Method, device, equipment and medium for monitoring polyurethane diffusion in porous media

Abstract

The present invention relates to the field of porous media monitoring technology, and more particularly to a method, apparatus, device, and medium for monitoring polyurethane diffusion in porous media. The method comprises selecting a diffusion model based on the diffusion characteristics of polyurethane in the porous medium, winding a distributed optical fiber around a sensing cage to form a helical structure, mapping the coordinates of each temperature measurement point on the helical structure to a rectangular coordinate system in the porous medium space, measuring the initial moisture field before polyurethane infiltration in the porous medium, monitoring the post-infiltration moisture field in a stable state of temperature transfer fluctuations as the polyurethane diffuses in the porous medium during the polyurethane infiltration process, analyzing changes in moisture content based on the initial moisture field and the post-infiltration moisture field, and identifying the polyurethane diffusion distribution field in the porous medium in combination with the diffusion model. The present invention utilizes distributed optical fiber sensing technology and exploits the characteristic of changes in thermal conductivity of polyurethane after curing to achieve a comprehensive and accurate assessment of the diffusion of polyurethane in the porous medium.

Description

Technical Field

[0001] The present invention relates to the technical field of porous medium monitoring, and in particular to a method, device, equipment and medium for monitoring the diffusion of polyurethane in porous media. Background Art

[0002] Chemical grouting has long been considered the most effective means of preventing and controlling sudden water inrush in underground projects. Among them, polyurethane, as a quick-setting slurry, can significantly enhance the engineering performance of rock and soil due to its strong permeability and low expansion properties when granular materials such as cement-based materials are difficult to exert their effects. However, as a hidden underground project, grouting is mainly achieved by controlling the grouting volume or grouting pressure. However, in actual applications, these methods are difficult to intuitively obtain the diffusion of slurry in porous media. Current underground hidden project monitoring technologies mostly use point monitoring, which is not only costly, but also prone to missed detection in actual projects, making it difficult to achieve comprehensive monitoring of the slurry diffusion process. In summary, traditional underground engineering monitoring technologies cannot obtain the diffusion of polyurethane in rock and soil over a large area and intuitively. There is an urgent need to develop new monitoring technologies to improve monitoring accuracy and coverage.

[0003] To overcome these shortcomings of existing technologies, distributed temperature sensing systems (DTS) have been applied to calcareous sand moisture field monitoring due to their advantages such as long distance, low maintenance cost and high precision. For example, using heatable optical fiber sensing cable (AHFO) at different moisture contents and seepage velocities, the difference in heat diffusion rate to the surrounding area is used to establish a moisture inversion function, thereby obtaining distribution monitoring of the soil moisture field. During the slurry infiltration process, the polyurethane slurry not only displaces the moisture in the porous medium, but also reacts chemically with the water. In this process, the thermal conductivity of the slurry during the phase change process is different from that after solidification. This phenomenon causes the heat transfer performance of the solidified porous medium to change. Therefore, the application of distributed optical fiber temperature sensing technology to monitor the diffusion of polyurethane in porous media has become an urgent problem that needs to be solved. Summary of the Invention

[0004] The purpose of the present invention is to provide a method, device, equipment and medium for monitoring the diffusion of polyurethane in porous media, which realizes accurate monitoring of the diffusion range of polyurethane by utilizing distributed optical fiber monitoring technology combined with the change characteristics of the thermal conductivity of the porous medium after the water-reactive polyurethane is cured.

[0005] In order to solve the above technical problems, the present invention provides a method, device, equipment and medium for monitoring the diffusion of polyurethane in porous media.

[0006] In a first aspect, the present invention provides a method for monitoring the diffusion of polyurethane in a porous medium, the method comprising the following steps:

[0007] A diffusion model is selected according to the diffusion characteristics of polyurethane in a porous medium, and a distributed optical fiber is wound around at least one sensing cage according to predetermined helical parameters to form a helical structure;

[0008] Taking the polyurethane penetration point as the origin, a rectangular coordinate system of the porous medium space is established, and the coordinates of each temperature measurement point on the spiral structure are mapped to the rectangular coordinate system of the porous medium space;

[0009] Connecting the optical fiber to a distributed temperature sensing system, calibrating the distributed temperature sensing system to an initial value, and measuring the initial moisture field of the porous medium before polyurethane infiltration;

[0010] During the polyurethane infiltration process, the distributed temperature sensing system is used to monitor the temperature transfer fluctuation along the optical fiber when the polyurethane diffuses in the porous medium, and obtain the moisture field after infiltration when the temperature transfer fluctuation is stable;

[0011] The change in moisture content is analyzed according to the initial moisture field and the moisture field after infiltration, and the polyurethane diffusion distribution field in the porous medium is identified in combination with the diffusion model.

[0012] In a further embodiment, the helix parameters include the number of fiber windings, the pitch, and the helix angle of the helix structure on each sensing cage, and the mathematical expressions of the number of fiber windings, the pitch, and the helix angle are:

[0013]

[0014]

[0015] Where N is the number of fiber windings; H is the height of the sensing cage; P is the pitch; D is the diameter of the sensing cage; L is the winding length of the optical fiber on each sensing cage; and θ is the helical angle.

[0016] In a further embodiment, when there is only a single sensing cage, the coordinates of each temperature measurement point on the spiral structure mapped to the rectangular coordinate system in the porous medium space are specifically:

[0017]

[0018] in,

[0019]

[0020] Where (x, y, z) represents the coordinates of the temperature measurement point on the helical structure mapped to the rectangular coordinate system in the porous medium space; θ represents the helix angle; p0 and d are intermediate variables; l1 represents the length of the optical fiber between the starting end of the sensing cage and the demodulator; L represents the winding length of the optical fiber on each sensing cage; n represents the number of spiral turns of the point on the helical structure; D represents the diameter of the sensing cage; and P represents the pitch.

[0021] In a further embodiment, when there are at least two sensing cages, the coordinates of each temperature measurement point on the spiral structure mapped to the rectangular coordinate system in the porous medium space are specifically:

[0022]

[0023] in,

[0024]

[0025]

[0026] Where (x, y, z) represents the coordinates of the temperature measurement point on the spiral structure mapped to the rectangular coordinate system of the porous medium space; i represents the i-th sensing cage, where 1≤i≤m, and m represents the number of sensing cages; θ i represents the helical angle of the helical structure on the i-th sensing cage; p0′ and d′ are intermediate variables; L i represents the winding length of the internal optical fiber on the i-th sensing cage; l i represents the length of the optical fiber between the starting end of the i-th sensing cage and the demodulator; n i Indicates the number of spiral turns where the temperature measurement point is located on the spiral structure of the i-th sensing cage; D i represents the diameter of the i-th sensor cage; P i represents the pitch of the helical structure on the i-th sensing cage.

[0027] In a further embodiment, the step of analyzing the change in moisture content based on the initial moisture field and the post-infiltration moisture field and identifying the polyurethane diffusion distribution field in the porous medium in combination with the diffusion model includes:

[0028] determining a moisture content reduction area according to the initial moisture field and the post-infiltration moisture field;

[0029] Determining the region of reduced thermal conductivity in the porous medium using a functional relationship between thermal conductivity and moisture content according to the region of reduced moisture content;

[0030] The polyurethane diffusion distribution field in the porous medium is identified based on the thermal conductivity reduction area in the porous medium and combined with the diffusion model.

[0031] In further embodiments, the diffusion model comprises a spherical diffusion model or a cylindrical-hemispherical diffusion model.

[0032] In a further embodiment, the step of identifying the polyurethane diffusion distribution field in the porous medium based on the region of reduced thermal conductivity in the porous medium and in combination with the diffusion model comprises:

[0033] Map the pre-measured sensing cage optical fiber length data to the porous medium spatial rectangular coordinate system to obtain the three-dimensional structural data of the porous medium;

[0034] Identifying pore structure data of the porous medium in a region where thermal conductivity is reduced based on the three-dimensional structural data of the porous medium, and quantifying a quantitative index of heterogeneity of the porous medium in the region where thermal conductivity is reduced using a statistical method based on the pore structure data;

[0035] Taking the quantitative index of porous medium heterogeneity as input, microscopic molecular dynamics simulation is performed in the region of reduced thermal conductivity to predict the microscopic diffusion characteristic parameters of polyurethane in the microstructure of the porous medium. The microscopic diffusion characteristic parameters are then integrated into the diffusion model to obtain a polyurethane diffusion model that takes heterogeneity into account.

[0036] A chemical reaction kinetics model for the diffusion of polyurethane in porous media was established. The chemical reaction kinetics model was used to analyze the time delay effect of the polyurethane diffusion process in the region of reduced thermal conductivity, and the time delay parameters of the polyurethane diffusion process were extracted.

[0037] A time delay parameter is introduced and the Galerkin finite element method is used to dynamically simulate the polyurethane diffusion model considering heterogeneity to capture the migration characteristics of polyurethane in porous media and obtain the polyurethane diffusion distribution field considering the time delay effect.

[0038] In a second aspect, the present invention provides a device for monitoring polyurethane diffusion in a porous medium, the device comprising:

[0039] a device establishment module for selecting a diffusion model based on the diffusion characteristics of polyurethane in a porous medium, and winding a distributed optical fiber around at least one sensing cage according to predetermined helical parameters to form a helical structure;

[0040] A coordinate mapping module is used to establish a rectangular coordinate system in the porous medium space with the polyurethane penetration point as the origin, and map the coordinates of each temperature measurement point on the spiral structure to the rectangular coordinate system in the porous medium space;

[0041] An initial measurement module, used to connect the optical fiber to the distributed temperature sensing system, perform initial value calibration on the distributed temperature sensing system, and measure the initial moisture field of the porous medium before polyurethane infiltration;

[0042] A diffusion monitoring module is used to monitor the temperature transfer fluctuation along the optical fiber when the polyurethane diffuses in the porous medium using the distributed temperature sensing system during the polyurethane infiltration process, and obtain the post-infiltration moisture field when the temperature transfer fluctuation is stable;

[0043] The diffusion identification module is used to analyze the change of moisture content according to the initial moisture field and the moisture field after penetration, and identify the polyurethane diffusion distribution field in the porous medium in combination with the diffusion model.

[0044] In a third aspect, the present invention also provides a computer device comprising a processor and a memory, wherein the processor is connected to the memory, the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory so that the computer device performs the steps of implementing the above method.

[0045] In a fourth aspect, the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0046] The present invention provides a method, device, equipment and medium for monitoring polyurethane diffusion in a porous medium. The method comprises the following steps: winding a distributed optical fiber around at least one sensing cage to form a helical structure; establishing a rectangular coordinate system in the porous medium space with the polyurethane penetration point as the origin, and mapping the coordinates of each temperature measurement point on the helical structure to the rectangular coordinate system in the porous medium space; connecting the optical fiber to a distributed temperature sensing system, calibrating the distributed temperature sensing system for initial values, and measuring the initial moisture field of the porous medium before polyurethane penetration; during the polyurethane penetration process, monitoring temperature transfer fluctuations along the optical fiber when polyurethane diffuses in the porous medium using the distributed temperature sensing system, and obtaining a post-penetration moisture field in a stable temperature transfer fluctuation state; analyzing changes in moisture content based on the initial moisture field and the post-penetration moisture field, and identifying the polyurethane diffusion distribution field in the porous medium in combination with a diffusion model. Compared with the existing technology, this method uses distributed fiber optic sensing technology to monitor the temperature changes along the optical fiber in the process of polyurethane diffusion in porous media in real time, thereby realizing low-cost and high-efficiency monitoring of large-area porous media, improving the comprehensiveness and economy of monitoring. At the same time, by utilizing the physical properties of the change in thermal conductivity of polyurethane after curing, the diffusion of slurry in the porous medium is indirectly determined by comparing the changes in the moisture field of the porous medium before and after grouting. It can accurately monitor the diffusion of polyurethane in porous media and provide strong technical support for engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a schematic flow chart of a method for monitoring polyurethane diffusion in porous media provided by an embodiment of the present invention;

[0048] Figure 2 Schematic diagram of the cylindrical sensor cage structure provided by an embodiment of the present invention;

[0049] Figure 3 1 is a schematic diagram of a planar expansion of a spiral structure provided by an embodiment of the present invention;

[0050] Figure 4 Schematic diagram of the length of the portion of the helical line that does not satisfy the single-turn requirement provided by an embodiment of the present invention;

[0051] Figure 5 Schematic diagram of a polyurethane diffusion distribution field distributed temperature sensing system provided by an embodiment of the present invention;

[0052] Figure 6 Schematic diagram of a polyurethane diffusion monitoring device in a porous medium provided by an embodiment of the present invention;

[0053] Figure 7 It is a structural diagram of a computer device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0054] The following describes the embodiments of the present invention in detail with reference to the accompanying drawings. The embodiments are provided for illustrative purposes only and are not to be construed as limiting the present invention. The accompanying drawings are provided for reference and illustration only and do not constitute a limitation on the scope of protection of the present invention. Many changes may be made to the present invention without departing from the spirit and scope of the present invention.

[0055] refer to Figure 1 , the embodiment of the present invention provides a method for monitoring the diffusion of polyurethane in a porous medium, such as Figure 1 As shown, the method includes the following steps:

[0056] S1. A diffusion model is selected based on the diffusion characteristics of polyurethane in a porous medium, and a distributed optical fiber is wound around at least one sensing cage according to predetermined helix parameters to form a helix structure.

[0057] S2. Establish a rectangular coordinate system in the porous medium space with the polyurethane penetration point as the origin, and map the coordinates of each temperature measurement point on the spiral structure to the rectangular coordinate system in the porous medium space.

[0058] When monitoring the slurry diffusion during the grouting process of porous media, this embodiment can select a diffusion model based on the diffusion characteristics of polyurethane in the porous medium. The diffusion model can adopt a spherical diffusion model or a column-hemispherical diffusion model. Its diffusion mode can be determined according to the number of grouting holes and the permeability of the foundation. In order to realize polyurethane diffusion monitoring, this embodiment can use epoxy resin material to wrap the distributed optical fiber around the sensing cage during the optical fiber layout stage to form a spiral structure on the sensing cage. For the convenience of explanation, as shown in FIG. Figure 2 As shown, this embodiment will be described in detail by taking the structure of a cylinder as an example. In this case, the optical fiber wound on the sensing cage is equivalent to a helical line wound on the cylinder. Those skilled in the art can set the shape of the sensing cage according to the specific implementation situation. It is not limited to the embodiment of the present invention. In three-dimensional space, a helical line is a curve that rotates along a certain axis (such as the axis of a cylinder) and extends along the axis at the same time. When the helical line structure is unfolded on a two-dimensional plane, as shown in FIG. Figure 3 、 Figure 4 As shown, the helical parameters of the distributed optical fiber when wound on the sensing cage include the number of optical fiber windings, the pitch, and the helical angle of the helical structure on each sensing cage. The mathematical expressions of the number of optical fiber windings, the pitch, and the helical angle are:

[0059]

[0060] The relationship between the pitch P and the helix angle θ is expressed as:

[0061]

[0062] Where N is the number of fiber windings; H is the height of the sensing cage; P is the pitch; D is the diameter of the sensing cage; L is the winding length of the optical fiber inside each sensing cage; and θ is the helical angle.

[0063] During the actual deployment of distributed optical fibers, the length L of the optical fiber wound around each sensing cage is a fixed value. In this embodiment, the pitch P is determined based on the diameter and height of the sensing cage. One end of the optical fiber is connected to a distributed temperature sensing system (DTS) via a jumper. This distributed temperature sensing system can capture and transmit temperature changes at each temperature measurement point along the optical fiber to a terminal device in real time. The location where the temperature change occurs is the specific location where polyurethane spreads on the temperature measurement optical fiber. This location is the marking point where the polyurethane diffuses onto the optical fiber, thereby enabling monitoring of the diffusion range of polyurethane in porous media.

[0064] In order to accurately describe this diffusion process, this embodiment takes the polyurethane penetration point as the origin and the direction perpendicular to the porous medium as the z-axis to establish a porous medium space rectangular coordinate system, and maps the coordinates of each temperature measurement point on the spiral structure to the porous medium space rectangular coordinate system, so that the length L of each target position corresponding to the optical fiber corresponds to the coordinate in the porous medium space rectangular coordinate system. Thus, according to the corresponding coordinate changes of the initial moisture field and the moisture field after penetration after temperature stabilization in the porous medium space rectangular coordinate system, the diffusion of polyurethane in the porous medium is quantified. This embodiment can use MATLAB software to Real-time data is processed to visualize the diffusion process. Specifically, this embodiment uses MATLAB software combined with the Kd-Tree neighbor point search algorithm to select an arbitrary coordinate point, screen out the coordinate point closest to it on the adjacent sensing cage as the point on the slurry diffusion path in a certain direction, and traverse all coordinate points on the sensing cage to ensure that each coordinate point has a corresponding point; then, this embodiment performs three-dimensional interpolation on adjacent spatial coordinate points to determine the specific diffusion path of the slurry in this direction; finally, this embodiment obtains the diffusion situation of the slurry at any time through visualization processing, and derives the slurry diffusion distribution field.

[0065] In view of the specific situation of optical fiber layout, this embodiment discusses the following two situations: a single sensor cage and multiple sensor cages:

[0066] Single sensing cage: When there is only one sensing cage, this embodiment determines that the temperature measurement point is located on the nth coil of the sensing cage based on the coil length L of the optical fiber inside each sensing cage, the cage diameter D, the cage height H, and the length l1 of the connection between the starting end and the distributed temperature sensing system. The specific calculation formula for the number of coils n of the temperature measurement point on the sensing cage is:

[0067]

[0068] Then we have:

[0069]

[0070] From this, the coordinates of each temperature measuring point on the spiral line are further derived. In this embodiment, the coordinates of each temperature measuring point on the spiral line structure mapped to the rectangular coordinate system in the porous medium space are specifically:

[0071]

[0072] Where (x, y, z) represents the coordinates of the temperature measurement point on the helical structure mapped to the rectangular coordinate system in the porous medium space; θ represents the helical angle; L represents the winding length of the optical fiber inside each sensing cage; n represents the number of helical turns at the point on the helical structure; D represents the diameter of the sensing cage; P represents the pitch; l1 represents the length of the optical fiber between the starting end of the sensing cage and the demodulator; p0 represents the length of the portion that does not exceed the pitch length; and d represents the diameter corresponding to the portion that does not exceed the length of a single helical turn.

[0073] Overlapping of multiple sensor cages: When there are at least two sensor cages (m sensor cages with overlapping central axes), this embodiment uses the diameter D of each sensor cage as the i , height H i , the number of winding turns in each sensor cage n i , pitch p i 、Helix angle θ i And the optical fiber length l between each sensing cage i , where the value range of i is 1≤i≤m. It can be determined that each temperature measurement point is located on the nth circle of the tth sensing cage. The specific calculation formula for the number of winding circles n of the temperature measurement point on the sensing cage is:

[0074]

[0075]

[0076] Then we have:

[0077]

[0078] From this, the coordinates of each temperature measurement point on the spiral line are further deduced. The coordinates of each temperature measurement point on the spiral line structure mapped to the rectangular coordinate system in the porous medium space are specifically:

[0079]

[0080] Where (x, y, z) represents the coordinates of the temperature measurement point on the spiral structure mapped to the rectangular coordinate system of the porous medium space; i represents the i-th sensing cage, where 1≤i≤m, and m represents the number of sensing cages; θ i represents the helical angle of the helical structure on the i-th sensing cage; L i represents the winding length of the optical fiber inside the i-th sensing cage; n i Indicates the number of spiral turns where the temperature measurement point is located on the spiral structure of the i-th sensing cage; D i represents the diameter of the i-th sensor cage; P irepresents the pitch of the helical structure on the i-th sensing cage; l represents the length of the optical fiber from the starting part of the first sensing cage to the input port of the distributed temperature sensing system; p0′ represents the length of the part that does not exceed the pitch length; d′ represents the diameter corresponding to the part that does not exceed the length of a single turn of the helix; l i represents the length of the optical fiber between the starting end of the i-th sensing cage and the demodulator; n i Indicates the number of spiral turns where the temperature measurement point is located on the spiral structure of the i-th sensing cage; D i represents the diameter of the i-th sensor cage; P i represents the pitch of the helical structure on the i-th sensing cage.

[0081] S3. Connecting the optical fiber to the distributed temperature sensing system, calibrating the distributed temperature sensing system to an initial value, and measuring the initial moisture field of the porous medium before the polyurethane infiltrates.

[0082] S4. During the polyurethane infiltration process, the distributed temperature sensing system is used to monitor the temperature transfer fluctuation along the optical fiber when the polyurethane diffuses in the porous medium, and obtain the post-infiltration moisture field under the stable state of temperature transfer fluctuation.

[0083] S5. Analyze the change in moisture content based on the initial moisture field and the post-infiltration moisture field, and identify the polyurethane diffusion distribution field in the porous medium in combination with the diffusion model.

[0084] In this embodiment, the step of analyzing the change in moisture content based on the initial moisture field and the post-infiltration moisture field, and identifying the polyurethane diffusion distribution field in the porous medium in combination with the diffusion model includes:

[0085] determining a moisture content reduction area according to the initial moisture field and the post-infiltration moisture field;

[0086] Determining the region of reduced thermal conductivity in the porous medium using a functional relationship between thermal conductivity and moisture content according to the region of reduced moisture content;

[0087] The polyurethane diffusion distribution field in the porous medium is identified based on the thermal conductivity reduction area in the porous medium and combined with the diffusion model.

[0088] In this embodiment, the step of identifying the polyurethane diffusion distribution field in the porous medium based on the region of reduced thermal conductivity in the porous medium and in combination with the diffusion model includes:

[0089] Mapping pre-measured sensing cage fiber length data to a rectangular coordinate system in the porous medium space to obtain three-dimensional structural data of the porous medium; wherein the sensing cage fiber length data includes the winding length of the optical fiber on each sensing cage, the optical fiber length connecting adjacent sensing cages, and the optical fiber length from the starting part of the first sensing cage to the input port of the distributed temperature sensing system;

[0090] Identifying pore structure data of the porous medium in a region where thermal conductivity is reduced based on the three-dimensional structural data of the porous medium, and quantifying a quantitative index of heterogeneity of the porous medium in the region where thermal conductivity is reduced using a statistical method based on the pore structure data;

[0091] Taking the quantitative index of porous medium heterogeneity as input, microscopic molecular dynamics simulation is performed in the region of reduced thermal conductivity to predict the microscopic diffusion characteristic parameters of polyurethane in the microstructure of the porous medium. The microscopic diffusion characteristic parameters are then integrated into the diffusion model to obtain a polyurethane diffusion model that takes heterogeneity into account.

[0092] A chemical reaction kinetics model for the diffusion of polyurethane in porous media was established. The chemical reaction kinetics model was used to analyze the time delay effect of the polyurethane diffusion process in the region of reduced thermal conductivity, and the time delay parameters of the polyurethane diffusion process were extracted.

[0093] A time delay parameter is introduced and the Galerkin finite element method is used to dynamically simulate the polyurethane diffusion model considering heterogeneity to capture the migration characteristics of polyurethane in porous media and obtain the polyurethane diffusion distribution field considering the time delay effect.

[0094] Specifically, this embodiment calculates the moisture content change at each position based on the initial moisture field and the moisture field after infiltration, determines the area with reduced moisture content, and uses the functional relationship between thermal conductivity and moisture content to determine the area with reduced thermal conductivity in the porous medium. This converts the area with reduced moisture content into the area with reduced thermal conductivity, obtains the three-dimensional structural data of the porous medium, and identifies the pore structure data of the porous medium in the area with reduced thermal conductivity based on the three-dimensional structural data of the porous medium. For example, the pore structure data may include structural data such as pore distribution, size, and shape, and then Then, based on the pore structure data, a statistical method is used to quantify the heterogeneity quantitative index of the porous medium in the area where the thermal conductivity coefficient decreases. For example, the heterogeneity quantitative index of the porous medium can include permeability distribution, etc. This embodiment is based on the physical and chemical properties of polyurethane and porous media. Microscopic molecular dynamics simulation is performed in the area where the thermal conductivity coefficient decreases, and the heterogeneity quantitative index of the porous medium is introduced in the simulation process to predict the microscopic diffusion characteristic parameters of polyurethane in the microstructure of the porous medium. The microscopic diffusion characteristic parameters are converted to the macroscopic scale and integrated into the macroscopic diffusion model to obtain the desired effect. The microscopic diffusion characteristic parameters adjust the parameters of the diffusion model (such as the diffusion coefficient and boundary conditions), thereby reflecting the impact of the heterogeneity of the porous medium on the diffusion of polyurethane, and obtaining a polyurethane diffusion model that takes into account heterogeneity. Next, this embodiment establishes a chemical reaction kinetic model for the diffusion of polyurethane in porous media, while also considering processes such as physical adsorption and chemical reaction between polyurethane and the medium. The chemical reaction kinetic model is used to analyze the time delay effect of the polyurethane diffusion process in the region of reduced thermal conductivity. Time delay parameters in the polyurethane diffusion process, such as the reaction rate constant and adsorption equilibrium time, are extracted to quantitatively describe the non-instantaneous characteristics of polyurethane diffusion in porous media. Finally, this embodiment uses the Galerkin finite element method to establish a dynamic simulation of the polyurethane diffusion model that takes into account heterogeneity. The time delay parameter is introduced into the simulation process to capture the migration characteristics of polyurethane in porous media, and a polyurethane diffusion distribution field that takes into account the time delay effect is obtained. By introducing the heterogeneity of the porous medium and considering the time delay effect, this embodiment can more accurately predict the diffusion behavior of polyurethane in porous media and obtain a polyurethane diffusion distribution field.

[0095] It should be noted that the porous medium heterogeneity introduced in this embodiment mainly refers to the non-uniformity of the physical, chemical, or structural properties of the porous medium, such as the non-uniformity of the pore distribution and connectivity of the porous medium. In this embodiment, the corresponding porous medium geometric characteristics can be extracted through pore structure data, etc., and the corresponding porous medium geometric characteristics are quantified using statistical methods to obtain a quantitative index of the porous medium heterogeneity. Those skilled in the art can use other methods to calculate the quantitative index of the porous medium heterogeneity. This is not limited to the embodiment of the present invention. Introducing a quantitative index of heterogeneity through the porous medium can more effectively describe the complex diffusion behavior in the porous medium. The time delay effect mainly refers to the significant lag time between the occurrence of a process or phenomenon and its triggering factor or starting condition. In the diffusion process of polyurethane in porous media, the time delay effect causes a time delay in the diffusion process due to multiple factors such as the chemical reaction time of the polyurethane and the increased diffusion resistance and time due to the complexity of the medium structure. In this embodiment, the time delay effect is introduced into the polyurethane diffusion model to more accurately describe and predict the non-instantaneous characteristics of the actual diffusion process.

[0096] In summary, in this embodiment, a distributed optical fiber is connected to a distributed temperature sensing system (DTS) via a patch cord. The DTS can capture and transmit temperature changes at each location on the optical fiber in real time, thereby displaying temperature changes in real time. The distributed temperature sensing system is then calibrated, and its spatial resolution, temporal resolution, and heating power are set. The initial value of the distributed temperature sensing system is also calibrated. The distributed temperature sensing system is started and moisture measurement is performed to obtain an initial moisture field M1. During the polyurethane infiltration process, the distributed temperature sensing system is used to monitor the temperature changes of the distributed optical fiber during the polyurethane diffusion process in real time. After the temperature is substantially stable, the moisture field is measured again to obtain a post-infiltration moisture field M2 under a stable temperature state. Based on the functional relationship between thermal conductivity and moisture content, the regions with reduced moisture content in M1 and M2 are compared, i.e., the regions with reduced thermal conductivity, thereby obtaining the diffusion of polyurethane in the porous medium. In this embodiment, polyurethane diffusion behavior includes but is not limited to the diffusion path, range, and morphology of polyurethane in the porous medium. For clarity, the heat source theory and polyurethane diffusion distribution field monitoring principle in the polyurethane diffusion distribution field theory are specifically described below:

[0097] (1) Heat source theory

[0098] In a homogeneous, isotropic porous medium with uniform initial temperature, the heat transfer can be described by Fourier's law:

[0099]

[0100] For a heat pulse generated by an infinitely long heat source, if the influence of radial dimensions and cable material is neglected, the process of heat diffusion to the surroundings during heating can be expressed as:

[0101]

[0102] Where c represents specific heat capacity (unit: J / (kg·℃)); T represents temperature; t represents time; They represent the partial derivatives of temperature in different directions of the x-axis, y-axis, and z-axis respectively; t0 represents the heating time; λ represents the thermal conductivity (in W / (m·℃)); P represents the heating power per unit length of the linear heat source (in J / (m·s)); S is the distance from the test point to the heat source (in m); and b represents a constant.

[0103] When the heat source radius is considered, the heat diffusion during the heating process can be expressed as:

[0104]

[0105] Where R and γ are the interface impedance (unit: m 2 ℃ / W) and Euler constant, which are fitted by the least squares method; r is the heat source radius (in m), which is obtained by numerical simulation.

[0106] (2) Principle of polyurethane diffusion distribution field monitoring

[0107] Before grouting, the porous medium contains a moisture field. First, the active heated fiber optic method (AHFO) is used to calibrate the initial moisture field M1 in the porous medium. At this time, the soil is composed of air, soil particles and water. The thermal conductivity of the gas is relatively small and can be ignored. This embodiment uses The soil thermal conductivity prediction model established by Konrad (hereinafter referred to as the CK model) establishes the relationship between the thermal conductivity of soil and the saturation. The change in saturation directly affects the value of the thermal conductivity. In porous media, the increase or decrease in moisture will directly affect the saturation of the soil, that is, the change in moisture content directly reflects the change in saturation. Therefore, through the above two relationships, this embodiment indirectly associates the thermal conductivity with the moisture content. The change in moisture content leads to the change in saturation, which in turn affects the value of the thermal conductivity. The relationship between moisture content and saturation is the prior art and will not be repeated here. The calculation formula for the thermal conductivity of rock and soil before grouting is:

[0108] λ1=(λ sat -λ dry )K e1 +λ dry

[0109]

[0110] Where λ1 represents the thermal conductivity of rock and soil; λ sat Indicates the thermal conductivity of soil under saturated conditions; λ dry Indicates the thermal conductivity of the soil under dry conditions; K e1 represents the normalized thermal conductivity before grouting; λ dry represents; a represents the weight coefficient, which is a parameter related to the composition, structure and temperature of the soil; S r1 Indicates the soil saturation before grouting (%).

[0111] Under non-freezing conditions, the thermal conductivity of saturated sand is λ sat for:

[0112]

[0113] Where λ w Represents the thermal conductivity of water; λ s represents the thermal conductivity of sand particles; n represents the porosity of the soil (%).

[0114]

[0115] Where, represents the thermal conductivity of each mineral component; x j Indicates the volume fraction (%) of each mineral component.

[0116] The thermal conductivity of dry soil is:

[0117] λ dry =10 -ηn χ

[0118] Where χ and η are material parameters.

[0119] Thermal conductivity λ of polyurethane during phase change p1 Before grouting, use the probe method to mix polyurethane and water in a preset ratio and then insert the probe to start measuring λ p1 The test time is about 10 minutes. Since the initial mixing of polyurethane and water will release a lot of heat, causing the temperature to rise and affecting the accuracy of the data, the probe heating is started 3 minutes after mixing and the test is completed at about 13 minutes to measure the thermal conductivity λ of polyurethane during the phase change process. p1 .

[0120] When grouting begins, polyurethane slowly penetrates into the porous medium and reacts with water to start phase change, causing the thermal conductivity of the porous medium to change. During the grouting process, the water in the porous medium is continuously displaced and reacts, and the water field changes. It is difficult to accurately obtain the saturation of the porous medium during the phase change process. Therefore, it is assumed that the saturation of the porous medium during the phase change process is the saturation after the reaction S r2 Since the permeation grouting does not cause much disturbance to the porous medium itself, it can be assumed that the porous medium does not produce displacement during the polyurethane penetration, displacement and curing process. Therefore, during the phase change process, the thermal conductivity coefficient λ2 in the porous medium can be calculated using the CK model and can be expressed as:

[0121] λ2=(λ sat -λ dry )K e2 +λ dry +λ p1

[0122]

[0123] Where K e2 represents the normalized thermal conductivity during the grouting process and after the slurry solidifies; λ p1 Represents the thermal conductivity of polyurethane during phase change; S r2 Indicates the soil saturation during the grouting process (%).

[0124] At this time, the DTS is started synchronously to monitor the temperature field changes in the porous medium in real time, so that the slurry diffusion can be monitored in real time.

[0125] After the slurry solidifies, the volume occupied by the pores in the porous medium is partially replaced by polyurethane, the water and air are displaced by polyurethane, and the moisture field is redistributed. At this time, the thermal conductivity coefficient λ3 of the stone body can be expressed as:

[0126] λ3=(λ sat -λ dry )K e2 +λ dry +λ p2

[0127] Where λ p2 Indicates the thermal conductivity of cured polyurethane, which can be measured by a hot disk thermal constant analyzer or a corundum tube thermal probe method.

[0128] At this time, AHFO is used again to monitor the reconstructed moisture field to obtain the post-infiltration moisture field M2. By using AHFO to monitor before infiltration and after curing, and by comparing the initial moisture field M1 and the post-infiltration moisture field M2, the area with reduced moisture content can be determined. Specifically, the initial moisture field M1 and the post-infiltration moisture field M2 measured by AHFO before and after grouting are used to calculate the moisture content change of each monitoring point, thereby identifying the area with significantly reduced moisture content. Then, by analyzing the change in thermal conductivity, the diffusion of polyurethane can be inferred. When λ3<λ1, it is the diffusion distribution field of polyurethane.

[0129] (2) Design and calibration of distributed fiber optic sensing system for polyurethane diffusion distribution field

[0130] like Figure 5 As shown in the figure, the distributed temperature sensing system for the polyurethane diffusion distribution field consists of a distributed temperature sensing system 1, a host computer 2, a data transmission line 3, a data processor 4, a time-controlled switch 5, a DC power supply 6, a copper conductor 7, a porous medium 8, an optical fiber 9 and a sensing cage 10. Among them, the heating module composed of a DC power supply and a time-controlled switch is used to heat the optical fiber, and the time-controlled switch is used to accurately control the heating time with an accuracy of 1 second; the distributed temperature sensing system is used to monitor temperature changes; the demodulation module of the distributed temperature sensing system is used to convert the measured Raman optical signal into temperature information; the data transmission line uses the mobile 5G network to send data to the terminal; the data processor has two major functions: one is the control function to ensure the coordinated work between the modules; the other is the data post-processing function, which converts the temperature fluctuation information into the analyzed moisture content change and infers the diffusion distribution field of the polyurethane based on this.

[0131] In terms of system calibration, the active heating fiber method AHFO is used to calibrate the initial moisture field of the porous medium to obtain the initial moisture field. During the infiltration process, DTS is started synchronously to monitor the temperature changes in real time and record the temperature changes caused by the reaction and diffusion of polyurethane, thereby realizing real-time monitoring of the diffusion of slurry in the porous medium. In the post-processing stage, after the grouting is completed, the post-infiltration moisture field M2 is measured and reconstructed again. According to the functional relationship between thermal conductivity and moisture content, the area with reduced thermal conductivity is determined by comparing the area with reduced moisture content, that is, the diffusion distribution field of polyurethane is identified.

[0132] Traditional fiber optic sensing-based grouting engineering analysis techniques primarily involve substituting temperature data monitored by fiber optic sensing technology into MATLAB to obtain a slurry temperature field cloud map or directly using temperature data as a basis for judgment to visually display the slurry diffusion range. However, this traditional method is easily affected by multiple factors, such as the external ambient temperature, the thermal conductivity of the medium, and temperature loss during the grouting process. This can cause a deviation between the temperature field and the actual slurry diffusion range, leading to serious deviations in the final measurement results. The flow of polyurethane in porous media is a relatively complex physical process involving fluid mechanics, thermodynamics, and the physical properties of porous media. Considering the thermal effect characteristics of the polyurethane curing process, directly determining the slurry diffusion range based on temperature changes makes it difficult for temperature data to accurately reflect the diffusion situation. Therefore, the polyurethane diffusion monitoring method in porous media provided in this embodiment monitors the moisture field changes in the porous medium and, combined with the relationship between thermal conductivity and moisture content, can more accurately analyze the diffusion behavior of the slurry in the porous medium. This method, based on physical principles, can more accurately reflect changes in the internal state of the porous medium, providing a scientific basis for the design and construction of grouting projects.

[0133] An embodiment of the present invention provides a method for monitoring polyurethane diffusion in a porous medium. The method comprises the following steps: winding a distributed optical fiber around at least one sensing cage to form a helical structure; establishing a rectangular coordinate system in the porous medium space with the polyurethane penetration point as the origin, and mapping the coordinates of each temperature measurement point on the helical structure to the rectangular coordinate system in the porous medium space; connecting the optical fiber to a distributed temperature sensing system, calibrating the distributed temperature sensing system to an initial value, and measuring the initial moisture field of the porous medium before polyurethane penetration; during the polyurethane penetration process, monitoring temperature transfer fluctuations along the optical fiber as polyurethane diffuses in the porous medium using the distributed temperature sensing system, and obtaining a post-penetration moisture field in a stable temperature transfer fluctuation state; analyzing changes in moisture content based on the initial moisture field and the post-penetration moisture field, and identifying the polyurethane diffusion distribution field in the porous medium in combination with a diffusion model. Compared with the existing technology, the method provided in the embodiment of the present invention uses a distributed temperature sensing system to monitor the temperature changes of distributed optical fibers in the polyurethane diffusion process in real time, and combines the functional relationship between thermal conductivity and moisture content to achieve a comprehensive and accurate assessment of the diffusion of polyurethane in porous media from the analysis of moisture field changes in the porous medium. This not only improves the comprehensiveness and economy of monitoring, but also avoids the serious errors caused by directly using temperature to measure the diffusion range, thereby improving the accuracy of monitoring and having broad application prospects.

[0134] It should be noted that the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of this application.

[0135] In one embodiment, Figure 6 As shown, an embodiment of the present invention provides a device for monitoring the diffusion of polyurethane in a porous medium, the device comprising:

[0136] The device establishment module 101 is used to select a diffusion model according to the diffusion characteristics of polyurethane in a porous medium, and to wind a distributed optical fiber around at least one sensing cage according to predetermined helical parameters to form a helical structure;

[0137] A coordinate mapping module 102 is used to establish a rectangular coordinate system in the porous medium space with the polyurethane penetration point as the origin, and map the coordinates of each temperature measurement point on the spiral structure to the rectangular coordinate system in the porous medium space;

[0138] An initial measurement module 103 is used to connect the optical fiber to the distributed temperature sensing system, perform initial value calibration on the distributed temperature sensing system, and measure the initial moisture field of the porous medium before polyurethane infiltration;

[0139] The diffusion monitoring module 104 is used to monitor the temperature transfer fluctuation along the optical fiber when the polyurethane diffuses in the porous medium using the distributed temperature sensing system during the polyurethane infiltration process, and obtain the post-infiltration moisture field when the temperature transfer fluctuation is stable;

[0140] The diffusion identification module 105 is used to analyze the change of moisture content according to the initial moisture field and the moisture field after penetration, and identify the polyurethane diffusion distribution field in the porous medium in combination with the diffusion model.

[0141] For the specific definition of a device for monitoring the diffusion of polyurethane in a porous medium, please refer to the above-mentioned definition of a method for monitoring the diffusion of polyurethane in a porous medium, which will not be repeated here. A person of ordinary skill in the art will appreciate that the various modules and steps described in conjunction with the embodiments disclosed in this application can be implemented in hardware, software, or a combination of both. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0142] An embodiment of the present invention provides a device for monitoring the diffusion of polyurethane in a porous medium. The device uses a device establishment module to wrap a distributed optical fiber around at least one sensing cage to form a helical structure. A coordinate mapping module uses a polyurethane penetration point as an origin to establish a rectangular coordinate system in the porous medium space, and maps the coordinates of each temperature measurement point on the helical structure to the rectangular coordinate system in the porous medium space. An initial measurement module connects the optical fiber to a distributed temperature sensing system, calibrates the distributed temperature sensing system for initial values, and measures the initial moisture field of the porous medium before polyurethane penetration. During the polyurethane penetration process, the diffusion monitoring module uses the distributed temperature sensing system to monitor temperature transfer fluctuations along the optical fiber when polyurethane diffuses in the porous medium, and obtains a post-penetration moisture field in a stable state of temperature transfer fluctuations. A diffusion identification module analyzes changes in moisture content based on the initial moisture field and the post-penetration moisture field, and identifies the polyurethane diffusion distribution field in the porous medium in combination with a diffusion model. Compared with the existing technology, the device provided by the embodiment of the present invention uses a distributed temperature sensing system to monitor the temperature changes of the distributed optical fiber in the polyurethane diffusion process in real time, and combines the functional relationship between thermal conductivity and moisture content to achieve a comprehensive and accurate assessment of the diffusion of polyurethane in porous media, which has broad application prospects.

[0143] Figure 7 A computer device provided in an embodiment of the present invention includes a memory, a processor and a transceiver, which are connected via a bus; the memory is used to store a set of computer program instructions and data, and can transmit the stored data to the processor, and the processor can execute the program instructions stored in the memory to perform the steps of the above method.

[0144] The memory may include volatile memory or non-volatile memory, or may include both volatile and non-volatile memory; the processor may be a central processing unit, a microprocessor, an application-specific integrated circuit, a programmable logic device, or a combination thereof. By way of example and not limitation, the programmable logic device may be a complex programmable logic device, a field programmable gate array, a general purpose array logic, or any combination thereof.

[0145] Additionally, the memory may be a physically separate unit or integrated with the processor.

[0146] It can be understood by those skilled in the art that Figure 7 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have the same component arrangement.

[0147] In one embodiment, the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the above method are implemented.

[0148] Embodiments of the present invention provide a method, device, equipment, and medium for monitoring the diffusion of polyurethane in a porous medium. The method for monitoring the diffusion of polyurethane in a porous medium combines optical fiber technology with the characteristics of changes in the thermal conductivity coefficient of polyurethane after curing to achieve high-precision, real-time, and comprehensive monitoring of the diffusion of polyurethane in the porous medium, thereby achieving not only low-cost and high-efficiency monitoring but also improving the accuracy and comprehensiveness of monitoring.

[0149] In the above embodiments, all or part of the embodiments can be implemented by software, hardware, firmware, or any combination thereof. When implemented using software, all or part of the embodiments can be implemented in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) method. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or data center that includes one or more available media. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., an SSD).

[0150] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing related hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods.

[0151] The above-described embodiments merely represent several preferred implementations of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art could make several improvements and substitutions without departing from the technical principles of the present invention, and these improvements and substitutions should also be considered within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be based on the scope of protection of the claims.

Claims

1. A method for monitoring the diffusion of polyurethane in porous media, characterized in that: The following steps are involved: A diffusion model is selected according to the diffusion characteristics of polyurethane in a porous medium, and a distributed optical fiber is wound around at least one sensing cage according to predetermined helical parameters to form a helical structure; Taking the polyurethane penetration point as the origin, a rectangular coordinate system of the porous medium space is established, and the coordinates of each temperature measurement point on the spiral structure are mapped to the rectangular coordinate system of the porous medium space; Connecting the optical fiber to a distributed temperature sensing system, calibrating the distributed temperature sensing system to an initial value, and measuring the initial moisture field of the porous medium before polyurethane infiltration; During the polyurethane infiltration process, the distributed temperature sensing system is used to monitor the temperature transfer fluctuation along the optical fiber when the polyurethane diffuses in the porous medium, and obtain the moisture field after infiltration when the temperature transfer fluctuation is stable; Analyzing the change in moisture content according to the initial moisture field and the moisture field after infiltration, and identifying the polyurethane diffusion distribution field in the porous medium in combination with the diffusion model; The helix parameters include the number of fiber windings, the pitch, and the helix angle of the helix structure on each sensing cage. The mathematical expressions of the number of fiber windings, the pitch, and the helix angle are: Where N is the number of fiber windings; H is the height of the sensing cage; P is the pitch; D is the diameter of the sensing cage; L is the winding length of the optical fiber inside each sensing cage; represents the helix angle; When there is only a single sensing cage, the coordinates of each temperature measurement point on the spiral structure mapped to the rectangular coordinate system in the porous medium space are specifically: in, Where (x, y, z) represents the coordinates of the temperature measurement point on the spiral structure mapped to the rectangular coordinate system in the porous medium space; represents the helix angle; and is an intermediate variable; It represents the length of the optical fiber between the starting end of the sensing cage and the demodulator; L represents the winding length of the optical fiber on each sensing cage; n represents the number of spiral turns at that point on the helical structure; D represents the diameter of the sensing cage; and P represents the pitch.

2. The method for monitoring polyurethane diffusion in porous media according to claim 1, wherein: When there are at least two sensing cages, the coordinates of each temperature measurement point on the spiral structure mapped to the rectangular coordinate system in the porous medium space are specifically: in, Where (x, y, z) represents the coordinates of the temperature measurement point on the spiral structure mapped to the rectangular coordinate system of the porous medium space; i represents the i-th sensing cage, where, , m represents the number of sensor cages; represents the helical angle of the helical structure on the i-th sensing cage; and is an intermediate variable; represents the winding length of the internal optical fiber on the i-th sensing cage; represents the length of the optical fiber between the starting end of the i-th sensing cage and the demodulator; Indicates the number of spiral turns where the temperature measurement point is located on the spiral structure of the i-th sensing cage; represents the diameter of the i-th sensor cage; represents the pitch of the helical structure on the i-th sensing cage.

3. The method for monitoring polyurethane diffusion in porous media according to claim 1, wherein: The step of analyzing the change in moisture content according to the initial moisture field and the moisture field after infiltration, and identifying the polyurethane diffusion distribution field in the porous medium in combination with the diffusion model includes: determining a moisture content reduction area according to the initial moisture field and the post-infiltration moisture field; Determining the region of reduced thermal conductivity in the porous medium using a functional relationship between thermal conductivity and moisture content according to the region of reduced moisture content; The polyurethane diffusion distribution field in the porous medium is identified based on the thermal conductivity reduction area in the porous medium and combined with the diffusion model.

4. The method for monitoring polyurethane diffusion in a porous medium according to claim 3, wherein: The diffusion model includes a spherical diffusion model or a cylindrical-hemispherical diffusion model.

5. The method for monitoring polyurethane diffusion in a porous medium according to claim 3, wherein: The step of identifying the polyurethane diffusion distribution field in the porous medium based on the region of reduced thermal conductivity in the porous medium and in combination with the diffusion model includes: Map the pre-measured sensing cage optical fiber length data to the porous medium spatial rectangular coordinate system to obtain the three-dimensional structural data of the porous medium; Identifying pore structure data of the porous medium in a region where thermal conductivity is reduced based on the three-dimensional structural data of the porous medium, and quantifying a quantitative index of heterogeneity of the porous medium in the region where thermal conductivity is reduced using a statistical method based on the pore structure data; Taking the quantitative index of porous medium heterogeneity as input, microscopic molecular dynamics simulation is performed in the region of reduced thermal conductivity to predict the microscopic diffusion characteristic parameters of polyurethane in the microstructure of the porous medium. The microscopic diffusion characteristic parameters are then integrated into the diffusion model to obtain a polyurethane diffusion model that takes heterogeneity into account. A chemical reaction kinetics model for the diffusion of polyurethane in porous media was established. The chemical reaction kinetics model was used to analyze the time delay effect of the polyurethane diffusion process in the region of reduced thermal conductivity, and the time delay parameters of the polyurethane diffusion process were extracted. A time delay parameter is introduced and the Galerkin finite element method is used to dynamically simulate the polyurethane diffusion model considering heterogeneity to capture the migration characteristics of polyurethane in porous media and obtain the polyurethane diffusion distribution field considering the time delay effect.

6. A computer device, characterized in that: The computer device comprises a processor and a memory, wherein the processor is connected to the memory, the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the computer device performs the method according to any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed, the method according to any one of claims 1 to 5 is implemented.

Images