Method for calculating borehole wall collapse pressure of boreholes with different sizes and related equipment

Abstract

The invention discloses a method for calculating borehole wall collapse pressure of boreholes with different sizes and related equipment, and belongs to the technical field of drilling engineering. Comprising the following steps: calculating crustal stress characteristic parameters of a target horizon based on logging parameters; establishing a target horizon borehole wall collapse pressure calculation model based on the crustal stress characteristic parameters; a size effect is introduced into the target horizon borehole wall collapse pressure calculation model, and a target horizon borehole wall collapse pressure mathematical model is obtained; and substituting the crustal stress characteristic parameters into the well wall collapse pressure mathematical model to obtain collapse pressure equivalent densities of well walls with different borehole sizes. According to the method, the influence of the size effect on the stability of the well wall is fully considered, the collapse pressure equivalent density of the well wall under different borehole sizes can be obtained, scientific design of the well body structure before drilling is facilitated, accurate control over the drilling fluid density in the drilling process is facilitated, the stability of the well wall is improved, and the conformity of the calculation result reaches 90% or above.

Description

Technical Field

[0001] The invention belongs to the technical field of drilling engineering, and relates to a method for calculating the wellbore collapse pressure of wellbores with different sizes and related equipment. Background Art

[0002] In the process of drilling and development of oil and gas resources, most of the oil and gas layers are distributed at around 6000m, and a multi-layer casing combination needs to be set up. At present, most of the wellbore instability occurs in mud shale formations. In addition, during the drilling of ultra-deep wells, carbonate rock fractures develop, and drilling fluid filtrate enters the rock micro-fractures, affecting the cementation strength of the formation rock and causing brittle failure. Once the wellbore instability occurs, if it is not handled properly, it will lead to collapse and block falling, or even collapse and drilling or wellbore expansion. Some wellbore expansion rates exceed 30%, which will eventually extend the drilling cycle and cause a significant increase in drilling costs. In the existing technical field, most of the analysis of wellbore stability is based on the Mohr-Coulomb criterion. When a certain functional relationship between rock normal stress and shear stress is considered, shear failure occurs. However, the conventional Mohr-Coulomb criterion ignores the influence of size effect on wellbore stability. Wellbores of different sizes have different effects on the stress concentration of the wellbore, making it difficult to calculate the collapse pressure of the wellbore. For example, the Chinese invention patent application with publication number CN1966934A discloses "A method for calculating the collapse pressure and fracture pressure of the formation under the drill bit while drilling", and the Chinese invention patent application with publication number CN109555515A discloses "A method and device for determining the collapse pressure of the formation". Summary of the invention

[0003] The purpose of the present invention is to solve the technical problem that the size effect is ignored in the prior art when performing wellbore stability analysis, resulting in difficulty in calculating the wellbore collapse pressure, and to provide a method for calculating the wellbore collapse pressure of wellbores of different sizes. The quantitative calculation problem of collapse pressure under different wellbore size conditions is solved, and the optimization design of wellbore structure and the selection of drilling fluid density for safe drilling are guided by this method, which can effectively reduce the occurrence of complex accidents such as wellbore collapse and drill sticking during drilling.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a method for calculating the wellbore collapse pressure of wellbores of different sizes, comprising the following steps:

[0007] Calculate the ground stress characteristic parameters of the target layer based on the logging parameters;

[0008] Establish a calculation model for the wellbore collapse pressure at the target layer based on the ground stress characteristic parameters;

[0009] The size effect is introduced into the calculation model of the wellbore collapse pressure of the target layer, and the mathematical model of the wellbore collapse pressure of the target layer is obtained;

[0010] Substituting the geostress characteristic parameters into the mathematical model of wellbore collapse pressure, the equivalent density of wellbore collapse pressure of different wellbore sizes is obtained.

[0011] A further improvement of the present invention is:

[0012] The following steps are also included:

[0013] The in-situ stress characteristic parameters of the target layer calculated based on the well logging parameters are obtained by the following steps:

[0014] σ v =∫G z dH (1)

[0015]

[0016]

[0017]

[0018]

[0019] Among them, σ v is the overburden pressure of the target layer; σ h is the minimum horizontal principal stress of the target layer; σ H is the maximum horizontal principal stress of the target layer; G z is the vertical pressure gradient; H is the well depth; μ is the Poisson's ratio; α is the effective stress coefficient, which is taken as 0.85; P p is the formation pore pressure, which can be obtained by Eaton's method; E is the elastic modulus, GPa; ε h is the minimum construction coefficient, ε H is the maximum structural coefficient, which can be obtained through inversion of indoor rock mechanics experiments.

[0020] The method of establishing a target layer wellbore collapse pressure calculation model based on the ground stress characteristic parameters includes:

[0021] According to the effective stress state of the wellbore, combined with the Mohr-Coulomb criterion, shear failure occurs when the effective stress difference of the wellbore is the largest. The effective angles are θ = 90° and θ = 270°, and the mathematical model P for calculating the wellbore collapse pressure at the target layer is obtained. m :

[0022]

[0023]

[0024] Among them, γ is the collapse pressure correction coefficient, dimensionless; η is the stress nonlinear correction coefficient, taken as 0.95; C is the rock cohesion, MPa; φ is the internal friction angle; p m is the collapse pressure equivalent density, g / cm 3 ; K is the attribute slope.

[0025] The size effect is introduced into the target layer wellbore collapse pressure calculation model to obtain the target layer wellbore collapse pressure mathematical model, which includes:

[0026] Based on the size effect, a failure model of rock samples with the same lithology and similar shapes under uniaxial compressive strength is established;

[0027] Establish the correlation model between the destruction model and the cohesion;

[0028] On the basis of the calculation model of wellbore collapse pressure at the target layer, the destruction model and the correlation model are introduced to obtain the mathematical model of wellbore collapse pressure at the target layer.

[0029] The damage model is:

[0030]

[0031] Among them, UCS 50 is the compressive strength of the rock sample with a diameter of 50 mm, MPa; UCS is the compressive strength of the rock to be tested, MPa; D is the rock diameter, mm; n is the empirical derivative coefficient, which is taken as 0.18.

[0032] The association model is:

[0033]

[0034] The target layer wellbore collapse pressure calculation model is based on the introduction of the destruction model and the correlation model to obtain the target layer wellbore collapse pressure mathematical model P wm :

[0035]

[0036] In a second aspect, the present invention provides a system for calculating the wellbore collapse pressure of wellbores of different sizes, comprising:

[0037] A parameter calculation unit, which calculates the ground stress characteristic parameters of the target layer based on the well logging parameters;

[0038] Preliminary modeling unit, establishing a calculation model for wellbore collapse pressure at the target layer based on the ground stress characteristic parameters;

[0039] The final modeling unit introduces the size effect into the target layer wellbore collapse pressure calculation model to obtain the target layer wellbore collapse pressure mathematical model;

[0040] The pressure calculation unit substitutes the ground stress characteristic parameters into the wellbore collapse pressure mathematical model to obtain the collapse pressure equivalent density of the wellbore of different wellbore sizes.

[0041] In a third aspect, the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned method for calculating the wellbore collapse pressure of wellbores of different sizes when executing the computer program.

[0042] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the method for calculating the wellbore collapse pressure of wellbores of different sizes as claimed in the claim.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] The present invention discloses a method for calculating the wellbore collapse pressure of wellbores of different sizes. First, the geostress characteristic parameters of the target layer are calculated through logging data, and a continuous target layer wellbore collapse pressure calculation model is established, which fully considers the influence of the geostress characteristic parameters of the wellbore rock mass on the collapse of the wellbore; the size effect is introduced into the wellbore collapse pressure calculation model of the target layer, and the geostress characteristic parameters of the target layer wellbore collapse pressure mathematical model are obtained, and the collapse pressure equivalent density of the wellbore of different wellbore sizes is calculated, and the collapse pressure values ​​of the same layer and different wellbore sizes are obtained. It is conducive to the scientific design of the wellbore structure before drilling, and the drilling fluid density is accurately controlled during the drilling process to improve the wellbore stability. The present invention fully considers the influence of the size effect on the wellbore stability, and can obtain the collapse pressure equivalent density of the wellbore under different wellbore sizes, which is conducive to the scientific design of the wellbore structure before drilling, and the drilling fluid density is accurately controlled during the drilling process to improve the wellbore stability. The calculation result conformity reaches more than 90%. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0046] Figure 1A flow chart of a method for calculating the wellbore collapse pressure of wellbores of different sizes in the present invention;

[0047] Figure 2 This is the correlation diagram between the formation collapse pressure and the wellbore size of Well X1;

[0048] Figure 3 A system diagram for calculating the wellbore collapse pressure of wellbores of different sizes in the present invention;

[0049] Figure 4 This is a module diagram of an electronic device in the present invention. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0051] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. 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.

[0052] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0053] The present invention is further described in detail below in conjunction with the accompanying drawings:

[0054] See also Figure 1 The embodiment of the present invention provides a method for calculating the wellbore collapse pressure of wellbores of different sizes, comprising the following steps:

[0055] S1, calculating the ground stress characteristic parameters of the target layer based on the logging parameters;

[0056] S2, establishing a calculation model for the wellbore collapse pressure at the target layer based on the ground stress characteristic parameters;

[0057] S3, introducing the size effect into the target layer wellbore collapse pressure calculation model, and obtaining the target layer wellbore collapse pressure mathematical model;

[0058] S4, substituting the geostress characteristic parameters into the wellbore collapse pressure mathematical model to obtain the wellbore collapse pressure equivalent density of different wellbore sizes.

[0059] This method fully considers the influence of size effect on wellbore stability, and can obtain the equivalent density of wellbore collapse pressure under different wellbore sizes, which is conducive to the scientific design of wellbore structure before drilling, precise control of drilling fluid density during drilling, and improvement of wellbore stability. The conformity of the calculated results reached more than 90%.

[0060] The content of the present invention is described in detail below in conjunction with specific embodiments:

[0061] Step 1: Calculate the geostress characteristic parameters of the target layer based on the logging parameters

[0062] Among them, the target layer is determined based on the electrical logging data of adjacent wells, such as the well section with serious well wall collapse, such as the mud shale formation. The logging data mainly include: Poisson's ratio, acoustic wave time difference, mud content, lithology density, and a mathematical model of the vertical change of ground stress with well depth is established based on the logging parameters; combined with the specific well depth of the target layer, the ground stress state of the target layer is obtained.

[0063] σ v =∫G z dH (1)

[0064]

[0065]

[0066]

[0067]

[0068] Among them, σ v is the overburden pressure of the target layer; σ h is the minimum horizontal principal stress of the target layer; σ H is the maximum horizontal principal stress of the target layer; G z is the vertical pressure gradient; H is the well depth; μ is the Poisson's ratio; α is the effective stress coefficient, which is taken as 0.85; P p is the formation pore pressure, which can be obtained by Eaton's method; E is the elastic modulus, GPa; ε h is the minimum construction coefficient, ε H is the maximum structural coefficient, which can be obtained through inversion of indoor rock mechanics experiments.

[0069] The maximum horizontal tectonic stress coefficient (ε H ) and the minimum horizontal stress structural coefficient (ε h), taking the X1 well in the Junggar Basin as an example, the target layer is cored through the adjacent wells, and the relevant rock mechanics parameters are obtained by indoor rock mechanics experiments and acoustic emission tests. Finally, the maximum horizontal tectonic stress coefficient (ε H ) and the minimum horizontal stress structural coefficient (ε h ). The relevant parameters of the target layer stress are shown in Table 1:

[0070]

[0071] Table 1

[0072] Step 2: Establish a calculation model for the wellbore collapse pressure of the target layer based on the ground stress characteristic parameters.

[0073] After clarifying the target layer's geostress characteristic parameters, considering the effective stress state of the wellbore, the Mohr-Coulomb failure criterion is used to obtain the target layer's wellbore collapse pressure calculation model. As shown in the following formula:

[0074]

[0075]

[0076] Among them, γ is the collapse pressure correction coefficient, dimensionless; η is the stress nonlinear correction coefficient, taken as 0.95; C is the rock cohesion, MPa; φ is the internal friction angle; p m is the collapse pressure equivalent density, g / cm 3 ; K is the attribute slope.

[0077] The collapse pressure correction coefficient designed in this step is obtained by combining indoor rock mechanics experiments with the actual collapse pressure on site, as shown in Table 2:

[0078] Lithology γ value shale 0.95 Mudstone 1.31 Conglomerate 0.85 Limestone 0.88

[0079] Table 2

[0080] Step 3: Establish a mathematical model of wellbore collapse pressure under the influence of size effect. The specific steps are as follows:

[0081] 1) Based on the size effect, a failure model of rock samples with the same lithology and similar shape under uniaxial compressive strength is established

[0082] Among them, the influence of size effect on rock strength is that for rock samples with the same lithology and similar shape, the uniaxial compressive strength decreases with the increase of size, and eventually failure occurs. The specific manifestation is shown in the following model:

[0083]

[0084] Among them, UCS 50is the compressive strength of the rock sample with a diameter of 50 mm, MPa; UCS is the compressive strength of the rock to be tested, MPa; D is the rock diameter, mm; n is the empirical derivative coefficient, which is taken as 0.18.

[0085] 2) Considering the wellbore damage mode, a correlation model between size effect and rock cohesion is established.

[0086] Among them, the failure mode of the well wall is shear failure. The correlation between cohesion and size effect is introduced, and the following correlation model is established:

[0087]

[0088] 3) Based on the calculation model of the wellbore collapse pressure at the target layer, the destruction model and the correlation model are introduced to obtain the mathematical model of the wellbore collapse pressure at the target layer.

[0089] In this step, in order to ensure the calculation accuracy, the influence of size effect on wellbore collapse pressure is introduced on the basis of the collapse pressure calculation model, and the correlation model between size effect and wellbore collapse pressure is obtained:

[0090]

[0091] Step 4: Substitute the geostress characteristic parameters into the wellbore collapse pressure mathematical model to obtain the collapse pressure equivalent density of the wellbore with different wellbore sizes.

[0092] According to the mathematical model of wellbore collapse pressure under the influence of size effect, the equivalent density of collapse pressure of different wellbore sizes is calculated. The calculation results are as follows: Figure 2 shown.

[0093] See also Figure 3 The embodiment of the present invention provides a system for calculating the wellbore collapse pressure of wellbores of different sizes, comprising:

[0094] A parameter calculation unit, which calculates the ground stress characteristic parameters of the target layer based on the well logging parameters;

[0095] Preliminary modeling unit, establishing a calculation model for wellbore collapse pressure at the target layer based on the ground stress characteristic parameters;

[0096] The final modeling unit introduces the size effect into the target layer wellbore collapse pressure calculation model to obtain the target layer wellbore collapse pressure mathematical model;

[0097] The pressure calculation unit substitutes the ground stress characteristic parameters into the wellbore collapse pressure mathematical model to obtain the collapse pressure equivalent density of the wellbore of different wellbore sizes.

[0098] This system fully considers the impact of size effect on wellbore stability, which is conducive to scientific design of wellbore structure before drilling, precise control of drilling fluid density during drilling, and improvement of wellbore stability.

[0099] See also Figure 4 The third object of the present invention is to provide an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method for calculating the wellbore collapse pressure of wellbores of different sizes when executing the computer program.

[0100] The method for calculating the wellbore collapse pressure of wellbores of different sizes comprises the following steps:

[0101] Calculate the ground stress characteristic parameters of the target layer based on the logging parameters;

[0102] Establish a calculation model for the wellbore collapse pressure at the target layer based on the ground stress characteristic parameters;

[0103] The size effect is introduced into the calculation model of the wellbore collapse pressure of the target layer, and the mathematical model of the wellbore collapse pressure of the target layer is obtained;

[0104] Substituting the geostress characteristic parameters into the mathematical model of wellbore collapse pressure, the equivalent density of wellbore collapse pressure of different wellbore sizes is obtained.

[0105] A fourth object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the method for calculating the wellbore collapse pressure of wellbores of different sizes.

[0106] The method for calculating the wellbore collapse pressure of wellbores of different sizes comprises the following steps:

[0107] Calculate the ground stress characteristic parameters of the target layer based on the logging parameters;

[0108] Establish a calculation model for the wellbore collapse pressure at the target layer based on the ground stress characteristic parameters;

[0109] The size effect is introduced into the calculation model of the wellbore collapse pressure of the target layer, and the mathematical model of the wellbore collapse pressure of the target layer is obtained;

[0110] Substituting the geostress characteristic parameters into the mathematical model of wellbore collapse pressure, the equivalent density of wellbore collapse pressure of different wellbore sizes is obtained.

[0111] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0112] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0113] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0114] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0115] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the wellbore collapse pressure of wellbores of different sizes, characterized in that: The following steps are involved: Calculate the ground stress characteristic parameters of the target layer based on the logging parameters; Establish a calculation model for the wellbore collapse pressure at the target layer based on the ground stress characteristic parameters; The size effect is introduced into the calculation model of the wellbore collapse pressure of the target layer, and the mathematical model of the wellbore collapse pressure of the target layer is obtained; Substituting the geostress characteristic parameters into the mathematical model of wellbore collapse pressure, the equivalent density of wellbore collapse pressure of different wellbore sizes is obtained.

2. The method for calculating the wellbore collapse pressure of wellbores of different sizes according to claim 1, characterized in that: The in-situ stress characteristic parameters of the target layer calculated based on the well logging parameters are obtained by the following steps: σ v =∫G z dH (1) Among them, σ v is the overburden pressure of the target layer; σ h is the minimum horizontal principal stress of the target layer; σ H is the maximum horizontal principal stress of the target layer; G z is the vertical pressure gradient; H is the well depth; μ is the Poisson's ratio; α is the effective stress coefficient, which is taken as 0.85; P p is the formation pore pressure, which can be obtained by Eaton's method; E is the elastic modulus, GPa; ε h is the minimum construction coefficient, ε H is the maximum structural coefficient, which can be obtained through inversion of indoor rock mechanics experiments.

3. The method for calculating the wellbore collapse pressure of wellbores of different sizes according to claim 2, characterized in that: The method of establishing a target layer wellbore collapse pressure calculation model based on the ground stress characteristic parameters includes: According to the effective stress state of the wellbore, combined with the Mohr-Coulomb criterion, shear failure occurs when the effective stress difference of the wellbore is the largest. The effective angles are θ = 90° and θ = 270°, and the mathematical model P for calculating the wellbore collapse pressure at the target layer is obtained. m : Among them, γ is the collapse pressure correction coefficient, dimensionless; η is the stress nonlinear correction coefficient, taken as 0.95; C is the rock cohesion, MPa; φ is the internal friction angle; p m is the collapse pressure equivalent density, g / cm 3 ; K is the attribute slope.

4. The method for calculating the wellbore collapse pressure of wellbores of different sizes according to claim 3, characterized in that: The size effect is introduced into the target layer wellbore collapse pressure calculation model to obtain the target layer wellbore collapse pressure mathematical model, which includes: Based on the size effect, a failure model of rock samples with the same lithology and similar shapes under uniaxial compressive strength is established; Establish the correlation model between the destruction model and the cohesion; On the basis of the calculation model of wellbore collapse pressure at the target layer, the destruction model and the correlation model are introduced to obtain the mathematical model of wellbore collapse pressure at the target layer.

5. The method for calculating the wellbore collapse pressure of wellbores of different sizes according to claim 4, characterized in that: The damage model is: Among them, UCS 50 is the compressive strength of the rock sample with a diameter of 50 mm, MPa; UCS is the compressive strength of the rock to be tested, MPa; D is the rock diameter, mm; n is the empirical derivative coefficient, which is taken as 0.

18.

6. The method for calculating the wellbore collapse pressure of wellbores of different sizes according to claim 4, characterized in that: The association model is:

7. The method for calculating the wellbore collapse pressure of wellbores of different sizes according to claim 4, characterized in that: The target layer wellbore collapse pressure calculation model is based on the introduction of the destruction model and the correlation model to obtain the target layer wellbore collapse pressure mathematical model P wm :

8. A system for calculating the wellbore collapse pressure of wellbores of different sizes, characterized in that: include: A parameter calculation unit, which calculates the ground stress characteristic parameters of the target layer based on the well logging parameters; Preliminary modeling unit, establishing a calculation model for wellbore collapse pressure at the target layer based on the ground stress characteristic parameters; The final modeling unit introduces the size effect into the target layer wellbore collapse pressure calculation model to obtain the target layer wellbore collapse pressure mathematical model; The pressure calculation unit substitutes the ground stress characteristic parameters into the wellbore collapse pressure mathematical model to obtain the collapse pressure equivalent density of the wellbore of different wellbore sizes.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method for calculating the wellbore collapse pressure of wellbores of different sizes as described in any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the method for calculating the wellbore collapse pressure of wellbores of different sizes as claimed in any one of claims 1 to 7.

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