Optimization Extraction Method of Coal-based n-alkane Phase Change Materials Based on Data-driven Model

Abstract

The present invention discloses an optimized extraction method for coal-based n-alkane phase change materials based on a data-driven model, which relates to the technical field of data processing; the method includes: Step 1: Collect experimental data of coal-based n-alkane; construct a coal sample feature vector based on the experimental data; Step 2: Based on the coal sample feature vector and the solubility parameter matrix of the coal sample, construct a solubility selectivity prediction model; Step 3: Construct a multi-field coupling transport equation; then according to the multi-field coupling transport equation, establish a separation efficiency prediction model and construct a phase change performance prediction function; establish a crystallization process control equation, solve the crystallization process control equation, and obtain the crystallinity; Step 4: Construct a multi-objective optimization function; by solving the multi-objective optimization function, obtain the optimal process parameter combination; the present invention significantly reduces energy consumption and production costs while ensuring material purity and extraction efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and particularly to an optimized extraction method of coal-based n-alkane phase change materials based on a data-driven model. Background Art

[0002] In the research on the extraction and application of coal-based n-alkane phase change materials, the existing technologies mainly focus on the deep processing and separation methods of coal-based raw materials. Coal-based n-alkanes are an important type of phase change materials, with unique thermophysical properties such as high latent heat and adjustable phase change temperature, which endow them with broad application potential in energy storage, temperature regulation, and thermal management. However, due to the complex composition, high carbon-hydrogen ratio, and many impurities of coal-based raw materials themselves, the extraction and purification processes of coal-based n-alkanes face great technical challenges. Most of the existing technologies rely on traditional chemical separation methods and heat treatment technologies, but these methods have many deficiencies in terms of energy consumption, separation efficiency, material purity, etc. Therefore, how to efficiently extract high-purity n-alkanes from complex coal-based raw materials while reducing energy consumption and improving the extraction quality has become a technical problem urgently to be solved in the industry.

[0003] In the existing technology, the most common methods for extracting coal-based n-alkanes include solvent extraction, distillation, fractionation, and hydrodewaxing, etc. The solvent extraction method uses the selective solubility of solvents for different components to extract the n-alkanes in coal-based raw materials from other components. This method has a certain selectivity, but its solvent recovery cost is relatively high, and impurities may be introduced during the dissolution process, affecting the purity of the extracted materials. In addition, due to the weak selectivity of solvents for n-alkanes with different carbon chain lengths, it is difficult to effectively extract n-alkanes with specific carbon chain lengths in complex coal-based raw materials by this method. Distillation and fractionation technologies separate different boiling point components, but this method requires high-temperature conditions, which easily leads to thermal decomposition of raw materials, reducing the thermal stability of materials, and the energy consumption problem associated with high-temperature operation has not been solved either.

[0004] Hydrodewaxing is another common method for extracting n-alkanes. It uses a hydrogenation reaction to remove non-n-alkane components and improve the purity of n-alkanes. However, this method usually requires high pressure and catalysts, is relatively complex in operating conditions, has a large equipment investment cost, and the selection and activity maintenance of catalysts are also key issues. The high pressure and hydrogenation atmosphere will also cause changes in the molecular structure of coal-based raw materials, resulting in instability during the conversion process. The by-products generated in this process may increase the difficulty of subsequent purification and further reduce the utilization efficiency of materials. Therefore, although hydrodewaxing has advantages in extraction purity, it shows obvious deficiencies in terms of energy consumption and equipment requirements. Summary of the Invention

[0005] The object of the present invention is to provide an optimized extraction method for coal-based n-alkane phase change materials based on a data-driven model. Through multi-field coupling and multi-objective optimization, the present invention can efficiently extract n-alkanes with specific carbon chain lengths from complex coal-based raw materials, while achieving the best balance between separation efficiency and energy consumption. During the extraction process, the data-driven model is used to combine the dynamic adjustment of variables such as temperature, pressure, and reaction time, enabling the extraction process to be optimized under different conditions, thereby significantly reducing energy consumption and production costs while ensuring material purity and extraction efficiency.

[0006] To solve the above technical problems, the present invention provides an optimized extraction method for coal-based n-alkane phase change materials based on a data-driven model, and the method includes:

[0007] Step 1: Collect experimental data of coal-based n-alkanes, including: coal sample component data, reaction temperature, reaction pressure, and reaction time; construct a coal sample feature vector based on the experimental data;

[0008] Step 2: Based on the coal sample feature vector and the solubility parameter matrix of the coal sample, construct a dissolution selectivity prediction model; the output result of the dissolution selectivity prediction model is the solubility of coal-based n-alkanes in the coal sample at a specific reaction temperature;

[0009] Step 3: Based on the specific heat capacity and density of the coal sample, combined with the output result of the dissolution selectivity prediction model, construct a multi-field coupling transport equation, solve the multi-field coupling transport equation to obtain the concentration of coal-based n-alkanes; then, based on the multi-field coupling transport equation, establish a separation efficiency prediction model and construct a phase change performance prediction function; the output result of the separation efficiency prediction model is the separation efficiency; solve the phase change performance prediction function to obtain the phase change temperature of coal-based n-alkanes; based on the separation efficiency prediction model and the constructed phase change performance prediction function, establish a crystallization process control equation, and solve the crystallization process control equation to obtain the crystallinity;

[0010] Step 4: Based on the crystallinity, separation efficiency, phase change temperature of coal-based n-alkanes, and concentration of coal-based n-alkanes, construct a multi-objective optimization function; by solving the multi-objective optimization function, obtain the optimal process parameter combination; the optimal process parameter combination includes: optimal reaction temperature, optimal reaction pressure, and optimal reaction time; use the optimal process parameter combination to optimize the extraction of coal-based n-alkane phase change materials.

[0011] Further, the coal sample component data includes: reaction degree, volume change, number of components, carbon content, hydrogen content, and oxygen content in the components.

[0012] Further, the coal sample feature vector is represented by the following formula:

[0013]

[0014] Among them, X(t) is the characteristic vector of the coal sample at the reaction time t; N is the number of components in the coal sample; i is an integer subscript index, with a value range of 1 to N; C i is the carbon content of the i-th component; e is the natural base; T is the reaction temperature; E i is the activation energy of the i-th component; α j is the reaction degree of the j-th component, where j is an integer subscript index with a value range of 1 to N and j≠i; H i is the hydrogen content of the i-th component; P is the reaction pressure; P0 is the standard pressure; O i is the oxygen content of the i-th component; ΔV i is the volume change of the i-th component; ΔG mix is the mixed Gibbs free energy; τ i is the characteristic relaxation time of the i-th component, and the calculation formula is:

[0015]

[0016] Furthermore, the dissolution selectivity prediction model is expressed by the following formula:

[0017]

[0018] Among them, S(n,T) represents the solubility of the n-alkane based on coal with a carbon chain length of n in the coal sample at the reaction temperature T; K d is a preset dissolution constant; X Z (t) is the transpose of X(t); μ is the average carbon chain length of the n-alkane based on coal; σ is the standard deviation of the carbon chain length of the n-alkane based on coal; D(T) is the dissolution parameter matrix, and the expression is:

[0019]

[0020] Among them, ΔH1 is the heat of dissolution of the first component, ΔH2 is the heat of dissolution of the second component, and ΔH N is the heat of dissolution of the N-th component; E1 is the activation energy of the first component, E2 is the activation energy of the second component, and E N is the activation energy of the N-th component; κ 12 (T) represents the dissolution influence coefficient of the first component on the second component at the temperature T, and so on, κ ij (T) represents the dissolution influence coefficient of the i-th component on the j-th component at the temperature T; Z is the transpose operation.

[0021] Furthermore, the multi-field coupling transport equation is expressed by the following formula:

[0022]

[0023] Among them, C n is the concentration of coal-based n-alkanes with a carbon chain length of n; is the gradient operator; k is the thermal conductivity of the coal sample; ρ is the density of the coal sample; C p is the specific heat capacity of the coal sample; is the change value of the reaction temperature; is the change value of the reaction pressure; D eff is the effective diffusion coefficient, which is calculated by the following formula:

[0024] D eff = φ·τ·D m ·S(n, T);

[0025] Among them, φ is the porosity of the coal sample; D m is the molecular diffusion coefficient of the medium, that is, the free diffusion coefficient of coal-based n-alkanes in the coal sample; τ is the tortuosity, which is a set value greater than 1.

[0026] Furthermore, the separation efficiency prediction model is expressed by the following formula:

[0027]

[0028] Among them, θ(t) represents the separation efficiency at the reaction time t; X(0) represents the characteristic vector of the coal sample at the initial reaction time.

[0029] Furthermore, the phase change performance prediction function is expressed by the following formula:

[0030]

[0031] Among them, T m (n) is the phase change temperature of coal-based n-alkanes with a carbon chain length of n; ΔH f is the latent heat of phase change; T0 is the preset parameter reference temperature.

[0032] Furthermore, the crystallization process control equation is expressed by the following formula:

[0033]

[0034] Among them, X c is the crystallinity; k0 is the crystallization rate constant; is the saturation concentration of coal-based n-alkanes with a carbon chain length of n, which is calculated based on the Wilson equation:

[0035]

[0036] Among them, ΔH sol is the enthalpy change of dissolution; C0 is the saturation concentration at the reference temperature T0.

[0037] Furthermore, the multi-objective optimization function is calculated using the following formula:

[0038]

[0039] where T target is the target phase transition temperature; E total is the total energy consumption; P opt is the optimal combination of process parameters.

[0040] The optimized extraction method of coal-based n-alkane phase change materials based on a data-driven model of the present invention has the following beneficial effects:

[0041] In the extraction process of the present invention, a data-driven multi-objective optimization model is introduced. Most traditional extraction methods rely on a single process parameter, while the present invention comprehensively incorporates factors such as crystallinity, separation efficiency, dissolution selectivity, and total energy consumption into the multi-objective optimization model to achieve global optimization of reaction conditions. This method ensures that the temperature, pressure, and time during the extraction process can operate under the optimal combination, thereby achieving the best balance between extraction efficiency and energy consumption and avoiding the cost problem caused by excessive energy consumption in traditional methods. At the same time, the multi-objective optimization model makes the extraction process flexible and adaptable to changes in different raw material characteristics or production requirements. By dynamically balancing energy consumption and separation efficiency, the present invention significantly improves the industrial extraction efficiency of coal-based n-alkanes.

[0042] Secondly, the multi-field coupling transport equation and dissolution selectivity prediction model of the present invention significantly improve the accuracy and stability of the extraction process. During the extraction process of coal-based n-alkanes, the solubility and transport path of the material vary significantly at different temperatures and pressures. Through the multi-field coupling transport equation, the present invention can simultaneously consider the effects of factors such as temperature gradient, pressure gradient, and concentration diffusion, comprehensively simulate the dissolution and transport behavior of coal-based n-alkanes, and thus achieve precise control of concentration and transport path during the extraction process. The dissolution selectivity prediction model accurately predicts the dissolution selectivity of different carbon chain structures at different temperatures based on the dissolution characteristics of n-alkanes with specific carbon chain lengths. This process not only ensures the separation of specific target components during the extraction process but also effectively improves the purity of the extraction product, making the finally obtained n-alkane material have a uniform carbon chain distribution and ensuring the performance stability of the material.

[0043] The phase change performance prediction function and the crystallization process control equation of the present invention play a crucial role in the temperature control during the extraction process and the regulation of the crystallization behavior. The phase change temperature is the core performance parameter of coal-based n-alkanes as phase change materials, directly affecting their energy storage and temperature regulation performance. The present invention predicts and adjusts the phase change temperature in real time during the extraction process through the phase change performance prediction function, ensuring that the final product can meet the temperature requirements of specific application scenarios. The phase change performance prediction function can dynamically adjust the phase change temperature of the carbon chain length according to the heat accumulation situation during the extraction process, thereby controlling the phase change behavior of n-alkanes during the extraction process. Combining with the crystallization process control equation, the present invention precisely regulates the crystallinity of coal-based n-alkanes during the extraction process, thus ensuring the thermal stability of the material after phase change. The crystallization process control equation ensures the adaptability of the crystallinity under different conditions by adjusting factors such as temperature and concentration, making the phase change temperature and crystallization state of the material reach the best. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to the provided drawings.

[0045] Figure 1 It is a schematic structural diagram of a system for an optimized extraction method of coal-based n-alkane phase change materials based on a data-driven model provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0047] Example 1, refer to Figure 1 : An optimized extraction method of coal-based n-alkane phase change materials based on a data-driven model, the method includes:

[0048] Step 1: Collect experimental data of coal-based n-alkanes, including: coal sample component data, reaction temperature, reaction pressure, and reaction time; construct a coal sample feature vector based on the experimental data;

[0049] As a phase change material, the extraction process of coal-based n-alkanes highly depends on the composition of coal samples and the changes in reaction conditions. In traditional methods, the extraction process often requires repeated experiments to verify the reaction effects of different coal samples under various conditions. This is not only time-consuming and laborious, but also the accuracy of data is limited by the subtle errors in experiments, making it difficult to efficiently obtain accurate prediction results for extraction conditions. The present invention introduces a data-driven method. First, by collecting experimental data of coal samples, including core parameters such as coal sample components, reaction temperature, reaction pressure, and reaction time, basic data for comprehensively describing each coal sample is formed. These data are no longer just experimental observations, but are transformed into "feature vectors" of coal samples through feature extraction and vectorization processing, representing the reaction behaviors and properties of coal samples under different conditions. The process of constructing the feature vectors of coal samples is not simply data aggregation, but through mathematical methods to analyze the weights of each experimental parameter to ensure that the feature vectors can cover multi-dimensional information of coal samples. Specifically, the composition data of coal samples includes the relative contents of different components, such as the percentages of elements like carbon, hydrogen, oxygen, sulfur, etc., as well as trace elements that may affect the solubility of n-alkanes. These component information play a decisive role in the extraction process of coal-based n-alkanes, while reaction temperature, pressure, and time directly affect the dissolution behavior of coal-based n-alkanes under dynamic conditions. The construction of feature vectors effectively compresses this information into a multi-dimensional space, forming a unified numerical vector, so that the similarities or differences between different coal samples under the same or different conditions can be compared through the distances between vectors. The feature vectors generated in this way have the basis for data-driven models and can predict the dissolution behavior of coal samples under different conditions, especially the relationship between the solubility of n-alkanes in coal samples and specific experimental conditions. The role of feature vectors in data-driven models is similar to a kind of "fingerprint", which is the unique response of coal samples under this specific experimental condition. Through repeated training and iteration, the data-driven model can learn the solubility differences of different coal samples under different conditions based on a large number of coal sample feature vectors and experimental conditions. In future predictions, even the feature vectors of unknown coal samples can be used as input data, and the model will generate corresponding prediction results based on existing knowledge, greatly improving the accuracy and efficiency of the n-alkane extraction process.

[0050] Step 2: Based on the feature vectors of coal samples and the dissolution parameter matrix of coal samples, construct a dissolution selectivity prediction model; the output result of the dissolution selectivity prediction model is the solubility of coal-based n-alkanes in coal samples at a specific reaction temperature;

[0051] In the method of the present invention, the basis of the dissolution selectivity prediction model is the dissolution parameter matrix constructed from experimental data. This matrix contains the dissolution characteristics of different coal samples at different reaction temperatures, integrating multi-dimensional data of the dissolution behavior to form a characteristic correlation relationship that can be learned by the model. This dissolution parameter matrix not only describes the solubility of a single coal sample at a single temperature, but through the accumulation of a large amount of experimental data, integrates various characteristics of the coal sample (such as composition, density, specific heat capacity, etc.) and reaction conditions (such as temperature, pressure, etc.) into an overall entity, enabling the model to find the corresponding solubility relationship under the combined conditions of different variables. During the training process, the model repeatedly learns these characteristic combinations, and through a data-driven approach, identifies the dissolution selectivity law of coal-based n-alkanes, ensuring efficient and accurate prediction under specific reaction conditions. The dissolution selectivity prediction model is not just a simple mapping of solubility data, but through machine learning methods, enables the model to "memorize" the correlation between different feature vectors. In actual operation, when the feature vector of a coal sample is input, the model will automatically find the sample data in the existing dissolution parameter matrix that is closest to this feature, and through methods such as interpolation and fitting, obtain the solubility of this coal sample under the current conditions. This method can significantly improve the accuracy of prediction because the model does not rely on a single solubility data for judgment, but organically links each experimental data through the overall characteristic correlation, forming a way to expand the dissolution behavior from the known to the unknown. The training of the model not only improves its accurate prediction ability for known samples, but also when faced with new coal samples or new conditions, through the similarity between data, can quickly give the prediction result of solubility. This flexibility enables the model to have strong adaptability and generalization ability.

[0052] By combining the coal sample feature vector and the solubility parameter matrix, the model can predict the solubility of a specific coal sample at a specific reaction temperature, thus providing guidance for the extraction process. This method has significant advantages compared with traditional experimental methods. Traditional methods usually require multiple experiments at different temperatures to observe the dissolution of n-alkanes in coal samples, which not only consumes manpower and time but also may lead to prediction errors due to the discreteness of data. The dissolution selectivity prediction model makes the influence of temperature on the dissolution behavior a quantifiable functional relationship through systematic training and integration of data. After obtaining the coal sample feature vector, the model directly uses the vector and the data in the solubility parameter matrix for calculation, thus quickly obtaining the solubility result. This efficiency is particularly important in industrial applications because the dissolution selectivity of different coal samples varies significantly. Through the prediction of the model, the dissolution of n-alkanes at a specific temperature can be directly obtained, avoiding the cumbersome steps of temperature control and sample testing in traditional experiments. Further, the dissolution selectivity prediction model is not only a data mapping tool. It essentially utilizes the complex non-linear relationship between the coal sample feature vector and the solubility parameter matrix, enabling the model to have a deep understanding of the dissolution behavior of coal-based n-alkanes. Through training, this model can automatically identify the influence pattern of different temperatures on solubility, making the prediction results closer to the actual situation. Whether under high-temperature or low-temperature conditions, the model can quickly find the appropriate solubility prediction value based on the known data pattern. This flexible response ability greatly improves the extraction efficiency of n-alkanes. During the process of data input and output, the dissolution selectivity prediction model is like a "virtual laboratory". It can give accurate solubility values at any time through the existing data, not only shortening the experimental time but also making the prediction of the dissolution behavior more reliable through systematic model analysis. Finally, the solubility value output by the dissolution selectivity prediction model becomes the key input for the subsequent steps, providing basic data for the establishment and optimization of the multi-field coupling transport equation. Through this prediction method, the present invention reduces the dependence on experimental steps in the extraction process, making the extraction process of coal-based n-alkanes more automated and intelligent. At the same time, it also makes the prediction of the data-driven model an indispensable part of the extraction method. This model not only provides an accurate basis for the selective dissolution of coal samples but also maintains high prediction ability under the influence of multiple variables such as temperature and coal sample components, thus ensuring the stability and controllability of the extraction process.

[0053] Step 3: Based on the specific heat capacity and density of the coal sample, combined with the output results of the dissolution selectivity prediction model, construct a multi-field coupled transport equation, solve the multi-field coupled transport equation to obtain the concentration of coal-based n-alkanes; then, according to the multi-field coupled transport equation, establish a separation efficiency prediction model and construct a phase change performance prediction function; the output result of the separation efficiency prediction model is the separation efficiency; solve the phase change performance prediction function to obtain the phase change temperature of the coal-based n-alkanes; based on the separation efficiency prediction model and the constructed phase change performance prediction function, establish a crystallization process control equation, solve the crystallization process control equation to obtain the crystallinity;

[0054] The main task of Step 3 is to further construct and solve a multi-field coupled transport equation based on the output results of the dissolution selectivity prediction model, combined with the specific heat capacity and density of the coal sample, so as to accurately simulate the transport process of n-alkanes in the coal sample and obtain their concentration distribution under different conditions. This step is not only a static prediction of solubility, but also needs to simulate the dynamic changes of solubility under specific reaction conditions by coupling the transport behaviors of multiple physical fields. Through the introduction of parameters such as specific heat capacity and density, the multi-field coupled transport equation realizes the comprehensive description of various effects such as heat transfer, mass transfer, and flow, thus truly reproducing the dynamic characteristics of the extraction process. On this basis, Step 3 further establishes a separation efficiency prediction model and a phase change performance prediction function, and constructs a control equation for the crystallization process based on these models to obtain the phase change temperature, separation efficiency, and crystallinity of the coal-based n-alkanes. This delicate coupled calculation provides a scientific basis for subsequent optimization. In the construction of the transport equation, the introduction of specific heat capacity and density plays an important role. The specific heat capacity reflects the amount of heat absorbed or released by the coal sample during heating, while the density is closely related to the transport speed and distribution state of the substance. During the transport process, the differences in specific heat capacity and density under different temperature conditions will cause local changes in solubility, which in turn affect the phase change process of n-alkanes. By combining these parameters, the multi-field coupled transport equation can capture the concentration distribution of n-alkanes in the coal sample and predict the change trend of solubility under different reaction conditions. The equation not only considers the distribution of n-alkanes in time and space, but also introduces variables such as temperature and concentration to form a dynamic correlation between the output results of the dissolution selectivity prediction model and the transport equation. Based on the solution of the transport equation, the system can deduce the distribution concentration of the coal-based n-alkanes, and then judge the efficiency of its transport and dissolution process through the concentration change trend.

[0055] In addition to the construction of the transport equation, Step 3 also introduces a separation efficiency prediction model and a phase change performance prediction function to further achieve precise control of the separation and phase change processes of coal-based n-alkanes. The separation efficiency prediction model uses the results of the transport equation to judge the extraction efficiency of n-alkanes. Specifically, the separation efficiency reflects the proportion of n-alkanes in the coal sample extracted per unit time under specific transport conditions. With the solution of the multi-field coupling transport equation, the separation efficiency prediction model can make a quantitative prediction of the separation effect during the extraction process based on data such as the gradient change of concentration and the time evolution of solubility. This prediction can not only help determine the extraction effect of coal-based n-alkanes under the current process conditions but also serve as a basis for adjusting extraction parameters to further optimize the efficiency of the entire process. The phase change performance prediction function, on the other hand, models the phase change characteristics of coal-based n-alkanes during the extraction process by combining the results of the transport equation. Phase change is a crucial step in the change of properties of coal-based n-alkanes after separation from the coal sample, and this process is affected by multiple factors such as temperature and pressure. The phase change performance prediction function calculates the phase change temperature under specific conditions based on the dissolution characteristics of n-alkanes and their thermodynamic parameters. Through the linkage of the transport equation and the prediction function, the reaction conditions can be monitored and adjusted in real time to ensure that the n-alkanes complete the phase change at an appropriate temperature. The determination of this phase change temperature not only directly affects the extraction purity and quality of the material but also determines the stability and performance of the finally obtained phase change material. On the basis of establishing the transport equation, the separation efficiency prediction model, and the phase change performance prediction function, Step 3 further constructs the control equation for the crystallization process. The crystallization process is an indispensable part of the extraction process. By precisely controlling the crystallization conditions of n-alkanes, the crystallinity of the phase change material can be increased, thereby optimizing the material's performance. Crystallinity is an important indicator characterizing the degree of ordered arrangement inside the material, and a higher crystallinity usually means better thermodynamic stability and mechanical properties. The crystallization process control equation determines the key conditions such as temperature, time, and pressure of n-alkanes during the crystallization process based on the outputs of the separation efficiency prediction model and the phase change performance prediction function, thereby maximizing its crystallinity under specific conditions. By solving this equation, the system can precisely control the reaction conditions to ensure that coal-based n-alkanes precipitate under the optimal crystallization conditions, ultimately forming a phase change material with a high crystallinity.

[0056] Step 4: Based on the crystallinity, separation efficiency, phase change temperature of coal-based n-alkanes, and concentration of coal-based n-alkanes, construct a multi-objective optimization function; by solving the multi-objective optimization function, obtain the optimal combination of process parameters; the optimal combination of process parameters includes: the optimal reaction temperature, the optimal reaction pressure, and the optimal reaction time; use the optimal combination of process parameters to optimize the extraction of coal-based n-alkane phase change materials.

[0057] The core of Step 4 is to find the optimal combination of process parameters during the extraction process by constructing a multi-objective optimization function, including the optimal reaction temperature, reaction pressure, and reaction time. This step is based on the data and prediction results obtained in the previous steps, and uses crystallinity, separation efficiency, phase transition temperature, and concentration of coal-based n-alkanes as key optimization objectives. Through the multi-objective optimization method, fine adjustment of process parameters is achieved under complex conditions. The multi-objective optimization function plays a role in integrating all important influencing factors here, measuring and weighing different target parameters through a unified function, and ensuring that the final parameter combination can achieve the optimal balance in all indicators. The optimization process first introduces each target index into a unified evaluation framework. The construction of the evaluation framework involves the setting of weights for multiple important factors and the comprehensive consideration of influencing factors. Specifically, as a key index of the final product performance, crystallinity affects the structural stability and thermodynamic properties of the coal-based n-alkane phase change material, so it occupies an important proportion in the optimization. The separation efficiency determines the extraction rate and quality of coal-based n-alkanes, and directly affects the economy and efficiency of the extraction process. The phase transition temperature is an important property of the material in practical applications, which can determine the stability and performance of coal-based n-alkanes under different temperature conditions. Optimizing this temperature parameter can ensure the reliability and durability of the material in applications. As an immediate variable during the reaction process, concentration reflects the content and distribution state of coal-based n-alkanes under reaction conditions, and can reflect the uniformity and effect of the dissolution process under different reaction conditions. Through the introduction of these target factors, the optimization function integrates them in a multi-dimensional space to find the combination of process conditions that can meet all indicators simultaneously.

[0058] A systematic solution method is adopted in the multi-objective optimization during this process, gradually adjusting the reaction temperature, pressure, and time to find a balance point among all target factors. This optimization solution method not only considers the individual extreme values of each target, but also identifies and adjusts the mutual restraint relationships among the targets through multiple iteration processes. Since there may be competitive relationships among different targets, such as higher separation efficiency often being accompanied by higher energy consumption or higher reaction temperature, through the optimization process, the system can achieve an ideal balance between separation efficiency and other targets, optimizing all aspects of the extraction process. In actual solution, the optimization function will adjust the combination of process conditions with the changes of the weights and conditions of each target factor, and finally find the best extraction conditions under the comprehensive evaluation of multiple target parameters. The optimal combination of process parameters obtained by solving the multi-objective optimization function enables the extraction of coal-based n-alkanes to achieve the highest extraction efficiency and quality. The entire optimization process is completed through multiple iterative calculations of the model, enabling the system to dynamically respond to and adjust different condition combinations, thus ensuring the optimal extraction effect in each extraction.

[0059] Example 2: The coal sample component data includes: reaction degree, volume change, number of components, carbon content, hydrogen content, and oxygen content in the components.

[0060] Specifically, the reaction degree, as the reaction depth of the coal sample under specific conditions, reveals the process of dissolution and transformation of n-alkanes from the coal sample. In the data-driven model, the reaction degree reflects the degree of chemical change inside the coal sample, which determines the extraction effect of n-alkanes and their performance in subsequent separation steps. Therefore, the reaction degree is not only an experimental variable but also an important input in the solubility prediction model, affecting the judgment of the extraction process by the dissolution selectivity prediction model. The volume change is another key parameter. The coal sample may undergo significant physical structure changes due to dissolution and separation during the extraction process, thereby changing the dissolution path and transport characteristics. The volume change captures this microscopic structural transformation, which affects the transport efficiency and path of n-alkanes during the dissolution process. By recording the volume change, the data-driven model can better simulate and predict the behavior of the coal sample under different conditions. The volume change data enables the model to dynamically adapt to the changes in the coal sample structure during the reaction process, thereby providing accurate parameters for the transport equation. The change in volume also reflects the adjustment of the internal pore structure, which has an important impact on the solubility and transport efficiency of coal-based n-alkanes. The input of volume data ensures the precise control of the coal sample dissolution process at the microscopic level. The carbon, hydrogen, and oxygen contents in the coal sample represent the basic chemical composition of the coal sample, which have a direct impact during the extraction process. The level of carbon content not only affects the basic properties of the coal sample but also determines the generation potential of n-alkanes. The hydrogen content is directly related to the saturation and chemical stability of n-alkanes and plays an important role during the dissolution and extraction processes. The oxygen content may affect the redox characteristics of the coal sample, thereby changing the reaction activity and affecting the dissolution and extraction efficiency. The chemical composition of the coal sample, through the ratio of carbon, hydrogen, and oxygen, determines the solubility and dissolution selectivity of different coal samples during the dissolution process. By analyzing these chemical data, the data-driven model can more accurately predict the extraction effect of n-alkanes under specific reaction conditions and can dynamically adjust process parameters such as temperature and pressure during the extraction process to achieve the best extraction effect. The number of components, as a structural characteristic of the coal sample, has important applications during the extraction process. The number of components not only determines the macroscopic characteristics of the coal sample but also indirectly affects the influence degree of reaction conditions on solubility. Different numbers of components may lead to significant differences in the microscopic structure of the coal sample, thereby changing the transport path of n-alkanes. The data-driven model can use the data of the number of components to adjust the parameters of the dissolution selectivity prediction model, making the extraction process more adaptable and flexible. The data-driven model, by means of information such as reaction degree, volume change, number of components, and carbon, hydrogen, and oxygen contents, enables the dissolution selectivity prediction model to make corresponding adjustments according to the characteristics of different coal samples, thereby precisely controlling the extraction process.

[0061] Example 3: The characteristic vector of the coal sample is represented by the following formula:

[0062]

[0063] where X(t) is the characteristic vector of the coal sample at reaction time t; N is the number of components in the coal sample; i is an integer subscript index with a value range of 1 to N; C i is the carbon content of the i-th component; e is the natural logarithm base; T is the reaction temperature; E i is the activation energy of the i-th component; α j is the reaction degree of the j-th component, where j is an integer subscript index with a value range of 1 to N and j≠i; H i is the hydrogen content of the i-th component; P is the reaction pressure; P0 is the standard pressure; O i is the oxygen content of the i-th component; ΔV i is the volume change of the i-th component; ΔG mix is the mixed Gibbs free energy; τ i is the characteristic relaxation time of the i-th component, and its calculation formula is:

[0064]

[0065] Specifically, each term in the characteristic vector corresponds to the behavior of the three key elements, carbon, hydrogen, and oxygen, in the coal sample during the reaction process. The first term involves the description of the carbon content C i and combines variables such as the activation energy E i , the reaction temperature T, and the reaction degree α j to represent the reaction trend of carbon under different reaction conditions. The activation energy and reaction temperature determine the reaction rate of each component. Among them, represents the dependence of the reaction rate on the activation energy and temperature. The higher the temperature or the lower the activation energy, the larger the value of this term, indicating that the reaction rate of the carbon component is faster under these conditions. This part of the formula effectively relates parameters such as temperature and activation energy, enabling the data-driven model to accurately describe the reaction behavior of carbon during the extraction process of coal-based n-alkanes based on these variables. The second term involves the hydrogen content H iThe change combines the ratio of the pressure P to the standard pressure P0 and the exponential term of the reaction extent. This formula describes the diffusion behavior of the hydrogen component during the dissolution and reaction processes through the combination of pressure and reaction conditions. Pressure directly affects the transport rate of the hydrogen component, while the reaction extent in the exponential term reflects the reaction state of hydrogen at different process stages. Through the ratio of pressure to the standard pressure, this formula not only captures the influence of pressure on the reaction but also enables the model to predict the dissolution and diffusion characteristics of hydrogen under different pressure conditions. The dynamic change of the hydrogen content provides crucial support for predicting the dissolution selectivity of n-alkanes. Therefore, the model can predict the behavior of the hydrogen component under different conditions based on the actual reaction pressure, thus providing effective guidance for the extraction process. The third term is about the oxygen content O i The description combines the volume change ΔV i and temperature, reflecting the dynamic transport behavior of oxygen during the reaction process due to volume changes. The oxygen content is crucial for the extraction process of coal-based n-alkanes, and the volume change significantly affects the transfer efficiency of the oxygen component during the dissolution and transport processes. The exponential term of this formula reflects the dissolution characteristics of oxygen under pressure, volume, and temperature conditions. An increase in pressure or a contraction in volume will limit the transport of oxygen, while an increase in temperature will promote the transport. The design of this term enables the data-driven model to accurately capture the behavior of the oxygen component under different volume changes and temperature conditions, thus achieving more precise control during the extraction process. In addition, the entire eigenvector is multiplied by an exponential correction term to further incorporate the effects of the energy state and reaction time of the coal sample. Here, the mixed Gibbs free energy ΔG mix describes the energy interaction between different components of the coal sample, and its negative value indicates that the reaction is more stable under lower free energy conditions. The combination of the reaction temperature T and the mixed Gibbs free energy can capture the energy change characteristics of the system during the temperature change process. Therefore, the model can evaluate the stability of each component in the coal sample through the calculation of temperature and free energy. In addition, represents the influence of the characteristic relaxation time of each component on the entire reaction time. The characteristic relaxation time τ i is defined by the formula which describes the reaction rate and delay of each component under different temperature and pressure conditions. This time scale enables the model to capture the time variation of different components during the reaction process. Especially when the reaction conditions change, the model can quickly respond based on the adjustment of these parameters to ensure the stability and efficiency of the extraction and dissolution processes of coal-based n-alkanes.

[0066] Example 4: The dissolution selectivity prediction model is represented by the following formula:

[0067]

[0068] Among them, S(n,T) represents the solubility of coal-based n-alkanes with a carbon chain length of n in the coal sample at the reaction temperature T; K d is a preset solubility constant; X Z (t) is the transpose of X(t); μ is the average carbon chain length of the coal-based n-alkanes; σ is the standard deviation of the carbon chain length of the coal-based n-alkanes; D(T) is the solubility parameter matrix, and the expression is:

[0069]

[0070] Among them, ΔH1 is the heat of solution of the first component, ΔH2 is the heat of solution of the second component, and ΔH N is the heat of solution of the Nth component; E1 is the activation energy of the first component, E2 is the activation energy of the second component, and E N is the activation energy of the Nth component; κ 12 (T) represents the solubility influence coefficient of the first component on the second component at the temperature T, and so on, κ ij (T) represents the solubility influence coefficient of the ith component on the jth component at the temperature T; Z is the transpose operation.

[0071] Specifically, the model first introduces the transpose X Z (t) of the characteristic vector of the coal sample. The role of this step in the model is to directly integrate the chemical composition, physical properties, and reactivity characteristics of the coal sample into the calculation of solubility. Through the transpose operation, the coal sample characteristic vector is multiplied by the solubility parameter matrix D(T), ensuring that the dissolution behavior is directly related to the proportions and reactivities of different components, making the calculation results have a higher material matching. This approach of directly introducing the coal sample characteristics into the solubility calculation enables the model to quickly reflect the internal structure changes of the coal sample under different temperatures and reaction conditions, reflecting the importance of data-driven characteristic analysis in the prediction of dissolution behavior. The solubility parameter matrix D(T) is one of the key components of the model, which includes the heat of solution ΔH i and activation energy E i of each component, as well as the solubility influence coefficient κ ij (T) between different components. The heat of solution and activation energy represent the absorption of energy and the "difficulty" of the reaction in the model, respectively. They determine the driving force and resistance of the dissolution process at a specific temperature. Specifically, the heat of solution describes the energy requirement, and the activation energy reflects the threshold of the reaction. These two together affect the temperature dependence of the dissolution behavior. For example, when the temperature increases, the contribution of the heat of solution decreases, promoting the acceleration of the dissolution process; while a lower activation energy makes the dissolution behavior more likely to occur. Through this relationship between temperature and energy, the solubility parameter matrix enables the solubility to be dynamically adjusted in actual temperature changes, thus truly simulating the temperature response of solubility.

[0072] In addition, the dissolution influence coefficient κ ij (T) represents the nature of the interaction between different components during the dissolution process. These coefficients indicate how one component affects the behavior of another component during dissolution, that is, there are cooperative or competitive effects among the dissolved molecules. For example, the presence of the i-th component may accelerate or inhibit the dissolution of the j-th component, resulting in the dissolution efficiency of a certain n-alkane being affected by other components. This interaction is represented by the dissolution influence coefficients in the matrix, making the dissolution behavior not just the result of a single component but the cooperative effect of the overall components. This design ensures that the solubility prediction model can reasonably represent the actual dissolution process when faced with complex components. To reflect the selectivity of the dissolution behavior, a Gaussian distribution function based on the carbon chain length is added to the model. The distribution of the carbon chain length n is described centered around the mean value μ and the standard deviation σ. This design makes the solubility show a certain distribution trend as the carbon chain length changes. For example, when the carbon chain length approaches the mean value, the solubility reaches a peak; while when the carbon chain length deviates significantly from the mean value, the solubility gradually decreases. Through this distribution function, the model realizes the simulation of the dissolution selectivity of n-alkanes. Specifically, the model can identify the differences in the influence of carbon chains of different lengths on solubility. This difference reflects the structural preference of n-alkane molecules, enabling long-chain or short-chain molecules to be selectively dissolved or retained during the extraction process. The entire formula also includes a normalization constant K d , which is a preset dissolution constant to ensure that the calculated results of solubility can be standardized and compared under different conditions. This constant provides a benchmark, enabling the solubility prediction results of the model under different temperature, component, and structural conditions to be analyzed and compared consistently, ensuring that the results of dissolution selectivity have a basis for quantification and comparison. Under different operating conditions, the model is adjusted through the combination of various variables to reflect the dissolution behavior during the extraction process, making the solubility prediction of the entire system more accurate and effective.

[0073] Example 5: The multi-field coupling transport equation is expressed by the following formula:

[0074]

[0075] where C n is the concentration of coal-based n-alkanes with a carbon chain length of n; is the gradient operator; k is the thermal conductivity of the coal sample; ρ is the density of the coal sample; C p is the specific heat capacity of the coal sample; is the change value of the reaction temperature; is the change value of the reaction pressure; D eff is the effective diffusion coefficient, which is calculated by the following formula:

[0076] D eff = φ·τ·Dm ·S(n,T);

[0077] where φ is the porosity of the coal sample; D m is the molecular diffusion coefficient of the medium, i.e., the free diffusion coefficient of the coal-based n-alkanes in the coal sample; τ is the tortuosity, which is a set value greater than 1.

[0078] Specifically, the first term of the equation describes the diffusion effect through the combination of the effective diffusion coefficient D eff and the concentration gradient . The effective diffusion coefficient plays a regulatory role in the transmission process. It not only depends on the internal pore structure of the coal sample but is also limited by the molecular characteristics and dissolution selectivity of the coal-based n-alkanes. The calculation formula for the effective diffusion coefficient is D eff = φ·τ·D m ·S(n,T), where the porosity φ represents the size of the space for the free flow of molecules in the coal sample, and the tortuosity τ is used to characterize the complexity of the transmission path. These factors work together to reflect the permeability and passage difficulty of molecules in the coal sample. The molecular diffusion coefficient D m describes the free diffusion rate of the coal-based n-alkanes in the coal sample medium, while the dissolution selectivity S(n,T) combines the effects of the carbon chain length n and the reaction temperature T on solubility. As an important factor, the dissolution selectivity controls the transmission rate of n-alkanes under specific conditions, enabling the model to accurately simulate the transmission behavior at different carbon chain structures and temperatures. Through the combined influence of these several parameters, the effective diffusion coefficient becomes the core for expressing the diffusion behavior of coal-based n-alkanes in the coal sample. The second term of the transport equation involves the thermal diffusion effect, which is described by the combination of the thermal conductivity k, the density ρ of the coal sample, and the specific heat capacity C p to describe the influence of the temperature gradient on the concentration change. The thermal conductivity k describes the ability of the coal sample to transfer heat from the high-temperature region to the low-temperature region, while the density ρ and the specific heat capacity C p reflect the characteristics of the coal sample to absorb and release heat during the heat conduction process. The specific heat capacity C p represents the ability of the coal sample to absorb heat per unit mass, while the density ρ represents the mass of the coal sample per unit volume. These characteristics are reflected in the transport model as the regulatory mechanism of thermal diffusion on the transmission behavior of n-alkanes. By introducing the temperature gradient, the equation can reflect the distribution change of temperature at different spatial positions and the direct influence of this change on dissolution and diffusion. The temperature gradient will cause the coal-based n-alkanes to diffuse from the high-temperature region to the low-temperature region because molecules have higher kinetic energy in the high-temperature environment and are thus more likely to enter the pores of the coal sample for transmission.

[0079] The third term is the expression of the pressure-driven effect, through the pressure gradient With the introduction of , the equation can describe the driving effect of pressure change on the transport of normal alkanes. During the extraction process, the pressure change will significantly affect the movement trend and transport speed of coal-based normal alkanes in coal samples. The solubility selectivity S(n,T) in this item appears again, combining the solubility under specific temperature and carbon chain length conditions, and combining with the gas constant R and temperature T to form

[0080] Example 6: The separation efficiency prediction model is expressed by the following formula:

[0081]

[0082] where η(t) represents the separation efficiency at reaction time t; X(0) represents the characteristic vector of the coal sample at the initial reaction time.

[0083] Specifically, in the separation efficiency prediction model, the numerator part of the formula contains the integral term used to describe the cumulative effect of the dissolution rate of coal-based normal alkanes over time. The solubility selectivity s(n,T) represents the selectivity preference for dissolution at carbon chain length n and temperature T, which means that the dissolution behavior of normal alkanes with a specific carbon chain length will be different under different temperature conditions. And the concentration change rate is the kinetic index during the dissolution process, indicating the concentration change of normal alkanes with carbon chain length n per unit time. The integral result of this term provides the cumulative amount of the dissolution rate from the initial moment to reaction time t, and this cumulative value reflects the total amount of dissolved normal alkane molecules within a specific time. Therefore, this part describes the process of gradual dissolution and separation of normal alkanes under reaction conditions. The denominator part X Z(0)·X(0) is the product of the initial coal sample characteristic vector X(0) and its transpose. As a normalization factor, it is used to quantify the overall characteristics of the initial coal sample. This normalization operation ensures that the calculated separation efficiency is comparable under different coal samples and conditions. The initial coal sample characteristic vector X(0) contains key component information of the coal sample, such as the contents of carbon, hydrogen, oxygen, etc., as well as other dissolution characteristics and physical parameters. These characteristics determine the basic dissolution behavior of the coal sample at the initial moment of the extraction process. By dividing by the result of the time integral, the model can normalize the separation efficiency, making it have a relatively consistent separation metric under different coal samples and extraction conditions. In the last part of the formula, the exponential term introduces the influence of the mixing Gibbs free energy ΔG mix . This term reflects the regulatory effect of the system thermodynamic stability on the separation efficiency. The mixing Gibbs free energy describes the energy interaction of different components in the mixed state. A negative value indicates that the system tends to a higher thermodynamic stability at the current temperature T. A lower free energy means that the system is more likely to remain dissolved in this state, thereby improving the separation efficiency. Conversely, if the Gibbs free energy is higher, the system is unstable, and the solubility and separation efficiency will decrease accordingly. By combining the mixing Gibbs free energy term with the gas constant R and the temperature T, the exponential term affects the prediction of the separation efficiency under different temperature conditions, ensuring that the model can adaptively adjust the separation efficiency results under various thermodynamic states. The separation efficiency prediction model thus accurately describes the separation effect of n-alkanes under specific reaction conditions from both kinetic and thermodynamic aspects. The structure of the formula ensures a reasonable trade-off of various factors. Kinetically, the accumulation of the dissolution rate reflects that the separation efficiency gradually increases with time, while thermodynamically, the mixing Gibbs free energy term regulates the upper limit and stability of the separation efficiency. The coupling of these two factors ensures that the model can provide accurate separation efficiency predictions under different reaction times and temperature conditions, enabling each moment of the extraction process to be carried out under optimal conditions, providing a scientific basis for the optimized extraction of coal-based n-alkanes.

[0084] Example 7: The phase change performance prediction function is represented by the following formula:

[0085]

[0086] where T m (n) is the phase change temperature of the coal-based n-alkane with a carbon chain length of n; ΔH f is the latent heat of transformation; T0 is the preset parameter reference temperature.

[0087] Specifically, in the first part of this formula, the integral term Used to calculate the total heat released during the separation process of n - paraffins within the reaction time t. The separation efficiency η(t) in this term represents the dissolution and extraction effect at the reaction time t. Its introduction in the formula ensures the time - dependence of heat calculation and reflects the dynamic changes of the reaction process over time. The level of separation efficiency directly affects the rate of the dissolution process, and thus determines the rate of heat release, while the concentration change rate describes the dissolution and extraction rate of n - paraffins, further incorporating the kinetic factors of the extraction process into the model. The product of this rate, the separation efficiency, and the latent heat of phase change ΔH f , when integrated over time, can give a dynamic heat accumulation value, describing the total heat of dissolution from the initial moment to the current moment. This heat directly reflects the reaction situation of the n - paraffin extraction process near the phase change temperature, thus providing a basis for predicting the phase change temperature. The latent heat of phase change ΔH f is another key parameter, which describes the energy conversion required for n - paraffins during the phase change process. Generally, the latent heat represents the heat required for a substance to undergo a phase change, whether from solid to liquid or from liquid to gas. The introduction of this term ensures that in the prediction of the phase change temperature, the energy requirements of n - paraffins in a specific state are considered, so as to accurately calculate how the accumulated energy during its dissolution process drives the phase change process. The combination of the latent heat of phase change and the separation efficiency enables the model to accurately predict the change trend of the phase change temperature based on the energy accumulated within the current reaction time. The denominator part of represents the heat capacity of the coal sample, where C p is the specific heat capacity of the coal sample. The specific heat capacity C p represents the heat absorbed by a unit mass of the coal sample under temperature change. This term directly affects the heat absorption ability of the coal sample during the dissolution process. By integrating the concentration C n of n - paraffins over time and multiplying it by the specific heat capacity C p , this term is designed to express the heat absorption ability of the coal sample throughout the reaction process. The larger the heat capacity of the coal sample, that is, the specific heat capacity C pThe higher the value, the smaller the rate of temperature change of the system, which means that higher heat capacity will make it more difficult for the system to reach the phase change temperature. Therefore, by using heat capacity as the denominator, the model achieves a reasonable balance between heat accumulation and temperature change, ensuring that the calculation results of the phase change temperature are accurate and adaptable under different coal samples and reaction conditions. The preset reference temperature T0 is the benchmark temperature of the model. By adding it to the heat accumulation value, the actual phase change temperature prediction under different reaction times is obtained. The setting of this reference temperature provides a basic value for the model, so that the temperature can return to the initial benchmark level in the absence of reaction or heat change. This temperature benchmark makes the prediction of phase change temperature more flexible and adaptable. By accumulating heat effects on the basis of the benchmark temperature, the model can accurately adjust the temperature prediction value under different environments and reaction conditions.

[0088] Example 8: The crystallization process control equation is expressed using the following formula:

[0089]

[0090] Among them, X c is the crystallinity; k0 is the crystallization rate constant; is the saturated concentration of coal-based normal alkanes with a carbon chain length of n, calculated based on the Wilson equation:

[0091]

[0092] Where ΔH sol is the dissolution enthalpy change; C0 is the saturation concentration at the reference temperature T0.

[0093] Specifically, the main structure of the formula is based on the crystallinity X c The rate of change Where k0 is the crystallization rate constant, which determines the crystallization speed under given conditions. This rate constant is related to factors such as the properties of the material, solubility, and solution environment. Through model settings, it is ensured that the crystallization process has high adaptability under different conditions. The separation efficiency η(t) is introduced into the formula to describe the extraction efficiency of normal alkanes at a specific time point, which directly affects the crystallization rate. The higher the separation efficiency, the more normal alkanes are separated from the solution per unit time, thereby providing more nucleation materials for the crystallization process. In the formula, The term reflects the effect of temperature on the crystallization process. T is the actual reaction temperature, T m(n) is the phase transition temperature of the n-alkane with a carbon chain length of n, and the absolute value of the difference between the two represents the deviation degree of the actual temperature from the phase transition temperature. By introducing the combined term of the gas constant R and temperature T, this exponential term indicates that when the actual temperature is close to the phase transition temperature, the crystallization rate will increase significantly; conversely, when the temperature deviation is large, the crystallization rate will slow down. This term optimizes the crystallization process by adjusting the driving effect of temperature on the crystallization process, ensuring that the crystallization process is optimized when the temperature condition is close to the phase transition temperature, so as to achieve the best crystallization effect. The closer the actual temperature is to the phase transition temperature, the closer the exponential term value is to 1, the greater the change rate of crystallinity, and the more efficient the crystallization process of n-alkane. The last part in the formula is the dynamic feedback control term for the concentration of n-alkane. Here C n is the concentration of the n-alkane with a carbon chain length of n at the current moment, is the saturation concentration of this carbon chain length at a specific temperature. The saturation concentration represents the maximum amount of n-alkane that the solution can dissolve at the current temperature T. By controlling the ratio of C n to , the formula ensures that when the current concentration is close to the saturation concentration, the increase rate of crystallinity will gradually slow down to avoid the instability of the crystallization process caused by supersaturation. The design of the saturation concentration control term enables the crystallization process to proceed rapidly when the concentration of n-alkane is much lower than the saturation concentration; while when the concentration is close to the saturation state, the crystallization rate slows down, thus forming a stable crystal structure. In addition, the saturation concentration is calculated based on the Wilson equation, and its formula is This equation describes the relationship between the saturation concentration of n-alkane and the heat of solution change ΔH sol , the gas constant R, the current temperature T and the reference temperature T0. The heat of solution change ΔH sol represents the energy conversion required for the dissolution process of n-alkane; when the temperature changes, the saturation concentration will be adjusted accordingly, so that the equation can dynamically calculate the saturation concentration of n-alkanes with different carbon chain lengths according to the actual temperature conditions, thereby further affecting the results of the crystallization process control equation. This calculation formula of the saturation concentration based on the heat of solution ensures the temperature dependence of the crystallization process, enabling the crystallization behavior of n-alkanes to be precisely regulated at different reaction temperatures.

[0094] Example 9: The multi-objective optimization function is calculated using the following formula:

[0095]

[0096] where, T target is the target phase transition temperature; E total is the total energy consumption; P opt is the optimal combination of process parameters.

[0097] Specifically, the first part of the multi-objective optimization function Combines crystallinity, separation efficiency, dissolution selectivity, and total energy consumption to form a core measure of extraction efficiency. The crystallinity X C Is a key parameter describing the degree of order in the internal structure of the material. A higher crystallinity often means better stability and performance of the phase change material in applications. Therefore, combinations with higher crystallinity are given priority in the optimization process. The separation efficiency η(t) represents the extraction efficiency of coal-based n-alkanes within the reaction time t, reflecting the speed and proportion at which the material separates from the solution. Since the separation efficiency is affected by the dissolution rate and solution concentration, it gradually increases over time, ensuring that the optimization function can provide dynamic feedback on the extraction process. The dissolution selectivity S(n,T) is a dissolution characteristic index based on the carbon chain length n and temperature T, used to represent the dissolution behavior under specific conditions. The dissolution tendencies of n-alkanes with different carbon chain lengths vary at different temperatures. By incorporating the dissolution selectivity into the optimization model, the best dissolution effect can be achieved at the target temperature. The product of these three represents the overall performance of the extraction efficiency under specific conditions. By integrating them, the optimization function can accurately evaluate the extraction effects of different combinations of process parameters. Energy consumption is an important constraint in this optimization function. The formula standardizes the extraction efficiency through the denominator of the total energy consumption E total . The total energy consumption refers to the total energy consumed during the extraction process. In actual operation, the lower the energy consumption, the more beneficial it is for cost savings and improving the economic viability of the extraction process. Therefore, by placing the total energy consumption in the denominator, the optimization function tends to select combinations of process conditions with high efficiency and low energy consumption. The standardization operation ensures the comparability of extraction efficiencies under different parameter combinations, enabling the model to find the best solution at different energy consumption levels. The optimization function uses the ratio of extraction effect to energy consumption as the evaluation criterion, ensuring the economic feasibility of the process while improving the extraction quality. Another key part of this formula is This exponential term measures the proximity of the actual temperature T to the target phase change temperature T target by the degree of temperature matching. T m (n) represents the actual phase change temperature at the current carbon chain length, while T target is the pre-set target temperature. In this term, the absolute difference between the actual temperature and the target temperature is standardized by the gas constant R and temperature T and characterized exponentially. This design ensures that when the actual temperature is close to the target temperature, the exponential term approaches 1 and the overall value of the optimization function increases; when the deviation between the two is large, the exponential term approaches 0 and the overall optimization effect decreases. This term not only ensures that the extraction process is as close as possible to the ideal temperature conditions but also incorporates a tolerance for temperature changes in the selection of process parameters, ensuring that the model can still find the best combination of process parameters under a wide range of temperature adjustments.

[0098] The present invention has been introduced in detail above. Specific examples are used herein to illustrate the principle and implementation of the present invention. The description of the above embodiments is only for helping to understand the method and its core idea of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for optimizing the extraction of coal-based n-alkane phase change materials based on a data-driven model, characterized in that, The method includes: Step 1: Collect experimental data of coal-based n-alkanes, including: coal sample component data, reaction temperature, reaction pressure, and reaction time; construct a coal sample feature vector based on the experimental data; Step 2: Construct a dissolution selectivity prediction model based on the coal sample feature vector and the solubility parameter matrix of the coal sample; the output result of the dissolution selectivity prediction model is the solubility of coal-based n-alkanes in the coal sample at a specific reaction temperature; Step 3: Based on the specific heat capacity and density of the coal sample, combined with the output result of the dissolution selectivity prediction model, construct a multi-field coupling transport equation, solve the multi-field coupling transport equation to obtain the concentration of coal-based n-alkanes; then, based on the multi-field coupling transport equation, establish a separation efficiency prediction model and construct a phase change performance prediction function; the output result of the separation efficiency prediction model is the separation efficiency; solve the phase change performance prediction function to obtain the phase change temperature of coal-based n-alkanes; based on the separation efficiency prediction model and the constructed phase change performance prediction function, establish a crystallization process control equation, solve the crystallization process control equation to obtain the crystallinity; Step 4: Construct a multi-objective optimization function based on the crystallinity, separation efficiency, phase change temperature of coal-based n-alkanes, and concentration of coal-based n-alkanes; by solving the multi-objective optimization function, obtain the optimal process parameter combination; the optimal process parameter combination includes: optimal reaction temperature, optimal reaction pressure, and optimal reaction time; use the optimal process parameter combination to optimize the extraction of coal-based n-alkane phase change materials; The dissolution selectivity prediction model is expressed by the following formula: Among them, S(n, T) represents the solubility of coal-based n-alkanes with a carbon chain length of n in the coal sample at the reaction temperature T; K d is a preset solubility constant; X Z (t) is the transpose of X(t); X(t) is the characteristic vector of the coal sample at the reaction time t; μ is the average carbon chain length of the coal-based n-alkanes; σ is the standard deviation of the carbon chain length of the coal-based n-alkanes; D(T) is the solubility parameter matrix, and the expression is: Among them, ΔH1 is the heat of solution of the first component, ΔH2 is the heat of solution of the second component, and ΔH N is the heat of solution of the Nth component; E1 is the activation energy of the first component, E2 is the activation energy of the second component, and E N is the activation energy of the Nth component; κ 12 (T) represents the dissolution influence coefficient of the first component on the second component at temperature T, and so on, k ij (T) represents the dissolution influence coefficient of the ith component on the jth component at temperature T; Z is the transpose operation; R is the gas constant; The separation efficiency prediction model is expressed by the following formula: Among them, η(t) represents the separation efficiency at the reaction time t; X(0) represents the characteristic vector of the coal sample at the initial reaction time; C n is the concentration of n-alkanes with a carbon chain length of n; ΔG mix is the mixing Gibbs free energy; The phase change performance prediction function is expressed by the following formula: Among them, T m (n) is the phase change temperature of coal-based n-alkanes with a carbon chain length of n; ΔHf is the latent heat of change; T0 is the preset parameter reference temperature; The crystallization process control equation is expressed by the following formula: Among them, X c is the crystallinity; k0 is the crystallization rate constant; is the saturation concentration of n-alkanes based on coal with a carbon chain length of n, calculated based on the Wilson equation: Among them, ΔH sol is the enthalpy change of dissolution; C0 is the saturation concentration at the reference temperature T0.

2. The optimized extraction method of coal-based n-alkane phase change material based on data-driven model according to claim 1, characterized in that The coal sample component data includes: reaction degree, volume change, number of components, carbon content, hydrogen content, and oxygen content in the components.

3. The optimized extraction method of coal-based n-alkane phase change materials based on a data-driven model according to claim 2, wherein The coal sample feature vector is expressed by the following formula: Among them, N is the number of components in the coal sample; i is an integer subscript index, with a value range of 1 to N; C i is the carbon content of the i-th component; e is the natural base; T is the reaction temperature; E i is the activation energy of the i-th component; α j is the reaction degree of the j-th component, j is an integer subscript index, with a value range of 1 to N, j≠i; H i is the hydrogen content of the i-th component; P is the reaction pressure; P0 is the standard pressure; O i is the oxygen content of the i-th component; ΔV i is the volume change of the i-th component; τ i is the characteristic relaxation time of the i-th component, and the calculation formula is:

4. The method for optimizing the extraction of coal-based n-alkane phase change materials based on a data-driven model according to claim 3, characterized in that, The multi-field coupling transport equation is expressed by the following formula: Among them, is the gradient operator; k is the thermal conductivity of the coal sample; ρ is the density of the coal sample; C p is the specific heat capacity of the coal sample; is the change value of the reaction temperature; is the change value of the reaction pressure; D eff is the effective diffusion coefficient, which is calculated by the following formula: D eff = φ·τ·D m ·S(n, T); where φ is the porosity of the coal sample; D m is the molecular diffusion coefficient of the medium, that is, the free diffusion coefficient of the coal-based n-alkanes in the coal sample; τ is the tortuosity, which is a set value greater than 1.

5. The method for optimizing the extraction of coal-based n-alkane phase change materials based on a data-driven model according to claim 4, wherein The multi-objective optimization function is calculated by the following formula: Among them, T target is the target phase transition temperature; E total is the total energy consumption; P opt is the optimal process parameter combination.

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