A method, device, medium and product for crystallization simulation of multi-salt electrolyte system based on solubility function model

Abstract

The application discloses a multi-salt electrolyte system crystallization simulation method and device based on a solubility function model, a medium and a product, relates to the field of chemical thermodynamics and crystallization process simulation, and comprises the following steps: obtaining saturation solubility experimental data of target components under different experimental conditions; constructing a solubility function model of the target components based on the saturation solubility experimental data, and fitting solubility function model parameters of each electrolyte system; calculating the theoretical saturation solubility of the target components under the current conditions based on the solubility function model and the fitted solubility function model parameters, so as to determine whether the multi-salt electrolyte system is in a supersaturated state; and if the multi-salt electrolyte system is in a supersaturated state, calculating the crystallization amount of the target components based on material balance relations, and obtaining the mother liquor composition, the flow rate of the mother liquor stream and the flow rate of the solid product. The application can improve the accuracy and universality of the crystallization simulation of complex electrolyte systems.

Description

Technical Field

[0001] This application relates to the field of chemical thermodynamics and crystallization process simulation technology, and in particular to a method, equipment, medium and product for simulating the crystallization of multi-salt electrolyte systems based on a solubility function model. Background Technology

[0002] Crystallization is a key unit operation in the separation, purification, and resource recovery of multi-salt electrolyte systems, and is widely used in inorganic salt chemistry, hydrometallurgy, pharmaceuticals, and environmental protection. For such systems, the core of the crystallization process lies in accurately describing the solid-liquid phase equilibrium relationship under given temperature and composition conditions, and in determining supersaturation and calculating the amount of crystallization.

[0003] Solid-liquid equilibrium calculations for multi-salt electrolyte systems are a crucial foundation for crystallization process simulation, process design, and process optimization. The solubility function model, serving as a vital bridge between experimental solubility data and engineering thermodynamic calculations, plays a key role in establishing a quantitative relationship between the saturated solubility of the target component and temperature and the composition of coexisting salts, thereby enabling the determination of the system's saturation state and the calculation of crystallization amounts. In multi-salt electrolyte systems, due to the prevalent common ion effect, hydration competition, and non-ideal deviations under high concentration conditions, the solubility of the target component is not only affected by temperature but also closely related to the types and concentrations of coexisting salts. Especially in systems with multiple hydrates or multiple crystallization branches, the dissolution behavior often exhibits significant differences across different temperature ranges or composition intervals. Existing unified empirical methods struggle to simultaneously ensure wide-range applicability, fitting accuracy, and model stability.

[0004] While the solubility data method can directly interpolate based on experimental data, avoiding errors caused by missing thermodynamic parameters, its extrapolation ability is poor, and it requires experimental data to cover the entire operating range, limiting its engineering applicability. The solubility function method can fit discrete experimental data into continuous analytical equations, offering advantages such as smooth expression and easy modular application; however, existing solubility function models are only established for binary systems and only use temperature as a variable, making it difficult to accurately describe the different segmented changes in bound water of the target component at different temperatures, as well as the salting-out effect and phase shift problems in multi-component coexisting salt systems.

[0005] Therefore, this invention proposes a solubility function model suitable for multi-salt electrolyte systems and fits the model parameters to improve the accuracy and stability of crystallization process simulation under wide temperature range and multi-salt coexistence conditions. Summary of the Invention

[0006] The purpose of this application is to provide a method, device, medium, and product for simulating the crystallization of multi-salt electrolyte systems based on a solubility function model, which can improve the accuracy and versatility of crystallization simulation of complex electrolyte systems.

[0007] To achieve the above objectives, this application provides the following solution: Firstly, this application provides a method for simulating the crystallization of multi-salt electrolyte systems based on a solubility function model, including: Acquire saturated solubility experimental data of the target component under different experimental conditions; when the multi-salt electrolyte system is a binary system, the saturated solubility experimental data includes the saturated solubility experimental data of the target component as precipitated crystals or containing crystalline crystals under different temperature conditions; when the multi-salt electrolyte system is a ternary or multi-component system, the saturated solubility experimental data includes the saturated solubility experimental data of the target component under different temperatures and different coexisting salt compositions. Based on the saturated solubility experimental data, a solubility function model for the target component was constructed, and the solubility function model parameters for each electrolyte system were fitted. The theoretical saturated solubility of the target component under the current conditions is calculated based on the solubility function model and the fitted solubility function model parameters to determine whether the multi-salt electrolyte system is in a supersaturated state. If the multi-salt electrolyte system is in a supersaturated state, the amount of crystallization of the target component is calculated based on the material balance relationship, and the composition of the mother liquor and the flow rate of the solid product are obtained.

[0008] Secondly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method for simulating the crystallization of a multi-salt electrolyte system based on a solubility function model.

[0009] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for simulating the crystallization of a multi-salt electrolyte system based on a solubility function model.

[0010] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method for simulating the crystallization of a multi-salt electrolyte system based on a solubility function model.

[0011] According to the specific embodiments provided in this application, this application has the following technical effects: By obtaining experimental data on saturated solubility under different temperatures and different coexisting salt compositions, a solubility function model for the target component was successfully constructed. This model can be widely adapted to complex multi-salt electrolyte systems such as binary, ternary, and multi-component systems, breaking through the bottleneck of the limited applicability of traditional models and possessing strong universality. Based on the constructed solubility function model, the theoretical saturated solubility is calculated and compared in real time with the actual concentration of the target component in the electrolyte solution. This allows for high-precision and rapid determination of whether the system is in a supersaturated state, providing a core theoretical basis for the precise control of the crystallization process and solving the problems of lagging and insufficient precision in the existing technology. Furthermore, after determining supersaturation, the amount of crystallization of the target component, the composition of the mother liquor, and the flow rate of the solid product can be quantitatively calculated based on material balance relationships. This provides precise data support and theoretical guidance for the optimization of crystallization process parameters, improvement of product yield, and process scale-up, contributing to the efficient development and optimization of crystallization production processes. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a flowchart illustrating a method for simulating the crystallization of a multi-salt electrolyte system based on a solubility function model, provided in one embodiment of this application.

[0014] Figure 2 This is a schematic diagram of the regression results of the solubility function of the H2O-NaHCO3 binary system in one embodiment of this application.

[0015] Figure 3 This is a schematic diagram of the isothermal phase diagram and model calculation results of the crystallization region of the H2O-NaHCO3-Na2CO3 ternary system in one embodiment of this application.

[0016] Figure 4 This is a schematic diagram showing the regression results of the solubility function of the H2O-Na2CO3 binary hydrate system on Na2CO3 ⇌ 10H2O in one embodiment of this application.

[0017] Figure 5 This is a schematic diagram showing the regression results of the solubility function of the H2O-Na2CO3 binary hydrate system on Na2CO3 ⇌ 7H2O in one embodiment of this application.

[0018] Figure 6This is a schematic diagram showing the regression results of the solubility function of the H2O-Na2CO3 binary hydrate system on Na2CO3H2O in one embodiment of this application.

[0019] Figure 7 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0021] The purpose of this application is to address the problems in the prior art, such as inaccurate description of solid-liquid phase equilibrium relationship in multi-salt electrolyte systems, insufficient stability of fitting over a wide temperature range, difficulty in characterizing the segmentation characteristics of multihydrates, and the salting-out effect of coexisting salts in multi-component systems, thereby improving the accuracy and engineering applicability of crystallization process simulation and crystallization amount prediction.

[0022] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, this application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] In one exemplary embodiment, such as Figure 1 As shown, a method for simulating the crystallization of a multi-salt electrolyte system based on a solubility function model is provided. This method is executed by a computer device, specifically by a computer device such as a terminal or server alone, or by a terminal and server together. In the embodiments of this application, the method includes the following steps 101 to 104.

[0024] Step 101: Obtain experimental data on the saturated solubility of the target component under different experimental conditions.

[0025] When the multi-salt electrolyte system is a binary system, the saturation solubility experimental data include the saturation solubility experimental data of the target component under different temperature conditions for precipitated crystals or crystalline bodies.

[0026] When the multi-salt electrolyte system is a ternary or multi-component system, the saturation solubility experimental data includes the saturation solubility experimental data of the target component under different temperatures and different coexisting salt compositions.

[0027] Step 102: Based on the saturated solubility experimental data, construct a solubility function model for the target component and fit the solubility function model parameters for each electrolyte system. The solubility function model is used to calculate the saturated solubility of the target component under the current conditions.

[0028] For different multi-salt electrolyte systems, the solubility function models constructed in this application fall into the following three categories: (i) When the multi-salt electrolyte system is a binary system of precipitated solids (i.e., a binary system that does not contain crystalline hydrates), based on the experimental data of saturated solubility, a solubility function model of the target component is constructed, and the solubility function model parameters of each electrolyte system are fitted, including the following steps 11 to 12.

[0029] Step 11: Establish a semi-logarithmic polynomial saturated solubility function model for the target component with temperature as the variable, as the solubility function model: ;in, For the first i Experimental values ​​of saturated solubility at various temperature points T For temperature, A , B , C , D These are all parameters of the solubility function model. i This refers to the serial number of the temperature point.

[0030] Step 12: Fit the parameters of the solubility function model using the least squares method.

[0031] Specifically, the objective function for fitting the solubility function model parameters using the least squares method is: ;in, OBJ To approximate the function value of the target, N This represents the total number of experimental data points for saturated solubility at different temperatures used in the fitting process. For the first i Calculated values ​​of saturated solubility at each temperature point.

[0032] (ii) When the multi-salt electrolyte system is a binary system in which the precipitated solid contains water of crystallization, based on the experimental data of saturated solubility, a solubility function model of the target component is constructed, and the solubility function model parameters of each electrolyte system are fitted, including the following steps 21 to 23.

[0033] Step 21: Divide the saturation solubility experimental data into zones according to the temperature ranges corresponding to hydrates containing different amounts of water of crystallization in the precipitated crystals.

[0034] Step 22: For hydrates containing different amounts of water of crystallization, establish semi-logarithmic polynomial saturated solubility function models of the target hydrate components with temperature as the variable, respectively, to obtain solubility function models of different hydrates in different temperature ranges: ;in, The experimental values ​​represent the saturated solubility of the target hydrate component. TFor temperature, A , B , C , D These are all parameters of the solubility function model. i This refers to the serial number of the temperature point.

[0035] Step 23: Fit the solubility function model parameters using the least squares method to obtain the solubility function model of the target hydrate component; wherein, the optimization objective function when fitting the solubility function model parameters using the least squares method is: ;in, OBJ To approximate the function value of the target, N This represents the total number of experimental data points for saturated solubility at different temperatures used in the fitting process. For the first i Calculated values ​​of saturated solubility at each temperature point.

[0036] (iii) When the multi-salt electrolyte system is a ternary or multi-component system, based on the saturated solubility experimental data, a solubility function model of the target component is constructed, and the solubility function model parameters of each electrolyte system are fitted, including the following steps 31 to 32.

[0037] Step 31: Based on the established solubility function model of the target component in the binary electrolyte system, a salt effect correction term is added to establish a saturated solubility function model with the mass fraction of coexisting salts and temperature as two variables in the multi-electrolyte system: ;in, Multi-salt electrolyte system m The target component in the first Experimental values ​​of saturated solubility under various experimental conditions. For the first i Experimental values ​​of saturated solubility at various temperature points w j Salt components coexisting in multi-salt electrolyte solutions j mass fraction, T For temperature, This is the first-order salt effect coefficient. , It is a second-order nonlinear correction term. , b 0、 b 1. c 0、 c 1. Empirical parameters characterizing the salt effect of interactions between components.

[0038] Step 32: Fit the parameters in the bivariate saturated solubility function model using the least squares method to obtain the solubility function model of the target component; the optimization objective function when fitting the parameters in the bivariate saturated solubility function model using the least squares method is: ;in, OBJ To approximate the function value of the target, N This represents the total number of experimental data points for saturated solubility at different temperatures used in the fitting process. For multi-salt electrolyte systems calculated using the bivariate saturation solubility function model... m The target component in the first Calculated values ​​of saturated solubility under various experimental conditions. Multi-salt electrolyte system m The target component in the first Experimental values ​​of saturated solubility under specific experimental conditions.

[0039] In another exemplary embodiment, the application also includes a process for refitting the solubility function model.

[0040] Specifically, the coefficient of determination R of the solubility function model is calculated. 2 When the coefficient of determination R 2 When the value is less than 0.95, a refitting step is performed. The refitting step includes: merging duplicate values ​​and screening for outliers in the saturated solubility experimental data; identifying outliers based on residuals and relative deviations; when the multi-salt electrolyte system exhibits multihydrate transitions, crystallization zone switching, or local nonlinear changes, re-dividing the temperature or composition ranges and performing regressions accordingly; based on the processed data, resetting initial parameter values ​​or constraints, and refitting the parameters using least squares or weighted least squares methods; and recalculating the coefficient of determination R after fitting. 2 When R 2 When R is not less than 0.95, the final parameters are output and used for subsequent crystallization calculations; when R... 2 If it is still less than 0.95, continue with the refitting step.

[0041] Step 103: Calculate the theoretical saturated solubility of the target component under the current conditions based on the solubility function model and the fitted solubility function model parameters, in order to determine whether the multi-salt electrolyte system is in a supersaturated state.

[0042] When the multi-salt electrolyte system is a binary system, the temperature inside the crystallizer is obtained, and the theoretical saturated solubility of the target component under the current conditions is calculated based on a solubility function model. When the multi-salt electrolyte system is a ternary or multi-component system, the temperature inside the crystallizer and the concentration of coexisting salts in the electrolyte solution are obtained, and the theoretical saturated solubility of the target component under the current conditions is calculated based on a solubility function model.

[0043] In a specific application example, the solubility function model and the fitted model parameters are written into the crystallizer unit. During crystallization calculations, the system temperature inside the crystallizer and the concentrations of each coexisting salt in the multi-salt electrolyte solution are obtained, and the corresponding solubility function model is called to calculate the theoretical saturated solubility of the target component under the current conditions. C In binary systems, temperature is the only variable, while in multi-component systems, the effects of both temperature and the concentration of coexisting salts are considered.

[0044] Specifically, if the actual concentration of the target component in the multi-salt electrolyte solution system is less than the theoretical saturation solubility, the target component in the multi-salt electrolyte system is determined to be unsaturated; if the actual concentration of the target component in the multi-salt electrolyte solution system is equal to the theoretical saturation solubility, the target component in the multi-salt electrolyte system is determined to be saturated; if the actual concentration of the target component in the multi-salt electrolyte solution system is greater than the theoretical saturation solubility, the target component in the multi-salt electrolyte system is determined to be supersaturated, and solid crystals will precipitate out.

[0045] Step 104: If the multi-salt electrolyte system is in a supersaturated state, calculate the amount of crystallization of the target component based on the material balance relationship, and obtain the composition of the mother liquor, the flow rate of the mother liquor stream and the flow rate of the solid product.

[0046] In a specific application example, when a multi-salt electrolyte system is in a supersaturated state, the solute exceeding the saturation limit precipitates from the liquid phase as a pure solid phase or a stable hydrate solid phase at the corresponding temperature range; the crystallization process continues until the concentration of the target component in the mother liquor decreases and reaches the theoretical saturation solubility under the current conditions. C It also outputs the crystallization simulation results.

[0047] The crystallization simulation method for multi-salt electrolyte systems based on the solubility function model calculates the amount of crystals precipitated from the liquid phase to form solid crystals based on the material balance relationship reaching equilibrium, following the mass conservation equation, namely: ; ; in, F The mass flow rate of the total feed stream. L The mass flow rate of the mother liquor stream. S To determine the mass flow rate of the precipitated solid stream, Target component k Mass fraction in the feed stream Target component k Mass fraction in the mother liquor stream Target component k The mass fraction in the precipitated solid stream.

[0048] This application employs a semi-logarithmic polynomial solubility function to provide a continuous analytical expression for binary systems. Compared to simple table lookup or interpolation methods, this approach more smoothly describes the solubility variation with temperature, improving computational continuity and stability. For multihydrate systems, a segmented regression strategy based on stable temperature zones is adopted to avoid the accuracy degradation caused by uniform fitting across phase regions, enabling a more accurate characterization of dissolution behavior at different hydrate stages. Furthermore, a salt effect correction term based on a temperature-coexisting salt concentration dual-variable is introduced into the binary system to correct prediction biases of traditional empirical models in complex electrolyte systems, thereby improving the model's performance in multi-salt coexisting systems. The ability to describe liquid phase equilibrium can effectively characterize common ion effects, hydration competition, and nonlinear salting-out behavior under high concentration conditions, thereby improving the accuracy of solubility prediction in ternary and multi-component systems. Furthermore, combining the solubility function model with the crystallization calculation logic of "saturation determination—crystallization amount calculation—material balance" ensures thermodynamic consistency while improving the numerical stability and engineering applicability of the crystallization process simulation. In addition, the method established in this application is applicable to solid-liquid phase equilibrium calculations under wide temperature ranges and multiple salt coexistence conditions, providing a reliable model foundation for process simulation, crystallization process design, and modular software implementation.

[0049] The following is a specific embodiment of the crystallization simulation method for multi-salt electrolyte systems based on the solubility function model described above.

[0050] S1: Obtain experimental data on the saturated solubility of H2O-NaHCO3 and H2O-NaHCO3-Na2CO3 in an electrolyte system with NaHCO3 as the target substance.

[0051] Specifically, experimental data on the saturated solubility of the H2O-NaHCO3 and H2O-NaHCO3-Na2CO3 components of the electrolyte system with NaHCO3 as the target substance were obtained from literature, as shown in Tables 1 and 2.

[0052] Table 1. Experimental data on the saturated solubility of the H2O-NaHCO3 binary system.

[0053] Table 2. Experimental data on the saturated solubility of the H2O-NaHCO3-Na2CO3 ternary system.

[0054] S2: First, taking the H2O-NaHCO3 binary system as the research object, a semi-logarithmic polynomial empirical equation is used to describe the relationship between the saturation solubility data of the target component NaHCO3 and temperature.

[0055] Specifically, based on the experimental data of NaHCO3 saturation solubility obtained from S1, the parameters of the H2O-NaHCO3 binary system were regressed. A , B , C , D The above semi-logarithmic polynomial empirical equation model is: ;in, These are experimental values ​​for saturated solubility.

[0056] S3: Establish the least squares method to perform regression analysis on the dependent and independent variables, solve for the empirical regression coefficients of the binary system, and then use the coefficient of determination R0 to determine the regression coefficients. 2 To determine the accuracy of empirical regression coefficients.

[0057] Specifically, based on the logarithmic polynomial empirical equation model of S2, least squares regression is established. A , B , C , D The parameter optimization objective for solving the empirical regression coefficients using the least squares method described above is: ;in, OBJ To approximate the function value of the target, N This represents the total number of experimental data points on saturated solubility at different temperatures participating in the regression. For the first i Experimental values ​​of saturated solubility of NaHCO3 at various temperature points For the first i Calculated values ​​of saturated solubility at each temperature point.

[0058] The regression results of the solubility function of the H2O-NaHCO3 binary system are as follows: Figure 2 As shown, the R of the H2O-NaHCO3 binary system 2 The value of 0.9959 is higher than 0.95, which meets the accuracy requirement for regression. The regression result... A , B , C , D The values ​​are listed in Table 3, where, T min The lowest temperature, T max This is the highest temperature.

[0059] Table 3. Fitting results of the solubility function model parameters for the H2O-NaHCO3 binary system.

[0060] Further based on regression A , B , C , DCalculate the solubility of the H2O-NaHCO3 binary system: .

[0061] The relative deviation and mean relative deviation are used to represent the deviation between the calculated results and the experimental data, and to evaluate the accuracy of the calculated results. The calculation formula is: ; ; in, RD This is a relative deviation. ARD The average relative deviation, For the first i Calculated saturated solubility at each temperature point For the first i Experimental values ​​of saturated solubility at specific temperature points.

[0062] Based on regression A , B , C , D The calculated solubility data for the H₂O-NaHCO₃ binary system are within the temperature range of 273.15K-473.15K. ARD The result is only 0.38%, which meets the accuracy requirements.

[0063] S4: Based on the binary system, introduce the coexisting salt concentration variable to establish a ternary system temperature-composition bivariate model.

[0064] Specifically, the empirical parameters of the H2O-NaHCO3 binary system in S3 regression A , B , C , D Based on this, a temperature-composition bivariate model of the ternary system is established by introducing the coexisting salt concentration variable: .

[0065] in, NaHCO3 in electrolyte solution m The calculated value of the mass fraction in. In electrolyte solution m The mass fraction of Na2CO3 stored in the CCP.

[0066] S5: Solve for the empirical parameters of the salt effect in the ternary system using the least squares method in S3, and then use the coefficient of determination R... 2 To determine the accuracy of empirical regression coefficients.

[0067] The optimization objective of solving the empirical parameters of the salt effect using the least squares method is: .

[0068] S6: Substitute the binary empirical regression coefficients and the ternary salt effect parameters to obtain the specific model for the saturated dissolution of the ternary system, calculate the saturated solubility data of NaHCO3 in the ternary system, and evaluate the error.

[0069] Specifically, the regression results of the empirical parameters of the solubility function and salt effect of the H2O-NaHCO3-Na2CO3 ternary system are listed in Table 4. The R-value of the H2O-NaHCO3-Na2CO3 ternary system... 2 The value of 0.9956 is higher than 0.95, which meets the accuracy requirements for regression.

[0070] Table 4. Regression results of empirical parameters for solubility function and salt effect in the H2O-NaHCO3-Na2CO3 ternary system.

[0071] Furthermore, the solubility of the H2O-NaHCO3-Na2CO3 system was calculated based on the empirical parameter values ​​of the salt effect in the ternary system obtained from regression analysis: .

[0072] The calculation results are as follows Figure 3 As shown, the ARD values ​​between the model calculations and experimental values ​​were 2.09%, 1.41%, 1.45%, 1.17%, and 1.57% at five operating temperatures ranging from 293.15K to 333.15K, respectively. The overall average relative deviation of the 50 sets of data within the 293.15K-333.15K temperature range was as low as 1.54%. The calculated trend is consistent with the experimental prediction results.

[0073] S7: Saturation determination based on ternary solubility data.

[0074] Specifically, read the current temperature T Mass fraction of Na2CO3 in actual electrolyte solutions and the mass fraction of NaHCO3 in the actual electrolyte solution ;Will T and Substituting into the above ternary model, we obtain the theoretical saturated mass fraction of NaHCO3. .when When the electrolyte solution system is in an unsaturated state, it is determined that the electrolyte solution system is in an unsaturated state; when When, determine the saturation state of the electrolyte solution system; when When the electrolyte solution system is determined to be in a supersaturated state, the crystallization amount calculation module is triggered.

[0075] S8: Calculate the amount of NaHCO3 crystals based on material balance.

[0076] The following section uses the H2O-Na2CO3 binary hydrate system as an example to introduce the construction process of the solubility function model.

[0077] (1) The H2O-Na2CO3 binary hydrate system was selected to obtain experimental data on the solubility of Na2CO3 in pure water. Since Na2CO3 exists in different crystalline hydrate forms at different temperatures, the H2O-Na2CO3 binary hydrate system includes three stable solid phase regions: Na2CO3·10H2O, Na2CO3·7H2O, and Na2CO3·H2O.

[0078] (2) Input the component information involved in the solid-liquid equilibrium calculation of the H2O-Na2CO3 binary system, and divide the system into zones according to the type of stable solid phase in different temperature ranges. Specifically, in the temperature range of 273.15K to 303.15K, the stable solid phase is Na2CO3·10H2O, and a total of 15 experimental data points are selected; in the narrow temperature range of 306.15K to 308.55K, the stable solid phase is Na2CO3·7H2O, and a total of 5 experimental data points are selected; in the temperature range of 311.15K to 368.15K, the stable solid phase is Na2CO3·H2O, and a total of 36 experimental data points are selected. Thus, the solubility calculation of the H2O-Na2CO3 binary system is divided into three independent hydrate stability ranges for separate processing.

[0079] (3) For each stable temperature range, a semi-logarithmic polynomial solubility function of Na2CO3 with respect to temperature was established, and the least squares method was used to perform piecewise regression on the experimental data to obtain the parameters corresponding to each hydrate range, as shown in Table 5.

[0080] Table 5. Fitting results of the solubility function model parameters for the H2O-Na2CO3 binary hydrate system.

[0081] (4) Input the parameters obtained from the fitting of each segment into the crystallization calculation module to calculate the saturated solubility of Na2CO3 in different temperature ranges. Specifically, when predicting solubility, first determine the stable hydrate range of the system based on the current operating temperature; then call the semi-logarithmic polynomial solubility function corresponding to the range to calculate the theoretical saturated solubility of Na2CO3 under the current temperature conditions; then compare the theoretical calculation results with the experimental values ​​to obtain the prediction results of the model.

[0082] (5) Compare the calculated solubility of the H2O-Na2CO3 binary system with the experimental value, record it as the prediction result of the established model, and use the average relative deviation ARD as the evaluation index to analyze the calculation accuracy of the model.

[0083] Taking the H2O-Na2CO3 binary system as an example, a semi-logarithmic polynomial solubility function of Na2CO3 with respect to temperature was established, and the least squares method was used to perform piecewise regression on the experimental data, with the coefficient of determination R0... 2 All values ​​were above 0.95, indicating good linear fit. The average relative deviations (ARDs) of the three subsystems Na₂CO₃·10H₂O, Na₂CO₃·7H₂O, and Na₂CO₃·H₂O, calculated based on the solubility function model parameters in Table 5, were 0.84%, 0.62%, and 0.58%, respectively, all below 1%. Regression results are shown in [Table 5]. Figures 4 to 6 As shown.

[0084] In summary, this application can stably characterize the solubility variation law under wide temperature range and multi-salt coexistence conditions, improve the accuracy of solid-liquid phase equilibrium description of multi-salt electrolyte system and the numerical stability of crystallization process simulation, and provide reliable support for process simulation, process design and modular software implementation.

[0085] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 7 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and databases. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a crystallization simulation method for a multi-salt electrolyte system based on a solubility function.

[0086] Those skilled in the art will understand that Figure 7 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer equipment to which the present application is applied. Specific computer equipment may include, for example, [the following is a list of possible additional structures]. Figure 7 The diagram shows more or fewer components, or combinations of certain components, or different component arrangements.

[0087] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0088] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0089] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0090] In this application, all actions to acquire signals, information, or data are carried out in compliance with the relevant data protection laws and policies of the country where the location is situated, and with the authorization granted by the owner of the relevant device.

[0091] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0092] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, etc., and are not limited to these.

[0093] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0094] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for simulating the crystallization of multi-salt electrolyte systems based on a solubility function model, characterized in that, The crystallization simulation method for multi-salt electrolyte systems based on a solubility function model includes: Acquire saturated solubility experimental data of the target component under different experimental conditions; when the multi-salt electrolyte system is a binary system, the saturated solubility experimental data includes the saturated solubility experimental data of the target component as precipitated crystals or containing crystalline crystals under different temperature conditions; when the multi-salt electrolyte system is a ternary or multi-component system, the saturated solubility experimental data includes the saturated solubility experimental data of the target component under different temperatures and different coexisting salt compositions. Based on the saturated solubility experimental data, a solubility function model for the target component was constructed, and the solubility function model parameters for each electrolyte system were fitted. The theoretical saturated solubility of the target component under the current conditions is calculated based on the solubility function model and the fitted solubility function model parameters to determine whether the multi-salt electrolyte system is in a supersaturated state. If the multi-salt electrolyte system is in a supersaturated state, the amount of crystallization of the target component is calculated based on the material balance relationship, and the composition of the mother liquor, the flow rate of the mother liquor stream and the flow rate of the solid product are obtained.

2. The method for simulating the crystallization of multi-salt electrolyte systems based on a solubility function model according to claim 1, characterized in that, When the multi-salt electrolyte system is a binary system that precipitates solids, based on the saturated solubility experimental data, a solubility function model for the target component is constructed, and the solubility function model parameters for each electrolyte system are fitted, including: A semi-logarithmic polynomial saturated solubility function model of the target component with temperature as the variable is established as the solubility function model: ;in, For the first i Experimental values ​​of saturated solubility at various temperature points T For temperature, A , B , C , D These are all parameters of the solubility function model. i The temperature point number; The solubility function model parameters are fitted using the least squares method; wherein, the optimization objective function for fitting the solubility function model parameters using the least squares method is: ;in, OBJ To approximate the function value of the target, N This represents the total number of experimental data points for saturated solubility at different temperatures used in the fitting process. For the first i Calculated values ​​of saturated solubility at each temperature point.

3. The method for simulating the crystallization of multi-salt electrolyte systems based on a solubility function model according to claim 1, characterized in that, When the multi-salt electrolyte system is a binary system in which the precipitated solid contains water of crystallization, based on the saturated solubility experimental data, a solubility function model for the target component is constructed, and the solubility function model parameters for each electrolyte system are fitted, including: The saturation solubility experimental data were partitioned according to the temperature range corresponding to hydrates containing different amounts of water of crystallization in the precipitated crystals. For hydrates containing different amounts of water of crystallization, semi-logarithmic polynomial saturated solubility function models of the target hydrate components with temperature as the variable were established, resulting in solubility function models of different hydrates in different temperature ranges: ;in, For the first i Experimental values ​​of saturated solubility at various temperature points T For temperature, A , B , C , D These are all parameters of the solubility function model. i The temperature point number; The solubility function model parameters are fitted using the least squares method to obtain the solubility function model of the target hydrate component; wherein, the optimization objective function when fitting the solubility function model parameters using the least squares method is: ;in, OBJ To approximate the function value of the target, N This represents the total number of experimental data points for saturated solubility at different temperatures used in the fitting process. For the first i Calculated values ​​of saturated solubility at each temperature point.

4. The method for simulating the crystallization of multi-salt electrolyte systems based on a solubility function model according to claim 2 or 3, characterized in that, When the multi-salt electrolyte system is a ternary or multi-component system, based on the saturated solubility experimental data, a solubility function model for the target component is constructed, and the solubility function model parameters for each electrolyte system are fitted, including: Based on the established solubility function model of the target component in the binary electrolyte system, a salt effect correction term is added to establish a saturated solubility function model with the mass fraction of coexisting salts and temperature as two variables in the multi-electrolyte system: ;in, Multi-salt electrolyte system m The target component in the first Experimental values ​​of saturated solubility under various experimental conditions. For the first i Experimental values ​​of saturated solubility at various temperature points w j Salt components coexisting in multi-salt electrolyte solutions j mass fraction, T For temperature, This is the first-order salt effect coefficient. , It is a second-order nonlinear correction term. , b 0、 b 1. c 0、 c 1. Empirical parameters characterizing the salt effect in relation to the interactions between components; The parameters in the bivariate saturated solubility function model are fitted using the least squares method to obtain the solubility function model of the target component. The optimization objective function when fitting the parameters in the bivariate saturated solubility function model using the least squares method is: ;in, OBJ To approximate the function value of the target, N This represents the total number of experimental data points for saturated solubility at different temperatures used in the fitting process. For multi-salt electrolyte systems calculated using the bivariate saturation solubility function model... m The target component in the first Calculated values ​​of saturated solubility under various experimental conditions.

5. The method for simulating the crystallization of multi-salt electrolyte systems based on a solubility function model according to claim 1, characterized in that, The theoretical saturated solubility of the target component under current conditions is calculated based on the solubility function model and the fitted solubility function model parameters, including: When the multi-salt electrolyte system is a binary system, the temperature inside the crystallizer is obtained, and the theoretical saturated solubility of the target component under the current conditions is calculated based on the solubility function model. When the multi-salt electrolyte system is a ternary or multi-component system, the internal temperature of the crystallizer and the concentration of coexisting salts in the electrolyte solution are obtained, and the theoretical saturated solubility of the target component under the current conditions is calculated based on the solubility function model.

6. The method for simulating the crystallization of multi-salt electrolyte systems based on a solubility function model according to claim 1, characterized in that, If the actual concentration of the target component in the multi-salt electrolyte system is less than the theoretical saturation solubility, the target component in the multi-salt electrolyte system is determined to be unsaturated; if the actual concentration of the target component in the multi-salt electrolyte system is equal to the theoretical saturation solubility, the target component in the multi-salt electrolyte system is determined to be saturated; if the actual concentration of the target component in the multi-salt electrolyte system is greater than the theoretical saturation solubility, the target component in the multi-salt electrolyte system is determined to be supersaturated, and solid crystals will precipitate out.

7. The method for simulating the crystallization of multi-salt electrolyte systems based on a solubility function model according to claim 1, characterized in that, The material balance relationship reaches a state of equilibrium, that is: ； ； in, F The mass flow rate of the total feed stream. L The mass flow rate of the mother liquor stream. S To determine the mass flow rate of the precipitated solid stream, Target component k Mass fraction in the feed stream Target component k Mass fraction in the mother liquor stream Target component k The mass fraction in the precipitated solid stream.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the crystallization simulation method for a multi-salt electrolyte system based on a solubility function model as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the crystallization simulation method for multi-salt electrolyte systems based on a solubility function model as described in any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the crystallization simulation method for multi-salt electrolyte systems based on a solubility function model as described in any one of claims 1-7.

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