Cement elastic parameter calculation method and system based on hollow microsphere cement system

Abstract

The invention relates to a cement elastic parameter calculation method and system based on a hollow microbead cement system, and the method comprises the steps: building a characterization unit model of hollow microbead cement based on a homogenization theory; calculating the volume fraction and strain parameters of each phase in the hollow microsphere cement according to the model parameters of the characterization unit body model; and calculating the elastic parameter of the hollow microsphere cement according to the volume fraction and the strain parameter of each phase in the hollow microsphere cement. According to the invention, on the premise of not carrying out a mechanical test, the elastic modulus of the hollow microsphere cement after curing can be quickly obtained through the mechanical parameters and the ratio of the cement matrix and the hollow microsphere; in addition, the influence of poor interface cementation quality between the hollow microspheres and the cement matrix on the macromechanical parameters of the cured cement is also considered, so that the calculation of the elastic parameters is more accurate.

Description

Technical Field

[0001] The invention relates to the field of elastic parameter calculation, and in particular to a cement elastic parameter calculation method and system based on a hollow microsphere cement system. Background Art

[0002] In the development of geothermal, oil and gas, CO2 storage, etc., cementing operations are very important for achieving interlayer isolation, formation support and casing protection in deep wells. In cementing operations, the density of cement slurry should be kept moderate, both to maintain a certain formation pressure to prevent wellbore extrusion damage and to avoid excessive cement slurry density causing leakage. In some cases, especially in low pressure gradient rock formations, lightweight cement is required. Lightweight and ultra-lightweight cement slurries are usually added with diluents, foams and lightweight materials. Diluents are when added to the slurry, the slurry has a higher water content without seriously affecting the properties of the cement paste. Foamed cement is a slurry that is made by injecting nitrogen to form nitrogen microbubbles to achieve a low specific weight. Lightweight materials can also be added to cement, and since their specific gravity is lower than that of cement, they reduce the density of the cement slurry. The final properties of the hardened cement paste will vary depending on the lightweight material. In fact, among the different lightweight materials, hollow glass microspheres are particularly interesting. This material has a very low weight but a compressive strength of up to 200MPa. It can reduce the density of the cement slurry without affecting the final cement strength. Compared with the traditional cement slurry system, the hollow microsphere lightweight cement slurry has a lower equivalent density and lower circulation loss during the cementing process, which can avoid the occurrence of complex situations downhole.

[0003] In deep well cementing construction, the compressive strength of cement is not the only important performance parameter of cement. Elastic parameters are also important. The change in contact stress between cement sheath and rock formation and casing directly depends on its own elastic modulus. However, when the formation rock creeps or the internal pressure of the casing increases, the internal stress of cement sheath with low elastic modulus is lower. Therefore, the risk of plastic strain and sealing failure of low modulus cement is lower. Similarly, cement in deep wells also produces thermo-mechanical stress with the change of temperature in the well, such as mud circulation or thermal recovery process, and the possibility of low modulus cement failure is lower. Using cement with sufficient elasticity also has advantages in the perforation process. The perforating charge will penetrate the casing and cement sheath after detonation. In the process of penetrating the casing and cement sheath, the perforating charge should minimize the damage to the casing and cement around the hole caused by its shaped energy jet as much as possible. However, according to the characteristics of the cement sheath, this is impossible under actual working conditions. The cement sheath of downhole cementing should have high toughness and low elastic modulus to reduce the propagation of internal cracks in the cement.

[0004] Therefore, it is necessary to obtain the elastic parameters of cement sheath, especially the elastic parameters of hollow microsphere cement. The most classic and common way to obtain elastic parameters is to conduct indoor tests on prepared cement samples. Indoor experimental tests require time to prepare samples and maintain them. In addition to indoor tests, theoretical calculation methods or empirical formulas need to be developed based on mix design and some basic information of the materials used to replace experimental methods to estimate the mechanical properties of cement. The empirical formula is to find out the mathematical relationship between the elastic parameters of cement paste and other parameters of cement slurry, such as water-cement ratio, hollow particle ratio, etc., through a large number of experiments with different cement slurry formulas and different additives. Although the empirical formula is more accurate in predicting the performance of cement in the later stage, it is very time-consuming and has great limitations. The mathematical relationship is limited to one cement slurry system. Therefore, it is necessary to provide a relatively easy-to-use analytical method to calculate the elastic parameters of cement after curing with hollow microsphere lightweight cement slurry. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method and system for calculating cement elastic parameters based on a hollow microsphere cement system, which can quickly obtain the elastic parameters of the hollow microsphere cement after curing.

[0006] The technical solution of the present invention to solve the above technical problem is as follows: a method for calculating cement elastic parameters based on a hollow microsphere cement system, comprising the following steps:

[0007] Based on the homogenization theory, a characterization unit model of hollow microsphere cement is established;

[0008] According to the model parameters of the characterization unit body model, the volume fraction and strain parameter of each phase in the hollow microsphere cement are calculated;

[0009] The elastic parameters of hollow microsphere cement are calculated according to the volume fraction of each phase and strain parameters in the hollow microsphere cement.

[0010] Based on the above technical solution, the present invention can also be improved as follows.

[0011] Further, the strain parameter includes a volumetric strain parameter and / or a deviatoric strain parameter; correspondingly, the elastic parameter includes a bulk modulus and / or a shear modulus;

[0012] The formula for calculating the bulk modulus and / or shear modulus of hollow microsphere cement is:

[0013] or / and

[0014] Among them, K hom is the bulk modulus of hollow microsphere cement, G homis the shear modulus of hollow microsphere cement, m is the phase sequence number of each phase in hollow microsphere cement, M is the total number of phases in hollow microsphere cement, and f m is the volume fraction of the mth phase in hollow microsphere cement, k m is the bulk modulus of the mth phase in hollow microsphere cement, g m is the shear modulus of the mth phase in hollow microsphere cement, is the volume strain parameter of the mth phase in hollow microsphere cement, is the deviatoric strain parameter of the mth phase in hollow microsphere cement.

[0015] Furthermore, hollow microsphere cement is specifically an inclusion formed by hollow microspheres embedded in a cement matrix, and the hollow microsphere cement has three phases, which are the first phase corresponding to the voids in the hollow microspheres, the second phase corresponding to the glass in the hollow microspheres, and the third phase corresponding to the cement matrix;

[0016] The model parameters characterizing the unit cell model include the volume fraction, inner diameter and outer diameter of the hollow microspheres in the hollow microsphere cement;

[0017] The formula for calculating the volume fraction of each phase in hollow microsphere cement is:

[0018] f 3 =1-f 1 -f 2 =1-f HGMS ;

[0019] Among them, f 1 is the volume fraction of the first phase in hollow microsphere cement, f 2 is the volume fraction of the second phase in hollow microsphere cement, f 3 is the volume fraction of the third phase in hollow microsphere cement, f HGMS is the volume fraction of hollow microspheres in hollow microsphere cement, r 1 is the inner diameter of the hollow microsphere, r 2 is the outer diameter of the hollow microsphere.

[0020] Furthermore, the strain parameter includes a volumetric strain parameter, and the formula for calculating the volumetric strain parameter of each phase in the hollow microsphere cement is:

[0021]

[0022] in, is the volume strain parameter of the mth phase in the hollow microsphere cement, m is the phase sequence number of each phase in the hollow microsphere cement, M is the total number of phases in the hollow microsphere cement, is the volume strain correlation coefficient of the mth phase in hollow microsphere cement, f m is the volume fraction of the mth phase in hollow microsphere cement.

[0023] Furthermore, hollow microsphere cement is specifically an inclusion formed by hollow microspheres embedded in a cement matrix, and the hollow microsphere cement has three phases, which are the first phase corresponding to the voids in the hollow microspheres, the second phase corresponding to the glass in the hollow microspheres, and the third phase corresponding to the cement matrix; then M = 3, m = 1, 2, 3;

[0024] The formula for calculating the volume strain correlation coefficient of the mth phase in hollow microsphere cement is:

[0025]

[0026]

[0027]

[0028] Among them, k 2 and g 2 They correspond to the bulk modulus and shear modulus of the second phase in hollow microsphere cement, k 3 and g 3 They correspond to the bulk modulus and shear modulus of the third phase in hollow microsphere cement, r 1 and r 2 They correspond to the inner and outer diameters of the hollow microspheres, ξ 2 , 2 and λ 2 They are dimensionless parameters of the second phase in hollow microsphere cement, which are a second-order tensor introduced when there is a gap between the cement matrix and the hollow microsphere bonding interface.

[0029] Furthermore, the dimensionless parameter ξ 2 , 2 and λ 2 The expressions are:

[0030]

[0031] in, and They correspond to the normal stiffness and tangential stiffness of the second-order tensor at the bonding interface relative to the second phase, R 2 is the radius of the second phase in hollow microsphere cement;

[0032] When the cement matrix and hollow microspheres are completely bonded, 2 =ξ 2 =0.

[0033] Furthermore, the strain parameter includes a deviatoric strain parameter, and the formula for calculating the deviatoric strain parameter of each phase in the hollow microsphere cement is:

[0034]

[0035] in, is the deviatoric strain parameter of the mth phase in the hollow microsphere cement, m is the phase sequence number of each phase in the hollow microsphere cement, M is the total number of phases in the hollow microsphere cement, is the deviatoric strain correlation coefficient of the mth phase in hollow microsphere cement, f m is the volume fraction of the mth phase in hollow microsphere cement.

[0036] Furthermore, hollow microsphere cement is specifically an inclusion formed by hollow microspheres embedded in a cement matrix, and the hollow microsphere cement has three phases, which are the first phase corresponding to the voids in the hollow microspheres, the second phase corresponding to the glass in the hollow microspheres, and the third phase corresponding to the cement matrix; then M = 3, m = 1, 2, 3;

[0037] The formula for calculating the deviatoric strain correlation coefficient of the mth phase in hollow microsphere cement is:

[0038]

[0039]

[0040]

[0041] in, and is a 4×4 matrix P (2) The weight, ν 2 is the Poisson's ratio of the second phase in hollow microsphere cement, r 1 and r 2 They correspond to the inner diameter and outer diameter of the hollow microspheres respectively.

[0042] Furthermore, the matrix P (2) The expression is:

[0043]

[0044] in:

[0045]

[0046]

[0047] Specifically, r is r 1 or 2 , ν m is the Poisson's ratio of the mth phase in hollow microsphere cement, and They correspond to the normal stiffness and tangential stiffness of the mth phase on the bonding interface of a second-order tensor introduced when there is a gap between the cement matrix and the hollow microspheres, respectively. mis the bulk modulus of the mth phase in hollow microsphere cement, g m is the shear modulus of the mth phase in hollow microsphere cement;

[0048] When the cement matrix and hollow microspheres are completely bonded, L′ 2 (r 2 ) is a zero matrix.

[0049] On the basis of the above-mentioned cement elasticity parameter calculation method based on the hollow microsphere cement system, the present invention also provides a cement elasticity parameter calculation system based on the hollow microsphere cement system.

[0050] The cement elastic parameter calculation system based on hollow microsphere cement system includes the following modules:

[0051] A modeling module, which is used to establish a characterization unit model of hollow microsphere cement based on homogenization theory;

[0052] A volume fraction and strain parameter calculation module, which is used to calculate the volume fraction and strain parameter of each phase in the hollow microsphere cement according to the model parameters of the characterization unit body model;

[0053] The elastic parameter calculation module is used to calculate the elastic parameters of the hollow microsphere cement according to the volume fraction and strain parameters of each phase in the hollow microsphere cement.

[0054] The beneficial effects of the present invention are as follows: the present invention provides a cement elastic parameter calculation method and system based on a hollow microsphere cement system, and the elastic modulus of the hollow microsphere cement after curing can be quickly obtained through the mechanical parameters and proportions of the cement matrix and the hollow microspheres without conducting a mechanical test; in addition, the present invention also considers the influence of poor interface bonding quality between the hollow microspheres and the cement matrix on the macroscopic mechanical parameters of the cement after curing, so that the calculation of the elastic parameters is more accurate; the present invention can provide an engineering tool for the design of lightweight cement with hollow microspheres, and provide a reference for the performance evaluation of cement rings in drilling projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flow chart of the cement elastic parameter calculation method based on the hollow microsphere cement system of the present invention;

[0056] Figure 2 This is a microscopic diagram of hollow microbead cement;

[0057] Figure 3 is a relationship curve diagram of hollow microsphere volume fraction and microsphere radius ratio versus dimensionless bulk modulus;

[0058] Figure 4 Another relationship curve diagram of hollow microsphere volume fraction f and microsphere radius ratio versus dimensionless bulk modulus;

[0059] Figure 5 is a graph showing the relationship between the interface microgap size and the dimensionless bulk modulus;

[0060] Figure 6 is a graph showing the relationship between the normal interface micro-gap size and the tangential interface micro-gap size and the dimensionless shear modulus;

[0061] Figure 7 It is a structural block diagram of the cement elastic parameter calculation system based on the hollow microsphere cement system of the present invention. DETAILED DESCRIPTION

[0062] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0063] like Figure 1 As shown, the cement elastic parameter calculation method based on the hollow microsphere cement system includes the following steps:

[0064] Based on the homogenization theory, a characterization unit model of hollow microsphere cement is established;

[0065] According to the model parameters of the characterization unit body model, the volume fraction and strain parameter of each phase in the hollow microsphere cement are calculated;

[0066] The elastic parameters of hollow microsphere cement are calculated according to the volume fraction of each phase and strain parameters in the hollow microsphere cement.

[0067] Wherein, the strain parameters include volumetric strain parameters and / or deviatoric strain parameters; correspondingly, the elastic parameters include bulk modulus and / or shear modulus.

[0068] The method of the present invention is specifically described below:

[0069] The present invention firstly needs to establish a characterization unit volume (REV) model of hollow microsphere cement based on homogenization theory.

[0070] The hollow microsphere cement is regarded as a heterogeneous material composed of multiple (M) different phases, each (mth) phase has a certain volume fraction f m Under isotropic solid phase conditions, the bulk modulus and shear modulus of each phase are expressed by k m and g m The bulk modulus and shear modulus of the entire hollow microsphere cement at a homogeneous macroscopic scale can be calculated using the following formula:

[0071]

[0072] Among them, K homis the bulk modulus of hollow microsphere cement, G hom is the shear modulus of hollow microsphere cement, m is the phase sequence number of each phase in hollow microsphere cement, M is the total number of phases in hollow microsphere cement, and f m is the volume fraction of the mth phase in hollow microsphere cement, k m is the bulk modulus of the mth phase in hollow microsphere cement, g m is the shear modulus of the mth phase in hollow microsphere cement, is the volume strain parameter of the mth phase in hollow microsphere cement, is the deviatoric strain parameter of the mth phase in hollow microsphere cement.

[0073] From formula (1), we can see that the effective elastic modulus is the weighted average of the elastic moduli of each phase; and are the coefficient weights of each microphase, and their values ​​depend on the material elasticity, surrounding matrix and geometric dimensions of each phase.

[0074] like Figure 2 As shown, hollow microsphere cement is formed by hollow microspheres 2 embedded in cement matrix 3 to form inclusions, and hollow microspheres 2 are voids 1. Hollow microspheres 2 are composed of a siliceous spherical shell filled with gas, which can be used as a density regulator for cement slurry. Lightweight cement (hollow microsphere cement) slurry is used for deep well cementing operations, and the integrity of the cementing ring needs to be ensured to avoid mud loss.

[0075] according to Figure 2 The microstructure of hollow microsphere cement shown in FIG. 1 is a microstructure of hollow microsphere cement having three microphases (referred to as three phases), which are the first phase corresponding to the voids in the hollow microspheres, the second phase corresponding to the glass in the hollow microspheres, and the third phase corresponding to the cement matrix.

[0076] The establishment of the micromechanical model of hollow microsphere cement first requires the definition of a complete REV model to represent the microstructure of the material. The REV model assumes the separation of cement matrix and hollow microspheres in terms of scale, in which the microscale of hollow microsphere cement can be regarded as consistent with that of cement. However, considering that the volume fraction and geometric size of hollow microspheres in the REV model are smaller than those of cement matrix particles, the assumption of scale separation between cement matrix and hollow microspheres does not seem to have a significant impact on the model prediction. The degree of simplification of the selected REV model depends greatly on the model parameters and experimental conditions. The mechanical parameters of the cement matrix can be measured on the specimen hardened with a slurry without hollow microspheres. The mechanical parameters of hollow microspheres are usually provided by the manufacturer, and the volume fraction information of each phase can be easily calculated from the slurry formula. In contrast, more complex REV models require more detailed information, including the microstructural phase composition, volume fraction and mechanical parameters of different phases of cement.

[0077] The hollow microspheres in hollow microsphere cement have good contact with the cement matrix. The hollow microspheres act as growth nuclei, which means that cement hydration products are formed on their surfaces. In addition, the hollow microspheres can accelerate the reaction process of calcium hydroxide in the slurry during cement hydration, further forming hydrated calcium silicate. Considering that the bonding between the hollow microspheres and the cement matrix is ​​not perfect in practice, simple assumptions cannot meet the accuracy requirements for most practical applications. Therefore, it is necessary to analyze the establishment and solution of the model when the quality of the bonding interface is poor.

[0078] Another point that should be mentioned is that the active reaction of hollow microspheres consumes part of the siliceous shell. The amorphous silica formed will react with the silicate in the cement paste to form calcium hydrated silicate. This process will reduce the thickness of the sphere and affect the chemical composition and microstructure of the microspheres, and will eventually affect the mechanical parameters of the hollow microspheres near the cement matrix. Generally speaking, the degree of active reaction is not 100%, and in most cases it is less than 50%. Since the chemical reaction is relatively complex, the present invention assumes that the hollow microspheres and the cement matrix maintain the initial value.

[0079] The evaluation of the homogenized elastic parameters (bulk modulus and shear modulus of hollow microsphere cement) in formula (1) requires knowing the volume fractions of different microphases.

[0080] Volume fraction of hollow microspheres f HGMS It can be obtained by the mass of hollow microspheres per unit volume and the density of hollow microspheres. The volume fractions of the three microscopic phases (voids, glass and cement matrix) can be evaluated by the inner and outer diameters of hollow microspheres. Specifically, the formula for calculating the volume fraction of each phase in hollow microsphere cement is as follows:

[0081]

[0082] Among them, f 1 is the volume fraction of the first phase (void phase) in hollow microsphere cement, f 2 is the volume fraction of the second phase (glass phase) in hollow microsphere cement, f 3 is the volume fraction of the third phase (cement matrix phase) in hollow microsphere cement, f HGMS is the volume fraction of hollow microspheres in hollow microsphere cement, r 1 is the inner diameter of the hollow microsphere, r 2 is the outer diameter of the hollow microsphere.

[0083] In addition, the density ρ of hollow microsphere cement can be calculated as:

[0084]

[0085] where ρ 2 and ρ 3are the densities of glass beads and cement matrix, respectively.

[0086] Due to the special geometric shape of inclusions (hollow spheres, i.e. cenospheres) in the cement matrix, it is assumed that the interface between the cenospheres and the cement matrix is ​​well bonded.

[0087] In formula (1) and They are expressed by the following relations:

[0088]

[0089] in, is the volume strain parameter of the mth phase in hollow microsphere cement, is the volume strain correlation coefficient of the mth phase in hollow microsphere cement, is the deviatoric strain parameter of the mth phase in hollow microsphere cement, is the deviatoric strain correlation coefficient of the mth phase in hollow microsphere cement.

[0090] and It can be obtained through the geometric dimensions of the REV model (i.e., the model parameters that characterize the unit cell model), mainly the inner diameter r of the hollow microsphere 1 and the outer diameter r of the hollow microsphere 2 .

[0091] Given by:

[0092]

[0093]

[0094]

[0095] It is worth noting that The homogeneous bulk modulus (bulk modulus of hollow microsphere cement) obtained by formula (1) depends only on the ratio of the inner and outer diameters of the hollow microspheres r 2 / r 1 , and the actual value r 1 and r 2 Not relevant.

[0096] In order to get It is necessary to calculate the 4×4 matrix P (2) , P (2) Given by:

[0097]

[0098] Among them, L 3 (r 2 )、L2 (r 2 )、L 2 (r 1 )、L 1 (r 1 ) is as follows:

[0099]

[0100] Note (2) The superscript (2) in is not a power, but indicates the second phase. (2) The mathematical expressions for each component are quite long because they can be obtained by matrix multiplication, so The equation of the matrix P (2) The amount To indicate that the physical units of these matrices are not the same, and The unit is dimensionless, The unit is L 2 , The unit is L -2 ; r is r 1 or 2 ; ν m is the Poisson's ratio of the mth phase in the hollow microsphere cement. By integrating equations (8) and (9), we can get:

[0101]

[0102]

[0103]

[0104] Among them, ν 2 is the Poisson's ratio of the second phase in the hollow microsphere cement. The elastic parameters of the first phase should be considered as 0.

[0105] Considering The complexity of the expression is similar to the above The macroscopic homogenized elastic modulus (shear modulus of hollow microsphere cement) calculated by formula (1) and the inner diameter r of the hollow microsphere 1 and the outer diameter r of the hollow microsphere 2 The specific value of is irrelevant, it only depends on the ratio of the inner and outer diameters of the hollow microspheres r 2 / r 1 .

[0106] The above mathematical model can be extended to the case where the bonding between microspheres and cement matrix is ​​poor. The poor compatibility of the bonding interface between microspheres and the matrix causes the displacement to show a jump-like mutation on the bonding interface. Assuming that the gap at the bonding interface is proportional to the continuous traction vector on the bonding interface, the gap Δu at the bonding interface is i It can be expressed by the following formula:

[0107] Δu i =n ij σ jm n m (13)

[0108] Among them, σ jm is the stress of the mth phase, n m is the stress vector of the mth phase, i and j are sequence numbers (1, 2), n ij is a second-order tensor representing the continuity of the interface; n ij = 0 corresponds to a completely bonded interface; it has a tangential stiffness η t and a normal stiffness η n The simple form of ij It can be expressed as:

[0109] n ij =η t δ ij +(η n -η t ) i n j (14)

[0110] Among them, δ ij is the tangential stiffness tensor, n i and n j They are two tensors separated from the normal stiffness and the tangential stiffness difference;

[0111] In the case of incomplete interface bonding, the strain localization coefficient of each phase is and can be written as:

[0112]

[0113]

[0114] The following dimensionless parameters are introduced and the simplified formula is expressed as follows:

[0115]

[0116] Among them, R m is the radius of the mth phase in hollow microsphere cement;

[0117] but Given by:

[0118]

[0119] According to formula (6), It can be expressed as Function of Same as formula (7).

[0120] When the hollow microspheres are completely bonded to the cement matrix, that is, 2 =ξ 2 When =0, equation (17) is simplified to equation (5).

[0121] In the case of incomplete interface bonding, the matrix P (2) The following formula can be used to solve:

[0122]

[0123] The matrix L′ m The expression of (r) is as follows:

[0124]

[0125] Matrix L m (r) is given by equation (9); and Calculate using equations (10), (11), and (12) respectively.

[0126] In order to show the influence of model parameters on macroscopic elastic mechanical parameters, sensitivity analysis was carried out. First, keeping other parameters unchanged, the ratio of the inner and outer diameters of hollow microspheres was analyzed. 2 / r 1 The influence of the volume ratio of hollow microspheres on the homogenized elastic parameters of hollow microsphere cement. The Young's modulus and Poisson's ratio of silica glass and cement matrix are E 2 =64GPa, ν 2 =0.2; E 3 =22GPa, ν 3 =0.25. The bulk modulus and shear modulus of silica glass and cement matrix can be calculated using the following formula:

[0127]

[0128] Assuming that the hollow microspheres are well bonded to the cement matrix, Figure 3 and Figure 4 are the volume ratio of hollow microspheres and the ratio of inner and outer diameters r 2 / r 1 The influence of cement bulk modulus and shear modulus.

[0129] When the volume fraction of hollow microsphere cement is constant, the bulk modulus and shear modulus both increase with r 2 / r 1 The ratio of glass (phase 2) to void (phase 1) increases, that is, the ratio of glass (phase 2) to void (phase 1) in the composite material increases. If the volume fraction of glass increases and the volume fraction of voids decreases, the addition of hard glass increases the stiffness of the composite material. Therefore, the use of thick-walled hollow microspheres will lead to a higher elastic modulus, but this will also indirectly increase the density of hollow microsphere cement slurry. Under the condition that other parameters of hollow microspheres remain unchanged, the increase in the volume fraction of hollow microspheres will reduce the density of cement, but also reduce its elastic parameters.

[0130] When the bonding quality between the hollow microspheres and the cement matrix is ​​poor, the interface bonding quality will affect the final elastic modulus of the cement. For this part of the sensitivity analysis, the inner and outer diameters of the hollow microspheres are fixed as r 1 =18μm and r 2 = 20 μm. The volume fraction of hollow microspheres is 0.24. The macroscopic bulk modulus and shear modulus of cement are analyzed under a wide range of normal and tangential stiffness of the interface. The macroscopic homogeneous bulk modulus of cement depends only on the normal stiffness and has nothing to do with the tangential stiffness. Its relationship curve with the normal stiffness is shown in Figure 5 As shown. η = 0 corresponds to the case of complete interface bonding. The results show that the macroscopic bulk modulus of cement decreases with the increase of interface stiffness, but tends to an asymptotic value. That is, the degree of interface bonding between hollow microspheres and cement has limited influence on the overall bulk modulus of cement. The influence of interface normal and tangential stiffness on the macroscopic shear modulus of cement is shown in Figure 6 As shown, the relationship between the interface normal stiffness, tangential stiffness and cement macroscopic shear modulus is in the form of elliptical contour lines.

[0131] In summary, the present invention can obtain the elastic modulus of hollow microsphere cement after curing by the mechanical parameters and ratio of cement matrix and hollow microspheres without mechanical testing. In addition, the influence of the geometric size and volume proportion of hollow particles on the macro elastic parameters of cement after curing can also be obtained, and the hollow microsphere cement system can be adjusted in the design stage.

[0132] The present invention is also applicable to special cements added with solid materials such as rubber and barite, and can realize the prediction of performance parameters of special cements, providing a basis for the optimal design of cement formulas.

[0133] On the basis of the above-mentioned cement elasticity parameter calculation method based on the hollow microsphere cement system, the present invention also provides a cement elasticity parameter calculation system based on the hollow microsphere cement system.

[0134] like Figure 7As shown in the figure, the cement elastic parameter calculation system based on the hollow microsphere cement system includes the following modules:

[0135] A modeling module, which is used to establish a characterization unit model of hollow microsphere cement based on homogenization theory;

[0136] A volume fraction and strain parameter calculation module, which is used to calculate the volume fraction and strain parameter of each phase in the hollow microsphere cement according to the model parameters of the characterization unit body model;

[0137] The elastic parameter calculation module is used to calculate the elastic parameters of the hollow microsphere cement according to the volume fraction and strain parameters of each phase in the hollow microsphere cement.

[0138] The specific functions of each module in the cement elasticity parameter calculation system based on the hollow microsphere cement system of the present invention refer to the specific steps of the cement elasticity parameter calculation method based on the hollow microsphere cement system of the present invention, which will not be repeated here.

[0139] The present invention discloses a cement elastic parameter calculation method and system based on a hollow microsphere cement system. The elastic modulus of the hollow microsphere cement after curing can be quickly obtained through the mechanical parameters and proportions of the cement matrix and the hollow microspheres without conducting a mechanical test. In addition, the present invention also considers the influence of poor interface bonding quality between the hollow microspheres and the cement matrix on the macroscopic mechanical parameters of the cement after curing, so that the calculation of the elastic parameters is more accurate. The present invention can provide an engineering tool for the design of lightweight cement with hollow microspheres, and provide a reference for the performance evaluation of cement sheath in drilling engineering.

[0140] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. Calculation method of cement elastic parameters based on hollow microsphere cement system, It is characterized in that The following steps are involved: Based on the homogenization theory, a characterization unit model of hollow microsphere cement is established; According to the model parameters of the characterization unit body model, the volume fraction and strain parameter of each phase in the hollow microsphere cement are calculated; The elastic parameters of hollow microsphere cement are calculated according to the volume fraction of each phase and strain parameters in the hollow microsphere cement.

2. The method for calculating cement elastic parameters based on hollow microsphere cement system according to claim 1, It is characterized in that The strain parameters include volumetric strain parameters and / or deviatoric strain parameters; correspondingly, the elastic parameters include bulk modulus and / or shear modulus; The formula for calculating the bulk modulus and / or shear modulus of hollow microsphere cement is: or / and Among them, K hom is the bulk modulus of hollow microsphere cement, G hom is the shear modulus of hollow microsphere cement, m is the phase sequence number of each phase in hollow microsphere cement, M is the total number of phases in hollow microsphere cement, and f m is the volume fraction of the mth phase in hollow microsphere cement, k m is the bulk modulus of the mth phase in hollow microsphere cement, g m is the shear modulus of the mth phase in hollow microsphere cement, is the volume strain parameter of the mth phase in hollow microsphere cement, is the deviatoric strain parameter of the mth phase in hollow microsphere cement.

3. The method for calculating cement elastic parameters based on hollow microsphere cement system according to claim 1, It is characterized in that Hollow microsphere cement is specifically an inclusion formed by hollow microspheres embedded in a cement matrix. Hollow microsphere cement has three phases, which are the first phase corresponding to the voids in the hollow microspheres, the second phase corresponding to the glass in the hollow microspheres, and the third phase corresponding to the cement matrix. The model parameters characterizing the unit cell model include the volume fraction, inner diameter and outer diameter of the hollow microspheres in the hollow microsphere cement; The formula for calculating the volume fraction of each phase in hollow microsphere cement is: Among them, f 1 is the volume fraction of the first phase in hollow microsphere cement, f 2 is the volume fraction of the second phase in hollow microsphere cement, f 3 is the volume fraction of the third phase in hollow microsphere cement, f HGMS is the volume fraction of hollow microspheres in hollow microsphere cement, r 1 is the inner diameter of the hollow microsphere, r 2 is the outer diameter of the hollow microsphere.

4. The method for calculating cement elastic parameters based on hollow microsphere cement system according to claim 1, It is characterized in that The strain parameters include volumetric strain parameters. The formula for calculating the volumetric strain parameters of each phase in the hollow microsphere cement is: in, is the volume strain parameter of the mth phase in the hollow microsphere cement, m is the phase sequence number of each phase in the hollow microsphere cement, M is the total number of phases in the hollow microsphere cement, is the volume strain correlation coefficient of the mth phase in hollow microsphere cement, f m is the volume fraction of the mth phase in hollow microsphere cement.

5. The method for calculating cement elastic parameters based on hollow microsphere cement system according to claim 4, It is characterized in that Hollow microsphere cement is specifically an inclusion formed by hollow microspheres embedded in a cement matrix. Hollow microsphere cement has three phases, which are the first phase corresponding to the voids in the hollow microspheres, the second phase corresponding to the glass in the hollow microspheres, and the third phase corresponding to the cement matrix; then M = 3, m = 1, 2, 3; The formula for calculating the volume strain correlation coefficient of the mth phase in hollow microsphere cement is: Among them, k 2 and g 2 They correspond to the bulk modulus and shear modulus of the second phase in hollow microsphere cement, k 3 and g 3 They correspond to the bulk modulus and shear modulus of the third phase in hollow microsphere cement, r 1 and r 2 They correspond to the inner and outer diameters of the hollow microspheres, ξ 2 , 2 and λ 2 They are dimensionless parameters of the second phase in hollow microsphere cement, which are a second-order tensor introduced when there is a gap between the cement matrix and the hollow microsphere bonding interface.

6. The method for calculating cement elastic parameters based on hollow microsphere cement system according to claim 5, It is characterized in that Dimensionless parameter ξ 2 , 2 and λ 2 The expressions are: in, and They correspond to the normal stiffness and tangential stiffness of the second-order tensor at the bonding interface relative to the second phase, R 2 is the radius of the second phase in hollow microsphere cement; When the cement matrix and hollow microspheres are completely bonded, 2 =ξ 2 =0.

7. The method for calculating cement elastic parameters based on hollow microsphere cement system according to claim 1, It is characterized in that The strain parameters include deviatoric strain parameters. The formula for calculating the deviatoric strain parameters of each phase in the hollow microsphere cement is: in, is the deviatoric strain parameter of the mth phase in the hollow microsphere cement, m is the phase sequence number of each phase in the hollow microsphere cement, M is the total number of phases in the hollow microsphere cement, is the deviatoric strain correlation coefficient of the mth phase in hollow microsphere cement, f m is the volume fraction of the mth phase in hollow microsphere cement.

8. The method for calculating cement elastic parameters based on hollow microsphere cement system according to claim 7, It is characterized in that Hollow microsphere cement is specifically an inclusion formed by hollow microspheres embedded in a cement matrix. Hollow microsphere cement has three phases, which are the first phase corresponding to the voids in the hollow microspheres, the second phase corresponding to the glass in the hollow microspheres, and the third phase corresponding to the cement matrix; then M = 3, m = 1, 2, 3; The formula for calculating the deviatoric strain correlation coefficient of the mth phase in hollow microsphere cement is: in, and is a 4×4 matrix P (2) The weight, ν 2 is the Poisson's ratio of the second phase in hollow microsphere cement, r 1 and r 2 They correspond to the inner diameter and outer diameter of the hollow microspheres respectively.

9. The method for calculating cement elastic parameters based on hollow microsphere cement system according to claim 8, It is characterized in that Matrix P (2) The expression is: in: Specifically, r is r 1 or 2 , ν m is the Poisson's ratio of the mth phase in hollow microsphere cement, and They correspond to the normal stiffness and tangential stiffness of the mth phase on the bonding interface of a second-order tensor introduced when there is a gap between the cement matrix and the hollow microspheres, respectively. m is the bulk modulus of the mth phase in hollow microsphere cement, g m is the shear modulus of the mth phase in hollow microsphere cement; When the cement matrix and hollow microspheres are completely bonded, L′ 2 (r 2 ) is a zero matrix.

10. Cement elastic parameter calculation system based on hollow microsphere cement system, It is characterized in that Includes the following modules: A modeling module, which is used to establish a characterization unit model of hollow microsphere cement based on homogenization theory; A volume fraction and strain parameter calculation module, which is used to calculate the volume fraction and strain parameter of each phase in the hollow microsphere cement according to the model parameters of the characterization unit body model; The elastic parameter calculation module is used to calculate the elastic parameters of the hollow microsphere cement according to the volume fraction and strain parameters of each phase in the hollow microsphere cement.

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