A method for predicting three-dimensional stress field around a well during spiral perforation and fracturing

Abstract

The present invention relates to a method for predicting a three-dimensional stress field around a spiral perforating and fracturing well, comprising the following steps: S1, constructing a formation-wellbore-perforation three-dimensional model of a target block according to actual basic parameters; S2, discretizing the formation-wellbore-perforation three-dimensional model and performing grid division; S3, constructing a finite element equation of the three-dimensional model, solving the finite element equation, and predicting the stress field. The method of the present invention can accurately predict the stress field distribution around the spiral perforating well and the wellbore under any phase angle condition, thereby providing a basis for fracturing optimization design.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas reservoir development, and in particular to a method for predicting a three-dimensional stress field around a spiral perforating and fracturing well. Background Art

[0002] In the process of hydraulic fracturing, most of the operations are carried out in casing perforated wells. Whether it is the initiation and expansion of cracks, it is necessary to determine the stress field distribution around the perforated wellbore and the hole, which lays the foundation for the calculation of the fracture pressure and the study of the crack expansion path. Therefore, accurate prediction of the stress field around the perforated wellbore is of great significance for the selection of hydraulic fracturing equipment and the optimization of construction parameters.

[0003] Due to the in-situ three-dimensional ground stress of the rock, the formation of the wellbore and the distribution of the stress field around the wellbore under the action of the internal pressure of the wellbore and the wellbore, a series of partial differential equations such as the rock constitutive equation, equilibrium equation, strain-displacement equation, strain compatibility equation, etc. need to be solved jointly, and the geometric shape of the perforated well is complex, so it is impossible to obtain it through accurate analytical solution in the existing technology. In the existing technology, most of the predictions of the stress field around the perforated well are simplified as two-dimensional plane strain, simplified to a hole intersecting the wellbore on several planes, and analytical solutions are performed, but this is not completely consistent with the fact that most of the actual perforated wells are spiral perforated at a certain phase angle.

[0004] Therefore, how to construct a three-dimensional model that conforms to the actual situation and obtain accurate stress field distribution is of great significance for hydraulic fracturing fracture pressure prediction and crack propagation simulation. Summary of the invention

[0005] In order to overcome the problems in the prior art, the present invention provides a method for predicting the three-dimensional stress field around a spiral perforating fracturing well. The method constructs a model by the finite element method, takes into account the actual situation of three-dimensional spiral perforating, and can accurately predict the stress field distribution around the spiral perforating well and the wellbore under any phase angle condition, thereby providing a basis for fracturing optimization design. To achieve the above purpose, the present invention provides the following solutions:

[0006] A method for predicting a three-dimensional stress field around a spiral perforating and fracturing well comprises the following steps:

[0007] S1. Construct a three-dimensional formation-wellbore-perforation model of the target area based on actual basic parameters;

[0008] S2, discretizing the formation-wellbore-perforation three-dimensional model and performing grid division;

[0009] S3. Construct the finite element equation of the three-dimensional model, solve the finite element equation, and predict the stress field.

[0010] A further technical solution is that the step S1 also includes

[0011] S11, constructing a geological three-dimensional model, constructing a vertical wellbore in the middle of the geological three-dimensional model, and constructing spirally distributed perforation holes in the radial direction of the vertical wellbore;

[0012] S12. Setting boundary conditions and assigning material characteristic parameters to the formation.

[0013] A further technical solution is that the step S11 further includes

[0014] Set the tip of the perforation hole to be hemispherical.

[0015] A further technical solution is that the boundary condition setting in step S12 includes:

[0016] Dirichlet boundary conditions are applied to the left, bottom and back of the reservoir, the minimum horizontal principal stress of the reservoir is applied to the right boundary of the reservoir, the maximum horizontal principal stress is applied to the front boundary of the reservoir, the vertical principal stress is applied above the reservoir, and the bottom hole construction pressure is applied in the wellbore and perforation holes.

[0017] A further technical solution is that the step S2 also includes

[0018] The three-dimensional geological model is divided by tetrahedral mesh, and the wellbore and perforation holes are processed by encrypted mesh.

[0019] A further technical solution is that the step S3 also includes

[0020] Constructing the finite element equation of rock deformation using tetrahedral elements

[0021] [K] e {u e}={f} e

[0022] Among them, [K] e is the element stiffness matrix; {f} e is the unit load array; u is the rock displacement,

[0023] A further technical solution is that step S3 further includes:

[0024] After obtaining the rock deformation finite element equation of the unit tetrahedron, the coefficient matrices of all units are assembled to obtain the finite element form of the porous medium deformation equation of the entire target area. The finite element form is:

[0025]

[0026] A further technical solution is that step S3 further includes:

[0027] The elastic constitutive model of the reservoir can be used to calculate the stress distribution inside each unit, thereby predicting the stress field around the well.

[0028] On the other hand, the present invention provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that when the processor executes the computer program, the steps of the three-dimensional stress field prediction method described in any one of the above claims are implemented.

[0029] On the other hand, the present invention provides a computer-readable storage medium having a computer program stored thereon, characterized in that when the computer program is executed by a processor, the steps of the three-dimensional stress field prediction method described in any one of the above claims are implemented.

[0030] The present invention has the following advantages: the present invention takes into account the actual engineering conditions of three-dimensional spiral perforation, and provides a method for predicting the three-dimensional stress field around a spiral perforation fracturing construction well, which can accurately predict the stress field distribution around the spiral perforation well and the wellbore under any phase angle conditions, thereby providing a basis for fracturing optimization design. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0032] Figure 1 It is a schematic diagram of a formation-wellbore-perforation three-dimensional model in an embodiment of the present invention;

[0033] Figure 2 It is a schematic diagram of the tip of the perforation hole in the embodiment of the present invention;

[0034] Figure 3 This is a diagram showing the calculation results of the circumferential stress at the hole edge when the phase angle is 0° in an embodiment of the present invention;

[0035] Figure 4 is a diagram showing the calculation results of mises stress when the phase angle is 0° in an embodiment of the present invention;

[0036] Figure 5 This is a diagram showing the calculation results of the mises stress at the hole edge when the phase angle is 0° in an embodiment of the present invention;

[0037] Figure 6 Graph showing the calculation results of the circumferential stress at the hole edge when the phase angle is 0° in an embodiment of the present invention;

[0038] Figure 7 A vertical well perforation model diagram under spiral perforation conditions in an embodiment of the present invention;

[0039] Figure 8 This is a stress prediction result diagram when 8 holes / m is used in an embodiment of the present invention;

[0040] Fig. 9 This is a stress prediction result diagram at 12 holes / m in an embodiment of the present invention;

[0041] Fig.10 This is a diagram of stress prediction results when 16 holes / m is used in an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0043] The purpose of the present invention is to provide a method for predicting the three-dimensional stress field around a spiral perforating and fracturing well. In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0044] In the prior art, the finite element method is often used to predict the stress field around the perforated well. However, due to the complex geometry of the three-dimensional spiral perforation and the presence of curved surfaces on the perforation end faces, it is difficult to build models, efficiently and accurately divide the grid, and solve the problem. In the prior art, the numerical simulation of the stress field around the perforated well is mostly based on single-hole or single-phase multi-hole finite element numerical simulation, which is not completely consistent with the fact that most actual perforated wells are spirally perforated at a certain phase angle.

[0045] Therefore, in order to accurately simulate the stress field around the hydraulic fracturing well of the inversion perforation well, the present invention provides a method for predicting the three-dimensional stress field around the spiral perforation fracturing well, comprising the following steps:

[0046] S1. Construct a three-dimensional formation-wellbore-perforation model of the target area based on actual basic parameters.

[0047] In a specific embodiment, the size of the research block may be determined according to the geological model parameters of the reservoir, thereby determining the geological three-dimensional model.

[0048] In a specific embodiment, Figure 1 As shown, a square geological three-dimensional model is first constructed.

[0049] In order to reduce the differentiation of model grids, the reservoir size is about 6 times the perforation hole depth h-perf. A vertical wellbore with a radius of rw is constructed in the middle of the geological 3D model. Perforations with a phase angle of alph are constructed in the radial direction of the vertical wellbore. The tip of the perforation hole is considered to be hemispherical.

[0050] When dividing the grid and constructing the perforation holes, Figure 1 The formation model is divided into grids as shown in Figure 2 As shown, the tip of the hole is considered to be hemispherical. After the geological three-dimensional model is constructed, the material characteristic parameters of the formation are given, and the material characteristic parameters include elastic modulus E, Poisson's ratio V, and rock density.

[0051] Then the boundary conditions are set, where Dirichlet boundary conditions are applied to the left, bottom and back of the reservoir, a stress boundary condition equal to the minimum horizontal principal stress of the reservoir is applied to the right boundary of the reservoir, the maximum horizontal principal stress is applied to the front boundary of the reservoir, the vertical principal stress is applied above the reservoir, and the bottom hole construction pressure P is applied in the wellbore and perforation holes.

[0052] S2. Discretize the formation-wellbore-perforation three-dimensional model and perform grid division.

[0053] like Figure 1 As shown, the three-dimensional geological model is divided by tetrahedral grids, and the wellbore and perforation holes are divided by encrypted grids, so that a discrete grid model of the geological three-dimensional model can be obtained.

[0054] Specifically, the perforation hole grid size is set first, and the grid size is set to 0.8 times the hole radius at the wellbore and hole boundary, and then the remaining grids are divided, where the minimum grid size is 0.2 times the hole radius and the maximum grid size is 5 times the hole radius.

[0055] The three-dimensional model construction method in the present application can reduce the differences between different grids of the model, and can also simplify the calculation and improve the accuracy of the calculation results around the wellbore and perforation.

[0056] S3. Construct the finite element equation of the three-dimensional model, solve the finite element equation, and predict the stress field.

[0057] When analyzing the mechanical properties of the meshed tetrahedral elements, the second-order Lagrangian element is selected, in which the displacement mode is a polynomial with the orders of constant term, linear term and quadratic term.

[0058] The finite element equation of rock deformation of tetrahedron unit is:

[0059] [K] e {u e}={f} e

[0060] Among them, [K] e is the element stiffness matrix; {f} e is the unit load array; u is the rock displacement,

[0061] Among them, [K] e =∫B T DBdΩ;

[0062]

[0063] B is the strain matrix, expressed as:

[0064] D is the elasticity matrix, expressed as:

[0065] G is the shear modulus of the porous medium,

[0066] λ is the Lame constant of the porous medium,

[0067] Unit load array {f} e The expression is:

[0068]

[0069] ε is the unit displacement:

[0070] After obtaining the rock deformation finite element equation of the unit tetrahedron, the coefficient matrices of all units are assembled to obtain the finite element form of the porous media deformation equation of the entire target area, as shown in the following formula:

[0071]

[0072] By solving the above-mentioned global stiffness matrix, the displacement of each node can be obtained. Specifically, in one embodiment, the MIUMPS method can be used for solving.

[0073] Afterwards, the elastic constitutive equation of the reservoir can be used to calculate the stress inside each unit, thereby predicting the stress field. The elastic constitutive equation is:

[0074] {σ}=[D e ]{ε}=[D e ][B]{u e}.

[0075] Calculation Example

[0076] The prediction was conducted for an actual case in a certain block, where the basic parameters of the model include: the formation is a 2m×2m×2m cube, the wellbore length is 1.5m, the perforation length is 0.4m, the hole radius is 0.02m, and the wellbore radius is 0.1m; σ x =30MPa,σ y =25MPa, bottom hole pressure is 24MPa, overburden stress σ z =28MPa.

[0077] in, Figure 3-4 is the calculation result of the hole edge circumferential stress and mises stress when the phase angle is 0°, Figure 5-6 The calculation results of the mises stress and circumferential stress at the hole edge when the phase angle is 0°. It can be seen that the stress concentration at the root and tip of the hole is most obvious.

[0078] In order to simulate the influence of stress superposition in the spiral perforation holes on the stress field during the actual perforation process, the above basic parameters are set to σ x =30MPa,σ y =25MPa,σ z =28MPa, such as Figure 7 As shown in the figure, a vertical well perforation model under spiral perforation conditions is constructed, and the models are respectively constructed for the embodiments under three conditions of 8 holes / m, 12 holes / m, and 16 holes / m, and the results are shown in Figures 8-10. It can be seen that at 8 holes / m, the influence of the stress field between the holes can only be observed on the contour line. As the number of holes increases to 12 holes and 16 holes, the holes produce areas of increased stress along the lines connecting the wellbore walls, and the larger the number of holes, the smaller the hole spacing, that is, the more obvious the stress influence between the holes; at the same time, the influence between the holes in the close direction is significantly lower than the influence of the holes in the close direction. Therefore, during the hydraulic fracturing process, if the cement sheath coagulation quality is poor, it may cause the wellbore wall to crack during the fracturing process and cause channeling.

[0079] It can be seen from the above embodiments that the present invention takes into account the complex geometry of three-dimensional spiral perforation and provides a method for predicting the three-dimensional stress field around a fracturing construction well under spiral perforation conditions. It can accurately predict the stress field distribution around the spiral perforation well and the wellbore under any phase angle conditions, thereby providing theoretical support for fracturing optimization design.

[0080] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for predicting the three-dimensional stress field around a spiral perforating and fracturing well, comprising the following steps: S1. Construct a three-dimensional formation-wellbore-perforation model of the target area based on actual basic parameters; These include: S11, constructing a geological three-dimensional model, constructing a vertical wellbore in the middle of the geological three-dimensional model, and constructing spirally distributed perforation holes in the radial direction of the vertical wellbore; S12, setting boundary conditions and assigning material characteristic parameters to the stratum; The boundary condition settings include: Dirichlet boundary conditions are applied to the left, bottom and back of the reservoir, the minimum horizontal principal stress of the reservoir is applied to the right boundary of the reservoir, the maximum horizontal principal stress is applied to the front boundary of the reservoir, the vertical principal stress is applied above the reservoir, and the bottom hole construction pressure is applied in the wellbore and perforation holes; S2, discretizing the formation-wellbore-perforation three-dimensional model and performing grid division; S3, construct the finite element equation of the three-dimensional model, solve the finite element equation, and predict the stress field; These include: Constructing the finite element equation of rock deformation using tetrahedral elements [K] e {u e }={f} e Among them, [K] e is the element stiffness matrix; {f} e is the unit load array; u is the rock displacement, Among them, [K] e =∫B T DBdΩ; B is the strain matrix, expressed as: D is the elasticity matrix, expressed as: G is the shear modulus of the porous medium, λ is the Lame constant of the porous medium, Unit load array {f} e The expression is: ε is the unit displacement: After obtaining the rock deformation finite element equation of the unit tetrahedron, the coefficient matrices of all units are assembled to obtain the finite element form of the porous medium deformation equation of the entire target area. The finite element form is: The reservoir elastic constitutive model is used to obtain the stress distribution inside each unit, thereby predicting the stress field around the well.

2. The method for predicting the three-dimensional stress field around a spiral perforating and fracturing well according to claim 1, wherein step S11 further comprises Set the tip of the perforation hole to be hemispherical.

3. The method for predicting the three-dimensional stress field around a spiral perforating and fracturing well according to claim 1, wherein step S2 further comprises: The three-dimensional geological model is divided by tetrahedral mesh, and the wellbore and perforation holes are processed by encrypted mesh.

4. A computer device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the computer program, the steps of the three-dimensional stress field prediction method described in any one of claims 1 to 3 are implemented.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the three-dimensional stress field prediction method described in any one of claims 1 to 3 are implemented.

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