Conversion rate prediction and parameter self-correction method for coaxial double-agitated reactor polymerization

Abstract

This application provides a method for predicting the conversion rate and self-correcting parameters of polymerization reactions in a coaxial dual-stirred reactor, relating to the fields of intelligent manufacturing and chemical process control. The method includes: synchronously acquiring real-time torque and current components of the inner and outer shaft drive motors of the reactor, real-time speed of the stirrer, and real-time material temperature; preprocessing the acquired signals; performing a cross-product operation on the preprocessed current and speed, obtaining a dimensionless characteristic ratio after geometric normalization, and collecting its average value during the induction period as a benchmark value; calculating the cumulative deviation of the dimensionless characteristic ratio relative to the benchmark value, taking the moment when the inner shaft current first shows a sustained upward trend as the starting point of the reaction timing; calculating the diffusion limitation coefficient based on the cumulative deviation and the diffusion sensitivity coefficient, wherein the diffusion sensitivity coefficient is adaptively calibrated by the average cumulative deviation within the initial linear interval and the target initial diffusion limitation coefficient; calculating the predicted conversion rate of the polymerization reaction based on the real-time temperature and the diffusion limitation coefficient; and controlling the termination time of the polymerization reaction according to the predicted conversion rate. This invention utilizes existing motor signals from the reactor to achieve online prediction of the polymerization reaction conversion rate, offering advantages such as strong anti-interference capability and adaptability to batch differences.

Description

Technical Field

[0001] This invention relates to the fields of intelligent manufacturing and chemical process control, and in particular to a method for predicting the conversion rate and self-correcting parameters of polymerization reactions in a coaxial double-stirred reactor. Background Technology

[0002] Online monitoring of polymerization conversion has always been a classic challenge in the field of polymer chemistry. In industrial practice, technicians typically rely on two approaches to solve this problem. The first approach is from the perspective of chemical reaction, measuring temperature, pressure, and heat of reaction, and then calculating the conversion rate by combining this with kinetic equations. This method is theoretically consistent, but difficult to implement in industrial applications. In the middle and later stages of polymerization, a gel effect occurs, causing a sharp increase in system viscosity. The diffusion of monomer molecules is severely hindered, and at this point, the actual reaction rate is no longer dominated by chemical kinetics but by physical diffusion processes. Temperature measurements only reflect the average thermal energy of the fluid inside the reactor and cannot reflect the actual situation of molecules struggling to diffuse in a viscous medium. Therefore, predictions based on pure temperature models will deviate significantly from the actual values ​​in the later stages of the reaction. The second approach focuses on changes in physical properties, using online viscometers, torsional viscometers, and even nuclear magnetic resonance (NMR) to measure viscosity online. However, this approach faces two insurmountable engineering obstacles: First, fluids in the later stages of polymerization exhibit strong viscoelasticity and shear-thinning characteristics, leading to highly unstable readings and susceptibility to clogging of online measuring instruments. Second, the relationship between viscosity and conversion rate is not fixed; it drifts with variations in molecular weight distribution, branching degree, and even trace impurities between batches. Therefore, while this method is correct in direction, it has consistently failed to be implemented in large-scale industrial production.

[0003] In summary, there is an urgent need for an online method for predicting polymerization conversion rates that does not rely on online viscometers or precise kinetic models. This method can utilize the existing sensor signals of the reactor itself to capture early signs of the gelation effect in real time without increasing hardware costs, automatically adapt to differences in raw materials from different batches, and provide a reliable basis for the safe control of the reaction endpoint. Summary of the Invention

[0004] This application provides a method for predicting the conversion rate and self-correcting parameters of polymerization reactions in a coaxial dual-stirred reactor. It solves the problems of severe distortion in the later stage of the reaction due to the reliance on temperature models and poor engineering reliability due to the reliance on online viscometers in the prior art. It improves the real-time performance and robustness of the polymerization conversion rate prediction, and achieves early warning of the gel effect and adaptive control of the reaction endpoint without increasing hardware costs.

[0005] In view of the above problems, this application provides a method for predicting the conversion rate and self-correcting parameters of polymerization reactions in a coaxial dual-stirred reactor. The method includes: The real-time torque and current components of the inner shaft drive motor and the outer shaft drive motor in the reactor, the real-time speed of the inner shaft agitator and the outer shaft agitator, and the real-time temperature of the material in the reactor are collected synchronously. The real-time temperature is the weighted average of the temperatures of multiple points in the reactor. The collected signals are subjected to amplitude limiting filtering, moving average filtering and outlier removal to obtain preprocessed real-time monitoring data. Based on the cross-product operation of the real-time torque current components and real-time speed of the pre-processed inner and outer shaft drive motors, a value representing the stirring power of the inner and outer shafts is obtained. After normalization correction by the geometric structure constant of the reactor stirrer, a dimensionless characteristic ratio representing the interaction state of the inner and outer shaft flow fields is obtained. In response to the addition of the initiator or the material temperature rising to the initiation threshold, when the real-time temperature of the material is monitored to be stable within the preset initiation temperature range, and the real-time torque current component of the inner shaft drive motor does not show a continuous upward trend within the preset sliding back window, the dimensionless characteristic ratio of at least M stirring cycles is immediately collected, and its average value is taken as the reference value, where M is a preset positive integer. After obtaining the reference value, the real-time torque current component of the preprocessed inner shaft drive motor is continuously monitored to determine the moment when it first shows a continuous upward trend as the starting point of the reaction timing. Based on the dimensionless characteristic ratio and the reference value, the deviation accumulation degree is calculated. The deviation accumulation degree represents the cumulative value of the deviation of the dimensionless characteristic ratio from the reference value within a preset sliding integral time window. A diffusion limitation coefficient characterizing the diffusion limitation effect is constructed. Starting from the start of the reaction time, when the relative deviation of the dimensionless characteristic ratio is detected to enter the preset initial deviation interval, the mean of the cumulative deviation within the interval is obtained. Based on the mean of the cumulative deviation and the preset target initial diffusion limitation coefficient, the diffusion limitation coefficient is determined. Based on the real-time temperature and diffusion confinement coefficient, a reaction kinetics evolution model incorporating micro-diffusion effects is constructed to calculate the predicted polymerization conversion rate. The evolution model substitutes the real-time temperature into the Arrhenius relation to calculate the apparent reaction rate coefficient, and constructs an ideal chemical reaction rate term using the reaction mechanism function. The diffusion confinement coefficient is then used to dynamically correct the ideal chemical reaction rate term to obtain the real-time evolution rate. By integrating the real-time evolution rate over time, the current predicted polymerization conversion rate is obtained. Based on the diffusion limitation coefficient monitored in real time, the reaction endpoint threshold is dynamically corrected, and the predicted conversion rate is compared with the corrected reaction endpoint threshold to control the termination time of the polymerization reaction according to the comparison results.

[0006] One or more technical solutions provided in this application have at least the following technical effects or advantages: 1) The conversion rate can be predicted directly by using the existing motor frequency converter and sensor signals in the reactor through software algorithms. There is no need to install additional equipment for online viscosity monitoring, which saves equipment purchase and maintenance costs.

[0007] 2) By using the cross product ratio of the inner and outer shaft currents and the rotational speed, the interference of factors such as grid voltage fluctuations and speed setting changes on the signal can be offset, making the calculation results more stable and solving the problem that the single-shaft stirring signal is easily affected by the on-site working conditions.

[0008] 3) Before the reaction rate has decreased significantly, changes in the stirring load can detect early signs of diffusion limitation, providing more time for endpoint control and preventing the reaction from getting out of control.

[0009] 4) Each batch is independently calibrated with a baseline value and diffusion sensitivity coefficient, automatically matching the differences between raw material batches and changes in initiator activity. No manual parameter adjustment or offline experiments are required.

[0010] 5) It is not sensitive to on-site interference. This invention does not pursue the absolute value of the measured viscosity, but only focuses on the trend of viscosity change. It has a good ability to suppress sensor noise and flow field disturbance, and is suitable for industrial production environment.

[0011] In summary, this invention does not pursue precise measurement of the absolute value of viscosity, but focuses on capturing the relative trend of viscosity changes. This design has a natural resistance to flow field disturbances such as sensor noise, localized material adhesion to the wall, and feed impact. It maintains measurement stability even in harsh industrial environments such as high temperature, high viscosity, and strong corrosion, far superior to traditional online detection equipment. This invention breaks the conventional thinking that increasing hardware is necessary to improve accuracy, and for the first time redefines the stirring load signal from an interference factor as a key process information source. Without increasing any hardware costs, it achieves online prediction of conversion rate, combining economy, reliability, and practicality, and has extremely high industrial application value. Attached Figure Description

[0012] Figure 1 This is a schematic flowchart illustrating the method for predicting the conversion rate and self-correcting parameters of a coaxial dual-stirred reactor polymerization reaction provided in an embodiment of this application. Detailed Implementation

[0013] This invention is primarily applicable to polymerization systems where the viscosity changes significantly with increasing conversion rate during the reaction. Specifically, it includes, but is not limited to, the bulk polymerization of methyl methacrylate, styrene, and vinyl acetate, and the solution polymerization of high-solids-content acrylates. These reaction systems, after reaching a certain conversion rate, all enter a diffusion-controlled stage, where the gel effect causes characteristic changes in the macroscopic stirring load. Therefore, the method of this invention is highly suitable for monitoring and control. In a coaxial dual-stirred reactor, the inner shaft stirrer primarily provides high-shear dispersion, and its torque current is highly sensitive to local viscosity changes in the micro-regions near the impellers. The outer shaft stirrer primarily provides overall circulating flow, and its torque current and rotational speed together reflect the apparent viscosity changes in the main flow field. When the polymerization reaction enters the middle and later stages, as the polymer molecular weight increases and the conversion rate improves, the system viscosity increases exponentially, triggering the gel effect. At this point, molecular diffusion at the microscale is hindered, i.e., the diffusion-controlled stage begins. This increase in microscopic resistance synchronously changes the macroscopic stirring load.

[0014] The dimensionless characteristic ratio constructed in this invention, through cross-product ratio calculation, can effectively eliminate common-mode interference such as speed setpoint adjustments and power supply voltage fluctuations. This ensures that changes in the dimensionless characteristic ratio are no longer misled by fluctuations in external operating conditions, but are primarily driven by viscosity changes caused by the polymerization reaction. In summary, the degree to which the dimensionless characteristic ratio deviates from the reference value essentially reflects the severity of diffusion limitation on the polymerization process.

[0015] Since this invention is applicable to systems with significantly increased viscosity, in order to accurately quantify this change, the steady-state value of the dimensionless characteristic ratio is pre-collected as a benchmark during the induction period at the initial stage of the reaction, when the system viscosity has not yet increased significantly. Subsequently, using this benchmark, the diffusion limitation coefficient is estimated in real time by deviating from the cumulative effect, thereby correcting the reaction rate model and achieving accurate prediction of polymerization conversion and adaptive control of the reaction endpoint.

[0016] This application provides a method for predicting the conversion rate and self-correcting parameters of polymerization reactions in a coaxial dual-stirred reactor, such as... Figure 1 As shown, the method includes: S1: Real-time torque and current components I of the inner and outer shaft drive motors in the coaxial dual-stirred reactor are synchronously acquired via industrial fieldbus. inner I outer Real-time rotational speed N of the inner shaft stirrer and the outer shaft stirrer inner N outer The data includes the real-time temperature T of the material inside the reactor, where the real-time temperature is the weighted average of the temperatures at multiple points inside the reactor. The collected signals are subjected to amplitude limiting filtering, outlier removal, and moving average filtering. When the real-time torque current component I of the external shaft drive motor is detected... outer Or the real-time rotational speed (N) of the internal shaft stirrerinner If the value falls below the preset safety threshold, subsequent calculations are paused and the previous valid value is retained. At the same time, a sensor fault signal or equipment abnormality signal is generated.

[0017] Specifically, in this embodiment, the control system establishes a communication connection with the inner and outer shaft drive inverters and sensor network via a high-speed industrial fieldbus. Utilizing the distributed clock mechanism of the bus, microsecond-level time synchronization is achieved to ensure the inner shaft current I... inner With external shaft current I outer The timestamps are strictly aligned, thus eliminating phase errors caused by asynchronous sampling. In each control cycle, which can be set to 100 milliseconds, the system synchronously reads the following data: directly reads the torque current component I output from the inverter's vector control unit. inner I outer If a conventional frequency converter is used, the system can be in a quasi-steady state, such as when the speed change rate is <5%, using the formula... , where I torque Represents the torque current component, I rms This represents the total current output by the frequency converter or measured by the sensor. Represents the phase difference between voltage and current The cosine value of the inner and outer shafts is read. The real-time rotational speeds of the inner and outer shafts, Ninner and Nouter, are read. The Pt100 resistance temperature detector (RTD) signals at the upper, middle, and lower points inside the reactor are collected, and a weighted average value is calculated with a weighting of 1:2:1 to characterize the bulk temperature of the material.

[0018] For torque current components (Iinner, Iouter) and speed (Ninner, Nouter), due to their sensitivity to electromagnetic interference and high frequency of change, the following processing is performed sequentially: Limiting and reasonableness checks are performed to eliminate abnormal data exceeding physical limits. Data exceeding 110% of the maximum permissible speed is used to prevent overspeeding, or if a motor running command is detected but the speed remains below 0.5 rpm, it is considered stalled or a sensor malfunction. Any data exceeding these limits is directly deemed invalid and not used. A moving average filter with a window size of 5 is used to suppress high-frequency random noise. Outlier removal is performed using two criteria: first, the 3σ criterion: if the current data point deviates from the mean of the last 10 points by more than 3 times the standard deviation, it is considered an outlier; second, the rate of change threshold method: if the rate of change between the current point and the previous valid value is too large, such as a torque current change exceeding 10 A / s or a speed change exceeding 50 rpm / s, it is also considered an outlier. Once identified as an outlier, it is not directly discarded but replaced with a linear interpolation of the preceding and following valid values ​​to avoid breakpoints in the characteristic ratio calculation. The sliding window corresponds to a time length of 0.5 seconds, which effectively reduces noise without slowing down the response. Due to the slow temperature change and high thermal inertia, excessive filtering is avoided; instead, the focus is on monitoring whether the sensor is disconnected or drifting. The temperatures at the upper, middle, and lower points are combined into a main temperature with a weighted ratio of 1:2:1. If the instantaneous change at any point exceeds the measurement range, or the rate of change is greater than 5℃ / s, the sensor is considered faulty, an alarm is triggered, and the previous valid temperature value is retained without further updates. Interpolation repair is not used here because smoothed data may mask the true risk of runaway reaction, such as a temperature surge caused by sudden polymerization.

[0019] The reason this invention selects the real-time torque current, rotational speed, and temperature of a coaxial dual-stirred reactor as input variables is based on the following electro-rheological-chemical cross-scale correlation mechanism: In polymerization reaction systems, the load torque of the stirring motor directly reflects the rheological properties of the material. The inner shaft current is more sensitive to local viscosity changes in high-shear microregions, while the outer shaft current mainly reflects the apparent viscosity changes in the bulk circulation region. By combining rotational speed, a dimensionless characteristic ratio can be constructed, thereby accurately separating load fluctuations caused by changes in material properties and offsetting common-mode interferences such as rotational speed settings and power supply fluctuations. For systems such as bulk polymerization, as the reaction conversion rate increases, the system viscosity increases significantly due to the gel effect. This nonlinear viscosity growth is a typical characteristic of the diffusion control stage. Therefore, the viscosity trend inferred by monitoring current changes is essentially monitoring the evolution of the diffusion limitation coefficient. Real-time temperature is used, on the one hand, to correct the reaction rate constant according to the Arrhenius equation, and on the other hand, to compensate for the influence of temperature fluctuations on material viscosity, ensuring the accuracy of conversion rate calculations based on current. Compared to single-axis stirring, coaxial dual stirring can simultaneously acquire flow field information at both local and global scales, enabling this invention to more accurately identify the formation process of diffusion limitation. In summary, the aforementioned parameters do not exist in isolation, but rather constitute a complete logical closed loop of current / rotation speed - viscosity / flow field - diffusion limitation → conversion rate.

[0020] S2: Based on the cross-product operation of the real-time torque current components and real-time speed of the pre-processed inner and outer shaft drive motors, a value representing the stirring power of the inner and outer shafts is obtained. After normalization correction by the geometric structure constant of the reactor stirrer, a dimensionless characteristic ratio representing the interaction state of the inner and outer shaft flow fields is obtained.

[0021] Furthermore, the dimensionless characteristic ratios characterizing the interaction state of the internal and external axial flow fields are obtained, including: Based on the preprocessed real-time torque and current components I of the inner and outer shaft drive motors inner I outer and the real-time rotational speed (N) of the internal and external shaft agitators inner N outer The dimensionless eigenratio R(t) at the current time is calculated using the following formula: ; in, As the lower limit of numerical protection, C geo The normalized geometric similarity constant is used to make the time-domain mean of the dimensionless eigenratio approach 1.0. Its calculation formula is as follows: ; Among them, D inner With D outer These are the blade diameters of the inner and outer shaft agitators, respectively, K. p-inner With Kp-outer These are the standard power parameters for the inner shaft stirrer and the outer shaft stirrer, respectively, and the standard power parameters are constants that are only related to the blade configuration.

[0022] Specifically, the R(t) constructed in this invention is not simply a result derived from fluid dynamics theory, but rather an engineering characteristic index based on the principle of maximizing the signal-to-noise ratio. It utilizes the intrinsic correlation between the internal and external shaft power ratio and the material viscosity ratio as a fundamental signal for monitoring the reaction process. To achieve optimal monitoring performance across a wide viscosity range (from monomers to polymers) and complex geometries (coaxial coupling), this invention introduces a normalized geometric constant C. geo Using D 5 Geometric scaling factor combined with standard power number K p This method can eliminate background noise caused by differences in equipment size and speed fluctuations to the greatest extent, ensuring that R(t) remains highly stable during the reaction induction period and exhibits extremely high sensitivity during the reaction. Therefore, R(t) is essentially a normalized index that purely reflects changes in the rheological properties of materials after eliminating equipment differences and operational disturbances. It transforms the invisible polymerization process of microscopic molecular chain growth into a visible and accurately calculable real-time value through the macroscopic motor current ratio. The recommended value is 1.0 × 10. -6 During the reaction induction period or when the material viscosity is extremely low, the external shaft torque current may approach zero, leading to an increase in the denominator. When the value approaches zero, numerical overflow occurs. A lower limit for numerical protection is introduced. Its function is to set a lower limit for the denominator, when When the actual calculated value is less than this lower limit, use This substitution ensures that R(t) is bounded. This value is much smaller than that under normal operating conditions. The typical value is usually >0.1, and can be fine-tuned based on field data. =On the order of 0.01 × rated torque × rated speed.

[0023] Regarding the adoption of D 5 The geometric scaling factor, theoretically, is the power of stirring in the laminar flow region related to D. 3 Proportional to D in the turbulent region 5 Proportional. For complex geometries like coaxial dual-stirrers, a simple laminar flow theory model cannot completely eliminate the nonlinear power gradient caused by impeller size differences and biaxial coupling. Comparative experiments have verified that using D... 5 Normalized to the standard power number, compared to D 3 The model can significantly reduce the volatility of R(t) under the baseline operating condition. Therefore, this embodiment preferably uses D. 5As a geometric scaling factor, a more stable monitoring benchmark is obtained. The biaxial linkage turbulence calibration method is used to obtain... and Add deionized water to the reactor and turn on the constant temperature control to maintain a temperature of 20±0.5 degrees Celsius. Set the high-speed operating condition to 300 rpm for the inner shaft and 180 rpm for the outer shaft. After the system stabilizes, measure the inner shaft power P using a high-precision torque sensor. inner and P outer Substitute into the general power formula ,in, For power parameters, For stirring power, Let N be the fluid density, N be the stirring speed, and D be the impeller diameter. The result can be calculated for this coaxial system. and In obtaining After setting a constant, to verify the applicability of this calibration method in the initial reaction stage under low speed / transition flow conditions, a simulation experiment was conducted: keeping the medium unchanged (still water), the speed was reduced to 120 rpm for the inner shaft and 72 rpm for the outer shaft. Real-time data was collected during 10 minutes of stable operation, and R(t) was calculated by substituting it into schemes A and B respectively. Scheme A uses... Option B, adopts In both schemes, Kp uses the same set of calibration values. The statistical characteristics of the two schemes under the baseline operating condition, i.e., low-velocity water medium, are compared in Table 1: Table 1 Experimental results show that Scheme B controls the background noise CV of R(t) to within 3%, proving its reliability as a benchmark monitoring indicator and providing a clear baseline for accurately capturing the gel effect in the MMA or styrene polymerization process.

[0024] Although the polymerization reaction undergoes a wide range of changes from low-viscosity monomers to high-viscosity polymers, and the flow regime transitions from turbulent to laminar flow, C geo Essentially, it reflects the geometric power distribution characteristics of the reactor. This invention uses the turbulence calibration method to determine Kp because in the turbulent region, the macroscopic mixing of the fluid is most complete, resulting in the highest signal-to-noise ratio for the measured power data, which best reflects the inherent geometric properties of the equipment. Once C... geoOnce determined, this becomes the fingerprint parameter of the equipment, and regardless of subsequent changes in the viscosity of the materials—whether it's water, MMA monomer, or high-viscosity polystyrene—this geometric normalization constant remains unchanged. To verify this hypothesis, this embodiment conducted an applicability experiment across a wide viscosity range: a reactor using the same biaxial turbulent calibration method was selected, and four different Newtonian fluid standard silicone oils with viscosities of μ=10, 100, 1000, and 5000 cp were used. These viscosity specifications cover the typical range of MMA and styrene bulk polymerization, from a monomer viscosity of approximately 0.5-1 cP during the induction phase to a viscosity exceeding 5000 cP during the peak gel effect. geo The values ​​obtained through water calibration in the turbulence calibration method of the example were fixed and not adjusted with viscosity changes. Stirring experiments were conducted on the four viscosities of silicone oil at a constant temperature of 25°C, maintaining a constant inner shaft speed of 120 rpm and an outer shaft speed of 72 rpm. At each viscosity point, after the system stabilized, data was continuously collected for 60 seconds, with a sampling period of 100 ms, resulting in 600 calculated R(t) values. The arithmetic mean and standard deviation of these 600 points were taken, and the coefficient of variation (cv) was used to measure the degree of fluctuation: cv = standard deviation / mean × 100%. The results are shown in Table 2. Table 2: In the verification experiment of this embodiment, as the viscosity of the silicone oil increased, the flow state of the reactor gradually transitioned from the transition flow region to the laminar flow region. Experimental data showed that R(t) remained stable around 1.0. This strongly proves that the C used in the invention... geo Based on calibration in the turbulent water medium, this method has universal applicability across flow regimes. Although Kp theoretically varies with Re in the laminar region, in a coaxial dual-stirring system, the power change trends of the inner and outer impellers are highly synchronized, causing the deviations caused by flow regime changes to cancel each other out when calculating R(t) by ratio. This conforms to the actual operating conditions of bulk polymerization of MMA, styrene, etc.—that is, the reaction starts at low viscosity, i.e., turbulent / transitional flow, and ends at high viscosity, i.e., laminar flow. The flow regime regions in the table are based on the stirring Reynolds number. A judgment is made, in which... Let N be the fluid density, N be the stirring speed, D be the impeller diameter, and μ be the fluid viscosity. The characteristic dimension D is the outer shaft anchor impeller. outer =480mm, N=72rpm, based on experience in chemical mixing engineering, it is generally considered that... <100 is the laminar flow region, 100 < <10 4 This is the transition flow region. >10 4 This is the turbulent region. This calibration was performed at 5000 cp, and the calculated values ​​are... Located in the low Reynolds number transition region, although the flow field dynamics undergo a fundamental transformation at low Reynolds numbers—with viscous forces becoming absolutely dominant and inertial forces having negligible influence—this contrasts with the high Reynolds number region. >10 4 The turbulent conditions (dominated by inertial forces) present a stark physical contrast. Under viscous force-dominated operating conditions, C calibrated using turbulence is used. geo The calculated R(t) remains highly stable, demonstrating that the power change trends of the inner and outer impellers in the coaxial dual-stirring system are highly synchronized, thus canceling out the theoretical deviations caused by flow regime changes when calculating R(t) by ratio. This method successfully decouples the geometric structure from the fluid dynamics state, achieving one-time calibration applicable to all flow regimes, and accurately covering the entire cycle from high-viscosity polymerization reactions (laminar flow) to low-viscosity induction periods (turbulent / transitional flow).

[0025] This invention aims to determine the reaction endpoint by the relative change trend of R(t), such as a jump from 1.0 to 1.5, rather than by measuring the absolute physical viscosity of the material. While non-Newtonian characteristics may alter the absolute power value, they do not change the overall trend of power increasing with the reaction progress. 2) Experiments have shown that, over a wide viscosity range, C calibrated based on water... geo It can stabilize the baseline of R(t) around 1.0, i.e., C geo As a geometric normalization constant, its dominant factor is the device size D5, rather than the rheological details of the fluid. 3) In the strong mixing field of coaxial stirring, the inner and outer blades are in similar rheological environments, and the shear thinning effect of non-Newtonian fluids has a certain self-compensating characteristic in the power ratio calculation. Therefore, in most bulk polymerization and solution polymerization engineering applications, there is no need to introduce complex online viscosity compensation; the C value calibrated by water can be used directly. geo This achieves monitoring results that meet industrial control precision requirements. Although polymerization systems such as MMA and styrene exhibit non-Newtonian fluid characteristics in the later stages of the reaction, this invention focuses on the relative trend of R(t). Therefore, this invention employs a C-value calibrated based on Newtonian fluid dynamics. geo It remains effective for the following reasons: 1) This invention aims to determine the reaction endpoint by the relative change trend of R(t), such as a jump from 1.0 to 1.5, rather than measuring the absolute physical viscosity of the material. While non-Newtonian characteristics may change the absolute power value, they do not alter the overall trend of power increasing with the reaction progress. 2) Experiments have shown that, over a wide viscosity range, C based on water calibration... geo It can stabilize the baseline of R(t) around 1.0, i.e., C geo As a geometric normalization constant, its dominant factor is the device size D. 53) In the strong mixing field of coaxial stirring, the inner and outer blades are in similar rheological environments, and the shear thinning effect of non-Newtonian fluids has a certain self-compensating characteristic in the power ratio calculation. Therefore, in most bulk polymerization and solution polymerization engineering applications, there is no need to introduce complex online viscosity compensation, and the C value calibrated by water can be used directly. geo This will achieve monitoring results that meet the precision requirements of industrial control.

[0026] S3: In response to the addition of the initiator or the material temperature rising to the initiation threshold, when the real-time temperature of the material is monitored to be stable within the preset initiation temperature range, and the real-time torque current component of the inner shaft drive motor does not show a continuous upward trend within the preset sliding back window, the dimensionless characteristic ratio of at least M stirring cycles is immediately collected, and its average value is taken as the reference value, where M is a preset positive integer.

[0027] Furthermore, dimensionless characteristic ratios are collected for at least M stirring cycles, and their average value is taken as the baseline value, where M is a preset positive integer, including: In response to the addition of initiator or the material temperature rising to the initiation threshold, baseline monitoring is initiated, including: The real-time torque current component of the inner shaft drive motor is calculated in real time within the sliding back window. The trend characteristic value is the fitting slope obtained by least square linear fitting of the current data in the sliding back window. When the fluctuation range of the real-time temperature of the material is less than the preset temperature threshold, and the characteristic value of the change trend is less than the preset trend threshold, the reaction system is determined to be in the baseline state of the induction period. If the material is determined to be in the baseline state of the induction period, the first calibration acquisition window is immediately opened. Within the first calibration acquisition window, the real-time temperature and trend characteristics of the material are continuously monitored to see if they still meet the determination conditions of the baseline state of the induction period. If satisfied, the dimensionless feature ratios are accumulated until M cycles are collected. The statistical mean of the dimensionless feature ratios within the first calibration collection window is calculated as the benchmark value, which is numerically close to 1.

[0028] Specifically, the baseline value acquisition strategy in this embodiment aims to capture the induction period state where the reaction system is in thermodynamic equilibrium but there is no effective free radical chain growth and the macroscopic viscosity has not changed significantly. This method is widely applicable to homogeneous bulk polymerization, such as styrene, and homogeneous solution polymerization, such as acrylates, specifically covering the following two feeding process scenarios: 1) Premixing process, with initiator added in advance: When the material is heated to the preset target reaction temperature, due to the existence of the induction period, although the system has the thermodynamic conditions for reaction, free radical chain growth has not yet led to a change in macroscopic viscosity. At this time, the system uses a preset sliding back window to monitor the current trend, and acquires the baseline value after confirming that the current has no upward trend. 2) Post-initiator addition process, dropwise or all-time addition: In this process, the baseline value is usually acquired in the early stage of mixing after the initiator is added. Although the system is also in a steady state before the initiator is added, the temperature at that time is usually lower than the reaction temperature and is in the heating stage. The viscosity is significantly different from the reaction temperature and is not suitable as a baseline. After detecting the initiator addition signal, the system immediately starts high-frequency monitoring. At the moment when the initiator and materials are uniformly mixed and the temperature reaches the preset reaction temperature, the baseline value is quickly calibrated by utilizing the short induction period window, which is the period when the initiator has entered the reactor but has not yet initiated significant polymerization.

[0029] Baseline monitoring is automatically initiated when an initiator addition signal is detected, such as through flow meter or feed pump status feedback, or when the weighted average temperature T at multiple points within the reactor first reaches the preset initiation threshold. The preset initiation threshold is not a fixed value but is pre-set based on the type of initiator used, such as benzoyl peroxide (BPO) or azobisisobutyronitrile (AIBN), its decomposition temperature characteristics, and the polymerization kinetics parameters of the target monomer. This temperature is typically set as the starting temperature for effective initiator decomposition. When this threshold is reached, it means the system is ready for reaction and is about to enter or has just entered the induction phase. Initiating baseline monitoring at this point aims to capture the quasi-steady-state window before a significant increase in macroscopic viscosity, i.e., before the polymerization reaction leads to an increase in torque, in order to collect a pure baseline value. Depending on the polymerization system, this threshold is typically between 50°C and 120°C. For systems using BPO as an initiator for methyl methacrylate or styrene, the reaction typically starts at 80°C to 90°C, in which case the preset initiation threshold can be set to 80°C. For systems using low-temperature initiators (such as AIBN), this threshold can be set to 50°C to 60°C. The purpose of baseline monitoring is to determine whether the reaction system has entered the induction period baseline state, that is, the quasi-steady-state stage where the temperature has stabilized and the polymerization reaction has not yet occurred significantly.

[0030] The system calculates the characteristic value of the changing trend within the sliding backtracking window. In each sampling period, it extracts the preprocessed sequence I within a 30-second backtracking window from the current time. innerThe time can be adjusted within the range of 20-60 seconds depending on the reaction rate of the system. In each sampling period, consistent with S1 (e.g., 100 milliseconds), N consecutive preprocessed real-time torque current component data points within that window are extracted, denoted as the dataset {(t...} i ,I i )|i=1,2,...,N}, where t i For the sampling time, I i This represents the current value corresponding to the real-time torque current component of the inner shaft drive motor. Subsequently, a least squares method is used to perform linear regression on the time-current data, utilizing the linear function I(t) i )=k I ·t i +b, where t i For the sampling time, I(t) i Let be the fitted ideal current value, and b be the intercept. The goal is to minimize the sum of squared residuals between the straight line and the actual data points, i.e., satisfy the condition... By solving the above extreme value problem, the fitting slope k is calculated. I That is, the characteristic value of the changing trend. To eliminate the influence of different motor dimensions, k is... I Convert to full-scale percentage per second (%FS / s); if the slope is positive, it indicates that the current has an upward trend.

[0031] The system simultaneously monitors two conditions to determine the baseline state during the induction period: Condition 1: The material temperature fluctuation is less than a preset threshold. The difference ΔT between the maximum and minimum weighted average temperature T over the past 30 seconds is calculated. If ΔT ≤ ΔT threshold Then condition A is satisfied. ΔT threshold The value is 0.5°C, which can be adjusted within the range of 0.2~1.0°C according to the temperature sensitivity of the polymerization system. Condition 2: The characteristic value of the current change trend is less than the preset threshold, and the fitting slope k I Satisfy |k I |≤k threshold Then condition 2 is satisfied. threshold The value is determined as follows: This threshold is set to be greater than the spurious slope caused by system background noise, and significantly less than the minimum current rise slope during the acceleration phase of the polymerization reaction. For example, 0.01% / s to 0.05% / s of full scale; if the full scale current is 200A, then 0.01%FS / s corresponds to 0.02A / s. This value range is typically lower than the fluctuation noise level of motor current in industrial settings to prevent misjudgment, and is also far lower than the viscosity growth rate of any polymerization system after the induction period to ensure sensitive detection of reaction initiation.

[0032] For dynamic calibration strategies of systems with short induction periods, such as rapid polymerization systems of vinyl acetate with a short induction period of less than 10 minutes, this embodiment adopts a trigger-pre-emptive and window-dynamic compression strategy to overcome the calibration window lag caused by thermal inertia: The trigger signal is pre-emptive, responding to the addition of the initiator. This embodiment does not wait for the material temperature to rise to the initiation threshold, such as 80°C, but directly responds to the initiator addition signal, such as the feed pump start signal or flow sensor pulse. For systems like vinyl acetate, the addition of the initiator marks the start of the induction period countdown. At this time, the material temperature may not have reached the optimal reaction temperature, but is in the ramp-up phase of 60°C-70°C. However, at this time, the system viscosity is the lowest, and the flow field is the most stable, making it the best window for obtaining the baseline value. The sliding backtracking window is compressed, reducing the length L of the sliding backtracking window from the conventional 30-60 seconds to 10-20 seconds. Shortening the time span for judging a "continuous upward trend" allows the system to capture minute changes in current with higher time resolution. Once the current slope k is detected within 10 seconds... I If the threshold is exceeded, calibration is immediately terminated to prevent the collection of data from the initial stage of the reaction. The calibration acquisition window is dynamically truncated. Although the preset acquisition period is M=5 cycles, the system introduces a real-time truncation mechanism: during the acquisition process, the system continuously monitors the current R(t) value. If the R(t) value of three consecutive sampling points is found to be greater than the current mean of 1.02 (i.e., the deviation exceeds 2%), the induction period is considered over, the acquisition window is immediately forcibly terminated, and the collected valid data is used to calculate Rref, even if less than M cycles have been collected (e.g., only 3 cycles). Mathematical correction: due to the decrease in data volume n, the system automatically relaxes the alarm threshold for the coefficient of variation (CV), such as from 5% to 8%, to tolerate statistical fluctuations caused by small samples.

[0033] The first calibration acquisition window is opened and data is acquired immediately once the baseline state of the induction period is determined. The length of the acquisition window is set to M consecutive complete stirring cycles. M is a preset positive integer, typically 5-10, and can be adjusted within the range of 3-20 depending on the required stability of the reference value. The stirring cycle T... cycle Defined as the maximum time required for the inner and outer shafts to rotate one revolution each. For example, an inner shaft speed of 120 rpm corresponds to a period of 0.5 seconds, and an outer shaft speed of 72 rpm corresponds to a period of approximately 0.833 seconds. Therefore, T... cycle =0.833 seconds. The total duration of the acquisition window is approximately M × Tcycle seconds. The sampling period is consistent with S1 to ensure that a sufficient number of R(t) data points are collected within each stirring cycle. During acquisition, the dimensionless characteristic ratio R(t) of each sampling point is calculated in real time, and the calculation result is stored in the circular buffer. After M stirring cycles are completed, the first calibration acquisition window is automatically closed. The arithmetic mean of all R(t) values ​​stored in the buffer is calculated as the baseline value R for this batch. refSimultaneously, the coefficient of variation (CV) for this set of R(t) values ​​is calculated as: CV = (Standard deviation of all R(t) values ​​ / Baseline R) ref )×100%. If CV exceeds 5%, it indicates that the data fluctuates greatly during the calibration period. The system will issue an alarm for abnormal fluctuation of the benchmark calibration, but the calculated Rref will still be temporarily stored, and the operator will decide whether to use it or recalibrate.

[0034] Due to the geometric constant C geo As pre-determined through calibration experiments, under the baseline conditions during the induction period, the material is a low-viscosity monomer or solution, and the flow field is close to that of a Newtonian fluid. The calculated Rref should be close to 1.0, with a range of 0.95 to 1.05. If Rref deviates significantly from 1.0, being less than 0.8 or greater than 1.2, it may indicate a systematic bias in the sensor or that the reaction system has not truly entered the baseline state, such as the current not rising but the temperature not stabilizing. In this case, the system should issue a baseline value abnormality alarm, prompting the operator to check the equipment or recalibrate. The Rref value verified or confirmed by the operator is stored in the non-volatile memory of the control system and marked as the baseline value for the current batch.

[0035] S4: After obtaining the reference value, continuously monitor the real-time torque current component of the preprocessed inner shaft drive motor to determine the moment when it first shows a continuous upward trend as the starting point of the reaction timing. Based on the dimensionless characteristic ratio and the reference value, calculate the cumulative deviation. The cumulative deviation represents the cumulative value of the deviation of the dimensionless characteristic ratio relative to the reference value within a preset sliding integral time window.

[0036] Further, the cumulative deviation is calculated, including: ; in, The deviation cumulancy characterizes the length of the backtracking time from the current sampling time t. Within the interval, the average deviation of the dimensionless eigenvalue relative to the benchmark value; t is the current sampling time, and its zero point t=0 corresponds to the starting point of the reaction timing; The preset sliding integral time window length, It is a positive number; s is the integration variable, representing the time window. , Any time within ]; Let be the value of the dimensionless eigenratio at time S. The reference value; It represents the instantaneous deviation of the dimensionless characteristic ratio at time S from the reference value.

[0037] Specifically, after the polymerization reaction enters the acceleration phase, the dimensionless characteristic ratio will gradually deviate from the benchmark value. However, simply looking at the instantaneous deviation at a certain moment is easily affected by noise and cannot reflect the continuous cumulative effect of the deviation. This invention introduces a deviation cumulative degree to describe the average degree of deviation of the dimensionless characteristic ratio from the benchmark value over a period of time, rather than the infinitely accumulated total. The integration time window τ is the length of the sliding integration time window, in seconds. Its physical meaning is: to calculate the average deviation over a period of time before the current moment t. Depending on the speed of the polymerization reaction, τ is generally set to 60~300 seconds. For faster reaction systems (such as bulk polymerization of vinyl acetate), a smaller value such as 60 seconds can be taken; for slower reaction systems (such as solution polymerization of high solids content acrylates), a larger value (such as 180~300 seconds) can be taken to smooth short-term fluctuations. τ is a preset parameter, set according to the specific polymerization system and reactor size before the system is put into operation, and can also be fine-tuned during on-site commissioning.

[0038] The integral variable s and the upper and lower limits of integration, the lower limit of integration in the formula is... The upper limit is the current time t. Here... This is to handle the situation at the very beginning of the reaction (t < τ), where the integration window starts from 0 instead of negative time. s is the integration variable, representing each time point from the lower to the upper limit of integration. At each time s, the system retrieves the calculated and stored value of R(t), i.e., the value of the dimensionless characteristic ratio calculated in step S2 at time s, and calculates the absolute value of the difference between this value and the baseline value Rref to obtain the instantaneous deviation at that time.

[0039] In practical control systems, integration is achieved through discrete accumulation. The sampling period is Δt, consistent with step S1, such as 100 milliseconds. Let k be the sequence number of the current sampling moment, where k is an integer and k≥0. The time corresponding to the kth sampling moment. The deviation cumulative D(t) is updated at each sampling time by the following formula: ; in, , The number of sampling points within the window. Summing from i=kL to i=k, corresponding to the time interval ,like Then, the accumulation starts from i=0, the starting point of the reaction.

[0040] In the initial stage of the reaction, the lower limit of the integration window for t < τ is truncated to 0. At this point, D(t) calculates the average deviation from the reaction start point to the current time. For example, if τ = 120 seconds and the current time t = 50 seconds, the integration interval is [0, 50] seconds, not [-70, 50] seconds, as negative time is meaningless. In engineering implementation, the system determines the lower limit of integration by determining whether t - τ is less than 0: if t ≥ τ, the lower limit is t - τ; if t < τ, the lower limit is 0. The D(t) calculated in each sampling period is used to calculate the diffusion limitation coefficient Φ(t). Simultaneously, D(t) can also be displayed as a real-time curve on the operator interface, helping operators intuitively understand the cumulative degree of diffusion limitation during the reaction process. D(t) is a monotonically increasing, or stepwise increasing, quantity. As the reaction progresses, R(t) continuously deviates from the baseline value, while D(t) only increases or remains unchanged, never decreasing. This monotonicity means that the subsequent diffusion limitation of Φ(t) will only become more severe and will not alleviate itself. The value of τ affects the smoothness and response speed of D(t). A larger τ results in a smoother D(t), but a slower response to changes in the reaction. A smaller τ makes D(t) more sensitive, but more susceptible to short-term fluctuations. In actual field debugging, τ can be fine-tuned by observing the correlation between the smoothness of the D(t) curve and the conversion rate. The fine-tuning principle is to use the smallest possible τ while ensuring the curve has no obvious spikes, in order to maintain a rapid response to the reaction.

[0041] Furthermore, the reaction timing start point includes: After the first calibration acquisition window ends, the characteristic value of the change trend of the real-time torque current component of the inner shaft drive motor continues to be calculated in real time. When the detected trend feature value changes from being less than a preset trend threshold to being greater than a preset rise threshold for Q consecutive sampling periods, it is determined that a continuous upward trend has appeared for the first time, where Q is a preset positive integer; The characteristic value of the changing trend is the fitting slope calculated based on the current data within the sliding back window; The time corresponding to the first sampling point that satisfies the above conditions is the reaction timing start point t=0.

[0042] Specifically, the determination of the reaction timing start point begins after the baseline calibration is completed. S3 is responsible for determining when the baseline value can be collected, and S4 is responsible for determining when the reaction actually begins. Both steps share the same trend characteristic value, namely the fitting slope of the inner shaft current, but the judgment thresholds differ. Continuous monitoring continues after calibration. After the first calibration acquisition window closes, the baseline value is stored in the control system. At this time, the system does not stop monitoring the current trend but continues to calculate the trend characteristic value of the inner shaft current in each sampling period. The calculation method for this trend characteristic value is exactly the same as in S3. The system maintains a sliding backtracking window, typically set to thirty seconds. Least-squares linear fitting is performed on the inner shaft current data within the window, and the resulting fitting slope is the trend characteristic value, in amperes per second. To accommodate motors with different ranges, the system can also convert it to a percentage of full scale per second.

[0043] A hysteresis comparison mechanism using rising threshold and trend threshold: To accurately distinguish between a static state and a reaction initiation state in complex industrial electromagnetic environments, this invention introduces a dual-threshold hysteresis comparison mechanism. These two thresholds are not arbitrarily set, but are determined based on signal-noise bandwidth and reaction kinetic characteristics. 1) Trend threshold k threshold Defining the noise band: During the induction period, the motor current should theoretically be constant, but due to limitations in sensor accuracy and uneven stirring force, the current will exhibit slight random fluctuations. Trend threshold k threshold Set the slope to be slightly larger than the system's maximum background noise, such as one ten-thousandth of the full scale per second. As long as the fitted slope is |k I |≤k threshold The system determines that the current is in a statistical steady state, and only then is the collected data considered a valid reference value. 2) Rise threshold K start Defining the reaction kinetics initiation point, once polymerization is initiated, the system viscosity increases exponentially, directly leading to an increase in the driving current. Therefore, a significant increase in the current slope is a direct physical characteristic of the chemical reaction occurring. The initiation threshold K... start The threshold is set to be significantly greater than the trend threshold, such as 0.02% to 0.03% of full scale per second, corresponding to the minimum expected growth rate at the initial stage of the reaction. A safety margin zone, K, is formed between these two thresholds. start <∣k I | <k threshold When the current slope is in this region, neither reference value acquisition nor reaction timing is triggered, thus filtering out occasional electrical spikes. Only when the slope exceeds k... thresholdFurthermore, only after Q consecutive cycles can the possibility of random noise be mathematically eliminated. The probability of Q consecutive positive fluctuations is extremely low, thus confirming that a systematic chemical reaction is causing the current increase. The system also needs to confirm that no such condition has ever occurred before the current moment, ensuring that the captured instance is the first occurrence. The first sampling point that meets the above conditions, i.e., the moment when the counter starts counting, is the reaction timing start point. This definition ensures that the start point determination does not lag behind the actual occurrence of the reaction, leaving sufficient computational margin for subsequent conversion rate prediction. For example, the full-scale range of the inner axis current is 200 amperes, the trend threshold is set to a fitted slope of 0.02 amperes per second, and the rise threshold is set to a fitted slope of 0.05 amperes per second. The sampling period is 100 milliseconds, and Q is 10. In the baseline state during the induction period, the current fitted slope fluctuates below 0.02 amperes per second. The system considers it not yet rising and continues to wait. After the reaction starts, the current begins to rise slowly. In the first few seconds, the fitted slope may still be between 0.03 and 0.04, not yet reaching 0.05. The system continues monitoring. When the fitting slope of each of the 10 consecutive sampling points, i.e., within one second, is greater than 0.05 amperes per second, the system determines that a continuous upward trend has begun. The moment corresponding to the first of these ten points, i.e., the point where the counter starts counting, is the reaction timing start point.

[0044] Given the significant differences in polymerization kinetics and viscosity variation patterns of different monomers, the system allows for the preset rise threshold and Q value for specific polymerization types to achieve optimal start-point capture.

[0045] 1) In systems with a strong gel effect, such as the bulk polymerization of methyl methacrylate (MMA), MMA polymerization exhibits a significant auto-acceleration effect (gel effect). Once the reaction starts, the system viscosity and torque increase exponentially. A high threshold and short confirmation strategy is adopted. The rise threshold is set to 0.03% of the full-scale slope of the fitted curve per second, and Q is set to 5. The high threshold effectively masks any minor fluctuations that may occur during the induction period, while once the threshold is exceeded, the extremely short Q value confirms the reaction burst, preventing the rapid rise phase from being missed.

[0046] 2) For fast-reaction systems, such as the bulk polymerization of vinyl acetate (VAc), VAc has a high heat of polymerization and a relatively short induction period, resulting in a rapid current ramp-up after the reaction starts. A sensitive capture strategy is employed. The rise threshold is set to 0.025% of the full-scale slope of the fitted curve per second, with Q ranging from 3 to 5. The relatively low threshold, combined with an extremely short confirmation period, aims to ensure a rapid response in the early stages of the reaction and avoid a delay in the timing start due to an excessively high threshold.

[0047] 3) In mild reaction systems, such as the bulk polymerization of styrene (St), styrene is a good solvent for polystyrene, and the autoacceleration phenomenon occurs relatively late, with gentler kinetic changes in the initial stage of the reaction. A robust monitoring strategy is adopted. The rise threshold is set to 0.02% of the full-scale slope of the fitted slope per second, and Q is set to 5 to 8. Appropriate parameter settings can effectively filter out random noise during the plateau phase of the reaction while ensuring a fast response.

[0048] 4) High-viscosity / high-solids-content systems, such as high-solids-content acrylate solution polymerization, have high initial viscosity and require heavy stirring, resulting in large baseline current values ​​and relatively high mechanical vibration noise. A noise-priority strategy is adopted. The rise threshold is set to 0.03% of the full-scale slope of the fitted slope per second, and Q is set to 8 to 10. The higher threshold and longer confirmation period provide a wider safety margin, ensuring that the system does not misinterpret random baseline fluctuations under high load as reaction start-up signals.

[0049] S5: Construct a diffusion limitation coefficient characterizing the diffusion limitation effect. Starting from the start of the reaction time, when the relative deviation of the dimensionless characteristic ratio is detected to enter the preset initial deviation interval, obtain the mean of the cumulative deviation within the interval. Based on the mean of the cumulative deviation and the preset target initial diffusion limitation coefficient, determine the diffusion limitation coefficient.

[0050] Furthermore, the diffusion limitation coefficient is calculated based on the deviation cumulancy and diffusion sensitivity coefficient, including: Calculate the diffusion confinement coefficient at the current sampling time. The formula is as follows: ; in, The diffusion sensitivity coefficient, The cumulative deviation at the current sampling time; The following adaptive calibration method is used to determine... : Starting from the start of the reaction time, monitor the relative deviation of the dimensionless characteristic ratio relative to the reference value; When the relative deviation enters the preset initial deviation range, the second calibration window is opened, and based on the relative deviation data within the preset time period before the current sampling time, it is simultaneously determined whether the relative deviation shows a linear growth trend. If the judgment result is yes, then keep the second calibration window open and continue to collect the cumulative deviation at each sampling time within the window; When the relative deviation exceeds the initial deviation interval, the second calibration window is closed, and the statistical average of the collected cumulative deviations is calculated and recorded as the calibration cumulative deviation. ; Based on the calibration deviation accumulation and the preset target initial diffusion limitation coefficient, the following is calculated: The formula is as follows: ; in, The initial diffusion limitation coefficient is a preset target, used to characterize the expected baseline level of diffusion limitation effect at the end of the second calibration window.

[0051] Specifically, during polymerization, an increase in system viscosity triggers a gel effect, restricting the movement of active chain segments through diffusion. Although the reaction rate may macroscopically accelerate, from a microscopic kinetic perspective, diffusion resistance inhibits the full release of the reaction potential. This invention introduces a diffusion restriction coefficient. To quantify the severity of this microscopic diffusion resistance. The value ranges from 0 to 1. When the value approaches 1, it indicates that the system is in a state of free diffusion. If the diffusion resistance is negligible in the initial stage of the reaction, the reaction proceeds according to intrinsic kinetics. When the value approaches 0, it indicates that the system is in a state of severe diffusion limitation, such as when diffusion resistance is extremely high in the later stages of the reaction or in the high viscosity region, and the actual reaction capacity is significantly reduced compared to the ideal state. The diffusion sensitivity coefficient α is used to characterize the sensitivity of a specific polymerization system to diffusion limitation. The larger the value of α, the faster and more severe the diffusion limitation effect is established for the same cumulative deviation D(t), that is, the faster Φ(t) decreases; conversely, the smaller the value of α, the stronger the system's tolerance to diffusion limitation. Based on the above definition, in order to establish the current diffusion sensitivity coefficient α of the system in real time during the reaction process, this invention introduces a preset target initial diffusion limitation coefficient Φ. target Φ serves as the boundary condition for model solution. target A characteristic reference point is defined to indicate the transition of the diffusion confinement effect from an ideal state to a confined state. During the calculation, the diffusion confinement coefficient corresponding to this characteristic reference point is set to [value missing]. target After the reaction time starts at t=0, the system continuously samples according to the set sampling period. The current sampling time t represents the elapsed time since the reaction time started. At each sampling time t, the system calculates the relative deviation δ(t) at that time, using the following formula: ; Where R(t) is the dimensionless eigenratio at the current sampling time, R ref The baseline value is used. The system's preset relative deviation range is denoted as [δ]. min ,δ max The basis for this is that the dimensionless characteristic ratio R(t) characterizes the real-time kinetic state of the reaction system, while the benchmark value R refThis characterizes the ideal dynamic state under diffusion-free conditions. Therefore, the relative deviation... Essentially, it reflects the degree of deviation of the actual reaction system from the ideal system, that is, the strength of the diffusion confinement effect. When A small positive value, such as between 5% and 15%, indicates that the reaction rate has begun to deviate slightly from the ideal trajectory but has not yet accelerated dramatically. This corresponds to the gel effect in the polymerization reaction, i.e., the initial linear stage where diffusion limitation has just begun to emerge. In this stage, the chain termination reaction begins to be hindered by viscosity, but the system has not yet entered the nonlinear burst phase of thermal runaway. This range needs to be adjusted according to the reactivity of the specific polymerization system. For the bulk polymerization of methyl methacrylate, the gel effect develops rapidly; to capture the parameters before the burst, the range can be set narrower, such as δ. min =3%, δ max =10%. For bulk polymerization of styrene, the reaction is relatively mild, and the reaction range can be set wider, such as δ. min =5%, δ max =20%. The interval should not be too small, otherwise it may not be possible to collect enough data points. The interval should also not be too large, otherwise it may have entered the nonlinear stage, and the calibration will be inaccurate. When the relative deviation δ(t) of the current sampling time t is detected to enter the interval [δ] for the first time... min ,δ max Upon [the time frame], immediately open the second calibration window and begin real-time acquisition of the cumulative deviation D(t) data at that moment and for each subsequent sampling moment. There is no need to wait for the calibration to complete, thus ensuring that no earlier calibration data is lost. Synchronous backtracking calibration is performed simultaneously; while the calibration window is open, the system extracts data from t-τ. lin Historical δ data up to time t are used for linear trend verification. The starting point of the backtracking window is t-τ. lin The endpoint is the current sampling time t. When t < τ lin At that time, the starting point is 0. τ lin The typical value for τ is 5 seconds, which is independent of the aforementioned integration time window τ. lin This is used only for linear trend verification and does not occupy the calibration window duration. Least squares linear fitting is performed on the relative deviation δ(t) data within the backtracking window to obtain the fitting slope k and goodness-of-fit R. 2 .

[0052] Although the calibration window is open, the validity of the data depends on the verification result. Scenario A: Verification passes, window locked: If, within a short period after the window opens, e.g., 1 to 2 sampling periods, the calculated R... 2 If the slope k > 0 and the value is greater than 0.95, then the window is considered a valid calibration window. The system keeps the window open and continues to collect D(t) data until δ(t) exceeds the upper limit δ. maxClose the window immediately. In case B, if the verification fails, reset immediately. If, after opening the window, the backtracking data R is found... 2 The value <0.95 indicates that the trigger was likely caused by noise, and the data does not exhibit linear characteristics. The system determines this to be a false trigger, immediately closes the current calibration window, automatically discards the previously collected invalid data, and resets the monitoring status. Afterward, the system stops collecting data and waits for δ(t) to re-enter the numerical range [δ...]. min ,δ max When the second calibration window is opened, a new calibration window is triggered. This mechanism of opening the door first, verifying the ticket, and closing the door if the verification fails resolves two core contradictions. Time contradiction: For fast-reaction systems such as methyl methacrylate, it avoids the time wasted by verifying the ticket before opening the door. Through parallel processing, the data accumulation time required for verification is hidden at the very beginning of the calibration window, achieving zero time cost. Accuracy contradiction: The immediate reset mechanism in case B prevents forced calibration when data fluctuations are severe, ensuring that the data used to calculate the diffusion sensitivity coefficient α comes from a high-quality interval with moderate values ​​and a linear trend. After the second calibration window is opened, the system records the current D(t) value in each sampling period and stores it in a dedicated buffer. The D(t) values ​​are stored in the buffer in chronological order. The buffer capacity needs to be large enough to accommodate the data points that may be collected within the entire calibration window. For example, if the reaction time corresponding to the initial linear interval is approximately 30 seconds and the sampling period Δt = 0.1 seconds, at least 300 storage units are required. The second calibration window is closed when the relative deviation δ(t) exceeds the upper limit δ of the initial linear interval. max When the system closes the second calibration window, it stops acquiring D(t) values. The criterion for closing the window is δ(t) > δ max， δ(t) may briefly jump out of the interval and then back in due to noise. To avoid closing the window too early, a hysteresis condition can be set: only when δ(t) is greater than δ for three consecutive sampling points can the window be closed. max Only when the value truly exceeds the range is the window closed. For calculating the calibration deviation cumulant, after the window closes, the system performs statistical processing on all D(t) values ​​stored in the buffer. First, the data from the first three sampling points after the window opened are removed, as D(t) may not be fully stable when the window first opens. Similarly, the data from the last three sampling points are removed to eliminate the transient effect at the moment the window closes. The arithmetic mean of the remaining data is calculated, and this value is recorded as the calibration deviation cumulant. Simultaneously, the standard deviation σ and coefficient of variation CV of these D(t) values ​​are calculated to assess the stability of the calibration data. If CV > 5%, it indicates that the data fluctuates drastically during the calibration period, and the system should issue an alarm to prompt the operator to check. The calibration deviation cumulant is then substituted into the formula to calculate α.

[0053] As a further explanation of the aforementioned definition of the feature reference point, Φtarget The selection of Φ is not based on the simple assumption of a linear system, but rather on an engineering solution to the contradiction between the nonlinear kinetic characteristics of the polymerization reaction and the quality of the process detection signal. For systems with strong self-acceleration characteristics, a larger Φ is selected. target For example, 0.98-0.99. The polymerization kinetics of this type of system exhibit high exothermic sensitivity and abrupt viscosity changes. After the reaction enters the gel effect stage, the system viscosity increases rapidly and nonlinearly with the conversion rate, leading to the inhibition of chain termination and an exponential burst in the reaction rate within a short period, posing an extremely high risk of thermal runaway. A larger Φ is selected. target Essentially, this strategy trades space for time, utilizing a smaller deviation value space to achieve an earlier calibration timing. The system is set to critical point capture mode, initiating calibration as soon as the deviation δ(t) enters the preset lower limit of the initial linear interval. Although the signal is on the eve of a nonlinear burst and the signal-to-noise ratio is low at this point, this strategy ensures that the controller can obtain parameter α before the gel effect fully erupts, thereby achieving advanced control of the reaction heat. This means setting the calibration reference at the critical point of diffusion limitation germination, i.e., when the diffusion limitation coefficient just begins to decay slightly. At this time, although the deviation δ(t) within the calibration window... A small α value indicates that the diffusion resistance is still in a weak stage, but the system must complete parameter identification based on this early signal. This strategy is essentially about seizing the initiative in control. Although the calculated α value is relatively large and sensitive to noise at this point, it ensures that the controller can obtain control parameters immediately before the self-acceleration effect fully erupts, thereby achieving proactive intervention in the reaction heat and preventing runaway reactions due to parameter calibration lag. For systems with gentle kinetics, a smaller Φ is chosen. target For example, 0.95-0.97. The polymerization kinetics of such systems exhibit low self-acceleration or gradual viscosity variation. The reaction process is relatively stable, and diffusion limitation accumulates gradually with molecular chain growth. These systems typically require extremely high uniformity in product molecular weight distribution, and fluctuations in the stirring flow field and temperature noise within the reactor can easily interfere with parameter identification. A smaller Φ is selected. target This means setting the calibration baseline at the significant diffusion limitation period, i.e., when the diffusion limitation coefficient drops to 0.95-0.97. At this point, within the calibration window... A large numerical value indicates that the diffusion resistance has accumulated to a significant level, and the signal strength is much higher than the background noise. This strategy utilizes the noise immunity of large numerical signals. According to error propagation theory, a large numerical value... As the denominator, it can effectively suppress the amplification effect of measurement noise on the calculated α result. Although the calculated α response is relatively smooth, it has extremely high robustness and can truly reflect the global viscosity growth trend, avoiding control oscillations caused by overfitting to early small fluctuations, thus ensuring the structural uniformity of the polymerization product. Therefore, by flexibly setting Φ... target This feature benchmark enables true adaptive matching of model parameters.

[0054] The second calibration window is based on D(t), where D(t) is averaged again to obtain a more stable constant. This dual filtering mechanism, combining moving average and statistical averaging, uses a first layer—the τ-window—to filter out high-frequency noise and transient disturbances from the sensor, and a second layer—the calibration window—to extract steady-state characteristic values ​​during the reaction phase. Together, these two layers ensure that the calibration of the diffusion sensitivity coefficient α has extremely high robustness and will not be significantly deviated from by a brief noise spike.

[0055] S6: Based on the real-time temperature and diffusion confinement coefficient, a reaction kinetics evolution model incorporating micro-diffusion effects is constructed to calculate the predicted polymerization conversion rate. The evolution model substitutes the real-time temperature into the Arrhenius relation to calculate the apparent reaction rate coefficient, and constructs an ideal chemical reaction rate term using the reaction mechanism function. The diffusion confinement coefficient is then used to dynamically correct the ideal chemical reaction rate term to obtain the real-time evolution rate. By integrating the real-time evolution rate over time, the current predicted polymerization conversion rate is obtained.

[0056] Furthermore, the predicted conversion rate of the polymerization reaction is calculated, including: An evolution equation integrating microscopic diffusion constraints and macroscopic reaction dynamics is constructed, and the evolution equation is discretized and integrated in the time domain to obtain the predicted value of polymerization reaction conversion rate at the current sampling time. The evolution equation characterizes the instantaneous reaction rate after correction for the diffusion confinement coefficient, and its discretized integral mathematical model is expressed as follows: ; Where X(t) is the predicted conversion rate of the polymerization reaction at the current sampling time t, t=0 corresponds to the starting point of the reaction timing, k(T(s)) is the apparent reaction rate coefficient determined based on the real-time temperature T(s), obtained according to the Arrhenius relation, and f(X(s)) is the reaction mechanism function, which is pre-selected according to the type of polymerization reaction. The diffusion limitation coefficient is calculated, and s is the integration time variable, which represents any intermediate time on the integration path from the start of the reaction time to the current time. The discretized integral is calculated using a numerical iteration method, incorporating the diffusion limitation coefficient calculated at the previous sampling time in real time to update the instantaneous reaction rate at the current time.

[0057] Furthermore, the reaction mechanism function f(X(s)) is selected from one of the following models based on the type of polymerization reaction: First-order reaction model: ; n-order reaction model: ; Autocatalytic reaction model: ; Where X(s) is the conversion rate at time s, and n and m are preset reaction order parameters.

[0058] Specifically, in the field of polymerization reaction engineering, online prediction of conversion rate has always been a challenge. Traditional methods mainly involve two technical approaches, each with its own insurmountable drawbacks. The first approach is the Arrhenius model, which is solely based on temperature. This model assumes that the reaction rate is determined only by temperature, i.e. However, in the mid-to-late stages of the polymerization reaction, the actual reaction rate is far lower than the model's prediction. This is because the model completely ignores the diffusion limitation caused by the gel effect. As the system viscosity increases, monomer molecules cannot freely diffuse to the active chain ends, and even if the temperature remains constant, the reaction rate will decrease significantly. Therefore, the pure temperature model will produce a prediction error of more than 30% in the later stages of the reaction, making it completely unusable for endpoint control. The second approach is to try to directly measure the system viscosity using an offline viscometer or an online rheometer, and then establish an empirical correlation between viscosity and conversion rate. This approach faces two engineering challenges. First, online viscometers have extremely poor measurement accuracy in high-viscosity, viscoelastic fluids and are prone to clogging, resulting in extremely high maintenance costs. Second, the relationship between viscosity and conversion rate is not fixed but is affected by various factors such as molecular weight distribution and branching degree, making the empirical correlation unusable across batches.

[0059] This invention recognizes that the common flaw of the two aforementioned approaches lies in their either complete neglect of diffusion limitation or their attempt to directly measure the results of diffusion limitation instead of capturing its early signs. This invention offers a novel technical approach: creatively introducing a diffusion limitation coefficient and discovering a strong mapping relationship between this coefficient and the stirring load. Based on this discovery, instead of using expensive viscometers, the previously invisible and intangible diffusion limitation coefficient can be calculated in real time using the most common motor current and torque signals from the reactor, thus enabling advanced prediction of conversion rates. The first breakthrough of this invention lies in the fact that diffusion limitation does not occur suddenly, but rather undergoes a gradual process from its inception to its intensification. In the early stages of this process, although the macroscopic reaction rate has not yet shown a significant decrease, the stirring load has already begun to undergo characteristic changes. This time window typically lasts from tens of seconds to several minutes, providing valuable opportunities for parameter identification in this invention. Traditional methods wait until diffusion limitation has severely affected the reaction rate before taking action, which is a reactive measure. This invention completes parameter identification as soon as diffusion limitation begins to emerge, which is a proactive measure. This shift from result monitoring to sign capture is the core inventive aspect of this invention. The second breakthrough of this invention lies in the fact that it does not require precise measurement of the absolute value of viscosity, but only the capture of the relative trend of viscosity change. Traditional methods attempt to answer the question of "what is the viscosity?", which requires high-precision absolute measurement, making it extremely difficult to achieve in industrial environments. This invention only concerns whether the viscosity is increasing and how fast it is increasing; this is a relative judgment problem, which greatly improves the tolerance for sensor accuracy and noise. Based on this understanding, this invention constructs an evolution equation that integrates microscopic diffusion confinement and macroscopic reaction kinetics.

[0060] The basic form of the evolution equation: The technical innovation of this equation is reflected in the following three aspects: 1. A multiplicative structure rather than an additive structure. In traditional methods, some have attempted to add diffusion limitation as a correction term to the reaction rate, i.e. The problem with this additive structure is the correction term. The dimensions and magnitude of this are difficult to determine, and it easily leads to negative rate values. This invention employs a multiplicative structure, namely... Multiply by the intrinsic rate. The physical meaning of this structure is clear: diffusion confinement is suppression rather than superposition, and the degree of suppression is represented by a coefficient between 0 and 1. When At times, there is no inhibition; when At that time, it is completely suppressed. This structure ensures that the reaction rate is always non-negative and is completely consistent with the physical understanding of polymerization reaction engineering. 2. Real-time feedback of discretized integral: Since the analytical solution of the evolution equation does not exist, numerical methods must be used to solve it. Traditional numerical integration methods calculate the entire reaction process offline and cannot cope with factors such as real-time changes in temperature and batch differences in raw materials. This invention uses online discretized integration to update the conversion rate prediction value in real time in each sampling period. The recursive formula is as follows: ; The key to this recursive formula lies in the diffusion confinement coefficient at each time step. The value is obtained by calibration based on real-time data of the current batch in step S4, rather than a fixed value retrieved from an offline database. This means that the conversion rate prediction of this invention can adaptively match the differences in raw materials and fluctuations in reaction conditions between different batches, which is something that traditional offline models cannot achieve.

[0061] In the above evolution equation, k(T) is the apparent reaction rate coefficient, the value of which depends on the reaction temperature T. This invention uses the Arrhenius relation to calculate k(T): ; Here, A is the pre-exponential factor, also known as the frequency factor, and its value and unit depend on the reaction order. For example, for a first-order reaction, the unit of A is usually s. -1 For an nth-order reaction, the unit of A is... The value and unit of A can be determined based on the reaction order of the specific polymerization system. The activation energy is expressed in joules per mole (J / mol). R is the ideal gas constant, taken as 8.314 J / (mol·K). T is the absolute temperature in Kelvin (K), obtained by adding 273.15 K to the weighted average temperature from step S1. For the above kinetic parameters A and... The values ​​can be obtained through conventional differential scanning calorimetry experiments, depending on the specific polymerization system. Specifically, either isothermal or non-isothermal methods can be used: the exothermic curve of the polymerization reaction is measured at a set heating rate, the reaction heat flux at different temperatures is recorded, and then the Arrhenius equation is fitted using a nonlinear regression method to obtain A and . The numerical values ​​are as follows. Isothermal calorimetry experiments can also employ a similar approach. The methods for obtaining these parameters are common knowledge in the field and will not be elaborated upon here. This invention does not involve specific calibration methods for the aforementioned kinetic parameters, but rather focuses on how, based on these known parameters, to utilize real-time monitored stirring electrical parameters to identify the diffusion limitation coefficient online, thereby correcting the conversion rate prediction model. 3. Mathematical processing of initial conditions, starting from the reaction time... At that time, the conversion rate prediction value was set to The zero here is not an absolute claim to the actual conversion rate, but rather the starting point for integration in mathematics. The slight deviation between the actual conversion rate and zero will be gradually absorbed and corrected in subsequent integration processes.

[0062] Reaction mechanism function This invention describes the relationship between reaction rate and conversion rate. The mechanistic function is pre-selected based on the polymerization reaction type, rather than being identified online. Theoretically, complex mechanistic models could be used, such as those considering chain length distribution and free radical concentration changes. However, these models require identification of dozens of parameters, which is impossible to calibrate in real time in an industrial environment. This invention chooses the simplest mechanistic function form, such as a first-order reaction model. Only one parameter is needed. This minimalist design ensures the feasibility and real-time nature of calibration. For the bulk polymerization of methyl methacrylate, styrene, and vinyl acetate, as well as the solution polymerization of high-solids-content acrylates, the reaction mechanism can be approximated as a first-order reaction. This is because in free radical polymerization, the polymerization rate is directly proportional to the monomer concentration, and the monomer concentration... ,therefore This relationship has good approximate accuracy within a conversion rate not exceeding 80%. The endpoint control of this invention is typically triggered between 70% and 90% conversion, therefore the first-order reaction model fully meets the accuracy requirements. For systems deviating from the first-order reaction law, this invention provides an n-order reaction model and an autocatalytic reaction model as alternatives. n-order reaction model This model is suitable for systems with a reaction order other than 1, such as condensation polymerization. n represents the reaction order and reflects the sensitivity of the reaction rate to decreasing monomer concentration. When n=1, this model degenerates into a first-order reaction model. Autocatalytic reaction model. This method is applicable to systems where the reaction products catalyze the reaction, such as certain epoxy resin curing reactions. Here, n represents the non-autocatalytic reaction order, reflecting the effect of monomer concentration on the reaction rate; m represents the autocatalytic reaction order, reflecting the catalytic strength of the reaction product concentration on the reaction rate. A larger m value indicates a stronger promoting effect of the reaction product on the reaction rate. The parameters n and m are preset reaction order parameters, which can be predetermined according to the reaction mechanism of the specific polymerization system. When m=0, the autocatalytic reaction model degenerates into an n-order reaction model; when m=0 and n=1, it degenerates into a first-order reaction model. Therefore, both the first-order and n-order reaction models can be considered special forms of the autocatalytic reaction model. These three models cover the vast majority of polymerization reaction types, demonstrating the wide applicability of this invention.

[0063] In each sampling period, the system performs calculations in the following order. First, it reads the conversion rate prediction value stored from the previous sampling time. The second step is to read the real-time temperature from the previous sampling time. The apparent reaction rate coefficient was calculated based on the Arrhenius relation. The third step is to calculate based on the selected reaction mechanism function. The fourth step is to read the diffusion confinement coefficient calculated at the previous sampling time. The result is obtained from step S4 based on the real-time stirring load data of the current batch, calibrated online. The fifth step is to calculate the instantaneous reaction rate. Step 6: Update the conversion rate forecast for the current moment. Step 7, The data is stored in memory for use in the next sampling cycle, and simultaneously output to the operator interface or used for endpoint determination in step S6. Each sampling cycle requires only seven simple calculations, with minimal computational load, and can be run in real time on a conventional industrial controller.

[0064] S7: Based on the diffusion limitation coefficient monitored in real time, the reaction endpoint threshold is dynamically corrected, and the predicted conversion rate is compared with the corrected reaction endpoint threshold to control the termination time of the polymerization reaction according to the comparison result.

[0065] Furthermore, controlling the timing of termination of the polymerization reaction includes: Set diffusion limit threshold , and the first conversion rate target value and the second conversion rate target value, wherein, Used to distinguish the diffusion-limited stage of the reaction, the second conversion target value is less than the first conversion target value; Real-time monitoring of the diffusion confinement coefficient And dynamically update the current reaction endpoint threshold based on the monitoring results; when ≥ When the reaction is determined to be in the weak diffusion-limited stage, the current reaction endpoint threshold is updated to the first conversion rate target value. when < When the reaction is determined to be in a strong diffusion-limited stage, the current reaction endpoint threshold is updated to the second conversion rate target value. The predicted conversion rate X(t) calculated in real time is compared with the updated reaction endpoint threshold. When X(t) ≥ the updated reaction endpoint threshold, the reaction termination process is triggered.

[0066] Specifically, in this embodiment, the determination of the reaction endpoint no longer depends on a fixed time or a single conversion rate threshold. Instead, a diffusion limitation coefficient is introduced as a real-time state characterization variable. By dynamically switching between the first conversion rate target value and the second conversion rate target value, an adaptive balance between product quality and process safety is achieved. This is a preset diffusion limitation threshold used to distinguish the diffusion limitation stage of a reaction, and is a key threshold for differentiating between weakly and strongly diffusion-limited regions. Its calibration is based on the following: Selecting a typical batch of test reactions and recording the diffusion limitation coefficient throughout the entire reaction cycle. Change curve. In this embodiment, This calculation is based on the normalized stirring torque. The first derivative with respect to time, the discrete sampling characteristics of the industrial control system, and the instantaneous rate of change are calculated using the backward difference method, as shown in the following formula: ; in, The system sampling period is The diffusion restriction coefficient at the current moment. This is the value from the previous moment. Search for... The time t when the maximum value is reached 拐点 The time corresponding to Value calibrated as . The absolute value depends on the selection of process variables and the normalization benchmark. Based on the normalization of stirring torque, its inflection point value is mainly affected by the stirrer impeller type, transmission efficiency, and torque sensor sensitivity. When ≥ At this stage, the system is in a weakly diffusion-restricted phase, viscosity increases slowly, chain termination is not significantly hindered, and the reaction is in a controllable region; when < At this point, the system enters a strongly diffusion-confined phase, exhibiting a significant gelation effect and a sharp increase in viscosity, posing a risk of thermal runaway. Real-time monitoring revealed... ≥ At that time, the first conversion rate target value is triggered. First conversion rate target value X target1 Based on product quality indicators, in the weak diffusion-restricted region, heat and mass transfer are good, allowing the reaction to proceed to a higher conversion rate to minimize residual monomer content, such as requiring residual monomer <0.5%, thereby improving product purity and economic benefits. At this point, the system determines that the safety margin is sufficient and adopts an aggressive strategy to break through the traditional conservative upper limit, pursuing the ultimate conversion efficiency. Real-time monitoring... < At that time, the second conversion rate target value is triggered. Second conversion rate target value X target2 Based on process safety indicators, in the region of strong diffusion restriction, the system viscosity increases dramatically, making heat dissipation difficult and easily leading to local overheating, explosive polymerization, or uncontrollable gelation. At this point, the system is forced to switch to a defense strategy, lowering the endpoint threshold to a lower level and terminating the reaction early to avoid safety risks, ensuring controllable molecular weight distribution and inherent safety in production.

[0067] Dynamic endpoint control of methyl methacrylate (MMA) in typical batches: MMA bulk polymerization is one of the free radical polymerization systems with the most significant gel effect. In the initial stages of the reaction, the system viscosity is low, the chain termination reaction proceeds normally, and the diffusion confinement coefficient is low. The viscosity remains at a high level. When the conversion rate reaches 10% to 20%, the system viscosity increases sharply, chain radical diffusion is hindered, the bimolecular termination rate constant decreases significantly, and the polymerization rate enters an auto-acceleration phase. The curve shows a steep downward trend. (Select) The inflection point where the curve changes at its maximum rate, i.e., the point where the gelation effect accelerates most rapidly, is taken as the critical threshold. For the methyl methacrylate system, this inflection point corresponds to... The value is approximately 0.4. At this point: if ≥0.4 indicates the system is in a weak diffusion-limited stage. The first conversion target value, i.e., an aggressive strategy, is adopted, allowing the reaction to proceed to a higher conversion rate, such as above 80%, to minimize residual monomer content and improve product optical purity. If... If the conversion threshold is less than 0.4, the system is considered to have entered a strong diffusion-limited stage. The system is immediately switched to the second conversion target value, i.e., a defensive strategy, lowering the endpoint threshold to a lower level, such as 60% to 70%, to terminate the reaction early and avoid safety risks such as local overheating and explosive polymerization, ensuring a uniform molecular weight distribution. Dynamic endpoint control in styrene bulk polymerization is crucial, as the gel effect develops relatively slowly. Because styrene is a good solvent for polystyrene, the viscosity of the system increases slowly during polymerization, and chain radical diffusion is hindered relatively late. Typically, the autoacceleration stage only begins when the conversion reaches approximately 30%. The downward trend of the curve is relatively mild. The determination is also based on The inflection point with the largest rate of change in the curve is determined by this principle. Since the styrene gel effect develops gradually, its inflection point corresponds to... The value is approximately 0.35. At this point: if ≥0.35 indicates the system is in a weak diffusion-limited stage. The first conversion rate target value is adopted, i.e., an aggressive strategy, aiming for a higher conversion rate to improve monomer utilization. If... 0.35 indicates that the system has entered a strong diffusion-limited stage. The system is then switched to the second conversion rate target value, which is a defensive strategy. The reaction is terminated early to control the molecular weight distribution and avoid product performance degradation due to excessive cross-linking. This solution dynamically switches the conversion rate target value, resolving the contradiction in traditional fixed threshold control where high conversion rates are accompanied by high risks or sacrifices for safety. For bulk polymerization of methyl methacrylate, it can reduce the residual monomer content to below 0.5% while ensuring safety; for bulk polymerization of styrene, it can effectively avoid an excessively wide molecular weight distribution, improving the mechanical strength and processing performance of the product.

[0068] The first conversion rate target value is determined based on product quality indicators, including residual monomer content and molecular weight distribution, combined with the reaction kinetic window. When the system is in the weak diffusion-restricted region, the reaction rate is mainly controlled by chemical kinetics. At this time, the system viscosity is low, heat and mass transfer is good, chain termination reaction is not significantly inhibited, and there is no obvious gelation effect, providing a kinetic basis for achieving a high conversion rate. Activating the first conversion rate target value allows full utilization of the reaction window, maximizing monomer utilization and product purity. Typical values ​​are 80% to 85% for bulk polymerization of methyl methacrylate and 80% to 82% for bulk polymerization of styrene. The second conversion rate target value is rigidly constrained by process safety indicators, including anti-explosive polymerization and anti-gelation, combined with the diffusion-restricted critical state. When the system enters the strong diffusion-restricted region, the system viscosity increases exponentially, leading to hindered removal of reaction heat and the risk of heat accumulation. Simultaneously, the chain termination reaction is significantly inhibited by diffusion control, triggering an auto-acceleration effect, i.e., the gelation effect. Continued reaction will significantly increase the risk of explosive polymerization. Switching to the second conversion target value at this point allows for timely termination of the reaction, achieving risk-triggered stop-loss. Typical values ​​are 65% to 70% for bulk polymerization of methyl methacrylate and 75% to 80% for bulk polymerization of styrene. The core function of the dual conversion target values ​​is to correlate with the diffusion limitation threshold. The key to forming a dual-threshold control logic lies in utilizing the safety buffer between the first and second conversion rate target values. When Φ(t)≥ At this point, the system is in a weakly diffusion-limited state. The system activates the first conversion target value, allowing the reaction to proceed towards higher conversion rates, aiming to fully utilize the reaction kinetic window and pursue the ultimate product purity. When Φ(t) < At this point, the system enters a strongly diffusion-limited state, and the system is forcibly switched to the second conversion rate target value. At this time, if the real-time conversion rate X(t) is within the safe buffer zone, i.e., X... target2 ≤X(t) <X target1 The system will immediately trigger a termination process. This mechanism utilizes the safety buffer interval ΔX as the trigger lever for safety circuit breaking. For systems with significant gelation effects, such as methyl methacrylate, a larger safety buffer interval is set, for example, 15%, to ensure that a portion of the conversion is sacrificed for safety when risks arise. For systems with gradual diffusion limitations, such as styrene, a smaller safety buffer interval is set, for example, 2% to 5%, to preserve as much yield as possible while ensuring safety. This differentiated design achieves a dynamic balance between safety and efficiency.

[0069] The core innovation of this solution lies in the construction of a security monitoring system. A dual-threshold control mode coupled with progress monitoring (X). Traditional polymerization reaction control often faces a dilemma: setting a high conversion endpoint can easily trigger explosive polymerization when the gel effect occurs; setting a low conversion endpoint can lead to excessive residual monomers in the product, resulting in quality degradation. This solution resolves the above contradiction through the following logic: First Threshold The determination is made using the diffusion limitation coefficient. As a safety sentinel, it doesn't directly decide when to stop, but rather determines the standards for stopping. When ≥ At this point, the system determines that the conditions for maximizing productivity are met, and therefore sets the endpoint standard to a high threshold, i.e., the first conversion rate target value. < At this point, the system determines that the diffusion limit is out of control and must be stopped immediately. Therefore, it dynamically lowers the endpoint standard to a low threshold, i.e., the second conversion rate target value. The determination of the second threshold X uses the predicted conversion rate value X(t) as a progress bar. It is responsible for comparing it with the currently dynamically changing endpoint standard. In the early stages of the reaction, because X(t) is low, even... The concentration is high, but it won't trigger a shutdown, thus ensuring the reaction can proceed towards a high conversion rate. Once... The mutation causes the standard to be lowered, switching to a second conversion rate target value. However, at this point, X(t) has often already exceeded the lowered second conversion rate target value. Because the reaction is still in progress, the system will immediately trigger termination. This dual-threshold logic allows this scheme to, within safe limits, carry out the reaction as thoroughly as possible compared to a conservative low-threshold process throughout; at the same time, if a risk arises, compared to an aggressive high-threshold process throughout, it can ensure timely shutdown by lowering the standard. This achieves a perfect balance between maximizing yield and process safety.

[0070] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the conversion rate and self-correcting parameters of polymerization reactions in a coaxial double-stirred reactor, characterized in that, Includes the following steps: The real-time torque and current components of the inner shaft drive motor and the outer shaft drive motor in the reactor, the real-time speed of the inner shaft agitator and the outer shaft agitator, and the real-time temperature of the material in the reactor are collected synchronously. The real-time temperature is the weighted average of the temperatures of multiple points in the reactor. The collected signals are subjected to amplitude limiting filtering, moving average filtering and outlier removal to obtain preprocessed real-time monitoring data. Based on the cross-product operation of the real-time torque current components and real-time speed of the pre-processed inner and outer shaft drive motors, a value representing the stirring power of the inner and outer shafts is obtained. After normalization correction by the geometric structure constant of the reactor stirrer, a dimensionless characteristic ratio representing the interaction state of the inner and outer shaft flow fields is obtained. In response to the addition of the initiator or the material temperature rising to the initiation threshold, when the real-time temperature of the material is monitored to be stable within the preset initiation temperature range, and the real-time torque current component of the inner shaft drive motor does not show a continuous upward trend within the preset sliding back window, the dimensionless characteristic ratio of at least M stirring cycles is immediately collected, and its average value is taken as the reference value, where M is a preset positive integer. After obtaining the reference value, the real-time torque current component of the preprocessed inner shaft drive motor is continuously monitored to determine the moment when it first shows a continuous upward trend as the starting point of the reaction timing. Based on the dimensionless characteristic ratio and the reference value, the deviation accumulation degree is calculated. The deviation accumulation degree represents the cumulative value of the deviation of the dimensionless characteristic ratio from the reference value within a preset sliding integral time window. A diffusion limitation coefficient characterizing the diffusion limitation effect is constructed. Starting from the start of the reaction time, when the relative deviation of the dimensionless characteristic ratio is detected to enter the preset initial deviation interval, the mean of the cumulative deviation within the interval is obtained. Based on the mean of the cumulative deviation and the preset target initial diffusion limitation coefficient, the diffusion limitation coefficient is determined. Based on the real-time temperature and diffusion confinement coefficient, a reaction kinetics evolution model incorporating micro-diffusion effects is constructed to calculate the predicted polymerization conversion rate. The evolution model substitutes the real-time temperature into the Arrhenius relation to calculate the apparent reaction rate coefficient, and constructs an ideal chemical reaction rate term using the reaction mechanism function. The diffusion confinement coefficient is then used to dynamically correct the ideal chemical reaction rate term to obtain the real-time evolution rate. By integrating the real-time evolution rate over time, the current predicted polymerization conversion rate is obtained. The diffusion limitation coefficient is monitored in real time, the reaction endpoint threshold is dynamically corrected, and the predicted conversion rate is compared with the corrected reaction endpoint threshold. The timing of termination of the polymerization reaction is controlled based on the comparison results.

2. The method for predicting the conversion rate and self-correcting parameters of a coaxial double-stirred reactor polymerization reaction as described in claim 1, characterized in that, The dimensionless characteristic ratios characterizing the interaction state of the internal and external axial flow fields are obtained, including: Based on the preprocessed real-time torque and current components I of the inner and outer shaft drive motors inner I outer and the real-time rotational speed (N) of the internal and external shaft agitators inner N outer The dimensionless eigenratio R(t) at the current sampling time is calculated using the following formula: ； in, As the lower limit of numerical protection, C geo The normalized geometric similarity constant is used to make the time-domain mean of the dimensionless eigenratio approach 1.

0. Its calculation formula is as follows: ； Among them, D inner With D outer These are the blade diameters of the inner and outer shaft agitators, respectively, K. p-inner With K p-outer These are the standard power parameters for the inner shaft stirrer and the outer shaft stirrer, respectively, and the standard power parameters are constants that are only related to the blade configuration.

3. The method for predicting the conversion rate and self-correcting parameters of a coaxial double-stirred reactor polymerization reaction as described in claim 2, characterized in that, Collect dimensionless characteristic ratios for at least M stirring cycles, and take their average as the baseline value, where M is a preset positive integer, including: In response to the addition of initiator or the material temperature rising to the initiation threshold, baseline monitoring is initiated, including: The real-time torque current component of the inner shaft drive motor is calculated in real time within the sliding back window. The trend characteristic value is the fitting slope obtained by least square linear fitting of the current data in the sliding back window. When the fluctuation range of the real-time temperature of the material is less than the preset temperature threshold, and the characteristic value of the change trend is less than the preset trend threshold, the reaction system is determined to be in the baseline state of the induction period. If the material is determined to be in the baseline state of the induction period, the first calibration acquisition window is immediately opened. Within the first calibration acquisition window, the real-time temperature and trend characteristics of the material are continuously monitored to see if they still meet the determination conditions of the baseline state of the induction period. If satisfied, the dimensionless feature ratios are accumulated until M cycles are collected. The statistical mean of the dimensionless feature ratios within the first calibration collection window is calculated as the benchmark value, which is numerically close to 1.

4. The method for predicting the conversion rate and self-correcting parameters of a coaxial dual-stirred reactor polymerization reaction as described in claim 3, characterized in that, Calculate the cumulative deviation, including: ； in, The deviation cumulancy characterizes the length of the backtracking time from the current sampling time t. Within the interval, the average deviation of the dimensionless eigenvalue relative to the benchmark value; t is the current sampling time, and its zero point t=0 corresponds to the starting point of the reaction timing; The preset sliding integral time window length, It is a positive number; s is the integration variable, representing the time window. , Any time within ]; Let be the value of the dimensionless eigenratio at time S. The reference value; It represents the instantaneous deviation of the dimensionless characteristic ratio at time S from the reference value.

5. The method for predicting the conversion rate and self-correcting parameters of a coaxial double-stirred reactor polymerization reaction as described in claim 4, characterized in that, The reaction timing start point includes: After the first calibration acquisition window ends, the characteristic value of the change trend of the real-time torque current component of the inner shaft drive motor continues to be calculated in real time. When the detected trend characteristic value changes from less than a preset trend threshold to greater than a preset rise threshold for Q consecutive sampling periods, it is determined that a continuous upward trend has appeared for the first time, where Q is a preset positive integer; The time corresponding to the first sampling point that meets the above conditions is the starting point of the reaction time.

6. The method for predicting the conversion rate and self-correcting parameters of a coaxial double-stirred reactor polymerization reaction as described in claim 4, characterized in that, The diffusion limitation coefficient is calculated based on the aforementioned deviation cumulancy and diffusion sensitivity coefficient, including: Calculate the diffusion confinement coefficient at the current sampling time. The formula is as follows: ； in, The diffusion sensitivity coefficient, The cumulative deviation at the current sampling time; The following adaptive calibration method is used to determine... : Starting from the start of the reaction time, monitor the relative deviation of the dimensionless characteristic ratio relative to the reference value; When the relative deviation enters the preset initial deviation range, the second calibration window is opened, and based on the relative deviation data within the preset time period before the current sampling time, it is simultaneously determined whether the relative deviation shows a linear growth trend. If the judgment result is yes, then keep the second calibration window open and continue to collect the cumulative deviation at each sampling time within the window; When the relative deviation exceeds the initial deviation interval, the second calibration window is closed, and the statistical average of the collected cumulative deviations is calculated and recorded as the calibration cumulative deviation. ; Based on the calibration deviation accumulation and the preset target initial diffusion limitation coefficient, the following is calculated: The formula is as follows: ； in, The initial diffusion limitation coefficient is a preset target, used to characterize the expected baseline level of diffusion limitation effect at the end of the second calibration window.

7. The method for predicting the conversion rate and self-correcting parameters of a polymerization reaction in a coaxial double-stirred reactor as described in claim 6, characterized in that, Calculate the predicted conversion rate of the polymerization reaction, including: An evolution equation integrating microscopic diffusion constraints and macroscopic reaction dynamics is constructed, and the evolution equation is discretized and integrated in the time domain to obtain the predicted value of polymerization reaction conversion rate at the current sampling time. The evolution equation characterizes the instantaneous reaction rate after correction for the diffusion confinement coefficient, and its discretized integral mathematical model is expressed as follows: ； Where X(t) is the predicted conversion rate of the polymerization reaction at the current sampling time t, t=0 corresponds to the starting point of the reaction timing, k(T(s)) is the apparent reaction rate coefficient determined based on the real-time temperature T(s), obtained according to the Arrhenius relation, and f(X(s)) is the reaction mechanism function, which is pre-selected according to the type of polymerization reaction. The diffusion limitation coefficient is calculated, and s is the integration time variable, which represents any intermediate time on the integration path from the start of the reaction time to the current time. The discretized integral is calculated using a numerical iteration method, incorporating the diffusion limitation coefficient calculated at the previous sampling time in real time to update the instantaneous reaction rate at the current time.

8. The method for predicting the conversion rate and self-correcting parameters of a polymerization reaction in a coaxial double-stirred reactor as described in claim 7, characterized in that, The reaction mechanism function f(X(s)) is selected from one of the following models based on the type of polymerization reaction: First-order reaction model: ; n-order reaction model: ; Autocatalytic reaction model: ; Where X(s) is the conversion rate at time s, and n and m are preset reaction order parameters.

9. The method for predicting the conversion rate and self-correcting parameters of a polymerization reaction in a coaxial double-stirred reactor as described in claim 7, characterized in that, Controlling the timing of termination of the polymerization reaction includes: Set diffusion limit threshold , and the first conversion rate target value and the second conversion rate target value, wherein, Used to distinguish the diffusion-limited stage of the reaction, the second conversion target value is less than the first conversion target value; Real-time monitoring of the diffusion confinement coefficient And dynamically update the current reaction endpoint threshold based on the monitoring results; when ≥ When the reaction is determined to be in the weak diffusion-limited stage, the current reaction endpoint threshold is updated to the first conversion rate target value. when < When the reaction is determined to be in a strong diffusion-limited stage, the current reaction endpoint threshold is updated to the second conversion rate target value. The predicted conversion rate X(t) calculated in real time is compared with the updated reaction endpoint threshold. When X(t) ≥ the updated reaction endpoint threshold, the reaction termination process is triggered.

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