the length of bottom hole pocket

and the length of perforated string can effectively reducethe peak pressure at packer.

Figure 11 shows the relationship between the perfor-ating peak pressure on the packer and the tubing length.

As shown in Figure 11, the relationship between theperforating peak pressure on the packer and the tubinglength shows an exponential function. The long tubingcan increase the underground explosion space and makethe packer farther away from the source of perforationcharge explosion, and the flexibility of tubing can alsoplay a shock absorption effect. The impact of perforationpressure on the packer will be reduced.

Through the aforementioned analysis, the influencelaws of the factors on the perforating peak pressure onthe packer pressure have been obtained, which can beapplied to the optimization of field perforation operation.

Figure 8: Influence of the number of perforating bullets on peakpressure of the packer.

Figure 9: Influence of single charge per hole on peak pressure of thepacker.

Figure 10: Influence of casing inner diameter on peak pressure of thepacker.

Study of dynamic pressure on the packer for deep-water perforation 221

4 Field case study

A deep-water well perforation case is used for the study,and the length of the perforation gun section, ratholesection, and perforated section are, respectively, 9, 10,and 20m. The rated working pressure of the packer is70 MPa. The operation parameters of the deep-water fieldwell are shown in Table 3. According to the predictionmodel of perforation peak pressure on the packer ofequation (12), the peak pressure on the packer in thecase can be calculated to be 105 MPa, which is beyondthe range of packer (70 MPa) and the packer will bedamaged.

When the material of the packer, the type of the per-forated string, the number of perforating bullets and thesingle charge are fixed, increasing tubing length is a goodoptimization measure, as shown in Figure 11.

In order to improve the safety of deep-water perfora-tion, the longitudinal shock absorbers are often installedunder the packer. Due to the complex environmentof deep-water wells, the shock absorbers of rubber com-ponents are often easily damaged, which brings greattrouble to perforation operation. Therefore, the shockabsorbers of spring components are often used in theperforation of deep-water wells. Based on the numericalmodel established in Section 2, the shock absorbers aresimplified into spring elements and added into the model.

The numerical model with shock absorbers can be used tocarry out simulation calculations. The peak perforatingpressure on the packer under different tubing lengthswith different number of shock absorbers can be obtained,as shown in Figure 12.

The figure reveals that with the increase in thenumber of shock absorbers, the perforating peak pres-sure on the packer can be more reduced, by which theeffect of shock-absorbing is better. As the tubing lengthincreases, the perforating peak pressure on the packerdecreases. If only one shock absorber is installed, thesafety of packer is still seriously threatened, whichcannot meet the safety requirements for deep-water per-foration operation. The minimum value of the perforatingpeak pressure (73 MPa) on the packer still exceeds therange of the packer (70MPa). If the number of shockabsorbers is two or three, the packer during deep-waterperforating is safely combined with the optimization oftubing length. The color area in Figure 12 represents thatthe peak pressure on the packer during perforating islower than the range of that, by which the safety of thepacker can be ensured.

Based on the aforementioned analysis, the optimiza-tion measure is put forward for perforation operation ofthis deep-water well case. The tubing length is 16 m, andthree shock absorbers are installed in series in the

Figure 11: Influence of tubing length on peak pressure of the packer.

Table 3: Operation parameters

Casing inner diameter 0.22 m Tubing outer diameter 0.11 mPerforating gun outer diameter 0.18 m Wellbore pressure 10MPaNumber of perforating bullets 360 Single charge 40 gFormation elastic modulus 1.27 GPa Formation pressure 12MPa

Figure 12: Peak pressure on packer with different tubing lengths andnumber of shock absorbers.

222 Hao Huang et al.

perforated string. After perforation operation, the integ-rity of the packer is good with no damage or releasing.

5 Conclusion

The numerical model of the actual deep-water perfora-tion has been established to study the dynamic perfor-ating pressure on the packer, and a series of numericalsimulations have been carried out by using orthogonaltests. The simulated result has been verified by the per-foration software, the database has been established, andthe model of the perforating peak pressure on the packerhas been fitted. The following conclusions can be obtained:1. Combining with the reflection and transmission of

shock waves on the packer during deep-water perfor-ating, the prediction model of the perforating peakpressure on the packer has been obtained, which canstudy the sensitivity of different factors.

2. The analysis results show that the perforating peakpressure on the packer peak is linearly related to thewellbore pressure, has a logarithm function relation-ship with the number of perforating bullets and singlecharge, and has an exponential function relationshipwith the inner diameter of casing and tubing length.

3. By the combination of increasing tubing length andinstalling shock absorbers, the safety optimization mea-sures of perforation packer of deep-water wells are putforward. The case study shows that the effect is good.

Acknowledgement: The authors gratefully acknowledgethe Natural Science Foundation of China (Grant Nos:U19B6003, 72001026, U19B6003-05, U1762211, 51734010,51774063, 51774304, 51821092, and 51774063), the StrategicCooperation Technology Projects of CNPC and CUPB(ZLZX2020-01), and the State Key Laboratory of PetroleumResources and Engineering.

Conflict of interest: Authors state no conflict of interest.

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