Simulation method of cement sheath sealing performance considering wellbore mud cake and fracturing conditions

Abstract

The present invention discloses a method for simulating cement ring sealing performance considering the mud cake of the wellbore and the fracturing working conditions, comprising the following steps: establishing a three-dimensional deformable solid model of the wellbore, and then dividing the model from the inside to the outside into casing, cement ring, mud cake and formation in turn and performing meshing; assigning material parameters to the casing, cement ring and formation; establishing an element set for defining the mud cake material, and then assigning the element set to the grid of the mud cake, considering the heterogeneity of the mud cake, and obtaining the material parameters of the mud cake based on Python code; setting boundary conditions, and applying loads to the casing at the same time; inserting cohesive units for the interface between the casing and cement ring, the interface between the cement ring and the mud cake, and the interface between the mud cake and the formation, respectively, performing linear damage evolution based on Maxs damage, and then obtaining the equivalent plastic strain of the cement ring during the load loading process and the size of the micro-gap. The present invention takes into account the actual existence of the mud cake of the wellbore, and can simulate the development of the interface micro-gap of the cementing interface.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas field development, and in particular to a method for simulating cement ring sealing performance taking into account well wall mud cake and fracturing conditions. Background Art

[0002] In the field of oil and gas exploration and development, unconventional resources have great potential. The use of large-scale fracturing technology is one of the key measures to increase the production capacity of unconventional oil and gas. However, during fracturing operations, the cement sheath is not only prone to fatigue damage under extreme conditions such as cyclic loads, high temperature and high pressure, but may also produce interface micro-gaps and even cracks, which seriously threaten the sealing integrity of the cement sheath. The wellbore cement sheath consists of two interfaces, the casing and the cement sheath as the first interface, and the cement sheath and the formation as the second interface. During the drilling process, a large amount of mud cake will adhere to the well wall. This mud cake is difficult to remove by circulating drilling fluid before cementing construction, which leads to the contact between cement slurry and mud cake during cementing. The mud cake has low strength and is prone to form a weak bonding surface. This weak bonding surface is prone to failure during fracturing, resulting in interface micro-gaps. Therefore, it is of great academic value and practical significance to conduct in-depth research on the mechanical behavior and damage mechanism of the cement sheath during fracturing under the conditions of the second interface mud cake characteristics.

[0003] In addition, with the increasing maturity of the application of numerical calculation methods in engineering problems and scientific research, most scholars use numerical simulation methods to study the sealing integrity of cement sheaths. However, in the research process, the ideal elastic-plastic model is often used to describe the stress-strain characteristics of cement sheaths, ignoring the changes of microcracks and micropores inside cement stone under fracturing alternating stress loads and their influence on the overall performance of cement sheaths. In fact, these microcracks and micropores will change under the action of loads, which may form connections and cause cement stone damage, showing characteristics such as stiffness degradation. Therefore, the ideal model cannot accurately reflect the mechanical behavior of cement sheaths under actual working conditions. The simulation results calculated by the ideal model are quite different from the actual results and do not have a high reference value. In order to obtain a more realistic model, some scholars have proposed a strain softening model to describe the stress-strain characteristics of cement sheaths to improve the accuracy of the model. At present, in theoretical research, some scholars have introduced damage mechanics theory to explore the mechanical properties of cement sheaths after plastic deformation under alternating loads. The research results show that the tensile and compressive elastic deformation properties of cement sheaths are crucial to the formation of microgap and tensile failure of cement sheaths. These theoretical results provide new ideas for more accurate evaluation of the sealing performance of cement sheaths. Summary of the invention

[0004] In order to solve at least one of the above problems, the present invention proposes a method for simulating cement ring sealing performance taking into account well wall mud cake and fracturing conditions.

[0005] The technical solution of the present invention is: a method for simulating cement ring sealing performance considering well wall mud cake and fracturing conditions, comprising the following steps:

[0006] S1. Based on Abaqus software, a three-dimensional deformable solid model of the wellbore is established, and then the model is divided into casing, cement ring, mud cake and formation from the inside to the outside and meshed;

[0007] S2. Assign material parameters to the casing, cement sheath and formation based on measured values;

[0008] S3, establish an element set for defining the mud cake material, then assign the element set to the grid of the mud cake, consider the heterogeneity of the mud cake, and obtain the material parameters of the mud cake based on Python code;

[0009] S4, insert cohesive units into the interface between casing and cement sheath, the interface between cement sheath and mud cake, and the interface between mud cake and formation, and perform linear damage evolution based on Maxs damage;

[0010] S5. Set boundary conditions for the model and apply loads to the casing based on actual working conditions. Then solve the model to obtain the interface separation of the cement sheath and the equivalent plastic strain during load loading.

[0011] Beneficial effects: The present invention takes into account the actual existence of mud cake on the well wall. When alternating loads are applied to the wellbore, the existence of mud cake has a significant impact on the stress-strain response of the cement sheath. It can also simulate the development of the interface micro-gap between the cementing interface (between the cement sheath and the formation), and explains the potential risk of sealing failure, providing a reference for the study of cement sheath sealing and related engineering evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 A model diagram of an embodiment of the present invention;

[0013] Figure 2 is an equivalent plastic strain cloud diagram of an embodiment of the present invention;

[0014] Figure 3 This is a diagram of the interface micro-gap after a load is applied in an embodiment of the present invention;

[0015] Figure 4 This is a graph showing the change of equivalent plastic strain of the inner wall of the cement sheath with the number of cycles according to an embodiment of the present invention;

[0016] Figure 5 The micro-gap development diagram of the interface of the cement sheath under different cycle times of the embodiment of the present invention;

[0017] Figure 6 This is the interface micro-gap diagram after the load is applied to the comparative scale;

[0018] Figure 7 This is the interface micro-gap development diagram of the comparative cement sheath under different cycle numbers. DETAILED DESCRIPTION

[0019] The specific implementation modes of the present invention will be described clearly and completely below with reference to examples and drawings. Obviously, the described examples are only some embodiments of the present invention, rather than all embodiments.

[0020] A method for simulating cement sheath sealing performance considering well wall mud cake and fracturing conditions, comprising the following steps:

[0021] S1. Based on Abaqus software, a three-dimensional deformable solid model of the wellbore is established, and then the model is divided into casing, cement ring, mud cake and formation from the inside to the outside and meshed;

[0022] Specifically, this embodiment is a redevelopment and application based on Abaqus software, which is a finite element simulation software. In this embodiment, a three-dimensional deformable solid model of the wellbore is first established in the Part module of the Abaqus software. In actual operation, we usually need to set the size of the model to at least 10 times the actual wellbore size, which is mainly to reduce the boundary effect of the model: when the model size is small, the conduction of stress and strain cannot be fully developed, which in turn affects the accuracy of the simulation.

[0023] After modeling, it is necessary to divide the model from the inside to the outside into casing, cement ring, mud cake and formation according to the actual situation. The thickness ratio between each layer is set according to the actual situation. At the same time, for the overall size of the model, the inventors found that if the size of the model is small, in the subsequent simulation process, due to the influence of the boundary effect, the stress and strain of the cement ring may not be able to be carried out, thereby affecting the accuracy of the model. To this end, after a large number of experiments, the inventors found that when the size of the model is set to at least 10 times the actual wellbore size, the final model established can effectively overcome the influence of the boundary effect and has a higher accuracy. The final model is as follows Figure 1 shown.

[0024] S2. Assign material parameters to the casing, cement sheath and formation based on measured values;

[0025] The measured values ​​are parameters obtained from indoor tests or logging data according to actual conditions, including elastic modulus, yield strength and Poisson's ratio. In actual operation, this step is performed in the Property module to assign material parameters to the casing, cement sheath and formation respectively.

[0026] At the same time, in the present invention, in addition to the above-mentioned material parameters, considering the characteristics of the cement sheath that it is easy to undergo plastic deformation and plastic damage under external load conditions, while the formation and casing change little and are not the research focus of the embodiments of the present invention, therefore, in this embodiment, it is also necessary to set the cement sheath as a plastic damage material, and set the casing and formation as elastic materials, in order to facilitate subsequent model calculations.

[0027] The plastic damage model of the cement sheath is as follows:

[0028]

[0029] In the formula, σ ij is the Cauchy stress; ij and are the total strain and plastic strain, respectively; is elastic stiffness, MPa; d s is the damage variable;

[0030] The damage variable d s Obtained by the following formula: W ε =∫σdε=∫f(ε)dε, where W0 is the strain energy density in the lossless state; E0 is the initial elastic modulus; ε is the compressive strain; σ is the stress tensor; W ε is the strain energy density in the damaged state.

[0031] In this embodiment, material parameters are shown in Table 1.

[0032] Table 1 Material parameter data table of casing / cement / mud cake / formation

[0033]

[0034] At the same time, it can be seen from Table 1 that in this embodiment, the material parameters of the casing, cement ring and formation are relatively uniform, so they can be uniformly assigned values. However, for the mud cake, its parameter range spans a large range and it is difficult to uniformly assign values.

[0035] S3, establish an element set for defining the mud cake material, then assign the element set to the grid of the mud cake, consider the heterogeneity of the mud cake, and obtain the material parameters of the mud cake based on Python code;

[0036] S31. Use Tool to create an element set. First, use Tool to create an element set and name it all. Import the sys module from the Python library provided by Abaqus to operate the Python runtime environment; import the os module for environment variable access, path operations, etc.; import the random module and use the randint function in the module to achieve random distribution in subsequent steps.

[0037] S32, creating a function of material parameters and mud cake elastic properties, dividing the element set into a plurality of element subsets, and randomly assigning a cross section containing mud cake material parameters to each subset;

[0038] Define the function Cre_mat_pro, which is used to create section properties, including material name, elastic modulus, yield strength, and Poisson's ratio; create a material in Model-1, including elastic properties and plastic properties; create a homogeneous solid section in Model-1, which is associated with the material just created, and does not need to specify the thickness;

[0039] Define the function Crea_elem_sets, which contains parameters n and matifo, to divide all elements of Part-1 in Model-1 into several element sets and randomly assign a section to each set. Introduce the variable p to obtain the reference of Part-1 in Model-1; introduce the variable elsts to obtain all elements in the element set named all; call the function len to calculate the number of elements in the all set and define it as elenum; call the function len to calculate the length of the matifo list, that is, the number of available section names, and define it as matnum;

[0040] S33, create a variable p to obtain a model reference, store it in the variable p, and then access and operate the component through p; create a variable p to obtain a model reference, store it in the variable p, and then access and operate the component through p. Get a list of all elements from the Element Set created by the component, call the len function to calculate the number of elements in the set as elenum and the number of available sections as matnum.

[0041] S34, use a for loop to traverse the required number of sets, and use the total number of elements in the element set / n+1 as the upper limit of the loop, where n represents the number of elements expected in each element subset in S32;

[0042] Use a for loop to create an element set, set the number of iterations to i, and the total number of elements to elenum. If elenum is not an integer multiple of n, the last set will be skipped, so elenum / n+1 is used as the upper limit of the loop. Inside the loop, first determine whether it is the last set. If (i!=elenum / n) it is not the last set, then create a new set set2 with a block size of n elements. Otherwise, include all the remaining elements and create a new set set2.

[0043] Call the randint function to randomly select an index of a section name from the matifo list 0 to matnum-1, assign the section to the newly created set set2, and define the region variable as region. Call the SectionAssignment function to specify the section parameters of the region region, including sectionName (the section name to be assigned, a section name randomly selected from the matifo list), offset (the offset of the section relative to the mid-surface of the element, set to 0.0), offsetType (offset type, set to MIDDLE_SURFACE), and thicknessAssignment (thickness assignment method, set to FROM_SECTION);

[0044] S35. Based on the measured values ​​and heterogeneity of the mud cake material parameters, the functions and element subsets in S32 are assigned values, and then solved using Python to obtain the material parameters of the mud cake in the model.

[0045] Define the function main_function, which is used to input the actual parameters of the mud cake and call the function defined in S32 to assign the material properties of the mud cake part. When inputting the actual parameters, randomly select them within the range of the measured values ​​of the mud cake, and these input parameters need to cover the upper and lower limits of the measured values, so that the final parameters are more in line with the actual situation.

[0046] In this embodiment, the material attribute matifo list is set to ('mat1', 1800, 2, 0.2), ('mat2', 2000, 3, 0.18), ('mat3', 2200, 4, 0.18), and the 4 parameters in the elements are material name, elastic modulus, yield strength, and Poisson's ratio. The three elements in the matifo list are temporarily assigned to the variable ma using a for loop, and ma is introduced into the function Cre_mat_pro to create a section and assign attributes; then the Crea_elem_sets function is called to set the number of elements n in the set to 50, and a section related to the material defined in the matifo list is randomly assigned to each set. Although three groups of parameters are selected for assignment within the mud cake parameter range in this embodiment, it is clear to those skilled in the art that different numbers of parameters can be selected for assignment according to actual conditions.

[0047] Run the function main_function to assign material properties to the entire mud cake part of the model.

[0048] Through the steps of the embodiment of the present invention, the mud cake can be well assigned a value, so that the mud cake parameters are closer to the existing mud cake and the final result is more accurate.

[0049] S4, insert cohesive units into the interface between casing and cement sheath, the interface between cement sheath and mud cake, and the interface between mud cake and formation, and perform linear damage evolution based on Maxs damage;

[0050] In this step, the following sub-steps are included: inserting cohesive units on the meshes of the interface between casing and cement sheath, the interface between cement sheath and mud cake, and the interface between mud cake and formation and setting properties, and then performing damage evolution based on the Maxs damage mechanism, and the damage evolution type is the Energy type.

[0051] Among them, when inserting the cohesive unit, it specifically includes: creating a material for the Cohesive unit in the Property module, setting the elastic property of the material to surface force, and setting the elastic modulus to 10GPa.

[0052] At the same time, the damage evolution includes the following sub-steps:

[0053] a) The cohesive unit is particularly suitable for simulating interfacial bonding behavior. It can accurately capture the normal and tangential stress-strain relationships at the interface, thereby providing high-precision simulation results, fully simulating the interfacial separation behavior of composite materials, and is fully suitable for the calculation of the development of interfacial micro-gap in the present invention.

[0054] b) Based on the damage mechanics theory and following the "Traction-Separation" law, the cohesive unit is inserted into the contact surface to simulate the cohesive performance between the two parts. During the numerical simulation, when the displacement of the contact surface increases to the displacement when the cohesive unit is completely destroyed, the contact surface will separate and produce a micro gap on the interface.

[0055] c) The process of interface separation mainly has three stages. Stress calculation in the elastic stage: At the beginning of loading, the cohesive unit behaves as linear elastic, that is, stress is proportional to strain. At this time, the stress on the interface has not reached the damage threshold and the interface remains intact. Assuming that the interface is in an elastic state, the stress is calculated based on the current strain. The stress vector σ and the strain vector ε can be multidimensional, including a normal component and two tangential components. The stress-strain relationship in the elastic stage can be expressed as:

[0056] σ=Kε

[0057] Where K is the 3×3 stiffness matrix of the Cohesive unit, including normal and tangential stiffness coefficients; σ is the stress vector, MPa; ε is the strain vector, %.

[0058] d) Damage criterion evaluation: evaluate whether the current stress state meets the damage criterion. For the energy-based damage criterion, it is necessary to calculate the current energy release rate G and compare it with the damage threshold G.c The energy release rate G can be calculated by the following formula:

[0059] The current energy release rate is obtained by the following formula:

[0060]

[0061] In the formula, σ n , σ s , σ t are the stresses in the normal direction and two tangential directions respectively; Δε n , Δε s , Δε t are the strain increments corresponding to the normal phase and the two tangential directions respectively.

[0062] e) If the current energy release rate G reaches the damage threshold G c , the interface begins to be damaged. The damage variable D will be iteratively calculated according to the damage evolution law. When the damage variable D reaches 1, it is considered that the interface has been completely destroyed and separated. For the linear damage evolution model, the damage variable can be expressed as:

[0063]

[0064] Where G is the energy release rate, MN / m; G c is the damage threshold, MN / m.

[0065] S5. Set boundary conditions for the model and apply loads to the casing based on actual working conditions. Then solve the model to obtain the interface separation of the cement sheath and the equivalent plastic strain during load loading.

[0066] In this embodiment, the following sub-steps are specifically included: creating an analysis step, the analysis step type is a static analysis step, and the step length of the analysis step is set; creating a load, the load is an alternating load, applied to the inner wall of the casing; creating boundary conditions, in the analysis step, defining three degrees of freedom in three directions of the model.

[0067] Among them, the analysis step is set to step1, the type is static, the time length is 1, the maximum number of incremental steps is 1000, the minimum incremental step is 0.01, and the maximum incremental step is 0.05.

[0068] The boundary conditions are set as follows: define three degrees of freedom U1, U2, and U3 on the left, bottom, and front of the model, representing displacement along the x-axis, displacement along the y-axis, and displacement along the z-axis, respectively, and set displacement / rotation limits in each direction;

[0069] When applying load to the casing, set the load in the Load module, create a pressure load in Step 1, and act on the inner wall of the casing. The amplitude change of the load is established using the table type. The load type is an alternating load, and each load cycle is completed within 1 analysis step.

[0070] In this embodiment, the maximum load is set to 75 MPa and the minimum is set to 40 MPa to simulate the alternating load change process during the fracturing process.

[0071] Then, create Job1 to solve the combined model, view the calculation results after solving, and extract the required unit data in the Visualization module for analysis. The final result is as follows: Figures 2 to 5 As shown, Figure 2 The equivalent plastic strain contour of the model (PEEQ) Figure 3 This is the interface separation diagram. Figure 4 is the graph of equivalent plastic strain of cement sheath inner wall changing with the number of cycles, Figure 5 The figure is a diagram of the interface micro-gap development of the cement sheath under different cycle times. The interface between the casing and the cement sheath is the first interface, and the interface between the cement sheath and the formation is the second interface. According to the existing logging data, both the first interface and the second interface have micro-gap and interface separation under the condition of external load, and the results of the embodiment of the present invention well confirm this point.

[0072] In order to illustrate the advantages of the method of the embodiment of the present invention, a comparative example is provided. In the comparative example, the model is not provided with a mud cake, and the analysis method of the embodiment is used to analyze it. The final result is Figures 6-7 As shown. Among them, Figure 6 is the interface micrograph after the load is applied, Figure 7 The development diagram of interface micro-gap of cement sheath under different cycle times. From the figure, when mud cake is not considered, only the first interface has certain micro-gap and interface separation, which is obviously inconsistent with the actual situation.

[0073] From the comparison of the figures, it can be seen that the results of the method in the embodiment of the present invention are more consistent with the actual situation.

[0074] The above description is only a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A method for simulating cement sheath sealing performance considering well wall mud cake and fracturing conditions, characterized in that: The following steps are involved: S1. Based on Abaqus software, a three-dimensional deformable solid model of the wellbore is established, and then the model is divided into casing, cement ring, mud cake and formation from the inside to the outside and meshed; S2. Based on the measured values, material parameters are assigned to the casing, cement sheath and formation; the material parameters include plasticity or elasticity, the formation and casing are elastic materials, the cement sheath is a plastic material, and the plastic damage model of the cement sheath is as follows: In the formula, σ ij is the Cauchy stress; ij and are the total strain and plastic strain, respectively; is elastic stiffness, MPa; d s is the damage variable; The damage variable d s Obtained by the following formula: W ε =∫σdε=∫f(ε)dε, where W0 is the strain energy density in the lossless state; E0 is the initial elastic modulus; ε is the compressive strain; σ is the stress tensor; W ε is the strain energy density under damage state; S3, establish an element set for defining the mud cake material, then assign the element set to the grid of the mud cake, consider the heterogeneity of the mud cake, and obtain the material parameters of the mud cake based on Python code; this step includes the following sub-steps: S31. Use Tool to create an element set; S32, creating a function of material parameters and mud cake elastic properties, dividing the element set into a plurality of element subsets, and randomly assigning a cross section containing mud cake material parameters to each subset; S33, creating a variable p to obtain a model reference, storing it in the variable p, and subsequently accessing and operating the component through p; S34, use a for loop to traverse the required number of sets, and use the total number of elements in the element set / n+1 as the upper limit of the loop, where n represents the number of elements expected in each element subset in S32; S35, based on the measured values ​​and heterogeneity of the mud cake material parameters, assign values ​​to the functions and element subsets in S32, and then solve them using Python to obtain the material parameters of the mud cake in the model; S4, insert cohesive units into the interface between casing and cement sheath, the interface between cement sheath and mud cake, and the interface between mud cake and formation, and perform linear damage evolution based on Maxs damage; S5. Set boundary conditions for the model and apply loads to the casing based on actual working conditions. Then solve the model to obtain the interface separation of the cement sheath and the equivalent plastic strain during load loading.

2. The method according to claim 1, characterized in that The size of the model is at least 10 times the actual wellbore size.

3. The method according to claim 1, characterized in that The material parameters also include elastic modulus, yield strength and Poisson's ratio.

4. The method according to claim 1, characterized in that: S4 includes the following sub-steps: inserting cohesive units and setting properties on the meshes of the interface between casing and cement sheath, the interface between cement sheath and mud cake, and the interface between mud cake and formation, and then performing damage evolution based on the Maxs damage mechanism. The damage evolution type is the Energy type. According to the damage evolution results, the damage is solved and analyzed based on the Jobs module to obtain an equivalent plastic deformation cloud map and an interface separation diagram, thereby obtaining the sealing performance of the cement sheath under external load conditions.

5. The method according to claim 4, characterized in that During the damage evolution process, the damage result is obtained based on the current energy release rate and damage threshold of the interface; the current energy release rate is obtained by the following formula: In the formula, σ n , σ s , σ t are the stresses in the normal direction and two tangential directions respectively; Δε n , Δε s , Δε t are the strain increments corresponding to the normal direction and the two tangential directions respectively.

6. The method according to claim 1, characterized in that In S5, setting boundary conditions and applying loads include the following sub-steps: creating an analysis step, the analysis step type is a static analysis step, and the step length of the analysis step is set; creating a load, the load is an alternating load, applied to the inner wall of the casing; creating boundary conditions, in the analysis step, defining three degrees of freedom in three directions of the model.

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