A method for testing cement-casing cementing strength based on friction effect

Abstract

The present application relates to the technical field of oil exploitation, and particularly relates to a method for testing cement-casing cementing strength based on friction effect, which comprises the following steps: performing cement-casing interface cementing strength experiment, collecting displacement, pressure and strain data of strain gauge of cement extrusion, and drawing load-displacement curve; performing rock mechanics experiment to obtain cement stone elastic parameters; establishing cement-casing interface cementing strength model of friction effect; constructing cohesive unit of friction effect by using Fortran; establishing cement-casing geometric model in ABAQUS software, inputting elastic parameters of cement-casing into unit body of the geometric model; and obtaining calculation results of cement-casing cementing surface according to finite element simulation results. In the present application, the cement-casing interface cementing strength is characterized by pressure when the interface is damaged, but in the damage process, there is friction effect in addition to cementing effect, and it is inaccurate to use shear strength to characterize cementing strength.

Description

Technical Field

[0001] This invention relates to the field of oil extraction technology, and in particular to a method for testing the cement-casing bond strength based on the friction effect. Background Technology

[0002] Cementing is a crucial step in oil extraction, and its quality directly impacts the safety and future prospects of an oilfield. The casing-cement sheath-formation assembly formed after cementing is subjected to complex thermo-baric stress changes under high temperature and pressure, making it prone to micro-annular gaps and cement sheath seal failure. Formation fluids then intrude into these gaps and migrate upwards, damaging the cement sheath itself or the cemented interface, leading to annular pressure and posing a serious threat to well life, well quality, and the safety of personnel. Therefore, experimentally measuring the cement slurry system's bonding strength and identifying the main factors affecting interfacial bonding strength is of great significance for optimizing the cement slurry system.

[0003] The bonding strength testing method proposed in CN105092465B mainly consists of a hydraulic power system, a top column, and a pressure sensor. The hydraulic power system drives the top column to move the bonding cylinder upwards until the cement loosens from the inner wall of the cylinder. The pressure sensor records the pressure value at this point and calculates the bonding strength. The bonding strength testing method proposed in CN109342195B mainly includes a metal tensile rod and a hydraulic tensile testing machine. The two ends of the sleeve-cement sample are clamped on the hydraulic tensile testing machine. Loading is stopped immediately after the sample breaks, and the load value is recorded. The bonding strength of the cement-sleeve interface is obtained by dividing the load by the area of ​​the cement paste. Both methods characterize the cement-sleeve interface bonding strength by the pressure at interface failure. However, in addition to bonding, friction also occurs during interface failure, making it inaccurate to characterize bonding strength using shear strength. CN111504898B proposes a method for testing the bonding strength of cement rings using the gas channeling method. A pressure gauge is connected to the air inlet of the casing, and a water tank is connected to the air outlet. A high-pressure gas cylinder is turned on until bubbles emerge from the water tank. The value on the pressure gauge is used to characterize the bonding strength of the cement-casing interface. This method is not only complex to operate and involves safety issues, but the accuracy of the results is also affected by the permeability of the cement stone during the test. Summary of the Invention

[0004] To address the shortcomings of existing methods, the technical solution adopted in this invention is: a method for testing the cement-casing bond strength based on friction effect, comprising the following steps:

[0005] Step 1: Collect displacement, pressure, and strain data of strain gauges of cement ejected through cement-casing interface bonding strength test, and plot load-displacement curves;

[0006] Step 2: Conduct rock mechanics tests to obtain the elastic parameters of the cement stone;

[0007] Step 3: Establish a cement-casing interface bonding strength model based on friction effects;

[0008] Furthermore, the formula for the cement-casing interface bond strength model is as follows:

[0009] τ=fσ r +C (5)

[0010] In the formula, τ is the tangential stress at the contact interface, f is the interfacial friction coefficient, and σ is the tangential stress at the contact interface. r C is the normal stress at the cement-casing interface, and C is the bonding force at the contact interface.

[0011] Step 4: Construct cohesive units for friction effects using Fortran;

[0012] Furthermore, step four specifically includes:

[0013] By introducing damage variables to measure the damaged and undamaged areas of the interface, and introducing friction effects during the damage process, the change in the bonding strength of the cement-casing interface is described.

[0014] The formula for calculating the displacement of the damaged portion is:

[0015] δ d =δ dc +δ di (6)

[0016] In the formula, δ dc It is elastic displacement, δ di It is an inelastic displacement;

[0017] The stress in the undamaged portion is calculated using the following formula:

[0018] τ u =K1δ u =K1δ (7)

[0019] In the formula, δ u δ represents the displacement of the damaged part, and K1 is the current displacement; K1 is the initial shear stiffness.

[0020] The formula for calculating the stress in the damaged area is:

[0021] τ d =K2(δ-δ di (8)

[0022] In the formula, δ di It is an inelastic displacement;

[0023]

[0024] In the formula, δr σ represents the displacement at the end of the damage; N For normal stress, δ is the friction angle; p This represents the displacement at the onset of the damage.

[0025] The stress evolution law of the damaged part is as follows:

[0026]

[0027] when When, the stress τ in the damaged part d for:

[0028]

[0029] when At that time, the tangential stress τ at the contact interface is:

[0030] τ=(1-D)τ u +Dτ d (12)

[0031] In the formula, τ u The shear stress is in the undamaged portion;

[0032] Furthermore, the formula for the damage variable D is:

[0033]

[0034] Where δ is the current displacement;

[0035]

[0036] The formula for calculating the tangential stress τ at the contact interface is:

[0037]

[0038] Step 5: Based on the indoor experimental conditions, establish a cement-casing geometric model in ABAQUS software and input the elastic parameters of the cement-casing into the element body of the geometric model.

[0039] Step 6: Based on the finite element simulation results, obtain the calculation results of the cement-casing bonding surface;

[0040] Furthermore, specifically including:

[0041] Stress-displacement curves are plotted using stress contour plots;

[0042] By fitting the simulated stress-displacement curve with the experimentally measured stress-displacement curve, the interfacial friction coefficient f and the contact interface adhesion force C are obtained, which inversely derive the constitutive relationship of the cement-casing interface bonding strength.

[0043] Calculate the cement-casing interface bonding strength.

[0044] Furthermore, the formula for the cement-casing interface bond strength is:

[0045] F = C * A (16)

[0046] In the formula, F is the cement-casing interface bonding strength, C is the contact interface adhesion force, and A is the shear area of ​​the sample.

[0047] The beneficial effects of this invention are:

[0048] 1. Based on the coupling of interfacial adhesion and friction, numerical simulation is performed on the cement-casing interface bonding strength test. A cohesive element considering the friction effect is introduced to derive the bonding strength parameters, which can accurately characterize the bonding strength of the cement-casing interface.

[0049] 2. The numerical simulation results are highly consistent with the experimental results, verifying the feasibility of the cement sleeve interface bonding strength model for experimental research on interface bonding strength, which is of great significance for optimizing the cement slurry system. Attached Figure Description

[0050] Figure 1 This is a flowchart of the method for testing the cement-casing bond strength based on the friction effect of the present invention;

[0051] Figure 2 It is a model diagram of the cohesion-damage-friction at the cement-casing interface;

[0052] Figure 3 This is a schematic diagram of the experimental setup;

[0053] Figure 4 (a) and (b) are schematic diagrams of the cement-casing geometric model and the mesh generation of the cement-casing geometric model, respectively;

[0054] Figure 5 This is a contour plot of the stress calculation results for the cement-casing geometric model.

[0055] Figure 6 The stress-displacement results are shown in the figure for the cement-casing geometric model.

[0056] Figure 7 This is a magnified view of the local stress-displacement of the cement-casing geometry model;

[0057] Figure 8 A comparison chart of experimental and numerical simulation results;

[0058] In the diagram, 1 is the steel cylinder, 2 is the base, 3 is the top cover, 4 is the piston, 5 is the heating jacket, 6 is the strain gauge, 7 is the sealing ring, and 8 is the constant pressure pump. Detailed Implementation

[0059] The present invention will be further described below with reference to the accompanying drawings and embodiments. The drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0060] like Figure 1 As shown, a method for testing the cement-casing bond strength based on the friction effect includes the following steps:

[0061] Conduct cement-casing interface bonding strength tests;

[0062] like Figure 3 The diagram shows the experimental setup, which consists of a steel cylinder 1, a base 2, a top cover 3, a sealing ring 7, a constant pressure pump 8, a piston 4, and a heating jacket 5. The sealing base 2 is assembled, the prepared cement slurry is poured into the steel cylinder 1, the piston 4 is placed inside the steel cylinder 1 to expel the air inside the steel cylinder 1, the top cover 3 is sealed and assembled, and strain gauges 6 are installed on the outside of the steel cylinder 1.

[0063] Curing: Wrap a heating jacket 5 around the outer wall of the steel cylinder and cure it under certain temperature and confining pressure.

[0064] Experimental loading: After curing, once the sample has cooled to room temperature, remove base 1 and heating jacket 5, turn on constant pressure pump 8, and inject water through constant pressure pump 8 to push piston 4 until the cement is pushed out.

[0065] Step 1: Collect the pressure applied by the piston, the displacement of the cement, and the strain of the strain gauges, and plot the load-displacement curve;

[0066] Based on the strain of the circumferential strain gauge 6 on the outer side of the steel cylinder 1 collected during the experiment, the circumferential stress σ on the outer side of the steel cylinder 1 is obtained. θ The calculation formula is:

[0067] σ θ =Eε θ (1)

[0068] In the formula, E is the elastic modulus of the casing, and ε θ The value represents the circumferential strain on the outer side of the steel cylinder.

[0069] Based on the thick-walled cylinder theory, the normal stress σ at the cement-casing interface is obtained. r The calculation formula is:

[0070]

[0071]

[0072] σ r =p1 (4)

[0073] Where a is the inner radius of the steel cylinder, b is the outer radius of the steel cylinder, r is any radius (a≤r≤b), σ r This refers to the normal stress at the cement-casing interface.

[0074] Step 2: Conduct rock mechanics tests to obtain the elastic parameters of the cement stone. The test sample is the cement stone obtained from the cement-casing interface bonding strength test.

[0075] The elastic parameters of cement stone include the elastic modulus E of cement. c Poisson's ratio is a parameter of the cement model that is entered into the numerical simulation interface.

[0076] Step 3: Establish a cement-casing interface bonding strength model based on friction effects;

[0077] The formula for the cement-casing interface bond strength model is:

[0078] τ=fσ r +C (5)

[0079] In the formula, τ is the tangential stress at the contact interface, f is the interfacial friction coefficient, and σ is the tangential stress at the contact interface. r C is the normal stress at the cement-casing interface, and C is the bonding force at the contact interface.

[0080] Step 4: Construct cohesive units for friction effects using Fortran;

[0081] Since the bilinear structural model inherent in cohesive elements cannot simulate frictional effects, it is necessary to develop new cohesive force models that incorporate frictional effects, such as... Figure 2 As shown, the 'damaged' and 'undamaged' regions of the interface are measured by introducing a damage variable (0 <= D <= 1), and the friction effect is introduced during the 'damage' process to describe the change in the bonding strength of the cement-casing interface.

[0082] The interface is divided into two parts: fully damaged and undamaged. Assuming that friction occurs only in the fully damaged part, the interfacial tension of the undamaged part is directly added to the contact action (contact pressure and friction) of the fully damaged part, thus combining interfacial damage and friction.

[0083] When δ < δ p At this time, in the linear elastic stage, the interface deformation is elastic, and the damage variable D = 0;

[0084] When δ p <δ<δ r At this time, the interface begins to gradually deteriorate, and the frictional action begins to evolve. <D<1;

[0085] When δ > δ rAt this point, the interface is completely damaged, and only kinetic friction is in effect; therefore, D = 1.

[0086] Within the undamaged portion of the infinitesimal region, the relative displacement of the interface is considered perfectly elastic. In the damaged portion, the relative displacement of the interface can be divided into two stages: the elastic displacement stage and the inelastic displacement stage. The displacement δ of the damaged portion is calculated. d The formula is:

[0087] δ d =δ dc +δ di (6)

[0088] In the formula, δ dc It is elastic displacement, δ di This is an inelastic displacement.

[0089] The stress-strain relationship in the undamaged portion is linear:

[0090] τ u =K1δ u =K1δ (7)

[0091] In the formula, δ u δ represents the displacement of the damaged portion, and K1 is the initial shear stiffness, which can be obtained from the experimental data. δ p τ is the displacement at the onset of damage. P τ is the shear stress at the onset of damage. f This represents the shear stress at the end of the damage.

[0092] Stress τ in the damaged area d for:

[0093] τ d =K2(δ-δ di (8)

[0094] In the formula, δ di For inelastic displacement, K2 is used to describe the elastic interaction caused by interface roughness. K2 is related to the normal pressure acting on the interface and the interface friction angle, and can be expressed by the following formula:

[0095]

[0096] In the formula, δ r σ represents the displacement at the end of the damage; N The normal stress is numerically equal to σ calculated based on the theory of thick-walled cylinders. r , Let δ be the friction angle. r This represents the displacement at the end of the damage.

[0097] The stress evolution law of the damaged part is as follows:

[0098]

[0099] when When, the stress τ in the damaged part d for:

[0100]

[0101] when At that time, the tangential stress τ at the contact interface is:

[0102] τ=(1-D)τ u +Dτ d (12)

[0103] In the formula, τ u The shear stress is in the undamaged portion;

[0104] The formula for damage variable D is:

[0105]

[0106] Where δ is the current displacement;

[0107]

[0108] In summary, the formula for the tangential stress at the contact interface is:

[0109]

[0110] The corresponding pseudocode is as follows:

[0111]

[0112]

[0113] Step 5: Based on the indoor experimental conditions, establish a cement-casing geometric model in ABAQUS software, and input the elastic parameters of the cement and casing into the element cells of the geometric model; the established geometric model is as follows. Figure 4 As shown in (b). Figure 4 (a) is a schematic diagram of the corresponding experimental model. The model dimensions are shown in Table 1, and the material parameters are shown in Table 2.

[0114] Table 1 Geometric Model Dimensions of Cement-Casing

[0115] Material Outer diameter (mm) Thickness (mm) Height (mm) casing 127 5.21 180

[0116] Table 2 Material Parameters

[0117] Material Elastic modulus E / Gpa Poisson's ratio cement 13.8 0.25 casing 210 0.3

[0118] The input parameters for the cohesive material interface are shown in Table 3. The analysis step, load, and boundary conditions are then determined. The component is meshed, selecting the default element type. A zero-thickness cohesive element is inserted at the cement-sleeve interface, selecting the cohesive element type. The meshing result is shown below. Figure 3 As shown in Table 3, the mechanical parameters obtained from the cementation strength experiment are entered into the cohesive material interface, which correspond to props(n) in the program.

[0119] Table 3 Cohesive material parameters

[0120] Create an analysis step, select an initial increment step of 0.01, a minimum increment step of 1e-5, and leave the rest as default settings.

[0121] Define the loads and boundary conditions, input the displacement load P acting on the cement in the model, constrain the bottom of the casing, constrain all degrees of freedom, and ensure the convergence of the calculation results.

[0122] Step Six: Based on the finite element simulation results, obtain the calculation results of the cement-casing bonding surface, and perform contour plot analysis. The stress contour plot is shown below. Figure 5 As shown. Extract the data and plot the corresponding stress-displacement curves, as shown. Figure 6 and Figure 7 As shown, the curve was fitted to the experimental curve, and the interface friction coefficient f was adjusted based on the fitting result. The fitting result is shown in the figure. Figure 8 As shown, f and C are required to derive the constitutive relationship of the cement-casing interface bonding strength, thus completing the construction of the constitutive model of the cement-casing interface bonding strength.

[0123] The cement-casing interface bonding strength is characterized by the following formula, calculated based on numerical simulation inversion results:

[0124] F = C * A (16)

[0125] In the formula, F is the cement-casing interface bonding strength, C is the contact interface adhesion force, and A is the shear area of ​​the sample.

[0126] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for testing the cement-casing bond strength based on the friction effect, characterized in that, Includes the following steps: Step 1: Conduct a cement-casing interface bonding strength test, collect displacement, pressure and strain data of the cement ejection and strain gauges, and plot the load-displacement curve; Step 2: Conduct rock mechanics tests to obtain the elastic parameters of the cement stone; Step 3: Establish a cement-casing interface bonding strength model based on friction effects; Step 4: Construct cohesive units for friction effects using Fortran; Specifically, it includes: By introducing damage variables to measure the damaged and undamaged areas of the interface, and introducing friction effects during the damage process, the change in the bonding strength of the cement-casing interface is described. The formula for calculating the displacement of the damaged portion is: （6） In the formula, It is elastic displacement. It is an inelastic displacement; The stress in the undamaged portion is calculated using the following formula: （7） In the formula, The displacement of the damaged part. This is the current displacement; It is the initial shear stiffness; The formula for calculating the stress in the damaged area is: （8） In the formula, It is an inelastic displacement; （9） In the formula, This represents the displacement at the end of the damage; For normal stress, It is the friction angle; This represents the displacement at the onset of the damage. The stress evolution law of the damaged part is as follows: （10） when At that time, the stress in the damaged part for: （11） when At that time, the tangential stress at the contact interface for: （12） In the formula, The shear stress is in the undamaged portion. D For damage variables; The formula for the damage variable is: （14） Calculate the tangential stress at the contact interface The formula is: （15） Step 5: In ABAQUS software, establish a cement-casing geometric model and input the elastic parameters of the cement-casing into the element body of the geometric model; Step 6: Based on the finite element simulation results, obtain the calculation results of the cement-casing bonding surface; Specifically, it includes: Stress-displacement curves are plotted using stress contour plots; By fitting the simulated stress-displacement curve with the experimentally measured stress-displacement curve, the interfacial friction coefficient of the constitutive relationship of the cement-casing interface bonding strength was derived. f and the adhesion of the contact interface ; Calculate the cement-casing interface bond strength; The formula for the cement-casing interface bond strength is: F = A （16） In the formula, F For the cement-casing interface bonding strength, For the bonding force at the contact interface, A This represents the shear area of ​​the sample.

2. The method for testing cement-casing bond strength based on friction effect according to claim 1, characterized in that, The formula for the cement-casing interface bond strength model is: （5） In the formula, τ is the tangential stress at the contact interface. f The coefficient of interfacial friction, For the normal stress at the cement-casing interface, This refers to the adhesive force at the contact interface.

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