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

Hao Huang; Qiao Deng; Hui Zhang

doi:10.1515/phys-2021-0025

Article Open Access

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

Hao Huang , Qiao Deng and Hui Zhang

Published/Copyright: April 28, 2021

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From the journal Open Physics Volume 19 Issue 1

Abstract

The packer is one of the most important tools in deep-water perforation combined well testing, and its safety directly determines the success of perforation test operations. The study of dynamic perforating pressure on the packer is one of the key technical problems in the production of deep-water wells. However, there are few studies on the safety of packers with shock loads. In this article, the three-dimensional finite element models of downhole perforation have been established, and a series of numerical simulations are carried out by using orthogonal design. The relationship between the perforating peak pressure on the packer with the factors such as perforating charge quantity, wellbore pressure, perforating explosion volume, formation pressure, and elastic modulus is established. Meanwhile, the database is established based on the results of numerical simulation, and the calculation model of peak pressure on the packer during perforating is obtained by considering the reflection and transmission of shock waves on the packer. The results of 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 the safety of the packer during deep-water perforating.

Keywords: deep-water perforation; downhole packer; numerical simulation; prediction model; optimization program

1 Introduction

With the rapid development of oil and gas industry in recent years, the exploration of offshore oil and gas resources has gradually become the focus, especially in deep water [1]. The perforation combined well testing is one of the most important links in the development of deep-water well operations. The researchers focus on the safety of downhole perforation, which is an important technical problem in deep-water well completion [2]. The study of dynamic pressure on the downhole packer in the wellbore during perforation is a key step for the safety analysis of deep-water perforation jobs. Tubing-conveyed perforating (TCP) combined well testing is an advanced technology, which has been widely used in offshore completion operations, especially in deep-water wells [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 the wellbore during TCP, as shown in Figure 1. The packer is one key tool connected to the perforated string, and the failure of the packer will lead to huge economic damage and seriously threaten the safety of field operators. Since 2011, the safety of the packers has been seriously threatened during deep-water well perforating in the Gulf of Mexico, with sealing failure and central pipe fracture [4]. Therefore, it is necessary to study the safety of packer during deep-water perforating. However, there is a lack of safety analysis for the packer during deep-water well perforating at present. The relevant research in detail has been carried in this study.

Figure 1

Downhole TCP system.

As we know, perforation is an intensely violent explosion process. In a few microseconds, the shaped charges inside the perforating gun explode and form a high-speed jet to penetrate the casing to the reservoir. Meanwhile, part of the perforating explosion energy will be released into the downhole wellbore, and the downhole space is long and narrow with the packer completely set. The wellbore is filled with perforation fluid, and the interaction between perforating explosion products with wellbore fluid is the beginning of the hydrodynamics effects with shock loads during perforating. The dynamic perforating pressure in the wellbore has been formed, and the packer has been impacted [5]. In recent years, in order to maximize the productivity and reduce the costs, larger perforating guns with higher-shot densities and propellants have been rapidly developed, which are widely adopted in deep-water oil and gas wells, resulting in a large increase in shock loads in the wellbore by using such perforating systems [6]. All the tools in the TCP system exposed to perforation fluid will be subjected to the pulsating pressure during perforating, and the safety of the TCP system will be seriously threatened, especially for the packer. As the perforation process of deep-water well is more complex and difficult with the increase in water depth, to predict downhole perforation pressure on the packer is the key to ensure the safety of downhole perforation.

Researchers have come to realize the importance of studying the dynamic pressure of perforation in recent years. Some research work has been carried out in theory, experiment, and simulation of perforating pressure. Combining theory with experiment, the characteristics of perforation pressure fluctuation during composite perforating have been studied [7]. Based on the empirical formula, the dynamic load of downhole perforation has been analyzed [8]. It is concluded that the dynamic pressure from perforation will increase the damage risk of downhole equipment of deep-water wells [9]. The perforation process is simulated by using the finite element software, and a prediction model is obtained based on the simulation data [10]. These studies have promoted the research progress of downhole perforation pressure. However, the dynamic perforation pressure on the packer under actual deep-water conditions is not clear.

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

In this article, the numerical simulation of actual deep-water conditions has been carried out by the software LS-DYNA to simulate the physical process of perforation, the peak pressure on the packer during perforating is obtained, and the safety analysis of the packer is proposed and the measures of shock absorption are put forward.

2 Numerical model

Some previous studies have focused on the numerical simulation for downhole perforation. A 2D Euler coding was used to simulate the process of jet formation and penetration into the casing during perforating [11]. The process of perforation has been studied by the software LS-DYNA, and the results have been verified by the field case [12]. The process of perforation to cement damage has been studied by the software LS-DYNA [13]. A pressure field model of shaped charge was set up to study the downhole perforation, which can simulate the changing process of shell, charge, and liner during perforating by the software LS-DYNA [14]. A model for estimating perforating depth has been obtained by considering the factors such as the number of bullets, the charge, the wellbore pressure, and the formation pressure. A prediction model based on simulated data has been fitted under different perforating conditions [15]. These studies promote the numerical simulation process of modern perforation completion.

However, due to the complexity of deep-water perforation model, previous studies mostly focused on a single or a small number of perforation bullets, without considering the influence of various factors in the perforation process of deep-water wells, while the study of perforation pressure on the packer has not been reported. The process of perforation is composed of complex physical and chemical changes, and some simplifications can be applied for the simulation. As the string system consists of different rods, the components of the string are regarded as isotropic, and the physical model of deep-water perforation can be established, as shown in Figure 2.

Figure 2

Numerical model.

Some perforating bullets are distributed in the perforating gun at a certain phase. The string system involves the perforating gun (177.80/152.53 mm), tubing (73.02/62.00 mm), and casing (244.40/220.50 mm). The air fills inside the remaining space of the gun, and the perforation fluid fills the annulus space of tubing and casing. The packer restrains the upper end of the string radially, and the circumference of the string is restrained by the casing with reservoir surrounding. The parameters of the perforation model for the deep-water wells are shown in Table 1.

Table 1

Model parameters

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

Since the physical process of perforation includes complex fluid–structure interaction with high strain rate, the Arbitrary Lagrange–Euler (ALE) algorithm in LS-DYNA can be used for the calculation. The ALE algorithm can accurately simulate the formation and penetration of a shaped charge jet with high strain rate and large deformation, which can be used in RDX (Royal Demolition Explosive) explosives, air, fluid, and the space position of the ALE grid remain unchanged with the material flows among the grids. The Lagrange algorithm is used in the perforated string. The Lagrange algorithm can be first executed by the ALE algorithm at each time step.

The hexahedral meshing is used in the perforation model. In order to capture the deformation and movement process of the material structure effectively, all parts of the material needs have common nodes on the contact interfaces, which can ensure the effective transfer of energy between the parts of the mesh. Figure 5 shows the local mesh of the cross perforated string and perforating gun. The grid size is an important factor affecting the speed and accuracy of simulation calculation. The larger size cannot guarantee the accuracy of calculation. The smaller size will greatly increase the amount of calculation. The appropriate mesh size is the prerequisite for the success of numerical simulation. After many times of test calculations, the average mesh spacing is set to 4–5 mm, and the total number of meshes is about 1 million (Figure 3).

Figure 3

Local mesh of perforating gun and perforated string.

The material model of HIGH_EXPLOSIVE_BURN is used for the charge, and its characteristics such as pressure, volume, and energy can be accurately described by the state equation of EOS_JWL during perforating, as shown in ref. [16]:

(1) P = A 1 − ω R 1 V e − R 1 V + B 1 − ω R 2 V e − R 2 V + ω E 0 V ,

where V is the relative volume of explosives; E 0 is the initial internal energy value per unit volume of explosives; and A , B , R 1 , R 2 , and ω are the physical properties of explosives.

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

(2) P = ρ J C J 2 α J 1 + 1 − γ 0 2 α J − δ J 2 α J 2 1 − ( S 1 − 1 ) α J − S 2 2 α J 2 α J 2 + 1 − S 3 α J 3 ( α J + 1 ) 2 + ( γ 0 + δ J α J ) E J ,

where ρ J is the initial density of medium; C J is the curve intercept of shock wave velocity; α J is the compressibility of medium; γ 0 and δ J are the constant coefficients and corrections of state equation; and S 1 , S 2 , and S 3 are the constant coefficients of stress wave velocity curve in materials.

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

(3) P = ( C 0 + C 1 μ + C 2 μ 2 + C 3 μ 3 ) + ( C 4 + C 5 μ + C 6 μ 2 ) E ,

where C 0 , C 1 , C 2 , C 3 , C 4 , C 5 , C 6 is the equation of state coefficients.

3 Numerical analysis

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

3.1 Simulation results

The dynamic response process of perforated gun under perforating pressure from 50 to 350 µs with an interval of 100 µs can be obtained, as shown in Figure 4. The unit system is cm–g–µs, and the unit of the fringe level is 10⁵ MPa.

Figure 4

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

As shown in Figure 4, when the perforator begins to detonate, the equivalent stress changes appear in the perforating gun under the action of perforating dynamic pressure. With the dynamic pressure of perforation produced by subsequent explosion of perforating bullets, the equivalent stress changes at different positions of perforating gun body begin to appear. The dynamic pressure of downhole perforation is formed in this way. The phenomenon of equivalent stress concentration between the adjacent blind holes occurs, which is the weak part of perforating gun.

In order to obtain the perforating pressure, some main methods are used by researchers: empirical formula calculation, experimental test, downhole actual measurement by high-speed P–T testing instruments, or special perforation software simulation. The results from the empirical formulas often refer to underwater explosion theory, which is inaccurate. The experimental test is limited by the various conditions, which cannot reflect the actual working conditions of perforation. The field measured data are often one-time, and the data obtained by special perforation software are relatively single, but both are very accurate, which can be used as the important reference of the verification of numerical simulation calculation results. Therefore, the pressure–time curve can be drawn by extracting the simulated data, which can be verified by the result calculated by the perforation software.

The simulated perforating pressure–time curve in this article (blue solid line) and that calculated by the perforation software (red dashed line) are shown in Figure 5. The time of numerical simulation is 0–5,000 µs.

Figure 5

Perforating pressure–time curves.

As shown in Figure 5, as the perforation bullets explode, the perforating pressure rises sharply, reaching a peak value of 106.54 MPa in 800 µs. After the explosion, the pressure decreases instantaneously and tends to be stable after showing a trend of oscillation attenuation, which truly reflects the law of the perforating pressure changing with time in deep-water wells. The time curve of perforation pressure calculated by the perforation software is relatively smooth because the dynamic theoretical calculation model adopted by it is calculated on the basis of many assumptions. Although the above differences exist, there are similarities between the two trends with rising rapidly at first and then decreasing sharply. Moreover, the peak pressures of the two are very close. The peak pressure of the perforation software result is 102.36 MPa. The error between both peak values can be calculated by:

(4) δ = 106.54 − 102.23 102.23 × 100 % = 4.22 % .

The comparative analysis of the aforementioned formulas shows that the simulated result is accurate, which shows that the numerical simulation method proposed in this study is reasonable. Therefore, a large number of numerical simulation calculations can be carried out to analyze perforation dynamic pressure on packers by changing model parameters.

3.2 Prediction model

The perforating pressure on the packer can be got from the perforation fluid under the lower end of packer in the wellbore according to the unit. In order to obtain the downhole perforation pressure on the packer under different perforation conditions, the method of orthogonal test is applied to carry out a series of numerical simulation calculations on a large computer. Five influence factors are considered: perforating charge quantity, wellbore pressure, perforating explosion volume, formation pressure, and elastic modulus. In this orthogonal design, there are five factor variables and four-level values. The orthogonal table design is shown in Table 2.

Table 2

Model parameters

Orthogonal level	Perforating charge (kg)	Wellbore pressure (MPa)	Explosion volume (m³)	Formation pressure (MPa)	Elastic modulus (GPa)
Level 1	5	10	1	5	5
Level 2	10	50	2	45	10
Level 3	15	90	3	85	15
Level 4	20	130	4	125	20

A database can be established based on the aforementioned simulation results. In order to obtain a model that can be used to predict the perforating peak pressure on the packer, the database can be fitted. The function by considering multi-factor changes can be expressed as:

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

where p is the perforation peak pressure on the packer; M is the perforating charge quantity; P is the wellbore pressure; V is the perforating explosion volume; F is the formation pressure; and G is the formation elastic modulus.

The modified multivariate nonlinear regression model can be established by using the least square method, and the peak perforating pressure on the lower end of the packer can be obtained [18,19,20,21]. The dimensionless form can be written as follows:

(6) p = a 1 × P + a 2 × L n ( M ) × F a 3 G a 4 × e a 5 ⋅ V + a 6 ,

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

The perforating charge quantity can be calculated by:

(7) M = n × m ,

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

The downhole volume for perforation can be obtained by:

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

where V 1 , V 2 , V 3 is the volume of the perforated string section, perforation section, and rathole section, respectively, which can be calculated as follows:

(9) V 1 = π 4 × ( φ c 2 − ϕ t 2 ) × L 1 , V 2 = π 4 × ( φ c 2 − ϕ g 2 ) × L 2 , V 3 = π 4 × φ c 2 × L 3 ,

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

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

(10) p = A 1 × P + A 2 × L n ( n ⋅ m ) × F A 3 G A 4 × A 5 ⋅ e { φ c 2 ( L 1 + L 2 + L 3 ) − ϕ t 2 × L 1 − ϕ g 2 × L 2 } + A 6 ,

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

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

Figure 6

Interfaces of the packer in the perforation fluid.

When the dynamic pressure of perforation acts on the lower interface of the packer, the reflection and transmission will occur. According to the principle of reflection and transmission, the perforating pressure acting on the packer will increase, and the pressure on the packer is the difference between the overpressure and transmission pressure, as shown in:

(11) P p = p + P f − P t = 2 p × ( ρ c ) 2 [ ( ρ c ) 2 − ( ρ c ) 1 ] [ ( ρ c ) 1 + ( ρ c ) 2 ] 2 ,

where P p is the perforating peak pressure on the packer; p is the pressure on the lower end of the packer; P f is the reflected pressure; P t is the transmitted pressure; and ( ρ c ) 1 / ( ρ c ) 2 = 1/5 .

Combining equation (10) with equation (11), the final prediction model of the perforating dynamic peak pressure acting on the packer can be expressed as follows:

(12) p = k 1 × P + k 2 × L n ( n ⋅ m ) × F k 3 G k 4 × e { φ c 2 ( L 1 + L 2 + L 3 ) − ϕ t 2 × L 1 − ϕ g 2 × L 2 } + k 5 .

3.3 Factor analysis

Under the condition that the material of deep-water perforated string and downhole formation conditions remain unchanged, the influencing factors such as wellbore pressure, number of perforating bullets, single charge per hole, inner diameter of casing, and length of tubing are analyzed, respectively. Figure 7 shows the relationship between the wellbore pressure and the peak perforation pressure on the packer.

Figure 7

Influence of wellbore pressure on peak pressure of the packer.

As shown in Figure 7, the peak perforation pressure on the packer increases linearly with the increase in wellbore 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 impact pressure on the packer will be greater, which is consistent with the actual operation. The reason is that the wellbore pressure provides the basis for the dynamic pressure of perforation. It is necessary to control the wellbore pressure effectively during perforating.

The relationship between the number of bullets and the peak perforation pressure on the packer is shown in Figure 8, and the relationship between the charge per hole and the peak perforation pressure on the packer is shown in Figure 9. As shown in the aforementioned figures, it can be seen that the perforating peak pressure on the packer and the number of perforation bullets show a logarithm function. The perforating peak pressure on the packer increases with the increase of the number of perforating bullets, and it also has a logarithmic relationship with the charge per hole. With the increase of the charge per hole, the perforating peak pressure on packer increases. The reason is that the dynamic pressure of downhole perforation mainly comes from the explosive energy of perforation bullets with the shaped charge.

Figure 8

Influence of the number of perforating bullets on peak pressure of the packer.

Figure 9

Influence of single charge per hole on peak pressure of the packer.

The perforating peak pressure on the packer increases with the increase of the number of perforating bullets and single charge. It is necessary to design perforation density and charge quantity reasonably to ensure the safety of packer during deep-water perforating.

Figure 10 illustrates the relationship between the perforating peak pressure on the packer and the inner diameter of the casing.

Figure 10

Influence of casing inner diameter on peak pressure of the packer.

As shown in Figure 10, the relationship between the perforating peak pressure on the packer and the inner diameter of the casing shows an exponential function. The value of the peak pressure gradually becomes smaller with the increase in the inner diameter of the casing. The reason is that with the packer seated, the downhole wellbore is in a closed space. With the increase in the inner diameter of the casing, the energy generated by perforation explosion has more space to release, and the perforating peak pressure on the packer becomes smaller. Therefore, increasing the length of bottom hole pocket and the length of perforated string can effectively reduce the peak pressure at packer.

Figure 11 shows the relationship between the perforating peak pressure on the packer and the tubing length.

Figure 11

Influence of tubing length on peak pressure of the packer.

As shown in Figure 11, the relationship between the perforating peak pressure on the packer and the tubing length shows an exponential function. The long tubing can increase the underground explosion space and make the packer farther away from the source of perforation charge explosion, and the flexibility of tubing can also play a shock absorption effect. The impact of perforation pressure on the packer will be reduced.

Through the aforementioned analysis, the influence laws of the factors on the perforating peak pressure on the packer pressure have been obtained, which can be applied to the optimization of field perforation operation.

4 Field case study

A deep-water well perforation case is used for the study, and the length of the perforation gun section, rathole section, and perforated section are, respectively, 9, 10, and 20 m. The rated working pressure of the packer is 70 MPa. The operation parameters of the deep-water field well are shown in Table 3. According to the prediction model of perforation peak pressure on the packer of equation (12), the peak pressure on the packer in the case can be calculated to be 105 MPa, which is beyond the range of packer (70 MPa) and the packer will be damaged.

Table 3

Operation parameters

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

When the material of the packer, the type of the perforated string, the number of perforating bullets and the single charge are fixed, increasing tubing length is a good optimization measure, as shown in Figure 11.

In order to improve the safety of deep-water perforation, the longitudinal shock absorbers are often installed under the packer. Due to the complex environment of deep-water wells, the shock absorbers of rubber components are often easily damaged, which brings great trouble to perforation operation. Therefore, the shock absorbers of spring components are often used in the perforation of deep-water wells. Based on the numerical model established in Section 2, the shock absorbers are simplified into spring elements and added into the model. The numerical model with shock absorbers can be used to carry out simulation calculations. The peak perforating pressure on the packer under different tubing lengths with different number of shock absorbers can be obtained, as shown in Figure 12.

Figure 12

Peak pressure on packer with different tubing lengths and number of shock absorbers.

The figure reveals that with the increase in the number of shock absorbers, the perforating peak pressure on the packer can be more reduced, by which the effect of shock-absorbing is better. As the tubing length increases, the perforating peak pressure on the packer decreases. If only one shock absorber is installed, the safety of packer is still seriously threatened, which cannot meet the safety requirements for deep-water perforation operation. The minimum value of the perforating peak pressure (73 MPa) on the packer still exceeds the range of the packer (70 MPa). If the number of shock absorbers is two or three, the packer during deep-water perforating is safely combined with the optimization of tubing length. The color area in Figure 12 represents that the peak pressure on the packer during perforating is lower than the range of that, by which the safety of the packer can be ensured.

Based on the aforementioned analysis, the optimization measure is put forward for perforation operation of this deep-water well case. The tubing length is 16 m, and three shock absorbers are installed in series in the perforated string. After perforation operation, the integrity of the packer is good with no damage or releasing.

5 Conclusion

The numerical model of the actual deep-water perforation has been established to study the dynamic perforating pressure on the packer, and a series of numerical simulations have been carried out by using orthogonal tests. The simulated result has been verified by the perforation software, the database has been established, and the model of the perforating peak pressure on the packer has been fitted. The following conclusions can be obtained:

Combining with the reflection and transmission of shock waves on the packer during deep-water perforating, the prediction model of the perforating peak pressure on the packer has been obtained, which can study the sensitivity of different factors.
The analysis results show that the perforating peak pressure on the packer peak is linearly related to the wellbore pressure, has a logarithm function relationship with the number of perforating bullets and single charge, and has an exponential function relationship with the inner diameter of casing and tubing length.
By the combination of increasing tubing length and installing shock absorbers, the safety optimization measures of perforation packer of deep-water wells are put forward. The case study shows that the effect is good.

Acknowledgement

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

Conflict of interest: Authors state no conflict of interest.

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Received: 2019-09-09

Revised: 2021-02-16

Accepted: 2021-03-11

Published Online: 2021-04-28

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/phys-2021-0025

Keywords for this article

deep-water perforation; downhole packer; numerical simulation; prediction model; optimization program

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