Casing-cement sheath corrosion rate prediction method in chloride corrosion environment
By constructing a rust diffusion model through a chemical-mechanical coupling model, the problem of the inability to predict the properties of well cement cracks after downhole casing corrosion in existing technologies is solved, enabling accurate prediction of downhole corrosion conditions and providing effective pipeline protection support.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-27
- Publication Date
- 2026-03-27
AI Technical Summary
Existing technologies lack effective models to predict the nature of cement cracks in oil wells after downhole casing corrosion, making it difficult to accurately predict downhole corrosion conditions.
A chemical-mechanical coupling model was adopted. By constructing a rust diffusion model, the deterioration performance of cement material around steel casing under chloride ion corrosion was simulated, and the corrosion rate of casing-cement ring was predicted. This included setting initial conditions, discretizing the matrix, determining the relationship between the rust volume and interfacial pressure of cement expansion, and finally obtaining the corrosion rate.
It can accurately predict the corrosion pattern of the casing-cement ring, providing support for pipeline protection and showing good application prospects.
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Figure CN121744579A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of oilfield wellbore corrosion protection technology, and relates to a method for predicting the corrosion rate of casing-cement sheath under chloride corrosion environment. Background Technology
[0002] For nearly four decades, steel casing used in the oil and gas industry, embedded in wellbore systems after cementing, has been exposed to underground water containing high concentrations of chlorides, making it susceptible to corrosion. The corrosion durability of the casing-cement sheath has become one of the most critical issues for wellbore integrity. One of the main causes of steel corrosion is the intrusion of chloride ions into the concrete. In chloride-induced corrosion, chloride ions form electrolytes in the pore solution of the concrete, causing corrosion of the steel. Due to chloride ion intrusion, the corrosion deterioration process of steel in cement-based materials has three stages: first, chloride ions penetrate into the concrete; second, rust formation and accumulation at the interface between the steel reinforcement and concrete; and third, cracks develop in the surrounding cement-based materials. Once the corrosion process begins, it is irreversible; therefore, characterizing the process of chloride penetration into the surrounding environment is crucial. The volume of rust produced by corroded steel generates expansion pressure at the steel / cement interface. As corrosion continues, the expansion pressure gradually increases. When the expansion pressure exceeds the tensile strength of the cement material, the cement will crack. For oil and gas well systems, the pressure, temperature, and humidity underground are higher than at the surface. The chloride permeability downhole is high, and the chloride diffusion process lasts for a very short time. Chloride ions penetrate the cement around the well and come into contact with the steel casing. The corrosion of the steel produces rust products that accumulate at the interface between the casing and the cement. The volume expansion of the rust layer generates circumferential tensile stress, leading to cracking of the well cement. At the same time, long-term corrosion reduces the casing wall thickness, and the strength of the casing and cement sheath decreases due to the corrosion process.
[0003] Currently, there is no suitable model to predict the properties of cement cracks in oil wells after downhole casing corrosion. Therefore, it is urgent to develop a new method to predict downhole corrosion conditions. Summary of the Invention
[0004] The purpose of this invention is to provide a method for predicting the corrosion rate of casing-cement sheath under chloride corrosion environment, which solves the problem that the existing technology does not have a suitable model to predict the properties of cement cracks in oil wells after downhole casing corrosion, making it difficult to accurately predict downhole corrosion conditions.
[0005] The technical solution adopted in this invention is a method for predicting the corrosion rate of casing-cement ring under chloride corrosion environment, which is implemented according to the following steps:
[0006] Step 1: Set initial conditions and construct a preliminary rust diffusion model;
[0007] Step 2: Discretize the matrix to obtain the rust concentration pressure distribution;
[0008] Step 3: Determine the volume of rust caused by cement expansion and determine the radial expansion value around the cement.
[0009] Step 4: Determine the relationship between radial expansion and interfacial pressure;
[0010] Step 5: Determine the critical value of the interfacial pressure at which cracks occur;
[0011] Step 6: Obtain the law of change of interfacial pressure and obtain the final corrosion rate of the casing-cement ring under chloride corrosion environment.
[0012] The beneficial effects of this invention are that it uses a chemical-mechanical coupling model to simulate and predict the deterioration performance of cement materials around steel casings under chloride ion corrosion conditions, focusing on the corrosion process, and can accurately predict the corrosion law of casing-cement ring, providing strong support for pipeline protection and showing great application prospects. Attached Figure Description
[0013] Figure 1 A simplified diagram of the cement ring thick-walled model constructed by the method of the present invention;
[0014] Figure 2 This refers to the relationship curve between tangential stress and crack size mentioned in the method of this invention;
[0015] Figure 3 This is a schematic diagram of the stress balance relationship caused by corrosion products;
[0016] Figure 4 This is the curve of interface pressure changing over time in Embodiment 1 of the method of the present invention;
[0017] Figure 5 This is the curve showing the change in interface pressure with displacement at point ri in Embodiment 1 of the method of the present invention;
[0018] Figure 6 This refers to the percentage of corrosion products at different radius positions in Embodiment 1 of the present invention. Detailed Implementation
[0019] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.
[0020] The present invention provides a method for predicting the corrosion rate of casing-cement ring under chloride corrosion environment, which is implemented according to the following steps:
[0021] Step 1: Set initial conditions and construct a preliminary rust diffusion model.
[0022] For downhole steel casing, once corrosion begins, it can be assumed that under normal circumstances, chloride content, moisture, and oxygen levels are always sufficient, and the corrosion process continues. Reducing these influencing factors would decrease the corrosion rate, but it is believed that the underground environment will provide a continuous supply. The mass loss m of the steel product during corrosion is... s It can be obtained by Faraday's law, as shown in equation (1). Then, dividing equation (1) by time gives the steel loss rate μ, as shown in equation (2). The corrosion depth d per unit area is calculated by dividing equation (3) by the density, as shown in the following expression:
[0023]
[0024] Among them, a s It is the atomic mass of steel, n is the number of equal parts exchanged, F is the Faraday constant, and i corr Let ρ be the annual average corrosion density, t be time, μ be the steel loss rate, and ρ be the corrosion density. s Let d be the density of the steel, and d be the corrosion depth per unit area.
[0025] Once the corrosion depth of the steel is obtained, the radius R is then calculated. i The volume of corrosion products within the cement ring is shown in equation (4):
[0026] V rust =απ(2R) i dd 2 (4)
[0027] Wherein, α is the volume ratio of corrosion products to the corroded material (casing). The value of α mainly depends on the chemical composition of the rust, and the value of α ranges from 0 to 1.
[0028] The above formula shows the variation of total corrosion amount over time. However, not all rust leads to increased pressure and penetration into the cement material. Generally, there is a porous region between the casing and the cement ring, called the interfacial transition zone (ITZ). Corrosion products will first occupy the space left by the casing corrosion, and then move into the interfacial transition zone. Rust stored in these two spaces will not generate any pressure. Therefore, the rust in the corroded casing area and the interfacial transition zone must be subtracted from the total amount of rust generated, as shown in formula (5):
[0029] V eff =V rust -V ITZ -V cs (5)
[0031] Among them, V ITZ V represents the volume of the interface transition region. cs V represents the volume of the corroded casing.eff It is the volume of rust that can generate pressure and further penetrate into the cement matrix, V nist The relevant expression for the volume of rust is:
[0032]
[0033] V ITZ =d ITZ A Steel (7)
[0034]
[0035] Among them, V rust It is the volume in which rust is produced; d ITZ A is the volume of a porous region per unit area that can absorb corrosion. steel It is the surface area of the casing, h i The thickness of the interface transition zone; The porosity of the interface transition zone;
[0036] When V eff When the value is greater than zero, it indicates that the voids left by casing corrosion and the voids in the interface transition zone are filled with corrosion products. Once these spaces are filled, the rust will begin to penetrate into the surrounding cement matrix. This diffusion process is simulated by Darcy's law, and the diffusion equation is shown in equation (9):
[0037]
[0038] Among them, C rust It is the concentration of rust in the pores, κ rust It is the viscosity of the corrosion products, η rust P is the diffusion coefficient of rust. rust This refers to the pressure distribution based on rust concentration, which largely depends on the rust concentration; the diffusion equation is called the chemical-mechanical coupled diffusion equation.
[0039] Step 2: Discretize the matrix to obtain the rust concentration pressure distribution.
[0040] As can be seen from the equations above, in order to solve this chemical-mechanical coupled diffusion equation, another connection C is needed. rust and P rust Therefore, a simple linear state equation is adopted, as shown in equation (10):
[0041] C rust =βP rust (10)
[0042] Where β is a state function determined by the permeation process; C p f represents the porosity of the cement matrix.t Let C be the tensile strength of the cement matrix; when all the porous media are filled in the cement matrix, then C = ... rust =C p At the same time, P rust =f t ;
[0043] Additional corrosion formation leads to pressure buildup in the cement. When the pressure generated by corrosion exceeds the tensile strength of the cement, cracks will form in the cement, leading to the conclusion shown in equation (11):
[0044]
[0045] Combining equations (9) and (11), the diffusion equation (9) is revised as follows:
[0046]
[0047] Where r is the radius of the surrounding cement.
[0048]
[0049] The diffusion equations for the boundary and initial conditions of equation (13) are shown below:
[0050] C rust (r,0)=0 (14)
[0052] C rust (R i ,t)=βP int (t) (15)
[0054] C rust (R0,t)=0 (16)
[0055] Among them, R i The inner diameter of the cement ring is equal to the outer diameter of the sleeve, and R0 is the outer diameter of the cement ring. Figure 1 As shown;
[0056] Initially, the rust concentration in the cement pores at the boundary is zero. At the start of the diffusion process, the rust concentration at the interface between the casing and the surrounding cement is obtained by equation (15). The interface between the casing and the surrounding cement is considered as a thick-walled cylinder, where R0 is a point far from the outer surface of the casing; the only unknown value is P. int (t), does it have a pressure matrix at the interface between the steel casing and the cement, because P int Since (t) has no expression, it is calculated using numerical methods, such as the finite difference method.
[0057] The radial backward Euler discretization method is used here, and the expression is as follows:
[0058]
[0059] From equation (17) to equation (20), the diffusion equation is discretized by n in time and by j in space, resulting in a tridiagonal matrix, which is then solved using the Thomas algorithm.
[0060] Step 3: Determine the volume of rust caused by cement expansion, and determine the radial expansion value around the cement.
[0061] The volume of rust penetrating into the cement matrix at each time step is calculated by integrating the concentration of rust products in the cement matrix. The expression is as follows:
[0062]
[0063] It should be noted that the total amount of rust is generated in several parts: including rust that has already filled the cement pores, rust stored in the interface transition zone, rust stored in the space left by the casing corrosion, and rust that causes expansion and further creates cracks around the cement.
[0064] Let the volume of rust causing the cement to expand be ΔV. rust The radial expansion around the cement, calculated from equation (22), is derived from equation (23) and expressed as follows:
[0065]
[0066] Where, δ Ri For R i Radial expansion caused by interfacial pressure.
[0067] Step 4: Determine the relationship between radial expansion and interfacial pressure.
[0068] Since the total volume of rust produced by corrosion is much larger than the volume of rust stored in the cement matrix, this problem can be considered as a hydrostatic pressure problem of a hollow, thick-walled cylinder at each time interval. When the pressure level is low, the interfacial pressure will not cause any cracks around the cement. Therefore, this step gives the linear elastic condition of the thick-walled cylinder, thereby deriving the relationship between radial expansion and interfacial pressure.
[0069] First, the stress expressions for hollow thick walls in different directions are shown in equations (24)-(26):
[0070]
[0071]
[0072] σrθ =0 (26)
[0073] Where, σ rr For radial stress, σ θθ Tangential stress;
[0074] Then, the relationship between tangential stress and radial displacement is established, as shown in equation (27);
[0075] Finally, combining equations (25) and (27), the linear elastic solution of the interfacial pressure is calculated, as shown in equation (28):
[0076]
[0077] Step 5: Determine the critical value of the interfacial pressure at which cracks occur.
[0078] Based on the above equation, the interfacial pressure before cement cracks form in oil and gas wells can be calculated using linear elasticity. As corrosion products penetrate, the interfacial pressure will continue to increase until it reaches a critical value, at which point cracks will form.
[0079] When the pressure accumulation caused by the tangential stress at the inner diameter exceeds the tensile strength of the surrounding cement, nonlinear fracture mechanics analysis must be used to calculate the interfacial pressure. In this step, a computational model is constructed, employing a virtual crack model to calculate the pressure change after the formation of an interfacial crack. The aim is to establish a relationship between crack size and radial propagation, and further derive the pressure generated by radial displacement.
[0080] Before constructing the virtual crack model, it is assumed that cracks will appear when the pressure exceeds the tensile strength of the cement material. As the crack size increases, the tangential stress will gradually decrease over time. When the crack size reaches a critical value, the tangential stress will decrease to zero.
[0081] like Figure 2 As shown, in the virtual crack model, the relationship between tangential stress and crack size is simplified to a linear function. When the tangential stress equals the tensile strength of the cement, there is no crack in the cement; during crack propagation, when the critical crack size (w) is reached... c When the tangential stress is zero, equation (29) describes this process;
[0082] like Figure 3 As shown, the area of the lower curve is the total energy absorbed during the entire crack propagation process, calculated by equation (30); combined with equations (29) and (30), the expression for the critical crack length is generated, calculated by equation (32); in addition, the critical fracture energy of oil well cement is obtained by testing through a three-point bending test, and the expression is as follows:
[0083]
[0084] In the virtual crack model, after the crack forms, the surrounding cement can be divided into two parts: the linear elastic part of the uncracked section and the softened part of the cracked section. Both parts have crack resistance, and the energy balance equation is shown in equation (32):
[0085]
[0086] Among them, P cr R is the resistance of the elastic part. cr The critical radius of the elastic and softened parts is given by , and the second part on the right side of equation (32) is the resistance from the cracked part. In equation (32), there is a constant "2" on both sides of the equation, which is due to the symmetry of the stress field under consideration.
[0087] Assuming two cracks are in opposite directions on the cross-section of the wellbore, such as... Figure 3 As shown. It should be mentioned that the number of cracks does not affect the form of formula (32), the only change is to replace "2" with "n", and calculate P based on the elastic solution. cr The value of is shown in equation (33); the critical radius will be determined based on R. i The radial displacement at the point is calculated as shown in equation (34):
[0088]
[0089]
[0090] The only unknown variable in equation (32) is the tangential stress σ. θθ (r), to obtain this tangential stress, first calculate the tangential elongation, from Figure 3 It can be seen that the total tangential elongation consists of two parts: the elongation of the elastic part and the width of the two cracks. Therefore, the elongation is obtained by equation (35), and the expression is as follows:
[0091] e(r)=2w(r)+(2πr-2w(r))ε t (r) (35)
[0092] Where εt is the tangential strain, because 2w(r)ε t The value of (r) is much smaller than 2πrε t (r) can be ignored, which means that equation (35) can be simplified to equation (36), as follows:
[0093] e(r)=2w(r)+2πrε t (r) (36)
[0094] When the radius r reaches the critical radius R crAt this point, the tangential stress of the cement equals its tensile strength; therefore, the crack will appear at the critical radius R. cr The crack width at point (36) is zero, and the Poisson effect is ignored here. The crack width equation is derived using equations (36) and (38). Finally, combining equations (39) and (31), the general expression for the tangential stress is obtained from equation (40), as follows:
[0095] e(R cr )=2πR cr ε cr (37)
[0096]
[0097] Combining the derived equations (33) and (41), the interfacial pressure P int The expression is:
[0098]
[0099] The equation can be solved numerically, and the expression is as follows:
[0100]
[0101] From this point on, the interfacial pressure after the crack appears can be calculated using equation (42).
[0102] Step 6: Analyze the interfacial pressure change pattern to obtain the final corrosion rate of the casing-cement ring under chloride corrosion environment.
[0103] It is worth noting that the chemical-mechanical coupling phenomenon still exists during crack propagation. The diffusion process in equation (13) needs to be considered in both crack-free and crack-containing calculations. Finally, the law of interface pressure change can be obtained through theoretical analysis, and the corrosion rate of the casing-cement ring under chloride corrosion environment can be clarified.
[0104] As the cementing interface pressure increases, the radial displacement of the wellbore also increases. This is due to the formation of a large amount of rust. The wellbore displacement-interface pressure curve can be divided into three parts: the linear elastic stage, the slope inflection stage, and the product compaction stage. In the first stage, there are no cracks in the cement, and the interface pressure is entirely subject to the linear resistance of the cement environment. In the second stage, the slope changes, the cement crack propagation time is fast, and the resistance is small. In the third stage, the cement crack propagation rate decreases, and there is greater resistance. To modify the corrosion process of the casing-cement sheath and delay the appearance of the second stage in the wellbore displacement-interface pressure curve as much as possible, it is recommended to add corrosion inhibitors to the cementing slurry to prevent premature appearance of cement cracks.
[0105] Example
[0106] The following four embodiments are based on specific working conditions and the aforementioned steps of the present invention, yielding relevant numerical values. The parameters are shown in the table below, and the calculation results of the four embodiments are obtained based on the parameters in the table.
[0107] Example 1 generally follows the steps outlined above. First, the degree of rust formation is calculated, then the radial expansion is calculated, and the interfacial pressure variation is calculated based on the displacement to obtain the interfacial pressure at different times (see...). Figure 4 The proportion of corrosion products; the final interfacial pressure distribution and corrosion product distribution, as shown in the figure. Figure 5 , Figure 6 As shown. The intermediate processes are omitted here.
[0108] Table 1. Relevant parameters and calculation results for the four embodiments.
[0109] Serial Number <![CDATA[R i (mm)]]> <![CDATA[R o (mm)]]> E(MPa) <![CDATA[f t (MPa)]]> <![CDATA[i corr / (μA / cm 2 )]]> <![CDATA[T model ]]> Example 1 8 34.88 27000 3.3 3.75 0.67 Example 2 8 56 27000 3.3 2.41 1.84 Example 3 8 78.3 27000 3.3 1.79 3.54 Example 4 8 86.2 27000 3.3 1.32 5.12
[0110] Following the steps outlined above in this invention, the wellbore corrosion in Example 1 was predicted, and the calculation results are shown below. Figure 4 , Figure 5 , Figure 6 As shown. Figure 4 This is the curve of interface pressure changing over time in Embodiment 1 of the method of the present invention; Figure 5 This is the curve showing the change in interface pressure with displacement at point ri in Embodiment 1 of the method of the present invention; Figure 6 This refers to the percentage of corrosion products at different radius positions in Embodiment 1 of the present invention.
[0111] Example 1: Field monitoring of the wellbore of well No. 1 in a certain well area showed that the cement sheath cracking time was 0.72 years, while the actual model prediction value was 0.67 years. Example 2: Field monitoring of the wellbore of well No. 2 in a certain well area showed that the cement sheath cracking time was 1.89 years, while the actual model prediction value was 1.84 years. Example 3: Field monitoring of the wellbore of well No. 3 in a certain well area showed that the cement sheath cracking time was 3.34 years, while the actual model prediction value was 3.54 years. Example 4: Field monitoring of the wellbore of well No. 4 in a certain well area showed that the cement sheath cracking time was 5.62 years, while the actual model prediction value was 5.57 years. It can be seen that the overall error rate of the prediction process according to the method of the present invention is 8%, which fully meets the quality requirements of field technology.
Claims
1. A method for predicting the corrosion rate of casing-cement sheath under chloride corrosion environment, characterized in that, Follow these steps: Step 1: Set initial conditions and construct a preliminary rust diffusion model. Step 2: Discretize the matrix to obtain the rust concentration pressure distribution. Step 3: Determine the volume of rust caused by cement expansion, and determine the radial expansion value around the cement. Step 4: Determine the relationship between radial expansion and interfacial pressure. Step 5: Determine the critical value of the interfacial pressure at which cracks occur; Step 6: Obtain the law of change of interfacial pressure and obtain the final corrosion rate of the casing-cement ring under chloride corrosion environment.
2. The method for predicting the corrosion rate of the casing-cement ring under chloride corrosion environment according to claim 1, characterized in that, In step 1, the specific process is as follows: The mass m lost by steel products during corrosion s The corrosion depth d per unit area is obtained by Faraday's law, as shown in equation (1). Then, equation (1) is divided by time to obtain the steel loss rate μ, as shown in equation (2). The corrosion depth d per unit area is calculated by dividing the density by equation (3), as shown in the following expression: Among them, a s It is the atomic mass of steel, n is the number of equal parts exchanged, F is the Faraday constant, and i corr Let ρ be the annual average corrosion density, t be time, μ be the steel loss rate, and ρ be the corrosion density. s Let d be the density of the steel, and d be the corrosion depth per unit area. Once the corrosion depth of the steel is obtained, the radius R is then calculated. i The volume of corrosion products within the cement ring is shown in equation (4): V rust =απ(2R i dd 2 ) (4) Wherein, α is the volume ratio of corrosion products to corroded material, and the value of α mainly depends on the chemical composition of rust. The rust in the corroded casing area and the interface transition zone must be subtracted from the total amount of rust generated, as shown in equation (5): V eff =V rust -V ITZ -V cs (5) Among them, V ITZ V represents the volume of the interface transition region. cs V represents the volume of the corroded casing. eff It is the volume of rust that can generate pressure and further penetrate into the cement matrix, V nist The relevant expression for the volume of rust is: V ITZ =d ITZ A Steel (7) Among them, V rust It is the volume of rust formation, h i The thickness of the interface transition zone; The porosity of the interface transition zone; d ITZ A is the volume of a porous region per unit area that can absorb corrosion. steel It is the surface area of the sleeve; When V eff When the value is greater than zero, it indicates that the voids left by casing corrosion and the voids in the interface transition zone are filled with corrosion products. Once these spaces are filled, rust will begin to penetrate into the surrounding cement matrix. The equation for this diffusion process is shown in equation (9): Among them, C rust It is the concentration of rust in the pores, κ rust It is the viscosity of the corrosion products, η rust P is the diffusion coefficient of rust. rust This refers to the pressure distribution based on rust concentration.
3. The method for predicting the corrosion rate of the casing-cement ring under chloride corrosion environment according to claim 1, characterized in that, In step 2, the specific process is as follows: A linear state equation is adopted, as shown in equation (10): C rust =βP rust (10) Where β is a state function determined by the permeation process; C p f represents the porosity of the cement matrix. t C is the tensile strength of the cement matrix; when all the porous media are filled in the cement matrix. rust =C p At the same time, P rust =f t ; Additional corrosion formation leads to pressure buildup in the cement. When the pressure generated by corrosion exceeds the tensile strength of the cement, cracks will form in the cement, leading to the conclusion shown in equation (11): Combining equations (9) and (11), the diffusion equation is revised as follows: Where r is the radius of the surrounding cement; The boundary conditions and initial conditions of equation (13) are shown below: C rust (r,0)=0 (14) C rust (R i ,t)=βP int (t) (15) C rust (R0,t)=0 (16) Among them, R i R0 is the inner diameter of the cement ring, which is equal to the outer diameter of the sleeve. Initially, the rust concentration in the cement pores at the boundary is zero. At the start of the diffusion process, the rust concentration at the interface between the casing and the surrounding cement is obtained by equation (15). The interface between the casing and the surrounding cement is considered as a thick-walled cylinder, where R0 is a point far from the outer surface of the casing; the unknown value is P. int (t), does it have a pressure matrix at the interface between the steel casing and the cement, because P int (t) has no expression; it is calculated using numerical methods. The radial backward Euler discretization method is used here, and the expression is as follows: From equation (17) to equation (20), the diffusion equation is discretized by n in time and by j in space, resulting in a tridiagonal matrix, which is then solved using the Thomas algorithm.
4. The method for predicting the corrosion rate of the casing-cement ring under chloride corrosion environment according to claim 1, characterized in that, In step 3, the specific process is as follows: The volume of rust penetrating into the cement matrix at each time step is calculated by integrating the concentration of rust products in the cement matrix. The expression is as follows: The total amount of rust is divided into several parts: rust that has already filled the cement pores, rust stored in the interface transition zone, rust stored in the space left by the casing corrosion, and rust that causes expansion and further creates cracks around the cement. Let the volume of rust causing the cement to expand be ΔV. rust The radial expansion around the cement, calculated from equation (22), is derived from equation (23) and expressed as follows: Where, δ Ri For R i Radial expansion caused by interfacial pressure.
5. The method for predicting the corrosion rate of the casing-cement ring under chloride corrosion environment according to claim 1, characterized in that, In step 4, the specific process is as follows: First, the stress expressions for hollow thick walls in different directions are shown in equations (24)-(26): s rθ =0 (26) Where, σ rr For radial stress, σ θθ Tangential stress; Then, the relationship between tangential stress and radial displacement is established, as shown in equation (27); Finally, combining equations (25) and (27), the linear elastic solution of the interfacial pressure is calculated, as shown in equation (28):
6. The method for predicting the corrosion rate of the casing-cement ring under chloride corrosion environment according to claim 1, characterized in that, In step 5, the specific process is as follows: Before constructing the virtual crack model, it is assumed that cracks will appear when the pressure exceeds the tensile strength of the cement material. As the crack size increases, the tangential stress will gradually decrease over time. When the crack size reaches the critical value, the tangential stress will decrease to zero. In the virtual crack model, the relationship between tangential stress and crack size is simplified to a linear function. When the tangential stress equals the tensile strength of the cement, there is no crack in the cement; during crack propagation, when the critical crack size (w) is reached... c When the tangential stress is zero, equation (29) describes this process; The area under the curve represents the total energy absorbed during the entire crack propagation process, calculated using equation (30). Combining equations (29) and (30), the expression for the critical crack length is derived, calculated using equation (32). Furthermore, the critical fracturing energy of oil well cement is obtained through a three-point bending test, expressed as follows: In the virtual crack model, after the crack forms, the surrounding cement is divided into two parts: the linear elastic part of the uncracked section and the softened part of the cracked section. The energy balance equation is shown in equation (32). Among them, P cr R is the resistance of the elastic part. cr The critical radius of the elastic and softened parts is given by , and the second part on the right side of equation (32) is the resistance from the cracked part. Assuming two cracks are in opposite directions on the cross-section of the wellbore, P is calculated based on the elastic solution. cr The value of is shown in equation (33); the critical radius will be determined based on R. i The radial displacement at the point is calculated as shown in equation (34): The unknown variable in equation (32) is the tangential stress σ. θθ (r), in order to obtain the tangential stress, the tangential elongation is first calculated. The total tangential elongation includes two parts: the elongation of the elastic part and the width of the two cracks. Therefore, the elongation is obtained by equation (35), and the expression is as follows: e(r)=2w(r)+(2πr-2w(r))ε t (r) (35) Where εt is the tangential strain, because 2w(r)ε t The value of (r) is much smaller than 2πrε t If (r) is ignored, then equation (35) simplifies to equation (36), as follows: e(r)=2w(r)+2πrε t (r) (36) When the radius r reaches the critical radius R cr At this point, the tangential stress of the cement equals its tensile strength; therefore, the crack will appear at the critical radius R. cr The crack width at point (36) is zero, and the Poisson effect is ignored here. The crack width equation is derived using equations (36) and (38). Finally, combining equations (39) and (31), the tangential stress is obtained from equation (40), and the expression is as follows: e(R cr )=2πR cr e cr (37) Combining the derived equations (33) and (41), the interfacial pressure P int The expression is: The equation can be solved numerically, and the expression is as follows: From this point on, equation (42) can be used to calculate the interfacial pressure after the crack appears.
7. The method for predicting the corrosion rate of the casing-cement ring under chloride corrosion environment according to claim 1, characterized in that, In step 6, the specific process is as follows: The interfacial pressure variation law was obtained through theoretical analysis, and the corrosion rate of the casing-cement ring under chloride corrosion environment was clarified. The wellbore displacement-interface pressure curve is divided into three parts: linear elastic stage, slope inflection stage, and product compaction stage. In the first stage, there are no cracks in the cement, and the interfacial pressure is completely subject to the linear resistance of the cement environment. In the second stage, the slope changes, the cement crack propagation time is fast, and the resistance is small. In the third stage, the cement crack propagation rate decreases, and there is greater resistance.