Static melt crystallization process prediction method, optimization method, device and medium

Abstract

The invention discloses a static melt crystallization process prediction method, an optimization method, a device and a medium. The prediction method comprises the following steps: determining melt parameters, crystal layer parameters and the mass fraction of impurities on the surface of a crystal layer at the current moment; determining the equilibrium temperature of the crystal surface at the current moment according to the impurity mass fraction of the crystal layer surface; predicting the growth condition of the crystal layer in a first time period after the current moment by using a preset crystal layer growth rate model to obtain a first growth prediction result, wherein the first growth prediction result comprises melt parameters, crystal layer parameters and the impurity mass fraction of the surface of the crystal layer at the end moment of the first time period; determining the equilibrium temperature of the crystal surface again according to the impurity mass fraction of the crystal layer surface at the end of the first time period; and according to the melt parameters, the crystal layer parameters and the equilibrium temperature of the crystal surface at the last moment of the first time period, predicting the growth condition of the crystal layer in the next time period by using a preset crystal layer growth rate model. According to the method, the static melt crystallization process can be accurately predicted and optimized.

Description

Technical Field

[0001] The present invention relates to the technical field of static crystallization, and particularly to a method and device for predicting and optimizing a static melting crystallization process, as well as a medium. Background Art

[0002] In recent years, with the booming development of industries such as electric vehicles, materials, chemical engineering, food, and medicine, the market's demand for the purity of related products has been increasing day by day. Especially for high-end fine chemicals and high-value-added products, their quality standards have become increasingly strict, and the requirements for purification processes have reached a new level.

[0003] Crystallization, as a key unit operation in the fields of chemical engineering, food, and medicine, is widely used in component separation and purification. This technology utilizes the difference in melting points of different components to achieve separation. Compared with the distillation method, it has higher safety, lower energy consumption, and can also break through the limitations of the distillation method to effectively separate substances with similar boiling points such as isomers; compared with the solvent method, the crystallization method not only has less pollution to the product, but also has a significant purity advantage for the purified product.

[0004] Classified by the way of obtaining supersaturation from a solution, the crystallization method is divided into evaporation crystallization and cooling crystallization; if classified by whether a third substance is introduced, cooling crystallization includes solvent crystallization and melting crystallization. Melting crystallization has significant characteristics such as simple process, high product purity, and low energy consumption when separating and purifying because it does not require the introduction of additional substances. Based on different operating methods, melting crystallization is further divided into suspension melting crystallization and layer melting crystallization. According to the flow state of the molten liquid around the crystallization layer, layer melting crystallization can be further subdivided into static layer crystallization and dynamic layer crystallization (i.e., falling film crystallization).

[0005] In the process of suspension melting crystallization, solid-liquid separation needs to be achieved by means of filtration or centrifugal separation to obtain crystal products. This method is easy to realize industrial scale-up and continuous production; in the process of layer melting crystallization, crystals directly grow on the cooling interface, and after crystallization, the crystals and the mother liquor can be directly separated, avoiding the problem of crystal breakage caused by mechanical separation and reducing the use of moving equipment. Each has its own advantages. For the separation problem of high-melting-point systems, suspension crystallization faces difficulties in high-temperature filtration with large difficulty and poor effect. At this time, the static crystallization process often becomes the first choice for separation and purification.

[0006] The crystallization process is inseparable from a crystallizer. Common crystallizers include kettle crystallizers, columnar crystallizers, plate crystallizers, and shell-and-tube crystallizers, etc. For static crystallization, plate crystallizers and shell-and-tube crystallizers are mainly used, which use fins and tubes as heat exchange elements. Compared with the jacketed kettle crystallizer, the heat transfer area of the crystallization process is significantly enlarged. However, insufficient material fluidity easily causes problems such as uneven crystallization, low heat transfer efficiency, and large temperature difference between the material and the coolant in the crystallizer, which has an adverse impact on product purity and yield.

[0007] There are not many principles in the design of existing static melting crystallizers. The design of existing melting crystallizers is blind, and small-scale experiments cannot guide the design of the crystallizer after magnification. It mainly relies on the experience of designers or research through experiments, which easily leads to unreasonable designs. In the patents of existing static melting crystallization processes, the influence of crystallization temperature conditions on melting crystallization is mainly explored through experiments. Although the cooling surfaces of different structures such as plate type or tube type are considered, in-depth research and analysis on the optimized design of melting crystallization equipment have not been carried out. Therefore, the optimal crystallization operation plan developed through small-scale laboratory research and development is often no longer the best after magnification and is difficult to be directly used for industrial scale-up design.

[0008] Aiming at the deficiencies of the existing technology, the Chinese patent application with the publication number CN119049601A uses Computational Fluid Dynamics (CFD) to simulate the fluid flow conditions in the reactor, couples the heat transfer equation and the phase change equation, can predict the crystal layer distribution under different operating conditions and device designs, and can reduce the cycle and cost of experiments and scale-up development.

[0009] The disclosure of the above background technical content is only used to assist in understanding the inventive concept and technical solution of the present invention. It does not necessarily belong to the prior art of this application and does not necessarily give technical guidance; in the case where there is no clear evidence indicating that the above content was publicly available before the filing date of this application, the above background technology should not be used to evaluate the novelty and inventiveness of this application. Summary of the Invention

[0010] The object of the present invention is to provide a method, an optimization method, a device and a medium for predicting the static melting crystallization process, which can more accurately predict the growth status of the crystal layer during the static melting crystallization process.

[0011] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0012] A method for predicting the static melting crystallization process includes the following steps:

[0013] Determine the melt parameters, crystal layer parameters and impurity mass fraction on the crystal layer surface at the current moment;

[0014] Based on the energy balance on the surface of the moving crystal layer, determine the equilibrium temperature on the crystal surface at the current moment according to the impurity mass fraction on the crystal layer surface;

[0015] Predict the growth status of the crystal layer within the first time period after the current moment using a preset crystal layer growth rate model to obtain a first growth prediction result. The crystal layer growth rate model is a functional relationship between the growth rate of the crystal layer, melt parameters, crystal layer parameters, and the equilibrium temperature of the crystal surface. The first growth prediction result includes the melt parameters, crystal layer parameters, and the impurity mass fraction on the crystal layer surface at the end moment of the first time period.

[0016] Determine the equilibrium temperature of the crystal surface at the end moment of the first time period according to the impurity mass fraction on the crystal layer surface at the end moment of the first time period.

[0017] Predict the growth status of the crystal layer in the next time period using the preset crystal layer growth rate model based on the melt parameters, crystal layer parameters, and the equilibrium temperature of the crystal surface at the end moment of the first time period.

[0018] Further, based on any one of the foregoing technical solutions or a combination of multiple technical solutions, determine the impurity mass fraction on the crystal layer surface at the end moment of the first time period as the first mass fraction. The first mass fraction is determined by the following method:

[0019] Determine the total volume of the crystallized product obtained after crystallization in the first time period according to the first growth prediction result. The crystallized product includes the crystal layer and the mother liquor wrapped in the crystal layer.

[0020] Determine the volume fraction of the mother liquor in the crystallized product.

[0021] Calculate the first mass fraction according to the volume fraction, the total volume of the crystallized product, the density of the crystal layer, and the melt density.

[0022] Further, based on any one of the foregoing technical solutions or a combination of multiple technical solutions, calculating the first mass fraction according to the volume fraction, the total volume of the crystallized product, the density of the crystal layer, and the melt density includes:

[0023] Calculate the mass fraction \(w\) of impurities in the remaining melt after crystallization in the first time period according to the volume fraction, the total volume of the crystallized product, the crystal density, and the melt density i And use it as the second mass fraction.

[0024] Determine the first mass fraction according to the second mass fraction.

[0025] Further, based on any one of the foregoing technical solutions or a combination of multiple technical solutions, determine that the first mass fraction is equal to the second mass fraction.

[0026] Further, based on any one of the foregoing technical solutions or a combination of multiple technical solutions, calculate the first mass fraction \(w\) using the following formula i,eq :

[0027]

[0028] Among them, w i,eq is the impurity concentration on the crystal surface, i.e., the first mass fraction, w i,L is the impurity concentration in the bulk phase, i.e., the second mass fraction, ρ L is the melt density, ρ s is the crystal density, D i,cr is the mass transfer coefficient, δ is the boundary layer thickness, G is a function of the crystal layer thickness and the crystal growth rate, and e is the base of the natural logarithm.

[0029] Furthermore, based on any one of the foregoing technical solutions or a combination of multiple technical solutions, the first mass fraction w is calculated by the following formula i,eq :

[0030]

[0031] Among them, w i,eq is the impurity concentration on the crystal surface, i.e., the first mass fraction, w i,L is the impurity concentration in the bulk phase, i.e., the second mass fraction, w i,S is the mass fraction of impurities on the solid surface, ρ L is the melt density, ρ s is the crystal density, D i,cr is the mass transfer coefficient, δ is the boundary layer thickness, G is a function of the crystal layer thickness and the crystal growth rate, x represents the distance from a point in the boundary layer outside the crystal layer to the crystal layer boundary, and e is the base of the natural logarithm.

[0032] Furthermore, based on any one of the foregoing technical solutions or a combination of multiple technical solutions, the second mass fraction is calculated by the following formula:

[0033]

[0034] Among them, w i is the second mass fraction, w is the mass fraction of impurities in the melt at the initial moment of the first time period, M ini is the mass of the melt at the initial moment of the first time period, M is the mass of the remaining melt after crystallization in the first time period, and mz is the mass of impurities included in the crystallized substance;

[0035] mz and M are calculated by the following formulas:

[0036] mc = (1 - φ)·ΔV·ρ cr

[0037] ml = φ·ΔV·ρ l

[0038] mz = ml·w i,eq

[0039] M = M ini -mc - ml

[0040] Wherein, mc is the mass of the target crystal in the crystallized product, ml is the mass of the mother liquor in the crystallized product, mz is the mass of the impurities contained in the mother liquor in the crystallized product, and w i,eq is the first mass fraction, φ is the volume fraction, △V is the total volume of the crystallized product, and ρ l is the density of the melt, and ρ cr is the density of the target crystal.

[0041] Further, based on any one of the foregoing technical solutions or a combination of multiple technical solutions, the volume fraction is determined by the following method:

[0042] After separating and removing the mother liquor in the crystallized product, measure the porosity of the crystallized product, and determine the volume fraction according to the porosity.

[0043] Further, based on any one of the foregoing technical solutions or a combination of multiple technical solutions, the volume fraction is determined by the following method:

[0044] Embed the volume fraction as an unknown into the crystal layer growth rate model;

[0045] For the static melt crystallization process, measure the experimental data of the crystal layer growth condition;

[0046] Use the experimental data to fit the volume fraction in the crystal layer growth rate model to determine the volume fraction.

[0047] Further, based on any one of the foregoing technical solutions or a combination of multiple technical solutions, the following steps are further included: Without correcting the crystal layer crystallization thermal conductivity k s in the crystal layer parameters, use the preset crystal layer growth rate model to predict the crystal layer growth condition and compare it with the experimental data. If the comparison result is a match, then do not correct the crystallization thermal conductivity k s and the first mass fraction; if the comparison result is a mismatch, then correct the crystallization thermal conductivity k s and / or the first mass fraction. Wherein, the error between the predicted result and the experimental data is within the preset error range, and the experimental data is the actual crystal layer growth condition obtained through experiments based on the conditions and parameters (including melt parameters and crystal layer parameters, etc.) used for prediction.

[0048] Further, based on any one of the foregoing technical solutions or a combination of multiple technical solutions, the following steps are further included:

[0049] Determine the density of the crystal layer grown within the first time period;

[0050] If the density is less than the preset density, then for the crystal layer thermal conductivity k in the crystal layer parameters s make the following correction:

[0051] k s ′ = k s ·(1 - C l ) + k l ·C l

[0052] where k s ′ is the corrected crystal layer thermal conductivity, k l is the thermal conductivity of the melt, and C l is the liquid phase fraction for correction;

[0053] Calculate C through the following formula l :

[0054]

[0055] where T eu is the eutectic temperature, T f is the melting point, and T cf is the cold end temperature.

[0056] Furthermore, based on any one of the foregoing technical solutions or a combination of multiple technical solutions, the crystal layer growth rate model is constructed as follows:

[0057] Based on the energy balance at the surface of the moving crystal layer, the following basic equation can be derived:

[0058]

[0059] where T cr , λ cr , ρ s and v are the temperature, thermal conductivity, density, and growth rate of the crystal layer respectively, T m is the melt temperature, T eq is the equilibrium temperature of the crystal surface, t is time, Δh' is the heat that must be transferred through the crystal layer during crystal growth, including the heat of fusion and the heat that the solidified melt must cool from the melt temperature T m to the equilibrium temperature T eq of the crystal surface, h L is the convective heat transfer coefficient, r refers to the radial direction, r cf is the cold end radius, s is the thickness of the crystallization crystal layer, and r cf + s represents the cold end radius plus the crystal layer thickness.

[0060]

[0061] Among them, c p,n is the specific heat capacity of the melt.

[0062] The temperature of the crystal surface is the equilibrium temperature T eq and the mass fraction w i,eq of the impurity components on the crystal surface have the following functional relationship:

[0063]

[0064] Among them, and are respectively the enthalpy of fusion and the melting temperature of the crystalline compound, and R is the ideal gas constant.

[0065] According to the characteristics of the crystal fingers, determine the relationship between the temperature of the crystal layer changing with time and the crystal finger size distribution. Taking the parabolic temperature distribution changing with time in the crystal of the cylindrical crystal finger as an example, the temperature of the crystal layer is expressed by the following formula:

[0066] T cr (r, t) = a(t)·(r - r cf ) 2 + b(t)·(r - r cf ) + c(t)

[0067] Differentiate the above formula with respect to time as the following formula, and substitute it into the one-dimensional unsteady Fourier equation, and combine the following boundary condition equation to obtain the coefficients a(t), b(t) and c(t).

[0068]

[0069] T cr (r = r cf ) = T cf,w

[0070] T cr (r = r cf+s ) = T eq

[0071] Among them, T cf,w is the temperature of the cold end wall surface, and k is the thermal diffusivity of the crystal layer.

[0072] Thus, the crystal layer growth rate model shown by the following formula can be obtained. This model includes an implicit differential equation among the growth rate of the crystal layer, the equilibrium temperature of the crystal surface, the melt temperature, the heat transfer coefficient, the mass transfer coefficient and the physical properties:

[0073]

[0074] Among them, h L is the convective heat transfer coefficient, k s is the crystallization thermal conductivity, ρ s is the crystal layer density, r0 is the initial radius of the crystal layer, s(t) is the crystal layer thickness at time t, α is the thermal diffusion coefficient, and r0 is the initial radius of the crystal layer.

[0075] Based on the implicit multi-step BDF (Backward Differentiation Formula) method, the above implicit differential equation can be solved to predict the growth condition of the crystal.

[0076] According to another aspect of the present invention, the present invention provides a method for optimizing the static melting crystallization process, which optimizes the process parameters and / or device parameters of the static melting crystallization process by using the static melting crystallization process prediction method described in any one of the above technical solutions or a combination of multiple technical solutions. Among them, the process parameters include the cooling rate, the initial cooling temperature, the final cooling temperature, etc., and the device parameters include the cold end parameters and the crystallizer parameters.

[0077] The cold end parameters include the radius of the cooling heat exchanger and the shape of the cold end;

[0078] The crystallizer parameters include the shape of the crystallizer and the size of the crystallizer.

[0079] Specifically, according to different process parameters and / or device parameters, the static melting crystallization process is predicted by using the static melting crystallization process prediction method described in any one of the above technical solutions or a combination of multiple technical solutions, and the process parameters and device parameters corresponding to the optimal prediction result are determined as the process parameters and device parameters for controlling the static melting crystallization process.

[0080] According to another aspect of the present invention, the present invention provides a static melting crystallization device, which includes a crystallizer and a cold end. The shape and size of the crystallizer and the shape and size of the cold end are determined by the static melting crystallization process optimization method described in any one of the above technical solutions or a combination of multiple technical solutions.

[0081] According to another aspect of the present invention, the present invention provides a computer-readable storage medium for storing program instructions, and the program instructions are configured to be called to execute the steps of the method described in any one of the above technical solutions or a combination of multiple technical solutions.

[0082] The beneficial effects brought by the technical solutions provided by the present invention are as follows:

[0083] a. By discretizing the time of the crystal layer growth process, the present invention obtains the impurity concentration of crystallization at different moments and updates the impurity mass fraction on the crystal layer surface. Using the updated impurity mass fraction on the crystal layer surface to update the equilibrium temperature on the crystal surface, it can predict the growth status of the crystal layer in the next time period, and can more accurately predict the growth status of the crystal layer;

[0084] b. The static melting crystallization process prediction method proposed by the present invention uses the crystal growth situation calculated by the crystal layer growth rate model and does not require experimental fitting. Therefore, it is not affected by parameters such as the crystallizer parameters and experimental parameters in the experiment, and there will be no situation where it works well in a small crystallizer but poorly in a large crystallizer. It is applicable to crystallizers of various sizes, and by continuously iteratively updating the parameters for prediction calculation, it is also applicable to various static melting crystallization objects;

[0085] c. The present invention fully considers the key factor that the impurity concentration in the mother liquor gradually increases during the crystallization process. With advanced algorithms and model construction, it can not only accurately estimate the purity achieved by the crystallization crystal, but also synchronously calculate the change trend of the impurity concentration in the mother liquor. In this way, there is no need to rely on a large number of repetitive experiments to explore the process and equipment parameters of melting crystallization, greatly improving the R & D efficiency and saving the research time and capital costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments recorded in the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0087] Figure 1 It is a flowchart of the static melting crystallization process prediction method provided for an exemplary embodiment of the present invention;

[0088] Figure 2 It is a schematic diagram of the qualitative temperature distribution during the crystal growth process provided for an exemplary embodiment of the present invention;

[0089] Figure 3 It is a prediction result diagram of the relationship between the crystal layer growth thickness and the crystallization time under two conditions of correcting and not correcting the impurity concentration on the crystal surface provided for an exemplary embodiment of the present invention;

[0090] Figure 4 It is a comparison diagram of the influence of different crystallizer volumes on the crystal layer growth provided for an exemplary embodiment of the present invention;

[0091] Figure 5Comparison diagram of the influence of different crystallizer volumes on the impurity concentration of the crystal layer provided for an exemplary embodiment of the present invention;

[0092] Figure 6 Schematic comparison diagram of the change of crystal layer growth thickness with time under the conditions of corrected and uncorrected thermal conductivity provided for an embodiment of the present invention with a melt temperature of 64°C;

[0093] Figure 7 Schematic comparison diagram of the change of crystal layer growth thickness with time and experimental data under the conditions of corrected and uncorrected thermal conductivity provided for an embodiment of the present invention with a melt temperature of 70°C. Detailed implementation manners

[0094] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0095] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described here can be implemented in an order other than those illustrated or described here. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, device, product or equipment comprising a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or equipment.

[0096] Although based on the hydrodynamic simulation of the fluid flow conditions in the reactor, coupling the heat transfer equation and the phase change equation, the crystal layer distribution under different process parameters and device designs can be predicted, the numerical simulation method has a large amount of calculation, a long time consumption, and high requirements for hardware. Moreover, the existing crystal layer distribution prediction methods do not consider the influence of component concentration changes on crystallization, which will cause certain deviations in the calculation results, especially when the crystallizer is small or the impurity concentration is high, the deviation is large.

[0097] Therefore, based on the deficiencies of the existing technology, the present application proposes a faster and more efficient calculation method for melt crystallization on the basis of considering the influence of component concentration changes on crystallization, aiming to predict the crystal layer growth rate as a function of process conditions to reduce the experimental workload of developing crystallization processes.

[0098] In one embodiment of the present invention, a method for predicting a static melt crystallization process is provided. Refer to Figure 1 , the prediction method includes the following steps:

[0099] Determine the melt parameters, crystal layer parameters, and impurity mass fraction on the crystal layer surface at the current moment. The melt parameters generally include melt temperature, melt density, etc.; the crystal layer parameters generally include the temperature, thermal conductivity, density, crystal layer thickness, and heat conductivity of the crystal layer, etc.;

[0100] Based on the energy balance on the surface of the moving crystal layer, determine the equilibrium temperature on the crystal surface at the current moment according to the impurity mass fraction on the crystal layer surface;

[0101] Use a preset crystal layer growth rate model to predict the growth condition of the crystal layer within the first time period after the current moment to obtain a first growth prediction result. The crystal layer growth rate model is a functional relationship between the growth rate of the crystal layer and the melt parameters, crystal layer parameters, and equilibrium temperature on the crystal surface. The first growth prediction result includes the melt parameters, crystal layer parameters, and impurity mass fraction on the crystal layer surface at the end of the first time period;

[0102] Determine the equilibrium temperature on the crystal surface at the end of the first time period according to the impurity mass fraction on the crystal layer surface at the end of the first time period;

[0103] According to the melt parameters, crystal layer parameters, and equilibrium temperature on the crystal surface at the end of the first time period, use the preset crystal layer growth rate model to predict the growth condition of the crystal layer in the next time period.

[0104] It should be noted that there can be various preset crystal layer growth rate models. For existing crystal layer growth rate models, usually, the growth rate of the crystal layer is the dependent variable, and the melt parameters, crystal layer parameters, and equilibrium temperature on the crystal surface are the independent variables. Among them, the equilibrium temperature on the crystal surface is determined according to the melt parameters at the initial stage of crystallization.

[0105] However, as the crystallization process progresses, with the precipitation of crystals, the impurity mass fraction in the melt will also change. In this application, the time of the crystal layer growth process is discretized to obtain the impurity concentration of crystallization at different moments and update the impurity mass fraction on the crystal layer surface, and use the updated impurity mass fraction on the crystal layer surface to update the equilibrium temperature on the crystal surface to predict the growth condition of the crystal layer in the next time period, which can more accurately predict the growth condition of the crystal layer.

[0106] In one embodiment of the present invention, a crystal layer growth rate model is further provided. In this embodiment, the crystal layer growth rate model is constructed in the following manner.

[0107] Figure 2 Schematically shows a qualitative temperature distribution diagram during the crystal growth process in a static melt on the cross-section of a static melting crystallizer, where the arrow indicates natural convection. Based on the energy balance at the surface of the moving crystal layer, the following basic equation can be derived:

[0108]

[0109] Where, T cr , λ cr , ρ s and v are respectively the temperature, thermal conductivity, density and growth rate of the crystal layer, T m is the melt temperature, T eq is the equilibrium temperature of the crystal surface, t is time, Δh' is the heat that must be transferred through the crystal layer during the crystal growth process, including the heat of fusion and the heat that the solidified melt must be cooled from the melt temperature T m to the equilibrium temperature T eq of the crystal surface, h L is the convective heat transfer coefficient, r refers to the radial direction, r cf is the radius of the cold end, s is the thickness of the crystallization crystal layer, r cf + s represents the radius of the cold end plus the thickness of the crystal layer.

[0110]

[0111] Where, c p,m is the specific heat capacity of the melt.

[0112] The temperature of the crystal surface is the equilibrium temperature T eq and the mass fraction w i,eq of the impurity components on the crystal surface have the following functional relationship:

[0113]

[0114] Where, and are respectively the enthalpy of fusion and melting temperature of the crystallization compound, and R is the ideal gas constant.

[0115] According to the characteristics of the crystal fingers, determine the relationship between the temperature of the crystal layer changing with time and the crystal finger size distribution. Taking the parabolic temperature distribution changing with time in the crystal of a cylindrical crystal finger as an example, the temperature of the crystal layer is expressed as the following formula:

[0116] T cr (r, t) = a(t)·(r - r cf ) 2 + b(t)·(r - r cf ) + c(t) (4)

[0117] Differentiate equation (4) with respect to time as shown in equation (5) below, and substitute it into the one-dimensional unsteady Fourier equation. Combining the following boundary condition equations (6) and (7) to obtain the coefficients a(t), b(t), and c(t).

[0118]

[0119] T cr (r = r cf ) = T cf,w (6)

[0120] T cr (r = r cf+s ) = T eq (7)

[0121] where, T cf,w is the cold-end surface temperature, and k is the thermal diffusivity of the crystal layer.

[0122] Thus, a crystal layer growth rate model as shown in equation (8) can be obtained. This model includes an implicit equation among the growth rate of the crystal layer, the equilibrium temperature with the crystal surface, the melt temperature, the heat transfer coefficient, the mass transfer coefficient, and the physical properties:

[0123]

[0124] where, h L is the convective heat transfer coefficient, k s is the crystallization thermal conductivity (consistent with the following text), ρ s is the crystal layer density, r0 is the initial radius of the crystal layer, s(t) is the crystal layer thickness at time t, α is the thermal diffusivity, and r0 is the initial radius of the crystal layer.

[0125] Based on the implicit multi-step BDF (Backward Differentiation Formula) method, solving the implicit differential equation (8) can predict the growth condition of the crystal. This model is only based on physical equations, so the calculated crystal growth is purely predictive and does not require experimental fitting. Therefore, it is not affected by the parameters of the crystallizer and experimental parameters in the experiment, and there will be no situation where it works well in a small crystallizer but poorly in a large crystallizer.

[0126] In another embodiment of the present invention, for flat crystal fingers, the temperature varying with time in the crystal is not a parabolic distribution as described in equation (4) but a linear distribution. Therefore, the crystal layer growth rate model constructed based on the linearly distributed crystal layer temperature is different from the crystal layer growth rate model shown in equation (8).

[0127] During the crystal growth process, the impurity concentration in the melt continuously increases, and the equilibrium temperature T of the crystal surfaceeq It is directly related to the impurity mass fraction on the crystal surface, that is, the impurity concentration at the crystal interface, and will continue to decrease. Therefore, in this embodiment, based on the change in the impurity mass fraction on the crystal surface, the crystal layer growth rate model is modified as follows.

[0128] The calculation time of crystal layer growth is discretized, and each discrete time is △t. In order to solve the discrete time, the pre-constructed crystal layer growth rate model (for example, for a cylindrical cold end, the constructed model is as shown in equation (8)) is used to obtain the relationship between s and t. According to the shape of the cooling wall surface (for a cylindrical cold end, it is the side of the cold end, and for a flat cold end, it is its plane), the time of △t can be easily calculated, and the growth rate of the crystal layer in △t time can also be obtained.

[0129] The crystal layer actually crystallized includes pure target crystals and mother liquid wrapped in the crystal layer, assuming that the volume fraction occupied by the mother liquid in the crystal layer is φ. The volume fraction φ occupied by the mother liquid in the crystal can be determined in a variety of ways, one of which is to determine it by experimental measurement: after separating and removing the mother liquid in the crystal, the porosity of the crystal is measured, and the volume fraction is determined according to the porosity.

[0130] Another way is through experimental fitting: embedding the crystal layer growth rate model with the volume fraction as the unknown quantity, obtaining the actual crystal layer growth condition through experimental measurement to obtain the corresponding experimental data, and using the experimental data to fit the volume fraction in the crystal layer growth rate model, thereby obtaining the volume fraction.

[0131] The volume fraction of the mother liquid in the crystal layer is φ, then the mass of the target product crystallized in △t time is:

[0132] mc=(1-φ)·ΔV·ρ cr (9)

[0133] Where mc is the mass of the target crystal in the crystallization, △V is the crystal layer volume, i.e. the total volume of the crystallization, and ρ cr is the density of the target crystal.

[0134] The mass of the mother liquor mixed in the crystal layer or crystals is:

[0135] ml=φ·ΔV·ρ l (10)

[0136] Among them, ml is the mass of mother liquor in the crystallization, ρ l is the density of the melt.

[0137] The mass of impurities contained in the mother liquor mixed with the crystals is:

[0138] mz = ml·w i,eq (11)

[0139] Wherein, mz is the impurity mass, and w i,eq is the impurity concentration on the surface of the crystal layer.

[0140] Furthermore, the impurity mass fraction W crystallized within the time period Δt can be calculated as follows:

[0141]

[0142] Before Δt starts, i.e., at the start time of the first time period, the initial mass of the material is M ini , and the impurity mass fraction is w. Then, after Δt, the mass M of the melt is:

[0143] M = M ini - mc - ml (13)

[0144] At the end of the first time period, the remaining impurity mass fraction w i in the melt is calculated by the following formula:

[0145]

[0146] Using the newly obtained melt mass M and w i to replace the original M ini and w as the calculation parameters at the start time of the next time period for solving the crystal layer thickness s and time t in the next stage.

[0147] Specifically, using the newly obtained impurity mass fraction w i in the melt and the above formula (3) to update the equilibrium temperature on the crystal surface, and accordingly update the crystal layer parameters and melt parameters. Then, using the updated crystal layer parameters, melt parameters, and the equilibrium temperature on the crystal surface to predict the crystal layer growth condition in the second time period. Similarly, using the prediction result of the crystal layer growth condition in the second time period to update the crystal layer parameters, melt parameters, and the equilibrium temperature on the crystal surface again, and then using the updated crystal layer parameters, melt parameters, and the equilibrium temperature on the crystal surface to predict the crystal layer growth condition in the second time period again. In this way, the crystal layer growth rate model is corrected through iterative updating, and thus the crystal layer growth condition can be predicted more accurately.

[0148] It should be noted that in the above embodiments of the static melting crystallization process prediction method and the construction method of the crystal layer growth rate model, if the impurity mass fraction on the crystal layer surface at the end of the first time period is determined as the first mass fraction, then the first mass fraction is determined by the following method:

[0149] Determine the total volume of the crystallized product obtained after crystallization for the first time period according to the first growth prediction result, where the crystallized product includes crystal layers and mother liquor wrapped in the crystal layers;

[0150] Determine the volume fraction of the mother liquor in the crystallized product;

[0151] Calculate the mass fraction w of impurities in the remaining melt after crystallization for the first time period according to the volume fraction, the total volume of the crystallized product, crystal density, and melt density i And use it as the second mass fraction;

[0152] Determine the first mass fraction according to the second mass fraction. There are various possibilities for the relationship between the second mass fraction and the first mass fraction. In some embodiments, if they are close, it is determined that the second mass fraction is equal to the first mass fraction. In some other embodiments, if they are not close but have a corresponding relationship, the first mass fraction is determined according to the corresponding relationship between the two based on the second mass fraction.

[0153] For example, for the growth of completely pure crystals, preferably, the first mass fraction is calculated using the following formula:

[0154]

[0155] where w i,eq is the impurity concentration on the crystal surface, i.e., the first mass fraction, w i,L is the impurity concentration in the bulk phase, i.e., the second mass fraction, ρ L is the melt density, ρ s is the crystal density, D i,cr is the mass transfer coefficient, δ is the boundary layer thickness, G is a function of the crystal layer thickness and crystal growth rate, and e is the base of the natural logarithm.

[0156] If impurities are embedded in liquid inclusions, the impurity concentration on the crystal surface is less than that in the case of complete separation. Then, the first mass fraction is calculated using the following equation:

[0157]

[0158] where w i,eq is the impurity concentration on the crystal surface, i.e., the first mass fraction, w i,L is the impurity concentration in the bulk phase, i.e., the second mass fraction, w i,S is the mass fraction of impurities on the solid surface, i.e., the impurity content on the solid surface, ρ L is the melt density, ρ s is the crystal density, D i,cris the mass transfer coefficient, δ is the boundary layer thickness, G is a function of the crystal layer thickness and the crystal growth rate, x represents the distance from a point in the boundary layer outside the crystal layer to the crystal layer boundary, and e is the base of the natural logarithm.

[0159] In one embodiment of the present invention, 3,5-dimethylphenol is used as the target crystal, and the growth process thereof is predicted by using the static melting crystallization process prediction method provided by the present invention.

[0160] Set the impurity mass fraction w in the melt at the initial moment i,L to be 7%, the melt temperature T m to be 63 °C, and the cooling rate CR to be 8 °C / h. Figure 3 shows the relationship between the crystal layer growth thickness s and the time t obtained by respectively correcting and not correcting the impurity concentration (the first mass fraction) on the crystal surface. It can be seen that when the impurity concentration on the crystal surface is not corrected, the growth thickness of the crystal layer increases relatively fast; while after the concentration correction, the growth rate will be reduced, because the impurity concentration on the crystal surface at the interface concentration will continuously increase, and the temperature T on the crystal surface eq continually decreases. Therefore, predicting the growth of the actual crystal layer after the interface concentration correction is more accurate.

[0161] In one embodiment of the present invention, on the basis of the above 3,5-dimethylphenol embodiment, 3,3,5-trimethylcyclohexanone is used as the target crystal. The system is changed, a crystal growth rate model is established by using the physical properties of 3,3,5-trimethylcyclohexanone, and the initial volume of the crystallizer is changed. The initial volume is doubled and increased tenfold to obtain the relationship between the crystal layer thickness and the time, as Figure 4 shown. If the existing calculation model without correcting the impurity concentration is used, it is obvious that the volume of the crystallizer has no effect on the crystal growth, which is unreasonable. Figure 4 In, the curves corresponding to doubling and increasing the volume of the crystallizer by 10 times are both the curves corresponding to the corrected concentration. By comparing the curves of doubling and increasing the volume by 10 times with the original uncorrected curves, it can be seen that different volumes have an impact on the crystallization rate, mainly by affecting the equilibrium temperature through the equilibrium concentration. When the crystallizer is large enough, the impurity concentration in the mother liquor changes little with time during the entire crystallization process, and this effect can be ignored. However, when the volume of the crystallizer is small, ignoring this effect will cause a large deviation. The original calculation method will overestimate the crystallization growth rate. Only when the container volume is relatively large, the enrichment of the impurity concentration has little effect on the crystallization growth rate. When the container is relatively small, the influence of the impurity concentration on the growth rate is more obvious, and the static melting crystallization process proposed in this application can accurately predict for crystallizers of different sizes.

[0162] In addition, the size of the crystallizer also has an impact on the purity of the crystallization product, as Figure 5As shown, when the crystallizer capacity is large, the impurity concentration in the crystal layer increases slowly. However, when the crystallizer capacity is small, the impurity concentration in the crystal layer increases rapidly. But a larger crystallizer requires more manufacturing costs, has a longer crystallization time, and a lower yield. The prediction method in the static melting crystallization process proposed in this application can achieve the magnification and optimization of the static melting crystallization process by comparing crystallizers with different volumes without experiments, saving costs.

[0163] In an embodiment of the present invention, based on the above embodiment of 3,5-dimethylphenol, the thermal conductivity of the crystal layer is corrected. Set the melt temperature T m to 64 °C and the cooling rate to 6 °C / h. Because the melt temperature is low, crystallization cannot form a relatively dense crystal layer, and the thermal conductivity of the crystal layer needs to be corrected. The thermal conductivity of the crystal layer has a significant impact on the crystal growth rate in layer melting crystallization. If the crystal layer grows relatively densely, the crystallization thermal conductivity is directly used for calculation. If the crystal layer grows relatively loosely, preferably, the crystallization thermal conductivity k s is corrected to obtain the corrected crystallization thermal conductivity k s '.

[0164] k s ' = k s ·(1 - C l ) + k l ·C l

[0165] Among them, k s is the crystallization thermal conductivity, k l is the thermal conductivity of the melt, and C l is the liquid phase ratio for correction.

[0166] C l is calculated by the following formula:

[0167]

[0168] Among them, T eu is the eutectic temperature, T f is the melting point, and T cf is the cold end temperature.

[0169] Figure 6 shows the influence of whether to correct the thermal conductivity. If the thermal conductivity is not corrected, the estimated thermal conductivity of the initial crystal layer will be too high, and the crystal layer will grow faster. The result after correcting the thermal conductivity is more consistent with the experimental results.

[0170] Based on the above embodiment where the melt temperature T m is 64 °C, the melt temperature is increased to 70 °C, and the thermal conductivity of the crystal layer is corrected again. Figure 7Shows the comparison of the crystal growth rate corresponding to whether the thermal conductivity is corrected with the experimental results. It can be found that under this working condition, the fitting with the experimental results is better without correcting the thermal conductivity, indicating that the crystal layer grows more closely. By comparing with the experiment, if the model needs to be corrected, it means that the crystal layer growth rate is too fast and it is easy to incorporate more impurities in the crystal layer. If the model does not need to be corrected, it means that the growth rate is appropriate and impurities are not easily incorporated into the crystal layer. Therefore, the fastest crystal layer growth rate can be found by judging whether the model needs to be corrected.

[0171] As can be seen from the above embodiments, in order to achieve rapid and accurate calculation of melt crystallization and provide a basis for static melt crystallization scaling-up and process parameter determination, the static melt crystallization process prediction method proposed by the present invention takes into account the implicit relationship between the growth rate and natural convection, and also takes into account the change of the mother liquor impurity concentration during the crystallization process. In addition, the influence of the crystallization state on the thermal conductivity is also considered, and the model of the crystallization thickness is corrected. Without using fitting parameters, the prediction results of the static melt crystallization process prediction method proposed in this application have achieved good consistency with the experimental data. It can be used to guide the design of melt crystallizers and reduce the experimental workload for developing crystallization processes. It should be noted that the scope of application of the present invention is not limited to 3,3,5-trimethylcyclohexanone, 3,3,5-trimethylcyclohexanol and 3,5-dimethylphenol. The method provided by the present invention is also applicable to the prediction and optimization of the static melt crystallization process of other chemicals.

[0172] In an embodiment of the present invention, the present invention provides a static melt crystallization process optimization method, which uses the static melt crystallization process prediction method described in any one of the above embodiments or a combination of multiple embodiments to simulate the crystallization process under different process parameters and / or device parameters, and then obtains the crystal layer growth conditions and impurity parameters under different conditions, thereby enabling the optimization of process parameters and device parameters.

[0173] Among them, the process parameters include the cooling rate, the initial cooling temperature, the end cooling temperature, etc., and the device parameters include the cold end parameters and the crystallizer parameters.

[0174] The cold end parameters include the radius of the cooling heat exchanger and the shape of the cold end;

[0175] The crystallizer parameters include the shape of the crystallizer and the size of the crystallizer.

[0176] In an embodiment of the present invention, according to another aspect of the present invention, the present invention provides a static melt crystallization device, which includes a crystallizer and a cold end, and the shape and size of the crystallizer and the shape and size of the cold end are determined by the static melt crystallization process optimization method described in the above embodiments.

[0177] In one embodiment of the present invention, a computer-readable storage medium is provided for storing program instructions, which are configured to be called and execute the steps of the method described in any of the above embodiments.

[0178] It should be noted that the above embodiments of the static melting crystallization process optimization method, the static melting crystallization device, and the computer-readable storage medium belong to the same inventive concept. By way of reference, all the content of the embodiment of the image stitching method is incorporated into the embodiments of the static melting crystallization process optimization method, the static melting crystallization device, and the computer-readable storage medium.

[0179] The present invention has unique advantages and can accurately predict the crystal layer distribution under different process parameters and different devices. Through this innovative prediction function, it is possible to effectively avoid the repeated experiments and cumbersome scale-up development processes in the traditional R & D mode, significantly reducing the corresponding cycle and cost investment, and especially opening up a new path for the design of melting crystallizers. It is worth emphasizing that the present invention fully considers the key factor that the impurity concentration in the mother liquor gradually increases during the crystallization process. With advanced algorithms and model construction, it can not only accurately estimate the purity of the final crystallized crystals, but also simultaneously calculate the change trend of the impurity concentration in the mother liquor. In this way, there is no need to rely on a large number of repeated experiments to explore the process and equipment parameters of melting crystallization, greatly improving the R & D efficiency and saving the research time and capital costs.

[0180] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "including a..." does not exclude the presence of additional identical elements in the process, method, article or device including the element.

[0181] The above are only specific embodiments of the present application. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present application, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present application.

Claims

1. A method for predicting a static melting crystallization process, characterized in that, It includes the following steps: Determine the melt parameters, crystal layer parameters, and impurity mass fraction on the surface of the crystal layer at the current moment; Based on the energy balance on the surface of the moving crystal layer, determine the equilibrium temperature of the crystal surface at the current moment according to the impurity mass fraction on the surface of the crystal layer; Use a preset crystal layer growth rate model to predict the growth condition of the crystal layer within the first time period after the current moment to obtain a first growth prediction result. The crystal layer growth rate model is a functional relationship between the growth rate of the crystal layer, the melt parameters, the crystal layer parameters, and the equilibrium temperature of the crystal surface. The first growth prediction result includes the melt parameters, crystal layer parameters, and impurity mass fraction on the surface of the crystal layer at the end of the first time period; Determine the equilibrium temperature of the crystal surface at the end of the first time period according to the impurity mass fraction on the surface of the crystal layer at the end of the first time period; According to the melt parameters, crystal layer parameters, and equilibrium temperature of the crystal surface at the end of the first time period, use the preset crystal layer growth rate model to predict the growth condition of the crystal layer in the next time period.

2. The static melting crystallization process prediction method according to claim 1, wherein Determine the impurity mass fraction on the surface of the crystal layer at the end of the first time period as the first mass fraction. The first mass fraction is determined in the following manner: Determine the total volume of the crystallized product obtained after crystallization for the first time period according to the first growth prediction result. The crystallized product includes the crystal layer and the mother liquor wrapped in the crystal layer; Determine the volume fraction of the mother liquor in the crystallized product; Calculate the first mass fraction according to the volume fraction, the total volume of the crystallized product, the density of the crystal layer, and the melt density.

3. The static melting crystallization process prediction method according to claim 2, characterized in that Calculating the first mass fraction according to the volume fraction, the total volume of the crystallized product, the density of the crystal layer, and the melt density includes: Calculate the mass fraction w of impurities in the remaining melt after crystallization for the first period according to the volume fraction, the total volume of the crystallized substance, the crystal density, and the melt density i and use it as the second mass fraction; Determine the first mass fraction according to the second mass fraction.

4. The static melting crystallization process prediction method according to claim 3, characterized in that, Determine that the first mass fraction is equal to the second mass fraction.

5. The method for predicting a static melt crystallization process according to claim 3, wherein The first mass fraction w is calculated by the following formula i,eq :[[]]END]] where, w i,eq is the impurity concentration on the crystal surface, i.e., the first mass fraction, w i,L is the impurity concentration in the bulk phase, the second mass fraction, ρ L is the melt density, ρ s is the crystal density, D i,cr is the mass transfer coefficient, δ is the boundary layer thickness, G is a function of the crystal layer thickness and the crystal growth rate, and e is the base of the natural logarithm.

6. The method for predicting a static melting crystallization process according to claim 3, characterized in that The first mass fraction w is calculated by the following formula i,eq : Among them, w i,eq is the impurity concentration on the crystal surface, i.e., the first mass fraction, w i,L is the impurity concentration in the bulk phase, i.e., the second mass fraction, w i,S is the mass fraction of impurities on the solid surface, ρ L is the melt density, ρ s is the crystal density, D i,cr is the mass transfer coefficient, δ is the boundary layer thickness, G is a function of the crystal layer thickness and the crystal growth rate, x represents the distance from a point in the boundary layer outside the crystal layer to the crystal layer boundary, and e is the base of the natural logarithm.

7. The static melting crystallization process prediction method according to any one of claims 3 to 6, characterized in that Calculate the second mass fraction through the following formula: Among them, w i is the second mass fraction, w is the impurity mass fraction in the melt at the initial moment of the first time period, M ini is the mass of the melt at the initial moment of the first time period, M is the mass of the remaining melt after crystallization in the first time period, and mz is the impurity mass included in the crystallized substance; Calculate mz and M through the following formula: mc = (1 - φ)·ΔV·ρ cr ml = φ·ΔV·ρ l mz = ml·w i,eq M = m ini -mc - ml Among them, mc is the mass of the target crystal in the crystallized product, ml is the mass of the mother liquor in the crystallized product, mz is the mass of impurities contained in the mother liquor in the crystallized product, w i,eq is the first mass fraction, φ is the volume fraction, △V is the total volume of the crystallized product, ρ l is the density of the melt, ρ cr is the density of the target crystal.

8. The static melting crystallization process prediction method according to claim 2, wherein Determine the volume fraction in the following manner: Measure the porosity of the crystallized product after separating and removing the mother liquor in the crystallized product, and determine the volume fraction according to the porosity; and / or The crystal layer parameters include the crystallization thermal conductivity k of the crystal layer s , and further include the following steps: Without correcting the crystallization thermal conductivity k of the crystal layer in the crystal layer parameters s and / or the first mass fraction, use the preset crystal layer growth rate model to predict the growth status of the crystal layer and compare it with the experimental data. If the comparison result is a match, do not correct the crystallization thermal conductivity k s and the first mass fraction; if the comparison result is a mismatch, correct the crystallization thermal conductivity k s and / or the first mass fraction.

9. The static melting crystallization process prediction method according to claim 2, characterized in that Determine the volume fraction in the following manner: Embed the volume fraction as an unknown quantity into the crystal layer growth rate model; For the static melting crystallization process, measure the experimental data of the crystal layer growth condition; Use the experimental data to fit the volume fraction in the crystal layer growth rate model to determine the volume fraction.

10. The static melting crystallization process prediction method according to claim 1, wherein It further includes the following steps: Determine the density of the crystal layer grown within the first time period; If the density is less than a preset density, then the crystal layer thermal conductivity k of the crystal layer in the crystal layer parameters s is corrected as follows: k′ s = k s · (1 - C l ) + k l · C l where k s ′ is the corrected crystal thermal conductivity, k l is the thermal conductivity of the melt, C l is the liquid fraction for correction; Calculate C using the following formula l : Among them, T eu is the eutectic temperature, T f is the melting point, and T cf is the cold-end temperature.

11. A method for optimizing a static melt crystallization process, characterized in that, Optimize the process parameters and / or device parameters of the static melting crystallization process by using the static melting crystallization process prediction method according to any one of claims 1-10. Among them, the process parameters include the cooling rate, the initial cooling temperature, and the end cooling temperature, and the device parameters include the cold end parameters and the crystallizer parameters; The cold end parameters include the radius of the cooling heat exchanger and the shape of the cold end; The crystallizer parameters include the shape of the crystallizer and the size of the crystallizer.

12. A static melt crystallization device, characterized in that, The static melt crystallization device includes a crystallizer and a cold end, and the shape and size of the crystallizer and the shape and size of the cold end are determined by the static melt crystallization process optimization method as described in claim 11.

13. A computer-readable storage medium for storing program instructions, characterized in that, The program instructions are configured to call and execute the steps of the method as described in any one of claims 1 to 11.

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