Introduction

Packer is widely used in oilfield water injection, oil production, fracturing, well completion, oil testing, log testing and other downhole operations (Sun et al. 2017; Liu et al. 2018; Lo et al. 2014; Zhou et al. 2018; Tong et al. 2018; Dong et al. 2021; Kao et al. 2020; Guo et al. 2020; Deng et al. 2020; Cheng et al. 2021; Franquet et al. 2019; Ishii 2020). The key structure of packer is super-elastic rubber tube with sealing function, which is adopted to achieve annular seal between tubing and casing and isolate production layer (Dong et al. 2020a, b; Yue et al. 2020; Zheng et al. 2021). At present, the commonly used rubber materials are mainly butadiene rubber and fluorine rubber (Chen et al. 2019; Dong et al. 2020a, b; Zhu et al. 2017b). According to the different requirements of working temperature (Zhu et al. 2017a; Zhang et al. 2021), pressure-bearing and gas immersion resistance, the application field and range are different.

The lithology and structure of deep volcanic gas reservoir in Daqing in China are complex, and the reservoir is characterized by low porosity, low permeability and strong heterogeneity (Liu et al. 2022; Han et al. 2023; Zhang et al. 2020; Wang et al. 2019; Li et al. 2023). The production capacity is low for single well in the study block, and most of them need large amount of sand and injection of fracturing before putting into production, which also results in a substantial increase in cost. The deep layer of Xushen gas field in China mainly adopts the way of fracturing in advance and then replacing the production completion string, which further increases the well construction cost.

Due to the characteristics of high temperature, high pressure and strong corrosivity of deep reservoir, the packing element elastomer of packer is confronted with extreme challenge. Nitrile (NBR) commonly adopted exhibits largely strength decreasing (> 100 °C). Hydrogenated Nitrile (HNBR), Fluorine rubber (FKM), Perfluoroelastomer (FFKM) or other polymers have been considered as alternatives to NBR for mechanical-set packers owing to the high heat resistance (Doane et al. 2012; Ren et al. 2012). Stress concentration is an important reason for the failure of the rubber barrel components of the packer (Dong et al. 2020a, b), and then, a novel dual cup packer concept was designed to achieve good sealing performance (Adan et al. 2016; Whaley et al. 2012). In addition, some shoulder ring structures were designed to protect the packer from stress concentration (Hu et al. 2017). High temperature and sulfur/CO2 corrosion are another important factors causing packer failure (Yue et al. 2021; Zhu et al. 2017a; Tong et al. 2019; Offenbacher et al. 2015; He et al. 2016; Liu et al., 2023a, b). Therefore, structural optimizations and rubber barrel material improvement are important means to improve the performance of the packer, which is of great significance to meet the site requirements (Ashena et al. 2021; Pervez et al. 2021; Zeinalabideen et al. 2021). Overall, based on the current research status at home and abroad, there are few reports on the research of completion tools for volcanic gas reservoirs. In addition, most packers only consider structural optimization or rubber material optimization and rarely optimize the design of packers based on the combined effects of the structure and rubber material. This article is of great significance for the efficient development of high temperature and high corrosion volcanic rock formations.

In order to further reduce the cost of exploratory well construction and avoid the secondary pollution of reservoir, the research on the integrated fracturing production technology is carried out, and the integrated packer as the core tool is studied to realize the technology. During the process of optimization design, the rubber formula was improved, the rubber cylinder shoulder’s structure and protection ring were optimized, and the performance of packer rubber cylinder was continuously improved, which provided theoretical guidance for the development of fracturing and completion integrated packer. The results of laboratory and field tests show that the optimized integrated packer cartridge can effectively seal the oil casing annulus and meet requirements for field operation, which provides an effective completion, fracturing, drainage and production integration tool for the risk exploration wells’ construction in volcanic rock, carbonate reservoirs.

Packer structure for gas well fracturing and completion

Integrated packer

The structure of fracturing and completion integrated packer for gas well is mainly composed of working barrel, anti-wear sleeve, spring claw, central pipe, slip, protective ring, spacer ring, rubber cylinder, protective umbrella, lower joint, etc., as shown in Fig. 1 The processing principle of the fracturing and production integrated packer is that shall be set by pumping water from the surface, when the completion tool reached to the design depth. When the pressure is up to the setting value, the water enters into channel of the central pipe, and the rubber cylinder is compressed, then the slip is anchored to the inner wall of casing.

Fig. 1
figure 1

Structural diagram of vertical well fracturing and completion integrated packer

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String structure and working principle

The fracturing and completion integrated string in Fig. 2 is mainly composed of working barrel, fracturing and completion integrated packer, fracturing packer, sand blasting sliding sleeve, ball seat, etc. The fracturing and completion integrated packer is set by hydraulic pressure, the slips are anchored into the casing, and the rubber barrel of the packer seals the annulus of the oil sleeve.

Fig. 2
figure 2

String structure of integrated fracturing and completion

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Numerical study of fracturing and completion packer rubber

Material optimization and treatment process of rubber

At present, the commonly used rubber materials mainly include nitrile rubber and fluororubber. In order to improve the performance of rubber materials for integrated packers for gas well fracturing production, the rubber materials are subjected to gas immersion resistance and high temperature resistance treatment. (1) The compound formula of “perfluoroether + nanomaterials” is preferred to prevent gas molecules from entering and rubber cylinder from expanding. (2) Add high-performance and stable resin to solve the oxidation problem of rubber in high-temperature environment. Double vulcanization system is adopted, and the process of subsection vulcanization, step-by-step heating and natural cooling is adopted for treatment. And the fluorosilicon and silico-carbon bonds are mainly introduced into the main molecular chain during the process, as shown in Fig. 3.

Fig. 3
figure 3

The molecular structure change diagram of the material for the rubber cylinder

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Rubber constitutive model

A key to improve the performance of packer is to calculate its stress results more accurately to optimize the structure and rubber materials of packer. There are some hyperelastic constitutive models to analyze the hyperelastic behavior of rubber, such as Mooney–Rivlin, Gent and Yeoh. Among them, Mooney–Rivlin model can better characterize the strain energy of incompressible materials in the medium strain range, while not suitable for materials in compression and large strain hardening. Gent model can analyze the strain energy of incompressible materials that undergo hardening during large deformations, which is mainly suitable for thin-walled spheres with internal pressure, rubber with voids, and thin-walled cylindrical tubular objects while not suitable for small and medium strains. The Yeoh model can simulate other deformation mechanical behaviors by simple uniaxial tensile tests, and the strain energy calculated under large deformation conditions is in good agreement with the test results. Therefore, Yeoh model is adopted in this paper to simulating the large deformation of the rubber cylinder. And the strain energy density function is,

$$\frac{\partial W}{{\partial I_{{1}} }} = C_{{{10}}} + {2}C_{{{20}}} \left( {I_{{1}} { - 3}} \right) + {3}C_{{{30}}} \left( {I_{{1}} { - 3}} \right)^{{2}}$$
(1)
$$\left\{ \begin{gathered} I_{{1}} = \lambda_{{_{{1}} }}^{{2}} + \frac{{2}}{{\lambda_{{1}} }} \hfill \\ I_{{2}} = {2}\lambda_{{1}} + \frac{{1}}{{\lambda_{{_{{1}} }}^{{2}} }} \hfill \\ \end{gathered} \right.$$
(2)

The commonly used test methods for measuring the material constant of the rubber cylinder are uniaxial tensile test and pure shear test (plane tensile test). In fact, the uniaxial compression state and the equal biaxial tension state are equivalent. Since the rubber material can be approximately regarded as an absolutely incompressible material, the hydrostatic pressure will not affect the strain state. Then, the hydrostatic pressure can be arbitrarily increased to strengthen the boundary conditions without affecting the equilibrium state. According to the working conditions of the packer cylinder and the convenience of uniaxial tensile test, uniaxial tensile test is conducted to determine the Yeoh model constants C10, C20 and C30.

Relationship between principal stress \(t_{i}\) and principal elongation ratio \(\lambda_{{\text{i}}}\) is,

$$t_{{1}} = \frac{{2}}{{\lambda_{{1}} }}\left( {\lambda_{{1}}^{{2}} { - }\frac{{1}}{{\lambda_{{1}}^{{2}} \lambda_{{2}}^{{2}} }}} \right)\left( {\frac{\partial W}{{\partial I_{{1}} }} + \lambda_{{2}}^{{2}} \frac{\partial W}{{\partial I_{{2}} }}} \right)$$
(3)

Substitute Eq. (1) into Eq. (3), then

$$\frac{{t_{1} }}{{2\left( {\lambda_{{1}} - \frac{{1}}{{\lambda_{1}^{2} }}} \right)}} = C_{{{10}}} + {2}C_{{{20}}} \left( {\lambda_{{1}}^{{2}} + \frac{{2}}{{\lambda_{{1}} }}{ - 3}} \right) + {3}C_{{{30}}} \left( {\lambda_{{1}}^{{2}} + \frac{{2}}{{\lambda_{{1}} }}{ - 3}} \right)^{{2}}$$
(4)

Equation (4) is the basic formula for determining C10, C20 and C30 by uniaxial tensile test. The curve of \(t_{{1}} { - }\lambda_{{1}}\) is determined from the test data, and then, the Yeoh model constants C10, C20 and C30 are calculated according to Eq. (4).

Tensile test of rubber sample

In order to test the mechanical properties of rubber, standard tensile specimens were prepared and uniaxial tensile tests were carried out. The test sample used in the test is dumbbell type I test piece, and the specification and size comply with the provisions of GB/t528-2009. The thickness of the test piece is 2 mm, the width is 6 mm, and the gauge distance is 25 mm, as shown in Fig. 4. Because the hardness of the side rubber cylinder and the middle rubber cylinder of the packer is different, they are shore hardness 84 and shore hardness 75, respectively. The two kinds of hardness rubber are tested. The test shall strictly comply with the national standard GB/t528-2009. Under normal temperature, the test piece shall be installed on microcomputer controlled electronic universal testing machine, as shown in Fig. 4.

Fig. 4
figure 4

Universal microcomputer control electronic testing machine

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Let \(y\left( {\lambda_{{1}} , \, t_{1} } \right) = y(u) = \frac{{t_{1} }}{{2\left( {\lambda_{{1}} - \frac{{1}}{{\lambda_{1}^{2} }}} \right)}}\), \(u(\lambda_{{1}} ) = \lambda_{{1}}^{{2}} + \frac{{2}}{{\lambda_{{1}} }}{ - 3}\), then formula (4) becomes

$$y = C_{{{10}}} + {2}C_{{{20}}} u + {3}C_{{{30}}} u^{{2}}$$
(5)

The tensile test data before and after vulcanization are obtained as shown in Fig. 5. Converting the measured stress and strain data of the tensile specimen into a “y-u” scatter plot, and the fitting curves are as shown in Fig. 6.

Fig. 5
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Tensile test data and Yeoh curve fitting diagram

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Fig. 6
figure 6

Parameter ‘y-u’ scatter conversion and curve fitting of tensile test data

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Numerical study of the gas well packer

According to the setting condition of the packer, a three-dimensional finite element model of the contact between the packer rubber cylinder and the casing is established. The following assumptions are put forward for the research content of this paper.

  1. (1)

    The influence of temperature changes on the simulation is not considered.

  2. (2)

    The influence of fluctuation on the force of the rubber cylinder is not considered.

  3. (3)

    The normal coefficient of friction varies with the contact area, positive pressure and temperature, and the coefficient of friction between different parts is different. Here, a fixed coefficient of friction of 0.2 is set between each part.

Establishment of rubber model

According to the structural parameters of the packer, 3D model is established as shown in Fig. 7.

Fig. 7
figure 7

Model establishment and mesh division of rubber cylinder

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Boundary conditions of rubber

In the boundary setting, 3D model boundary constraints are set for the outer boundary of the central pipe, bottom protective ring and casing, continuous contact is set for the contact surface between various components, and the friction coefficient is 0.2. In order to increase the convergence of nonlinear mechanics of rubber cylinder, nonlinear dynamics is used for calculation (Table 1).

Table 1 Result parameters of Yeoh model for rubber cylinder material
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Optimization design of shoulder chamfer of side rubber cylinder

During the setting process of the packer, the central pipe of the packer is stretched when the hydraulic pressure in the tubing entering into the setting chamber through the pressure guide channel, and the setting load further compresses the rubber cylinder. When the contact pressure between the rubber cylinder and the casing is greater than the working pressure difference, the packer plays the role of sealing (Liu et al. 2019). According to the compression simulation process of the rubber cylinder, it can be seen that the contact stress between the rubber cylinder and the casing increases continuously with the application of the acting load, and the protective parts of the upper and lower rubber cylinder edges are squeezed, and the stress and strain are the largest, and it shows obvious nonlinear increasing characteristics. The upper and lower end of the rubber cylinder is compressed first after bearing pressure, which is prone to strength failure. How to convert the stress concentration into uniform stress is the key to prolong the service life and improve the reliability of the packer.

By establishing the numerical model of the rubber cylinder setting, the optimization analysis of the rubber cylinder structure which affects the pressure performance of the rubber cylinder can effectively prevent the stress damage of the rubber cylinder and prolong the life of the rubber cylinder. In this paper, the structural optimization design of side rubber cylinder shoulder chamfer and its protection ring were carried out as shown in Fig. 8. The chamfer of the protection ring (20°, 30°, 40°) is, respectively, studied and analyzed. The rubber material parameters after vulcanization were calculated. The numerical results show that the packer begins to squeeze the central pipe and casing when the setting displacement is 15 mm. The packer stress state under the three sets of structures is analyzed. The results show that the stress decreases first and then increases with the increase in chamfer on the shoulder of the side rubber cylinder under the same setting displacement load. When the chamfer is 30°, the edge of the rubber cylinder has less stress, which can reduce stress damage and prolong the service life of the packer.

Fig. 8
figure 8

Structural optimization design of anti-shoulder burst packer (rubber cylinder protective ring)

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According to the structural optimization calculation results of the protection ring showed from Figs. 9, 10 and 11, the stress decreases from 553 to 393 MPa when the chamfer changes from 20° to 30° as shown in Fig. 12. When the chamfer becomes 40°, the stress of the protection ring is 260 MPa under the same compression load. In order to realize the sealing of the packer and ensure that the protective ring has a certain degree of opening under the load stress, the structural optimization of the protective ring needs to have moderate stress, so the chamfer of 30° is an optimization result.

Fig. 9
figure 9

The force and deformation results of the edge rubber cylinder under the compression distance of 15 mm when the chamfer is 20°

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Fig. 10
figure 10

The force and deformation results of the edge rubber cylinder under the compression distance of 15 mm when the chamfer is 30°

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Fig. 11
figure 11

The force and deformation results of the edge rubber cylinder under the compression distance of 15 mm when the chamfer is 40°

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Fig. 12
figure 12

Stress results under different protection ring chamfers

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Simulation of setting process

After setting the outer diameter of the rubber cylinder and the inner diameter of the casing, sealing property can be calculated by changing the setting load, and it also can be studied the relationship between the setting pressure and the setting distance of the rubber cylinder. Packer setting simulation results are shown in Figs. 13 and 14.

Fig. 13
figure 13

Cloud diagram of stress (MPa) and deformation (mm) when the setting displacement is 10 mm

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Fig. 14
figure 14

Cloud diagram of stress (MPa) and deformation (mm) when the setting displacement is 48 mm

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The analysis results show that the deformation degree and compression distance of rubber cylinder increase with the increase in setting load. In the initial state, the protection ring squeezes the upper and lower rubber under the compression load, which causes the rubber axial compression and radial expansion. Finally, it realizes the sealing of the entire annulus from the upper rubber to the lower rubber. The simulation results show that the packer rubber seals the annular between the fracturing tool and casing when setting displacement is 48 mm in the initial state, and the maximum stress of protection ring reaches 533 MPa. The stress of upper protection ring is the largest, and the stress of lower protection ring is least. Protection rings play an important role in improving the performance of sealing and pressure bearing.

In addition, the stress state of the packer before and after vulcanization of the rubber material was calculated, and the contact sealing effect of the rubber material on the inner wall of the central pipe and casing under the same setting state was analyzed. Taking 48 mm setting displacement load as the research object, the calculation and comparison results are as follows in Figs. 15 and 16.

Fig. 15
figure 15

Cloud diagram of stress (MPa) and deformation (mm) of unvulcanized rubber packer when the final setting displacement is 48 mm

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Fig. 16
figure 16

Cloud diagram of stress (MPa) and deformation (mm) of vulcanized rubber packer when the final setting displacement is 48 mm

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According to the comparison results, it can be seen that under 48 mm setting displacement load of the rubber material corroded by formation fluid immersion, the maximum stress of the protective ring of the packer rubber cylinder before vulcanization is 289 MPa, and the maximum stress of the protective ring of the packer rubber cylinder after vulcanization is 533 MPa. The vulcanized rubber cylinder could still keep the mechanical properties of the material in a good state after immersion of formation water, while the unvulcanized rubber material showed mechanical deterioration and even lost its working performance in the working fluid environment. Therefore, the vulcanized rubber material has good adaptability.

In order to analyze the variation rule of contact stress between packer rubber cylinder and casing in the setting process, grid node elements on the rubber cylinder were selected as the analysis object, and the variation law of contact stress between the side node position of rubber cylinder and the setting process was extracted, and the correlation curve was drawn as shown in Fig. 17.

Fig. 17
figure 17

Relationship between setting loads and total contact stress

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According to the compression relation curve, when the setting displacement of the three rubber cylinder reaches 48 mm, the contact stress between the upper rubber and casing is 4.5 MPa, the contact stress between the medium rubber and casing is 2.1 MPa, and the contact stress between lower rubber cylinder with casing 1.4 MPa. Therefore, it is necessary to optimize the chamfer and the protective ring improving the contact stress. It can be seen from the analysis results, the contact stress of the rubber cylinder to the casing shows a nonlinear increasing trend. According to the set result stress nephogram of the packer rubber, the force of the medium rubber cylinder is moderate with no stress concentration between the two ends and the protection ring. The rubber material with slightly softer material can be preferred to play a better role in sealing.

It can be seen from Fig. 18 that with the densification of the rubber cylinder grids, the stress shows a slight decrease with a small change, indicating that the current grid size has little impact on the results, which can meet the analysis requirements. In addition, with the increase of friction coefficient, under the same displacement load, the stress of packer rubber cylinder increases to a certain extent, indicating that friction and roughness will lead to a higher stress.

Fig. 18
figure 18

Simulation results under different grid sizes and different friction coefficients

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Indoor evaluation and field application of packer cylinder

Indoor test

Figure 19 is the indoor test result for rubber cartridge, and Fig. 20 is the pressure test result. During the limit test of the rubber cylinder, under the conditions of 150 °C and 70 MPa oil immersion, there was no obvious pressure drop and pressure channeling, indicating that the sealing effect of the rubber cylinder after pressure is good. During the rubber cylinder fatigue test, under the conditions of 150 °C, two-way pressure bearing of 35 MPa and 24 h oil immersion, there are no abnormal phenomena such as obvious pressure drop and pressure channeling, and the rubber cylinder has good pressure bearing sealing effect. After the test, it is observed that the rubber cylinder is in good appearance, good recovery performance, and the residual deformation is less than 5%, as well as that rubber cylinders are not broken and without any crack. The test results show that the rubber cylinder meets the requirements of indoor and field application.

Fig. 19
figure 19

Rubber cartridge of indoor experiment

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Fig. 20.
figure 20

70 MPa pressure test curve of packer

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Field application

The integrated packer for vertical well fracturing and production has been applied to 16 wells in total on site, and the on-site construction success rate is 100%. Among them, Fig. 21 is one of the on-site construction tests. The maximum number of fracturing construction layers are 6 layers, the maximum liquid addition is 8490 m3, the maximum sand addition is 403 m3, the maximum pressure can reach 79 MPa, the maximum temperature is 154 °C, the maximum construction displacement is 6 m3/min, and the average production increase is 9.0 × 104 m3/d. The maximum effective sealing time of the downhole packer has exceeded 4 years, and the field application effect is good.

Fig. 21
figure 21

Field test of integrated fracturing and completion packer

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Before the study, the temperature and pressure resistance of the rubber of the fracturing completion packer meet the requirements of 150 °C, 70 MPa and gas-resistant immersion, but the long-term sealing and reliability cannot be guaranteed, and there are also differences in the sealing capacity. Therefore, by further improving the rubber material and applying the mechanical experimental test means, the mechanical performance parameters of the rubber cylinder material are carefully evaluated, and the structural parameters and setting parameters that affect the temperature and pressure resistance performance of the rubber cylinder are simulated, so as to further improve the performance of integrated fracturing and completion tools of gas well. The integrated fracturing and completion process realizes one trip of string fracturing, gas testing and completion, reducing reservoir pollution caused by tripping in operation. The validity period of the rubber tube seal of the packer is extended to ensure that there is no pressure in the oil casing annulus of the wellbore, which plays an anti-corrosion protection role for the upper casing, and also increases safety factor of the completion string.

Conclusions

A new optimization application of the fracturing and completion integrated packer for risk exploration wells was presented and designed through the method combining the test of high temperature and high pressure curing kettle and the force analysis from Abaqus finite element simulation platform. And the integrated analysis process of determining rubber constitutive parameters and optimizing the structure of rubber cylinder components in high-temperature and high-pressure geological environments was completed, and the following conclusions are obtained:

  1. (1)

    The protective ring structure is designed to reduce the stress concentration of the packer rubber in sleeve shoulder, and the 30° included angle is an optimized angle, which can prevent stress failure and prolong the service life.

  2. (2)

    Perfluoroether, fluorinated polypropylene and fluorosilicone rubber are adopted in the integrated packer for fracturing and completion to solve the impact of high temperature and corrosive environment in deep volcanic formation.

  3. (3)

    A performance test and optimization scheme of the packer is designed by combining numerical simulation, laboratory and field experiments, which can simulate the packer setting and working conditions well. The field application of the optimized packer shows that it reaches temperature resistance at 154 °C and pressure resistance at 79 MPa, and the validity extends from one year to four years under the corrosive formation environment, which meets the development requirements of volcanic gas reservoirs in Daqing Oilfield.