A method and system for high temperature cement life prediction based on multifractal theory

Abstract

The application provides a high-temperature cement life prediction method and system based on a multi-fractal theory. The method comprises the following steps: obtaining an electron microscope picture of a cement section, wherein the cement section is obtained by slicing cement after high-temperature and high-pressure curing and high-temperature and high-pressure mechanical test; screening a required electron microscope picture according to the obtained electron microscope picture; splicing the screened required electron microscope picture to obtain a spliced picture; performing binaryzation processing on the spliced picture to obtain a binary picture; a pixel point in the binary picture corresponds to a small square; if the binary picture contains a pore, the corresponding small square is black, otherwise, the small square is white; performing multi-fractal analysis on the binary picture, and predicting the life of the high-temperature cement. The application establishes a correlation between a high-temperature cement fatigue damage factor and a fractal parameter based on multi-fractal analysis, and predicts the life of the high-temperature cement.

Description

Technical Field

[0001] This invention belongs to the field of oil well cement, and particularly relates to a method and system for predicting the life of high-temperature cement based on multifractal theory. Background Technology

[0002] Oil well cement is a crucial sealing material specifically used in cementing operations for oil and gas wells. Because cement slurry is pumped hundreds or thousands of meters downhole into the annular space between the wellbore and casing during cementing, and because downhole temperature and pressure increase with well depth, the performance requirements for oil well cement are much stricter than for general construction cement. For example, specific well depths correspond to varying bottomhole temperatures and pressures, resulting in significant variations in the chemical reaction environment of the cement slurry. Therefore, the prepared cement slurry must possess suitable density, good fluidity, and a reasonable pumpable time (commonly known as thickening time) during injection downhole. After the cement slurry reaches the designated sealing location and stops flowing, it should solidify quickly and reach a sufficient strength value within a relatively short time, avoiding prolonged setting time. The hardened cement stone should possess good sealing strength and bonding properties, good temperature stability and impermeability, and sufficient corrosion resistance, among other qualities. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention proposes a technical solution for predicting the lifespan of high-temperature cement based on multifractal theory.

[0004] The first aspect of this invention discloses a method for predicting the life of high-temperature cement based on multifractal theory, the method comprising:

[0005] Step S1: Obtain electron microscope images of cement slices, wherein the cement slices are obtained by slicing cement that has undergone high temperature and high pressure curing and has completed high temperature and high pressure mechanical tests.

[0006] Step S2: Based on the obtained electron microscope images, select the required electron microscope images and stitch them together to obtain a stitched image.

[0007] Step S3: Binarize the stitched image to obtain a binary image; each pixel in the binary image corresponds to a small square. If the binary image contains holes, the corresponding small square is black; otherwise, it is white.

[0008] Step S4: Perform multifractal analysis on the binary image and predict the lifespan of high-temperature cement.

[0009] According to the method of the first aspect of the present invention, in step S4, the multifractal analysis method includes: calculating the probability distribution function of the fractal and its moments of each order for the black and white small squares in the binary image, and constructing a continuous fractal spectrum of the fractal dimension; predicting the life of high-temperature cement by establishing the relationship between the fractal spectrum and fatigue life.

[0010] According to the method of the first aspect of the present invention, in step S4, the multifractal analysis method includes:

[0011] S41: Calculate the probability measure, as follows:

[0012] δ=L×2 -k

[0013] L is the total side length of the stitched electron microscope image, k is an integer greater than or equal to 0, and δ is the scale; each grid at scale δ is further subdivided into ε×ε small squares, where ε is an integer greater than or equal to 1;

[0014] Count the number N of black squares in ε×ε squares at the δ scale. ij And divide by the total number of black squares ∑N in the entire electron microscope image. ij The occupancy rate of each square with a scale of δ in the fractal image is obtained, which is the probability measure P. ij (δ), the specific formula is as follows:

[0015]

[0016] S42: Introducing the partition function of multifractal systems provides another representation for probability measures, as follows:

[0017] χ q (δ)~δ τ(q)

[0018] in,

[0019]

[0020] χq(δ) is the probability measure P ij The q-th moment, where q is a weighting factor, has a larger probability measure when q >> 1. ij For χ q The influence of (δ) is relatively large; conversely, when q << -1, P, which has a smaller probability measure, has a smaller influence. ij For χ q (δ) has a significant impact, where i and j represent the row and column positions of each small square, respectively.

[0021] The value of q is: -1 < q < 1;

[0022] S43: Based on the Legendre transformation in statistical physics, the multifractal spectrum α-f(α) of the fractal can be derived from the mass index. The relevant calculation formula for the singularity scaling index α is as follows:

[0023]

[0024] The relevant calculation formulas for the fractal spectrum f(α) are as follows:

[0025]

[0026] Where τ(q) is the quality index;

[0027] S44: Obtain the relationship between the fractal spectrum width and fractal spectrum height of high-temperature cement electron microscopy images under different loading conditions and different cycles, and predict the life of high-temperature cement.

[0028] The second aspect of this invention discloses a system for predicting the lifespan of high-temperature cement based on multifractal theory. The system employs the method for predicting the lifespan of high-temperature cement based on multifractal theory described in the first aspect. The system includes:

[0029] High-temperature and high-pressure curing equipment: used for conducting high-temperature and high-pressure mechanical tests;

[0030] Electron microscopy: Obtain electron micrographs of cement slices, wherein the cement slices are obtained by slicing cement that has undergone high-temperature and high-pressure curing and has completed high-temperature and high-pressure mechanical tests; based on the obtained electron micrograph images, select the required electron micrograph images, and stitch the selected electron micrograph images together to obtain a stitched image;

[0031] The binarization processing unit is configured to perform binarization processing on the stitched image to obtain a binary image; the pixels in the binary image correspond to a small square, and if the binary image contains holes, the corresponding small square is black, otherwise it is white;

[0032] A multifractal analysis unit is configured to perform multifractal analysis on the binary image and predict the lifespan of high-temperature cement.

[0033] According to the system of the second aspect of the present invention, a multifractal analysis unit is configured to calculate the probability distribution function of the fractal and its moments of each order for the black and white small squares in the binary image, and to construct a continuous fractal spectrum of the fractal dimension. By establishing the relationship between the fractal spectrum and the fatigue life, the life of high-temperature cement can be predicted.

[0034] According to a system of a second aspect of the present invention, a multifractal analysis unit is configured such that the multifractal analysis includes:

[0035] The probability measure is calculated as follows:

[0036] δ=L×2 -k

[0037] L is the total side length of the stitched electron microscope image, k is an integer greater than or equal to 0, and δ is the scale; each grid at scale δ is further subdivided into ε×ε small squares, where ε is an integer greater than or equal to 1;

[0038] Count the number N of black squares in ε×ε squares at the δ scale. ij And divide by the total number of black squares ∑N in the entire electron microscope image. ij The occupancy rate of each square with a scale of δ in the fractal image is obtained, which is the probability measure P. ij (δ), the specific formula is as follows:

[0039]

[0040] Introducing the partition function of multifractal systems provides another representation for probability measures, as follows:

[0041] χ q (δ)~δ τ(q)

[0042] in,

[0043]

[0044] χq(δ) is the probability measure P ij The q-th moment, where q is a weighting factor, has a larger probability measure when q >> 1. ij For χ q The influence of (δ) is relatively large; conversely, when q << -1, P, which has a smaller probability measure, has a smaller influence. ij For χ q (δ) has a significant impact, where i and j represent the row and column positions of each small square, respectively.

[0045] The value of q is: -1 < q < 1;

[0046] S43: Based on the Legendre transformation in statistical physics, the multifractal spectrum α-f(α) of the fractal can be derived from the mass index. The relevant calculation formula for the singularity scaling index α is as follows:

[0047]

[0048] The relevant calculation formulas for the fractal spectrum f(α) are as follows:

[0049]

[0050] Where τ(q) is the quality index;

[0051] The relationship between the fractal spectrum width and fractal spectrum height of high-temperature cement electron microscopy images under different loading conditions and different cycle numbers and fatigue life was obtained to predict the life of high-temperature cement.

[0052] According to a second aspect of the system of the present invention, the high-temperature and high-pressure curing device comprises:

[0053] Curing vessel, piston container, temperature control system, pressurization system, inlet and outlet pressure-resistant pipelines and valves;

[0054] The piston container and pressurization system are connected to the curing vessel via the inlet and outlet pressure-resistant pipelines and valves; the temperature control system is connected to the curing vessel.

[0055] The curing vessel is used for subsequent triaxial compression tests; the piston container is used to achieve the curing environment liquid required for different curing conditions; the temperature control system includes a temperature control heater and a temperature probe for heating and temperature control of the curing vessel; the pressurization system includes a pressure pump, a precision pressure gauge and a pressurization valve for providing a pressure environment for the curing vessel.

[0056] According to the system of the second aspect of the present invention, the working pressure of the curing vessel is greater than 50 MPa;

[0057] Before the curing process begins, the piston should be positioned in the middle of the piston container.

[0058] According to the system of the second aspect of the present invention, the high temperature and high pressure mechanical test includes: a triaxial compression test and a cyclic loading and unloading test;

[0059] The triaxial compression test determines the mechanical strength and deformation characteristics under complex stress and temperature conditions;

[0060] Based on the triaxial compression test, cyclic loading and unloading tests were conducted under different temperatures and confining pressures, different load levels, and different number of cycles.

[0061] According to the system of the second aspect of the present invention, the test procedure of the triaxial compression test is as follows: a pressure head is added to both ends of the cement specimen and then sealed with a sealing sleeve; a strain sensor is installed and placed in a pressure chamber; a lateral pressure is first applied to the specimen to reach a preset value; an axial pressure is applied to the specimen until the specimen fails while keeping the lateral pressure constant; and the load and strain values ​​of the specimen are recorded during the test.

[0062] The test procedure for the cyclic loading and unloading test is as follows: pressure heads are added to both ends of the specimen and then sealed with a sealing sleeve. Strain sensors are installed and placed in the pressure chamber. First, lateral pressure is applied to the specimen to reach a preset value. Under the condition of keeping the lateral pressure constant, axial pressure within a specific upper and lower limit and loading and unloading rate range is applied to the specimen for cyclic loading and unloading. During the test, the load and strain values ​​of the specimen are recorded.

[0063] A third aspect of this invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements steps S3-S4 of the method for predicting the life of high-temperature cement based on multifractal theory according to any one of the first aspects of this disclosure.

[0064] A fourth aspect of this invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements steps S3-S4 of the method for predicting the lifespan of high-temperature cement based on multifractal theory according to any one of the first aspects of this disclosure.

[0065] The proposed solution can simulate the curing conditions of cement materials and conduct fatigue tests to obtain crack evolution images of cement materials. Based on the crack evolution images, the fractal dimension of the series of images is obtained through programming, thereby obtaining the curve of the fractal dimension parameter changing with the life. Based on the curve, the life prediction value can be obtained, and the correlation between other fatigue damage factors and fractal parameters can be established. Attached Figure Description

[0066] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0067] Figure 1 This is a flowchart of a method for predicting the life of high-temperature cement based on multifractal theory according to an embodiment of the present invention;

[0068] Figure 2 This is a structural diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] The first aspect of this invention discloses a method for predicting the lifespan of high-temperature cement based on multifractal theory. Figure 1 This is a flowchart illustrating a method for predicting the lifespan of high-temperature cement based on multifractal theory according to an embodiment of the present invention. Figure 1 As shown, the method includes:

[0071] First, a high-temperature and high-pressure curing device was designed to simulate the actual confining pressure and temperature of downhole rock. Then, cement stone samples cured using the high-temperature and high-pressure curing device were subjected to high-temperature and high-pressure mechanical tests.

[0072] High temperature and high pressure mechanical tests have a special mechanical testing machine. For details, please refer to the American-made MTS815Flex Test GT programmable servo rock mechanics testing system in the example. The high temperature and high pressure curing device is only used to cure cement samples. The general process is: (1) prepare cement stone samples in the high temperature and high pressure curing kettle (high temperature and high pressure curing kettle), (2) carry out high temperature and high pressure rock mechanics tests in the rock mechanics testing machine, and (3) observe and analyze the samples after the test using SEM.

[0073] Step S1: Obtain electron microscope images of cement slices, wherein the cement slices are obtained by slicing cement that has undergone high temperature and high pressure curing and has completed high temperature and high pressure mechanical tests.

[0074] Specifically, the cement samples after the test need to be sliced, and then the slices are scanned or photographed by electron microscopy to obtain electron micrographs.

[0075] In some specific embodiments, step S1 involves obtaining electron micrographs of cement slices. These cement slices are obtained by slicing cement that has undergone high-temperature and high-pressure curing and completed high-temperature and high-pressure mechanical testing. Specifically, the electron microscopy analysis involves stitching together high-magnification electron micrographs. Regarding the microstructure of cement stone: cement hydration is an alternating chemical reaction between clinker components, calcium sulfate, and water, resulting in the continuous thickening and hardening of the cement paste. Cement stone hardened at room temperature typically consists of unhydrated cement clinker particles, hydrated cement, water, and a small amount of air, as well as a porous network occupied by water and air. Therefore, hardened cement is a bonding matrix material; it is itself a composite material, belonging to a solid-liquid-gas three-phase porous system. The properties of cement stone ultimately depend on the properties of these components, their relative content, and the interactions between them, i.e., the microstructure.

[0076] The phenomenon of decreased strength and increased permeability of cement paste under high-temperature conditions is commonly referred to as "strength decay" in cement paste. Under high-temperature curing conditions, the hydration products produced by cement hydration differ from those produced under normal-temperature conditions, exhibiting a series of complex changes including crystal transformation, gelation, and crystal dehydration. With increasing temperature, the microstructure and morphology of CSH gel, the most abundant hydration product in silicate cement, undergo certain changes. Most hydration products transform into fibrous structures, and a higher degree of silicate polymerization can be observed. Simultaneously, adding silica sand, silica fume, or silica ash to the cement paste can improve the carbon-silicon ratio in the cement, thereby improving the morphology and properties of the formed cement hydration products and ultimately mitigating the strength decay phenomenon of cement paste under high temperatures.

[0077] Characterization techniques that can intuitively demonstrate the spatial distribution characteristics of different pore sizes include electron microscopy, CT, and MRI. However, due to resolution limitations, only scanning electron microscopy (SEM) can achieve nanoscale observation. Electron microscopy is the most commonly used method for studying the size, morphology, surface structure, and micro-area chemical composition of nanopores. This method generally includes scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Relying on the interaction between electrons and matter, including the collection of secondary electrons and backscattered electrons, information about the microscopic morphology of the material can be obtained. This method is an absolute method for particle size observation because of its reliability, intuitiveness, and advantages such as large depth of field, high resolution, intuitive imaging, and a wide magnification range. High-magnification electron microscopy (up to 200,000x) can achieve nanoscale pore observation.

[0078] In this embodiment, a field emission scanning electron microscope (SEM) is used, a large and precise instrument for high-resolution morphological observation. SEM features a large depth of field, high resolution, intuitive imaging, strong stereoscopic effect, wide magnification range, and the ability to rotate and tilt the sample in three-dimensional space. It also offers advantages such as the ability to analyze a wide variety of samples, minimal damage or contamination to the original sample, and the simultaneous acquisition of morphological, structural, compositional, and crystallographic information. Currently, scanning electron microscopes are widely used in microscopic research in life sciences, physics, chemistry, earth sciences, materials science, and industrial production.

[0079] Step S2: Based on the obtained electron microscope images, select the required electron microscope images, and stitch the selected electron microscope images together to obtain a stitched image.

[0080] The specific method for selecting the required electron microscope images is as follows:

[0081] High-magnification electron microscopy images are stitched together to achieve simultaneous observation of multiple aperture scales; multiple images are used to increase the number of apertures to be analyzed, making them more representative.

[0082] In some embodiments, after the electron microscope is moved by the translation stage in step S2, the calibration of the before and after images should be ensured to be performed in areas of the sample with obvious features, and not in large areas without samples or in areas of samples with uniform structure.

[0083] Specifically, measurements at high magnification lack overall statistical significance. Therefore, it is necessary to stitch together high-magnification electron microscopy images to achieve simultaneous observation of multiple aperture scales. Multiple images increase the number of apertures to be analyzed, making the results more representative.

[0084] Multi-image stitching technology requires the use of a certain matching strategy to find the corresponding positions of feature points in the image to be stitched in the reference image, and then determine the transformation relationship between the stitched images.

[0085] Using the built-in camera and image processing software of the scanning electron microscope (SEM) to take pictures and stitch them together, it is important to note that after the SEM is moved by the translation stage, the calibration of the images before and after should be carried out in areas of the sample with obvious features, and not in large areas without samples or in areas of samples with uniform structure, otherwise the image coordinates cannot be accurately located when stitching the images.

[0086] Before capturing images, you need to pre-select the number of images to be stitched together, including the number of horizontal and vertical images. Then, the system will automatically take pictures in sequence according to the selection.

[0087] The above method can effectively expand the field of view of electron microscope cameras and solve the problem of the representativeness of small-scale particle size sampling.

[0088] Step S3: Binarize the stitched image to obtain a binary image; each pixel in the binary image corresponds to a small square. If the binary image contains holes, the corresponding small square is black; otherwise, it is white. Specifically, image binarization can be achieved using Matlab's toolbox Fraclab or ImageJ.

[0089] Electron microscope images are inherently grayscale images, typically displayed as grayscale levels ranging from the darkest black to the brightest white, with 256 grayscale levels. Binarization is used to reduce the image to only black and white.

[0090] Step S4: Perform multifractal analysis on the binary image and predict the lifespan of high-temperature cement.

[0091] In step S4, the multifractal analysis method includes: calculating the probability distribution function of the fractal and its moments of each order for the black and white small squares in the binary image, and constructing a continuous fractal spectrum of the fractal dimension; predicting the life of high-temperature cement by establishing the relationship between the fractal spectrum and fatigue life.

[0092] In step S4, the multifractal analysis method includes:

[0093] S41: Calculate the probability measure, as follows:

[0094] δ=L×2 -k

[0095] L is the total side length of the stitched electron microscope image, k is an integer greater than or equal to 0, and δ is the scale; each square at scale δ is further subdivided into ε×ε small squares, and when subdivided infinitely to the last pixel, ε is 1, so ε is an integer greater than or equal to 1.

[0096] Count the number N of black squares in ε×ε squares at the δ scale. ij And divide by the total number of black squares ∑N in the entire electron microscope image. ij The occupancy rate of each square with a scale of δ in the fractal image is obtained, which is the probability measure P. ij (δ), the specific formula is as follows:

[0097]

[0098] S42: Introducing the partition function of multifractal systems provides another representation for probability measures, as follows:

[0099] χ q (δ)~δ τ(q)

[0100] in,

[0101]

[0102] χq(δ) is the probability measure P ij The q-th moment, where q is a weighting factor, has a larger probability measure when q >> 1. ij For χ q The influence of (δ) is relatively large; conversely, when q << -1, P, which has a smaller probability measure, has a smaller influence. ij For χ q (δ) has a significant impact, where i and j represent the row and column positions of each small square, respectively.

[0103] The value of q is: -1 < q < 1;

[0104] S43: Based on the Legendre transformation in statistical physics, the multifractal spectrum α-f(α) of the fractal can be derived from the mass index. The relevant calculation formula for the singularity scaling index α is as follows:

[0105]

[0106] The relevant calculation formulas for the fractal spectrum f(α) are as follows:

[0107]

[0108] Where τ(q) is the quality index;

[0109] Δα is the spectral width of the fractal spectrum, and Δf is the spectral height of the fractal spectrum;

[0110] f(α max ) is the maximum value of f(α), f(α) min The minimum value of f(α) is given by f(α), and the spectral height Δf of the fractal spectrum is given by f(α). min )-f(α max The spectral height Δf of the fractal spectrum reflects the roughness of the crack on the damaged surface.

[0111] S44: Obtain the relationship between the fractal spectrum width and fractal spectrum height of high-temperature cement electron microscopy images under different loading conditions and different cycles, and predict the life of high-temperature cement; the fractal spectrum width and height can reflect the degree of damage, and the relationship between the degree of damage and the number of fatigue cycles can be used to predict the life. Specific implementation examples:

[0113] The following is a specific embodiment of step S4, performing multifractal analysis on the binary image, and predicting the lifespan of high-temperature cement.

[0114] To more accurately characterize the complexity and inhomogeneity of fractals, it is necessary to introduce the probability distribution function of fractals and the calculation of their moments, thereby constructing a continuous spectrum of fractal dimension, which allows for a hierarchical understanding of the internal fine structure of fractals.

[0115] Specifically, a multifractal is a complex fractal structure divided into multiple regions. Simple fractals use only one dimension to describe their overall characteristics, which cannot fully capture the complexity and diversity of nature.

[0116] To more precisely characterize the complexity and inhomogeneity of fractals, it is necessary to introduce their probability distribution function and the calculation of their moments, thus constructing a continuous spectrum of the fractal dimension, known as a multifractal or multiscale fractal. Using multifractals, a complex fractal can be divided into many small regions with different degrees of singularity for study, thereby enabling a hierarchical understanding of the fractal's internal fine structure.

[0117] The box dimension algorithm is used to count the number of boxes at different scales.

[0118] To perform multifractal analysis, probability measures need to be calculated. Specifically:

[0119] δ=L×2 -k L is the total side length of the entire electron microscope image, k is an integer greater than or equal to 0, and δ is the scale; each grid at scale δ is further subdivided into ε×ε small squares (i.e., pixels).

[0120] If each small square (corresponding pixel) in the overall electron microscope image contains a pore, then the small square is defined as black; otherwise, it is white. Then, the number N of black small squares within ε×ε small squares is counted at the δ-scale. ij And divide by the total number of black squares in the entire electron microscope image, ∑N. ij This yields the occupancy rate of each square with a scale of δ in the fractal image, which is the probability measure.

[0121]

[0122] Using relevant theories and calculations from statistical physics, a partition function for multifractal systems is introduced:

[0123]

[0124] The above formula is defined as the probability measure P. ij The q-th moment, where q ranges from -∞ to +∞, but in the calculation, the absolute value of q between 1 and 10 is sufficient. q is called the weighting factor. When q >> 1, P has a relatively large probability measure. ij For χ qThe influence of (δ) is relatively large; conversely, when q << -1, P, which has a smaller probability measure, has a smaller influence. ij For χ q The influence of (δ) is relatively large. Therefore, q usually takes values ​​from -1 to 1.

[0125] Ultimately, χ q (δ) provides another representation of probability measure P ij :

[0126] χ q (δ)~δ τ(q)

[0127] Here, τ(q) is called the mass index. Finally, based on the Legendre transformation in statistical physics, the multifractal spectrum α-f(α) of the fractal is derived from the mass index. The singularity scaling index α is calculated by the following formula:

[0128]

[0129] The fractal spectrum f(α) is obtained from the following equation:

[0130]

[0131] A single fractal dimension alone cannot fully reflect the complete information of the distribution of micro-defects during the fatigue damage process of materials. However, the two important characteristic parameters of multifractal spectrum, spectral height and spectral width, can make up for the deficiency, thereby achieving a comprehensive and systematic description of damage information.

[0132] From the calculation and theory of multifractals, we know that Δα is the spectral width of the fractal spectrum (the fractal spectrum f(α) is a convex function of α. Δα = αmax - αmin, which represents the difference between the maximum and minimum probabilities, and physically represents the degree of significance of the multifractal features of the fractal image), and Δf is the spectral height of the fractal spectrum (Δf = f(α)). min )-f(α max ));

[0133] f(α max ) is the maximum value of f(α), f(α) min The minimum value of f(α) is given by f(α), and the spectral height Δf of the fractal spectrum is given by f(α). min )-f(α max The spectral height Δf of the fractal spectrum reflects the roughness of the crack on the damaged surface.

[0134] The scaling exponent α and the fractal spectrum f(α) have a convex function relationship. When f(α) reaches its maximum value, f(α) max The larger ) is, the larger the interval [α] min ,α maxThe greater the width of f(α) and the better the symmetry of the f(α) spectrum curve, the stronger the multifractal property of the image sample.

[0135] The meaning represented is: as the number of cycles increases, the fractal spectrum f(α) max The increase in the fractal spectrum width Δ indicates an increase in the proportion of cracks on the fatigued surface; α An increase indicates an increase in the non-uniformity of fatigue surface cracks. Δα reflects the magnitude of the probability distribution range. The more non-uniform the probability distribution, the wider the corresponding f(α) curve, i.e., the larger Δα. In the field of fatigue research, the fractal spectrum height Δf = f(α) min )-f(α max This reflects the roughness of the cracks on the damaged surface.

[0136] The relationship between the spectral width and spectral height of damage images under different loading conditions and different cycle numbers as a function of fatigue life can be obtained. As the loading amplitude and the number of cycles increase, the change of Δα or Δf with fatigue life reflects the fatigue evolution process, which can be divided into three stages: the initial rapid growth stage, the middle stable damage stage, and the late jump failure stage.

[0137] In summary, the proposed solution can simulate the curing conditions of cement materials and conduct fatigue tests to obtain crack evolution images of cement materials. Based on the crack evolution images, the fractal dimension of the series of images is obtained through programming, thereby obtaining the curve of the fractal dimension parameter changing with the life. Based on the curve, the life prediction value can be obtained, and the correlation between other fatigue damage factors and fractal parameters can be established.

[0138] The second aspect of this invention discloses a system for predicting the lifespan of high-temperature cement based on multifractal theory. The system employs the method for predicting the lifespan of high-temperature cement based on multifractal theory described in the first aspect of this invention. The system includes:

[0139] High-temperature and high-pressure curing equipment: used for conducting high-temperature and high-pressure mechanical tests;

[0140] High-temperature and high-pressure curing device: This device realistically simulates the underground geological environment, obtaining cement samples at different depths, temperatures, and pressures. Since temperature and pressure significantly affect the cement hydration process, this device can more accurately evaluate cement samples under different geological conditions. According to the standard "General Portland Cement" (GB 175-2007), the cement paste is expected to reach its final strength (i.e., over 90%) after 28 days.

[0141] Once the cement stone has solidified and formed (with stable mechanical properties), it is removed for further mechanical testing. The high-temperature and high-pressure mechanical tests include triaxial compression tests and cyclic loading and unloading tests, using an MTS testing machine.

[0142] After the experiment, the cement samples were sliced ​​to obtain the samples needed for electron microscopy testing. The final electron micrographs were then obtained. Argon ion polishing was used for pretreatment to obtain smooth cross-sections without causing mechanical damage to the samples. After argon ion beam polishing, the cement samples, combined with scanning electron microscopy (SEM) and X-ray diffraction, can be analyzed for mineral composition, structure, and pore distribution. Furthermore, the reservoir structure in the cement stone can be observed, pore fractures can be quantitatively counted, and porosity can be determined.

[0143] Electron microscopy: Obtain electron micrographs of cement slices, wherein the cement slices are obtained by slicing cement that has undergone high temperature and high pressure curing and high temperature and high pressure mechanical testing; based on the electron micrographs taken, select the required electron micrographs, and stitch the selected electron micrographs together to obtain a stitched image;

[0144] The binarization processing unit is configured to perform binarization processing on the stitched image to obtain a binary image; the pixels in the binary image correspond to a small square, and if the binary image contains holes, the corresponding small square is black, otherwise it is white;

[0145] A multifractal analysis unit is configured to perform multifractal analysis on the binary image and predict the lifespan of high-temperature cement.

[0146] Specifically, the high-temperature and high-pressure curing device includes: a curing vessel, a piston container, a temperature control system, a pressurization system, inlet and outlet pressure-resistant pipelines and valves;

[0147] The piston container and pressurization system are connected to the curing vessel via the inlet and outlet pressure-resistant pipelines and valves; the temperature control system is connected to the curing vessel.

[0148] The curing vessel is used for subsequent triaxial compression testing; the piston container is used to provide the curing environment liquid required for different curing conditions; the temperature control system includes a temperature-controlled heater and a temperature probe for heating and temperature control of the curing vessel; the pressurization system includes a pressure pump, a precision pressure gauge, and a pressurization valve for providing a pressure environment for the curing vessel. The working pressure of the curing vessel is greater than 50 MPa; the dimensions of the curing vessel meet the minimum dimensions of the specimens required for subsequent triaxial compression testing, using a diameter of 120 mm and a height of 250 mm.

[0149] Before the curing process begins, the piston should be positioned in the middle of the piston container.

[0150] The high-temperature and high-pressure mechanical tests include: triaxial compression tests and cyclic loading and unloading tests;

[0151] The triaxial compression test determines the mechanical strength and deformation characteristics under complex stress and temperature conditions;

[0152] Based on the triaxial compression test, cyclic loading and unloading tests were conducted under different temperatures and confining pressures, different load levels, and different number of cycles.

[0153] The procedure for the triaxial compression test is as follows: indenters are added to both ends of the cement specimen and then sealed with a sealing sleeve. Strain sensors are installed and the specimen is placed in a pressure chamber. Lateral pressure is first applied to the specimen to reach a preset value. Under the condition of keeping the lateral pressure constant, axial pressure is applied to the specimen until the specimen fails. The load and strain values ​​of the specimen are recorded during the test.

[0154] The test procedure for the cyclic loading and unloading test is as follows: pressure heads are added to both ends of the specimen and then sealed with a sealing sleeve. Strain sensors are installed and placed in the pressure chamber. First, lateral pressure is applied to the specimen to reach a preset value. Under the condition of keeping the lateral pressure constant, axial pressure within a specific upper and lower limit and loading and unloading rate range is applied to the specimen for cyclic loading and unloading. During the test, the load and strain values ​​of the specimen are recorded.

[0155] In some specific embodiments, a high-temperature and high-pressure curing device is designed to simulate the actual confining pressure and temperature of downhole rock. The high-temperature and high-pressure curing device includes:

[0156] Curing vessel, piston container, temperature control system, pressurization system, and pressure-resistant inlet and outlet pipelines and valves for connection;

[0157] The piston container and pressurization system are connected to the curing vessel via the inlet and outlet pressure-resistant pipelines and valves; the temperature control system is connected to the curing vessel.

[0158] The curing vessel is used for subsequent triaxial compression tests; the piston container is used to achieve the curing environment liquid required for different curing conditions; the temperature control system includes a temperature control heater and a temperature probe for heating and temperature control of the curing vessel; the pressurization system includes a pressure pump, a precision pressure gauge and a pressurization valve for providing a pressure environment for the curing vessel.

[0159] The curing vessel reaches a high working pressure of more than 50 MPa, and the dimensions of the curing vessel meet the minimum size of the specimen required for the subsequent triaxial compression test, with a diameter of 120 mm and a height of 250 mm.

[0160] Before the curing process begins, the piston should be positioned as close to the center of the piston container as possible.

[0161] Specifically, the composition and structure of hydration products are mainly determined by the properties of cement clinker minerals and the hydration and hardening environment. For a given type of cement clinker, the curing temperature and the effect of admixtures can not only change the composition and structure of hydration products, but also change the pore structure and porosity of cement stone and the water content in cement stone (including free water, interlayer water of hydration products, and bound water of hydration products), thereby changing the mechanical properties of hardened cement stone.

[0162] In order to conduct a more objective and realistic study and evaluation of the hydration, hardening and performance of oil well cement, it is necessary to realistically simulate the downhole environment and meet different temperature and confining pressure conditions for cement stone curing.

[0163] The influence of temperature changes on the cement hydration process is quite complex. During the cement hydration process, there are complex processes such as cement hydration, free water evaporation, crystal water dehydration and evaporation, and crystal transformation of hydration products. These processes interact with each other within a specific temperature range, which makes the hydration process quite different from that under constant temperature conditions.

[0164] The high-temperature and high-pressure curing device was used to conduct high-temperature and high-pressure mechanical tests, which included triaxial compression tests and cyclic loading and unloading tests.

[0165] The triaxial compression test determines the mechanical strength and deformation characteristics under complex stress and temperature conditions;

[0166] Based on the triaxial compression test, cyclic loading and unloading tests were conducted under different temperatures and confining pressures, different load levels and number of cycles to study the cumulative evolution of damage in different cement stone.

[0167] The procedure for the triaxial compression test is as follows: indenters are added to both ends of the cement specimen and then sealed with a sealing sleeve. Strain sensors are installed and the specimen is placed in a pressure chamber. Lateral pressure is first applied to the specimen to reach a preset value. Under the condition of keeping the lateral pressure constant, axial pressure is applied to the specimen until the specimen fails. The load and strain values ​​of the specimen are recorded during the test.

[0168] The test procedure for the cyclic loading and unloading test is as follows: pressure heads are added to both ends of the specimen and then sealed with a sealing sleeve. Strain sensors are installed and placed in the pressure chamber. First, lateral pressure is applied to the specimen to reach a preset value. Under the condition of keeping the lateral pressure constant, axial pressure within a specific upper and lower limit and loading and unloading rate range is applied to the specimen for cyclic loading and unloading. During the test, the load and strain values ​​of the specimen are recorded.

[0169] In this embodiment, the equipment used is the American-made MTS815 Flex Test GT programmable servo rock mechanics testing system, mainly used for conventional mechanical tests of materials such as rock and concrete under electro-hydraulic servo control. It is equipped with a servo-controlled fully automatic triaxial pressurization and measurement system. The system consists of the following parts:

[0170] Loading section: consists of a hydraulic power source, a single-axis pressurization frame, a triaxial chamber, actuators, servo valves, and a booster.

[0171] The testing section consists of various sensors for load, pressure, displacement, strain, etc.

[0172] Control section: Consists of control hardware and software such as feedback control system, data acquisition unit, and computer;

[0173] Program control components include: test assistant, static test software, multi-functional test software, function generator control, etc.

[0174] The system's performance specifications are as follows: maximum vertical output force: 4600 kN, vertical piston stroke: 100 mm, maximum confining pressure: 140 MPa, strain rate adaptability range: 10⁻² to 10⁻². -7 1 / s, fatigue frequency: 0.001~0.5Hz, overall stiffness of the test frame: 11.0×10 9 The test system operates at a stable load of N / m and has high measurement and control accuracy. All test processes and data are controlled and collected by computer, avoiding misreading and errors caused by manual reading.

[0175] The procedure for the triaxial compression test is as follows: indenters are added to both ends of the cement specimen and then sealed with a sealing sleeve. Strain sensors are installed and the specimen is placed in a pressure chamber. Lateral pressure is first applied to the specimen to reach a preset value. Under the condition of keeping the lateral pressure constant, axial pressure is applied to the specimen until the specimen fails. The load and strain values ​​of the specimen are recorded during the test.

[0176] The test procedure for the cyclic loading and unloading test is as follows: pressure heads are added to both ends of the specimen and then sealed with a sealing sleeve. Strain sensors are installed and placed in the pressure chamber. First, lateral pressure is applied to the specimen to reach a preset value. Under the condition of keeping the lateral pressure constant, axial pressure within a specific upper and lower limit and loading and unloading rate range is applied to the specimen for cyclic loading and unloading. During the test, the load and strain values ​​of the specimen are recorded.

[0177] Electron microscopy: Obtain electron micrographs of cement slices, wherein the cement slices are obtained by slicing cement that has undergone high temperature and high pressure curing and high temperature and high pressure mechanical testing; based on the electron micrographs taken, select the required electron micrographs, and stitch the selected electron micrographs together to obtain a stitched image;

[0178] Binarization processing unit: configured to perform binarization processing on the stitched image to obtain a binary image; the pixels in the binary image correspond to a small square, and if the binary image contains holes, the corresponding small square is black, otherwise it is white;

[0179] A multifractal analysis unit is configured to perform multifractal analysis on the binary image and predict the lifespan of high-temperature cement.

[0180] The multifractal analysis includes: using the probability distribution function of the fractal and calculating its moments of each order, and constructing a continuous spectrum of the fractal dimension to reflect the internal structure of the fractal in a hierarchical manner.

[0181] According to the system of the second aspect of the present invention, a multifractal analysis unit is configured to calculate the probability distribution function of the fractal and its moments of each order for the black and white small squares in the binary image, and to construct a continuous fractal spectrum of the fractal dimension. By establishing the relationship between the fractal spectrum and the fatigue life, the life of high-temperature cement can be predicted.

[0182] According to a system of a second aspect of the present invention, a multifractal analysis unit is configured such that the multifractal analysis includes:

[0183] The probability measure is calculated as follows:

[0184] δ=L×2- k

[0185] L is the total side length of the stitched electron microscope image, k is an integer greater than or equal to 0, and δ is the scale; each grid at scale δ is further subdivided into ε×ε small squares.

[0186] Count the number N of black squares in ε×ε squares at the δ scale. ij And divide by the total number of black squares ∑N in the entire electron microscope image. ij The occupancy rate of each square with a scale of δ in the fractal image is obtained, which is the probability measure P. ij (δ), the specific formula is as follows:

[0187]

[0188] Introducing the partition function of multifractal systems provides another representation for probability measures, as follows:

[0189] χ q (δ)~δ τ(q)

[0190] in,

[0191]

[0192] χq(δ) is the probability measure P ij The q-th moment, where q is a weighting factor, has a larger probability measure when q >> 1. ij For χ q The influence of (δ) is relatively large; conversely, when q << -1, P, which has a smaller probability measure, has a smaller influence. ij For χ q (δ) has a significant impact;

[0193] The value of q is: -1 < q < 1;

[0194] S43: Based on the Legendre transformation in statistical physics, the multifractal spectrum α-f(α) of the fractal can be derived from the mass index. The relevant calculation formula for the singularity scaling index α is as follows:

[0195]

[0196] The relevant calculation formulas for the fractal spectrum f(α) are as follows:

[0197]

[0198] Where τ(q) is the quality index; Δα is the spectral width of the fractal spectrum; and Δf is the spectral height of the fractal spectrum.

[0199] f(α max ) is the maximum value of f(α), f(α) min The minimum value of f(α) is given by f(α), and the spectral height Δf of the fractal spectrum is given by f(α). min )-f(α max The spectral height Δf of the fractal spectrum reflects the roughness of the crack on the damaged surface.

[0200] The relationship between the fractal spectrum width and fractal spectrum height of high-temperature cement electron microscopy images under different loading conditions and different cycle numbers and fatigue life was obtained to predict the life of high-temperature cement.

[0201] A third aspect of this invention discloses an electronic device. The electronic device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements steps S3-S4 of the method for predicting the life of high-temperature cement based on multifractal theory according to any one of the first aspects of this invention.

[0202] Figure 2 This is a structural diagram of an electronic device according to an embodiment of the present invention, such as... Figure 2As shown, the electronic device includes a processor, memory, communication interface, display screen, and input device connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, Near Field Communication (NFC), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input device can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the device's casing, or an external keyboard, touchpad, or mouse.

[0203] Those skilled in the art will understand that Figure 2 The structure shown is merely a structural diagram of the part related to the technical solution of this disclosure and does not constitute a limitation on the electronic device to which the solution of this application is applied. The specific electronic device may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0204] A fourth aspect of this invention discloses a computer-readable storage medium. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements steps S3-S4 of the method for predicting the lifespan of high-temperature cement based on multifractal theory according to any one of the first aspects of this invention.

[0205] Please note that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. The above embodiments only illustrate several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for predicting the lifespan of high-temperature cement based on multifractal theory, characterized in that, The method includes: Step S1: Obtain electron microscope images of cement slices, wherein the cement slices are obtained by slicing cement that has undergone high temperature and high pressure curing and has completed high temperature and high pressure mechanical tests. Step S2: Based on the obtained electron microscope images, select the required electron microscope images and stitch them together to obtain a stitched image, so as to achieve the goal of simultaneous observation of multiple scale apertures. The calibration of the images before and after stitching is carried out in the areas of the sample with obvious features. Step S3: Binarize the stitched image to obtain a binary image; each pixel in the binary image corresponds to a small square. If the binary image contains holes, the corresponding small square is black; otherwise, it is white. Step S4: Perform multifractal analysis on the binary image and predict the lifespan of high-temperature cement; In step S4, the multifractal analysis method includes: For the black and white squares in the binary image, the probability distribution function of the fractal and its moments are calculated to form a continuous fractal spectrum of the fractal dimension. By establishing the relationship between the fractal spectrum and fatigue life, the life of high-temperature cement can be predicted. In step S4, the multifractal analysis method includes: S41: Calculate the probability measure, as follows: δ=L×2 -k L is the total side length of the stitched electron microscope image, k is an integer greater than or equal to 0, and δ is the scale; each grid at scale δ is further subdivided into ε×ε small squares; ε is an integer greater than or equal to 1; Count the number N of black squares in ε×ε squares at the δ scale. ij And divide by the total number of black squares ∑N in the entire electron microscope image. ij The occupancy rate of each square with a scale of δ in the fractal image is obtained, which is the probability measure. P ij (δ) The specific formula is as follows: S42: Introducing the partition function of multifractal systems provides another representation for probability measures, as follows: in, χq(δ) For probability measure P ij of q Step moment, q As a weighting factor, when q When >> 1, it has a relatively high probability measure. P ij right χ q (δ) The impact is relatively large; conversely, when q When << -1, it has a smaller probability measure. P ij right χ q (δ) The impact is significant; P ij Indicates the first i Line 1 j A probability measure of a column; q The value can be: -1 < q <1; S43: Based on the Legendre transformation in statistical physics, the multifractal spectrum α-f(α) of the fractal can be derived from the mass index. The relevant calculation formula for the singularity scaling index α is as follows: The relevant calculation formulas for the fractal spectrum f(α) are as follows: Where τ(q) is the quality index; S44: Obtain the relationship between the fractal spectrum width and fractal spectrum height of high-temperature cement electron microscopy images under different loading conditions and different cycles, and predict the life of high-temperature cement.

2. A system for predicting the lifespan of high-temperature cement based on multifractal theory, characterized in that, The system employs the high-temperature cement life prediction method based on multifractal theory as described in claim 1, and the system comprises: High-temperature and high-pressure curing equipment: used for conducting high-temperature and high-pressure mechanical tests; Electron microscopy: Obtain electron microscopic images of cement slices, wherein the cement slices are obtained by slicing cement that has undergone high temperature and high pressure curing and has completed high temperature and high pressure mechanical tests; Based on the electron microscopic images taken, select the required electron microscopic images, and stitch the selected electron microscopic images together to obtain a stitched image, so as to achieve the goal of simultaneous observation of multiple scale apertures. The binarization processing unit is configured to perform binarization processing on the stitched image to obtain a binary image; the pixels in the binary image correspond to a small square, and if the binary image contains holes, the corresponding small square is black, otherwise it is white; A multifractal analysis unit is configured to perform multifractal analysis on the binary image and predict the lifespan of high-temperature cement. The multifractal analysis unit is also used to calculate the probability distribution function of the fractal and its moments of each order for the black and white small squares in the binary image, and to construct a continuous fractal spectrum of the fractal dimension. By establishing the relationship between the fractal spectrum and fatigue life, the life of high-temperature cement can be predicted.

3. A system for predicting the lifespan of high-temperature cement based on multifractal theory according to claim 2, characterized in that, The high-temperature and high-pressure curing device includes: Curing vessel, piston container, temperature control system, pressurization system, inlet and outlet pressure-resistant pipelines and valves; The piston container and pressurization system are connected to the curing vessel via the inlet and outlet pressure-resistant pipelines and valves; the temperature control system is connected to the curing vessel. The curing vessel is used for subsequent triaxial compression tests; the piston container is used to achieve the curing environment liquid required for different curing conditions; the temperature control system includes a temperature control heater and a temperature probe for heating and temperature control of the curing vessel; the pressurization system includes a pressure pump, a precision pressure gauge and a pressurization valve, and the pressurization system is used to provide a pressure environment for the curing vessel.

4. A system for predicting the lifespan of high-temperature cement based on multifractal theory according to claim 3, characterized in that, The working pressure of the curing vessel is greater than 50 MPa; Before the curing process begins, the piston should be positioned in the middle of the piston container.

5. A system for predicting the lifespan of high-temperature cement based on multifractal theory according to claim 2, characterized in that, The high-temperature and high-pressure mechanical tests include: triaxial compression tests and cyclic loading and unloading tests; The triaxial compression test determines the mechanical strength and deformation characteristics under complex stress and temperature conditions; Based on the triaxial compression test, cyclic loading and unloading tests were conducted under different temperatures and confining pressures, different load levels, and different number of cycles.

6. A system for predicting the lifespan of high-temperature cement based on multifractal theory according to claim 5, characterized in that, The procedure for the triaxial compression test is as follows: indenters are added to both ends of the cement specimen and then sealed with a sealing sleeve. Strain sensors are installed and the specimen is placed in a pressure chamber. Lateral pressure is first applied to the specimen to reach a preset value. Under the condition of keeping the lateral pressure constant, axial pressure is applied to the specimen until the specimen fails. The load and strain values ​​of the specimen are recorded during the test. The test procedure for the cyclic loading and unloading test is as follows: pressure heads are added to both ends of the specimen and then sealed with a sealing sleeve. Strain sensors are installed and placed in the pressure chamber. First, lateral pressure is applied to the specimen to reach a preset value. Under the condition of keeping the lateral pressure constant, axial pressure within a specific upper and lower limit and loading and unloading rate range is applied to the specimen for cyclic loading and unloading. During the test, the load and strain values ​​of the specimen are recorded.

7. An electronic device, characterized in that, The electronic device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements steps S3-S4 in the method for predicting the life of high-temperature cement based on multifractal theory as described in claim 1.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which, when executed by a processor, implements steps S3-S4 of the method for predicting the life of high-temperature cement based on multifractal theory as described in claim 1.

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