A double-layer homotopy-based polyolefin reaction module circulating process convergence method

Abstract

The application discloses a kind of based on double-layer homotopy's polyolefin reaction module circulating process convergence method, belong to chemical industry process simulation field.This method sets up process level homotopy parameter and unit level homotopy parameter in computer process model, constructs tear stream initial value with non-reactive component as leading;Outer process level homotopy gradually increases λ, gradually loads real circulating stream, gradually increases recovery polymerization reaction term in inner layer, solves in each homotopy stage using full load priority, failure rollback and adaptive step length strategy, until λ=1 and α=1 When the convergent solution of original process model is obtained.The application can improve the robustness of steady-state solution of circulating process under unknown or disturbed tear initial value, and is suitable for polyolefin reaction module process simulation and online recalculation.

Description

Technical Field

[0001] This invention relates to the field of chemical process simulation, and in particular to a convergence method for a polyolefin reaction module cyclic process based on bilayer homotopy. Background Technology

[0002] Process simulation is a crucial foundation for process systems engineering and digital twins. Processes involving circulating streams typically require tearing the circulating stream and solving for fixed points. Polyolefin reaction module processes usually include fluidized bed reactors and circulating gas loops, involving multi-component gas-phase circulation, phase equilibrium of condensable components, Ziegler-Natta polymerization kinetics, and polymer property calculations. During operating condition switching or online recalculation, the reactor local equations are prone to failure due to the deep coupling of strong reaction terms and phase equilibrium. Furthermore, reliable initial values ​​for tearing the stream are difficult to predefine, and the reactor local equations may also fail due to the coupling of strong reaction terms and phase equilibrium.

[0003] Homotopy extension methods can reduce the dependence of nonlinear equation solutions on initial values ​​by constructing a continuous path from easily solvable auxiliary problems to the target problem. Chen et al. proposed a homotopy backtracking method with second-order correction, and Li Hongrui et al. proposed a cyclic homotopy convergence algorithm based on adaptive variable step size. WO2024074673A1 discloses a computer implementation method for generating digital twins of chemical processes or chemical plants, which obtains multiple simulation data points by gradually changing boundary condition parameters, and mentions that the homotopy method can be used to approach the target point when the simulation does not converge. WO2023093857A1 discloses a method for solving nonlinear equation systems based on quantum circuits, which uses the homotopy perturbation method to convert quadratic nonlinear equation systems or nonlinear ordinary differential equation systems into linear equation system information. US20160048150A1 discloses the use of homotopy extension methods to transition from simplified problems to complete nonlinear problems in the optimal power flow solution of large-scale power systems.

[0004] The above methods show that the homotopy concept has been used in scenarios such as solving nonlinear equations, process simulation, or generating digital twin data. Although it has improved the convergence performance of some processes with circulating flow streams, it usually uses the equation set level to unify the homotopy parameters, which cannot directly solve the dual problems of the initial value sensitivity of the polyolefin reaction module tearing and the strong local nonlinear coupling of the reactor.

[0005] To address the aforementioned problems, this invention proposes a convergence method with a clear process physical meaning: on the one hand, it can stably load the circulating gas stream under unknown or disturbed tearing initial values; on the other hand, it can gradually recover the strong polymerization reaction term within the reactor unit and proposes an inert component initial value strategy, thereby improving the robustness of the polyolefin reaction module process simulation and reducing the dependence of the circulating process on the tearing stream initial value. Summary of the Invention

[0006] This invention addresses the shortcomings of existing technologies by proposing a convergence method for a polyolefin reaction module loop process based on bilayer homotopy. This method constructs a bilayer homotopy framework consisting of an outer process loop and an inner unit model, using process-level homotopy parameters... Gradually advance the loading of cyclic logistics, based on reaction intensity parameters The reaction is gradually advanced, and an initial value strategy for the inert component in the tearing stream is proposed to improve the convergence robustness of the polyolefin reaction module cyclic process simulation.

[0007] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a convergence method for a polyolefin reaction module cyclic process based on bilayer homotopy, comprising: (1) Obtain the circulating process model of the polyolefin reaction module to be solved, wherein the circulating process includes an olefin polymerization reactor and a circulating loop connected between the gas phase outlet and the inlet of the reactor; (2) Construct a two-layer homotopy solution framework that includes inner-layer cell-level homotopy and outer-layer process-level homotopy, and set process-level homotopy parameters. Hotopism parameters at the unit level ,in Used to control the loading level of real-world circular logistics. Used to control the degree of recovery of polymerization reaction items in the reactor unit; (3) Construct inner-cell-level homotopy: Under the given process-level homotopy parameters The following section introduces the unit-level homotopy parameter into the steady-state material balance equation for the reactor unit. Construct unit-level homotopy equations and adaptively adjust them. Progressing from 0 to 1, gradually introducing polymerization reaction terms; (4) Constructing outer-layer process-level homotopy: Based on the inner-layer cell-level homotopy solution, the process-level homotopy parameter is introduced to address the problem of fixed points of torn flow strands in the cyclic process. Through adaptive adjustment Progressing from 0 to 1, gradually implementing real-world circular logistics, each... Each stage solves the problem of fixed points in the tearing flow strand; (5) Initial values ​​of the inert component in the tearing flow stream The scale of the recycle gas was determined with non-reactive components as the dominant components, serving as the initial basis for process-level isotope. (6) In both process-level homotopy and cell-level homotopy, a full-load priority, failure rollback, and adaptive step size strategy is adopted until... and And satisfy the process convergence conditions, output the convergence simulation results of the polyolefin reaction module cycle process.

[0008] Compared with the prior art, the beneficial effects of the present invention are: (1) The present invention introduces the homotopy method in the process of solving the process, and gradually transitions the complex process model from the easily convergent auxiliary model to the target model. Based on the continuous deformation effect of the homotopy path, the tear flow variable can gradually approach the target solution in the iteration process, thereby reducing the dependence of the process solution on the accuracy of the initial guess value of the tear flow, expanding the convergence initial value range of the process simulation, and improving the overall convergence stability of the process.

[0009] (2) This invention introduces a unit-level homotopy solution strategy for polymerization reactor units, and solves the strongly nonlinear reaction calculation process in polymerization reactors in stages. By reducing the degree of nonlinear mutation when directly solving the model, the non-convergence problem caused by poor initial values ​​or strong model rigidity in polymerization reactors can be reduced, thereby improving the solution robustness and convergence success rate of polymerization reactor units.

[0010] (3) In the simulation of new operating conditions, this invention combines an inert initial value strategy, using relatively stable inert or weakly coupled initial values ​​as the starting point for the solution, and gradually introduces the target operating condition conditions through process-level homotopy and / or cell-level homotopy. Thus, even in the absence of accurate initial guesses of the tearing flow stream, a relatively stable initial solution path can still be obtained, reducing the need for repeated manual adjustment of initial values ​​and improving the automation level and computational reliability of the simulation of new operating conditions. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the cyclic process of the polyolefin reaction module in an embodiment of the present invention; Figure 2 This is a schematic diagram of the circulating process of the gas-phase polyethylene reaction module in an embodiment of the present invention; Figure 3 This is the cell-level homotopy path diagram in this invention; Figure 4 This is the process-level homotopy path diagram in this invention. Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described in detail below with reference to specific embodiments. Specific embodiments are described below to simplify the invention. However, it should be understood that the invention is not limited to the described embodiments, and various modifications are possible without departing from the basic principles; these equivalent forms also fall within the scope defined by the appended claims.

[0013] The convergence method for the polyolefin reaction module cycle flow based on bilayer homotopy provided in this invention is applicable to the simulation and online recalculation of the polyolefin reaction module cycle flow.

[0014] refer to Figure 1 The polyolefin reaction module circulation process of the present invention includes: an olefin polymerization reactor, a reactor inlet pipeline, a reactor outlet pipeline, a circulation stream pipeline, a fresh material feed pipeline, and heat exchangers, pumps or compressors required for regulating the temperature and pressure of the stream. Part of the material in the reactor outlet pipeline returns to the reactor inlet through the circulation stream pipeline.

[0015] Typically, but not limited to, the polyolefin reaction module can be a gas-phase polyolefin module, such as... Figure 2 As shown, the gas-phase polyolefin module includes a fluidized bed reactor, a circulating gas compressor, a circulating gas cooler, and a distributor. The top gas-phase outlet of the fluidized bed reactor is connected to the distributor, the first outlet of which is connected to the inlet of the circulating gas compressor, and the second outlet is a gas-phase outlet stream. The outlet of the circulating gas compressor is connected to the inlet of the circulating gas cooler, and the outlet of the circulating gas cooler is connected to the inlet of the fluidized bed reactor. A liquid-phase outlet stream is provided at the bottom of the fluidized bed reactor. Furthermore, a first inlet stream is provided between the distributor and the inlet of the circulating gas compressor, a second inlet stream is provided between the compressor outlet and the inlet of the circulating gas cooler, a third inlet stream is provided between the outlet of the circulating gas cooler and the inlet of the fluidized bed reactor, and a fourth inlet stream is also provided on the sidewall of the fluidized bed reactor.

[0016] Typically, but not limited to, the polyolefin reaction module can also be a slurry polyolefin module, which includes a slurry reactor, a circulating gas compressor, a heat exchanger, and a flash separation tank; the top gas phase outlet of the slurry reactor is connected to the heat exchanger, the heat exchanger outlet is connected to the flash separation tank, the top gas phase outlet of the flash separation tank is connected to the inlet of the circulating gas compressor, the circulating gas compressor outlet is connected to the inlet of the slurry reactor, and the bottom liquid phase outlet of the flash separation tank is connected to the inlet of the slurry reactor; the slurry reactor is equipped with feed lines for fresh monomers, comonomers, hydrogen, catalyst, cocatalyst, and solvent.

[0017] The convergence method for the polyolefin reaction module cyclic process based on bilayer homotopy proposed in this invention mainly includes the following steps: (1) Obtain the circulating process model of the polyolefin reaction module to be solved, wherein the circulating process includes an olefin polymerization reactor and a circulating loop connected between the gas phase outlet and the inlet of the reactor; (2) Construct a two-layer homotopy solution framework that includes inner-layer cell-level homotopy and outer-layer process-level homotopy, and set process-level homotopy parameters. Hotopism parameters at the unit level ,in Used to control the loading level of real-world circular logistics. Used to control the degree of recovery of polymerization reaction items in the reactor unit; (3) Construct inner-cell-level homotopy: Under the given process-level homotopy parameters The following section introduces the unit-level homotopy parameter into the steady-state material balance equation for the reactor unit. Construct unit-level homotopy equations and adaptively adjust them. Progressing from 0 to 1, the polymerization reaction term is introduced gradually.

[0018] Specifically, the homotopy equation at the unit level takes the form of:

[0019] In the formula, Let the reactor state vector be... This is the feed molar flow vector, i.e., the feed term; This is the discharge molar flow vector, i.e., the discharge term; This is the reaction rate term, a vector representing the net rate of formation of each component due to the chemical reaction. Its specific form is determined based on the selected polymerization kinetic model and is related to the components, temperature, and pressure. For the volume of the reaction phase, when When the reaction rate term is turned off, the problem degenerates into a calculation of mixing and flash evaporation; when Then, restore the true reactor equation.

[0020] The solution process for inner-layer element-level homotopy is as follows: the solver first attempts to find the inner-layer element-level homotopy. Perform a local solution under full load conditions; if the solution fails, then proceed as follows: The sequence is backtracked to find a convergent starting point. ,in The maximum number of backtracking iterations is preset; a convergent starting point is determined. Afterwards, from Starting from this point, a secant prediction and adaptive step size strategy are employed. Progress gradually up to 1; if backtracking reaches the preset minimum value If the process still fails or the set limit for backtracking is reached, then the stage is considered a failure.

[0021] (4) Constructing outer-layer process-level homotopy: Based on the inner-layer cell-level homotopy solution, the process-level homotopy parameter is introduced to address the problem of fixed points of torn flow strands in the cyclic process. Through adaptive adjustment Progressing from 0 to 1, gradually implementing real-world circular logistics, each... The problem of fixing points in the tearing flow strand is solved in each stage.

[0022] Specifically, the process-level homotopy mapping is as follows:

[0023]

[0024]

[0025] In the formula, The tearing flow state vector includes the molar flow rate and temperature of each component. and pressure , For the actual process in the tearing flow state The returned result; This is the initial vector of molar flow rates of each component in the tearing flow stream. This is the return result for the torn flow under the initial value. When At that time, the process-level homotopy mapping degenerates into a basis system dominated by inert components; when This is a true cyclical system.

[0026] Each of the steps in (4) The problem of fixing points in the tearing flow stream during a given stage can be solved using the Wegstein method, Broyden method, or Newton-type method. In this embodiment, the Wegstein method is specifically used.

[0027] (5) Initial values ​​of the inert component in the tearing flow stream The scale of the recycle gas was determined with non-reactive components as the dominant component, serving as the initial basis for process-level isotope.

[0028] Specifically, the initial value of the inert component of the tearing stream In this process, the molar flow rate of non-reactive components constitutes the main body of the total molar flow rate of the circulating gas, while the molar flow rates of other components are set to a preset minimum positive flow rate; wherein, the non-reactive components include nitrogen, isopentane, methane, ethane, and n-butane.

[0029] When reliable initial values ​​for the tearing flow strands cannot be obtained in advance under changing operating conditions, new operating conditions, or online recalculation scenarios, the initial values ​​for the inert components of the tearing flow strands are adopted. An initial basis for process-level homotopy is constructed; wherein the molar flow rate of the non-reactive component is used to determine the total molar flow rate of the target recycle gas, and the preset minimum flow rate of the other components is taken as 10% of the total molar flow rate of the target recycle gas. -6 Up to 10 -2 times.

[0030] (6) In both process-level homotopy and cell-level homotopy, a full-load priority, failure rollback, and adaptive step size strategy is adopted until... and And satisfy the process convergence conditions, output the convergence simulation results of the polyolefin reaction module cycle process.

[0031] In the adaptive step size strategy, the step size update formula is:

[0032]

[0033] In the formula express or , To determine the next step length after a successful solution, To determine the backoff step size after a failure, Step size growth factor and >1, The step size contraction factor is 0 < <1, To limit the maximum step size, This is a minimum step size constraint.

[0034] In the aforementioned method of the present invention, the homotopy parameters, solution variables, iteration count and convergence state of each homotopy stage are further recorded and used for the step size and variable update of the next stage.

[0035] Example 1 This embodiment uses a circulating gas-phase polyethylene polymerization process as an example; for details, please refer to [link / reference needed]. Figure 2 In the embodiments, ethylene (monomer, C2H4) and hydrogen (chain transfer agent, H2) are combined into Feed1 stream, 1-butene (comonomer, C4H8), inert gas nitrogen (N2), and condenser isopentane (C5H4H8). 12 The components are summarized as Feed2 stream, catalyst (TiCl4), and co-catalyst (C6H). 15 The reaction mixture (Al) was aggregated into Feed3 stream, and the reactor gas phase outlet stream was a tear stream. Polyethylene (LLDPE) was discharged from the reactor liquid phase outlet. The reactor operating temperature was 360.15 K, and the operating pressure was 2.38 MPa. Property calculations were performed using the PC-SAFT equation of state (Perturbed-Chain Statistical Associating Fluid Theory). This method typically characterizes fluid molecules as chain molecules composed of chain segments and describes the thermodynamic properties of the system through contributions from hard chains, dispersion, and association. It can be used for property calculations of hydrocarbon and polymer systems. Reaction kinetics were performed using the Ziegler-Natta catalytic ethylene / 1-butene copolymerization kinetic model. This type of model is based on the coordination insertion polymerization of olefins at the active center of the Ziegler-Natta catalyst and typically includes elementary steps such as chain initiation, chain growth, ethylene / 1-butene copolymerization insertion, chain transfer, and deactivation / termination. The process convergence residual was 10.-4 The feed parameters are listed in Table 1.

[0036] Table 1 Feeding parameters for Example 1

[0037] In this embodiment, the process-level homotopy parameter The range of values ​​is Initial homotopy step size Take 0.05 as the minimum allowable step size. Take 1.0 × 10 -6 Maximum allowable step size Set the value to 0.1. When the current... When a phase convergence is successful, the step size of the next phase is multiplied by the growth factor. Enlarge it, and limit it to no more than ; when currently If a stage fails to solve, revert to the previous homotopic state and adjust the next stage step size by multiplying it by the shrinkage factor. Reduce the step size; if the reduced step size is lower than... If so, the homotopy process at the process level is deemed to have failed.

[0038] Reactor unit-level homotopy parameters The range of values ​​is The algorithm first tries The full-load reaction model can be solved directly; if the direct solution fails, the convergent starting point is determined by backtracking using a bisection method. The lower bound for backtracking is 1.0 × 10⁻⁶. -8 The maximum number of backtracking iterations is 50. Confirm. Then, the interval The initial division is into 5 advance steps, i.e. When a certain When the phase convergence is successful, the subsequent step size is pressed. Magnify, and be subject to the length of the remaining interval. Constraints; when a stage fails to solve, the step size is adjusted accordingly. Shrink. Minimum step size for cell-level homotopy. The maximum number of propulsion stages is set to 100. This embodiment employs an inert component initial value strategy to set the circulating gas tearing stream. The initial value of the tearing stream is set as: [10, 5000, 10, 10, 10, 10, 10, 10, 0, 0, 0]. The first eight terms correspond to the molar flow rates of hydrogen, nitrogen, methane, ethylene, ethane, 1-butene, n-butane, and isopentane, respectively, while the last three terms correspond to the molar flow rates of LLDPE, catalyst, and co-catalyst, respectively, in mol / s. Nitrogen dominates in this initial value, and the reaction composition deviates significantly from the actual circulating gas composition, used to simulate difficult initial conditions.

[0039] Under these initial conditions, both process-level and reactor-level isotope were simultaneously enabled. Calculation results show that the process eventually converged successfully, with a gas phase mole fraction of approximately 0.966 and a polymer mass flow rate of approximately 10.69 kg / s. Figure 3 This demonstrates how the reactor model solves variables with respect to the homotopy parameters at the element level. The evolutionary process. Figure 4 The flow rates of each component in the recirculating gas tear stream are shown as a function of process stage isotope parameters. The evolutionary process, when Nitrogen gas was maintained at around 5000 mol / s, effectively maintaining the circulating gas scale with the inert components; the reactive and condensable components... Gradually increase the amount of material entering the actual composition. to In the final stage, the concentrations of hydrogen, ethylene, and butane rapidly increased from 29.29, 1368.06, and 170.05 mol / s to 459.26, 2680.12, and 1493.79 mol / s, respectively, indicating an enhancement of the nonlinearity of the cyclic mapping near full load.

[0040] Example 2 This embodiment uses inaccurate initial values ​​for the tear stream. Specifically, based on the accurate estimated value of the tear stream, a random perturbation of ±20% is applied to the molar flow rates of the first eight components of the recirculating gas. The perturbation factor follows a uniform distribution within the interval [0.8, 1.2], while the initial values ​​for the remaining polymers, catalysts, and co-catalysts remain zero. The initial values ​​for the tear stream perturbation in this embodiment are [1410.23, 5225.32, 123.072, 3142.77, 447.589, 688.631, 2007.20, 1187.78, 0, 0, 0], where the first eight items correspond to the molar flow rates of hydrogen, nitrogen, methane, ethylene, ethane, 1-butene, n-butane, and isopentane, respectively, and the last three items correspond to the molar flow rates of LLDPE, catalyst, and co-catalyst, respectively, in mol / s.

[0041] Under this initial perturbation, both process-level and reactor-unit-level homotopy were enabled. The calculation results show that the process still converged successfully, with a gas phase mole fraction of approximately 0.974 and a polymer mass flow rate of approximately 10.69 kg / s. This result demonstrates that even with significant deviations in the initial values ​​of the tear stream, the bilayer homotopy algorithm can maintain solution stability through continuous parameter advancement.

[0042] Example 3 This embodiment uses a circulating gas-phase polypropylene polymerization process as an example. The process includes a mixer, a polymerization reactor, a compressor, and a heat exchanger. The gaseous stream from the reactor passes through the compressor and heat exchanger before returning to the mixer, where it mixes with the fresh feed and then enters the reactor. The gaseous stream from the reactor is selected as a tear stream, and the polypropylene product is discharged from the liquid phase outlet of the reactor.

[0043] In this embodiment, propylene (C3H6) is the polymerization monomer, hydrogen (H2) is the chain transfer agent, nitrogen (N2) is the inert gas, titanium tetrachloride (TiCl4) is the catalyst, and triethylaluminum (C6H) is the polymer. 15 TiCl₄ is used as a co-catalyst. The fresh feed includes catalyst feed, co-catalyst feed, nitrogen feed, hydrogen feed, and propylene feed. The catalyst feed is a liquid stream at 303.15 K and 3.0 MPa, with a molar flow rate of 0.004393 mol / s for TiCl₄, and also contains 1.9566 mol / s of propylene and 0.003780 mol / s of propane. The co-catalyst feed is also a liquid stream at 303.15 K and 3.0 MPa, with a molar flow rate of 0.024331 mol / s for C₆H₁₅Al. The nitrogen feed is a gaseous stream at 303.15 K and 3.0 MPa, with a molar flow rate of 0.018713 mol / s for nitrogen. The hydrogen feed is a gaseous stream at a temperature of 303.15 K and a pressure of 3.0 MPa, with a hydrogen molar flow rate of 0.263987 mol / s. The propylene feed is a liquid stream at a temperature of 303.15 K and a pressure of 3.0 MPa, with a propylene molar flow rate of 133.6118 mol / s and a propane molar flow rate of 0.5525 mol / s. The reactor operates at a temperature of 342.15 K and a pressure of 2.800 MPa, with a reactor volume of 90 m³. 3 The liquid phase volume is 60 m³. 3 The physical property analysis was performed using PC-SAFT, and the reaction kinetics were analyzed using the Ziegler-Natta catalytic polymerization model with 4 active sites on the catalyst.

[0044] This embodiment employs an inert component initial value strategy to set the recirculating gas tearing stream. The initial values ​​for the tearing stream are set as: [0,0, 10, 10, 0, 10, 50], where each term corresponds to the molar flow rate of TiCl4, C6H15Al, propylene, propane, polypropylene, hydrogen, and nitrogen, respectively, in mol / s. This initial value does not include catalysts, co-catalysts, or polymers, and uses nitrogen as the dominant component, significantly deviating from the compositional state where propylene dominates in real recirculating gas, thus simulating challenging tearing initial value conditions.

[0045] Under these initial conditions, both process-level and reactor-unit-level isotope methods were simultaneously implemented. Calculations showed that the process eventually converged successfully. After convergence, the molar flow rates of propylene, propane, hydrogen, and nitrogen in the recirculating gas tear stream were approximately 464.76 mol / s, 8.96 mol / s, 44.07 mol / s, and 9.20 mol / s, respectively; the mass flow rate of polypropylene in the liquid product stream was approximately 4.50 kg / s. These results demonstrate that the bilayer isotope method is applicable to recirculating gas-phase polypropylene polymerization processes and can achieve process convergence even when the initial tear stream values ​​deviate significantly from the actual recirculating gas composition.

[0046] Example 4 This embodiment uses a dual-reactor, dual-circulation slurry polymerization process for high-density polyethylene as an example. Ethylene (C2H4) and 1-butene (C4H8) are the monomers, hydrogen (H2) is the chain transfer-related component, and nitrogen (N2), methane (CH4), ethane (C2H6), and n-butane (C4H) are also present. 10 The solvent is n-hexane (HX), the catalyst is titanium tetrachloride (TiCl4), and the catalyst is triethylaluminum (C6H). 15 Al was used as a co-catalyst, and the target polymer was high-density polyethylene (HDPE). The fresh feed streams included H2, C2, CAT, HX, and ML1 from the first cycle, and N2, H22, HX2, C4, C22, ML2, and 221HX from the second cycle. In the first cycle, the H2 feed contained 0.407256 mol / s of H2 and 0.001189 mol / s of CH4; the C2 feed contained 55.31915 mol / s of C2H4, 0.00077 mol / s of H2, 0.009676 mol / s of CH4, and 0.005162 mol / s of C2H6; the CAT feed contained 0.001867 mol / s of TiCl4 and C6H4. 15Al 0.003102 mol / s and n-hexane 0.813731 mol / s; HX feed contains n-hexane 11.28167 mol / s; ML1 feed contains C2H4 0.022477 mol / s, C4H8 0.022427 mol / s, and C6H 15 Al 0.000462 mol / s, n-hexane 16.19181 mol / s, N2 0.007139 mol / s, and C2H6 0.010531 mol / s. In the second cycle, the N2 feed is 0.198317 mol / s; the H22 feed contains 0.098194 mol / s of H2 and 0.000287 mol / s of CH4; the HX2 feed is 6.446668 mol / s of n-hexane; and the C4 feed contains 0.467198 mol / s of C4H8 and C4H 10 0.007799 mol / s; C22 feed contains C2H4 53.57682 mol / s, H2 0.000746 mol / s, CH4 0.009371 mol / s and C2H6 0.005 mol / s; ML2 feed contains C2H4 0.037329 mol / s, C4H8 0.03723 mol / s, C6H 15 The feed consisted of Al 0.000779 mol / s, n-hexane 26.81991 mol / s, N2 0.0118 mol / s, and C2H6 0.017552 mol / s; the 221HX feed consisted of n-hexane 0.370683 mol / s. The first reactor operated at a temperature of 358.15 K, a pressure of 0.600 MPa, and a volume of 90 m³. 3 The liquid phase volume is 51.12 m³. 3 The second reactor operates at a temperature of 353.15 K, a pressure of 0.350 MPa, and a volume of 90 m³. 3 The liquid phase volume is 51.12 m³. 3 The physical property analysis was performed using PC-SAFT, and the reaction kinetics were analyzed using a five-active-center Ziegler-Natta catalytic ethylene / 1-butene copolymerization model, with the catalyst having five active centers.

[0047] In this embodiment, both the first and second cycles are equipped with relaxation branches to limit the accumulation of light components in the recycle streams. In the first cycle, the gas phase outlet stream recycle1 from the first reactor is selected as the tear stream; in the second cycle, the gas phase outlet stream recycle2 from the second reactor is selected as the tear stream. The component order of both tear streams is C2H4, C4H8, TiCl4, C6H4. 15 Al, H2, HX, HDPE, N2, CH4, C2H6 and C4H 10 An inert component initial value strategy was adopted. The initial value of the first tear stream, recycle1, was set to [1, 1, 0, 0, 1, 100, 0, 10, 1, 1, 0] mol / s. The initial value of the second tear stream, recycle2, was set to [10, 10, 0, 0, 10, 10, 0, 500, 10, 10, 10] mol / s. Under these initial values, both process-level homotopy and reactor unit-level homotopy were simultaneously initiated. The initial step size for process-level homotopy was set to 0.05, and the minimum step size was set to 1.0 × 10⁻⁵. -8 When homotopy parameter When the value is greater than 0.80, the maximum step size is limited to 0.02.

[0048] The calculation results show that both process-level homotopy were successfully advanced to The process eventually converged. After convergence, the molar flow rate of recycle1 was approximately 0.715 mol / s, with molar flow rates of C2H4, H2, and HX approximately 0.236 mol / s, 0.0957 mol / s, and 0.376 mol / s, respectively; the molar flow rate of recycle2 was approximately 20.476 mol / s, with molar flow rates of C2H4, C4H8, H2, HX, and N2 approximately 10.514 mol / s, 0.241 mol / s, 0.134 mol / s, 9.282 mol / s, and 0.259 mol / s, respectively. The total mass flow rate of the product stream was approximately 7.38 kg / s, with the HDPE component mass flow rate approximately 2.77 kg / s. These results demonstrate that the method combining process-level isotope and reactor unit-level isotope is applicable to the dual-circulation slurry method for high-density polyethylene polymerization, achieving stable convergence of the dual-circulation process.

[0049] Example 5 To further verify the applicability of the unit-level homotopy method to reactor models, two-dimensional temperature-pressure test grids were constructed for the reactor operating conditions of two industrial cases. The reactor feed composition for Industrial Case 1 was as follows: hydrogen 606.77 mol / s, nitrogen 4846.18 mol / s, methane 118.33 mol / s, ethylene 3835.26 mol / s, ethane 338.09 mol / s, 1-butene 1200.80 mol / s, n-butane 953.23 mol / s, isopentane 1301.21 mol / s, LLDPE polymer 0.00 mol / s, TiCl4 main catalyst 0.01 mol / s, and C6H15Al co-catalyst 0.02 mol / s. The reactor feed composition for Industrial Case 2 was as follows: hydrogen 559.33 mol / s, nitrogen 6160.72 mol / s, methane 72.45 mol / s, ethylene 3861.71 mol / s, ethane 389.79 mol / s, 1-butene 1190.44 mol / s, n-butane 1361.89 mol / s, isopentane 1299.88 mol / s, LLDPE polymer 0.00 mol / s, TiCl4 main catalyst 0.01 mol / s, and C6H15Al co-catalyst 0.02 mol / s. Each industrial case had 20 × 20 temperature and pressure operating points, with a pressure range of 2.20–2.60 MPa; the temperature range for Industrial Case 1 was 345–360 K, and for Industrial Case 2 it was 348.15–363.15 K. Methods, reaction kinetics models, solver types, and convergence criteria that maintain the same physical properties before and after enabling homotopy.

[0050] The cell-level homotopy test results of this embodiment are shown in Table 2.

[0051] Table 2. CSTR Test Results for Industrial Case 1 and Industrial Case 2

[0052] As shown in Table 2, out of a total of 800 temperature and pressure conditions, 570 points were successfully solved directly with unit-level homotopy disabled, a success rate of 71.2%; with unit-level homotopy enabled, 794 points were successfully solved, increasing the success rate to 99.2%. For the 230 conditions that failed to be solved directly, unit-level homotopy successfully recovered 224 points, a recovery rate of 97.4%. These results indicate that unit-level homotopy can significantly enhance the convergence stability of the polymerization reactor model over a wide temperature and pressure range.

[0053] Comparative Example 1 This comparative example uses accurate initial values ​​for the tearing stream. The accurate initial values ​​for the tearing stream are: [1204.33, 4926.1732, 127.88, 3550.42, 436.01, 615.23, 1866.21, 1099.77, 0, 0, 0]. The first eight terms correspond to the molar flow rates of hydrogen, nitrogen, methane, ethylene, ethane, 1-butene, n-butane, and isopentane, respectively, while the last three terms correspond to the molar flow rates of LLDPE, catalyst, and co-catalyst, respectively, in mol / s. The calculation results show that the process converges successfully, with a gas phase molar fraction of approximately 0.972 and a polymer mass flow rate of approximately 10.69 kg / s. This indicates that when the initial values ​​for the tearing stream are sufficiently close to the true solution, a convergent solution can be obtained through conventional direct solution.

[0054] Comparative Example 2 This comparative example uses the same accurate initial values ​​for the torn flow stream as Comparative Example 1. Calculations were performed with bilayer homotopy disabled and bilayer homotopy enabled, respectively, under these accurate initial values. The calculation results show that the process successfully converges, with a gas phase mole fraction of approximately 0.972 and a polymer mass flow rate of approximately 10.69 kg / s. This indicates that the bilayer homotopy method of this invention does not change the final rigorous model solution, but rather alters the solution path.

[0055] Comparative Example 3 This comparative example uses the same initial values ​​for the inert component as Example 1, but disables process-level and reactor unit-level isotope, i.e., directly uses the original rigorous process model for solution. The calculation results show that this condition failed to converge. This indicates that for tearing streams with inert components dominating and reactant components significantly deviating from their true values, conventional direct solution methods struggle to overcome the strongly nonlinear region.

[0056] Comparative Example 4 This comparative example uses the same ±20% perturbation to tear stream initial value as Example 2, but disables process-level homotopy and reactor unit-level homotopy. Calculation results show that this condition also failed to converge. This indicates that even with a finite-amplitude perturbation of the initial value relative to the accurate tear stream estimate, direct solutions may still fail under the combined effects of strong cyclic coupling and a strongly nonlinear reactor.

[0057] Table 3 Summary of Results

[0058] As shown in Examples 1 and 3, and Examples 2 and 4, under difficult initial conditions of inert component and ±20% perturbation, the process failed to converge when homotopy was disabled. However, by simultaneously enabling both process-level and reactor unit-level homotopy, a strictly convergent solution for the process model could be obtained. This result indicates that process-level homotopy can improve the global convergence difficulty caused by the initial value deviation of the circulating tear stream, while unit-level homotopy can improve the local convergence difficulty of the strongly nonlinear reactor model. The combination of the two can significantly improve the robustness of steady-state solutions in the simulation of polyolefin reaction module processes.

[0059] The above-described embodiments are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. Those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A convergence method for a polyolefin reaction module cyclic process based on bilayer homotopy, characterized in that, The method includes: (1) Obtain the circulating process model of the polyolefin reaction module to be solved, wherein the circulating process includes an olefin polymerization reactor and a circulating loop connected between the gas phase outlet and the inlet of the reactor; (2) Construct a two-layer homotopy solution framework that includes inner-layer cell-level homotopy and outer-layer process-level homotopy, and set process-level homotopy parameters. Hotopism parameters at the unit level ,in Used to control the loading level of real-world circular logistics. Used to control the degree of recovery of polymerization reaction items in the reactor unit; (3) Construct inner-cell-level homotopy: Under the given process-level homotopy parameters The following section introduces the unit-level homotopy parameter into the steady-state material balance equation for the reactor unit. Construct unit-level homotopy equations and adaptively adjust them. Progressing from 0 to 1, gradually introducing polymerization reaction terms; (4) Constructing outer-layer process-level homotopy: Based on the inner-layer cell-level homotopy solution, the process-level homotopy parameter is introduced to address the problem of fixed points of torn flow strands in the cyclic process. Through adaptive adjustment Progressing from 0 to 1, gradually implementing real-world circular logistics, each... Each stage solves the problem of fixed points in the tearing flow strand; (5) Initial values ​​of the inert component in the tearing flow stream The scale of the recycle gas was determined with non-reactive components as the dominant components, serving as the initial basis for process-level isotope. (6) An adaptive step size strategy is adopted in both process-level homotopy and cell-level homotopy until... and And satisfy the process convergence conditions, output the convergence simulation results of the polyolefin reaction module cycle process.

2. The method for convergence of a polyolefin reaction module cyclic process based on bilayer homotopy according to claim 1, characterized in that, The form of the unit-level homotopy equation is: ； In the formula, Let the reactor state vector be... This is the feed molar flow vector, i.e., the feed term; This is the discharge molar flow vector, i.e., the discharge term; This is the reaction rate term. For the volume of the reaction phase, when When the reaction rate term is turned off, the reaction rate term is turned off; when The equations are for a real reactor.

3. The method for convergence of a polyolefin reaction module cyclic process based on bilayer homotopy according to claim 1, characterized in that, The solution process for the inner-layer homotopy is as follows: the solver first attempts to solve the homotopy of the inner-layer elements. Local solutions are performed under full load conditions; If the solution fails, then press The sequence is backtracked to find a convergent starting point. ,in , The maximum number of backtracking iterations is preset; After determining the convergent starting point Afterwards, from Starting from this point, a secant prediction and adaptive step size strategy are employed. Progress gradually up to 1; if backtracking reaches the preset minimum value If the process still fails or the set limit for backtracking is reached, then the stage is considered a failure.

4. The method for convergence of a polyolefin reaction module cyclic process based on bilayer homotopy according to claim 1, characterized in that, The process-level homotopy mapping is: ； ； ； In the formula, The tearing flow state vector includes the molar flow rate and temperature of each component. and pressure , For the actual process in the tearing flow state The returned result; This is the initial vector of molar flow rates of each component in the tearing flow stream. The return result for the tearing flow under the initial value; when At that time, the process-level homotopy mapping degenerates into a basis system dominated by inert components; when This is a true cyclical system.

5. The method for convergence of a polyolefin reaction module cyclic process based on bilayer homotopy according to claim 4, characterized in that, The initial value of the inert component of the tearing stream In this process, the molar flow rate of non-reactive components constitutes the main body of the total molar flow rate of the circulating gas, while the molar flow rates of other components are set to a preset minimum positive flow rate; wherein, the non-reactive components include nitrogen, isopentane, methane, ethane, and n-butane.

6. The method for convergence of a polyolefin reaction module cyclic process based on bilayer homotopy according to claim 1, characterized in that, In the adaptive step size strategy, the step size update formula is: ； ； In the formula express or , To determine the next step length after a successful solution, To determine the backoff step size after a failure, Step size growth factor and >1, The step size contraction factor is 0 < <1, To limit the maximum step size, This is a minimum step size constraint.

7. The method for convergence of a polyolefin reaction module cyclic process based on bilayer homotopy according to claim 5, characterized in that, When reliable initial values ​​for the tearing flow strands cannot be obtained in advance under changing operating conditions, new operating conditions, or online recalculation scenarios, the initial values ​​for the inert components of the tearing flow strands are adopted. Construct an initial basis for process-level homotopy; wherein, the molar flow rate of the non-reactive component is used to determine the total molar flow rate of the target recycle gas, and the preset minimum flow rate of the other components is taken as 10% of the total molar flow rate of the target recycle gas. -6 Up to 10 -2 times.

8. The method according to claim 1, characterized in that, The polyolefin reaction module is a gas-phase polyolefin module, including a fluidized bed reactor, a circulating gas compressor, a circulating gas cooler, and a distributor; the top gas phase outlet of the fluidized bed reactor is connected to the distributor, the first outlet of the distributor is connected to the inlet of the circulating gas compressor, and the second outlet is a gas phase outlet stream. The outlet of the circulating gas compressor is connected to the inlet of the circulating gas cooler, and the outlet of the circulating gas cooler is connected to the inlet of the fluidized bed reactor. A liquid phase outlet stream is installed at the bottom of the fluidized bed reactor.

9. The method according to claim 1, characterized in that, The polyolefin reaction module is a slurry polyolefin module, including a slurry reactor, a circulating gas compressor, a heat exchanger, and a flash separation tank. The top gas phase outlet of the slurry reactor is connected to the heat exchanger, the heat exchanger outlet is connected to the flash separation tank, the top gas phase outlet of the flash separation tank is connected to the inlet of the circulating gas compressor, the circulating gas compressor outlet is connected to the inlet of the slurry reactor, and the bottom liquid phase outlet of the flash separation tank is connected to the inlet of the slurry reactor. The slurry reactor is equipped with feed lines for fresh monomers, comonomers, hydrogen, catalyst, cocatalyst, and solvent.

10. The method according to claim 1, characterized in that, Each of the steps in (4) The problem of fixed points in the tearing flow of a stage can be solved using the Wegstein method, Broyden method, or Newton-type method. The method also includes recording the homotopy parameters, solution variables, iteration count, and convergence state for each homotopy stage, and using this information for the step size and variable updates in the next stage.

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