A method for calculating strain transfer efficiency of a wellbore structure

Abstract

The present application relates to a kind of wellbore structure strain transmission efficiency calculation method, it is related to petroleum technical field, the wellbore structure includes casing, cement sheath and rock ring in turn from inside to outside along radial direction, the casing inner wall, casing outer wall, the outer wall of cement sheath are linearly arranged with optical fiber along axial direction, the rock-cement sheath casing structure is applied with stress along radial direction, the method comprises: obtaining the material mechanics parameter and geometric dimension of casing, cement sheath and rock ring;According to the interface cementation state of first interface and second interface, the interface transmission coefficient of first interface and second interface is determined respectively, wherein the first interface is the interface of rock ring and cement sheath, and the second interface is the interface of cement sheath and casing;Establish the displacement field and strain field model of each layer, and interface continuity condition and boundary condition;According to displacement field, the target strain at the key radial position of casing, cement sheath and rock ring is calculated.

Description

Technical Field

[0001] This invention relates to the field of petroleum technology, and in particular to a method for calculating the strain transfer efficiency of wellbore structures. Background Technology

[0002] Oil and gas wells, energy storage wells, and geothermal wells typically consist of a rock formation, a cement sheath, and casing, forming a typical three-layer composite structure system: rock-cement sheath-casing. Under engineering conditions such as hydraulic fracturing, injection-production circulation, temperature changes, and interference from adjacent wells, the formation stress state undergoes significant changes, leading to strain responses in the formation rock. This strain is transmitted stepwise to the casing structure through the rock-cement sheath interface and the cement sheath-casing interface. Distributed fiber optic sensing, which uses optical fibers deployed outside the casing, outside the tubing, or inside the tubing to achieve real-time strain monitoring, has become an important technical means for studying fracturing fracture propagation, inter-well interference, and wellbore integrity.

[0003] However, in actual wellbore environments, the strain signals measured by optical fibers are not the original strain of the formation rock, but rather the response result after the formation strain has been transmitted through multiple layers of media: rock-cement sheath-casing. Due to differences in the elastic modulus, Poisson's ratio, geometric dimensions, and interfacial cementation state of different materials, the strain will undergo varying degrees of attenuation or distortion during transmission, thus affecting the accuracy and reliability of the monitoring results. Therefore, it is necessary to establish a method for calculating the strain transmission efficiency of the rock-cement sheath-casing structure. By constructing the strain transmission relationship of the multi-layer structure, the attenuation law of formation strain transmission to the casing and its interior can be quantitatively characterized, providing a technical reference for the study of the mechanical behavior of the rock-cement sheath-casing structure and the diagnosis of fracturing fractures in oil and gas wells.

[0004] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0005] The main objective of this invention is to provide a method for calculating the strain transfer efficiency of a well shaft structure, aiming to solve the aforementioned technical problems in the prior art.

[0006] To achieve the above objectives, this invention provides a method for calculating the strain transfer efficiency of a wellbore structure. The wellbore structure, from the inside to the outside radially, includes a casing, a cement sheath, and a rock sheath. Optical fibers are arranged in a straight line along the axial direction on the inner wall of the casing, the outer wall of the casing, and the outer wall of the cement sheath. Stress is applied radially to the rock-cement sheath casing structure. The method includes:

[0007] Obtain the material mechanical parameters and geometric dimensions of the casing, cement ring, and rock ring;

[0008] Based on the interface bonding state of the first interface and the second interface, the interface transfer coefficients of the first interface and the second interface are determined respectively, wherein the first interface is the interface between the rock ring and the cement ring, and the second interface is the interface between the cement ring and the casing.

[0009] Establish displacement and strain field models for each layer, as well as interface continuity and boundary conditions;

[0010] Based on the displacement field, calculate the target strain at key radial positions of the casing, cement ring, and rock ring; based on the strain field, calculate the strain transfer efficiency of the rock ring and cement ring, the strain transfer efficiency of the cement ring and casing, and the strain transfer efficiency inside the casing wall.

[0011] The total strain transfer efficiency is calculated based on the strain transfer efficiency of the rock ring and cement ring, the strain transfer efficiency of the cement ring and casing, and the strain transfer efficiency inside the casing wall.

[0012] By changing the material mechanical parameters, geometric dimensions, and interface cementation state of the casing, cement sheath, and rock sheath, the process is repeated cyclically to determine the influence of these parameters on strain transfer efficiency. The actual formation strain and deformation are then inferred from the measured strain using the total strain transfer efficiency.

[0013] Preferably, in the method for calculating the strain transfer efficiency of the wellbore structure, the step of using the total strain transfer efficiency to infer the true formation strain and deformation from the measured strain includes:

[0014] Using radial strain as the target strain, obtain the inner wall strain r=r of the casing. i The measured radial strain and the total radial strain transfer efficiency were measured.

[0015] Based on the total radial strain transfer efficiency and the inner wall of the casing, r=r i Measured radial strain at the location, inverted and compared with the inner wall of the casing r=r i Rock rings located in the same radial direction, r=r m The actual radial strain is ;

[0016] Calculate r at any two positions of the rock ring a and r b The radial deformation between them is calculated using the following formula:

[0017] ;

[0018] in, The inner wall radius of the casing is r = r i Radial strain;

[0019] The radius of the rock ring is r = rm Radial strain;

[0020] The total radial strain transfer efficiency;

[0021] A p These are the constant coefficients in the general solution of rock ring displacement;

[0022] B p represents the constant coefficients in the general solution of rock ring displacement.

[0023] Preferably, in the method for calculating the strain transfer efficiency of the wellbore structure, the step of using the total strain transfer efficiency to infer the true formation strain and deformation from the measured strain includes:

[0024] Using circumferential strain as the target strain, obtain the inner wall strain r=r of the casing. i The measured circumferential strain and the total circumferential strain transfer efficiency were measured.

[0025] Based on the total circumferential strain transfer efficiency and the inner wall of the casing r=r i The measured circumferential strain was used to invert the position r=r in the rock ring. m The actual circumferential strain of the formation at that location is given by the following formula:

[0026] ;

[0027] Calculate the rock ring r m The formula for calculating the circumferential deformation at the location is:

[0028] ;

[0029] in, For the rock ring, r=r m Circumferential deformation at the location;

[0030] For the inner wall of the casing, r=r i Circumferential strain;

[0031] The total circumferential strain transfer efficiency;

[0032] For the rock ring at r=r m Circumferential strain.

[0033] Preferably, in the method for calculating the strain transfer efficiency of the wellbore structure, the step of using the total strain transfer efficiency to infer the true formation strain and deformation from the measured strain includes:

[0034] Using axial strain as the target strain, obtain the inner wall strain r=r of the casing. i The measured axial strain and the total axial strain transfer efficiency were measured.

[0035] Based on the total axial strain transfer efficiency and the inner wall of the casing r=r i The measured axial strain was used to invert the position r=r in the rock ring. m The actual axial strain of the formation at the specified location is given by the following formula:

[0036] ;

[0037] Calculate the rock ring from the axial coordinate z a To z b The axial deformation is calculated using the following formula:

[0038] ;

[0039] in, Let z be the circumferential deformation at the axial coordinate z in the rock ring;

[0040] For the inner wall of the casing, r=r i Measured axial strain at the location;

[0041] The total circumferential strain transfer efficiency;

[0042] For the rock ring r=r m Actual axial strain;

[0043] E j Let be the elastic modulus of the j-th layer material; j is p, and the p-th layer material is a rock ring.

[0044] Let J be the axial stress of the j-th layer material;

[0045] Let be the Poisson's ratio of the j-th layer material;

[0046] Let J be the radial stress of the j-th layer of material;

[0047] The table shows the circumferential stress of the j-th layer material.

[0048] Preferably, in the method for calculating the strain transfer efficiency of the well structure, establishing the displacement field and strain field models for each layer includes:

[0049] The radial displacement of each layer satisfies:

[0050] ;

[0051] Simplified to: ;

[0052] The radial strain, circumferential strain, and axial strain of each layer are as follows:

[0053] ;

[0054] ;

[0055] ;

[0056] in, Let be the radial displacement of the j-th layer of material at point r, where j is p, c, or s, where the p-th layer is a rock ring, the c-th layer is a cement ring, and the s-th layer is a casing.

[0057] r is the radial coordinate in the cylindrical coordinate system, that is, the distance from the center of the wellbore outwards;

[0058] A j These are the constant coefficients in the general solution of the displacement of the j-th layer;

[0059] B j These are the constant coefficients in the general solution of the displacement of the j-th layer;

[0060] Let be the radial strain of the j-th layer of material at point r;

[0061] Let be the circumferential strain of the j-th layer of material at point r;

[0062] Let J be the axial strain of the j-th layer material;

[0063] This represents the elastic modulus of the j-th layer material;

[0064] This represents the axial stress of the j-th layer of material;

[0065] Represents the Poisson's ratio of the j-th layer material;

[0066] Let J be the radial stress of the j-th layer of material;

[0067] This represents the circumferential stress of the j-th layer of material.

[0068] Preferably, in the method for calculating the strain transfer efficiency of the wellbore structure, the interface continuity condition and boundary condition include:

[0069] When the target strain is radial strain, at the rock-cement sheath interface r=r c The following conditions must be met:

[0070] Displacement compatibility conditions: ;

[0071] Interfacial stress continuity condition: ;

[0072] At the interface between the cement ring and the casing, r=r o At this location, the following conditions must be met: Displacement compatibility conditions: ;

[0073] Interfacial stress continuity condition: ;

[0074] On the inner wall of the casing, r=r i At this location, the inner wall of the casing is subjected to internal pressure p. i ,So ;

[0075] At the outer boundary of the rock ring, r=r R At the location, the outer boundary of the rock ring is subjected to an external load p R ,So ;

[0076] When the displacement of the outer boundary of the rock ring is known, and the displacement of the outer boundary of the rock ring is u R hour, ;

[0077] in, For the j-th layer material in r c The radial displacement at point j is p, c, or s, where the p-th layer is the rock ring, the c-th layer is the cement ring, and the s-th layer is the casing;

[0078] , Cement ring and rock ring, respectively, at r c Radial stress at the location;

[0079] , The sleeve and cement sheath are respectively located at r o Radial displacement at the location;

[0080] k pc k cs These are the interface transfer coefficients for the first interface and the second interface, respectively.

[0081] , The sleeve and cement ring are respectively located at r o Radial stress at the location;

[0082] For the casing at r i Radial stress at the location;

[0083] For rock rings in r R Radial stress at the location.

[0084] Preferably, in the method for calculating the strain transfer efficiency of the wellbore structure, the calculation of the strain transfer efficiency of the rock sheath and cement sheath includes:

[0085] The radial strain transfer efficiency of the rock ring and cement ring is:

[0086] ;

[0087] The circumferential strain transfer efficiency of the rock ring and cement ring is:

[0088] ;

[0089] The axial strain transfer efficiency of the rock ring and cement ring is:

[0090]

[0091] in, The formula for calculating the radial propagation effect within the rock ring is as follows:

[0092] ;

[0093] A j These are the constant coefficients in the general solution of the displacement of the j-th layer;

[0094] j is p, c, or s, where the p-th layer is a rock ring, the c-th layer is a cement ring, and the s-th layer is a casing;

[0095] B j These are the constant coefficients in the general solution of the displacement of the j-th layer;

[0096] The formula for calculating the radial transmission effect at the interface between the rock ring and the cement ring is as follows:

[0097] ;

[0098] The formula for calculating the circumferential propagation effect within the rock ring is as follows:

[0099] ;

[0100] The formula for calculating the circumferential transmission effect at the interface between the rock ring and the cement ring is as follows:

[0101] ;

[0102] The formula for calculating the axial propagation effect within the rock ring is as follows:

[0103] ;

[0104] The formula for calculating the axial transmission effect at the interface between the rock ring and the cement ring is as follows:

[0105] ;

[0106] This represents the axial stress of the j-th layer of material;

[0107] Represents the Poisson's ratio of the j-th layer material;

[0108] Let J be the radial stress of the j-th layer of material;

[0109] This represents the circumferential stress of the j-th layer of material;

[0110] This represents the elastic modulus of the j-th layer material;

[0111] r is the radial coordinate in the cylindrical coordinate system, that is, the distance from the center of the wellbore outwards. c r m .

[0112] Preferably, in the method for calculating the strain transfer efficiency of the wellbore structure, the strain transfer efficiency of the cement sheath and casing includes:

[0113] The radial strain transfer efficiency of the cement ring and sleeve is:

[0114] :

[0115] in, The formula for calculating the radial propagation effect of the cement ring is:

[0116] ;

[0117] The radial transmission effect at the interface between the cement ring and the casing is calculated using the following formula:

[0118] ;

[0119] The radial strain transfer efficiency of the cement ring and sleeve is simplified as follows:

[0120] ;

[0121] The circumferential strain transfer efficiency of the cement ring and the casing is:

[0122] ;

[0123] The engineering approximation of the circumferential strain transfer efficiency of the cement ring and casing is:

[0124] ;

[0125] The axial strain transfer efficiency of the cement ring and the casing is:

[0126] ;

[0127] in, , , The strain transfer efficiencies of the cement ring and the sleeve are respectively in the radial, circumferential, and axial directions;

[0128] This represents the elastic modulus of the j-th layer material; j is p, c, or s, where the p-th layer is a rock ring, the c-th layer is a cement ring, and the s-th layer is a casing.

[0129] , , These represent the radial strain, circumferential strain, and axial strain of the j-th layer material at point r, where r is the radial coordinate in the cylindrical coordinate system, i.e., the distance from the center of the wellbore outwards.

[0130] r is r o or r c ;

[0131] , , This represents the axial stress, radial stress, and circumferential stress of the j-th layer of material at point r;

[0132] A j These are the constant coefficients in the general solution of the displacement of the j-th layer;

[0133] B j These are the constant coefficients in the general solution of the displacement of the j-th layer;

[0134] k cs For the interface transfer coefficient of the second interface;

[0135] Let represent the Poisson's ratio of the j-th layer material.

[0136] Preferably, in the method for calculating the strain transfer efficiency of the wellbore structure, the strain transfer efficiency inside the casing wall includes:

[0137] The radial strain transfer efficiency of the outer and inner walls of the casing is:

[0138] ;

[0139] The circumferential strain transfer efficiency of the outer and inner walls of the casing is:

[0140] ;

[0141] The axial strain transfer efficiency between the outer and inner walls of the casing is:

[0142] ;

[0143] in, , , These represent the strain transfer efficiencies of the outer and inner walls of the casing in the radial, circumferential, and axial directions, respectively.

[0144] , , These represent the radial strain, circumferential strain, and axial strain of the j-th layer material at point r, where r is the radial coordinate in the cylindrical coordinate system, i.e., the distance from the center of the wellbore outwards; j is p, c, or s, where the p-th layer is the rock sheath, the c-th layer is the cement sheath, and the s-th layer is the casing.

[0145] r is r o or r i ;

[0146] A j These are the constant coefficients in the general solution of the displacement of the j-th layer;

[0147] B j These are the constant coefficients in the general solution of the displacement of the j-th layer;

[0148] Let represent the Poisson's ratio of the j-th layer material.

[0149] Preferably, in the method for calculating the strain transfer efficiency of the wellbore structure, the calculation formula for the step of calculating the total strain transfer efficiency based on the strain transfer efficiencies of the rock sheath and cement sheath, the strain transfer efficiency of the cement sheath and casing, and the strain transfer efficiency inside the casing wall is as follows:

[0150] The overall radial strain transfer efficiency is:

[0151] ;

[0152] The overall circumferential strain transfer efficiency is:

[0153] ;

[0154] The overall axial strain transfer efficiency is:

[0155] ;

[0156] in, , , These are the total radial strain transfer efficiency, the total circumferential strain transfer efficiency, and the total axial strain transfer efficiency, respectively.

[0157] , , These represent the strain transfer efficiencies of the outer and inner walls of the casing in the radial, circumferential, and axial directions, respectively.

[0158] , , The strain transfer efficiencies of the cement ring and the sleeve are respectively in the radial, circumferential, and axial directions;

[0159] , , The values ​​represent the strain transfer efficiencies of the rock ring and cement ring in the radial, circumferential, and axial directions, respectively.

[0160] The present invention has at least the following beneficial effects:

[0161] This invention obtains the material mechanical parameters and geometric dimensions of the casing, cement sheath, and rock sheath; determines the interface transfer coefficients of the first and second interfaces based on their interface bonding states, wherein the first interface is the interface between the rock sheath and the cement sheath, and the second interface is the interface between the cement sheath and the casing; establishes displacement and strain field models for each layer, as well as interface continuity and boundary conditions; calculates the target strain at key radial positions of the casing, cement sheath, and rock sheath based on the displacement field; calculates the strain transfer efficiency of the rock sheath and cement sheath, the strain transfer efficiency of the cement sheath and the casing, and the strain transfer efficiency inside the casing wall based on the strain field; calculates the total strain transfer efficiency based on the strain transfer efficiency of the rock sheath and cement sheath, the strain transfer efficiency of the cement sheath and the casing, and the strain transfer efficiency inside the casing wall; determines the influence of the material mechanical parameters, geometric dimensions, and interface bonding states on the strain transfer efficiency by changing the material mechanical parameters, geometric dimensions, and interface bonding states of the casing, cement sheath, and rock sheath through iterative execution; and uses the total strain transfer efficiency to infer the actual formation strain and deformation from the measured strain. In this way, the strain transfer efficiency of the rock-cement sheath-casing structure in adjacent wells can be quantitatively calculated under various working conditions, which can provide a theoretical reference for the real formation strain reconstruction, wellbore integrity evaluation and strain-based parameter inversion research.

[0162] Furthermore, this invention considers material mechanical parameters, structural geometry, and interface cementation state to quantitatively analyze the strain transmission process of formation rocks in the rock-cement sheath-casing system, thereby obtaining the rock-cement sheath-casing strain transmission efficiency and restoring the true formation strain. Attached Figure Description

[0163] Figure 1 A flowchart of a method for calculating the strain transfer efficiency of a well structure provided by the present invention in a first embodiment;

[0164] Figure 2 This invention relates to the relationship between the strain transfer efficiency and the elastic modulus ratio of the rock ring-cement ring.

[0165] Figure 3 This invention relates to the relationship between the strain transfer efficiency of the cement ring-sleeve and the interfacial bonding coefficient.

[0166] Figure 4 This invention relates the strain transfer efficiency of the outer and inner walls of the casing to the casing wall thickness.

[0167] Figure 5 This represents the total strain transfer efficiency under different interfacial bonding states in this invention.

[0168] The objectives, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0169] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The present invention will be described in detail below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0170] In this embodiment of the invention, the term "and / or" describes the relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The character " / " generally indicates that the preceding and following associated objects have an "or" relationship.

[0171] It should be noted that the terms "first," "second," etc., in the specification, claims, and drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0172] In this embodiment of the invention, the term "multiple" refers to two or more, and other quantifiers are similar.

[0173] In this invention, unless otherwise stated, directional terms such as "upper," "lower," "top," and "bottom" are generally used in relation to the direction shown in the accompanying drawings, or in relation to the vertical, perpendicular, or gravitational direction of the component itself; similarly, for ease of understanding and description, "inner" and "outer" refer to the inner and outer contours of each component itself, but the above directional terms are not intended to limit this invention.

[0174] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details are presented in the embodiments of the present invention to facilitate a better understanding of the invention. However, the technical solutions claimed in the present invention can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined with and referenced by each other without contradiction.

[0175] This invention provides a method for calculating the strain transfer efficiency of a wellbore structure, such as... Figure 1 As shown, the wellbore structure includes, from the inside to the outside, a casing, a cement sheath, and a rock sheath in a radial direction. Optical fibers are arranged in a straight line along the axial direction on the inner wall of the casing, the outer wall of the casing, and the outer wall of the cement sheath. The rock-cement sheath casing structure is subjected to radial stress. The method includes:

[0176] Step S1000: Obtain the material mechanical parameters and geometric dimensions of the casing, cement ring, and rock ring. The material mechanical parameters of the casing, cement ring, and rock ring include the elastic modulus and Poisson's ratio, specifically the elastic modulus and Poisson's ratio of the rock ring, the elastic modulus and Poisson's ratio of the cement ring, the elastic modulus and Poisson's ratio of the casing.

[0177] The geometry of the casing, cement sheath, and rock sheath includes the outer boundary radius r of the rock. R The outer radius r of the cement ring c Outer radius r of the casing o The inner radius of the casing is r i Among them, r i < r o <r c <r R .

[0178] Step S2000: Based on the interfacial bonding state of the first interface and the second interface, determine the interfacial transfer coefficients of the first interface and the second interface respectively, wherein the first interface is the interface between the rock ring and the cement ring, and the second interface is the interface between the cement ring and the casing.

[0179] The interfacial transport coefficient at the interface between the rock ring and the cement ring is k. pc The cement ring-sleeve interface transfer coefficient is k. cs .

[0180] Where 0 < k pc ≤1, 0<k cs ≤1; When the interface is fully bonded, the corresponding interface transfer coefficient is 1; When there is micro-slip, debonding or weak bonding at the interface, the corresponding interface transfer coefficient is less than 1.

[0181] In some implementations, the interface transfer coefficient can be obtained through experimental calibration, i.e., by loading an experiment to measure the strain or displacement on both sides of the interface and calculating it according to their ratio, or by numerical simulation inversion, i.e. by establishing a rock-cement ring-casing coupling model, adjusting the interface parameters to match the simulation results with the measured data, thereby determining the corresponding interface transfer coefficient.

[0182] Step S3000 establishes the displacement and strain field models for each layer, as well as the interface continuity and boundary conditions. Specifically, the radial displacement of each layer satisfies:

[0183] ;

[0184] Simplified to: ;

[0185] The radial strain, circumferential strain, and axial strain of each layer are as follows:

[0186] ;

[0187] ;

[0188] ;

[0189] The interface continuity condition and boundary condition include:

[0190] When the target strain is radial strain, at the rock-cement sheath interface r=r c The following conditions must be met:

[0191] Displacement compatibility conditions: ;

[0192] Interfacial stress continuity condition: ;

[0193] At the interface between the cement ring and the casing, r=r o At this location, the following conditions must be met: Displacement compatibility conditions: ;

[0194] Interfacial stress continuity condition: ;

[0195] On the inner wall of the casing, r=r i At this location, the inner wall of the casing is subjected to internal pressure p. i ,So ;

[0196] At the outer boundary of the rock ring, r=r R At the location, the outer boundary of the rock ring is subjected to an external load p R ,So ;

[0197] When the displacement of the outer boundary of the rock ring is known, and the displacement of the outer boundary of the rock ring is u R hour, .

[0198] Step S4000: Calculate the target strain at the critical radial positions of the casing, cement ring, and rock ring based on the displacement field; calculate the strain transfer efficiency of the rock ring and cement ring, the strain transfer efficiency of the cement ring and casing, and the strain transfer efficiency inside the casing wall based on the strain field.

[0199] The calculation of strain transfer efficiency of the rock ring and cement ring includes:

[0200] The radial strain transfer efficiency of the rock ring and cement ring is:

[0201] ;

[0202] The circumferential strain transfer efficiency of the rock ring and cement ring is:

[0203] ;

[0204] The axial strain transfer efficiency of the rock ring and cement ring is:

[0205]

[0206] in, The formula for calculating the radial propagation effect within the rock ring is as follows:

[0207] ;

[0208] The formula for calculating the radial transmission effect at the interface between the rock ring and the cement ring is as follows:

[0209] ;

[0210] The formula for calculating the circumferential propagation effect within the rock ring is as follows:

[0211] ;

[0212] The formula for calculating the circumferential transmission effect at the interface between the rock ring and the cement ring is as follows:

[0213] ;

[0214] The formula for calculating the axial propagation effect within the rock ring is as follows:

[0215] ;

[0216] The formula for calculating the axial transmission effect at the interface between the rock ring and the cement ring is as follows:

[0217] .

[0218] The radial strain transfer efficiency of the cement ring and sleeve is:

[0219] :

[0220] in, The formula for calculating the radial propagation effect of the cement ring is:

[0221] ;

[0222] The radial transmission effect at the interface between the cement ring and the casing is calculated using the following formula:

[0223] ;

[0224] The radial strain transfer efficiency of the cement ring and sleeve is simplified as follows:

[0225] ;

[0226] The circumferential strain transfer efficiency of the cement ring and the casing is:

[0227] ;

[0228] The engineering approximation of the circumferential strain transfer efficiency of the cement ring and casing is:

[0229] ;

[0230] The axial strain transfer efficiency of the cement ring and the casing is:

[0231] .

[0232] The strain transfer efficiency inside the casing wall includes:

[0233] The radial strain transfer efficiency of the outer and inner walls of the casing is:

[0234] ;

[0235] The circumferential strain transfer efficiency of the outer and inner walls of the casing is:

[0236] ;

[0237] The axial strain transfer efficiency between the outer and inner walls of the casing is:

[0238] .

[0239] Step S5000 calculates the total strain transfer efficiency based on the strain transfer efficiency of the rock ring and cement ring, the strain transfer efficiency of the cement ring and casing, and the strain transfer efficiency inside the casing wall.

[0240] The overall radial strain transfer efficiency is:

[0241] ;

[0242] The overall circumferential strain transfer efficiency is:

[0243] ;

[0244] The overall axial strain transfer efficiency is:

[0245] .

[0246] Step S6000 involves changing the material mechanical parameters, geometric dimensions, and interface cementation state of the casing, cement sheath, and rock sheath, and executing the process cyclically to determine the influence of these parameters on strain transfer efficiency. The actual formation strain and deformation are then inferred from the measured strain using the total strain transfer efficiency.

[0247] The step S6000, which uses the total strain transfer efficiency to infer the actual formation strain and deformation from the measured strain, includes steps S6100, S6200, and S6300.

[0248] Step S6100 uses radial strain as the target strain to obtain the measured radial strain at r=ri on the inner wall of the casing and the total radial strain transfer efficiency; based on the total radial strain transfer efficiency and the measured radial strain at r=ri on the inner wall of the casing, the true radial strain at r=rm of the rock ring located in the same radial direction as r=ri on the inner wall of the casing is inverted. The radial deformation between any two positions ra and rb of the rock ring is calculated using the following formula:

[0249] .

[0250] Step S6200 uses circumferential strain as the target strain to obtain the inner wall strain r=r of the casing. i The measured circumferential strain and the total circumferential strain transfer efficiency were measured.

[0251] Based on the total circumferential strain transfer efficiency and the inner wall of the casing r=r i The measured circumferential strain was used to invert the position r=r in the rock ring. m The actual circumferential strain of the formation at that location is given by the following formula:

[0252] ;

[0253] Calculate the rock ring r m The formula for calculating the circumferential deformation at the location is:

[0254] .

[0255] Step S6300 uses axial strain as the target strain to obtain the inner wall strain r=r of the casing. i The measured axial strain and the total axial strain transfer efficiency were determined; based on the total axial strain transfer efficiency and the inner wall of the casing, r=r i The measured axial strain was used to invert the position r=r in the rock ring. m The actual axial strain of the formation at the specified location is given by the following formula:

[0256] ;

[0257] Calculate the rock ring from the axial coordinate z a To z b The axial deformation is calculated using the following formula:

[0258] ;

[0259] in, Let be the radial strain of the j-th layer of material at radius r;

[0260] Let be the circumferential strain of the j-th layer of material at radius r;

[0261] Let be the axial strain of the j-th layer of material at radius r; where, Let z be the axial strain at the z-axis position of the j-th layer of material;

[0262] j is p, c, or s, where the p-th layer is a rock ring, the c-th layer is a cement ring, and the s-th layer is a casing;

[0263] r is the radial coordinate in the cylindrical coordinate system, that is, the distance from the center of the wellbore outwards; r can be, but is not limited to, r i r m、 rc、 r o、 r R .

[0264] , , These are the total radial strain transfer efficiency, the total circumferential strain transfer efficiency, and the total axial strain transfer efficiency, respectively.

[0265] A j These are the constant coefficients in the general solution of the displacement of the j-th layer material;

[0266] B j denoted as the constant coefficient in the general solution of the displacement of the j-th layer material.

[0267] in, For the rock ring, r=r m Circumferential deformation at the location;

[0268] E j Let J be the elastic modulus of the j-th layer material;

[0269] , , These are the radial stress, circumferential stress, and axial stress of the j-th layer material, respectively.

[0270] Let be the Poisson's ratio of the j-th layer material;

[0271] Let r be the radial displacement of the j-th layer of material at point r;

[0272] k pc k cs These are the interface transfer coefficients for the first interface and the second interface, respectively.

[0273] , , The strain transfer efficiencies of the cement ring and the sleeve are respectively in the radial, circumferential, and axial directions;

[0274] , , These represent the strain transfer efficiencies of the outer and inner walls of the casing in the radial, circumferential, and axial directions, respectively.

[0275] , , These are the total radial strain transfer efficiency, the total circumferential strain transfer efficiency, and the total axial strain transfer efficiency, respectively.

[0276] , , These represent the strain transfer efficiencies of the outer and inner walls of the casing in the radial, circumferential, and axial directions, respectively.

[0277] , , The values ​​represent the strain transfer efficiencies of the rock ring and cement ring in the radial, circumferential, and axial directions, respectively.

[0278] Example

[0279] S1. First, obtain the material mechanical parameters and geometric dimensions of the rock, cement sheath, and casing in the wellbore structure. Specifically: the rock's elastic modulus is 25 GPa, and its Poisson's ratio is 0.25; the cement sheath's elastic modulus is 12 GPa, and its Poisson's ratio is 0.22; the casing's elastic modulus is 210 GPa, and its Poisson's ratio is 0.30; the casing's inner radius r... i The outer radius of the casing is 50 mm. o It is 56 mm; the outer radius r of the cement ring c The diameter is 80 mm, and the outer boundary radius of the rock is 200 mm.

[0280] S2, based on the bonding state of the rock-cement sheath interface and the cement sheath-casing interface, an interface transfer coefficient is introduced. There are typically three methods for determining the interface transfer coefficient: empirical method, interface shear stiffness method, and experimental calibration method, which will not be elaborated upon here. In this case: the interface transfer coefficient (k) between the rock sheath and the cement sheath... pc =0.9; cement ring and casing interface transfer coefficient (k) cs =0.95; when the interface is fully cemented, take 1, and when there is weak cementation or slip, take less than 1.

[0281] S3. Establish expressions for the displacement and strain fields of each layer. The rock, cement sheath, and casing are simplified into a coaxial multi-layered cylindrical structure. Under axisymmetric, small deformation, and linear elastic conditions, expressions for the displacement and strain fields of each layer are established. The radial displacement of each layer satisfies the axisymmetric governing equations in the cylindrical coordinate system:

[0282] ;

[0283] Solving this equation yields the general solution for the radial displacement:

[0284] ;

[0285] The corresponding radial strain and circumferential strain are as follows:

[0286] ;

[0287] ;

[0288] If the object of analysis is axial strain transmission, then the axial strain of each layer is denoted as... This can be expressed by the generalized Hooke's Law as:

[0289] ;

[0290] Establish interface continuity conditions and boundary conditions:

[0291] Displacement compatibility conditions: ;

[0292] Interfacial stress continuity condition: ;

[0293] At the interface between the cement ring and the casing, r=r o At this location, the following conditions must be met: Displacement compatibility conditions: ;

[0294] Interfacial stress continuity condition: ;

[0295] On the inner wall of the casing, r=r i At this location, the inner wall of the casing is subjected to internal pressure p. i ,So ;

[0296] At the outer boundary of the rock ring, r=r R At the location, the outer boundary of the rock ring is subjected to an external load p R ,So ;

[0297] When the displacement of the outer boundary of the rock ring is known, and the displacement of the outer boundary of the rock ring is u R hour, .

[0298] Using the aforementioned displacement compatibility conditions, stress continuity conditions, and boundary conditions, the undetermined coefficients A for each layer are solved. j and B j In this invention, the rock ring, cement ring, and casing each correspond to six integration constants, uniquely determined by six independent conditions:

[0299] Under axisymmetric, small deformation, and linear elastic conditions, the general solutions for the radial displacements of the rock layer, cement sheath layer, and casing layer are respectively expressed as:

[0300] ;

[0301] Accordingly, there are 6 unknown integral constants in the three-layer structure, which are solved by solving the following 6 independent equations simultaneously:

[0302] Conditions for compatibility of displacement at the interface between the rock ring and cement ring Substituting into the general solution of the displacement, we get:

[0303] ;

[0304] Stress continuity condition at the rock ring and cement ring interface: ;

[0305] Substituting the general solution of the displacement into the constitutive relation, we obtain:

[0306] ;

[0307] Displacement compatibility conditions at the interface between the cement sheath and the casing: Substituting the general solution of the displacement into the constitutive relation, we get:

[0308] ;

[0309] On the inner wall of the casing, r=r i If the inner wall of the casing is not subjected to internal pressure, then: The inner wall of the casing is subjected to internal pressure p. i ,So ;

[0310] At the outer boundary of the rock at r=rR, if the outer boundary is subjected to an external load pR, then: ;

[0311] Alternatively, when the displacement of the outer boundary is known, we have Then there is ;

[0312] The above six equations can be uniformly written in the following matrix form:

[0313] ,Right now ;

[0314] M is a coefficient matrix composed of interface and boundary conditions, and b is a vector of constant terms composed of external loads, internal pressures, and boundary displacements. The integral constants in the general solution for displacements at each layer are uniquely determined through this matrix form.

[0315] S4, taking radial strain as the target strain as an example, at any position r of the rock ring m The radial strain at the point is

[0316] r c ≤r m ≤r R The radial strain on the outer side of the cement sheath at the interface between the rock sheath and the cement sheath is: The radial strain on the inner side of the cement sheath layer at the interface between the cement sheath and the casing is: Radial strain on the outer wall of the casing Radial strain of the inner wall of the casing .

[0317] S5, the radial strain transfer efficiency between the outer wall and inner wall of the casing can be expressed as:

[0318] ;

[0319] If circumferential strain is used as the target strain component, then:

[0320] ;

[0321] Similarly, the circumferential strain transfer efficiency between the outer wall and inner wall of the casing can be expressed as:

[0322] Its engineering approximate calculation form can be written as: ;

[0323] Similarly, the axial strain transfer efficiency between the outer wall and inner wall of the casing can be expressed as:

[0324] ;

[0325] The total circumferential strain transfer efficiency of the rock ring, cement ring, and casing can be expressed as:

[0326] Its engineering approximate calculation form can be written as:

[0327] ;

[0328] Similarly, the total axial strain transfer efficiency of the rock ring, cement ring, and casing can be expressed as:

[0329] ;

[0330] When radial strain is used as the target strain, the total strain transfer efficiency is determined by the displacement derivatives of each layer.

[0331] When circumferential strain is used as the target strain, the total strain transfer efficiency can be further approximated by an engineering form that combines the interface transfer coefficient with material and geometric correction functions.

[0332] When axial strain is used as the target strain, the total strain transfer efficiency needs to be calculated based on the generalized Hooke's law under three-dimensional stress state.

[0333] S6 involves altering the material mechanical parameters, geometric dimensions, and interfacial bonding state of the casing, cement ring, and rock ring, and cyclically executing S1 to S5 to determine the influence of these parameters on strain transfer efficiency. Figures 2 to 5 . Figure 5The numbers on the curve represent the total strain transfer efficiency, showing the relationship between the total strain transfer efficiency and the interface bonding state under different interfacial bonding conditions. By understanding the influence of material mechanical parameters, geometric dimensions, and interface bonding state on the strain transfer efficiency, the strain transfer efficiency of each layer A can be determined. j and B j As shown in Table 1.

[0334] Table 1. Constant coefficients in the general solution of displacement

[0335]

[0336] Thus, based on the obtained parameters, the actual formation strain and deformation can be calculated from the measured strain using the total strain transfer efficiency, as shown in Table 2.

[0337] Table 2 Calculation Results

[0338]

[0339] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for calculating the strain transfer efficiency of a well shaft structure, characterized in that, The wellbore structure, from the inside to the outside in the radial direction, includes a casing, a cement sheath, and a rock sheath. Optical fibers are arranged in a straight line along the axial direction on the inner wall of the casing, the outer wall of the casing, and the outer wall of the cement sheath. The rock-cement sheath casing structure is subjected to radial stress. The method includes: Obtain the material mechanical parameters and geometric dimensions of the casing, cement ring, and rock ring; Based on the interface bonding state of the first interface and the second interface, the interface transfer coefficients of the first interface and the second interface are determined respectively, wherein the first interface is the interface between the rock ring and the cement ring, and the second interface is the interface between the cement ring and the casing. Establish displacement and strain field models for each layer, as well as interface continuity and boundary conditions; Based on the displacement field, calculate the target strain at key radial positions of the casing, cement ring, and rock ring; based on the strain field, calculate the strain transfer efficiency of the rock ring and cement ring, the strain transfer efficiency of the cement ring and casing, and the strain transfer efficiency inside the casing wall. The total strain transfer efficiency is calculated based on the strain transfer efficiency of the rock ring and cement ring, the strain transfer efficiency of the cement ring and casing, and the strain transfer efficiency inside the casing wall. By changing the material mechanical parameters, geometric dimensions, and interface cementation state of the casing, cement sheath, and rock sheath, the process is repeated cyclically to determine the influence of these parameters on strain transfer efficiency. The actual formation strain and deformation are then inferred from the measured strain using the total strain transfer efficiency. In the step of calculating the total strain transfer efficiency based on the strain transfer efficiency of the rock ring and cement ring, the strain transfer efficiency of the cement ring and casing, and the strain transfer efficiency inside the casing wall, the calculation formula is as follows: The overall radial strain transfer efficiency is: ； The overall circumferential strain transfer efficiency is: ； The overall axial strain transfer efficiency is: ； The strain transfer efficiency of the cement ring and sleeve includes: The radial strain transfer efficiency of the cement ring and sleeve is: ： in, The formula for calculating the radial propagation effect of the cement ring is: ； The radial transmission effect at the interface between the cement ring and the casing is calculated using the following formula: ； The radial strain transfer efficiency of the cement ring and sleeve is simplified as follows: ； The circumferential strain transfer efficiency of the cement ring and the casing is: ； The engineering approximation of the circumferential strain transfer efficiency of the cement ring and casing is: ； The axial strain transfer efficiency of the cement ring and the casing is: ； in, , , The strain transfer efficiencies of the cement ring and the sleeve are respectively in the radial, circumferential, and axial directions; This represents the elastic modulus of the j-th layer material; j is p, c, or s, where the p-th layer is a rock ring, the c-th layer is a cement ring, and the s-th layer is a casing. , , These represent the radial strain, circumferential strain, and axial strain of the j-th layer material at point r, where r is the radial coordinate in the cylindrical coordinate system, i.e., the distance from the center of the wellbore outwards. r is r o or r c ; r o At the interface between the cement ring and the sleeve; r c The outer radius of the cement ring; , , This represents the axial stress, radial stress, and circumferential stress of the j-th layer of material at point r; A j These are the constant coefficients in the general solution of the displacement of the j-th layer; B j These are the constant coefficients in the general solution of the displacement of the j-th layer; k cs For the interface transfer coefficient of the second interface; Represents the Poisson's ratio of the j-th layer material; in, , , These are the total radial strain transfer efficiency, the total circumferential strain transfer efficiency, and the total axial strain transfer efficiency, respectively. , , These represent the strain transfer efficiencies of the outer and inner walls of the casing in the radial, circumferential, and axial directions, respectively. , , The strain transfer efficiencies of the cement ring and the sleeve are respectively in the radial, circumferential, and axial directions; , , The values ​​represent the strain transfer efficiencies of the rock ring and cement ring in the radial, circumferential, and axial directions, respectively.

2. The method for calculating the strain transfer efficiency of a wellbore structure as described in claim 1, characterized in that, The method of using total strain transfer efficiency to infer the true formation strain and deformation from the measured strain includes: Using radial strain as the target strain, obtain the inner wall strain r=r of the casing. i The measured radial strain and the total radial strain transfer efficiency were measured. Based on the total radial strain transfer efficiency and the inner wall of the casing, r=r i Measured radial strain at the location, inverted and compared with the inner wall of the casing r=r i Rock rings located in the same radial direction, r=r m The actual radial strain is ; Calculate r at any two positions of the rock ring a and r b The radial deformation between them is calculated using the following formula: ； in, The inner wall radius of the casing is r = r i Radial strain; The radius of the rock ring is r = r m Radial strain; The total radial strain transfer efficiency; A p These are the constant coefficients in the general solution of rock ring displacement; B p represents the constant coefficients in the general solution of rock ring displacement.

3. The method for calculating the strain transfer efficiency of a wellbore structure as described in claim 1, characterized in that, The method of using total strain transfer efficiency to infer the true formation strain and deformation from the measured strain includes: Using circumferential strain as the target strain, obtain the inner wall strain r=r of the casing. i The measured circumferential strain and the total circumferential strain transfer efficiency were measured. Based on the total circumferential strain transfer efficiency and the inner wall of the casing r=r i The measured circumferential strain was used to invert the position r=r in the rock ring. m The actual circumferential strain of the formation at that location is given by the following formula: ； Calculate the rock ring r m The formula for calculating the circumferential deformation at the location is: ； in, For the rock ring, r=r m Circumferential deformation at the location; For the inner wall of the casing, r=r i Circumferential strain; The total circumferential strain transfer efficiency; For the rock ring at r=r m Circumferential strain; A p These are the constant coefficients in the general solution of rock ring displacement; B p represents the constant coefficients in the general solution of rock ring displacement.

4. The method for calculating the strain transfer efficiency of a wellbore structure as described in claim 1, characterized in that, The method of using total strain transfer efficiency to infer the true formation strain and deformation from the measured strain includes: Using axial strain as the target strain, obtain the inner wall strain r=r of the casing. i The measured axial strain and the total axial strain transfer efficiency were measured. Based on the total axial strain transfer efficiency and the inner wall of the casing r=r i The measured axial strain was used to invert the position r=r in the rock ring. m The actual axial strain of the formation at the specified location is given by the following formula: ； Calculate the rock ring from the axial coordinate z a To z b The axial deformation is calculated using the following formula: ; in, Let z be the circumferential deformation at the axial coordinate z in the rock ring; For the inner wall of the casing, r=r i Measured axial strain at the location; The total circumferential strain transfer efficiency; For the rock ring r=r m Actual axial strain; E j Let be the elastic modulus of the j-th layer material; j is p, and the p-th layer material is a rock ring. Let J be the axial stress of the j-th layer material; Let be the Poisson's ratio of the j-th layer material; Let J be the radial stress of the j-th layer of material; The table shows the circumferential stress of the j-th layer material.

5. The method for calculating the strain transfer efficiency of a wellbore structure as described in claim 1, characterized in that, The establishment of displacement and strain field models for each layer includes: The radial displacement of each layer satisfies: ； Simplified to: ; The radial strain, circumferential strain, and axial strain of each layer are as follows: ； ； ； in, Let be the radial displacement of the j-th layer of material at point r, where j is p, c, or s, where the p-th layer is a rock ring, the c-th layer is a cement ring, and the s-th layer is a casing. r is the radial coordinate in the cylindrical coordinate system, that is, the distance from the center of the wellbore outwards; A j These are the constant coefficients in the general solution of the displacement of the j-th layer; B j These are the constant coefficients in the general solution of the displacement of the j-th layer; Let be the radial strain of the j-th layer of material at point r; Let be the circumferential strain of the j-th layer of material at point r; Let J be the axial strain of the j-th layer material; This represents the elastic modulus of the j-th layer material; This represents the axial stress of the j-th layer of material; Represents the Poisson's ratio of the j-th layer material; Let J be the radial stress of the j-th layer of material; This represents the circumferential stress of the j-th layer of material.

6. The method for calculating the strain transfer efficiency of a wellbore structure as described in claim 1, characterized in that, The interface continuity condition and boundary condition include: When the target strain is radial strain, at the rock-cement sheath interface r=r c The following conditions must be met: Displacement compatibility conditions: ; Interfacial stress continuity condition: ; At the interface between the cement ring and the casing, r=r o At this location, the following conditions must be met: Displacement compatibility conditions: ; Interfacial stress continuity condition: ; On the inner wall of the casing, r=r i At this location, the inner wall of the casing is subjected to internal pressure p. i ,So ; At the outer boundary of the rock ring, r=r R At the location, the outer boundary of the rock ring is subjected to an external load p R ,So ; When the displacement of the outer boundary of the rock ring is known, and the displacement of the outer boundary of the rock ring is u R hour, ; in, For the j-th layer material in r c The radial displacement at point j is p, c, or s, where the p-th layer is the rock ring, the c-th layer is the cement ring, and the s-th layer is the casing; , Cement ring and rock ring, respectively, at r c Radial stress at the location; , The sleeve and cement ring are respectively located at r o Radial displacement at the location; k pc k cs These are the interface transfer coefficients for the first interface and the second interface, respectively. , The sleeve and cement ring are respectively located at r o Radial stress at the location; For the casing at r i Radial stress at the location; For rock rings in r R Radial stress at the location.

7. The method for calculating the strain transfer efficiency of a wellbore structure as described in claim 1, characterized in that, The calculation of strain transfer efficiency of the rock ring and cement ring includes: The radial strain transfer efficiency of the rock ring and cement ring is: ； The circumferential strain transfer efficiency of the rock ring and cement ring is: ； The axial strain transfer efficiency of the rock ring and cement ring is: in, The formula for calculating the radial propagation effect within the rock ring is as follows: ； A j These are the constant coefficients in the general solution of the displacement of the j-th layer; j is p, c, or s, where the p-th layer is a rock ring, the c-th layer is a cement ring, and the s-th layer is a casing; B j These are the constant coefficients in the general solution of the displacement of the j-th layer; The formula for calculating the radial transmission effect at the interface between the rock ring and the cement ring is as follows: ； The formula for calculating the circumferential propagation effect within the rock ring is as follows: ； The formula for calculating the circumferential transmission effect at the interface between the rock ring and the cement ring is as follows: ； The formula for calculating the axial propagation effect within the rock ring is as follows: ； The formula for calculating the axial transmission effect at the interface between the rock ring and the cement ring is as follows: ； This represents the axial stress of the j-th layer of material; Represents the Poisson's ratio of the j-th layer material; Let J be the radial stress of the j-th layer of material; This represents the circumferential stress of the j-th layer of material; This represents the elastic modulus of the j-th layer material; r is the radial coordinate in the cylindrical coordinate system, that is, the distance from the center of the wellbore outwards. c r m； r=r m The radius is at the rock ring.

8. The method for calculating the strain transfer efficiency of a wellbore structure as described in claim 1, characterized in that, The strain transfer efficiency inside the casing wall includes: The radial strain transfer efficiency of the outer and inner walls of the casing is: ； The circumferential strain transfer efficiency of the outer and inner walls of the casing is: ； The axial strain transfer efficiency between the outer and inner walls of the casing is: ； in, , , These represent the strain transfer efficiencies of the outer and inner walls of the casing in the radial, circumferential, and axial directions, respectively. , , These represent the radial strain, circumferential strain, and axial strain of the j-th layer material at point r, where r is the radial coordinate in the cylindrical coordinate system, i.e., the distance from the center of the wellbore outwards; j is p, c, or s, where the p-th layer is the rock sheath, the c-th layer is the cement sheath, and the s-th layer is the casing. r is r o or r i ; r i The inner radius of the sleeve; A j These are the constant coefficients in the general solution of the displacement of the j-th layer; B j These are the constant coefficients in the general solution of the displacement of the j-th layer; Let represent the Poisson's ratio of the j-th layer material.

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