Method for designing a sustained-release agent component and method for preparing a sustained-release agent

Abstract

This application relates to a method for designing and preparing a sustained-release agent. The sustained-release agent includes quartz sand, paraffin wax, and an active ingredient. The method for designing the sustained-release agent components includes: pre-setting different component design schemes, each with the same volume of sustained-release agent. Each component design scheme has a first variable and a second variable. The first variable is the mass of active ingredient per unit volume, and the second variable is the wax-to-sand ratio. The method simulates the rapid dissolution process of the active ingredient on the surface of the sustained-release agent to obtain a first release curve of the active ingredient over time. The method simulates the dissolution process of the active ingredient inside the sustained-release agent to obtain a second release curve of the active ingredient over time. The simulation process includes: obtaining the effective diffusion coefficient based on the first and second variables, and simulating and solving the second release curve based on Fick's law and the effective diffusion coefficient. The method determines the optimal component design scheme that matches the desired stable concentration and the mass-time release curve.

Description

Technical Field

[0001] This application relates to the field of groundwater remediation, and in particular to a method for designing components of a slow-release agent and a method for preparing the slow-release agent. Background Technology

[0002] Groundwater is a crucial component of my country's water resources, accounting for 13.8% of the country's total water supply. Its quality and safety are vital to the healthy development of society. With the acceleration of urbanization, the groundwater environment has been polluted by various sources, including industrial wastewater, agricultural sewage, and urban waste. Among these, recalcitrant organic pollutants such as trichloroethylene, benzene rings, and aromatic hydrocarbons require hundreds of years to degrade in the natural environment. Furthermore, the hydrogeological conditions of groundwater are complex, making pollutant remediation challenging. Currently, commonly used technologies for recalcitrant organic pollutants include in-situ remediation and ex-situ remediation. In-situ chemical oxidation technology has advantages such as high remediation efficiency, wide treatment range, and low cost; however, it is affected by the oxidant materials and the groundwater environment during the remediation process, often resulting in problems such as back diffusion, tailing, rebound, and short oxidant lifetime.

[0003] In recent years, slow-release agents (CRMs) technology has been studied as an effective method to overcome the problems encountered by current in-situ chemical oxidation technologies. Slow-release agents have several advantages: stable and low release rates, enabling long-term remediation of pollutants; low cost; reduction of non-selective consumption and loss of oxidants; and environmental friendliness. Depending on the oxidant used, permanganate slow-release agents and persulfate slow-release agents are currently the most common. Persulfates have higher reduction potentials, better stability, and multiple activation mechanisms, making them more suitable for long-term stable remediation of groundwater.

[0004] The stable release of slow-release agents is a key factor in the in-situ remediation of groundwater, influenced by the composition and proportions of the agent itself, as well as environmental conditions. Accurately understanding and characterizing the release patterns and features of slow-release agents is crucial for their in-situ application. Mathematical algorithms and models are effective tools for studying slow-release agent release. While some studies have analyzed the release patterns, these methods are based on fitting experimental data and lack exploration of diffusion during the release process. Although existing technologies attempt to provide quantitative predictions of release time based on research models, common empirical models cannot adequately explain the release process or confirm their widespread applicability, thus hindering the successful implementation of slow-release agents. Summary of the Invention

[0005] Therefore, it is necessary to provide a method for designing sustained-release agent components and a method for preparing sustained-release agents to address the above-mentioned technical problems.

[0006] This application provides a method for designing a sustained-release agent component, wherein the sustained-release agent comprises quartz sand, paraffin wax, and an active ingredient, and the method for designing the sustained-release agent component includes:

[0007] Different component design schemes are preset, and the volume of the sustained-release agent in each component design scheme is the same. Each component design scheme has a first variable and a second variable. The first variable is the mass of active ingredient contained in a unit volume, and the second variable is the wax-sand ratio of the mass of paraffin to the mass of quartz sand.

[0008] Simulate the sustained-release process of different component design schemes to obtain the mass-time release curves of the active ingredients in each component design scheme, including:

[0009] The rapid dissolution process of the active ingredient on the surface of the sustained-release agent was simulated to obtain a first release curve of the active ingredient over time;

[0010] The dissolution process of the active ingredient inside the sustained-release agent is simulated to obtain a second release curve of the active ingredient over time. The simulation process includes: obtaining an effective diffusion coefficient based on the first and second variables, simulating and solving the second release curve based on Fick's law and the effective diffusion coefficient, and connecting the second release curve with the first release curve to form the mass-time release curve.

[0011] Based on the matching degree between the expected stable concentration in the application scenario and the mass-time release curve, a matching preferred component design scheme is determined.

[0012] Optionally, the active ingredient is persulfate.

[0013] Optionally, the rapid dissolution process of the active ingredient at the surface of the sustained-release agent is simulated to obtain a first release curve of the active ingredient over time, using the following formula:

[0014]

[0015] In the formula, M t1 M represents the mass of the active ingredient released at time t1, where t1 is the duration of the first release curve. 总 The total added mass of the active ingredient in each of the component design schemes is α, where α is the correction factor and k is the rapid release constant.

[0016] Optionally, the effective diffusion coefficient can be obtained based on the first variable and the second variable using the following formula:

[0017] De = AB * ln(X1) + C * X2

[0018] In the formula, De is the effective diffusion coefficient, A, B, and C are all constants, X1 represents the second variable, X2 represents the total added mass of the active ingredient in each component design scheme, and X2 is obtained based on the first variable and the volume of the sustained-release agent.

[0019] Optional, A is 1.36 × 10 -6 B is 1.27 × 10 -5 C is 2.45 × 10 -6 .

[0020] Optionally, the sustained-release agent is cubic in shape.

[0021] Optionally, in the process of simulating the second release curve, the mass of the active ingredient in the second release curve is simulated in the following manner:

[0022]

[0023] In the formula, a is half the side length of the cubic sustained-release agent;

[0024] x is half the side length of the cube-shaped sustained-release agent that has not yet dissolved inside the sustained-release agent;

[0025] M2 represents the mass of the active ingredient during the dissolution process of the active ingredient inside the sustained-release agent;

[0026] V represents the volume of the solution in the simulated scenario;

[0027] C S This represents the maximum solubility of the active ingredient in the simulated scenario solution.

[0028] C a The solubility of the active ingredient at the end of the first release curve;

[0029] De is the effective diffusion coefficient;

[0030] C represents the concentration of the active ingredient in the solution in the simulated scenario.

[0031] Optionally, the effective diffusion coefficient is obtained based on the first and second variables, and the second release curve is simulated using the effective diffusion coefficient. The result is obtained by simultaneously solving the following two equations:

[0032] M2=A(8a 3 -8x 3 )

[0033]

[0034] In the formula, a is half the side length of the cubic sustained-release agent;

[0035] x is half the side length of the cube-shaped sustained-release agent that has not yet dissolved inside the sustained-release agent;

[0036] A is the first variable;

[0037] M2 represents the mass of active ingredient released cumulatively over time t during the dissolution process of the active ingredient inside the sustained-release agent.

[0038] De is the effective diffusion coefficient;

[0039] t1 is the duration of the first release curve;

[0040] V represents the volume of the solution in the simulated scenario;

[0041] C S This represents the maximum solubility of the active ingredient in the simulated scenario solution.

[0042] This application provides a method for preparing a sustained-release agent, implemented using the preferred component design scheme obtained by the sustained-release agent component design method described in this application, including:

[0043] The volume of the sustained-release agent is determined according to the preferred component design scheme, and the mass of the active ingredient in the sustained-release agent is determined according to the volume of the sustained-release agent and the mass of the active ingredient contained in the unit volume.

[0044] The wax-to-sand ratio of the paraffin mass to the quartz sand mass is determined according to the preferred component design scheme.

[0045] Prepare the sustained-release agent.

[0046] Optionally, the active ingredient is sodium persulfate, and the process for preparing the sustained-release agent includes:

[0047] (I) First, add paraffin wax to anhydrous ethanol, heat and melt it, then add sodium persulfate, mesoporous manganese oxide, quartz sand, Span-80 and polyethylene glycol according to the ratio, mix and stir evenly at 65°C to obtain molten material; the mesoporous manganese oxide is prepared by hard template coupled nano-etching method;

[0048] (II) Quickly pour the molten material obtained in step (I) into a mold and cool it at room temperature to obtain the final product.

[0049] Optionally, the polyethylene glycol is polyethylene glycol-4000.

[0050] The method for designing the components of the sustained-release agent and the method for preparing the sustained-release agent in this application have at least the following technical advantages:

[0051] The sustained-release simulation of different component designs in this application consists of two processes: a first stage belonging to the liquid phase and a second stage belonging to the solid phase, forming a two-phase diffusion model. The first stage mainly simulates the rapid dissolution of the surface of the sustained-release agent when it first enters the solution, while the second stage mainly simulates the slow dissolution of the internal solid after the rapid dissolution of the surface of the sustained-release agent. This application obtains the effective diffusion coefficient through the first and second variables, and performs sustained-release process simulations with discrimination for different component conditions, further improving the broad applicability of the sustained-release agent simulation.

[0052] The slow-release agent component design method provided in this application can quantitatively adjust the content of quartz sand and sodium persulfate to change the release process, simulate and regulate the lifespan of the slow-release agent, help to more accurately simulate the release mechanism and process of the slow-release agent, assist in the design of the slow-release agent and effectively apply it to in-situ groundwater remediation in different environments. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the process for preparing a sustained-release agent in one embodiment of this application;

[0054] Figure 2 This is a schematic diagram of the preparation process of mesoporous manganese oxide used in the sustained-release agent preparation method in one embodiment of this application;

[0055] Figure 3 This is a flowchart illustrating the design method of the sustained-release agent component in one embodiment of this application;

[0056] Figure 4 for Figure 3 A schematic diagram of the simulation concept for step S220;

[0057] Figure 5a This is a schematic diagram of an electron microscope scan before the release of the sustained-release agent in a static release experiment.

[0058] Figure 5b This is a schematic diagram of an electron microscope scan after the release of the sustained-release agent in a static release experiment.

[0059] Figure 6a This is a schematic diagram showing the effect of different wax-to-sand ratios on the release of the sustained-release agent in a static release experiment.

[0060] Figure 6b This is a schematic diagram illustrating the effect of different sodium persulfate contents on the release of the sustained-release agent in a static release experiment.

[0061] Figure 7a This is a comparison chart of data from the static release experiment and the simulated control experiment (the wax-sand ratio in the figure is 1:1);

[0062] Figure 7bThis is a comparison chart of data from the static release experiment and the simulated control experiment (the wax-sand ratio in the figure is 1:2);

[0063] Figure 7c This is a comparison chart of data from the static release experiment and the simulated control experiment (the wax-sand ratio in the figure is 1:4);

[0064] Figure 7d This is a comparison chart of data from the static release experiment and the simulated control experiment (the wax-sand ratio in the figure is 1:6);

[0065] Figure 8a This is a comparison chart of data from a static release experiment and a simulated control experiment (sodium persulfate content: 2g).

[0066] Figure 8b This is a comparison chart of data from a static release experiment and a simulated control experiment (sodium persulfate content: 4g).

[0067] Figure 8c This is a comparison chart of data from a static release experiment and a simulated control experiment (sodium persulfate content: 6g).

[0068] Figure 8d This is a comparison chart of data from a static release experiment and a simulated control experiment (sodium persulfate content: 8g). Detailed Implementation

[0069] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0070] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0071] See Figure 1 This application provides a method for preparing a sustained-release agent, comprising preparing the sustained-release agent based on the volume of the sustained-release agent, the mass of the active ingredient per unit volume, and the wax-to-sand ratio of the paraffin mass to the quartz sand mass. The active ingredient is sodium persulfate, and the process for preparing the sustained-release agent includes:

[0072] (I) First, add paraffin wax to anhydrous ethanol, heat and melt it, then add sodium persulfate, mesoporous manganese oxide, quartz sand, Span-80 and polyethylene glycol according to the ratio, mix and stir evenly at 65°C to obtain molten material; mesoporous manganese oxide is prepared by hard template coupled nano-etching method;

[0073] (II) Quickly pour the molten material obtained in step (I) into a mold and cool it at room temperature to obtain the final product.

[0074] As a specific process disclosed in this embodiment, sodium persulfate (Na2S2O8) and manganese nitrate (Mn(NO3)2) were both analytical grade, and quartz sand (SiO2) was purchased from Shanghai Maclean Biochemical Technology Co., Ltd. Commercial manganese dioxide was purchased from Xilong Chemical Co., Ltd. Anhydrous ethanol (C2H6O) and sodium hydroxide (NaOH) were both analytical grade, and paraffin wax and polyethylene glycol-4000 were chemically pure and purchased from Sinopharm Chemical Reagent Co., Ltd. Span-80 was analytical grade and purchased from Shenzhen Biao Le Industrial Co., Ltd. SBA-15 was purchased from Nanjing Xianfeng Nanomaterials Technology Co., Ltd. Sodium bicarbonate (NaHCO3) and potassium iodide (KI) were both analytical grade and purchased from Shanghai Lingfeng Chemical Reagent Co., Ltd. The preparation instruments included: HC-2518 high-speed centrifuge (Anhui Zhongke Zhongjia Scientific Instrument Co., Ltd.); DF-101S thermal collector-type constant temperature magnetic stirrer (Hangzhou David Science and Education Instrument Co., Ltd.); and DL-I-15 benchtop enclosed electric furnace (Tianjin Tester Instrument Co., Ltd.).

[0075] The preparation process of the persulfate sustained-release agent is shown in the figure. For example, the sustained-release agent contains 12g of quartz sand and 4g of sodium persulfate, with wax-sand ratios of 1:1, 1:2, 1:4, and 1:6, while other components remain constant (polyethylene glycol-4000 mass is 1.0g, mesoporous manganese oxide mass is 0.5g, and Span-80 mass is 0.1ml). Another example is sustained-release agents with sodium persulfate contents of 2g, 4g, 6g, and 8g, containing 12g of quartz sand and 12g of paraffin wax, with other components remaining constant (polyethylene glycol-4000 mass is 1.0g, manganese dioxide mass is 0.5g, and Span-80 mass is 0.1ml). The mold for preparing the cubic sustained-release agent is, for example, a 1cm × 1cm × 1cm cube, yielding 12 sustained-release agents per batch, each weighing approximately 2.5g. The above preparation processes can be used to conduct static release experiments to demonstrate the rationality of the component design scheme. It is understandable that the absolute mass of a single sustained-release agent is difficult to control precisely due to various factors during preparation. However, this does not affect the implementation of the embodiments of this application. By controlling the wax-sand ratio and the mass of sodium persulfate per unit volume, the embodiments modify the preparation process of the sustained-release agent. Subsequent static release experiments and simulated control experiments are sufficient to demonstrate the feasibility of each embodiment.

[0076] See Figure 2Ordered mesoporous manganese oxide was prepared by hard template coupled nano-etching method (Wang Ting, Xu Kunmiao, Wu Liguang, et al. Construction and performance of slow-release agent for tetracycline removal in groundwater [J]. Journal of Environmental Science, 2022, 42(06):167-177.), and the preparation process is shown in the figure.

[0077] See Figure 3 One embodiment of this application provides a method for designing a sustained-release agent component. The sustained-release agent includes quartz sand, paraffin wax, and an active ingredient. The method for designing the sustained-release agent component includes:

[0078] Step S100: Preset different component design schemes. The volume of the sustained-release agent in each component design scheme is the same. The component design scheme has a first variable and a second variable. The first variable is the mass of active ingredients contained in a unit volume, and the second variable is the wax-sand ratio of the mass of paraffin to the mass of quartz sand.

[0079] Step S200: Simulate the sustained-release process of different component design schemes to obtain the mass-time release curves of the active ingredients in each component design scheme, including:

[0080] Step S210: Simulate the rapid dissolution process of the active ingredient on the surface of the sustained-release agent to obtain the first release curve of the active ingredient over time;

[0081] Step S220: Simulate the dissolution process of the active ingredient inside the sustained-release agent to obtain a second release curve of the active ingredient changing over time. The simulation process includes: obtaining the effective diffusion coefficient based on the first and second variables, simulating and solving the second release curve based on Fick's law and the effective diffusion coefficient, and connecting the second release curve with the first release curve to form a mass-time release curve.

[0082] Step S300: Based on the matching degree between the expected stable concentration and the mass-time release curve in the application scenario, determine the optimal component design scheme that matches the target composition.

[0083] In this embodiment, the sustained-release agent can be cubic in shape, and its application scenario can be, for example, groundwater ecological restoration, where it achieves the desired stable concentration of the active ingredient. Since the first and second release curves play a dominant role at different time periods, and both release the active ingredient within their respective time periods, the mass-time release curve of the active ingredient can be obtained by sequentially connecting the curves. The active ingredient can be a persulfate, such as sodium persulfate; each embodiment uses sodium persulfate as an example of the active ingredient for further explanation.

[0084] This embodiment simulates the sustained-release process of different component designs into two processes, namely steps S210 and S220, which improves the reliability of different component designs. Step S210 mainly simulates the rapid dissolution that occurs on the surface of the sustained-release agent when it first enters the solution, which belongs to the first stage of the liquid phase. Step S220 mainly simulates the slow dissolution of the solid inside the sustained-release agent after the rapid dissolution of the surface, which belongs to the second stage of the solid phase.

[0085] Furthermore, this embodiment obtains the effective diffusion coefficient through the first and second variables, and performs sustained-release process simulations with discriminative ability for different component conditions, further improving the applicability of sustained-release agent simulation release. The reliability of the auxiliary component design in this embodiment can be demonstrated through the comparative static release experiments and simulated control experiments provided in the following examples.

[0086] Step S200 can be viewed as a mathematical model for the release of a slow-release agent. This model divides the release process into two stages: a first stage corresponding to step S210 and a second stage corresponding to step S220. The first stage represents the rapid release process of the slow-release agent, which mainly involves the rapid dissolution of sodium persulfate on the surface of the slow-release agent and within a certain range of the surface through direct contact with water. The second stage is a stable release process, where water enters the interior of the slow-release agent along the pores, and sodium persulfate is mainly released through diffusion. At this stage, the amount of water in the pores is insufficient to rapidly dissolve the surrounding sodium persulfate, making diffusion the main rate-limiting step.

[0087] The following table explains the relevant parameters in step S200:

[0088]

[0089] For step S210, in the first few days after the release begins, the release rate is high and follows an exponential relationship, which can be represented by first-order kinetics:

[0090]

[0091] In the formula, t1 is the duration of the first release curve, the first release curve is the rapid release process, and the end of the continuous process is the number of days until the rapid release ends.

[0092] M t1 The mass of sodium persulfate released at time t1 (i.e., the total amount of sodium persulfate released in the first stage);

[0093] M 总 The total added mass of the active ingredient in each component design scheme is the raw material mass of sodium persulfate in one sustained-release tablet. In some embodiments, M 总 This indicates the release mass of sodium persulfate in the sustained-release agent at infinity.

[0094] α is a correction factor, ranging from 0.50 to 0.85, and k is the rapid release constant, ranging from 0.05 to 1.5. Accordingly, the curve showing the change in the mass of sodium persulfate released in the first stage over time is obtained, i.e., the first release curve.

[0095] See Figure 4 For step S220, i.e. the second stage, the dissolution and diffusion process of sodium persulfate in the slow-release agent can be solved based on Fick's law, as shown in formula (2):

[0096]

[0097] J is the diffusion flux;

[0098] M2 represents the mass of sodium persulfate during the dissolution process of sodium persulfate inside the simulated slow-release agent, which increases with time, i.e., the cumulative mass of sodium persulfate released in the second stage after time t.

[0099] C represents the concentration of the active ingredient in the solution in the simulated scenario, specifically the concentration of sodium persulfate dissolved in water constructed through a mathematical model.

[0100] De is the effective diffusion coefficient;

[0101] x is half the side length of the currently undissolved cubic slow-release agent inside the agent, simply referred to as the length of the undissolved area;

[0102] S represents the surface area of ​​the cubic sustained-release agent at a certain moment.

[0103] The effective diffusion coefficient can be obtained using the following formula based on the first and second variables:

[0104] De = AB * ln(X1) + C * X2

[0105] In the formula, De is the effective diffusion coefficient, A, B, and C are constants, X1 represents the second variable, and X2 represents the total mass of sodium persulfate added in each component design scheme. X2 is obtained based on the first variable and the volume of the slow-release agent. Specifically, A is 1.36 × 10⁻⁶. -6 B is 1.27 × 10 -5 C is 2.45 × 10 -6 .

[0106] The surface area of ​​a cubic sustained-release agent at a given moment can be calculated using the following formula:

[0107] S = 24x 2 (3)

[0108] Substituting formula (3) into formula (2) and moving S to the right side of the formula, we can obtain formula (4).

[0109]

[0110] In the process of simulating the solution of the second release curve, the mass of sodium persulfate in the second release curve is simulated in the following way. This includes: integrating equation (4) using boundary conditions, and when x is between 0 and a, the concentration C at the boundary of the undissolved zone is C = C s When x = a, C = C a Formula (5) for the mass release of sodium persulfate in the sustained-release agent was obtained, and further simplification yielded formula (6):

[0111]

[0112] In the formula, 'a' is half the side length of the cube-shaped sustained-release agent, and is simply referred to as the second-stage boundary length;

[0113] V represents the volume of the solution in the simulated scenario, or simply the volume of water;

[0114] C S The maximum solubility of sodium persulfate in the simulated scenario solution, i.e., the maximum solubility of sodium persulfate in water, is taken as 550 kg / m³. 3 ;

[0115] C a The concentration of sodium persulfate in the aqueous phase is C. a This represents the solubility of sodium persulfate at the end of the first release curve, i.e., the solubility of sodium persulfate at the end of the first stage.

[0116] The rate at which the undissolved diffusion zone migrates to the dissolved diffusion zone in the sustained-release agent is shown in formula (7):

[0117]

[0118] In the formula, A is the first variable, specifically representing the mass of sodium persulfate contained in a unit volume of the sustained-release agent.

[0119] According to the law of conservation of mass, equating formula (6) with formula (7) yields formula (8).

[0120]

[0121] Formula (9) for the cumulative mass of sodium persulfate released after time t (t≥t1).

[0122] M2=A(8a 3 -8x 3 (9)

[0123] At this point, the concentration of sodium persulfate in the aqueous phase (C) a The expression for is represented by formula (10).

[0124]

[0125] Substitute formula (10) into formula (8) to obtain formula (11).

[0126]

[0127] Simplify formula (11) to obtain formula (12).

[0128]

[0129] According to the boundary conditions, when t = t1, x = a, and when t ≥ t1, integrate x (0 ≤ x < a) to obtain the controlled release equation (13).

[0130]

[0131] Define the following dimensionless parameter form as shown in formula (14):

[0132]

[0133] Based on the above dimensionless parameters, convert equation (13) into formula (15).

[0134]

[0135] Since this equation is an implicit function, in this paper, the second-stage release amount M is jointly solved for formula (13) and (9) based on Matlab software. t2 . Since in the simultaneous equations, on the premise that the volume of the cubic sustained-release agent is determined, the first variable (the mass of the active ingredient contained per unit volume) and the second variable (the wax-sand ratio) are used as input parameters. Based on the fact that the effective diffusion coefficient De has been obtained in relation to the first variable and the second variable, the second-stage release amount M can be jointly obtained by combining the effective diffusion coefficient. t2 . Furthermore, the second-stage release amount M is obtained. t2 The curve of the second-stage release amount M with respect to time is obtained, that is, the second release curve obtained by simulation solution.

[0136] Based on this, the total release percentage can be further obtained:

[0137]

[0138] Static release experiment

[0139] To verify the feasibility of the sustained-release agent component design method of each embodiment of this application, the applicant conducts experimental verification according to several examples in the preparation process.

[0140] See Figure 5a and Figure 5bThe sustained-release agent was characterized before and after release using scanning electron microscopy (SEM). It was observed that the surface of the sustained-release agent was relatively smooth with few pores before release, while larger pores and voids appeared after release. This is likely because during the release process, water dissolves the sodium persulfate near the surface of the sustained-release agent, which then seeps into the interior of the agent along the pores, dissolving and diffusing the sodium persulfate within the matrix. The instruments used were an S-4800 scanning electron microscope (Hitachi, Japan) and a TU-1901 dual-beam UV-Vis spectrophotometer (Beijing Purkinje General Instrument Co., Ltd.).

[0141] See Figure 6a The figure shows the effect of different wax-to-sand ratios on the release of the slow-release agent. The M / M ratio in the figure... 总 This refers to the mass of sodium persulfate released by the slow-release agent over time divided by the maximum mass of sodium persulfate that a single slow-release agent can release. As shown in the figure, the release rate of the slow-release agent increases with the increasing proportion of quartz sand. When the ratio of paraffin wax to quartz sand is 1:1, the initial release rate is slow, reaching only 60% on day 9. This may be because the high proportion of paraffin wax results in a relatively dense structure in the slow-release agent, making it difficult for the sodium persulfate to dissolve and diffuse out. When the proportion of quartz sand increases, the initial release rate of the slow-release agent increases significantly. This may be because the larger particle size of quartz sand increases the porosity of the slow-release agent, making the structure looser and facilitating water penetration into the interior, thus increasing mass transfer efficiency. Therefore, a smaller wax-to-sand ratio is more conducive to the dissolution and diffusion of the slow-release agent.

[0142] See Figure 6b The figure shows the effect of different sodium persulfate contents on the release of the sustained-release agent. As shown, increasing the sodium persulfate content leads to a faster initial release rate of the sustained-release agent. When the sodium persulfate content is 2g, the low content and the presence of a large amount of paraffin wax, coupled with the fact that paraffin wax is hydrophobic, make it difficult for water to penetrate. When the sodium persulfate content increases to 4g and 6g, the release rate of the sustained-release agent increases significantly. When it is increased to 8g, the release rate reaches 60% on the first day. This indicates that increasing the sodium persulfate content can change the release time of the sustained-release agent.

[0143] Simulated control experiment

[0144] To verify the feasibility of the sustained-release agent component design method in each embodiment of this application, the applicant evaluated the sustained-release agent component design method based on several examples in the preparation process, specifically the evaluation of the simulation model provided in step S200. The model evaluation used the coefficient of determination (R²). 2 The test is performed using R and the root mean square error (RMSE). 2The larger the value, the closer it is to 1, and the smaller the RMSE value, the more accurate the model is. The calculation formula is as follows:

[0145]

[0146] In the formula, y i Y is the measured value. i For the predicted value, O i is the measured average value, i is the sample sequence, and n is the sample size.

[0147] As shown in the figure, the experimental conditions for different component controlled-release agents were calculated and the experimental data were fitted using a first-order kinetic model, a diffusion model, and the two-phase diffusion model proposed in this paper. The two-phase diffusion model, i.e., step S200, includes a first-stage simulation of the liquid phase and a second-stage simulation of the solid phase. Specifically, the coefficient of determination R was calculated using the table below. 2 We use the root mean square error (RMSE) to analyze the computational accuracy of different models.

[0148] Evaluation results (R) calculated by the three models 2 RMSE)

[0149]

[0150] See Figures 7a to 7d The slow-release agent initially exhibits a relatively rapid release trend, primarily because the sodium persulfate on and near the surface of the slow-release agent can directly contact water and dissolve rapidly. As the oxidant is released, the concentration gradient in the solution continuously decreases, and diffusion becomes the main rate-limiting step in the later stages of release. The R1 of the first-order kinetic model... 2 The value reached 0.976 when the wax-to-sand ratio was 1:1. However, as the wax-to-sand ratio decreased, R... 2 The RMSE value also decreased, reaching 0.0325. This is because the first-order kinetics mainly considered the concentration of sodium persulfate itself, neglecting the effect of diffusion and not treating diffusion as the main rate-limiting step, leading to a higher predicted value than the experimental value and an increased error. The diffusion-type model predicted higher values ​​than the experimental values ​​when the wax-sand ratio was 1:1. When the wax-sand ratio increased, the predicted value of the release in the early stage was lower than the experimental value, and R... 2 The coefficient of determination (R²) dropped below 0.9, while the RMSE was greater than 0.01. This may be because the model did not consider the rapid initial release of the slow-release agent. The increased proportion of quartz sand in the slow-release agent increased its permeability. As more water permeated in, more oxidant was released in the early stages, resulting in a smaller change in the concentration gradient in the later stages. Therefore, the diffusion driven by the concentration gradient became more stable in the later stages, showing a better fit to the experimental values. The two-phase diffusion model proposed in this paper considers both the rapid initial release of the slow-release agent and the subsequent diffusion process, with a fitting R² value of [missing value]. 2All values ​​are greater than 0.9, and RMSE is less than 0.007. Compared with the first two models, the fitting accuracy is the highest, and it can better calculate the release of the sustained-release agent.

[0151] See Figures 8a to 8d The figures show the release characteristics of the sustained-release agent with different sodium persulfate contents, compared with simulation results from a first-order kinetic model, a diffusion model, and a two-phase diffusion model. As can be seen from the figures, the two-phase diffusion model has the best overall fit, with R0... 2 All values ​​were above 0.9. The goodness of fit of the first-order kinetic model was better when the sodium persulfate content was 2g and 4g, but when the sodium persulfate content increased to more than 4g, R0 decreased. 2 Less than 0.9. As the sodium persulfate content increases, the fitting curve of the diffusion model shifts to the right. This is because the sodium persulfate near the surface of the initial slow-release agent dissolves in water, leading to a higher concentration of sodium persulfate in the water. The diffusion model calculates based on the concentration difference at the boundary; excessive sodium persulfate will prevent the model from recognizing the error caused by rapid early dissolution. When the sodium persulfate content is 0.6g, R... 2 It reached 0.984, while when the sodium persulfate content increased to 8g, R 2 The value decreased to 0.529. The two-phase diffusion model can stably calculate the release process with different sodium persulfate contents. 2 All are above 0.95.

[0152] In the embodiments of this application, sodium persulfate is used as an oxidant, paraffin and quartz sand are used as binders, and reaction kinetics and diffusion theory are combined to construct a two-phase diffusion model corresponding to step S200 to describe the release behavior of the slow-release agent.

[0153] To demonstrate the feasibility of the design method for the sustained-release agent components in each embodiment, this application prepared sustained-release agents with different wax-sand ratios and sodium persulfate contents, and conducted static release experiments. The release experiment data were simulated using a first-order kinetic model, a diffusion model, and the two-phase diffusion model of this study, and the results were compared with the experimental results to evaluate the accuracy and reliability of the models. Finally, the parameter variation law of the two-phase diffusion model was investigated.

[0154] Release experiments were designed to detect the release of the sustained-release agent with different wax-to-sand ratios and different persulfate contents, obtaining release data for more than 15 days. Simulations were performed using first-order kinetics, a diffusion model, and the two-phase diffusion model proposed in this paper. The results show that the determination coefficient R0 of the two-phase diffusion model is... 2 All values ​​were above 0.96, indicating an accuracy improvement of over 10% compared to single first-order kinetic and diffusion models, enabling more precise simulation of the sustained-release agent release process. The two-phase diffusion model, used for step S200, had a determination coefficient R0. 2 Most values ​​are above 0.95, indicating higher accuracy compared to first-order dynamical models and diffusion models.

[0155] The comparison of data from the static release experiment, first-order kinetic model, and diffusion model is sufficient to demonstrate the reliability of the controlled-release agent component design method in each embodiment of this application. The content of quartz sand and sodium persulfate can effectively change the release rate of the controlled-release agent. The controlled-release agent component design method provided in each embodiment can quantitatively adjust the content of quartz sand and sodium persulfate to change the release process and simulate and regulate the lifetime of the controlled-release agent. The controlled-release agent component design method provided in each embodiment helps to more accurately simulate the release mechanism and process of the controlled-release agent, assists in the design of the controlled-release agent, and effectively applies it to in-situ groundwater remediation in different environments. It is of great significance in guiding the design optimization of persulfate controlled-release agents, as well as the preparation and field application of persulfate controlled-release agents based on groundwater remediation.

[0156] The technical features of the embodiments described above can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered to be within the scope of this specification. When technical features of different embodiments are embodied in the same drawing, it can be regarded as the drawing also disclosing examples of combinations of the various embodiments involved.

[0157] The embodiments described above are merely examples of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application.

Claims

1. A method for designing sustained-release agent components, characterized in that, The sustained-release agent comprises quartz sand, paraffin wax, and active ingredients. The sustained-release agent is cubic in shape. The method for designing the components of the sustained-release agent includes: Different component design schemes are preset, and the volume of the sustained-release agent in each component design scheme is the same. Each component design scheme has a first variable and a second variable. The first variable is the mass of active ingredient contained in a unit volume, and the second variable is the wax-sand ratio of the mass of paraffin to the mass of quartz sand. Simulate the sustained-release process of different component design schemes to obtain the mass-time release curves of the active ingredients in each component design scheme, including: The rapid dissolution process of the active ingredient at the surface of the sustained-release agent was simulated to obtain a first release curve of the active ingredient over time, which was obtained using the following formula: In the formula, M t1 For the active ingredient in t Release quality over time t 1 represents the duration of the first release curve. M 总 The total added mass of the active ingredients in each of the aforementioned component design schemes. α For correction factor, k To quickly release the constant, t Release time; The dissolution process of the active ingredient inside the sustained-release agent is simulated to obtain a second release curve of the active ingredient over time. The simulation process includes: obtaining the effective diffusion coefficient based on the first variable and the second variable, using the following formula: De=AB*ln(X1)+C*X2, where De is the effective diffusion coefficient, A, B, and C are constants, X1 represents the second variable, X2 represents the total added mass of the active ingredient in each component design scheme, and X2 is obtained based on the first variable and the volume of the sustained-release agent; Based on Fick's law and the aforementioned effective diffusion coefficient, the second release curve was simulated and solved using the following two equations simultaneously: , In the formula, a It is half the side length of the cube-shaped sustained-release agent; x It is half the side length of the cube-shaped sustained-release agent that has not yet dissolved inside the sustained-release agent; A Let this be the first variable; M 2. To simulate the dissolution process of the active ingredient inside the sustained-release agent, t The cumulative mass of active ingredient released over time; De is the effective diffusion coefficient; t 1 represents the duration of the first release curve; V To simulate the solution volume in the scenario; C S This represents the maximum solubility of the active ingredient in the simulated scenario solution. The second release curve and the first release curve are connected to form the mass-time release curve; Based on the matching degree between the expected stable concentration in the application scenario and the mass-time release curve, a matching preferred component design scheme is determined.

2. The method for designing sustained-release agent components as described in claim 1, characterized in that, The active ingredient is persulfate.

3. The method for designing sustained-release agent components as described in claim 1, characterized in that, A is 1.36 × 10 -6 B is 1.27 × 10 -5 C is 2.45 × 10 -6 .

4. The method for designing sustained-release agent components as described in claim 1, characterized in that, In the process of simulating and solving the second release curve, the mass of the active ingredient in the second release curve is simulated in the following manner: In the formula, a It is half the side length of the cube-shaped sustained-release agent; x It is half the side length of the cube-shaped sustained-release agent that has not yet dissolved inside the sustained-release agent; M 2 is to simulate the mass of the active ingredient during the dissolution process of the active ingredient inside the sustained-release agent; V To simulate the solution volume in the scenario; C S This represents the maximum solubility of the active ingredient in the simulated scenario solution. C a The solubility of the active ingredient at the end of the first release curve; De is the effective diffusion coefficient; C represents the concentration of the active ingredient in the solution in the simulated scenario.

5. A method for preparing a sustained-release agent, characterized in that, Implementing the preferred component design scheme obtained by the sustained-release agent component design method according to any one of claims 1 to 4 includes: The volume of the sustained-release agent is determined according to the preferred component design scheme, and the mass of the active ingredient in the sustained-release agent is determined according to the volume of the sustained-release agent and the mass of the active ingredient contained in the unit volume. The wax-to-sand ratio of the paraffin mass to the quartz sand mass is determined according to the preferred component design scheme. Prepare the sustained-release agent.

6. The method for preparing a sustained-release agent as described in claim 5, characterized in that, The active ingredient is sodium persulfate, and the process for preparing the sustained-release agent includes: (I) First, add paraffin wax to anhydrous ethanol, heat and melt it, then add sodium persulfate, mesoporous manganese oxide, quartz sand, Span-80 and polyethylene glycol according to the ratio, mix and stir evenly at 65°C to obtain molten material; the mesoporous manganese oxide is prepared by hard template coupled nano-etching method; (II) Quickly pour the molten material obtained in step (I) into the mold and cool it at room temperature to obtain the final product.

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