A perforation azimuth angle optimization method for coiled tubing drag fracturing under stress superposition

Abstract

The application discloses a perforation azimuth optimization method for coiled tubing drag fracturing under stress superposition, and comprises the following steps: obtaining reservoir rock mechanics parameters, reservoir physical property parameters, thermodynamic parameters and wellbore parameters; according to the theory of elasticity, a total stress distribution model of a perforation tunnel is established; according to the obtained total stress distribution of the perforation tunnel, the magnitude of the principal stress on the perforation tunnel wall at any point can be deduced, and according to the method of elasticity and dichotomy, the maximum tensile stress of the reservoir rock and the fracture initiation azimuth angle are calculated; the calculated maximum tensile stress of the rock is substituted into the fracture criterion to calculate the formation fracture pressure when sand jet perforation is performed at different perforation azimuth angles. The application proposes a relatively accurate calculation method for optimizing the sand jet perforation azimuth of the coiled tubing drag fracturing, and discloses the influence law of the sand jet perforation azimuth of the coiled tubing drag fracturing on the fracture pressure, which will help to improve the development potential of low-permeability reservoir oil and gas resources.

Description

TECHNICAL FIELD

[0001] The present application relates to a perforation azimuth angle optimization method for coiled tubing drag fracturing under stress superposition, and belongs to the field of oil and gas stimulation. BACKGROUND

[0002] Compared with conventional fracturing technology, the coiled tubing drag fracturing technology has higher reservoir reconstruction accuracy and operation efficiency, and its operation time is more than half of that of the conventional fracturing technology, which effectively improves the operation effect and increases the application frequency in large-scale low-permeability reservoirs. Meanwhile, the coiled tubing drag fracturing technology has higher reservoir reconstruction accuracy and efficiency, can accurately position the crack initiation position, and the single crack size is controllable, which is beneficial to the implementation of targeted reservoir reconstruction measures and the integration of geology and engineering fracturing reconstruction.

[0003] At present, relevant scholars have carried out experimental and theoretical researches on the influence of the hydraulic jetting effect of the coiled tubing drag fracturing. Fu Gangdan, Xia Qiang, Xie Gangru, Zhang Jing, etc. studied the optimization of jetting speed, perforation time, nozzle size and fluid properties under different sandblasting perforation parameters through indoor test, and showed that the factors influencing the coiled tubing hydraulic sandblasting perforation capacity mainly include nozzle parameters, abrasive type, abrasive particle size and concentration, jet pressure, construction displacement, confining pressure and jetting time, among which the nozzle parameters, abrasive type, jet pressure, displacement and confining pressure are the key factors. Ouyang Mengdi, Wang Boxue, Li Zhaoyang, Gao Rongxing, Wang Zunze, etc. analyzed the influence of jet flow parameters, abrasive parameters, nozzle parameters and rock mechanics parameters on the hydraulic jetting effect by numerical simulation and computational fluid dynamics method combined with CFD software.

[0004] In summary, the experimental and theoretical researches mainly aim at the influence of sandblasting perforation parameters on the jetting effect, and the influence of the formation fracture pressure during perforation has not been studied. During the coiled tubing drag fracturing operation, the formation fracture pressure is greater than that of the conventional fracturing operation, and since the number of sandblasting perforation holes is small, the perforation hole position may not be on the principal stress position, thereby affecting the size of the formation fracture pressure.

[0005] Therefore, it is urgent to establish a perforation azimuth angle optimization method for coiled tubing drag fracturing under stress superposition, which will help to improve the scientificity and pertinence of the coiled tubing drag fracturing design and further improve the development potential of low-permeability reservoirs. SUMMARY

[0006] In order to overcome the problems in the prior art, the present application provides a perforation azimuth angle optimization method for coiled tubing drag fracturing under stress superposition, which can conveniently analyze the influence of the coiled tubing fracturing perforation azimuth angle on the formation fracture pressure and provide some insights for the parameter design and optimization of the coiled tubing drag fracturing.

[0007] The technical scheme provided by the present application to solve the above technical problems is: a perforation azimuth optimization method for coiled tubing drag fracturing considering stress superposition, comprising the following steps:

[0008] Step S1, obtaining reservoir rock mechanics parameters, reservoir physical property parameters, thermodynamic parameters and wellbore parameters;

[0009] Step S2, using the parameters obtained in step S1, according to the theory of elasticity, establishing a total stress distribution model of the perforation tunnel considering the influence of stress superposition caused by in-situ stress, wellbore internal pressure, fracturing fluid loss, cemented casing and temperature change of surrounding rock, and calculating the stress distribution around the perforated wellbore;

[0010] Step S3, according to the stress distribution around the perforated wellbore, and using the method of elasticity and dichotomy, the maximum tensile stress of the reservoir rock is calculated;

[0011] Step S4, substituting the maximum tensile stress of the reservoir rock into the fracture criterion to calculate the formation fracture pressure when sandblasting perforation is performed at different perforation azimuths.

[0012] Further technical solutions are that the reservoir mechanics parameters in step S1 include maximum horizontal principal stress, minimum horizontal principal stress, vertical stress, pore pressure, rock tensile strength, the reservoir physical property parameters include porosity, Young's modulus, Poisson's ratio, permeability coefficient, Biot porous elastic coefficient, Haimson correction coefficient, the thermodynamic parameters include linear thermal expansion coefficient, rock temperature difference, and the wellbore parameters include wellbore inclination angle, azimuth angle, casing outer diameter, inner diameter.

[0013] Further technical solutions are that the total stress distribution model of the perforation tunnel is:

[0014]

[0015] In the formula: σ s , σ θp , σ zz are the radial, circumferential and axial stresses in the perforation hole, MPa; τ sθ , τ zzθ , τ szz are three coordinate components of shear stress in the perforation hole, MPa; θ p is the circumferential angle of perforation, °; r hs is the radius of the perforation hole, m; s is the distance from a certain point in the perforation hole plane to the axial direction, m; P p is the pore pressure, MPa.

[0016] Further technical solutions are that the calculation process of the total stress distribution of the perforation tunnel in step S2 is as follows:

[0017] Step S21, according to the theory of elasticity, the stress field distribution caused by in-situ stress is calculated;

[0018] Step S22, the stress field distribution caused by wellbore internal pressure is calculated;

[0019] Step S23, the stress field distribution caused by fracturing fluid loss is calculated;

[0020] Step S24, the stress field distribution caused by cementing casing is calculated;

[0021] Step S25, the stress field distribution caused by temperature change of surrounding rock is calculated;

[0022] Step S26, the total stress field distribution of the perforation tunnel is obtained by combining the different stress field change distributions calculated above.

[0023] Further technical solutions are that the calculation formula in the step S22 is:

[0024]

[0025] In the formula, r is the wellbore radius, m; r is the distance from the wellbore axis to a point in the formation, m; θ is the polar angle of any radial and the x axis, °; σ w , σ r , σ θ , and σ z are the radial, hoop and axial stresses in the wellbore coordinates, MPa; τ θz , τ rθ , and τ rz are three components of the shear stress in the wellbore coordinates, MPa.

[0026] Further technical solutions are that the calculation formula in the step S23 is:

[0027]

[0028] In the formula, P w is the liquid column pressure in the wellbore, MPa; c is the Haimson correction coefficient, 0.9 < c < 1.

[0029] Further technical solutions are that the calculation formula in the step S24 is:

[0030]

[0031] The boundary conditions are:

[0032]

[0033] In the formula, α is the Biot porous elastic coefficient; C r, C b respectively are skeleton compression rate and volume compression rate of rock, %; φ is rock porosity, %; δ is permeability coefficient; P n (r) is net stress of stratum at radius r.

[0034] Further technical solutions are that the calculation formula in the step S25 is:

[0035]

[0036]

[0037] In the formula: is radial stress and tangential stress around wellbore caused by cement casing, MPa; TF is transfer coefficient, which represents wellbore pressure transferred to rock in stratum; v c is Poisson's ratio of cement casing, dimensionless; E c is Young's modulus of cement casing, MPa; R o , R i are respectively inner diameter and outer diameter of casing, m.

[0038] Further technical solutions are that the calculation formula of the maximum tensile stress of reservoir rock in the step S3 is:

[0039]

[0040]

[0041] In the formula: α is Biot porous elasticity coefficient; σ3 is the maximum tensile stress of reservoir rock, MPa.

[0042] Further technical solutions are that the fracture criterion is:

[0043] σ max (θ p )-αP p ≥σ t

[0044] In the formula: α is Biot porous elasticity coefficient; P p is pore pressure, MPa.

[0045] The present application has the following beneficial effects: the present application proposes a more accurate calculation method to optimize coiled tubing drag fracturing sandblasting perforation azimuth, and discloses the influence law of coiled tubing drag fracturing sandblasting perforation azimuth angle on fracture pressure, which will help to improve the development potential of low-permeability reservoir oil and gas resources. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is a flowchart of the present application;

[0047] Figure 2 The figure is a tangential stress distribution diagram of a perforation hole of the application;

[0048] Figure 3 The figure is a fracture initiation azimuth and initiation angle diagram of the application;

[0049] Figure 4 The figure is a curve diagram of the formation fracture pressure of Well A varying with the perforation azimuth angle;

[0050] Figure 5 The figure is a curve diagram of the formation fracture pressure of Well B varying with the perforation azimuth angle. DETAILED DESCRIPTION

[0051] The technical solutions of the application will be described clearly and completely below with reference to the drawings. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the application.

[0052] As shown in the figure, the method for optimizing the perforation azimuth angle of the coiled tubing drag fracturing considering stress superposition of the application comprises the following steps: Figure 1

[0053] Step S1, obtaining the reservoir mechanical parameters (maximum and minimum horizontal principal stress, vertical stress, pore pressure, rock tensile strength), reservoir physical parameters (porosity, Young's modulus, Poisson's ratio, permeability coefficient, Biot porous elastic coefficient, Haimson correction coefficient), thermodynamic parameters (linear thermal expansion coefficient, rock temperature difference), wellbore parameters (wellbore inclination angle, azimuth angle, casing outer diameter, inner diameter);

[0054] Step S2, using the parameters obtained in step S1, according to the theory of elasticity, establishing the total stress distribution model of the perforation hole considering the influence of stress superposition caused by the in-situ stress, wellbore internal pressure, fracturing fluid loss, cemented casing and temperature change of surrounding rock, and calculating the stress distribution around the perforation wellbore;

[0055] Step S21, according to the theory of elasticity, calculating the stress field distribution caused by the in-situ stress;

[0056]

[0057] In the formula, r is the wellbore radius, m; r is the distance from the wellbore axis to a certain point in the formation, m; θ is the polar angle of any radial direction and the x-axis, °; σ w , σ r , σ θ and σ z are the radial, hoop and axial stresses in the wellbore coordinates, MPa; τ​θz rθ rz are three components of shear stress in wellbore coordinate, MPa;

[0058] Step S22, calculating stress field distribution caused by wellbore pressure;

[0059]

[0060] wherein: P w is liquid column pressure in wellbore, MPa; c is Haimson correction coefficient, 0.9 < c < 1.

[0061] Step S23, calculating stress field distribution caused by fracturing fluid filtration;

[0062]

[0063] Boundary conditions thereof are:

[0064]

[0065] wherein: α is Biot porous elasticity coefficient, α = 1-β v = 1-C r / C b ; C r , C b are skeleton compression rate and volume compression rate of rock, %; φ is rock porosity, %; δ is permeability coefficient (δ = 1 when formation is permeable, δ = 0 when formation is impermeable); P n (r) is net stress of formation at radius r, P n (r) = P(r) - P0.

[0066] Step S24, calculating stress field distribution caused by cemented casing;

[0067]

[0068]

[0069] wherein: is radial stress and tangential stress around wellbore caused by cemented casing, MPa; TF is transfer coefficient, indicating wellbore pressure transferred to rock in formation. c is Poisson's ratio of cemented casing, dimensionless; E c is Young's modulus of cemented casing, MPa; R o , R i are inner diameter and outer diameter of casing, respectively, m;

[0070] Step S25, calculating stress field distribution caused by temperature change of surrounding rock; ​​

[0071]

[0072] wherein:

[0073]

[0074] wherein: σ x , σ y , σ z are normal stresses in x, y, z directions, MPa; v, v' are Poisson's ratios in three principal planes and perpendicular to the three principal planes, dimensionless; E, E' are Young's moduli in three principal planes and perpendicular to the three principal planes, MPa; a, a' are thermal expansion coefficients of the rock in the plane and perpendicular to the plane, 1 / ℃; T0 is an initial temperature of the formation rock, ℃; T is a temperature of the formation rock after being affected by drilling and fracturing fluid, ℃; a T is a thermal expansion coefficient of the rock, 1 / ℃.

[0075] Step S27, combined with the different stress field change distribution calculated by formula (1)-(7), according to the geometric model shown in Figure 2 , and the total stress distribution of the perforation tunnel is calculated by formula (8);

[0076]

[0077] wherein: σ s , σ θp , σ zz are radial, circumferential and axial stresses in the perforation hole, MPa; τ sθ , τ zzθ , τ szz are three coordinate components of shear stress in the perforation hole, MPa; θ p is a circumferential angle of the perforation, °; r hs is a radius of the perforation hole, m; s is a distance from a point in the perforation hole plane to the axial direction of the hole, m; P p is a pore pressure, MPa;

[0078] Step S3, according to the stress distribution around the perforated wellbore, and using the method of elastic mechanics and dichotomy, the maximum tensile stress of the reservoir rock is calculated;

[0079] The total stress distribution of the perforation tunnel is calculated by formula (8), and the principal stress on the perforation hole wall of any point can be expressed as:

[0080]

[0081] According to the theory of elastic mechanics, the maximum tensile stress of the rock is calculated as:

[0082]

[0083] For a perforation azimuth angle θ p , the fracture initiation azimuth angle is:

[0084]

[0085] Step S4, as shown in Figure 3 , according to the fracture criterion, when the maximum tensile stress in the well wall z-θ plane is greater than or equal to the tensile strength of the rock itself, that is:

[0086] σ max (θ p )-αP p ≥σ t (12)

[0087] Satisfying θ p is the initiation pressure when the well wall is stretched and fractured when the perforation azimuth angle is θ.

[0088] Where for any given perforation azimuth angle, the corresponding surrounding rock fracture pressure and initiation azimuth angle can be obtained, and the initiation azimuth angle calculation equation is shown in equation (13);

[0089]

[0090] Get γ1, γ2;

[0091]

[0092] According to the definition of function extreme value, when the second order function value is less than 0, the original function has a maximum value. The maximum tensile stress of the surrounding rock and its second order derivative expression are shown in equation (15);

[0093]

[0094] Substitute γ1 and γ2 into equation (15). If the numerical value is less than 0, the original function has a maximum value, and it is the true angle of crack initiation.

[0095] Example 1

[0096] The basic parameters of the coiled tubing drag hydraulic sandblasting perforation fracturing well in a domestic oilfield are used to study the relationship between the perforation azimuth angle and the fracture pressure. The basic parameters of the coiled tubing drag fracturing well in this example are shown in Table 1.

[0097] Table 1 Basic parameters of coiled tubing drag fracturing well

[0098]

[0099] According to the steps described above, the calculation results are shown inFigure 4 and 5 as shown.

[0100] The minimum formation fracture pressure of A well corresponds to the perforation azimuth angle of 160° or 340°, and the minimum formation fracture pressure of B well corresponds to the perforation azimuth angle of 6° or 180°. With the change of the perforation azimuth angle, the fracture pressure is reduced by 7-20 MPa. Since the horizontal wellbore is arranged along the direction of the horizontal minimum principal stress, the wellbore is subjected to the horizontal maximum principal stress and the vertical principal stress. When the horizontal maximum principal stress is greater than the vertical stress, the nozzle needs to be adjusted to the horizontal position, and when the horizontal maximum principal stress is less than the vertical stress, the nozzle needs to be adjusted to the vertical position, which can effectively reduce the fracture pressure. If the fracture pressure is not the optimal value when sandblasting perforation is performed, the integrity of the casing is reduced, the shear resistance is weakened, and the stability of the wellbore is not conducive.

[0101] The above description is not intended to limit the present application in any form, although the present application has been disclosed by the above examples, however, it is not intended to limit the present application, any skilled person in the art, within the scope of the technical scheme of the present application, can make some changes or modifications of the above disclosed technical content as equivalent examples of equivalent changes, but any simple modification, equivalent change and modification made to the above examples according to the technical essence of the present application, as long as it does not deviate from the content of the technical scheme of the present application, still belongs to the scope of the technical scheme of the present application.

Claims

1. A method for optimizing the azimuth of perforation for coiled tubing drag fracturing under stress superposition, characterized in that, The method comprises the following steps: Step S1, obtaining reservoir rock mechanics parameters, reservoir physical property parameters, thermodynamic parameters and wellbore parameters; Step S2, using the parameters obtained in step S1, according to the theory of elasticity, establishing a total stress distribution model of the perforation tunnel under the influence of stress superposition caused by in-situ stress, wellbore internal pressure, fracturing fluid loss, cemented casing and temperature change of surrounding rock, and calculating the stress distribution around the perforated wellbore; The total stress distribution model of the perforation tunnel is: wherein: σ s , σ θp , σ zz is the radial, circumferential and axial stress in the perforation hole, MPa; τ sθ , τ zzθ , τ szz is the three coordinate components of the shear stress in the perforation hole, MPa; θ p is the circumferential angle of the perforation, °; r hs is the radius of the perforation hole, m; s is the distance from a point in the plane of the perforation hole to the axial direction of the hole, m; P p is the pore pressure, MPa; Step S3, according to the stress distribution around the perforated wellbore, and using the method of elasticity and dichotomy to calculate the maximum tensile stress of the reservoir rock; Step S4, substituting the maximum tensile stress of the reservoir rock into the fracture criterion to calculate the formation fracture pressure when sandblasting perforation is performed at different perforation azimuth angles.

2. The method of claim 1, wherein, The reservoir mechanics parameters in step S1 include maximum horizontal principal stress, minimum horizontal principal stress, vertical stress, pore pressure, rock tensile strength, the reservoir physical property parameters include porosity, Young's modulus, Poisson's ratio, permeability coefficient, Biot porous elastic coefficient, Haimson correction coefficient, the thermodynamic parameters include linear thermal expansion coefficient, rock temperature difference, and the wellbore parameters include wellbore inclination angle, azimuth angle, casing outer diameter, inner diameter.

3. The method of claim 1, wherein, The calculation process of the total stress distribution of the perforation tunnel in step S2 is as follows: Step S21, according to the theory of elasticity, the stress field distribution caused by in-situ stress is calculated; Step S22, the stress field distribution caused by wellbore internal pressure is calculated; Step S23, the stress field distribution caused by fracturing fluid loss is calculated; Step S24, the stress field distribution caused by cemented casing is calculated; Step S25, the stress field distribution caused by temperature change of surrounding rock is calculated; Step S26, combining the above calculated different stress field change distributions, the total stress field distribution of the perforation tunnel is obtained.

4. The method of claim 3, wherein, The calculation formula in step S22 is: where: r w R is the wellbore radius, m; r r is the distance from the wellbore axis to a point in the formation, m; θ θ is the polar angle of the wellbore axis, °; x σ r , σ θ , σ z σrr, σθθ, and σzz are the radial, hoop, and axial stresses in wellbore coordinates, MPa; τ θz , τ rθ , τ rz γrr, γθθ, and γzz are the three components of shear stress in wellbore coordinates, MPa.​ 5. The method of claim 3, wherein, The calculation formula in step S23 is: In the formula: P w The pressure of the fluid column inside the wellbore, in MPa; c The Haimson correction factor is 0.9 < c < 1.

6. The method of optimizing the azimuth of perforation for coiled tubing drag fracturing considering stress superposition of claim 3, wherein, The calculation formula in step S24 is: Its boundary conditions are: In the formula: α The elastic modulus of Biot porous materials; C r , C b These represent the skeletal compression ratio and volumetric compression ratio of the rock, respectively, % . ϕ The porosity of the rock is %; δ Permeability coefficient; P n (r) is the radius r Net stress in the formation at that location.

7. The method of optimizing the azimuth of perforation for coiled tubing drag fracturing considering stress superposition of claim 3, wherein, The calculation formula in step S25 is: where: σ o r, σ o θ is the radial and tangential stress around the wellbore caused by the cement casing, MPa; TF is the transfer coefficient, which represents the transfer of wellbore pressure to the rock in the formation; v c is the Poisson's ratio of the cement casing, dimensionless; E c is the Young's modulus of the cement casing, MPa; R o , R i is the inner and outer diameter of the casing, respectively, m.

8. The method of claim 1, wherein, The calculation formula of the maximum tensile stress of the reservoir rock in step S3 is: where: α Biot's porous elastic coefficient; σ 3 is the maximum tensile stress of the reservoir rock, MPa.

9. The method of claim 1, wherein, The fracture criterion is: wherein: α Biot's porous elastic coefficient; P p Pp is the pore pressure, MPa.

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