Construction method for mechanical behavior analysis model of double-layer shaft of elastic stratum

Abstract

The invention belongs to the technical field of measuring stress in a pipe column or a pipe sleeve, and relates to a construction method of a double-layer shaft mechanical behavior analysis model of an elastic stratum, which comprises the following steps of: S1, simplifying a double-layer shaft mechanical behavior analysis object of the elastic stratum, and collecting relevant data of a target shaft; s2, constructing a mathematical model of mechanical behaviors of the double-layer shaft under uniform ground stress based on the collected data; s3, constructing a mathematical model under deflection crustal stress based on the constructed mathematical model under the uniform crustal stress; s4, constructing a double-layer shaft mechanical behavior simulation model of the elastic stratum under the deflection ground stress; s5, comparing and verifying the constructed deflection crustal stress mathematical model and the simulation model; according to the mechanical behavior analysis model for the double-layer shaft of the elastic stratum, the stress component and the displacement component of any position in the double-layer shaft can be calculated more accurately, and therefore a more reliable theoretical basis is provided for design and safety evaluation of the shaft.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of stress measurement in a pipe string or a pipe sleeve, and in particular to a method for constructing a double-layer wellbore mechanical behavior analysis model of an elastic formation. BACKGROUND

[0002] With the development of society, the demand for oil and gas resources continues to rise, but due to the frequent occurrence of wellbore integrity failure problems, it seriously restricts the safety and development efficiency of natural gas exploitation. As the entity protective barrier of the wellbore of the oil and gas well, the integrity of the casing is crucial to the overall safety of the wellbore, and the cement sheath, as the core component to protect the integrity of the casing, is easily damaged during the operation of the oil and gas well, resulting in the loss of sealing performance, the inability to effectively store and isolate oil, gas and water, and the inability to provide sufficient protection for the casing. In addition, the damage of the cementation degree between the casing and the cement sheath will cause local or even overall casing damage, and in severe cases, it will even cause excessive deformation or rupture of the casing, seriously affecting the reliability of the wellbore safety barrier and the wellbore passability, bringing great difficulties to the operation and workover construction, causing significant economic losses, and causing a series of safety problems.

[0003] Therefore, in order to prevent safety problems caused by the loss of integrity of the wellbore, it is necessary to further explore the mechanical behavior characteristics of the wellbore. However, the current research on the mechanical behavior characteristics of the wellbore by many scholars mainly focuses on the analysis of single-layer wellbores, and there is less research on double-layer wellbores, and the existing analysis model has low fidelity and poor reflection ability on the mechanical behavior of the actual wellbore.

[0004] Therefore, a method for constructing a double-layer wellbore mechanical behavior analysis model is needed to construct a more accurate mechanical behavior analysis model of a double-layer wellbore under actual stress conditions. SUMMARY

[0005] The present application provides a method for constructing a double-layer wellbore mechanical behavior analysis model of an elastic formation, which aims to solve the problem of poor reflection ability of the existing double-layer wellbore model on the mechanical behavior of the actual wellbore.

[0006] The technical solution of the present application is as follows:

[0007] A method for constructing a double-layer wellbore mechanical behavior analysis model of an elastic formation, comprising the following steps:

[0008] S1. Simplify the double-layer wellbore mechanical behavior analysis object of the elastic formation, and collect relevant data of the target wellbore;

[0009] S2. Construct a mathematical model of the mechanical behavior of the double-layer wellbore under uniform stress based on the collected data;

[0010] S3. Constructing a mathematical model under deviated stress based on the constructed mathematical model under uniform stress;

[0011] S4. Constructing a double-layer wellbore mechanical behavior simulation model of an elastic formation under deviated stress;

[0012] S5. Comparing and verifying the constructed mathematical model under deviated stress with the simulation model.

[0013] Further, the step S1 comprises the following steps:

[0014] S1.1. Simplifying the double-layer wellbore mechanical behavior analysis object of an elastic formation and constructing a simplified analysis model;

[0015] S1.2. Collecting target wellbore related data based on the constructed simplified analysis model.

[0016] Further, the simplified analysis model comprises a first casing, a second casing, a first cement sheath, a second cement sheath and surrounding rock, and the simplified analysis model is composed of the first casing, the first cement sheath, the second casing, the second cement sheath and the surrounding rock from the inner layer to the outer layer.

[0017] Further, the step S2 comprises the following steps:

[0018] S2.1. Constructing a thick-walled cylinder analysis model under uniform stress based on the simplified analysis model;

[0019] S2.2. Constructing a mathematical model of double-layer wellbore mechanical behavior under uniform stress based on the collected data and the constructed thick-walled cylinder analysis model.

[0020] Further, the step S3 comprises the following steps:

[0021] S3.1. Constructing a thick-walled cylinder analysis model under deviated stress based on the simplified analysis model;

[0022] S3.2. Constructing a calculation equation of stress component and displacement component of the thick-walled cylinder under deviated stress.

[0023] Further, the calculation equation constructed in the step S3.2 is:

[0024] The stress component of the thick-walled cylinder is:

[0025]

[0026] In the formula:

[0027] θ - phase angle;

[0028] σ r - radial stress of the thick-walled cylinder;

[0029] σ θ circumferential stress of thick-walled cylinder;

[0030] τ Rθ shear stress of thick-walled cylinder;

[0031] r - inner wall radius of thick-walled cylinder;

[0032] A, B, C, D - undetermined coefficients;

[0033] displacement component of thick-walled cylinder:

[0034]

[0035] wherein:

[0036] u r radial displacement of thick-walled cylinder;

[0037] u θ circumferential displacement of thick-walled cylinder;

[0038] μ - Poisson's ratio;

[0039] E - elastic modulus.

[0040] Further, the step S4 comprises the following steps:

[0041] S4.1. constructing a three-dimensional simulation model and setting geometric parameters;

[0042] S4.2. setting boundary load and meshing.

[0043] The present application has the following beneficial effects:

[0044] The present application provides a double-layer wellbore mechanical behavior analysis model of elastic formation, which simplifies and analyzes the structure of the double-layer wellbore, and considers the interaction between the casing, cement sheath and formation and the stress continuity condition. By simplifying them into a thick-walled cylinder model bearing uniform internal and external pressure, and constructing the corresponding stress component and displacement component calculation equation, the stress component and displacement component at any position in the double-layer wellbore can be more accurately calculated, thereby providing a more reliable theoretical basis for the design and safety evaluation of the wellbore, and to some extent, avoiding the engineering risks caused by calculation errors. BRIEF DESCRIPTION OF DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as a limitation to the scope, and for those skilled in the art, other related drawings can also be obtained without creative labor.

[0046] Figure 1 is a construction method flowchart provided by the present application;

[0047] Figure 2 is a casing, cement sheath and surrounding rock simplified thick-walled cylinder model schematic diagram provided by the present application;

[0048] Figure 3 is a double-layer wellbore parameter definition schematic diagram provided by the present application;

[0049] Figure 4 is a double-layer wellbore mechanical behavior simplified model schematic diagram under uniform ground stress provided by the present application;

[0050] Figure 5 is a double-layer wellbore mechanical behavior simplified model schematic diagram under deviated ground stress provided by the present application;

[0051] Figure 6 is a casing-cement sheath-surrounding rock combination three-dimensional model structure schematic diagram provided by the present application;

[0052] Figure 7 is a double-layer wellbore geometric parameter schematic diagram provided by the present application;

[0053] Figure 8 is a casing and cement sheath material attribute schematic diagram provided by the present application;

[0054] Figure 9 is a three-dimensional simulation model grid division quantity schematic diagram provided by the present application;

[0055] Figure 10 is a three-dimensional simulation model schematic diagram provided by the present application;

[0056] Figure 11 is a cement sheath stress component numerical solution and theoretical solution comparison schematic diagram under deviated ground stress provided by the present application;

[0057] Figure 12 is a casing stress component numerical solution and theoretical solution comparison schematic diagram under deviated ground stress provided by the present application. DETAILED DESCRIPTION

[0058] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present application.

[0059] Embodiment

[0060] A method for constructing a double-layer wellbore mechanical behavior analysis model of an elastic formation, comprising the following steps:

[0061] S1. Simplifying the double-layer wellbore mechanical behavior analysis object of the elastic formation, and collecting target wellbore related data;

[0062] S2. Constructing a mathematical model of the double-layer wellbore mechanical behavior under uniform ground stress based on the collected data;

[0063] S3. Constructing a mathematical model under deviated ground stress based on the constructed mathematical model under uniform ground stress;

[0064] S4. Constructing a simulation model of the double-layer wellbore mechanical behavior of the elastic formation under deviated ground stress;

[0065] S5. Comparing and verifying the constructed mathematical model under deviated ground stress with the simulation model.

[0066] It should be noted that the present application is a double-layer wellbore mechanical behavior mathematical model constructed based on non-uniform ground stress. In the technical field, the mechanical problem of the wellbore under non-uniform ground stress can be decomposed into the superposition of two mechanical problems under uniform ground stress and deviated ground stress. Based on this, the present application first constructs a mathematical model of the double-layer wellbore mechanical behavior under uniform ground stress, and then constructs a mathematical model of the double-layer wellbore mechanical behavior of the elastic formation under deviated ground stress based on the mathematical model of the double-layer wellbore mechanical behavior under uniform ground stress. At this time, the mathematical model of the double-layer wellbore mechanical behavior of the elastic formation under deviated ground stress is the mathematical model of the double-layer wellbore mechanical behavior under non-uniform ground stress. The following will not be described in detail.

[0067] Figure 3 、 Figure 7 、 Figure 8 、 Figure 11 and Figure 12The "casing 1", "casing 2", "cement sheath 1", and "cement sheath 2" in the above are "first casing", "second casing", "first cement sheath", and "second cement sheath".

[0068] Further, the step S1 comprises the following steps:

[0069] S1.1. simplifying and constructing a simplified analysis model for the double-layer wellbore mechanical behavior analysis object of the elastic stratum;

[0070] S1.2. collecting target wellbore related data based on the constructed simplified analysis model.

[0071] Further, the simplified analysis model comprises: the first casing, the second casing, the first cement sheath, the second cement sheath, and the surrounding rock, and the simplified analysis model is from the inner layer to the outer layer as the first casing, the first cement sheath, the second casing, the second cement sheath, and the surrounding rock.

[0072] The collected target wellbore related data are as follows:

[0073] (1) including the interfacial pressure and boundary conditions of the double-layer wellbore under the uniform stress field, the internal pressure p i of the casing, the confining pressure p0; the pressure p1 between the first casing and the first cement sheath; the pressure p2 between the first cement sheath and the second casing; the pressure p3 between the second casing and the second cement sheath; and the pressure p4 between the second cement sheath and the surrounding rock;

[0074] (2) including the interfacial pressure and boundary conditions of the double-layer wellbore under the non-uniform stress field, the cosine-distributed extrusion force s·cos2θ, the sine-distributed shear force s·sin2θ; the cosine-distributed extrusion force s1·cos2θ between the first casing and the first cement sheath, the sine-distributed shear force s2·sin2θ between the first casing and the first cement sheath; the cosine-distributed extrusion force s3·cos2θ between the first cement sheath and the second casing, the sine-distributed shear force s4·sin2θ between the first cement sheath and the second casing; the cosine-distributed extrusion force s5·cos2θ between the second casing and the second cement sheath, the sine-distributed shear force s6·sin2θ between the second casing and the second cement sheath; the cosine-distributed extrusion force s7·cos2θ between the second cement sheath and the surrounding rock, and the sine-distributed shear force s8·sin2θ between the second cement sheath and the surrounding rock; wherein s is half of the difference between the maximum stress σ H and the minimum stress σ h , and θ is the phase angle.

[0075] In the present embodiment, p i = 15 MPa; p0= 25 MPa; S = 5 MPa;

[0076] Further, the step S2 comprises the following steps:

[0077] S2.1. Constructing the thick-walled cylinder analysis model under uniform stress based on the simplified analysis model;

[0078] S2.2. Constructing the mathematical model of the mechanical behavior of the double-layer wellbore under uniform stress based on the collected data and the constructed thick-walled cylinder analysis model.

[0079] The specific process is as follows:

[0080] S2.1. Constructing the thick-walled cylinder analysis model under uniform stress based on the simplified analysis model;

[0081] Under uniform stress, the first casing, the first cement sheath, the second casing, the second cement sheath and the surrounding rock are all simplified as thick-walled cylinder models bearing uniform internal and external pressure, and the effects of the casing, the cement sheath and the surrounding rock are connected through the double-layer wellbore interface pressure and the boundary conditions;

[0082] It should be noted that the specific simplification method and principle are prior art, and will not be further described here.

[0083] S2.2. Constructing the mathematical model of the mechanical behavior of the double-layer wellbore under uniform stress based on the collected data and the constructed thick-walled cylinder analysis model.

[0084] The first casing, the first cement sheath, the second casing, the second cement sheath and the surrounding rock are brought into the radial displacement expression of the thick-walled cylinder through the displacement continuity condition and the stress continuity condition, the radial displacement is solved, and then the interface pressures p1, p2, p3 and p4 of the casing, the cement sheath and the surrounding rock are solved through the displacement continuity condition, and the interface pressures are substituted into the stress components σ r , σ θ and the displacement component u r of the thick-walled cylinder, so that the stress components and the displacement components at any position in the double-layer wellbore under uniform stress can be accurately calculated.

[0085] Under uniform stress, the stress components and the displacement components of the thick-walled cylinder are calculated as follows:

[0086] The stress components of the thick-walled cylinder are as follows:

[0087]

[0088] In the formula:

[0089] σ r , σ θ — the radial stress and the circumferential stress of the thick-walled cylinder;

[0090] r i , r0— the inner and outer radii of the thick-walled cylinder;

[0091] p i p0— pressure inside the casing and confining pressure;

[0092] Radial displacement of thick-walled cylinder:

[0093]

[0094] where:

[0095] u r Radial displacement of cylinder;

[0096] μ— Poisson's ratio;

[0097] E— Elastic modulus;

[0098] where the stress continuity conditions for the double-layer wellbore under uniform stress are as follows:

[0099] 1. The inner wall boundary stress of the first casing is equal to the pressure applied inside the wellbore (r = r i ):

[0100]

[0101] 2. The stress at the interface of the first casing and the first cement sheath is equal (r = r1):

[0102] σ 1 r1 = σ 2 r1

[0103] 3. The stress at the interface of the first cement sheath and the second casing is equal (r = r2):

[0104] σ 2 r2 = σ 3 r2

[0105] 4. The stress at the interface of the second casing and the second cement sheath is equal (r = r3):

[0106] σ 3 r3 = σ 4 r3

[0107] 5. The stress at the interface of the second cement sheath and the surrounding rock is equal (r = r4):

[0108] σ 4 r4 = σ F r4

[0109] 6. The outer wall boundary stress of the surrounding rock is equal to the pressure applied by the earth stress (r = r out ) The displacement continuity conditions of the double-layer wellbore under uniform stress are as follows:

[0110] 1. The interface displacement of the first casing and the first cement sheath is equal (r = r1):

[0111] u 1 r1 = u 2 r1

[0112] 2. The interface displacement of the first cement sheath and the second casing is equal (r = r2):

[0113] u 2 r2 = u 3 r2

[0114] 3. The interface displacement of the second casing and the second cement sheath is equal (r = r3):

[0115] u 3 r3 = u 4 r3

[0116] 4. The interface displacement of the second cement sheath and the surrounding rock is equal (r = r4):

[0117] u 4 r4 = u F r4

[0118] Wherein, under uniform stress, the calculation equations of the pressures p1, p2, p3, p4 on the interfaces of the casing, the cement sheath and the surrounding rock are as follows:

[0119] Wherein, the calculation equations of p1, p2, p3, p4 are as follows:

[0120]

[0121] In the formula:

[0122] P i — The internal pressure of the casing;

[0123] r1— The internal radius of the first casing;

[0124] r2— The external radius of the first casing (equal to the internal radius of the first cement sheath);

[0125] r3— The external radius of the first cement sheath (equal to the internal radius of the second casing);

[0126] r4——outer radius of the second casing;

[0127] r5——inner radius of surrounding rock;

[0128] r F ——Outer radius of surrounding rock.

[0129] Among them, k1-k 16 The calculation formula is as follows:

[0130]

[0131]

[0132] Specifically, the radial displacement expressions of casing, cement sheath and surrounding rock can be obtained by bringing stress conditions and displacement continuity conditions into the radial displacement expression of thick-walled cylinder. 16 The radial displacement expressions of casing, cement sheath and surrounding rock are simplified, and the displacement continuity condition is brought into the simplified radial displacement to obtain the pressures p1, p2, p3 and p4 on the interface of casing, cement sheath and surrounding rock.

[0133] It should be noted that k1~k 16 It is an intermediate variable used to assist in simplifying the radial displacement expression and plays a transitional role. It has no clear meaning in itself.

[0134] Substitute the pressure P1~P4 on the interface between casing, cement sheath and surrounding rock into the stress component σ of the thick-walled cylinder r , σ θ and displacement component u r The stress and displacement components at any position in a double-layer wellbore under uniform ground stress can be accurately calculated.

[0135] Will Figure 7 as well as Figure 8 Wellbore parameters shown are r i 、r1~r5、r F ;E1~E F 、μ1~μ F The pressure on the interface can be obtained by substituting the value of into the expression of pressure p1, p2, p3, p4 on the interface of casing, cement sheath and surrounding rock; the pressure on the interface of casing, cement sheath and surrounding rock is substituted into the stress component σ of the thick-walled cylinder. r , σ θ and displacement component u r In this paper, the stress component and displacement component at any position in the double-layer wellbore under uniform geostress can be accurately calculated, thereby completing the construction of the mathematical model of the mechanical behavior of the double-layer wellbore under uniform geostress.

[0136] For reference, in this embodiment, according to Figure 7The inner and outer radius of the double-layer wellbore casing, cement sheath, and Figure 8 The elastic modulus and Poisson's ratio of the casing and cement sheath, and k1-k 16 In order, 0.0021, 0.0024, 0.0117, 0.0131, 0.0095, 0.0115, 0.0052, 0.0055, 0.0050, 0.0053, 0.0256, 0.0278, 0.0225, 0.0252, 0.0190, 0.0272; p i = 15 MPa, p0= 25 MPa and k1-k 16 The expression is brought into the expression of p1-p4, and the pressure p1-p4 on the interface of the double-layer wellbore is -26.85 MPa, -26.29 MPa, -33.34 MPa, and -32.35 MPa, respectively; combined with the inner and outer radius of the double-layer wellbore casing and cement sheath and the wellbore interface pressure, the stress component and radial displacement function containing only the position r of the double-layer wellbore are brought into the stress component and radial displacement expression of the thick-walled cylinder model, so that the stress component and displacement component at any position in the double-layer wellbore can be solved; no more details are given here.

[0137] Further, step S3 comprises the following steps:

[0138] S3.1. Constructing a thick-walled cylinder analysis model under deviated stress based on the simplified analysis model;

[0139] S3.2. Constructing a calculation equation of stress component and displacement component of the thick-walled cylinder under deviated stress.

[0140] Specifically as follows:

[0141] S3.1. Constructing a thick-walled cylinder analysis model under deviated stress based on the simplified analysis model;

[0142] Under deviated stress, the first casing, the first cement sheath, the second casing, the second cement sheath, and the surrounding rock are all simplified as thick-walled cylinder models bearing uniform internal and external pressure, and the effects of the casing, the cement sheath, and the surrounding rock are linked together through the double-layer wellbore interface pressure and the boundary conditions;

[0143] It should be noted that the specific simplification method and principle are prior art, and will not be further described here.

[0144] S3.2. Constructing a calculation equation of stress component and displacement component of the thick-walled cylinder under deviated stress.

[0145] The mathematical model of the mechanical behavior of the double-layer wellbore under deviated stress is consistent with the mathematical model of the mechanical behavior of the double-layer wellbore under uniform stress in form, but the expressions are different;

[0146] Wherein, under the deviated stress, the stress component and displacement component calculation equation of thick-walled cylinder is as follows:

[0147] Thick-walled cylinder stress component:

[0148]

[0149] In the formula:

[0150] θ - phase angle;

[0151] σ r - radial stress of thick-walled cylinder;

[0152] σ θ - circumferential stress of thick-walled cylinder;

[0153] τ Rθ - shear stress of thick-walled cylinder;

[0154] r - inner wall radius of thick-walled cylinder;

[0155] A, B, C, D - undetermined coefficients;

[0156] Wherein, A, B, C, D can be solved by the following equation group:

[0157]

[0158] In the formula:

[0159] r0 - outer wall radius of thick-walled cylinder n = r0 / r i

[0160] q1, q2, q3, q4 - interface pressure under deviated stress

[0161] Displacement component of thick-walled cylinder:

[0162]

[0163] In the formula: u r , u θ - radial and circumferential displacement of thick-walled cylinder

[0164] Wherein, the stress continuity condition of double-layer wellbore under deviated stress is as follows:

[0165] 1. The inner wall boundary stress of the first casing is 0 (r = a):

[0166]

[0167] 2. The interface stress of the first casing and the first cement ring is equal (r = b):

[0168]

[0169] 3. The interface stress of the first cement sheath and the surrounding rock is equal (r = c):

[0170]

[0171] 4. The outer wall boundary stress of the surrounding rock is equal to the pressure applied by the earth stress (r = d):

[0172]

[0173] The displacement continuity conditions of the double-layer wellbore under the deviated earth stress are as follows:

[0174] 1. The interface displacement of the first casing and the first cement sheath is equal (r = b):

[0175]

[0176] 2. The interface displacement of the first cement sheath and the surrounding rock is equal (r = c):

[0177]

[0178] The unknowns s1, s2, s3, s4 can be obtained through the stress and displacement continuity conditions, and the stress components and displacement components of the casing, the cement sheath, and the surrounding rock need to be paid attention to the stress boundary conditions:

[0179] For the first casing, the following replacements should be made:

[0180] r i = a, r0 = b, n = n1 = b / a, q1 = 0, q2 = 0, q3 = s1, q4 = s2

[0181] For the first cement sheath, the following replacements should be made:

[0182] r i = b, r0 = c, n = n1 = c / b, q1 = s1, q2 = s2, q3 = s3, q4 = s4

[0183] For the second casing, the following replacements should be made:

[0184] r i = c, r0 = d, n = n1 = d / c, q1 = s3, q2 = s4, q3 = s5, q4 = s6

[0185] For the second cement sheath, the following replacements should be made:

[0186] r i = d, r0 = e, n = n1 = e / d, q1 = s5, q2 = s6, q3 = s7, q4 = s8

[0187] For the surrounding rock, the following replacements should be made:

[0188] r i =e, r0=f, n=n1=b=f / e, q1=s7, q2=s8, q3=s, q4=s

[0189] By the above substitution, the interface pressures q1, q2, q3, and q4 are substituted into the stress component σ r , σ θ , τ Rθ and displacement component u r 、u θ , the stress and displacement components at any position of the double-layer wellbore under deviated in-situ stress can be obtained;

[0190] At this point, the mathematical model for mechanical behavior analysis of a double-layer wellbore under a deflection stress field has been established.

[0191] For reference, under the deflected ground stress condition in this embodiment, according to Figure 7 The double-layer wellbore casing, inner and outer radii of the cement sheath, and Figure 8 The elastic modulus and Poisson's ratio of the casing and cement sheath are shown in Figure 2, and the obtained values ​​of s1 to s8 are: 10.6869 MPa, -30.3025 MPa, -3.1202 MPa, -20.6082 MPa, -2.7981 MPa, -26.0957 MPa, -9.9987 MPa, and -17.9375 MPa, respectively. By replacing the stress boundary conditions of s1 to s8 under deviated ground stress and combining the inner and outer radii of the double-layer wellbore casing and cement sheath, the pressures q1 to q4 on the first casing are 0, 0, 10.6869 MPa, and -30.3025 MPa, respectively. The interface pressures q1 to q4 on the first cement sheath are 10.6869 MPa, -30.3025 MPa, -3.1202 MPa, and -20.6082 MPa, respectively. The pressures on the second casing are: The interface pressures q1~q4 on the double-layer wellbore are -3.1202MPa, -20.6082MPa, -2.7981MPa, and -26.0957MPa; the interface pressures q1~q4 on the second cement sheath are -2.7981MPa, -26.0957MPa, -9.9987MPa, and -17.9375MPa; the interface pressures q1~q4 on the surrounding rock are -9.9987MPa, -17.9375MPa, 5MPa, and 5MPa; finally, the interface pressures q1~q4 of each part of the double-layer wellbore are substituted into the stress component and radial displacement expressions of the thick-walled cylinder model, and the stress component and radial displacement function containing the arbitrary position r and phase angle θ of the double-layer wellbore can be obtained, thereby solving the stress component and displacement component of each part of the double-layer wellbore at any position and in each phase.

[0192] Further, step S4 comprises the following steps:

[0193] S4.1. Constructing a three-dimensional simulation model and setting geometric parameters;

[0194] S4.2. Setting boundary loads and meshing.

[0195] Specifically as follows:

[0196] S4.1. Constructing a three-dimensional simulation model and setting geometric parameters;

[0197] It is assumed that the casing, cement sheath and surrounding rock are isotropic ideal elastic materials, and are tightly connected without relative sliding between them; based on the above premise, a three-dimensional geometric model of the casing-cement sheath-surrounding rock combination is established, in which the combination bears casing internal pressure, maximum ground stress, minimum ground stress, vertical ground stress, axial load and self weight. Figure 6

[0198] In the present embodiment, as shown in Figure 10 In order to prevent the formation boundary effect from affecting the stress distribution of the casing-cement sheath, according to the Saint-Venant principle, the length and width of the formation in the three-dimensional simulation model are taken as 10 times the borehole diameter, and the height is taken as 20 times the borehole diameter.

[0199] S4.2. Setting boundary loads and meshing.

[0200] In the present embodiment, by way of reference, the maximum ground stress is 110.13 MPa, the minimum ground stress is 89.52 MPa, the vertical ground stress is 102.36 MPa, the casing internal pressure is 44.1 MPa (the liquid density is 1 kg / m 3 ), and the formation temperature is 392.6 K; in addition, when constructing the three-dimensional simulation model, the axial load borne by the casing needs to be considered, and the calculated axial loads at the lower end of the inner and outer casings are 510874 N and 810166 N respectively, so the corresponding axial pressures are 77.84 MPa and 71.88 MPa respectively; the model is meshed with solid elements of the 3Dstress three-dimensional simulation model, and the meshing principle of inner dense and outer sparse is followed, and the number of meshes is as shown in Figure 9

[0201] S5. Comparing and verifying the constructed deviated ground stress mathematical model with the simulation model.

[0202] In the three-dimensional simulation model, the upper surface of the formation bears the vertical ground stress, the lower surface and the front surface bear the vertical simple support constraint perpendicular to the corresponding surface, the left surface and the right surface bear the maximum ground stress, the rear surface bears the minimum ground stress, the entire combination bears the self weight, the lower surface of the casing bears the axial load, and the inner surface bears the liquid column pressure, and the simulation model is as shown in Figure 10 .​​

[0203] By way of reference, in the present embodiment, the comparison results between the numerical solution of the mathematical model and the simulation solution of the simulation model are as follows:

[0204] Table 1 Comparison between numerical solution of mathematical model and simulation solution of simulation model

[0205]

[0206]

[0207] From Figure 11 , Figure 12 and Table 1, the average error between the numerical solution of the mathematical model and the simulation solution of the simulation model is less than 4%, verifying the correctness of the analysis model of the mechanical behavior of the double-layer wellbore in the elastic formation constructed by the present application; it should be noted that Figure 11 the "theoretical solution" in

[0208] The above description does not limit the present application in any form, although the present application has been disclosed as above through the embodiments, however, it is not intended to limit the present application, any person skilled in the art, without departing from the technical solution range of the present application, can make some changes or modifications to the above disclosed technical content for equivalent embodiments of equivalent changes, as long as it does not deviate from the technical solution of the present application, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, all still belong to the range of the technical solution of the present application.

Claims

1. A method for constructing a double-layer wellbore mechanical behavior analysis model for elastic formations, characterized in that: The following steps are involved: S1. Simplify the double-layer wellbore mechanical behavior analysis object in the elastic formation and collect relevant data of the target wellbore; S2. Construct a mathematical model of the mechanical behavior of a double-layer wellbore under uniform in-situ stress based on the acquired data; S3. constructing a mathematical model under skew in-situ stress based on the constructed mathematical model under uniform in-situ stress; S4. Construct a simulation model of the mechanical behavior of a double-layer wellbore in elastic formations under deflected in-situ stress; S5. Compare and verify the constructed deflective geostress mathematical model with the simulation model.

2. The method according to claim 1, characterized in that Described step S1 comprises the following steps: S1.

1. Simplify the double-layer wellbore mechanical behavior analysis object of the elastic formation and construct a simplified analysis model; S1.

2. Based on the constructed simplified analysis model, collect data related to the target wellbore.

3. The method according to claim 2, characterized in that The simplified analysis model includes: a first casing, a second casing, a first cement sheath, a second cement sheath and surrounding rock. The simplified model includes the first casing, the first cement sheath, the second casing, the second cement sheath and surrounding rock from inner layer to outer layer.

4. The method according to claim 1, wherein The step S2 comprises the following steps: S2.

1. Construct an analytical model for a thick-walled cylinder under uniform in-situ stress based on a simplified analytical model. S2.

2. Construct a mathematical model of the mechanical behavior of a uniformly stressed double-layer wellbore based on the collected data and the constructed thick-walled cylinder analysis model.

5. The method according to claim 1, wherein The step S3 comprises the following steps: S3.

1. Construct an analytical model for a thick-walled cylinder under deflected in-situ stress based on a simplified analytical model. S3.

2. Construct equations for the stress and displacement components of a thick-walled cylinder under deflection stress.

6. The method according to claim 5, characterized in that The calculation equation constructed in step S3.2 is: Stress components of a thick-walled cylinder: Where: θ——phase angle; σ r — radial stress in thick-walled cylinders; σ θ — circumferential stress in thick-walled cylinders; τ Rθ — shear stress in thick-walled cylinders; r——Inner wall radius of thick-walled cylinder; A, B, C, D – coefficients to be determined; Displacement components of a thick-walled cylinder: Where: u r — radial displacement of thick-walled cylinder; u θ — circumferential displacement of thick-walled cylinders; μ——Poisson’s ratio; E——elastic modulus.

7. The method according to claim 1, characterized in that The step S4 comprises the following steps: S4.

1. constructing a three-dimensional simulation model and setting geometric parameters; S4.

2. Set boundary loads and perform meshing.

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