Conversion rate space-time distribution prediction method for gas-solid in-situ preparation of micro-size charge

Abstract

The invention discloses a conversion rate spatial-temporal distribution prediction method for gas-solid in-situ preparation of micro-sized charge, and belongs to the field of energetic material performance prediction. The implementation method comprises the following steps: constructing a multi-physical field model, and calculating and extracting a time-varying rule of gas concentration in the gas-solid reactor under a given working condition; by taking the obtained change rule of the gas concentration in the gas-solid reactor as a known condition, and combining an identical relationship between the change characteristics of the internal structure of the micro-charge and the gas diffusion flux, constructing the change rule of the gas concentration at different cross section positions in the micro-charge; a single-particle gas-solid reaction kinetic model is established by considering island-shaped structure characteristics of a solid product, a micro-charge reaction kinetic model and a corresponding nonlinear equation set are established, and a spatial-temporal distribution result of the micro-charge conversion rate is obtained through iterative solution. According to the method, the full-process reaction model can be established according to the gas-solid reaction characteristics of the transition metal azide micro-charge, the complex reaction process in the gas-solid reactor is accurately represented, and the method has the advantages of high prediction efficiency, good reliability and the like.

Description

Technical Field

[0001] This invention belongs to the field of energetic material performance prediction, and relates to a method for predicting the spatiotemporal distribution of conversion rate in in-situ gas-solid preparation of micro-sized charges. Background Technology

[0002] Transition metal azides (M(N3)) n Metals such as Cu(N3)2, AgN3, Pb(N3)2, and Cd(N3)2 have advantages such as low ignition energy, short detonation growth distance, and strong initiation capability, and are commonly used as starting charges in weapon systems. However, traditional liquid-phase synthesis-weighing and pressing processes cannot meet the miniaturization requirements of weapon systems. Researchers have proposed a high-precision, batch-synthesized sub-milligram-level in-situ micro-sized charge (micro-charge) technology by utilizing the gas-solid reaction characteristics of transition metal elements and azidoic acid (HN3) gas. This effectively solves the contradiction between charge size, operational safety, and energy efficiency, and has become a research focus in this field. However, due to the high toxicity and explosiveness of the gaseous reactant HN3 gas, compared to the traditional liquid-phase synthesis method, the gas-solid in-situ reaction preparation process requires a specially designed gas-solid reaction device, in which the following reaction steps occur simultaneously: Step 1. NaN3 reacts with a low-volatility acid to generate HN3 gas (involving a chemical reaction and a liquid-gas phase mass transfer process). Step 2. Diffusion of HN3 gas within the gas-solid reactor (involving a gas diffusion process); Step 3. Diffusion of HN3 gas in the pores inside the transition metal (involving the gas pore diffusion process); Step 4. HN3 gas reacts with transition metal elements in a gas-solid reaction to produce solid products (involving a gas-solid reaction process). Step 5. Solid products alter the surface structure of the solid through solid-phase diffusion and accumulation (involving solid-phase diffusion and morphological evolution processes). Step 6. The HN3 gas diffuses through the solid product to the surface of the unreacted transition metal to continue the reaction (involving a solid-phase diffusion process).

[0003] As can be seen from the above steps, gas-solid reactions involve complex processes such as gas diffusion, chemical reactions, and solid product growth. As the reaction proceeds, each step influences and restricts the others. The physical / chemical processes involved in in-situ gas-solid reactions are as follows: Figure 1 As shown, due to the high toxicity and explosiveness of the reactants, researchers find it difficult to obtain real-time experimental data and establish the coupling relationship between multiple reaction steps in the gas-solid container. Optimizing the reaction conditions requires a large number of experiments, which is time-consuming and labor-intensive, and also increases safety risks.

[0004] To investigate the influence of reaction conditions on the conversion rate of micro-charges, researchers analyzed the effect of gas-solid reaction conditions on the conversion rate of copper azide micro-charges based on a core shrinking model (Zhang Lei, Zhang Fang, Wang Yanlan, et al. Analysis of influencing factors on the synthesis of porous copper azide based on unreacted core model [J]. Energetic Materials, 2018, 26(12): 1049-55; Wang Yanlan, Zhang Lei, Zhang Fang, et al. Study on reaction kinetics of copper azide nanowire array [J]. Explosives, 2020, (06): 50-3.). However, related studies assumed that the HN3 gas concentration in the gas-solid reaction was fixed and that the solid product continuously and uniformly covered the surface of the solid reactants, neglecting the influence of steps 1 and 5 on the gas-solid reaction process. Existing experimental results show that the gas-solid azide reaction rate is greatly affected by the HN3 gas concentration, and the gas-solid reaction products exhibit discontinuous growth (island growth) on the reactant surface. The core shrinkage model cannot accurately recreate the reaction process (Wu Xingyu, Li Mingyu, Zeng Qingxuan, et al. In-situ synthesis of copper azide chips and investigation of their initiation ability[J]. Chemical Engineering Journal, 2022, 427(1):131952-60; Ren Jie, Wang Jiabao, Zhang Weijing, et al. Morphologicalevolution mechanism of copper-based azide during gas-solid azidation process:Experiment and thermodynamic analysis[J]. Vacuum, 2023,217(1): 112564-73.). Therefore, it is urgent to construct a method for predicting the spatiotemporal distribution of micro-charge conversion rate based on the product morphology evolution process and the coupling matching relationship of multiple reaction rates, to accurately describe the complex reaction process in the gas-solid reactor and provide guidance for researchers to optimize reaction parameters. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a method for predicting the spatiotemporal distribution of conversion rate in in-situ gas-solid preparation of micro-sized charges. By constructing a coupling and matching relationship between the product morphology evolution process involved in the gas-solid reaction and multiple reaction rates, the complex reaction process within the gas-solid reactor can be described more accurately.

[0006] The objective of this invention is achieved through the following technical solution.

[0007] This invention discloses a method for predicting the spatiotemporal distribution of conversion rate in gas-solid in-situ preparation of micro-sized charges, comprising the following steps: S1. Construct a multiphysics model of the gas-solid reactor based on the diffusion of concentrated substances, turbulence, and heat transfer processes between solids and fluids. Calculate and extract the internal dynamics of the gas-solid reactor under given operating conditions. The pattern of gas concentration change over time.

[0008] S101. Select an appropriate physical model to describe the material diffusion, turbulence, solid-fluid heat transfer processes within the gas-solid reactor.

[0009] Described using chemical reaction rate equations The reaction process with low-volatility acids is described using a boiling mass transfer model. In the mass transfer process between gas and liquid phases, the mass transformation relationship is as follows: (1) In the formula, , These are liquid phase and gas phase mass source terms, respectively; This is the relaxation factor, with a value between 0.01 and 1. It is the liquid volume fraction; and These are the liquid temperature and saturation temperature, respectively, under standard atmospheric pressure. Saturation temperature of liquid It is 309.15K.

[0010] The HN3 gas transport process within the gas-solid reactor is considered a concentrated mass transport process. Fick's law is used to describe the transport mechanism, with mass fraction as a constraint and linear discretization performed. The transient concentrated mass transport field can be described as follows: (2) In the formula, For fluid density; Components The mass fraction; For matter Mass diffusion flux; For Hamiltonian operators; The average velocity is the mass. Reaction rate. Mass diffusion flux. The diffusion coefficient is proportional to the mole fraction gradient of the components and is calculated using the Fuller formula: (3) In the formula, for gas in The molecular diffusion coefficient in; Thermodynamic temperature; The relative molecular mass of the gaseous component; For system pressure; The volume of gas molecule diffusion. and The molecular diffusion volumes are 19.05. and 17.9 ; Mass and momentum transfer during gas flow within the reactor are governed by the incompressible Navier-Stokes equations: (4) In the formula, For pressure; For fluid dynamic viscosity; It is the identity matrix; It is the acceleration due to gravity; It is a volume force.

[0011] The heat conduction and convective heat transfer processes within the reactor are described using solid and fluid heat transfer equations, specifically: (5) In the formula, It is a constant pressure heat capacity; The convective heat transfer coefficient; Thermal conductivity; It is a heat source.

[0012] S102. Construct a multiphysics model by combining the geometry of the gas-solid reactor and the selected physical field, divide the grid reasonably, set relevant regions and point probes according to the initial reaction conditions, and calculate and extract the physical field information of the gas-solid reactor at different times and locations under the given conditions.

[0013] Taking the finite element simulation software COMSOL as an example, a two-dimensional axisymmetric model is established to match the actual reactor dimensions. Non-isothermal flow is coupled with fluid flow and heat transfer interface coupling with relevant physical fields. The physical field controls the mesh size, and the mesh is further refined in regions with large physical field gradients, such as near the wall and corners, to ensure computational accuracy. After defining the initial reaction conditions such as feed rate and heating temperature, corresponding boundary conditions and material properties are set, including the liquid reaction zone, inlet velocity, wall heating zone, and wall heating temperature. Through transient solution, continuous calculation of HN3 gas concentration in the gas-solid reactor under given conditions and at different times can be achieved. Point probes are set at different locations in the reactor to extract physical field information at different locations and times within the gas-solid reactor.

[0014] Preferably, the gas-solid reactor under different operating conditions is analyzed. When considering the gas concentration-time variation pattern, the heating temperature setting range is: , The feed rate can be set from 0.001 to 10 mol, the calculation time from 10 to 10000 s, and the step size from [missing value]. Optionally, point probes can be used to extract data at different locations and times within the gas-solid reactor. gas concentration, Gas flow rate, This invention focuses on discrete simulation data points such as gas temperature. Gas concentration.

[0015] S103. Based on the extracted discrete simulation data, fit the gas-solid reactor under given operating conditions. The pattern of gas concentration change over time.

[0016] Based on the above-extracted data at different times at a given location Using discrete data points of gas concentration as the object, the curve fitting toolbox in MATLAB software was used to fit them into a smooth and continuous numerical expression, and the coefficient of determination was employed. Evaluate the reliability of the fitted expression; The value should be no less than 0.95, and the fitting expression should be as concise as possible while meeting the accuracy requirements. The final numerical expression determined by the fitting is used to describe the variation law of HN3 gas concentration in the gas-solid reactor, and is used as input condition for subsequent micro-charge conversion rate prediction.

[0017] S2, the obtained gas-solid reactor Given the known gas concentration variation pattern, and combined with the internal structural variation characteristics of the micro-charge, a constant relationship is established between the gas consumption per unit time of the micro-element and the gas diffusion flux based on the law of conservation of mass. This yields the variation pattern of gas concentration at different cross-sectional locations inside the micro-charge with conversion rate and time. S201. The growth of solid products in gas-solid reactions leads to changes in the internal structure of the micro-charge, manifested as a continuous reduction in the porosity of the micro-charge, hindering... Gas diffuses inward; establish an appropriate physical model to describe it. The process of gas diffusing inward.

[0018] Carry the micro-charged medicine along the height Directional differential For a thickness of The infinitesimal element is described using Fick's diffusion law. The diffusion process of gas in a micro-element. (6) In the formula, The effective diffusion coefficient of gas within the pores; This represents the HN3 gas concentration at a specific location.

[0019] Local porosity With conversion rate The relationship between them is (7) In the formula, is the coefficient of thermal expansion, dimensionless; is the initial porosity. , For sample packing density and For theoretical density, The diffusion coefficient of the gas within the pore is the diffusion coefficient through the gas molecules. Knudsen diffusion coefficient The calculation is obtained using the following formula: ; It can be calculated from equation (3). The calculation formula is as follows: (8) In the formula, The molar mass of a gas molecule; Thermodynamic temperature; Where is the pore radius.

[0020] S202, the obtained gas-solid reactor Given the known variation law of gas concentration, the variation law of gas concentration at different cross-sectional positions inside the micro-charge with conversion rate and time is obtained based on the gas diffusion flux and the law of conservation of mass.

[0021] The amount of reactant gas consumed per unit time is equal to the height )Flow at the end face and height The difference in the amount of reactant gas flowing out at the end face, according to the law of conservation of mass: (9) In the formula, The charge radius of the micro-charge is... For gas flux, These are stoichiometric coefficients. The molar volume of the reactants. Let be the reaction time; Equation (9) simplifies to (10) Combined equations (6) and (10), at different cross-sectional positions inside the micro-charge Write the relationship between gas concentration and conversion rate and time. (11) In the formula, For gas-solid reactor Gas concentration is represented using a numerical expression determined by fitting. Adsorbed on solid surface Gas concentration; The external diffusion coefficient of the gas is calculated using the Sherwood number.

[0022] Preferably, the analysis is performed at different cross-sectional locations inside the micro-charge. When considering the relationship between gas concentration and conversion rate and time, the radius of the micro-charge is... for initial porosity ε 0 is Micro-packing and micro-layering for .

[0023] S3, Based on the island-like structure characteristics of solid products and surface chemical reaction rates Product diffusion rate Establish a single-particle gas-solid reaction kinetic model and obtain The influence of gas concentration on the conversion rate of single particles was investigated; a reaction kinetic model and corresponding nonlinear equations for micro-charge were established to accurately describe the complex reaction process in the gas-solid reactor; and the spatiotemporal distribution prediction results of the conversion rate of micro-charge were obtained by iterative solution, thus realizing the spatiotemporal distribution prediction of the conversion rate of micro-sized charges prepared in situ using gas-solid methods.

[0024] S301, Considering the island-like structure characteristics of solid products and surface chemical reaction rates Product diffusion rate Establish a single-particle gas-solid reaction kinetic model and obtain The influence of gas concentration on single-particle conversion rate.

[0025] Single particles are the basic building blocks of micro-charges. Existing experimental results show that gas-solid reaction products exhibit discontinuous growth (island growth) on the reactant surface. For single-particle gas-solid reaction processes, the growth process of solid product islands is described using rate equation theory, with the total volume of solid products... The growth rate is primarily determined by the rate of chemical reactions occurring on the exposed surface, expressed as... (12) (13) In the formula, The surface area of ​​the solid reactant; The proportion occupied by the surface of solid reactants is dimensionless. It is the surface chemical reaction rate constant; The critical height of the product island. Combining equations (12) and (13), the surface area occupied by the solid reactants is obtained. The expression is (14) The growth process of product islands involves a product diffusion-product island growth competition mechanism, and the critical height of the product islands is related to the surface diffusion coefficient of the product monomers. Product island capture monomer growth rate It is related to the surface monomer concentration distribution, and the expression is: (15) In the formula, The characteristic diffusion length of the product monomer. The dimensionless monomer concentration at which the height of the product island no longer continues to grow.

[0026] The single-particle gas-solid reaction process can be divided into two stages: In the initial stage, the surface of the reactants is partially covered by product islands, while the remaining parts are exposed and can directly participate in the gas-solid reaction. At this stage, the reaction conversion rate needs to consider both the surface reaction process and the product layer diffusion process. As the products completely cover the surface of the reactants, the single-particle gas-solid reaction process can be divided into two stages: the reactant gases can only carry out chemical reactions through diffusion of the product layer.

[0027] The relationship between single particle size and conversion rate can be expressed as follows: (16) In the formula, The initial radius of the reactants; The radius of the unreacted nucleus; denoted as , where is the radius of the reaction product.

[0028] Based on the two reaction steps of direct chemical reaction and diffusion of gaseous products, the rate of consumption of the volume of the diffused solid reactant is expressed as: (17) In the formula, At the solid product / reactant interface Gas concentration.

[0029] Substituting equation (16) into equation (17) and simplifying, we can obtain the expression for the single-particle conversion rate as follows: (18) Using Fick's diffusion law to describe The diffusion process of gas in the product layer, (19) In the formula, for Diffusion flux of gas in the product layer for The diffusion coefficient of the product layer of the gas. for The concentration of gas in the product layer.

[0030] because There is a conservation relationship between the consumption rate of gaseous chemical reactions and the gas diffusion flux. (20) In the formula, To obtain the stoichiometric coefficients, integrate equation (19) and combine it with equation (20) to get... (twenty one) The single-particle conversion rate expression based on product structure change is as follows: (twenty two) S302, combined with the gas-solid reactor The variation law of gas concentration, and the influence of changes in the internal structure of the micro-charge on the gas concentration at different cross-sectional locations. The influence of gas concentration on single-particle conversion rate was investigated. A micro-charge reaction kinetic model and corresponding nonlinear equations were established, which included changes in packing porosity and multiple single-particle gas-solid reaction processes. The complex reaction process in the gas-solid reactor was accurately described, and the spatiotemporal distribution prediction results of the micro-charge conversion rate were obtained by iterative solution.

[0031] Based on the above steps, the gas-solid reactor under given operating conditions is obtained. The regularity of gas concentration and the influence of changes in the internal structure of micro-charges on the gas concentration at different cross-sectional locations. The influence of gas concentration on single-particle conversion rate was investigated, and a micro-charge reaction kinetic model and corresponding nonlinear equations were established, incorporating changes in packing porosity and multiple single-particle gas-solid reaction processes, to accurately predict complex reaction processes within the gas-solid reactor.

[0032] Combining equations (11) and (22), the following set of nonlinear equations can be obtained: (twenty three) By iteratively solving the nonlinear equation system, the spatiotemporal distribution of micro-charge conversion rate under specific operating conditions can be obtained, providing guidance for researchers to optimize reaction parameters.

[0033] Preferably, when analyzing the spatiotemporal distribution of the microcharge conversion rate, the microcharge height is 2. H 0 sets the range to Single particle radius The setting range is The calculation time setting range is The step size setting range is .

[0034] Beneficial effects: 1. Compared to existing technologies that assume gas-solid reactions... With a fixed gas concentration, this invention discloses a method for predicting the spatiotemporal distribution of conversion rate in the in-situ preparation of micro-sized charges using a gas-solid process. Based on a multiphysics model constructed from the diffusion, turbulence, and solid-fluid heat transfer processes of concentrated substances, this method can more comprehensively describe the reaction, heat transfer, and mass transfer processes within the gas-solid reactor, and accurately obtain the conversion rate of the gas-solid reactor under given operating conditions. The changing patterns of gases.

[0035] 2. Compared to existing technologies that assume a continuous and uniform coverage of solid products on the surface of solid reactants, this invention discloses a method for predicting the spatiotemporal distribution of conversion rate in the in-situ preparation of micro-sized charges using gas-solid processes. Based on the discontinuous growth (island-like growth) of gas-solid products on the reactant surface, this method employs rate equation theory to describe the growth of solid product islands and their transformation into a solid product layer. This establishes a single-particle gas-solid reaction model that better matches experimental results, enabling accurate prediction of conversion rates. The influence of gas concentration on single-particle conversion rate.

[0036] 3. Compared to existing technologies that cannot accurately reproduce the complex reaction processes within a gas-solid reactor, this invention discloses a method for predicting the spatiotemporal distribution of conversion rate in the in-situ preparation of micro-sized charges using a gas-solid reactor. The variation law of gas concentration, and the influence of changes in the internal structure of the micro-charge on the gas concentration at different cross-sectional locations. The influence of gas concentration on single-particle conversion rate can accurately reconstruct the complex reaction process in a gas-solid reactor, and more accurately predict the spatiotemporal distribution of micro-charge conversion rate, providing guidance for researchers to optimize reaction parameters. Attached Figure Description

[0037] Figure 1 This is a diagram of the physical / chemical processes involved in the gas-solid in-situ reaction.

[0038] Figure 2 This is a gas-solid reactor built using COMSOL software in the embodiment. Gas diffusion model, in which: Figure 2 (a) Simulation model diagram; Figure 2 (b) is the grid division diagram.

[0039] Figure 3 The different operating conditions in the embodiments affect the reactor. The effects of gas concentration changes, including: Figure 3 (a) shows the effect of different feed amounts; Figure 3Figure (b) shows the effect of different heating temperatures.

[0040] Figure 4 This is a schematic diagram of the layered structure of the micro-charge model.

[0041] Figure 5 This is a schematic diagram of the structural changes of a single particle during a gas-solid reaction.

[0042] Figure 6 This is a diagram illustrating the influence of product island growth on the reaction control steps in a single-particle model.

[0043] Figure 7 This is a schematic diagram of the numerical solution algorithm for the micro-charge reaction kinetics model.

[0044] Figure 8 This is a spatiotemporal distribution diagram of microcharge conversion rate under different charge heights and initial porosities. Detailed Implementation

[0045] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0046] Example 1: This embodiment uses Cu nanoparticles and A case study of the gas-solid reaction to generate Cu(N3)2 micro-charges. Relevant parameter values ​​are shown in Table 1. The chemical reaction equations involved in the gas-solid reactor are as follows: (twenty four) (25) Table 1. Values ​​of physical properties of each component in the examples. like Figure 1 As shown in this embodiment, a method for predicting the spatiotemporal distribution of conversion rate in the in-situ preparation of micro-sized charges using a gas-solid process is disclosed. The specific implementation steps are as follows: S1. Construct a multiphysics model of the gas-solid reactor based on the diffusion of concentrated substances, turbulence, and heat transfer processes between solids and fluids. Calculate and extract the internal dynamics of the gas-solid reactor under given operating conditions. The pattern of gas concentration change over time.

[0047] The chemical reaction rate equation and boiling mass transfer model are used to describe the reaction. In the gas-liquid two-phase mass transfer process, the incompressible Navier-Stokes equations are used to control the mass and momentum transfer processes during gas flow within the reactor, while solid and fluid heat transfer equations are used to describe the heat conduction and convective heat transfer processes within the reactor. Geometric modeling, preprocessing, solving, and post-processing are all performed in COMSOL 6.1 software. The simulation geometry is consistent with the experimental dimensions, and the model adopts a two-dimensional axisymmetric mode, constructing the gas reaction source at the bottom of a circular flask. The final two-dimensional model structure of the gas-solid reactor is as follows. Figure 2 As shown in (a). Concentrated substance diffusion, turbulence, solid and fluid conjugate heat transfer physical fields are set for the gas reaction source, gas flow domain, and reactor outer wall, respectively. The relevant physical processes can be described by equations (1) to (5). Non-isothermal flow is selected to couple the fluid flow and heat transfer interface to associate each physical field. The physical field is used to control the mesh size and further refine the mesh. The mesh division is as follows. Figure 2 As shown in (b). Based on the multiphysics model established above, using point probe 3 as the observation point, the variation law of HN3 gas concentration under different reaction conditions was calculated, extracted, and fitted. The results are as follows. Figure 3 As shown. The calculation time setting range is 5000s, and the step size setting range is 0.10s.

[0048] As shown in the figure, the HN3 gas concentration in the reactor first increases rapidly and then slowly increases to a steady state. When the heating temperature is constant, increasing the feed rate can increase the rate of increase in gas concentration and the steady-state gas concentration. The gas concentration field can reach steady state more quickly. When the feed amount is constant... The gas generation rate increases with increasing temperature, but the steady-state gas concentration decreases at higher reaction temperatures. Simulation results show that the maximum achievable gas concentration in the gas-solid reactor is determined by both the feed rate and heating temperature, while the time to reach the maximum gas concentration is primarily determined by temperature. The simulation results show the gas-solid reactor under different operating conditions. The gas concentration change process showed significant differences, verifying the accuracy of calculations for the gas-solid reactor under given operating conditions. The necessity of understanding the pattern of gas concentration changes over time.

[0049] S2, in the obtained gas-solid reactor Given the known variation law of gas concentration, and combined with the internal structural variation characteristics of the micro-charge, a constant relationship is established between the amount of gas consumed per unit time in the micro-element and the gas diffusion flux based on the law of conservation of mass. This yields the variation law of gas concentration at different cross-sectional locations inside the micro-charge with conversion rate and time.

[0050] The selected heating temperature is 55℃ and the feeding amount is 0.03mol. The reaction conditions were used as the research object, and the specific location within the gas-solid reactor was calculated using COMSOL software. gas concentration To investigate the changes over time, numerical expressions obtained through MATLAB software were used as input parameters to study the relationship between gas concentration at different cross-sectional locations inside the micro-charge and the conversion rate and time. Since both ends of the gas-solid reaction are exposed to the reaction gas, the model can be symmetrically treated. Differentiation along the height direction of the cylindrical charge was performed, and the model was layered as follows: Figure 4 As shown. With the center of the cylinder as the origin, the entire particle is divided into equally spaced layers along the height direction. Parts, with a layer spacing of Numbered sequentially from the model center to the surface along the height direction as follows: In this embodiment, the number of micro-layers N is selected as 100.

[0051] Since the volume of the solid product generated during the gas-solid azide reaction is greater than the volume of the solid reactants consumed, the particle volume continuously expands as the reaction proceeds, leading to a continuous shrinkage of the micro-charge pore structure. This process can be described by equation (9). Local porosity When the porosity decreases to 0, pore blockage occurs, preventing the reacting gases from diffusing into the interior to react. When the local porosity... At that time, according to equation (9), the following relationship is obtained. (26) In the formula, The initial porosity when pores are blocked. The local conversion rate during pore blockage. ,but (27) According to the reaction expansion coefficient involved in this embodiment, when That is, the density of copper powder packing g / cm 3 At this time, the gas concentration at different cross-sectional locations inside the micro-charge is always equal to the gas concentration inside the gas-solid reactor. C g .when That is, the density of copper powder packing g / cm 3 At this time, pore blockage may occur, meaning that the gas concentration at different cross-sectional locations inside the micro-charge may vary with the conversion rate. and time The change in gas concentration at different cross-sectional locations inside the micro-charge can be described by equation (11) as a function of conversion rate. and time The changing relationship.

[0052] S3, Based on the island-like structure characteristics of solid products and surface chemical reaction rates Product diffusion rate Establish a single-particle gas-solid reaction kinetic model and obtain The influence of gas concentration on the conversion rate of single particles was investigated; a reaction kinetic model and corresponding nonlinear equations for micro-charge were established to accurately describe the complex reaction process in the gas-solid reactor; and the spatiotemporal distribution prediction results of the conversion rate of micro-charge were obtained by iterative solution, thus realizing the spatiotemporal distribution prediction of the conversion rate of micro-sized charges prepared in situ using gas-solid methods.

[0053] The gas-solid reaction process of a single particle can be divided into two stages, as shown in the schematic diagram of the structural changes of the single particle. Figure 5 As shown. In the initial stage, the surface of the reactants is partially covered by product islands, while the remaining parts are exposed and can directly participate in the gas-solid reaction. At this point, the reaction conversion rate needs to consider both the surface reaction process and the product layer diffusion process. Single-particle conversion rate. Based on the characteristic diffusion length of the product monomer , Diffusion coefficient of gas product layer Surface chemical reaction rate constant , reactant surface Gas adsorption concentration The common determination can be described by the system of differential equations (22). Using MATLAB software and the fourth-order Runge-Kutta method, the system of differential equations (22) is solved, and the conversion rate in the single-particle reaction model is obtained through numerical calculation. Surface area The curve showing the change over time is as follows: Figure 6 As shown, in the initial stage, the surface of the solid reactants can react directly with gas molecules, leading to a rapid increase in conversion rate. As solid product islands grow and gradually cover the surface of the reactants, the rate-determining step of the reaction gradually changes from surface reaction to gas diffusion reaction, the conversion rate gradually decreases, and is eventually completely controlled by the product layer diffusion step.

[0054] Combining gas concentration changes, internal structure changes of micro-charges, and single-particle gas-solid reaction processes, a micro-charge reaction kinetic model and corresponding nonlinear equation set are established. The spatiotemporal distribution of micro-charge conversion rate under specific working conditions is obtained through iterative calculation. The micro-charge reaction kinetic model describes multiple single-particle gas-solid reaction processes involving changes in packing porosity, which can be described by the differential equation set (23). MATLAB software is used for programming, and the parameters are initialized according to the actual working conditions. The nonlinear equation set is solved using the explicit difference method and Gaussian elimination method. The numerical solution algorithm is as follows: Figure 7 As shown. First, the parameters are input, assigned values, and initialized. Then, the local conversion rate at the current time step is calculated using the explicit difference method. and the proportion of particle surface Then the nonlinear difference equation system was calculated. By combining the coefficient matrix and solving the system of equations using Gaussian elimination, the change in gas concentration along height can be calculated. The gas concentration distribution and nonlinear equations are then updated. After the iteration calculations for this time step are completed, the numerical calculations for the next time step are performed by advancing the time step.

[0055] initial porosity and charge height Related to the diffusion resistance and diffusion path within the gas, respectively changing and The values ​​were selected, and the spatiotemporal distribution of microcharge conversion rate under different charge heights and initial porosities was calculated. The results are as follows: Figure 8 As shown, as the reaction proceeds, the porosity gradually decreases, the gas diffusion resistance increases, and the gas concentration rapidly decreases along the height direction. This causes the conversion rate of particles at the center to gradually decrease until the reaction stops, while particles at the end faces can continue to react, increasing the conversion rate. Therefore, the overall conversion rate of the micro-charge is... The conversion rate should be lower than the local conversion rate at the end face of the micro-charge but higher than the local conversion rate at the center.

[0056] Three typical operating conditions were selected, and Cu(N3)2 micro-charges were prepared using a gas-solid reactor. The Cu(N3)2 content was then tested using inductively coupled plasma atomic emission spectrometry (ICP-AES) for comparative verification. The results of this invention's method, compared with existing core shrinkage model methods and experimental testing methods, are shown in Table 2. Operating condition 1 involved a heating temperature of 55℃ and a feed rate of 0.03 mol. , charge height Initial porosity reaction time Reaction condition 2 is a heating temperature of 65℃ and a feed rate of 0.05 mol. , charge height Initial porosity reaction time Reaction condition 3 is characterized by a heating temperature of 65℃, a feed rate of 0.05 mol NaN3, and a charge height of [missing information]. Initial porosity reaction time As can be seen from Table 2, compared with the existing core shrinkage model method, this method simultaneously considers the gas-solid reactor... The variation law of gas concentration, and the influence of changes in the internal structure of the micro-charge on the gas concentration at different cross-sectional locations. The influence of gas concentration on single-particle conversion rate can accurately reconstruct the complex reaction process in the gas-solid reactor, more accurately predict the spatiotemporal distribution of micro-charge conversion rate, and help optimize reaction operating parameters.

[0057] Table 2 Comparison of predicted and experimental results of overall conversion rate of micro-charged drugs The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the spatiotemporal distribution of conversion rate in in-situ gas-solid preparation of micro-sized charges, characterized in that: Includes the following steps: S1. Construct a multiphysics model of the gas-solid reactor based on the diffusion of concentrated substances, turbulence, and heat transfer processes between solids and fluids. Calculate and extract the internal dynamics of the gas-solid reactor under given operating conditions. The pattern of gas concentration change over time; S2, the obtained gas-solid reactor Given the known gas concentration variation pattern, and combined with the internal structural variation characteristics of the micro-charge, a constant relationship is established between the gas consumption per unit time of the micro-element and the gas diffusion flux based on the law of conservation of mass. This yields the variation pattern of gas concentration at different cross-sectional locations inside the micro-charge with conversion rate and time. S3, Based on the island-like structure characteristics of solid products and surface chemical reaction rates Product diffusion rate Establish a single-particle gas-solid reaction kinetic model and obtain The influence of gas concentration on the conversion rate of single particles was investigated; a reaction kinetic model and corresponding nonlinear equations for micro-charge were established to accurately describe the complex reaction process in the gas-solid reactor; and the spatiotemporal distribution prediction results of the conversion rate of micro-charge were obtained by iterative solution, thus realizing the spatiotemporal distribution prediction of the conversion rate of micro-sized charges prepared in situ using gas-solid methods.

2. The method for predicting the spatiotemporal distribution of conversion rate in in-situ gas-solid preparation of micro-sized charges according to claim 1, characterized in that: The method for implementing step S1 is as follows: S101. Select an appropriate physical model to describe the material diffusion, turbulence, solid and fluid heat transfer processes in the gas-solid reactor; The reaction process of NaN3 with a low-volatility acid is described using a chemical reaction rate equation, and the mass transfer process of HN3 in the gas-liquid two-phase flow is described using a boiling mass transfer model. The mass conversion relationship is as follows: （1） In the formula, , These are liquid phase and gas phase mass source terms, respectively; This is the relaxation factor, with a value between 0.01 and 1. It is the liquid volume fraction; and These are the liquid temperature and saturation temperature, respectively, under standard atmospheric pressure. Saturation temperature of liquid It is 309.15K; The gas-solid reactor The gas transport process is considered as a concentrated mass transport process; Fick's law is used to describe the transport mechanism, with mass fraction as the constraint condition and linear discretization performed. Its transient concentrated mass transport field is described as follows: （2） In the formula, For fluid density; Components The mass fraction; For matter Mass diffusion flux; For Hamiltonian operators; The average velocity is the mass. For reaction rate; mass diffusion flux The diffusion coefficient is proportional to the mole fraction gradient of the components and is calculated using the Fuller formula: （3） In the formula, for gas in The molecular diffusion coefficient in; Thermodynamic temperature; The relative molecular mass of the gaseous component; For system pressure; The volume of gas molecule diffusion. and The molecular diffusion volumes are 19.

05. and 17.9 ; Mass and momentum transfer during gas flow within the reactor are governed by the incompressible Navier-Stokes equations: （4） In the formula, For pressure; For fluid dynamic viscosity; It is the identity matrix; It is the acceleration due to gravity; It is a volume force; The heat conduction and convective heat transfer processes within the reactor are described using solid and fluid heat transfer equations, specifically: （5） In the formula, It is a constant pressure heat capacity; The convective heat transfer coefficient; Thermal conductivity; As a heat source; S102. Construct a multiphysics model by combining the geometry of the gas-solid reactor and the selected physical field, divide the grid reasonably, set relevant regions and point probes according to the initial reaction conditions, and calculate and extract the physical field information of the gas-solid reactor at different times and locations under the given conditions. S103. Based on the extracted discrete simulation data, fit the gas-solid reactor under given operating conditions. The pattern of gas concentration change over time.

3. The method for predicting the spatiotemporal distribution of conversion rate in in-situ gas-solid preparation of micro-sized charges according to claim 2, characterized in that: The implementation method for step S2 is as follows: S201. The growth of solid products in gas-solid reactions leads to changes in the internal structure of the micro-charge, manifested as a continuous reduction in the porosity of the micro-charge, hindering... Gas diffuses inward; establish an appropriate physical model to describe it. The process of gas diffusing inward; Carry the micro-charged medicine along the height Directional differential For a thickness of The infinitesimal element is described using Fick's diffusion law. The diffusion process of gas in a micro-element. （6） In the formula, The effective diffusion coefficient of gas within the pores; The concentration of HN3 gas at a specific location; Local porosity With conversion rate The relationship between them is （7） In the formula, The coefficient of thermal expansion is dimensionless. The initial porosity, , For sample packing density and For theoretical density, The diffusion coefficient of the gas within the pore is the diffusion coefficient through the gas molecules. Knudsen diffusion coefficient The calculation is obtained using the following formula: ; It can be calculated from equation (3). The calculation formula is as follows: （8） In the formula, The molar mass of a gas molecule; Thermodynamic temperature; Where is the pore radius; S202, the obtained gas-solid reactor Given the known gas concentration variation law, the variation law of gas concentration at different cross-sectional positions inside the micro-charge with conversion rate and time was obtained based on the gas diffusion flux and the law of conservation of mass. The amount of reactant gas consumed per unit time is equal to the height )Flow at the end face and height The difference in the amount of reactant gas flowing out at the end face, according to the law of conservation of mass: （9） In the formula, The charge radius of the micro-charge is... For gas flux, These are stoichiometric coefficients. The molar volume of the reactants. Let be the reaction time; Equation (9) simplifies to （10） Combined equations (6) and (10), at different cross-sectional positions inside the micro-charge The relationship between gas concentration and conversion rate and time is as follows: （11） In the formula, For gas-solid reactor Gas concentration is represented using a numerical expression determined by fitting. Adsorbed on solid surface Gas concentration; The external diffusion coefficient of the gas is calculated using the Sherwood number.

4. The method for predicting the spatiotemporal distribution of conversion rate in in-situ gas-solid preparation of micro-sized charges according to claim 3, characterized in that: The implementation method for step S3 is as follows: S301, Considering the island-like structure characteristics of solid products and surface chemical reaction rates Product diffusion rate Establish a single-particle gas-solid reaction kinetic model and obtain The influence of gas concentration on single-particle conversion rate; Single particles are the basic building blocks of micro-charges; for single-particle gas-solid reaction processes, the growth process of solid product islands is described using rate equation theory, and the total volume of solid products... The growth rate is primarily determined by the rate of chemical reactions occurring on the exposed surface, expressed as... （12） （13） In the formula, The surface area of ​​the solid reactant; The proportion occupied by the surface of solid reactants is dimensionless. It is the surface chemical reaction rate constant; This represents the critical height of the product island. Combining equations (12) and (13), the surface area occupied by the solid reactants is obtained. The expression is （14） The growth process of product islands involves a product diffusion-product island growth competition mechanism, and the critical height of the product islands is related to the surface diffusion coefficient of the product monomers. Product island capture monomer growth rate It is related to the surface monomer concentration distribution, and the expression is: （15） In the formula, The characteristic diffusion length of the product monomer. The dimensionless monomer concentration at which the height of the product island no longer continues to grow; The single-particle gas-solid reaction process can be divided into two stages: In the initial stage, the surface of the reactant is partially covered by product islands, while the rest is exposed and can directly participate in the gas-solid reaction. At this time, the reaction conversion rate needs to consider both the surface reaction process and the product layer diffusion process. As the product completely covers the surface of the reactant, the single-particle gas-solid reaction process is divided into two stages: the reaction gas can only carry out chemical reactions through the diffusion of the product layer. The relationship between single particle size and conversion rate is expressed as follows: （16） In the formula, The initial radius of the reactants; The radius of the unreacted nucleus; The radius of the reaction product; Based on the two reaction steps of direct chemical reaction and diffusion of gaseous products, the rate of consumption of the volume of the diffused solid reactant is expressed as: （17） In the formula, At the solid product / reactant interface Gas concentration; Substituting equation (16) into equation (17) and simplifying, we obtain the expression for the single-particle conversion rate as follows: （18） Using Fick's diffusion law to describe The diffusion process of gas in the product layer, （19） In the formula, for Diffusion flux of gas in the product layer for The diffusion coefficient of the product layer of the gas. for The concentration of gas in the product layer; because There is a conservation relationship between the consumption rate of gaseous chemical reactions and the gas diffusion flux. （20） In the formula, To obtain the stoichiometric coefficients, integrate equation (19) and combine it with equation (20) to get... （21） The single-particle conversion rate expression based on product structure change is as follows: （22） S302, combined with the gas-solid reactor The variation law of gas concentration, and the influence of changes in the internal structure of the micro-charge on the gas concentration at different cross-sectional locations. The influence of gas concentration on single-particle conversion rate was investigated. A micro-charge reaction kinetic model and corresponding nonlinear equations were established, which included changes in packing porosity and multiple single-particle gas-solid reaction processes. The complex reaction process in the gas-solid reactor was accurately described, and the spatiotemporal distribution prediction results of the micro-charge conversion rate were obtained by iterative solution.

5. The method for predicting the spatiotemporal distribution of conversion rate in in-situ gas-solid preparation of micro-sized charges according to claim 4, characterized in that: The implementation method for step S302 is as follows: Obtain the gas-solid reactor under given operating conditions The regularity of gas concentration and the influence of changes in the internal structure of micro-charges on the gas concentration at different cross-sectional locations. The influence of gas concentration on single-particle conversion rate was investigated, and a micro-charge reaction kinetic model and corresponding nonlinear equations were established, including changes in packing porosity and multiple single-particle gas-solid reaction processes, to accurately predict complex reaction processes in the gas-solid reactor. Combining equations (11) and (22), the following set of nonlinear equations is obtained: （23） The spatiotemporal distribution of micro-charge conversion rate under specific working conditions is obtained by iteratively solving a system of nonlinear equations.

6. The method for predicting the spatiotemporal distribution of conversion rate in in-situ gas-solid preparation of micro-sized charges according to claim 5, characterized in that: In step S102, For the finite element simulation software COMSOL, a two-dimensional axisymmetric mode was adopted to establish a simulation geometric model consistent with the actual reactor size. Non-isothermal flow was coupled with fluid flow and heat transfer interface coupling with relevant physical fields. The mesh size was controlled using physical fields, and the mesh was further refined near the wall and corners to ensure computational accuracy. After defining the initial reaction conditions, corresponding boundary conditions and material properties were set. Transient solutions were used to realize the gas-solid reactor under given conditions and at different times. Gas concentration is continuously calculated; point probes are set at different locations in the reactor to extract physical field information at different locations and times in the gas-solid reactor.

7. The method for predicting the spatiotemporal distribution of conversion rate in in-situ gas-solid preparation of micro-sized charges according to claim 6, characterized in that: Analysis of gas-solid reactor under different operating conditions When considering the gas concentration-time variation pattern, the heating temperature setting range is: , The range of material feeding settings is: The calculation time setting range is The step size setting range is ; Based on point probe extraction at different locations and times in the gas-solid reactor gas concentration, Gas flow rate, Discrete simulation data points such as gas temperature.

8. The method for predicting the spatiotemporal distribution of conversion rate in in-situ gas-solid preparation of micro-sized charges according to claim 6, characterized in that: In step S103, Extracted at different times at a given location Using discrete data points of gas concentration as the object, the curve fitting toolbox in MATLAB software was used to fit them into a smooth and continuous numerical expression, and the coefficient of determination was employed. Evaluate the reliability of the fitted expression; The value should be no less than 0.95, and the fitting expression should be as concise as possible while meeting the accuracy requirements; the final numerical expression determined by the fitting should be used to describe the gas-solid reactor. The variation pattern of gas concentration was studied and used as an input condition for subsequent prediction of micro-charge conversion rate.

9. The method for predicting the spatiotemporal distribution of conversion rate in in-situ gas-solid preparation of micro-sized charges according to claim 5, characterized in that: In step S202, the positions of different cross sections inside the micro-charge are analyzed. When considering the relationship between gas concentration and conversion rate and time, the radius of the micro-charge is... for initial porosity ε 0 is Micro-packing and micro-layering for .

10. The method for predicting the spatiotemporal distribution of conversion rate in in-situ gas-solid preparation of micro-sized charges according to claim 5, characterized in that: When analyzing the spatiotemporal distribution of microcharge conversion efficiency, the microcharge height 2 H 0 sets the range to Single particle radius The setting range is The calculation time setting range is The step size setting range is .

Images