A kinetic model modeling method for the crystallization process of isophthalic acid

Abstract

The present invention discloses a method for modeling the kinetic model of the crystallization process of purified isophthalic acid, comprising the following steps: designing a crystallization experiment, and measuring and obtaining crystallization kinetic parameters by using an intermittent dynamic method; constructing a crystallization kinetic model, and fitting the parameters in the crystallization kinetic model; obtaining crystal nucleation kinetics and growth kinetics parameters based on the crystallization kinetic parameters and the fitted crystallization kinetic model; and obtaining the variation law of crystal characteristics with crystallization time based on the crystal nucleation kinetics and growth kinetics parameters, thereby completing the crystallization kinetic modeling method of purified isophthalic acid. The crystallization kinetic model established by the present invention provides a mathematical support for constructing an industrial crystallization reactor, and has important value for the industrial development of PIA.

Description

Technical Field

[0001] The present invention belongs to the technical field of chemical reaction engineering, and particularly relates to a method for modeling the kinetic model of the crystallization process of isophthalic acid. Background Art

[0002] Isophthalic acid (PIA) is a rapidly developing raw material for organic chemical industry intermediates. It has strong heat resistance, hydrolysis resistance and chemical resistance, and can undergo polymerization, hydrogenation, halogenation and other reactions. With the rapid development of the construction industry and the continuous improvement of people's living standards, the demand for high-grade polyester coatings, unsaturated polyesters, building materials, fiberglass products and sanitary ware products prepared from PIA has increased. The copolyester market in China is still in the development stage, but the future trend of high-end market products and the progress of R & D technology will inevitably drive the development of copolyesters into high-end polyester fabrics, food packaging, heat-resistant polyester bottles and other fields. At present, the preparation of high-performance alkyd resin paints and coatings using PIA in China is still in its infancy. Replacing phthalic anhydride with PIA not only enhances the performance of the coatings, but also saves a large amount of raw material costs, meeting the development needs of green environmental protection. In addition, the raw material MX for preparing PIA is abundantly present in steam cracking gasoline and catalytic reforming oil in the petrochemical field, and the content of MX in xylene (PX, MX, OX) is the highest. Therefore, high-quality and low-cost raw material PIA can be provided for the polyester industry through the MX oxidation method.

[0003] At present, the output of PIA in China is still very small, and there are only a few production plants. In 1999, Yanshan Petrochemical Corporation successfully converted its 36,000-ton / year PTA production unit into a PIA production unit, with a production capacity of 25,000 tons / year. After capacity expansion and transformation, the annual output reached 50,000 tons.

[0004] With the rapid development of the polyester industry, the market demand for PTA (terephthalic acid) has been increasing, and domestic PTA production units have expanded rapidly. However, in recent years, the supply of PTA has far exceeded the demand, and the market demand has gradually reached saturation. At present, the market situation of PTA at home and abroad is not optimistic, which has prompted some PTA production plants to start transforming to PIA production to seek greater profit margins and ensure the normal operation of PTA production units.

[0005] Industrially, isophthalic acid is usually produced by the liquid-phase oxidation method. The raw material m-xylene (MX) is oxidized to obtain crude isophthalic acid (CIA). The liquid phase is mainly acetic acid. The oxidation product is refined through processes such as crystallization, hydrogenation, and drying to remove impurities, and finally the product is obtained. The crude isophthalic acid is obtained by the liquid-phase oxidation method, but a new solvent needs to be replaced in the subsequent refining process. Therefore, isophthalic acid needs to be precipitated from the acetic acid solvent through the crystallization process. In this process, by establishing a crystallization kinetics model, the change of the crystallization process over time can be well reflected, and the influence of conditions such as temperature on crystallization can be predicted. A good crystallization kinetics model can provide mathematical support for constructing an industrial crystallization reactor, which is of great significance for the industrial development of PIA. Summary of the Invention

[0006] In order to overcome the deficiencies in the above problems, the present invention provides a method for modeling the crystallization kinetics of purified isophthalic acid, which provides mathematical support for constructing an industrial crystallization reactor.

[0007] To achieve the above object, the present invention provides a method for modeling the crystallization kinetics of purified isophthalic acid, comprising the following steps:

[0008] Design a crystallization experiment, and measure and obtain the crystallization kinetics-related parameters by using the batch dynamic method;

[0009] Construct a crystallization kinetics model and fit the parameters in the crystallization kinetics model;

[0010] Based on the crystallization kinetics-related parameters and the fitted crystallization kinetics model, obtain the crystal nucleation kinetics and growth kinetics parameters;

[0011] Based on the crystal nucleation kinetics and growth kinetics parameters, obtain the variation law of crystal characteristics with crystallization time, and complete the method for modeling the crystallization kinetics of purified isophthalic acid.

[0012] Optionally, in the crystallization experiment, the mother liquor is a pre-prepared mixture of PIA, 3-CBA, and water.

[0013] Optionally, the ratio of PIA to water is 1:5 - 1:9;

[0014] The mass concentration of 3-CBA is 350 - 1200 ppm.

[0015] Optionally, the temperature change range during the reaction process in the crystallization experiment is 220 - 150 °C.

[0016] Optionally, the stirring rate during the cooling crystallization process in the crystallization experiment is 100 - 200 ppm.

[0017] Optionally, the crystallization kinetics model includes a nucleation term equation and a growth term equation.

[0018] Optionally, the nucleation term equation B is constructed based on the classical crystal nucleation theory, and the expression of the nucleation term equation B is:

[0019]

[0020] where A is the rate constant of the nucleation process, σ is the surface tension, V m is the molar volume of the crystal, R is the gas constant, T is the temperature, and S is the solution supersaturation ratio;

[0021] The growth term equation G is constructed based on the power-law growth kinetics equation, and the expression of the growth term equation G is:

[0022]

[0023] where k is the rate constant of the growth process, g is the growth order, E g is the activation energy of the growth process, and S is the solution supersaturation ratio.

[0024] Optionally, the parameter in the crystallization kinetics model is the equilibrium concentration of purified isophthalic acid;

[0025] The method for fitting the equilibrium concentration of purified isophthalic acid includes:

[0026] Fitting the equilibrium concentration of purified isophthalic acid using the Apelblat equation and performing a third moment conversion;

[0027] where the Apelblat equation is:

[0028]

[0029] where w is the mass solubility and T is the solution temperature;

[0030] The converted expression is:

[0031]

[0032] where w is the mass solubility, w ini is the initial value of the mass solubility, m 3 is the third moment, with the unit of m 3 / kg; ρ c is the density of PIA, with the unit of kg / m 3 ; ρ L is the density of the solvent, with the unit of kg / m 3 , K V is the coefficient of variation, with the unit of kg / kg.

[0033] Optionally, the crystal kinetics related parameters are:

[0034] Θ = {A, σ, k, E g , g, L 0};

[0035] wherein, A is the rate constant of the nucleation process, g is the growth order, k is the rate constant of the growth process, E g is the activation energy of the growth process, L 0 is the critical crystal radius, and σ is the surface tension.

[0036] Optionally, the method for obtaining the crystal nucleation kinetics and growth kinetics parameters is as follows:

[0037] Substitute the crystallization kinetics parameters into the fitted crystallization kinetics model, and use the unconstrained optimization method to construct an objective function to obtain the crystal nucleation kinetics and growth kinetics parameters;

[0038] The expression of the objective function is:

[0039]

[0040] wherein, N e is the total number of experimental points, N j is the total number of moments, m i,j is each order moment, and the variables m i,j and represent the measured and predicted moments of each order.

[0041] Compared with the prior art, the present invention has the following advantages and technical effects:

[0042] The crystallization kinetics model established by the present invention can more accurately reflect the change curve of particle size with time during the crystallization process, and can quantitatively describe the change of particle size with time under industrial temperature and supersaturation, so as to guide the design of industrial reactors, the optimization of production operation conditions and the optimization of production processes, solve the problem that the PIA crystallization process is difficult to predict in the prior art, provide a design basis for the existing crystallizer design, and have great guiding significance for the industrial PIA refining process. The modeling method of the present invention is applicable to different types of isophthalic acid crystallization processes and has wide applicability. Description of the Drawings

[0043] The drawings constituting a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

[0044] Figure 1Schematic flow chart of a method for modeling the kinetic model of the crystallization process of purified isophthalic acid in an embodiment of the present invention;

[0045] Figure 2 Schematic diagram showing the relationship between the crystal characteristic particle size and the crystallization time in the crystallization process in an embodiment of the present invention;

[0046] Figure 3 Schematic diagram showing the change of supersaturation with crystallization time in the crystallization process in an embodiment of the present invention;

[0047] Figure 4 Schematic diagram showing the change of the number of particles with crystallization time in the crystallization process in an embodiment of the present invention;

[0048] Figure 5 Schematic diagram showing the change of the growth rate with crystallization time in the crystallization process in an embodiment of the present invention;

[0049] Figure 6 Schematic diagram showing the change of the nucleation rate with crystallization time in the crystallization process in an embodiment of the present invention. Detailed implementation manners

[0050] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the drawings and in conjunction with the embodiments.

[0051] It should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a set of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0052] Embodiment

[0053] As Figure 1 shown, this embodiment provides a method for modeling the kinetic model of the crystallization process of purified isophthalic acid, which specifically includes:

[0054] Design a crystallization experiment, and measure and obtain the crystallization kinetic parameters by using the batch dynamic method;

[0055] In the crystallization experiment, the mother liquor is a pre-prepared mixture of PIA, 3-CBA and water; the ratio of PIA to water is 1:5 - 1:9; the mass concentration of 3-CBA is 350 - 1200 ppm; the temperature change range of the reaction process in the crystallization experiment is 220 - 150 °C; the stirring rate during the cooling crystallization process in the crystallization experiment is 100 - 200 ppm.

[0056] In this embodiment, the specific crystallization experiment process is as follows:

[0057] (1) According to PIA: The ratio of water is 1:7, and then add 3-CBA (1000 ppm) for preparation. Under this solvent ratio condition, carry out the crystallization kinetics experiment. First, completely dissolve the raw materials at 220 °C to simulate the situation at the end of industrial hydrofining.

[0058] (2) For the crystallization raw materials in the reaction kettle, adjust the stirring rate to 150 rpm to keep the crystals in a completely suspended state. Control the kettle temperature at about 220 °C and stabilize it. Take samples three times, which is used as the starting point of the crystallization experiment, and set the cooling program.

[0059] (3) Start the cooling program. When the kettle temperature enters the cooling stage, start timing. Use a special sampler to take samples every 15 minutes. Send the mother liquor for analysis of its composition. After the solid phase is fully dried, take a part of it for analysis of particle size and a part for analysis of composition.

[0060] Construct a crystallization kinetics model and fit the parameters in the crystallization kinetics model; the crystallization kinetics model includes a nucleation term equation and a growth term equation.

[0061] In this embodiment, due to the batch crystallization process, there is no fluid mass exchange in the crystallizer, and the crystal disappearance term is ignored. The PBE model can be simplified to:

[0062]

[0063] Among them, n is the relationship between the crystal radius L and time t, t is the time, and L is the crystal radius;

[0064] From the definition of the method of moments:

[0065]

[0066] Among them, m k is the definition of the moment, k is the order, L is the crystal radius, n is the relationship between the crystal radius L and time t, and dL is the derivative with respect to the crystal radius;

[0067] The change equation of the moment can be deduced:

[0068]

[0069] Among them, dm k (t) is the derivative of the moment definition at time t, B(t) is the nucleation correlation formula, L 0 is the critical crystal radius, k is the order, G(t) is the growth correlation formula, and m k-1 (t) is the k - 1 order moment at time t;

[0070] To make the equation closed, intercept the first four moment equations and supplement them with the mass balance equation to solve:

[0071]

[0072] Among them, m 0 -m 3 are the 0th to 3rd order moments respectively;

[0073] Based on the classical crystal nucleation theory, the nucleation term equation is:

[0074]

[0075] Among them, A is the rate constant of the nucleation process, σ is the interfacial tension between the solid and liquid phases, V m is the molar volume of the crystal, m 3 / mol, R is the gas constant, taking 8.3145 J / mol·K, T is the temperature, and S is the solution supersaturation ratio;

[0076] Based on the power-law growth kinetic equation, the growth term equation is:

[0077]

[0078] Among them, k is the rate constant of the growth process, g is the growth order, E g is the activation energy of the growth process, and S is the solution supersaturation ratio;

[0079] The equilibrium concentration of PIA is fitted using the Apelblat equation, as shown in the formula:

[0080]

[0081] The concentration of PIA in the crystallizer can be obtained by converting the third-order moment, as shown in the formula:

[0082]

[0083] Among them, m 3 is the third-order moment, with the unit of m 3 / kg; ρ c is the density of PIA, with the unit of kg / m 3 ; ρ L is the density of the solvent, with the unit of kg / m 3 , K V is the coefficient of variation, with the unit of kg / kg, w ini is the initial value of the mass solubility, w is the mass solubility, m 3ini is the initial value of the third-order moment;

[0084] Based on the crystallization kinetic parameters and the fitted crystallization kinetic model, the crystal nucleation kinetics and growth kinetics parameters are obtained.

[0085] In this embodiment, first, the unknown crystallization kinetic parameters, namely the crystal kinetic related parameters, are determined, and then the objective function is selected for solution to obtain the crystal nucleation kinetics and growth kinetics parameters. Specifically:

[0086] Solve in Matlab. First, simulate the batch cooling crystallization process under a certain cooling curve, and transform the particle size distribution at each sampling point into the moment transformation of each order. Use the ode45 equation to solve the system of ordinary differential equations. The moment amounts at each sampling point can be obtained.

[0087] For each unknown crystallization kinetic parameter, namely the crystal kinetic related parameter Θ = {A, σ, k, E g , g, L 0}, an unconstrained optimization method is used to construct the objective function as shown in the formula:

[0088]

[0089] Among them, N e is the total number of experimental points, N j is the total number of moment amounts, m i,j is the moment of each order, and the variables m i,j and represent the measured and predicted moment amounts of each order.

[0090] Using the Matlab optimization toolbox, the simplex transformation method is used for least squares parameter estimation of the formula to solve the crystal kinetic related parameters, and then the crystal nucleation kinetics and growth kinetics parameters A, σ, k, E g , g, as shown in Table 1, the table of crystal nucleation kinetics and growth kinetics parameters.

[0091] Table 1

[0092]

[0093] Based on the crystallization kinetic parameters and the fitted crystallization kinetic model, the crystal nucleation kinetics and growth kinetics parameters are obtained.

[0094] In this embodiment, according to the nucleation kinetics and growth kinetics parameter data, the relationship between the crystal growth characteristic particle size and other characteristics changing with time can be obtained, such as Figures 2 - 6 shown.

[0095] The change of the characteristic particle size shows a trend of first increasing and then decreasing, presenting a mountain-shaped change, which is similar to the experimental results. The main reason for showing the mountain-shaped characteristic is that the growth rate gradually decreases with the change of crystallization time, while the nucleation rate remains almost unchanged. In the later stage of crystallization, a large number of very small crystal nuclei are generated, but the growth is very slow, resulting in the phenomenon that the characteristic particle size of the crystal first increases and then slowly decreases.

[0096] Meanwhile, since the change value of supersaturation is small, the nucleation rate of the system changes little and is basically a fixed value. For the growth rate, the growth rate of the system is faster under high supersaturation and slower under low supersaturation. Therefore, it can be judged that supersaturation is the main factor affecting the crystal nucleation and growth process. In industry, the most common methods to change supersaturation are to change temperature and pressure. When the cooling rate or pressure reduction rate is too fast, it is extremely easy to cause a large fluctuation of supersaturation beyond the metastable zone, generating a large number of fine crystals and resulting in a decrease in particle size. However, too low cooling and pressure reduction rates are not conducive to actual production operations and increase production costs.

[0097] Therefore, from nucleation kinetics and growth kinetics, if it is necessary to grow crystals of a larger size, the solution supersaturation can be appropriately increased, and crystal cultivation and growth can be carried out under low supersaturation. In addition, the crystal growth rate can be accelerated by enhancing mass transfer in the system.

[0098] The kinetic model in the present invention can guide the design of actual crystallizers in industry. For example, the kinetic parameters of the nucleation term and growth term obtained by the modeling method are used for kinetic model calculation. Specifically, kinetic parameters are obtained through laboratory experiments, and the actual crystallization process in industry can be predicted based on the obtained kinetic parameters, that is, how the changes in parameters such as temperature or supersaturation will affect the final crystallization, and adjustments can be made in combination with the actual situation.

[0099] As mentioned above, the above are only the preferred specific embodiments of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for modeling the kinetic model of the isophthalic acid crystallization process, characterized in that, it includes the following steps, design a crystallization experiment, and measure and obtain the kinetic parameters related to crystallization by using the batch dynamic method; construct a crystallization kinetic model and fit the parameters in the crystallization kinetic model; based on the crystallization kinetic parameters and the fitted crystallization kinetic model, obtain the crystal nucleation kinetics and growth kinetics parameters; obtain the variation law of crystal characteristics with crystallization time based on the crystal nucleation kinetics and growth kinetics parameters, and complete the kinetic modeling method of isophthalic acid crystallization; in the crystallization experiment, the mother liquor is a pre-prepared mixture of PIA, 3-CBA and water; the crystallization kinetic model includes a nucleation term equation and a growth term equation; construct the nucleation term equation B based on the classical crystal nucleation theory, and the expression of the nucleation term equation B is: where A is the rate constant of the nucleation process, σ is the surface tension, V m is the molar volume of the crystal, R is the gas constant, T is the temperature, and S is the solution supersaturation ratio; construct the growth term equation G based on the power-law growth kinetic equation, and the expression of the growth term equation G is: where k is the rate constant of the growth process, g is the growth order, and E g is the activation energy of the growth process; the parameter in the crystallization kinetic model is the equilibrium concentration of isophthalic acid; the method for fitting the equilibrium concentration of isophthalic acid includes: fit the equilibrium concentration of isophthalic acid by using the Apelblat equation and perform third-moment conversion; wherein, the Apelblat equation is: wherein, w is the mass solubility and T is the solution temperature; the converted expression is: Among them, w is the mass solubility, w ini is the initial value of the mass solubility, m 3 is the third moment, with the unit of m 3 / kg; ρ c is the density of PIA, with the unit of kg / m 3 ; ρ L is the density of the solvent, with the unit of kg / m 3 , K V is the coefficient of variation, with the unit of kg / kg; the method for obtaining the crystal nucleation kinetics and growth kinetics parameters is: substitute the crystallization kinetic parameters into the fitted crystallization kinetic model, and construct an objective function by using the unconstrained optimization method to obtain the crystal nucleation kinetics and growth kinetics parameters; the expression of the objective function is: Among them, N e is the total number of experimental points, N j is the total number of moments, m i,j is each order moment, the variable m i,j and m i,j are the measured and predicted moments of each order respectively.

2. The method for modeling the kinetic model of the isophthalic acid crystallization process according to claim 1, characterized in that, the ratio of PIA to water is 1:5 - 1:9; the mass concentration of 3-CBA is 350 - 1200 ppm.

3. The method for modeling the kinetic model of the isophthalic acid crystallization process according to claim 2, characterized in that, the temperature change range of the reaction process in the crystallization experiment is 220 - 150 °C.

4. The method for modeling the kinetic model of the isophthalic acid crystallization process according to claim 3, characterized in that, the stirring rate during the cooling crystallization process in the crystallization experiment is 100 - 200 rpm.

5. The method for modeling the kinetic model of the isophthalic acid crystallization process according to claim 1, characterized in that, the crystallization kinetic parameters are: Θ = {A, σ, k, E g , g, L 0}; where A is the rate constant of the nucleation process, g is the growth order, k is the rate constant of the growth process, E g is the activation energy of the growth process, L 0 is the critical crystal radius, and σ is the surface tension.

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