A method for predicting performance of silicon carbide phase transition filler based on RSM

Abstract

The application discloses a kind of based on RSM's silicon carbide phase transition filling body performance prediction method, it is related to mine filling material technical field, phase change material is phase change microcapsule, include: selecting the response of the performance of filling body and the factor of influencing the performance of filling body;The correlation between the response of the performance of filling body and the interaction between each factor, the correlation between the response of the performance of filling body and the correlation between the response of the performance of filling body are carried out test design and data analysis;According to test data, variance analysis is carried out, and the test results of the response of each corresponding performance are carried out multiple linear regression and binomial fitting analysis using multivariate quadratic polynomial model, verify the regression model of each response variable and the significance of factor;The performance of multiple response variables is comprehensively evaluated using comprehensive desirability, to predict the preferred factor combination.The application can predict the performance of filling body under different proportions in actual engineering based on RSM, can solve the problem of heat damage in deep mine and reduce mining cost during the operation of mine.

Description

Technical Field

[0001] This invention relates to the field of mine backfill material technology, and in particular to a method for predicting the performance of silicon carbide phase change backfill based on RSM. Background Technology

[0002] Geothermal energy, as a green, clean, and abundant renewable energy source, has significant advantages and development potential in reducing the cost of deep mining of mineral resources. Fully utilizing the geothermal energy contained in deep rock masses can not only effectively alleviate the heat hazards in mineral resource extraction but also promote the green, low-carbon, and sustainable development of the energy industry. Co-extraction of minerals and geothermal energy based on brine circulation systems, excavation technology, and backfilling mining methods are currently the three newest models.

[0003] In this type of mining, backfilling involves assembling and laying thermal pipelines in the goaf to establish a unique mine backfill coupled with a heat exchange system. Backfill slurry is transported to the goaf through pipelines, allowing the thermal pipelines and backfill material to solidify and form a thermodynamically efficient, integrated thermal storage / energy storage backfill. This achieves cooling of the mining area and co-extraction of mineral thermal resources through heat conduction and exchange. The entire geothermal extraction system is closed-loop, extracting heat through circulating fluid within the pipelines without extracting water, thus avoiding the groundwater pollution and land subsidence problems associated with conventional geothermal extraction. This technical solution not only solves the problem of heat hazards in deep mines and reduces mining costs during operation, but also allows for continued development of geothermal resources after mining is completed, extending the mine's lifespan and improving the long-term sustainability of the mining area.

[0004] Mine thermal / energy storage functional backfilling refers to a backfilling mining method that, while meeting the structural and volumetric requirements of traditional backfill bodies, also incorporates thermal / energy storage functions. Basic methods of thermal energy storage include sensible heat storage, latent heat storage, concentration gradient heat storage, and chemical reaction heat storage. Among these, latent heat storage utilizes material phase changes to store and release thermal energy, offering advantages such as high specific volumetric heat storage, a wide phase change temperature range, and constant heat storage / release temperature, thus attracting widespread attention. Therefore, the thermal properties of traditional backfill materials can be improved by adding phase change materials with good thermal / energy storage functions. Phase change materials should possess large latent heat of phase change and specific heat capacity to accumulate / release more thermal energy. While directly incorporating solid-liquid phase change materials into backfill materials is simple, liquid phase leakage is prone to occur during phase change. Therefore, encapsulating phase change materials to form shaped phase change materials and microencapsulated phase change materials is widely used in underground buried pipe heat exchange systems. However, the addition of microencapsulated phase change materials (MPCM) reduces their mechanical strength and thermal conductivity. Summary of the Invention

[0005] This invention provides a method for predicting the performance of silicon carbide phase change fillers based on RSM, in order to solve the problem of the inability to predict the performance of fillers. By adding phase change microcapsules, the thermal energy storage capacity of the filler material is improved without affecting the phase change capacity of the phase change microcapsules. This method can improve the thermal conductivity and mechanical strength of the filler, thereby taking into account the strength, thermal conductivity and thermal storage of the filler material.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] A method for predicting the performance of silicon carbide phase change infill materials based on RSM is proposed for enhancing the thermal energy storage performance of infill materials in deep and shallow mines, deep mines, and goaf areas. The phase change material is a silicon carbide-doped phase change microcapsule, comprising:

[0008] Select the response that characterizes the performance of the filling material and the factors that affect the performance of the filling material;

[0009] Experimental design and data analysis were conducted to investigate the correlation between individual changes in various factors and the interactions between these factors, and to examine the impact of these factors on the response of various properties of the filling material.

[0010] Analysis of variance was conducted based on the experimental data. Multiple linear regression and binomial fitting analysis were performed on the experimental results of the response of each corresponding performance using a multivariate quadratic polynomial model to verify the significance of the regression model and factors for each response variable.

[0011] Comprehensive desirability is used to comprehensively evaluate the performance of multiple response variables in order to predict the optimal combination of factors.

[0012] Optionally, the method of using comprehensive desirability to comprehensively evaluate the performance of multiple response variables in order to predict the optimal combination of factors includes: calculating the comprehensive desirability D by taking the geometric mean of the individual desirability functions. Where i is 1, 2, 3...n, n is the number of factors and responses included in the optimization process, ri is the relative importance of each factor and response, and di is the individual expectation of the factor and response.

[0013] Optionally, in the selection of the response characterizing the performance of the filling material and the factors affecting the performance of the filling material, the response characterizing the performance of the filling material includes compressive strength, thermal conductivity and specific heat capacity, and the factors affecting the performance of the filling material include ash-sand ratio, slurry concentration, MPCM ratio and silicon carbide ratio.

[0014] Optionally, in designing experiments to correlate the individual changes of each factor with the interactions between the factors and the responses of the infill material to various performance characteristics, the Box-Behnken Design software in Design-expert is used for experimental design and data analysis. At least 27 sets of experiments are designed according to four factors including ash-sand ratio, slurry concentration, proportion of phase change microcapsules and silicon carbide proportion, three responses including compressive strength, thermal conductivity and specific heat capacity, and a three-center BBD configuration.

[0015] Optionally, in designing experiments to correlate the individual changes of each factor with the interactions between the factors and the responses of the infill material to various performance characteristics, a central composite design is used for experimental design and data analysis.

[0016] Optionally, the step of performing variance analysis based on experimental data, and using a multivariate quadratic polynomial model to perform multiple linear regression and binomial fitting analysis on the experimental results of the responses of each corresponding performance to verify the significance of the regression model and factors for each response variable includes:

[0017] Regression simulation analysis was performed using Design-expert software to obtain a regression model for compressive strength, thereby revealing the significance of the effects of four factors on compressive strength, including the ash-sand ratio, slurry concentration, proportion of phase change microcapsules, and proportion of silicon carbide.

[0018] Optionally, the process of performing variance analysis based on experimental data, and using a multivariate quadratic polynomial model to perform multiple linear regression and binomial fitting analysis on the experimental results of the responses of each corresponding performance to verify the significance of the regression model and factors for each response variable, further includes:

[0019] Regression simulation analysis was performed using Design-expert software to obtain a regression model for thermal conductivity, thereby revealing the significance of the effects of four factors, including ash-sand ratio, slurry concentration, proportion of phase change microcapsules, and proportion of silicon carbide, on thermal conductivity.

[0020] Optionally, the process of performing variance analysis based on experimental data, and using a multivariate quadratic polynomial model to perform multiple linear regression and binomial fitting analysis on the experimental results of the responses of each corresponding performance to verify the significance of the regression model and factors for each response variable, further includes:

[0021] Regression simulation analysis was performed using Design-expert software to obtain a regression model for specific heat capacity, thereby determining the significance of the influence of four factors, including ash-sand ratio, slurry concentration, proportion of phase change microcapsules, and proportion of silicon carbide, on specific heat capacity.

[0022] Optionally, after employing comprehensive desirability to comprehensively evaluate the performance of multiple response variables to predict a preferred combination of factors, the method further includes: conducting experiments based on the preferred combination of factors, comparing the experimental values ​​with the predicted values, to verify the accuracy of the prediction method.

[0023] In the above embodiments, by incorporating silicon carbide into the phase change filler, the heat transfer capacity of the phase change filler is enhanced, which can ensure the heat storage capacity and mechanical properties of the filler. The optimal ratio of silicon carbide under different requirements can be predicted by the response surface methodology (RSM), which can also predict various factors affecting the performance of the filler, such as the ash-sand ratio, slurry concentration, MPCM ratio and silicon carbide ratio. Based on the predicted values, the proportioning test of various materials can be guided, thereby obtaining the ideal performance of the filler.

[0024] In some embodiments, Box-Behnken is used for experimental design and data analysis. With the same number of factors, fewer trials are required, and it can assess the nonlinear effects of factors. It is suitable for experiments where all factors are quantitative values, and does not require multiple consecutive trials. Therefore, using Box-Behnken for experimental design and data analysis is simple to operate and facilitates the rapid establishment of regression models. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart illustrating the method for predicting the performance of silicon carbide phase change fillers based on RSM, as provided in this embodiment of the invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0028] This embodiment provides a method for predicting the performance of silicon carbide phase change infill materials based on RSM. This method is used to enhance the thermal energy storage performance of infill materials in deep and shallow mines, deep mines, and goaf areas. The phase change material is phase change microcapsules (MPCMs), such as... Figure 1 As shown, it includes the following steps:

[0029] S100: Select the response that characterizes the performance of the filling material and the factors that affect the performance of the filling material;

[0030] S200: Experimental design and data analysis are conducted to investigate the correlation between individual changes in various factors and the interactions between these factors, and the impact of these factors on the response of various properties of the filling material.

[0031] S300: Based on the experimental data, perform analysis of variance, and use a multivariate quadratic polynomial model to perform multiple linear regression and binomial fitting analysis on the experimental results of the response of each corresponding performance to verify the significance of the regression model and factors of each response variable.

[0032] S400: Uses comprehensive desirability to comprehensively evaluate the performance of multiple response variables in order to predict the preferred combination of factors.

[0033] Since the thermal conductivity of the backfill is another key factor in evaluating the heat transfer rate between the composite backfill and the surrounding thermal environment and heat-carrying fluid, it affects the working efficiency of the entire heating system. The higher the thermal conductivity, the faster the heat storage and release rate of the backfill. Increasing the thermal conductivity of the backfill material can usually improve the efficiency of the underground buried pipe heat exchange system.

[0034] Therefore, this invention improves the thermal energy storage capacity of the filling material by adding MPCM without affecting the phase change capability of MPCM, thereby enhancing the thermal conductivity and mechanical strength of the filling. This combination achieves a balance between the strength, thermal conductivity, and thermal storage properties of the filling. Silicon carbide possesses high thermal conductivity, high hardness, strong oxidation resistance, strong thermal stability, and resistance to chemical corrosion. This invention incorporates silicon carbide into the phase change filling to compensate for the reduced thermal conductivity and strength of the filling when MPCM is added. Silicon carbide enhances the heat transfer capacity of the phase change filling while ensuring its thermal energy storage capacity and mechanical properties. Furthermore, the optimal ratio under different requirements is predicted using the response surface method (RSM).

[0035] The core material of the phase change microcapsules is an organic solid-liquid phase change material, with the phase change material content not exceeding 80%. The latent heat of phase change of the microcapsules ranges from 120 to 180 kJ / kg, the particle size ranges from 5 to 100 micrometers, and the thermal conductivity ranges from 0.2 to 0.5 W / (m·K). The tailings are metal ore tailings or copper tailings. In the copper tailings, the proportion of D10 is 3.530%, the proportion of D50 is 16.598%, and the proportion of D90 is 85.735%. The main components of the tailings include quartz, muscovite, and a very small amount of azurite.

[0036] In this invention, SiC and MPCM are used to replace tailings by equal mass. The silicon carbide in the SiC-reinforced thermal energy storage phase change filler is green silicon carbide with a particle size of approximately 10-30 micrometers, a specific gravity of 320-325, and a microhardness of 2840-3320 kg / mm². 2SiC particles exhibit irregular angular shapes, with numerous depressions and wrinkles on their surface.

[0037] Furthermore, the effect of phase change microcapsules on the performance of the filler is as follows: with the increase of MPCM doping (0-20%), the compressive strength of the PMCM filler decreases significantly, then the trend flattens out; the thermal conductivity decreases linearly; the specific heat capacity gradually increases and then slightly decreases; while the enthalpy value increases significantly. The SiC-reinforced thermal energy storage phase change filler of this invention is applied to the field of deep and shallow mine filling, including deep mines and filling of mined-out areas.

[0038] In the above embodiment, step S400 includes: calculating the overall desirability D by taking the geometric mean of each desirability function. Where i is 1, 2, 3...n, n is the number of factors and responses included in the optimization process, ri is the relative importance of each factor and response, and di is the individual expectation of the factor and response.

[0039] It should be noted that r i This represents the relative importance of each factor or response, with values ​​ranging from +1 to +5, corresponding to the lowest to the highest importance. In other words, these five levels specify the relative importance of a response relative to other responses. Finally, by comparing its value with the corresponding defined objective, d... i This represents the individual's expectation level for each factor and response, with values ​​ranging from 0 to 1 for both undesirable and desired responses.

[0040] In some embodiments, among the selection of responses characterizing the performance of the filling material and factors affecting the performance of the filling material, the responses characterizing the performance of the filling material include compressive strength, thermal conductivity and specific heat capacity, and the factors affecting the performance of the filling material include ash-sand ratio, slurry concentration, MPCM ratio and silicon carbide ratio.

[0041] Furthermore, to improve the strength and thermal conductivity of the phase change infill, based on the research results on the mechanical strength and thermal conductivity of silicon carbide-reinforced concrete, silicon carbide was incorporated to replace tailings by an equal mass. Silicon carbide has high thermal conductivity, high hardness, strong oxidation resistance, strong thermal stability, and resistance to chemical corrosion, thus improving the thermodynamic properties of the phase change infill. To explore the optimal proportion of the phase change infill after incorporating SiC, response surface methodology was used to determine the most suitable level among various influencing factors. This invention comprehensively considers heat exchange efficiency, heat storage capacity, and strength requirements, selecting MPCM mass fractions of 5%, 10%, and 15%, silicon carbide dosages of 2%, 4%, and 6%, and cement-sand ratios of 1:4, 1:6, and 1:8. To meet the flowability requirements of on-site preparation, mixing, and transportation of the infill, slurry concentrations of 72%, 75%, and 78% were selected.

[0042] Optionally, in step S200: the experimental design for the correlation between the individual changes of each factor and the interaction between each factor affecting the response of various properties of the filling body, the Box-Behnken Design (BBD) in Design-expert software (DX13) is used for experimental design and data analysis. At least 27 sets of experiments are designed according to four factors including ash-sand ratio, slurry concentration, MPCM ratio and silicon carbide ratio, three responses including compressive strength, thermal conductivity and specific heat capacity, and a three-center BBD configuration.

[0043] Following the above embodiments, for filling materials, individual changes in each factor and the interactions between them have a significant impact on their various properties. Four factors (A, B, C, and D) were selected: sand-cement ratio, slurry concentration, MPCM mass fraction, and SiC mass fraction; compressive strength, thermal conductivity, and specific heat capacity were selected as three levels. Box-Behnken Design (BBD) in Design-Expert software (DX13) was used for experimental design and data analysis. A total of 27 sets of experiments were designed according to the four-factor, three-level, three-center BBD configuration. For each experimental index in each set, three specimens were prepared in parallel, and the average value of the three specimens was taken as the experimental result. The definition boundaries of each factor in RSM are shown in Table 1, and detailed mixing ratios and main performance test results are shown in Table 2.

[0044] Table 1 RSM Factor Levels

[0045] factor Lime-sand ratio Slurry concentration (%) MPCM (%) SiC (%) coding A B C D 1 1：4 72 5 2 0 1：6 75 10 4 -1 1：8 78 15 6

[0046] Table 2. Mixture Design and Experimental Results

[0047] Grouping A B(％) C(％) D(％) 28-day compressive strength / MPa Thermal conductivity / W / (m·K) <![CDATA[Specific heat capacity / MJ / (m 3 ·K)]]> 1 1：6 78 10 2 3.91 0.92 2.22 2 1：6 75 5 2 3.53 0.94 2.05 3 1：6 78 10 6 5.64 1.12 2.22 4 1：6 78 5 4 5.87 1.14 2.41 5 1：8 78 10 4 3.88 0.94 2.27 6 1：8 75 15 4 2.52 0.91 2.34 7 1：6 75 10 4 4.93 0.98 2.13 8 1：6 75 10 4 4.88 0.97 2.11 9 1：6 75 15 2 2.86 0.91 2.24 10 1：6 72 10 2 2.15 0.87 1.67 11 1：8 75 10 2 2.34 0.85 1.88 12 1：6 78 15 4 3.90 1.00 2.43 13 1：4 75 15 4 3.81 1.01 2.73 14 1：8 75 10 6 3.59 0.93 2.12 15 1：8 72 10 4 1.83 0.87 1.82 16 1：4 75 10 2 4.49 0.97 2.45 17 1：6 72 15 4 2.24 0.91 2.14 18 1：6 72 10 6 2.46 0.89 2.00 19 1：4 78 10 4 6.49 1.19 2.62 20 1：4 75 5 4 5.65 1.21 2.72 21 1：4 72 10 4 3.27 0.97 2.37 22 1：6 75 10 4 4.95 0.98 2.12 23 1：4 75 10 6 5.13 1.15 2.44 24 1：6 75 5 6 4.91 1.14 2.30 25 1：6 72 5 4 2.71 0.95 1.95 26 1：6 75 15 6 3.28 0.95 2.31 27 1：8 75 5 4 3.23 0.95 2.19

[0048] In another optional implementation, in step S200, the experimental design and data analysis can also be carried out using a central composite design (CCD) to study the correlation between the individual changes of each factor and the interaction between the factors affecting the response of the various properties of the filling material.

[0049] Following the embodiments shown in Tables 1 and 2, in step S300: A variance analysis is performed based on the experimental data. A multivariate quadratic polynomial model is used to perform multiple linear regression and binomial fitting analysis on the experimental results of the response of each corresponding performance, and to verify the significance of the regression model and factors of each response variable. This includes: using DX13 software to perform regression simulation analysis on the experimental data to obtain the regression model of compressive strength, thereby obtaining the significance of the influence of four factors, including the ash-sand ratio, slurry concentration, MPCM ratio and silicon carbide ratio, on the three levels of compressive strength, thermal conductivity and specific heat capacity.

[0050] Analysis of variance (ANOVA) was performed using RSM-BBD based on the experimental data. Multiple linear regression and binomial fit analysis were conducted on the experimental results of each corresponding variable using a multivariate quadratic polynomial model to verify the significance of the regression model and the factors. Table 3 shows the ANOVA results of the regression model under different response quantities. The p-values ​​of all models were less than 0.0001, indicating a strong regression effect. The independent effects of each factor on the response variable and the interaction terms were all highly significant. The R-values ​​for compressive strength, thermal conductivity, and specific heat capacity were... 2 All are greater than 0.99, adjusted R 2 Compared with the predicted R 2 The difference was less than 5%. The p-value for the lack-of-fit term was not significant (>0.05), indicating that there were no factors causing the experiment to lack fit, and the regression model could fully reflect the actual situation. Therefore, the established model is effective and has high enough accuracy to predict the expected response value and the corresponding factor values.

[0051] Table 3. Analysis of Variance for Regression Models

[0052]

[0053] In Table 3, P≤0.01 indicates that the factor has a highly significant effect on the response value, and P≤0.05 indicates that the factor has a significant effect on the response value.

[0054] The experimental results in Table 3 were analyzed using DX13 software through regression simulation, and the following regression model for compressive strength was obtained:

[0055] Y1=5.33+0.955A+1.32B-0.6682C+0.445D+0.293AB-0.272AC-0.144AD-0.375BC+0.354BD-0.240CD-0.828A 2 -0.652B 2 -0.633C 2 -0.660D 2 ,

[0056] Wherein, Y1: compressive strength.

[0057] Based on the above formula, the response surfaces of A and B, A and C, and A and D for the compressive strength of MPSC filling bodies can be obtained, including three-dimensional response surface views and contour plots. As A and B decrease, the compressive strength of the filling body decreases from 6.49 MPa to 1.83 MPa (C: 0.1, D: 0.04). With increasing C, the compressive strength gradually decreases. As A decreases from 1:4 to 1:8, the decrease in compressive strength with increasing C decreases, from 1.74 MPa (31.3%) to 0.71 MPa (22.0%). With increasing D, the compressive strength shows a trend of first increasing and then slightly decreasing, with an overall increasing trend. As A decreases from 1:4 to 1:8, the decrease in compressive strength with increasing D increases, from 0.64 MPa (12.4%) to 1.25 MPa (34.8%). As shown in Table 3, the significance of each factor on the compressive strength of MPSC fillers is B>A>C>D.

[0058] Following the above embodiment, in step S300; performing variance analysis based on the experimental data, using a multivariate quadratic polynomial model to perform multiple linear regression and binomial fitting analysis on the experimental results of the responses of each corresponding performance, and verifying the significance of the regression model and factors for each response variable, the method further includes:

[0059] Regression simulation analysis was performed using experimental data from DX13 software to obtain a regression model for thermal conductivity. This model revealed the significance of the effects of four factors—ash-sand ratio, slurry concentration, MPCM ratio, and silicon carbide ratio—on thermal conductivity. The regression model for thermal conductivity is as follows:

[0060] Y2=1.01+0.0889A+0.0783B-0.0619C+0.0658D+0.0364AB-0.0392AC-0.0256A

[0061] D-0.0248BC+0.0445BD-0.0385CD-0.0113A2-0.0040B2-0.0278C2-0.0174D2.

[0062] Where Y2 is the thermal conductivity.

[0063] The influence of various factors on thermal conductivity can be obtained from the above formula. As A and B decrease, the thermal conductivity of the filling material continuously decreases. The thermal conductivity of the filling material decreases from 1.19 W / (m·K) to 0.87 W / (m·K). Furthermore, the rate of decrease is faster at higher A or B ratios. As A and B approach 1:8 and 72%, the decrease becomes more gradual. The addition of C causes a decreasing trend in thermal conductivity; the decreasing trend gradually slows down as the C addition increases from 5% to 15%, which is consistent with the preliminary experimental results. When A is 1:4, C decreases from 1.212 to 1.012; when A is 1:8, C decreases from 0.949 to 0.908, with a significantly smaller decrease in the rate of decrease. With the increase of D, the compressive strength shows a linear increasing trend. SiC has a high thermal conductivity, which can enhance the heat transfer characteristics of the filling material. Combined with the preliminary experiments, it can be seen that the addition of SiC effectively enhances the thermal conductivity of the phase change energy storage filling material, achieving the desired effect. Based on Table 3, the significance of each factor on the thermal conductivity of MPSC filler is A>B>D>C.

[0064] Following the above embodiment, in step S300: Based on the experimental data, an analysis of variance is performed. A multivariate quadratic polynomial model is used to perform multiple linear regression and binomial fitting analysis on the experimental results of the responses to each corresponding performance, verifying the significance of the regression model and factors for each response variable. This also includes:

[0065] Regression simulation analysis was performed using experimental data from DX13 software to obtain a regression model for specific heat capacity. This model identified the significant impact of four factors—ash-sand ratio, slurry concentration, MPCM ratio, and silicon carbide ratio—on specific heat capacity. The regression model for specific heat capacity is as follows:

[0066] Y3=2.18+0.2264A+0.1724B+0.0377C+0.0579D-0.0520AB-0.0364AC-0.0632A

[0067] D-0.0440BC-0.0842BD-0.0457CD+0.1253A2-0.0398B2+0.1712C2-0.0687D2.

[0068] Where Y3 represents specific heat capacity. The influence of each factor on specific heat capacity can be obtained from the above formula. As A and B decrease, the specific heat capacity of the filling material continuously decreases, from 2.612 MJ / (m³) 3 The concentration of K decreased to 1.818 MJ / (m 3 As B decreases from 78% to 71%, the specific heat capacity decreases more rapidly with decreasing A, from 0.343 (13.1%) to 0.554 MJ / (m³). 3(·K)(23.4%). With the addition of C, the specific heat capacity initially decreased and then increased, consistent with the preliminary experimental results; the specific heat capacity decreased slightly after the C addition exceeded 5%. With the increase of D, the specific heat capacity generally showed an increasing trend. When A was 1:4, the specific heat capacity initially increased and then decreased, but the fluctuation was small, generally changing from 2.449 to 2.442 MJ / (m³). 3 (·K). When A is 1:8, the specific heat capacity increases from 1.875 to 2.121 MJ / (m³). 3 • K) There is no decay process. In summary, D has no negative impact on the specific heat capacity of the phase change energy storage filling material, and can increase the specific heat capacity of the filling material when the addition amount is high. The significance of the effects of each factor on the thermal conductivity of the MPSC filling material is A>B>D>C.

[0069] Continuing with the above embodiments, since SiC-MPCM-Backfill needs to meet multiple performance requirements such as strength, thermal conductivity, and energy storage, it is difficult to obtain the optimal solution for all performance aspects. Therefore, after variance analysis and model validation, a multi-factor, multi-objective joint optimization is used to obtain the optimal solution, which can simultaneously satisfy the requirements of all responses. In the embodiments of the present invention, since all responses are equally important, a comprehensive desirability D is used to comprehensively evaluate the performance of multiple response variables to determine the optimal experimental conditions. D is calculated by taking the geometric mean of each desirability function, as shown below:

[0070] d iThe desirability of each response is defined as follows, where n is the number of independent variables (factors) and dependent variables (responses) included in the optimization process. This embodiment of the invention employs four factors: ash-sand ratio, slurry concentration, MPCM, and SiC, while simultaneously optimizing four responses: compressive strength, thermal conductivity, and specific heat capacity. Each factor and response has a certain importance during the optimization process; the number of "+" signs determines the importance, with more "+" signs indicating higher importance. During numerical optimization, the targets for factors and responses can be given options, such as "none," "maximize," "minimize," or "in range," to ensure that each factor and response is within a reasonable range, allowing the MPSC backfill to achieve optimal performance. The compressive strength of the backfill needs to be set within a range according to site requirements; in this embodiment, a compressive strength of 2-5 MPa is set, while higher thermal conductivity and specific heat capacity are preferred. Based on the above requirements, the optimal mix design was implemented, with thermal conductivity and specific heat capacity set to their maximum values. Specific targets for factors (A, B, C, D) and responses (Y1, Y2, Y3) are shown in Table 4. According to the standards given in the table, the optimal solution within a given range was selected for analysis. The high expected value of the optimal mix design for the filling material indicates its rationality.

[0071] Table 4 Standards for Optimized Response

[0072] Factors and Responses Target Lower Upper importance A scope 1：4 1：8 +++ B scope 72％ 78％ +++ C scope 5％ 15％ +++ D scope 2％ 6％ +++ <![CDATA[Y1]]> Maximum value 2 5 +++ <![CDATA[Y2]]> Maximum value 1.0 1.2 +++ <![CDATA[Y3]]> Maximum value 2.20 2.60 +++

[0073] Optionally, after step S400: using comprehensive desirability to comprehensively evaluate the performance of multiple response variables to predict the preferred combination of factors, the method further includes: conducting experiments based on the preferred combination of factors, comparing the experimental values ​​with the predicted values ​​to verify the accuracy of the prediction method.

[0074] To further verify the obtained filling conditions that meet the requirements for mine thermal energy storage, experiments were conducted on the optimized mix proportions. The optimal mix proportion for combination 1 was: a lime-sand ratio of 0.226, a slurry concentration of 77.8%, an MPCM content of 5.25%, and a SiC content of 3.25%. Then, experiments were conducted using this mix proportion, and the experimental and predicted values ​​are shown in Table 5. As can be seen from the table, the errors between the experimental results and the predicted values ​​are all less than 5%, indicating good agreement between the two results. The smaller the error value, the better the accuracy and predictability of the response model. Overall, the RSM-BBD method is a very effective method for determining the predictive value of each factor on the performance of SiC-MPCM-Backfill.

[0075] Table 5 Comparison of predicted and experimental values ​​from optimized mix design.

[0076]

[0077] In summary, the embodiments of this invention provide a novel silicon carbide-reinforced phase change infill body, explore the compressive strength, thermal conductivity, and thermal energy storage performance of the infill body, and use RSM to predict the various properties of the infill body under different proportions in actual engineering. This technical solution can not only solve the problem of heat hazards in deep mines and reduce mining costs during mine operation, but also continue to develop geothermal resources after the mine is completed, extend the life cycle of the mine, and improve the long-term sustainability of the mining area.

[0078] It should also be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0079] Finally, it should be noted that the above description represents a preferred embodiment of the present invention. It should be pointed out that although preferred embodiments have been described, those skilled in the art, once they understand the basic inventive concept of the present invention, can make various improvements and modifications without departing from the principles described herein. These improvements and modifications should also be considered within the scope of protection of the present invention. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the embodiments of the present invention.

Claims

1. A method for predicting the performance of silicon carbide phase change infill materials based on RSM, used to enhance the thermal energy storage performance of infill materials in deep and shallow mines, deep mines, and goaf areas, wherein the phase change material is a phase change microcapsule, characterized in that... include: Select the response that characterizes the performance of the filling material and the factors that affect the performance of the filling material; The responses characterizing the performance of the filling material include compressive strength, thermal conductivity, and specific heat capacity. The factors affecting the performance of the filling material include ash-sand ratio, slurry concentration, proportion of phase change microcapsules, and proportion of silicon carbide. Experimental design and data analysis were conducted to investigate the correlation between individual changes in various factors and the interactions between these factors, and to examine the impact of these factors on the response of various properties of the filling material. In the experimental design to investigate the correlation between the individual changes of each factor and the interaction between the factors affecting the response of various properties of the filling material, a central composite design was used for experimental design and data analysis. Analysis of variance was conducted based on the experimental data. Multiple linear regression and binomial fitting analysis were performed on the experimental results of the response of each corresponding performance using a multivariate quadratic polynomial model to verify the significance of the regression model and factors for each response variable. Comprehensive desirability is used to comprehensively evaluate the performance of multiple response variables in order to predict the optimal combination of factors.

2. The method for predicting the performance of silicon carbide phase change fillers based on RSM as described in claim 1, characterized in that, The method of using comprehensive desirability to comprehensively evaluate the performance of multiple response variables in order to predict the optimal combination of factors includes: calculating the comprehensive desirability D by taking the geometric mean of the desirability functions. , where i is 1, 2, 3... n, n is the number of factors and responses included in the optimization process, ri is the relative importance of each factor and response, and di is the individual expectation of the factor and response.

3. The method for predicting the performance of silicon carbide phase change fillers based on RSM as described in claim 1, characterized in that, In the experimental design for the correlation between the individual changes of each factor and the interaction between the factors affecting the response of various properties of the filling body, the Box-Behnken Design in Design-expert software was used for experimental design and data analysis. At least 27 sets of experiments were designed according to four factors including ash-sand ratio, slurry concentration, proportion of phase change microcapsules and silicon carbide proportion, three responses including compressive strength, thermal conductivity and specific heat capacity, and a three-center BBD configuration.

4. The method for predicting the performance of silicon carbide phase change fillers based on RSM as described in claim 3, characterized in that, The process of performing variance analysis based on experimental data, using a multivariate quadratic polynomial model to analyze the response of each corresponding performance item, and conducting multiple linear regression and binomial fitting analysis to verify the significance of the regression model and factors for each response variable includes: Regression simulation analysis was performed using Design-expert software to obtain a regression model for compressive strength, thereby revealing the significance of the effects of four factors on compressive strength, including the ash-sand ratio, slurry concentration, proportion of phase change microcapsules, and proportion of silicon carbide.

5. The method for predicting the performance of silicon carbide phase change fillers based on RSM as described in claim 4, characterized in that, The process of performing variance analysis based on experimental data, using a multivariate quadratic polynomial model to perform multiple linear regression and binomial fitting analysis on the experimental results of the responses of various performance parameters, and verifying the significance of the regression model and factors for each response variable, also includes: Regression simulation analysis was performed using Design-expert software to obtain a regression model for thermal conductivity, thereby revealing the significance of the effects of four factors, including ash-sand ratio, slurry concentration, proportion of phase change microcapsules, and proportion of silicon carbide, on thermal conductivity.

6. The method for predicting the performance of silicon carbide phase change fillers based on RSM as described in claim 4, characterized in that, The process of performing variance analysis based on experimental data, using a multivariate quadratic polynomial model to perform multiple linear regression and binomial fitting analysis on the experimental results of the responses of various performance parameters, and verifying the significance of the regression model and factors for each response variable, also includes: Regression simulation analysis was performed using Design-expert software to obtain a regression model for specific heat capacity, thereby determining the significance of the influence of four factors, including ash-sand ratio, slurry concentration, proportion of phase change microcapsules, and proportion of silicon carbide, on specific heat capacity.

7. The method for predicting the performance of silicon carbide phase change fillers based on RSM as described in claim 1, characterized in that, After employing comprehensive desirability to comprehensively evaluate the performance of multiple response variables in order to predict the preferred combination of factors, the method further includes: conducting experiments based on the preferred combination of factors, comparing the experimental values ​​with the predicted values, and verifying the accuracy of the prediction method.

Images