Predictive method for the optimization and scale-up of static melt crystallization of electronic chemicals

Abstract

The application provides a prediction method for static electronic chemical melt crystallization optimization and amplification, establishes heat transfer equations under different heat transfer mechanisms in different regions of a static melt crystallization process; establishes a liquid-solid phase change process theoretical model; establishes momentum equations and mass conservation equations for the calculation of the flow field of the coolant and the melt in different regions; combines static melt crystallization experimental results to determine the parameters in the coupling model of (1)-(3), and verifies the accuracy of the coupling model prediction; performs process simulation of the heat transfer-phase change-flow multi-physical field coupling of the static melt crystallization process, realizes numerical amplification, and optimizes the operation conditions and geometric structure. The "conjugate heat transfer" physical field is used, the "non-isothermal flow" interface is added to couple the "solid and fluid heat transfer" and "laminar flow or turbulent flow" interfaces, so as to ensure that the "fluid" characteristics in the "heat transfer" interface can use the velocity field calculated by the "flow" interface.

Description

Technical Field

[0001] This invention relates to the prediction of optimization and scale-up of static melt crystallization process for electronic chemicals, and more particularly to the prediction of optimization and scale-up of static melt crystallization process for preparing electronic-grade phosphoric acid. Background Technology

[0002] Electronic-grade chemicals, also known as electronic chemical materials, broadly refer to fine chemical materials specifically designed for use in the electronics industry. These include various chemicals and materials used in the production and packaging of integrated circuits, display panels, photovoltaic solar cells, printed circuit boards, and other electronic components, as well as industrial and consumer electronics. Due to their high technological content and high-performance parameters, electronic chemicals are hailed as the "crown jewel of fine chemicals." With the rapid development of emerging electronic information industries such as big data, artificial intelligence, and the Internet of Things, electronic chemicals are characterized by an increasing variety of products, higher quality requirements, more stringent purity requirements, and continuously increasing added value. Electronic chemicals have become one of the key materials prioritized for development by countries worldwide in their efforts to develop the electronics industry.

[0003] Purity is one of the key indicators of electronic chemicals; therefore, a purification process is usually involved in the preparation of electronic chemicals. Melt crystallization is an important method for purifying electronic chemicals. Compared with distillation, it has the advantage of low energy consumption; compared with ion exchange, electrodialysis, and other methods, it has the advantages of not requiring the introduction of other substances, simple operation, simple equipment, and easy industrialization. Therefore, melt crystallization is considered a highly selective and green purification method.

[0004] Electronic-grade phosphoric acid is primarily used for etching in the manufacturing processes of electronic devices such as integrated circuits and display panels. For example, electronic-grade phosphoric acid, used alone or in combination with other acids and additives, can be used in phosphoric acid etching solutions to treat various materials such as silicon nitride, silicon, and metals that require etching in the manufacture of logic chips and memory chips. It is an extremely important electronic chemical in chip manufacturing. With the continuous upgrading of the integrated circuit manufacturing industry, the purity requirements for phosphoric acid are becoming increasingly stringent. Currently, the purity of domestically produced electronic-grade phosphoric acid lags behind international advanced levels, and it can only be used for chip processes of 28 nm and below. Ultra-high purity electronic-grade phosphoric acid for the advanced 14nm technology node is basically dependent on imports.

[0005] Patents related to the study of the static melt crystallization process of electronic-grade phosphoric acid include patents 201110096758.6, 201310747117.1, 201310742213.7, and 201310747141.5. Patent 201110096758.6 uses a static multi-stage melt crystallization method to prepare electronic-grade phosphoric acid. The core invention lies in setting up multi-stage melt crystallization and controlling the temperature of each stage. The crystallization equipment used is a columnar jacketed crystallization tower, but the influence of the crystallization tower structure is not analyzed. Patent 201310747117.1 uses a partitioned crystallization method to prepare electronic-grade phosphoric acid, using a crystallizer with partitions for crystallization, but it also does not explain the influence of the partition structure on the melt crystallization efficiency. Patent 201310742213.7 describes a method for preparing electronic-grade phosphoric acid using a U-tube static multi-stage melt crystallization method. Phosphoric acid seed crystals are first applied to the outer wall of the U-tube by spraying or brushing, promoting crystal growth from the surface of the U-tube outwards. However, the structure of the U-tube is not described. Patent 201310747141.5 describes a method for producing electronic-grade phosphoric acid using a tubular crystallization method. A vertical tubular structure is installed in an acid storage tank. Cooling medium is introduced through the vertical tubular structure, and phosphoric acid semi-crystalline seed crystals are added to the outer wall of the tubular structure to induce crystallization. However, the influence of the structure and number of tubular structures is not explained.

[0006] In summary, existing patents on the static melt crystallization process of electronic-grade phosphoric acid primarily explore the influence of crystallization temperature on melting and crystallization through experiments. Although different cooling surface structures, such as plate or tubular, are considered, in-depth research and analysis on the optimization design of the melt crystallization equipment have not been conducted. Furthermore, the static melt crystallization process lacks intense stirring, making it prone to uneven temperature distribution, which severely affects the crystallization effect in scaled-up equipment. Therefore, the optimal crystallization operation scheme developed in laboratory-scale studies is often no longer optimal after scale-up and is difficult to directly apply to industrial-scale design.

[0007] Numerical simulation can significantly reduce the cycle and cost of experimental and scale-up development, making it an important tool for optimization and scale-up in industrial applications. Computational fluid dynamics (CFD) can be used to simulate fluid flow within reactors; by coupling heat transfer equations and phase transition equations, it is possible to predict crystal layer distribution under different operating conditions and device designs. However, currently, there is a lack of research in this field on numerical simulation methods for the melting and crystallization processes of electronic chemicals. Summary of the Invention

[0008] The purpose of this invention is to obtain a method for optimizing and scaling up the static melt crystallization process of electronic chemicals. Electronic-grade phosphoric acid is the specific research object of this patent, but the method of this invention is also applicable to the static melt crystallization process of other electronic chemicals.

[0009] This invention utilizes CFD to obtain flow field information of coolant and melt at different locations inside a static melting crystallizer. Combined with heat transfer equations and liquid-solid phase transition models, crystal growth trends are analyzed. Based on these models, a theoretical prediction model for the static melting crystallization process of electronic chemicals is established. After determining the model parameters and verifying the model's reliability through static melting crystallization experiments, numerical simulation methods are used to study the static melting crystallization process of electronic chemicals, optimize operating conditions and equipment structure, and conduct scientific scale-up. This is of great significance for accurately obtaining high-quality electronic chemicals. The method mainly includes the following:

[0010] (1) Establish heat transfer equations under different heat transfer mechanisms in different regions of the static melting and crystallization process;

[0011] (2) Establish a theoretical model for the liquid-solid phase transition process;

[0012] (3) Establish the momentum equation and mass conservation equation for the calculation of coolant and melt flow field in different regions;

[0013] (4) Determine the parameters in the coupling model (1)-(3) based on the results of the static melting and crystallization experiment, and verify the accuracy of the predictions made by the coupling model;

[0014] (5) Simulate the static melting and crystallization process to achieve numerical amplification, and further optimize the operating conditions and geometric structure.

[0015] In step (1), the overall static melting and crystallization region is divided into three parts: (i) the coolant flow region; (ii) the cooling pipe wall; and (iii) the phase change region. For the coolant flow region, the heat transfer mechanism is convective heat transfer and heat conduction, and the heat transfer equation is...

[0016] (1)

[0017] in, , , , , Let be the density, specific heat capacity, velocity, thermal conductivity, and viscous stress tensor of the fluid in the studied region, respectively.

[0018] For heat transfer through the cooling pipe wall, following the solid-state heat conduction mechanism, the heat transfer equation is:

[0019] (2)

[0020] In the phase transition region, the melt exhibits a density difference due to temperature variations, leading to natural convection. Furthermore, the heat of phase transition needs to be considered in this region. Q Therefore, its heat transfer equation is:

[0021] (3)

[0022] To calculate the heat of phase transition Q Further integration with a phase transition model is needed. In step (2), the apparent heat capacity method is used to describe the liquid-solid phase transition process. This method assumes that the phase transition occurs within a temperature interval Δ. T Therefore, the phase transition begins at a temperature of T fus -Δ T At / 2, as the temperature increases, the initial phase 1 begins to transform into phase 2; that is, the phase fraction of phase 1 gradually decreases, and the fraction of phase 2 gradually increases, but the sum of the phase fractions of the two always remains 1. When the temperature reaches T fus +Δ T At a phase fraction of 0, phase 1 has a phase fraction of 0, and phase 2 has a phase fraction of 1, indicating a complete phase transition. The phase fraction transformation equations for phases 1 and 2 throughout the process are described by the following equation.

[0023] (4)

[0024] For the process of transformation from melt to solid, phase 1 is the melt and phase 2 is the solid.

[0025] The apparent heat capacity method introduces phase transition heat by treating the heat capacity of the material in the phase transition region. The formula for calculating the apparent heat capacity of the phase transition region is:

[0026] (5)

[0027] Represents the phase transition heat distribution. This represents the equivalent heat capacity after the two phases are mixed together. (Mass fraction of the mixture) Thermal conductivity Defined respectively

[0028] (6)

[0029] (7)

[0030] (8)

[0031] The momentum equation and mass conservation equation for the coolant flow region in step (3) are calculated as follows:

[0032] (9)

[0033] (10)

[0034] The material properties, flow pattern, and geometry of a fluid determine whether heat transfer is laminar or turbulent, which can be determined using the Reynolds number. Re To determine:

[0035] (11)

[0036] ρ , μ Represents the density and viscosity of the fluid. L The characteristic length of the geometric structure, U It is the flow velocity of the fluid. The Reynolds number represents the ratio of inertial forces to viscous forces. When the Reynolds number is low, viscous forces dominate and laminar flow can be observed; if the Reynolds number is high enough, the flow field will eventually evolve into a turbulent flow pattern.

[0037] In the phase transition region, natural convection occurs. Unlike fluid flow driven by conventional external forces, natural convection often occurs in static fluids with varying temperatures. When a significant density difference arises due to an internal temperature difference, buoyancy is generated in the gravitational field, thus driving fluid flow. Therefore, the buoyancy F under the influence of molten gravity needs to be considered. The momentum equation for this region is:

[0038] (12)

[0039] Rayleigh number is used to characterize the flow pattern and heat transfer caused by natural convection. It is determined by fluid properties, cavity size, and temperature difference, and can be calculated by the following formula:

[0040] (13)

[0041] If Rayleigh number < 10 3 If the Rayleigh number is large, natural convection can be ignored, and most heat transfer is caused by thermal diffusion. If the Rayleigh number is large, natural convection needs to be considered. The Grashof number is another flow pattern indicator, which is the ratio of buoyancy to viscous force. When the buoyancy is large relative to the viscous force ( Gr >10 9 If the flow pattern is turbulent, it is laminar; otherwise, the Grashof number is calculated using the following formula:

[0042] (14)

[0043] ρ, g, α p 、C p μ, k, L These are the density, gravitational acceleration, coefficient of thermal expansion, specific heat capacity, viscosity, thermal conductivity, and characteristic length of the fluid in the studied region.

[0044] In step (5), a static melting and crystallization process simulation is performed. First, a geometric model of the static crystallizer is constructed, then a computational mesh is generated, and coupling relationships, boundary conditions, and initial conditions are defined. For the turbulent flow of the coolant, the standard k-epsilon turbulence model is used for description. For the melt region, a laminar flow field is set where all velocity components are zero, considering... z Gravitational acceleration in the negative axis direction.

[0045] During the simulation, a "conjugate heat transfer" physics field is used. A "non-isothermal flow" interface is added to couple the "solid and fluid heat transfer" and "laminar or turbulent" interfaces. This ensures that the "fluid" characteristics in the "heat transfer" interface can use the velocity field calculated by the "flow" interface. Simultaneously, the temperature dependence of material properties in the flow interface can be defined based on the temperature field calculated by the "heat transfer" interface. Specifically, in the "solid and fluid heat transfer" physics field, the cooling medium region is set as fluid heat transfer, the wall region as solid heat transfer, and the molten liquid region as a "phase change material," specifying solid and liquid phase properties and phase transition conditions respectively. A "laminar" physics field is added to the molten liquid region, and a "turbulent" physics field is added to the cooling medium region. The "solid and fluid heat transfer" physics field is coupled to the "laminar" physics field of the molten liquid region through the "non-isothermal flow" interface, and the "solid and fluid heat transfer" physics field is coupled to the "turbulent" physics field of the cooling medium region through the "non-isothermal flow" interface. The material properties of the flow field are all derived from the heat transfer interface.

[0046] Based on the above process, the operating conditions of the static melting and crystallization process and the geometry of the crystallizer were optimized and scaled up. Attached Figure Description

[0047] Figure 1 Different Δ T Under the given conditions, the relative deviation between the experimentally measured thickness of the phosphate crystal layer and the simulation calculation results.

[0048] Figure 2 Ion partition coefficients at different crystal layer growth rates.

[0049] Figure 3 Schematic diagram of a static melting crystallizer.

[0050] Figure 4 The effect of crystallizer height on crystal layer distribution.

[0051] Figure 5 Crystal layer distribution when the cooling tube radius is 20 mm and the ratio of the crystallizer radius to the cooling tube radius is 1 to 6.

[0052] Figure 6 Crystal layer distribution when the cooling tube radius is 40 mm and the ratio of the crystallizer radius to the cooling tube radius is 1 to 6.

[0053] Figure 7 Crystal layer distribution when the cooling tube radius is 60 mm and the ratio of the crystallizer radius to the cooling tube radius is 1 to 6.

[0054] Figure 8 Crystal layer distribution when the cooling tube radius is 80 mm and the ratio of the crystallizer radius to the cooling tube radius is 1 to 6.

[0055] Figure 9 Crystal layer distribution when the cooling tube radius is 100 mm and the ratio of the crystallizer radius to the cooling tube radius is 1 to 6.

[0056] Figure 10 The effect of cooling pipe outer wall temperature on crystal layer distribution.

[0057] Figure 11 The effect of crystallizer inner wall temperature on crystal layer distribution. Detailed Implementation

[0058] Example 1

[0059] (1) Based on the crystallizer size parameters, including the cooling pipe radius R i crystallizer radius R c Crystallizer height H c Establish a geometric model of the static melting crystallizer;

[0060] (2) Perform computational mesh generation on the established crystallizer geometric model;

[0061] (3) Based on equations (1)-(14), a static melting and crystallization process mathematical model involving multiple physical fields such as heat transfer, phase change and fluid flow is established for each computational grid;

[0062] Predictive models for the optimization and scale-up of static melt crystallization of electronic chemicals include the following:

[0063] (a) Establish heat transfer equations under different heat transfer mechanisms in different regions of the static melting and crystallization process;

[0064] (b) Establish a theoretical model for the liquid-solid phase transition process;

[0065] (c) Establish the momentum equation and mass conservation equation for the coolant and melt flow field calculation in different regions;

[0066] (d) Determine the parameters in the (1)-(3) coupled model by combining the results of static melting and crystallization experiments, and verify the accuracy of the predictions made by the coupled model;

[0067] (e) Perform process simulation of heat transfer-phase change-flow multiphysics coupling in static melting and crystallization process, realize numerical scale-up, and optimize operating conditions and geometry.

[0068] In step (a), the overall static melting and crystallization region is divided into three parts: (i) the coolant flow region; (ii) the cooling pipe wall; and (iii) the phase change region.

[0069] For the coolant flow region, the heat transfer mechanism is convective heat transfer and heat conduction, and the heat transfer equation is:

[0070] (1)

[0071] For heat transfer through the cooling pipe wall, following the solid-state heat conduction mechanism, the heat transfer equation is:

[0072] (2)

[0073] For the phase transition region, there exists a density difference in the melt due to the temperature difference, resulting in natural convection of the melt. Furthermore, the phase transition heat Q needs to be considered in this region; therefore, its heat transfer equation is:

[0074] (3)

[0075] From the above equations (a), (b), and (c), we can see that... , , , , Let Δ represent the density, specific heat capacity, velocity, thermal conductivity, and viscous stress tensor of the fluid in the studied region, respectively; T For temperature intervals.

[0076] In step (b), the apparent heat capacity method is used to describe the liquid-solid phase transition process. Throughout the process, the phase fraction transformation equations for phase 1 and phase 2 are described by the following equation.

[0077] (4)

[0078] For the process of transformation from melt to solid, phase 1 is the melt and phase 2 is the solid;

[0079] T fus -Δ T / 2 represents the temperature at which the phase transition begins;

[0080] T fus +Δ T / 2 means that the phase fraction of phase 1 is 0 and the phase fraction of phase 2 is 1, thus completing the complete phase transition process;

[0081] The apparent heat capacity method introduces phase transition heat by treating the heat capacity of the material in the phase transition region. The formula for calculating the apparent heat capacity of the phase transition region is:

[0082] (5)

[0083] Represents the phase transition heat distribution. This represents the equivalent heat capacity after the two phases are mixed together.

[0084] Mixture mass fraction Thermal conductivity Defined respectively

[0085] (6)

[0086] (7)

[0087] (8).

[0088] The momentum equation and mass conservation equation for the coolant flow region in step (c) are calculated as follows:

[0089] (9)

[0090] (10)

[0091] In the above formula, ρ Let ρ be the coolant density, ▽u be the coolant velocity gradient, and ∂u / ∂t represent the change in coolant velocity over time.

[0092] The material properties, flow pattern, and geometry of a fluid determine whether heat transfer is laminar or turbulent, as indicated by the Reynolds number. Re To determine:

[0093] (11)

[0094] ρ , μ Represents the density and viscosity of the fluid. L The characteristic length of the geometric structure, U It is the flow rate of the fluid;

[0095] For the phase transition region, the buoyancy force F under the action of the melt gravity must be considered. The momentum equation for this region is:

[0096] (12)

[0097] The Rayleigh number is used to characterize the flow pattern and heat transfer caused by natural convection. It is determined by fluid properties, cavity size, and temperature difference, and can be calculated by the following formula:

[0098] (13)

[0099] If Rayleigh number < 10 3 If natural convection is ignored, most heat transfer is caused by thermal diffusion, and the Rayleigh number is greater than or equal to 10. 3 Then the natural convection field must be considered;

[0100] ρ, g, α p 、C p μ, k, L These are the density, gravitational acceleration, coefficient of thermal expansion, viscosity, specific heat capacity, thermal conductivity, and characteristic length of the fluid in the studied region.

[0101] The Grashof number is used as a convection modulus, which is the ratio of buoyancy to viscous force. Gr >10 9 If the flow pattern is turbulent, otherwise it is laminar. The Grashof number is calculated by the following formula:

[0102] (14)

[0103] ρ, g, α p μ, L These are the density, gravitational acceleration, coefficient of thermal expansion, viscosity, and characteristic length of the fluid in the studied region, respectively.

[0104] (4) Based on the operating conditions parameters of the crystallization process, including the temperature of the outer wall of the cooling pipe. T i Temperature of the inner wall of the crystallizer T c Define the initial and boundary conditions for solving the mathematical model;

[0105] (5) Different temperature intervals Δ T The parameters are input into the mathematical model for solving, and the crystal layer thickness at different times under the given crystallizer size parameters and temperature operating conditions can be calculated.

[0106] (6) In the crystallization experiment, a fixed camera was used to take pictures of the static melting and crystallization process at certain time intervals. By comparing the scale, the thickness of the crystal layer at the outer wall of the cooling tube at different times was calculated, and the crystal growth rate was calculated. At the same time, the content of various metal impurities in the crystallized product was analyzed.

[0107] (7) Compare the crystal layer thickness calculated by the model with the experimentally measured crystal layer thickness, and find the Δ corresponding to the smallest error. T The value is then used for subsequent optimization and amplification simulation calculations.

[0108] Figure 1 For different Δ T Under certain conditions, the relative deviation between the experimentally measured thickness of the phosphate crystal layer and the simulation calculation results indicates that when Δ... T When K = 3.70, the simulation calculation error is minimized. Therefore, in this invention, the simulation calculation error is minimized for phosphoric acid Δ. T The optimal value is 3.70 K.

[0109] The removal efficiency of metal impurities under different growth rates was further analyzed. Figure 2 For different crystal layer growth rates G ion partition coefficients of Cr, Fe, and As K i The results showed that increasing the crystal growth rate had no significant impact on the removal of metal impurities. Therefore, the static melt crystallization process of phosphoric acid can be optimized and designed by increasing the crystal growth rate.

[0110] (8) Based on the optimal temperature interval parameter Δ T Further simulation studies will be conducted to predict different cooling pipe radii. R i crystallizer radius R c Crystallizer height H c Temperature of the outer wall of the cooling pipe T i Temperature of the inner wall of the crystallizer T c The predicted crystal layer thickness was used to optimize the structural parameters and operating conditions of the static melt crystallizer, and the process was scaled up.

[0111] Example 2

[0112] Based on Example 1, targeting Figure 3 The schematic diagram of the static melting crystallizer structure studied in this invention shows that coolant is circulated inside the internal cooling pipes for cooling and temperature reduction. The radius of the cooling pipes is... R i The radius of the crystallizer is R c The height of the crystallizer is H c The temperature of the outer wall of the cooling pipe is T i The temperature of the inner wall of the crystallizer is T c The temperatures of the cooling tube wall and the crystallizer wall were adjusted to allow phosphoric acid to grow outwards perpendicular to the outer wall of the cooling tube. The static melt crystallization process was optimized and scaled up by comparing the crystal layer thickness under different structural and operating temperature conditions.

[0113]

[0114] Example 2-1

[0115] The crystallizer used in the experiment had a cooling tube radius of 20 mm, a crystallizer radius of 67.5 mm, and a height of 300 mm. The effects of crystallizer heights of 300, 450, 600, 750, and 900 mm on crystal layer growth were compared through simulation calculations. Figure 4 The results show that the crystallizer height has no effect on the crystal layer distribution. Therefore, the scale-up can be achieved by directly increasing the crystallizer height, thereby increasing the yield per batch.

[0116] Example 2-2

[0117] Considering a cooling pipe radius of 20 mm and a crystallizer radius to cooling pipe radius ratio controlled between 1 and 6, that is, taking into account the differences in crystal layer distribution when the crystallizer inner diameter is 40, 60, 80, 100, and 120 mm, the crystallizer height is controlled at 600 mm. Figure 5 The results show that when the inner diameter of the crystallizer is only 40, 60, and 80 mm, the crystal layer thickness is significantly less than that of 100 and 120 mm. This indicates that for a cooling tube radius of 20 mm, the crystallizer radius needs to be designed to be at least 100 mm to obtain the maximum crystal yield. However, further increasing the radius will increase the manufacturing cost and floor space. Therefore, when the cooling tube radius is 20 mm, a crystallizer radius of 100 mm is the optimal crystallizer geometry design.

[0118] Example 2-3

[0119] Considering increasing the cooling pipe radius to 40 mm, and controlling the ratio of the crystallizer radius to the cooling pipe radius within 1-6, we take into account the differences in crystal layer distribution when the crystallizer inner diameter is 80, 120, 160, 200, and 240 mm. In this case, the crystallizer height is controlled at 600 mm. Figure 6 The results show that when the inner diameter of the crystallizer is only 80 mm, the crystal layer thickness is significantly less than that under the other four conditions. This indicates that for a cooling tube radius of 40 mm, the crystallizer radius needs to be designed to be at least 120 mm to ensure maximum crystal yield. However, further increasing the radius would increase manufacturing costs and floor space. Therefore, when the cooling tube radius is 40 mm, a crystallizer radius of 120 mm is the optimal crystallizer geometry design.

[0120] Examples 2-4

[0121] Considering increasing the cooling pipe radius to 60 mm, and controlling the ratio of the crystallizer radius to the cooling pipe radius within 1-6, we consider the differences in crystal layer distribution when the crystallizer inner diameter is 120, 180, 240, 300, and 360 mm. In this case, the crystallizer height is controlled at 600 mm. Figure 7 The results show that when the inner diameter of the crystallizer is only 120 mm, the crystal layer thickness is slightly less than that under the other four conditions. This indicates that for a cooling tube radius of 60 mm, the crystallizer radius needs to be designed to be at least 180 mm to ensure maximum crystal yield. However, further increasing the radius would increase manufacturing costs and floor space. Therefore, when the cooling tube radius is 60 mm, a crystallizer radius of 180 mm is the optimal crystallizer geometry design.

[0122] Examples 2-5

[0123] Considering increasing the cooling pipe radius to 80 mm, and controlling the ratio of the crystallizer radius to the cooling pipe radius within 1-6, we consider the differences in crystal layer distribution when the crystallizer inner diameter is 160, 240, 320, 400, and 480 mm. In this case, the crystallizer height is controlled at 600 mm. Figure 8 The results show that there is basically no significant difference in crystal layer distribution under the five conditions, indicating that for a cooling tube radius of 80 mm, the crystallizer radius needs to be designed to be at least 160 mm to ensure maximum crystal yield. However, further increasing the radius would increase manufacturing costs and floor space. Therefore, when the cooling tube radius is 80 mm, a crystallizer radius of 160 mm is the optimal crystallizer geometry design.

[0124] Examples 2-6

[0125] Considering increasing the cooling pipe radius to 100 mm, and controlling the ratio of the crystallizer radius to the cooling pipe radius within 1-6, we consider the differences in crystal layer distribution when the crystallizer inner diameter is 200, 300, 400, 500, and 600 mm. In this case, the crystallizer height is controlled at 600 mm. Figure 9 The results show that there is basically no significant difference in crystal layer distribution under the five conditions, indicating that for a cooling tube radius of 100 mm, designing the crystallizer radius to be at least 200 mm can ensure maximum crystal yield. Further increasing the crystallizer radius has no significant impact on increasing yield, but it will increase manufacturing costs and floor space. Therefore, when the cooling tube radius is 100 mm, a crystallizer radius of 200 mm is the optimal crystallizer geometry design.

[0126] Examples 2-7

[0127] As can be seen from the comparison of Examples 1-5, the crystallizer height has no effect on the crystal layer distribution, but increasing the radius of the cooling tube and the crystallizer radius is beneficial to increasing the crystal layer thickness, i.e., the crystal yield. Based on a crystallizer structure with a cooling tube radius of 100 mm, a crystallizer radius of 200 mm, and a crystallizer height of 600 mm, the influence of the outer wall temperature of the cooling tube is further considered. The inner wall temperature of the crystallizer is fixed at 296.15 K, and the differences in crystal layer distribution under the outer wall temperatures of the cooling tube of 275.15, 277.15, 279.15, 281.15, and 283.15 K are compared. Figure 10 The results show that the crystal layer thickness increases as the outer wall temperature of the cooling tube decreases. Therefore, the yield of the crystal can be improved by reducing the outer wall temperature of the cooling tube, thereby optimizing the overall yield of the process.

[0128] Examples 2-8

[0129] Based on a crystallizer structure with a cooling tube radius of 100 mm, a crystallizer radius of 200 mm, and a crystallizer height of 600 mm, and further considering the influence of the crystallizer inner wall temperature, the outer wall temperature of the cooling tube was fixed at 275.15 K. The differences in crystal layer distribution were compared under crystallizer inner wall temperatures of 295.15, 296.15, 297.15, 298.15, 301.15, and 303.15 K. Figure 11 The results show that the crystal layer thickness increases as the outer wall temperature of the cooling tube decreases. Therefore, the crystal yield can be increased by reducing the inner wall temperature of the crystallizer, thereby optimizing the overall yield of the process.

Claims

1. A method for predicting the optimization and scale-up of electrochemical static melt crystallization of chemicals, characterized in that, Comprise the following contents: (1) Establish heat transfer equation under different heat transfer mechanisms in different regions of static melt crystallization process; The whole static melt crystallization region is divided into three parts (i) coolant flow region; (ii) cooling pipe wall surface; (iii) phase change region; For the coolant flow region, the heat transfer mechanism is convective heat transfer and heat conduction, and the heat transfer equation is （1） For the cooling pipe wall surface heat transfer, it is a solid heat conduction mechanism, and its heat transfer equation is （2） For the phase change region, there is a density difference of melt due to temperature difference, so that the natural convection of melt is formed, in addition, the phase change heat Q needs to be considered, so its heat transfer equation is （3） In the above formulas (1), (2), (3) , , , , are the density, specific heat capacity, velocity, thermal conductivity and viscous stress tensor of the fluid in the region under study, respectively; (2) Establish the theoretical model of liquid-solid phase change process; (3) Establish the momentum equation and mass conservation equation for the calculation of the coolant and melt flow field in different regions; (4) Combine the static melt crystallization experimental results to determine the parameters in the coupling model of (1)-(3), and verify the accuracy of the coupling model prediction; (5) Perform process simulation of static melt crystallization process heat transfer-phase change-flow multi-physical field coupling, realize numerical amplification, and optimize the operating conditions and geometric structure.

2. The prediction method for static melt crystallization optimization and scale-up of electronic chemicals according to claim 1, characterized in that, In step (2), the apparent heat capacity method is used to describe the liquid-solid phase change process, and the phase 1 and phase 2 phase fraction transformation equation is described by the following formula （4） For the process of melt to solid, phase 1 is melt and phase 2 is solid; T fus - Δ T T2 is the temperature at which the phase transition begins; T fus + Δ T / 2 is the phase fraction of phase 1 and 1 is the phase fraction of phase 2, a complete phase transformation process is completed; The apparent heat capacity method introduces the phase change heat by processing the heat capacity of the material in the phase change region, and the calculation formula of the apparent heat capacity of the phase change region is （5） representing the distribution of phase change heat, representing the equivalent heat capacity after the two phases are mixed together; Mass fraction of mixture Thermal conductivity are defined as （6） （7） （8）。 3. The prediction method for static melt crystallization optimization and scale-up of electronic chemicals according to claim 2, characterized in that, In step (3), the momentum equation and mass conservation equation of the coolant flow region are as follows: （9） （10） In the above formula, ρ is the coolant density, and ∇u is the coolant velocity gradient, represents the change in coolant velocity over time; The material properties, flow pattern and geometry of the fluid determine whether heat transfer is by laminar or turbulent flow, judged by the Reynolds number Re : （11） ρ , μ representing the density and viscosity of the fluid, L denotes a characteristic length of the geometry, U is the flow rate of the fluid; For the phase change region, the buoyancy F under the action of melt gravity needs to be considered, and the momentum equation of the region is （12）。 4. The prediction method for optimization and amplification of electronic chemical static melt crystallization according to claim 3, characterized in that, The Rayleigh number is used to represent the flow pattern and heat transfer brought by natural convection, which is determined by fluid properties, cavity size and temperature difference, and can be calculated by the following formula: （13） If Rayleigh number < 10 3 then ignore natural convection, most heat transfer is by thermal diffusion, if Rayleigh number is greater than or equal to 10 3 then natural convection field is to be considered; ρ, g, α p 、C p , μ, k, L respectively the density, the gravitational acceleration, the thermal expansion coefficient, the specific heat capacity, the viscosity, the thermal conductivity and the characteristic length of the fluid of the region under study.

5. The prediction method for optimization and amplification of electronic chemical static melt crystallization according to claim 4, characterized in that, The Grashof number is used as a flow regime indicator, which is the ratio of buoyancy to viscous forces Gr > 10 9 , the flow regime is turbulent, otherwise it is laminar, the Grashof number is calculated from the following equation: （14） ρ, g, α p , μ, L respectively the density, the gravitational acceleration, the thermal expansion coefficient, the viscosity and the characteristic length of the fluid of the area under study.

6. The method of claim 1, wherein the method is a method of predicting the static melt crystallization optimization and amplification of electronic chemicals, characterized by, In step (5), the process simulation of static melt crystallization process is carried out, first the geometric model of static crystallizer is constructed, then the calculation grid is generated, the coupling relationship and boundary conditions, initial value conditions are defined; For the turbulent flow of coolant, the standard k-epsilon turbulent flow model is used for description, while for the melt region, the laminar flow field is set with each velocity component being 0, and the gravity acceleration in the negative direction of z axis is considered.

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