A design of experiment method suitable for high viscosity polymerization temperature gradient correction

Abstract

The application provides a design method for high-viscosity polymerization reaction temperature gradient correction, uses a reaction calorimeter to carry out styrene bulk thermal polymerization experiment under constant temperature conditions, and obtains the temperature change measured by a thermocouple and the average temperature change of the system. The changes of reaction parameters such as the viscosity, specific heat capacity and density of the mixture are obtained by consulting literatures. Then, a relationship between the temperature difference between the temperature measured by the thermocouple and the average temperature of the system and the Reynolds number Re and the Prandtl number Pr is established, and the heat balance equation under the high-viscosity system is further improved. By using the corrected heat balance model, the average temperature of the polymerization system can be effectively described. The method can correct the deviation introduced by a single temperature monitoring point, has good application value for the study of polymerization reaction thermal safety problems, effectively prevents the polymerization from running out of control due to uneven temperature distribution, and thus provides guidance for safety control and process parameter optimization.

Description

Technical Field

[0001] This invention belongs to the technical field of correcting temperature gradients in polymerization reactions, and specifically relates to an experimental design method suitable for correcting temperature gradients in high-viscosity polymerization reactions. Background Technology

[0002] Polymerization is an important type of chemical reaction, widely used in the production of materials such as plastics and adhesives. Its products possess excellent properties such as lightweight, strong plasticity, corrosion resistance, and high elasticity. However, polymerization reactions typically exhibit strong exothermic characteristics, posing a high thermal risk, especially bulk polymerization. Styrene polymerization is a typical example of bulk polymerization. During polymerization, as the reaction proceeds, the polymer chains continuously elongate, leading to a significant increase in the system's viscosity. Increased viscosity hinders efficient heat transfer, resulting in heat accumulation and causing uneven temperature distribution and gradients within the system. This creates hot spots in localized areas and exacerbates thermal runaway.

[0003] Temperature deviations of varying degrees are unavoidable in polymerization systems. Traditional calorimetric methods are prone to disrupting the thermal equilibrium of exothermic polymerization reactions. Therefore, ensuring that the temperature changes detected by thermocouples represent the overall temperature state of the reactant is crucial. In fact, the average temperature is the most accurate indicator of the global temperature state. However, the inability to precisely pinpoint the location representing the average temperature in an actual reactor, coupled with limitations on thermocouple installation and movement, makes accurate average temperature measurement even more challenging. Judging the reaction extent based on data from thermocouples at arbitrary locations is somewhat unreliable and can lead to inappropriate or untimely safety measures. Therefore, heat transfer correction for deviations between thermocouple-measured temperatures and the average temperature is essential. Summary of the Invention

[0004] To address the problems existing in the prior art, the purpose of this invention is to provide a method for establishing a temperature difference equation between the temperature measured by a thermocouple and the average temperature through a reaction calorimeter experiment, and for correcting the temperature rise difference in the polymerization system by combining it with a heat balance equation. This method can improve the efficiency and safety of the polymerization reaction.

[0005] Firstly, an experimental design method suitable for correcting the temperature gradient in high-viscosity polymerization reactions is provided. This experimental design method utilizes a reaction calorimeter, which includes a thermocouple and a stirring paddle.

[0006] Step 1: Install at least three temperature monitoring points around the thermocouple of the reaction calorimeter;

[0007] Step 2: After raising the wall of the reaction calorimeter to the target temperature, styrene is added to carry out a constant-temperature thermal polymerization reaction, and the temperature difference between the thermocouple temperature at each time point and the average temperature of the system is obtained.

[0008] Step 3: Using a multivariate nonlinear fitting method, construct the mathematical equations relating the temperature difference to the dimensionless numbers Re and Pr throughout the entire reaction process;

[0009] Step 4: Based on the mathematical equation, after correcting the temperature measured by the thermocouple to the average temperature of the system, substitute it together with the actual values ​​of the physical properties of the reactants into the heat balance equation of the polymerization reaction to calculate the corrected average temperature rise of the system.

[0010] Furthermore, the heat balance equation is shown in the following formula:

[0011] mC p (T t+1 -T t )+KA[(T rdo -ΔT)-T j ]Δt=VΔHRΔt

[0012] In the formula, m is the reaction mass (kg); C p It is specific heat capacity, J·kg -1 ·K -1 K is the overall heat transfer coefficient, W·m -2 ·K -1 A is the reaction area, in meters. 2 ;T rdo ΔT is the temperature measured by the thermocouple; ΔT is the temperature difference between the thermocouple temperature at each time point and the average temperature of the system; T j V is the jacket temperature, in K; V is the reaction volume, in m³. 3 ΔH is the enthalpy of polymerization, 7.1 × 10⁻⁶. 4 J·mol -1 R is the polymerization rate, mol·m -3 ·s -1 ;(T t+1 -T t ) represents the temperature rise of the system, in K; Δt is the time interval recorded in the experiment, in s.

[0013] Furthermore, the amount of styrene added should be selected according to the size of the reaction calorimeter, and the volume of styrene should not exceed 2 / 3 of the reactor volume.

[0014] Furthermore, at least three temperature monitoring points are installed around the thermocouple of the reaction calorimeter. The thermocouple is located on one side of the stirring shaft, the first temperature monitoring point is located directly below the thermocouple, and the distance between the two is 5-10 mm. The second and third temperature monitoring points are located on the other side of the stirring shaft, and the distances from them to the stirring shaft are the same as the distances from the thermocouple to the stirring shaft, which are 20-25 mm. The height difference between the second temperature monitoring point and the thermocouple is 5-8 mm, and the distance between the third temperature monitoring point and the second temperature monitoring point is 23-28 mm.

[0015] Furthermore, after raising the wall temperature of the reaction calorimeter to 80℃-130℃, styrene was added to carry out a constant-temperature thermal polymerization reaction, and the stirring speed was set to 50-250 rpm.

[0016] Furthermore, the temperature difference between the temperature measured by the thermocouple and the average temperature of the system is obtained. The average temperature of the system refers to the average of the temperatures obtained from the three temperature monitoring points and the thermocouple as the average temperature of the system of the reactants.

[0017] Furthermore, the temperature monitoring point is a temperature sensor or a thermocouple.

[0018] Furthermore, using a multivariate nonlinear fitting method, a mathematical equation is constructed relating the temperature difference to the dimensionless Reynolds number (Re) and Prandtl number (Pr) throughout the reaction process. The specific steps are as follows:

[0019] In a reaction calorimeter, Re is defined as:

[0020]

[0021] In the formula, N is the stirring speed (rps), D is the maximum distance between the two ends of the stirring blades (m), and ρ is the density of the reactant (kg·m³). -3 μ is the viscosity of the reactant, in Pa·s;

[0022] The expression for Pr is:

[0023]

[0024] In the formula, λ is the thermal conductivity of the reactant, W·m -1 ·K -1 ;

[0025] Through derivation, a multivariate nonlinear fitting was performed on the temperature difference between the thermocouple-measured temperatures at each time point and the system average temperature, which are exponential functions of Re and Pr, to obtain the mathematical equation between the temperature difference and the dimensionless numbers Re and Pr:

[0026] ΔT=f(Re a ,Pr b ).

[0027] Furthermore, the overall heat transfer coefficient K is expressed as:

[0028]

[0029] In the formula, α i and α o These are the convective heat transfer coefficients inside and outside the wall of the reaction calorimeter, respectively, in W·m. -2 ·K -1 .

[0030] Compared with the prior art, the advantages of the present invention are as follows: the present invention can correct the deviation of a single temperature monitoring point through the modified thermal balance model, improve the safety control effect of styrene polymerization, show that the thermocouple position is crucial for monitoring high viscosity polymerization, and guide temperature monitoring. It has good application value for the study of thermal safety issues in polymerization reactions and effectively prevents polymerization runaway caused by uneven temperature distribution. Attached Figure Description

[0031] Figure 1 This is a diagram showing the relative locations of the temperature monitoring points.

[0032] Figure 2 This is a comparison graph showing the changes in measured thermocouple temperature and average temperature.

[0033] Figure 3 The results of the multivariate nonlinear fitting are shown in the figure. (a) Re < 50, (b) 50 < Re < 1000.

[0034] Figure 4 This is a comparison chart of the measured average temperature and the average temperature calculated based on the modified thermal balance model. Detailed Implementation

[0035] The present invention will be further described below with reference to the accompanying drawings.

[0036] The experimental design method for correcting temperature gradients in high-viscosity polymerization reactions described in this invention employs a reaction calorimeter, which includes a built-in thermocouple and a stirring paddle.

[0037] Step 1: Install at least three temperature sensors around the thermocouple of the reaction calorimeter. The thermocouple is located on one side of the stirring shaft. The first temperature sensor is located directly below the thermocouple, with a distance of 5-10 mm between them. The second and third temperature sensors are located on the other side of the stirring shaft, with the distances from them to the stirring shaft being the same as the distances from the thermocouple to the stirring shaft, which is 20-25 mm. The height difference between the second temperature sensor and the thermocouple is 5-8 mm, and the distance between the third temperature sensor and the second temperature sensor is 23-28 mm.

[0038] Step 2: After raising the wall temperature of the reaction calorimeter to 80℃-130℃, add styrene to carry out a constant-temperature thermal polymerization reaction. Set the stirring speed of the stirrer to 50-250 rpm. Select the amount of styrene to be added according to the size of the reaction calorimeter. The volume of styrene should not exceed 2 / 3 of the reactor volume. Obtain the temperature difference between the temperature measured by the thermocouple at each time point and the average temperature of the system. The average temperature of the system refers to the average of the temperatures obtained by the three temperature sensors and the thermocouple as the average temperature of the system of the reactants.

[0039] Step 3: Using a multivariate nonlinear fitting method, construct the mathematical equations relating the temperature difference to the dimensionless numbers Re and Pr throughout the entire reaction process. The specific steps are as follows:

[0040] In a reaction calorimeter, Re is defined as:

[0041]

[0042] In the formula, N is the stirring speed (rps), D is the maximum distance between the two ends of the stirring blades (m), and ρ is the density of the reactant (kg·m³). -3 μ is the viscosity of the reactant, in Pa·s;

[0043] The expression for Pr is:

[0044]

[0045] In the formula, λ is the thermal conductivity of the reactant, W·m -1 ·K -1 ;

[0046] Through derivation, a multivariate nonlinear fitting was performed on the temperature difference between the thermocouple-measured temperatures at each time point and the system average temperature, which are exponential functions of Re and Pr, to obtain the mathematical equation between the temperature difference and the dimensionless numbers Re and Pr:

[0047] ΔT=f(Re a ,Pr b (3)

[0048] Step 4: Based on the mathematical equation, substitute the temperature measured by the thermocouple into formula (3) to obtain the corrected average system temperature. Then, substitute this temperature along with the actual values ​​of the physical properties of the reactants into the heat balance equation for the polymerization reaction, i.e., formula (4), to calculate the corrected average temperature rise of the system. The relevant reaction parameter data in the formula are obtained through experimental monitoring and calculation, as well as by consulting literature. Subsequently, the average value within Δt is taken and substituted into the calculation. Finally, the corrected average temperature rise of the system is compared with the experimental data to verify its reliability.

[0049] The heat balance equation is shown in formula (4):

[0050] mC p (T t+1 -T t )+KA[(T rdo -ΔT)-T j ]Δt=VΔHRΔt (4)

[0051] In the formula, m is the reaction mass (kg); C p It is specific heat capacity, J·kg -1 ·K -1 K is the overall heat transfer coefficient, W·m -2 ·K -1 A is the reaction area, in meters. 2 ;T rdo ΔT is the temperature measured by the thermocouple; ΔT is the temperature difference between the thermocouple temperature at each time point and the average temperature of the system; T j V is the jacket temperature, in K; V is the reaction volume, in m³. 3 ΔH is the enthalpy of polymerization, 7.1 × 10⁻⁶. 4 J·mol -1 R is the polymerization rate, mol·m -3 ·s -1 ;(T t+1 -T t ) represents the temperature rise of the system, in K; Δt is the time interval recorded in the experiment, in s.

[0052] Equation (4) is the extended heat balance equation, which is obtained by extending equation (5) below:

[0053]

[0054] Where dT / dt is the temperature rise change; T r This is the reaction temperature, K. At this point, the units for the three heat parameters are unified, all in J. Δt is the time interval recorded in the experiment, which is 0.5–1 s. Ignoring the thermal resistance of the reaction calorimeter wall, the overall heat transfer coefficient K is expressed as:

[0055]

[0056] In the formula, α i and α o These are the convective heat transfer coefficients inside and outside the wall of the reaction calorimeter, respectively, in W·m. -2 ·K -1 .

[0057] Example

[0058] Using the RC1e reaction calorimeter manufactured by Mettler Toledo as an example, this paper illustrates a method for correcting the temperature gradient of a styrene polymerization system based on RC1e experiments and combined with a heat balance model.

[0059] Step 1: Prepare 160g of styrene, with a volume of 178cm³ at room temperature. 3 And three additional temperature monitoring points are installed in the RC1e, such as Figure 1 ;

[0060] Step 2: The RC1e wall temperature was raised to 120°C, and styrene was added for a thermal polymerization reaction under constant temperature conditions of 120°C. The stirring speed was 100 rpm, and the highest temperature measured by the thermocouple was 158°C. The temperature difference curve between the temperature of the RC1e wall and the average temperature of the system was obtained. The experimental temperature curve is shown below. Figure 2 ;

[0061] Step 3: Using a multivariate nonlinear fitting method, the equation expression (1) between the temperature difference and the dimensionless numbers Re and Pr during the entire reaction process at a stirring speed of 100 rpm was established. The fitting results are as follows: Figure 3 :

[0062] ΔT=Re -2.445 Pr -0.1051 Re<50

[0063] ΔT=Re -0.9002 Pr -0.2746 50 < Re < 1000

[0064] ΔT≈0 Re>1000 (1)

[0065] Step 4: The corrected T r Substituting the actual values ​​of the physical properties of the reactants into the heat balance equation of the polymerization reaction, the corrected average temperature rise of the system is calculated and compared with the actual average value. The heat balance equation is shown in formula (2), where Δt is 0.5 s:

[0066] mC p (T t+1 -T t )+KA[(T rdo -ΔT)-T j ]Δt=VΔHRΔt (2)

[0067] Figure 4 To correct the results and compare them with the experiment, R 2 The value was 0.99, which is basically consistent with the data, verifying the reliability of the correction system.

Claims

1. An experimental design method suitable for correcting the temperature gradient in high-viscosity polymerization reactions, wherein the experimental design method is performed using a reaction calorimeter, the reaction calorimeter comprising a thermocouple and a stirring paddle, characterized in that, include: Step 1: Install at least three temperature monitoring points around the thermocouple of the reaction calorimeter; Step 2: After raising the wall of the reaction calorimeter to the target temperature, add styrene to carry out a constant-temperature thermal polymerization reaction, and obtain the temperature difference between the temperature measured by the thermocouple at each time point and the average temperature of the system. Step 3: Using a multivariate nonlinear fitting method, construct the mathematical equations relating the temperature difference to the dimensionless numbers Re and Pr throughout the entire reaction process; Step 4: Based on the mathematical equation, after correcting the temperature measured by the thermocouple to the average temperature of the system, substitute it together with the actual values ​​of the physical properties of the reactants into the heat balance equation of the polymerization reaction to calculate the corrected average temperature rise of the system.

2. The experimental design method as described in claim 1, characterized in that, The heat balance equation is shown in the following formula: mC p (T t+1 -T t )+KA[(T rdo -ΔT)-T j ]Δt=VΔHRΔt In the formula, m is the reaction mass (kg); C p It is specific heat capacity, J·kg -1 ·K -1 K is the overall heat transfer coefficient, W·m -2 ·K -1 ; A is the reaction area, m 2 ; T rdo ΔT is the temperature measured by the thermocouple; ΔT is the temperature difference between the thermocouple temperature at each time point and the average temperature of the system; T j V is the jacket temperature, in K; V is the reaction volume, in m³. 3 ΔH is the enthalpy of polymerization, 7.1 × 10⁻⁶. 4 J·mol -1 R is the polymerization rate, mol·m -3 ·s -1 ;(T t+1 -T t ) represents the temperature rise of the system, in K; Δt is the time interval recorded in the experiment, in s.

3. The experimental design method as described in claim 1, characterized in that, The amount of styrene added should be selected according to the size of the reaction calorimeter, and the volume of styrene should not exceed 2 / 3 of the reactor volume.

4. The experimental design method as described in claim 1, characterized in that, At least three temperature monitoring points are installed around the thermocouple in the reaction calorimeter. The thermocouple is located on one side of the stirring shaft, the first temperature monitoring point is located directly below the thermocouple, and the distance between the two is 5-10 mm. The second and third temperature monitoring points are located on the other side of the stirring shaft, and the distances from the second and third temperature monitoring points to the stirring shaft are the same as the distances from the thermocouple to the stirring shaft, which are 20-25 mm. The height difference between the second temperature monitoring point and the thermocouple is 5-8 mm, and the distance between the third temperature monitoring point and the second temperature monitoring point is 23-28 mm.

5. The experimental design method as described in claim 1, characterized in that, After raising the wall temperature of the reaction calorimeter to 80℃-130℃, styrene was added to carry out a constant-temperature thermal polymerization reaction, and the stirring speed was set to 50-250 rpm.

6. The experimental design method as described in claim 1, characterized in that, The temperature difference between the temperature measured by the thermocouple and the average temperature of the system is obtained. The average temperature of the system refers to the average of the temperatures obtained from the three temperature monitoring points and the thermocouple.

7. The experimental design method as described in claim 1, characterized in that, Temperature monitoring points are temperature sensors or thermocouples.

8. The experimental design method as described in claim 1, characterized in that, Using a multivariate nonlinear fitting method, a mathematical equation relating the temperature difference to the dimensionless numbers Re and Pr during the entire reaction process is constructed. The specific steps are as follows: In a reaction calorimeter, Re is defined as: In the formula, N is the stirring speed (rps), D is the maximum distance between the two ends of the stirring blades (m), and ρ is the density of the reactant (kg·m³). -3 μ is the viscosity of the reactant, Pa·s; The expression for Pr is: In the formula, λ is the thermal conductivity of the reactant, W·m -1 ·K -1 ; Through derivation, a multivariate nonlinear fitting was performed on the temperature difference between the thermocouple-measured temperatures at each time point and the system average temperature, which are exponential functions of Re and Pr, to obtain the mathematical equation between the temperature difference and the dimensionless numbers Re and Pr: ΔT=f(Re a ,Pr b )。 9. The experimental design method as described in claim 2, characterized in that, The overall heat transfer coefficient K is expressed as: In the formula, α i and α o These are the convective heat transfer coefficients inside and outside the wall of the reaction calorimeter, respectively, in W·m. -2 ·K -1 .

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