Nano calcium carbonate preparation method, device and equipment based on dynamic mathematical model

Abstract

The invention provides a nano calcium carbonate preparation method, device and equipment based on a dynamic mathematical model, and relates to the technical field of nano calcium carbonate preparation. The tail gas is subjected to compression treatment, pretreatment and atomization fusion treatment, and a liquid drop gas mixing system is obtained; inputting the current process parameters of the droplet-gas mixing system into a pre-established dynamic mathematical model for parameter coupling association, and outputting a state equation; state prediction and optimization are carried out based on the state equation, and candidate process parameters are obtained; and carrying out atomization fusion treatment through the candidate process parameters, and adjusting the state equation in real time until target nano calcium carbonate is generated. In the mode, the actual working condition change is accurately reflected, and the process parameters are updated in real time through the actual working condition change, so that the particle size distribution of the nano calcium carbonate product is more uniform, and the conversion rate fluctuation is further reduced.

Description

Technical Field

[0001] This invention relates to the field of nano-calcium carbonate preparation technology, and in particular to a method, apparatus and equipment for preparing nano-calcium carbonate based on a dynamic mathematical model. Background Technology

[0002] Nano-calcium carbonate refers to calcium carbonate products with a particle size ranging from 0 to 100 nm. Nano-calcium carbonate has advantages such as fine particles, large specific surface area, high surface activation rate, and high whiteness, and is one of the nanomaterials that can be produced and applied on a large scale industrially at present.

[0003] In the preparation of nano-calcium carbonate, the relevant technologies often rely solely on experience to set process parameters, which makes it difficult to accurately control the gas-liquid contact area and mass transfer efficiency during the reaction. This results in uneven particle size distribution and large fluctuations in conversion rate of the generated nano-calcium carbonate product. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method, apparatus and equipment for preparing nano-calcium carbonate based on a dynamic mathematical model, so as to accurately reflect the changes in actual working conditions, update the process parameters in real time through changes in actual working conditions, so as to make the particle size distribution of nano-calcium carbonate products more uniform, thereby reducing the fluctuation of conversion rate.

[0005] In a first aspect, embodiments of the present invention provide a method for preparing nano-calcium carbonate based on a dynamic mathematical model. The method includes: obtaining exhaust gas emitted from a combustion power plant; compressing, pretreating, and atomizing the exhaust gas to obtain a droplet-gas mixture system; inputting the current process parameters of the droplet-gas mixture system into a pre-established dynamic mathematical model for parameter coupling and correlation, and outputting a state equation; performing state prediction and optimization based on the state equation to obtain candidate process parameters; performing atomization and fusion processing using the candidate process parameters and adjusting the state equation in real time until the target nano-calcium carbonate is generated.

[0006] In a preferred embodiment of the present invention, the above-described process of compressing, pretreating, and atomizing the exhaust gas to obtain a droplet gas mixture system includes: compressing and collecting the exhaust gas into a carbon dioxide tank using an air compressor; connecting the outlet pipe of the carbon dioxide tank to a water washing bottle to remove sulfur dioxide and dust from the exhaust gas; connecting the outlet pipe of the water washing bottle to a carbon dioxide pressure swing adsorber to concentrate the carbon dioxide gas in the exhaust gas; connecting the outlet pipe of the carbon dioxide pressure swing adsorber to an air compressor to compress the carbon dioxide gas; connecting the outlet pipe of the air compressor to a pressure stabilizing tank, and connecting the outlet pipe of the pressure stabilizing tank to the bottom of a spray reaction tank to deliver carbon dioxide gas; the top of the spray reaction tank is provided with multiple spray heads, a pressure reducing valve, and a liquid inlet pipe; atomizing the Ca(OH) solution obtained by filtration through the spray heads to obtain droplets; and mixing the droplets with the carbon dioxide gas delivered from the outlet pipe of the pressure stabilizing tank to obtain the droplet gas mixture system.

[0007] In a preferred embodiment of the present invention, the above-mentioned inputting the current process parameters of the droplet-gas mixing system into a pre-established dynamic mathematical model for parameter coupling and correlation, and outputting a state equation, includes: inputting the current process parameters of the droplet-gas mixing system into a pre-established dynamic mathematical model to determine the correspondence between the current process parameters and product parameters; performing parameter coupling and correlation based on the correspondence, and outputting a state equation.

[0008] In a preferred embodiment of the present invention, the above-mentioned product parameters include: average droplet diameter, average particle size of CaCO3 product, and final product particle size. Determining the correspondence between the current process parameters and product parameters includes:

[0009] The relationship between the current process parameters and the average droplet diameter is determined based on the following formula: Where d represents the average droplet diameter, σ represents the liquid surface tension, and ρ g α1 represents the gas density, U represents the characteristic relative velocity between the gas and liquid phases, α1 represents the scaling coefficient, and β1 represents the scaling exponent.

[0010] The relationship between the current process parameters and the average particle size of the CaCO3 product is determined based on the following formula: Where p represents the average particle size of the CaCO3 product; k r A represents the reaction rate constant. contact V represents the gas-liquid contact area, and C represents the reactor volume. CO and C eq These represent the initial and equilibrium concentrations of carbon dioxide gas in the reaction, respectively. The relationship between the current process parameters and the final product particle size is determined based on the following formula: Where p represents the final product particle size, d represents the initial reactant droplet size, and Q... g Q represents the flow rate of carbon dioxide gas.l The flow rate of Ca(OH)2 liquid is represented by N, the stirring rate by p0 (where p0 represents the baseline or initial value of the target particle size), and d. * This indicates the droplet size under preset operating conditions. N represents the gas-liquid flow ratio under preset operating conditions. * α1 represents the stirring rate under preset operating conditions, α2 represents the sensitivity of the final product particle size to changes in the initial reactant droplet size, α3 represents the sensitivity of the final product particle size to changes in the gas-liquid flow ratio, and α4 represents the sensitivity of the final product particle size to changes in the stirring rate.

[0011] In a preferred embodiment of the present invention, the above-mentioned parameter coupling association based on the correspondence relationship to output the state equation includes: obtaining the state vector and the input vector by performing parameter coupling association based on the correspondence relationship of the following formula: z(t) represents the state vector, d(t) represents the droplet size, p(t) represents the product particle size, u(t) represents the input vector, and Q... g (t) represents the carbon dioxide gas flow rate, Q l (t) represents the liquid flow rate of Ca(OH)2, U spray (t) represents the adjustable parameters of the spray device, and N(t) represents the stirring rate; the state equation is obtained based on the state vector and input vector using the following formula: x(k+1)=A·x(k)+B·Δu(k); where, Δu(k)=u(k)-u ref , representing the adjustment amount relative to the reference operating condition, u ref Represents the steady-state condition; A represents matrix A, B represents matrix B, and matrix A ∈ R. 2×2 It is used to describe the dynamic coupling relationship between state variables; matrix B∈R 2×4 This indicates the regulatory effect of the input on the state variable.

[0012] In a preferred embodiment of the present invention, state prediction and optimization based on the state equation are used to obtain candidate process parameters, including: state prediction within the next H sampling steps based on the state equation using the following formula: x(k+j+1)=A·x(k+j)+B·Δu(k+j), j=0,1,…,H; where j represents the number of sampling steps, and H represents the total sampling step length; Δu(k)=u(k)-u ref , representing the adjustment amount relative to the reference operating condition, u ref The steady-state condition is represented by A and B, which represent matrices A and B, respectively. y(k+j)=C·x(k+j) represents the predicted output. Based on the predicted output, state optimization is performed to obtain candidate process parameters.

[0013] In a preferred embodiment of the present invention, the above-mentioned state optimization based on the predicted output to obtain candidate process parameters includes: constructing a target convergence function based on the predicted output using the following formula: Where J represents the target approach function, H represents the total sampling step size, y(k+j) represents the predicted output, and P target Let λ represent the target value, and let λ represent the weighting factor used to balance the state deviation and the change amplitude of the control quantity; Δu(k+j) represents the control quantity; under the input constraints, solve for the optimal control increment; the constraint condition is: u_min≤u≤u_max; based on the optimal control increment and the current process parameters, obtain the candidate process parameters.

[0014] Secondly, embodiments of the present invention also provide a nano-calcium carbonate preparation device based on a dynamic mathematical model. The device includes: a tail gas acquisition module for acquiring tail gas emitted from a combustion power plant; a tail gas treatment module for compressing, pretreating, and atomizing the tail gas to obtain a droplet-gas mixture system; a state equation output module for inputting the current process parameters of the droplet-gas mixture system into a pre-established dynamic mathematical model for parameter coupling and correlation, and outputting a state equation; a prediction and optimization module for performing state prediction and optimization based on the state equation to obtain candidate process parameters; and a target nano-calcium carbonate generation module for performing atomization and fusion treatment using the candidate process parameters and adjusting the state equation in real time until the target nano-calcium carbonate is generated.

[0015] Thirdly, embodiments of the present invention also provide an electronic device, including a processor and a memory, wherein the memory stores computer-executable instructions that can be executed by the processor, and the processor executes the computer-executable instructions to implement the above-described method for preparing nano-calcium carbonate based on a dynamic mathematical model.

[0016] Fourthly, embodiments of the present invention also provide a computer-readable storage medium storing computer-executable instructions. When the computer-executable instructions are invoked and executed by a processor, the computer-executable instructions cause the processor to implement the above-described method for preparing nano-calcium carbonate based on a dynamic mathematical model in the first aspect.

[0017] The embodiments of the present invention bring the following beneficial effects:

[0018] This invention provides a method, apparatus, and equipment for preparing nano-calcium carbonate based on a dynamic mathematical model. The method involves acquiring exhaust gas from a combustion power plant, compressing, pretreating, and atomizing the exhaust gas to obtain a droplet-gas mixture system. The current process parameters of this droplet-gas mixture system are input into a pre-established dynamic mathematical model for parameter coupling and correlation, outputting a state equation. Based on the state equation, state prediction and optimization are performed to obtain candidate process parameters. These candidate process parameters are then used for atomization and fusion processing, with the state equation adjusted in real time until the target nano-calcium carbonate is generated. This method accurately reflects changes in actual operating conditions, updating process parameters in real time based on these changes, resulting in a more uniform particle size distribution in the nano-calcium carbonate product and thus reducing conversion rate fluctuations.

[0019] Other features and advantages of this disclosure will be set forth in the following description, or some features and advantages may be inferred from the description or determined without doubt, or may be learned by practicing the techniques described above.

[0020] To make the above-mentioned objects, features and advantages of this disclosure more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0021] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0022] Figure 1 A flowchart illustrating a method for preparing nano-calcium carbonate based on a dynamic mathematical model, provided in an embodiment of the present invention;

[0023] Figure 2 A flowchart illustrating another method for preparing nano-calcium carbonate based on a dynamic mathematical model, provided in an embodiment of the present invention;

[0024] Figure 3 A process apparatus flow chart provided for an embodiment of the present invention;

[0025] Figure 4 A flowchart illustrating another method for preparing nano-calcium carbonate based on a dynamic mathematical model, provided as an embodiment of the present invention;

[0026] Figure 5 A schematic diagram of a nano-calcium carbonate preparation device based on a dynamic mathematical model provided in an embodiment of the present invention;

[0027] Figure 6This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] Nano-calcium carbonate refers to calcium carbonate products with a particle size ranging from 0 to 100 nm. Nano-calcium carbonate has advantages such as fine particles, large specific surface area, high surface activation rate, and high whiteness, and is one of the nanomaterials that can be produced and applied on a large scale industrially at present.

[0030] In the preparation of nano-calcium carbonate, the relevant technologies often rely solely on experience to set process parameters, which makes it difficult to accurately control the gas-liquid contact area and mass transfer efficiency during the reaction. This results in uneven particle size distribution and large fluctuations in conversion rate of the generated nano-calcium carbonate product.

[0031] Specifically, the main production methods for nano-calcium carbonate currently include mechanical methods, metathesis methods, precipitation methods, carbonation methods, and microemulsion methods. Among these, carbonation is the mainstream process, which is further divided into three main process routes: intermittent bubbling carbonation, multi-stage spray carbonation, and high-gravity carbonation.

[0032] Intermittent bubbling carbonation is a common method both domestically and internationally. 5-8°Be' lime slurry is cooled to below 25°C, pumped into a carbonation tower, and kept at a certain liquid level. Kiln gas is introduced from the bottom of the tower to bubble and carry out the carbonation reaction. By controlling process conditions such as reaction temperature, concentration, gas-liquid ratio, and additives, nano-calcium carbonate can be prepared intermittently.

[0033] The multi-stage spray carbonization method involves spraying Ca(OH)2 emulsion downwards from the top of a tower through a pressure nozzle, while simultaneously introducing CO2 gas upwards from the bottom of the tower. This ensures that the sprayed Ca(OH)2 and CO2 come into full contact and react. The resulting Ca(OH)2 slurry is then sprayed into another carbonization tower from the top, where CO2 gas is also introduced from the bottom, again ensuring that the sprayed Ca(OH)2 and CO2 come into full contact and react. This process is repeated in a cycle.

[0034] The hypergravity carbonation method refers to the process where a Ca(OH)₂ emulsion passes through a high-speed rotating packed bed in a hypergravity reactor, achieving centrifugal velocities 2-3 orders of magnitude greater than gravitational acceleration. Under these conditions, the Ca(OH)₂ emulsion is broken down into extremely small droplets, filaments, and very thin liquid films by the packing material, generating a large and rapid phase interface. This results in interphase mass transfer volume and rate that are 1-3 orders of magnitude greater than in a column reactor, thus significantly enhancing the carbonation reaction rate. Nano-sized calcium carbonate can be produced under this hypergravity environment.

[0035] Currently, the three methods for preparing nano-calcium carbonate mentioned above still have shortcomings. For example, the product obtained by intermittent bubbling carbonation has uneven particle distribution; although the products obtained by multi-stage spray carbonation and centrifugal carbonation are more uniform than those obtained by intermittent bubbling carbonation, the equipment has a large footprint and high energy consumption. Furthermore, the above methods have not yet used relevant calculations to obtain various operating conditions so that the equipment can operate under optimal conditions.

[0036] Based on this, the present invention provides a method, apparatus, and equipment for preparing nano-calcium carbonate based on a dynamic mathematical model. This method involves acquiring exhaust gas from a combustion power plant, compressing, pretreating, and atomizing the exhaust gas to obtain a droplet-gas mixture system. The current process parameters of this droplet-gas mixture system are input into a pre-established dynamic mathematical model for parameter coupling and correlation, outputting a state equation. Based on the state equation, state prediction and optimization are performed to obtain candidate process parameters. These candidate process parameters are then used for atomization and fusion processing, with the state equation adjusted in real time until the target nano-calcium carbonate is generated. This approach accurately reflects changes in actual operating conditions, updating process parameters in real time based on these changes, resulting in a more uniform particle size distribution in the nano-calcium carbonate product and thus reducing conversion rate fluctuations.

[0037] To facilitate understanding of this embodiment, a detailed description of a method for preparing nano-calcium carbonate based on a dynamic mathematical model, as disclosed in this embodiment of the invention, will be provided first.

[0038] Example 1

[0039] This invention provides a method for preparing nano-calcium carbonate based on a dynamic mathematical model. Figure 1 This is a flowchart illustrating a method for preparing nano-calcium carbonate based on a dynamic mathematical model, provided as an embodiment of the present invention. Figure 1 As shown, the method for preparing nano-calcium carbonate based on a dynamic mathematical model may include the following steps:

[0040] Step S101: Obtain the exhaust gas emitted by the combustion power plant.

[0041] The exhaust gas may contain carbon dioxide, sulfur dioxide, dust, etc.

[0042] Step S102 involves compressing, pretreating, and atomizing the exhaust gas to obtain a droplet gas mixture system.

[0043] Among these methods, the exhaust gas can be collected by compression; pretreatment can be gas washing and pressure swing adsorption. Gas washing can remove impurities from carbon dioxide gas, and pressure swing adsorption can enrich and release carbon dioxide concentration; atomization fusion treatment can be performed by atomizing Ca(OH) solution to obtain droplets, and then fusing the droplets with carbon dioxide gas to obtain a droplet gas mixture system.

[0044] Step S103: Input the current process parameters of the droplet-gas mixing system into the pre-established dynamic mathematical model for parameter coupling and correlation, and output the state equation.

[0045] This allows for real-time monitoring of current process parameters, enabling adjustments to the state equation and timely updates to candidate process parameters.

[0046] Step S104: Based on the state equation, perform state prediction and optimization to obtain candidate process parameters.

[0047] Among them, the state equation can be adjusted in real time to predict and optimize the state, reduce the fluctuation of conversion rate, and improve the efficiency of generating target nano-calcium carbonate.

[0048] Step S105 involves performing atomization fusion processing using candidate process parameters and adjusting the equation of state in real time until the target nano-calcium carbonate is generated.

[0049] By continuously adjusting the equation of state and then continuously optimizing the candidate process parameters, the candidate process parameters can be made closer to the target process parameters, thereby generating the target nano-calcium carbonate.

[0050] The present invention provides a method for preparing nano-calcium carbonate based on a dynamic mathematical model. This method involves acquiring exhaust gas from a combustion power plant, compressing, pretreating, and atomizing the exhaust gas to obtain a droplet-gas mixture system. The current process parameters of this system are input into a pre-established dynamic mathematical model for parameter coupling and correlation, outputting a state equation. Based on this state equation, state prediction and optimization are performed to obtain candidate process parameters. These candidate parameters are then used for atomization and fusion processing, with the state equation adjusted in real time until the target nano-calcium carbonate is generated. This method accurately reflects changes in actual operating conditions, updating process parameters in real time to ensure a more uniform particle size distribution in the nano-calcium carbonate product, thereby reducing conversion rate fluctuations.

[0051] Example 2

[0052] This invention also provides another method for preparing nano-calcium carbonate based on a dynamic mathematical model; this method is implemented based on the method in the above embodiments; the method focuses on describing the specific implementation of compressing, pretreating and atomizing the exhaust gas to obtain a droplet gas mixture system.

[0053] Figure 2 A flowchart illustrating another method for preparing nano-calcium carbonate based on a dynamic mathematical model, provided in this embodiment of the invention. Figure 3 This is a process apparatus flow chart provided for an embodiment of the present invention. Figure 2 As shown, the process of compressing, pretreating, and atomizing exhaust gas to obtain a droplet-gas mixture system may include the following steps:

[0054] Step S201: The exhaust gas is compressed and collected into a carbon dioxide tank using an air compressor.

[0055] like Figure 3 As shown, the exhaust gas discharged from the flue gas collection pipeline of the power plant is compressed and collected into a carbon dioxide tank (CO2 tank) by an air compressor.

[0056] In step S202, the outlet pipe of the carbon dioxide tank is connected to a water washing bottle to remove sulfur dioxide and dust from the exhaust gas.

[0057] like Figure 3 As shown, the outlet pipe of the carbon dioxide tank is connected to a water washing bottle to remove sulfur dioxide and dust from the exhaust gas.

[0058] In step S203, the outlet pipe of the water washing bottle is connected to a carbon dioxide pressure swing adsorber to concentrate the carbon dioxide gas in the tail gas.

[0059] like Figure 3 As shown, the outlet pipe of the water washing bottle is connected to a carbon dioxide pressure swing adsorber to concentrate the carbon dioxide gas in the exhaust gas.

[0060] In step S204, the outlet pipe of the carbon dioxide pressure swing adsorber is connected to an air compressor to compress the carbon dioxide gas.

[0061] like Figure 3 As shown, the outlet pipe of the carbon dioxide pressure swing adsorber is connected to an air compressor to compress carbon dioxide gas.

[0062] In step S205, the air compressor's outlet pipe is connected to the pressure stabilizing tank, and the pressure stabilizing tank's outlet pipe is connected to the bottom of the spray reaction tank to deliver carbon dioxide gas.

[0063] The top of the spray reaction tank is equipped with multiple spray heads, a pressure reducing valve, and an inlet pipe.

[0064] like Figure 3As shown, the air compressor's outlet pipe is connected to a pressure stabilizing tank, and the pressure stabilizing tank's outlet pipe is connected to the bottom of the spray reaction tank to deliver carbon dioxide gas.

[0065] Step S206: The Ca(OH) solution obtained by filtration is atomized through a spray head to obtain droplets.

[0066] like Figure 3 As shown, the Ca(OH) solution obtained by filtration is atomized through a spray head to obtain droplets.

[0067] In this process, Ca(OH)2 is first thoroughly stirred and dissolved in an aging tank to form a saturated solution. The saturated solution is then pumped into a Ca(OH)2 solution tank and then injected into the spray reaction tank through an inlet pipe using a delivery pump.

[0068] Step S207: The droplets and carbon dioxide gas supplied from the outlet pipe of the pressure stabilizing tank are mixed to obtain a droplet gas mixture system.

[0069] like Figure 3 As shown, droplets and carbon dioxide gas supplied from the outlet pipe of the pressure stabilizing tank are mixed to obtain a droplet-gas mixture system.

[0070] The process involves installing a discharge pipe at the bottom of the spray reaction tank to store the resulting suspension in a storage tank. This suspension is then placed into a filtration device to separate the nano-calcium carbonate and Ca(OH)₂ solution into solid and liquid components. The Ca(OH)₂ solution is refluxed back to a Ca(OH)₂ solution tank, while the nano-calcium carbonate is dried in an oven.

[0071] In practical applications, coal-fired power plants emit exhaust gas (mainly CO2). This exhaust gas is compressed and collected into several CO2 cylinders using an air compressor. The outlet pipes of the CO2 cylinders are connected to a water washing bottle to remove small amounts of SO2, dust, and other impurities from the gas. The outlet pipes of the water washing bottle are connected to a CO2 pressure swing adsorber (PSA), with the pressure set between 0.2-1 MPa. At this pressure, CO2 is adsorbed into the dehydrated silica gel, activated carbon, and zeolite mixture in the PSA. Afterward, the pressure is reduced to about 5-10 kPa, and the adsorbed CO2 is released. This process can concentrate 10%-20% CO2 to about 40%.

[0072] The pressure swing adsorber (PSA) outlet pipe is connected to an air compressor to compress the CO2 gas. The air compressor outlet pipe is connected to a pressure stabilizing tank, and the pressure stabilizing tank outlet pipe is connected to the inlet pipe at the bottom of the spray reactor. The inlet pipe has a diameter of 10-20 mm. Plastic pipes are installed at 2 cm intervals. Four pores are arranged on the same transverse cross section.

[0073] The top of the spray reaction tank is equipped with several spray nozzles, a pressure reducing valve (which releases pressure when it reaches 0.6 MPa), and an inlet pipe. Ca(OH)₂ is first thoroughly dissolved in an aging tank by stirring to form a saturated solution. This saturated solution is then pumped into a Ca(OH)₂ solution tank and subsequently injected into the spray reaction tank via the inlet pipe using a delivery pump. Through the spray reaction, the Ca(OH)₂ solution is atomized into fine droplets within the reactor, the particle size of which can be controlled by the nozzle parameters. The resulting fine droplets are thoroughly mixed with CO gas introduced from the bottom inlet pipe, achieving a large-area gas-liquid interface contact and promoting rapid alkalization to generate CaCO₃. In this spray reaction tank, the gas and liquid phases are continuously mixed, broken up, and recombined under the action of a stirrer (or through flow field design), resulting in a significant reaction linkage effect. The reaction mainly occurs at the interface between the atomized droplets and the gas, where the generated primary CaCO₃ crystals gradually grow into finished particles.

[0074] A discharge pipe is installed at the bottom of the spray reaction tank to store the suspension generated by the reaction in a storage tank. The suspension is then placed into a vacuum filter to separate the nano-calcium carbonate and Ca(OH)2 solution generated by the reaction into solid and liquid components.

[0075] The suspension after the reaction is vacuum filtered using a vacuum pump to accelerate the separation of nano-calcium carbonate from the liquid, reduce residual moisture, and improve drying efficiency. The Ca(OH)₂ solution is refluxed back to the Ca(OH)₂ solution tank, and the nano-calcium carbonate is placed in an oven at 60°C until it is completely dried.

[0076] Example 3

[0077] This invention also provides another method for preparing nano-calcium carbonate based on a dynamic mathematical model; this method is implemented based on the method described in the above embodiments.

[0078] Figure 4 A flowchart illustrating another method for preparing nano-calcium carbonate based on a dynamic mathematical model, as provided in this embodiment of the invention, is shown below. Figure 4 As shown, the method for preparing nano-calcium carbonate based on a dynamic mathematical model may include the following steps:

[0079] Step S301: Obtain the exhaust gas emitted by the combustion power plant.

[0080] Step S302 involves compressing, pretreating, and atomizing the exhaust gas to obtain a droplet gas mixture system.

[0081] Step S302 has been specifically described in Example 2 and will not be repeated here.

[0082] Step S303: Input the current process parameters of the droplet-gas mixing system into the pre-established dynamic mathematical model to determine the correspondence between the current process parameters and the product parameters.

[0083] Specifically, the product parameters include: average droplet diameter, average particle size of CaCO3 product, and final product particle size. Determining the correspondence between the current process parameters and the product parameters includes: determining the correspondence between the current process parameters and the average droplet diameter based on the following formula: Where d represents the average droplet diameter, σ represents the liquid surface tension, and ρ g Let α represent the gas density, U represent the characteristic relative velocity between the gas and liquid phases, α1 represent the scaling coefficient, and β1 represent the scaling exponent.

[0084] The characteristic relative velocity between the gas and liquid phases can be correlated with the CO2 flow rate and the stirring rate.

[0085] The scaling coefficient primarily determines the absolute size benchmark of the atomized droplet, with a value range of 0.5-1.0, and is an empirical parameter obtained through experimental fitting.

[0086] The scaling exponent characterizes the sensitivity of droplet size to the relative balance between surface tension (stabilizing effect) and airflow impact force (breaking effect), and depends on the power-law dependence of droplet size on factors such as relative velocity. The value ranges from 5 to 30, and is an empirical parameter obtained through experimental fitting.

[0087] It should be noted that in the spray reaction stage, the liquid is atomized into fine droplets by the spray device and thoroughly mixed with CO2 gas. The droplet size directly affects the reaction contact area and the reaction rate; therefore, a droplet breakup model can be established.

[0088] The relationship between the current process parameters and the average particle size of the CaCO3 product is determined based on the following formula: Where p represents the average particle size of the CaCO3 product; k r A represents the reaction rate constant. contact V represents the gas-liquid contact area, and C represents the reactor volume. CO and C eq These represent the initial and equilibrium concentrations of carbon dioxide gas in the gas, respectively.

[0089] It should be noted that the droplet size d directly affects the gas-liquid contact area, and the gas-liquid contact area A contact The reaction rate between the gas-liquid contact area A and the formation of nano-calcium carbonate, which is proportional to 1 / d², can be expressed by a first-order kinetic equation, i.e.

[0090] The relationship between the current process parameters and the final product particle size is determined based on the following formula: Where p represents the final product particle size, d represents the initial reactant droplet size, and Q...g Q represents the flow rate of carbon dioxide gas. l The flow rate of Ca(OH)2 liquid is represented by N, the stirring rate by p0, and the reference or initial value of the target particle size by d. * This indicates the droplet size under preset operating conditions. N represents the gas-liquid flow ratio under preset operating conditions. * α1 represents the stirring rate under preset operating conditions, α2 represents the sensitivity of the final product particle size to changes in the initial reactant droplet size, α3 represents the sensitivity of the final product particle size to changes in the gas-liquid flow ratio, and α4 represents the sensitivity of the final product particle size to changes in the stirring rate.

[0091] The preset operating condition is the standard operating condition, that is, the operating condition under normal atmospheric pressure.

[0092] The value of α2 ranges from +0.5 to +2.0 and can be obtained through experimental fitting.

[0093] The value of α3 ranges from -10 to -50 nm and can be obtained through experimental fitting; the value of α4 ranges from -0.01 to -0.04 nm / RPM and can be obtained through experimental fitting.

[0094] Step S304: Perform parameter coupling association based on the correspondence relationship and output the state equation.

[0095] Specifically, based on the correspondence, parameter coupling and association are performed to output state equations, including:

[0096] The state vector and input vector are obtained by coupling parameters based on the correspondence of the following formulas: z(t) represents the state vector, d(t) represents the droplet size, p(t) represents the product particle size, u(t) represents the input vector, and Q... g (t) represents the carbon dioxide gas flow rate, Q l (t) represents the liquid flow rate of Ca(OH)2, U spray (t) represents the adjustable parameters of the spray device, and N(t) represents the stirring rate.

[0097] The state vector is a core set of variables used to describe the dynamic behavior of the system, including the droplet size d(t) and the product particle size p(t).

[0098] Among them, the adjustable parameters of the spray device, such as the spray pressure or the nozzle orifice diameter, directly affect the droplet size.

[0099] The input vector can contain adjustable process parameters that directly affect droplet size and reaction rate.

[0100] The state equation is obtained based on the state vector and input vector using the following formula: x(k+1)=A·x(k)+B·Δu(k); where, Δu(k)=u(k)-u ref , representing the adjustment amount relative to the reference operating condition, u ref Represents the steady-state condition; A represents matrix A, B represents matrix B, and matrix A ∈ R. 2×2 It is used to describe the dynamic coupling relationship between state variables; matrix B∈R 2×4 This indicates the regulatory effect of the input on the state variable.

[0101] The state equation is based on the linearization assumption, discretizing the continuous-time dynamic model (sampling period T). s )get.

[0102] In matrix A, A11 represents the natural decay coefficient of droplet size d(t) over time (e.g., evaporation); A21 represents the transfer coefficient (hysteresis effect) of droplet size d(t) to product particle size p(t); A12 represents the influence coefficient of droplet size d(k) on product particle size p(k+1) at the next time step; and A22 represents the correlation coefficient of current product particle size p(k) to product particle size p(k+1) at the next time step.

[0103] Among them, A11 to A22 take values ​​between 0 and 1.

[0104] Matrix B quantifies the impact of adjusting CO2 flow rate, Ca(OH)2 flow rate, spray parameters, and stirring speed on the size of the generated droplets and particles in the next time step. Matrix B is a 2×4 matrix, where each column corresponds to the influence of a control input variable on the state variable, as detailed below:

[0105] B11, B12: Gas flow rate ΔQ g It affects d(k+1) and p(k+1).

[0106] B21, B22: Liquid flow rate ΔQ l It affects d(k+1) and p(k+1).

[0107] B31, B32: Spray parameter ΔU spray It affects d(k+1) and p(k+1).

[0108] B41, B42: The stirring rate N affects d(k+1) and p(k+1).

[0109] The output equation is: y(k)=C·x(k); where y(k) represents the product particle size p(k), and the corresponding matrix C=

[01] . The matrix C determines the transformation of the system state x(k) into the measurement output y(k). Essentially, it selects which states or combinations of states to observe or control.

[0110] Since the output y(k) is defined as the product granularity value (k) and x(k) is [d(k), p(k)], T Matrix C is simply the second element of the state vector. Therefore, C =

[01] . It depends on the selected value (k) for controlling / monitoring particle size.

[0111] Step S305: Based on the state equation, perform state prediction and optimization to obtain candidate process parameters.

[0112] Based on process parameters such as gas-liquid flow rate, spray state, and stirring rate, a model predictive control (MPC) framework is adopted to achieve the optimal product particle size. The current state x(k) = [d(k), p(k)] can be obtained using online sensors. T The system uses various input parameters (gas-liquid flow rate, spray state, stirring rate, etc.) and multivariate coupling relationships (gas-liquid flow rate, spray state, stirring rate, etc.) to achieve dynamic process control and predict the state within the next H sampling steps.

[0113] Specifically, the state prediction within the next H sampling steps is performed based on the state equation using the following formula: x(k+j+1)=A·x(k+j)+B·Δu(k+j), j=0,1,…,H; where j represents the number of sampling steps and H represents the total sampling step length; Δu(k)=u(k)-u ref , representing the adjustment amount relative to the reference operating condition, u ref The steady-state condition is represented by A and B, which represent matrices A and B, respectively. y(k+j)=C·x(k+j) represents the predicted output. Based on the predicted output, state optimization is performed to obtain candidate process parameters.

[0114] Among them, the target product particle size P target For reference, the difference between the actual output particle size and the target product particle size is used to construct a function J, which makes the system output (product particle size) as close as possible to and maintain the target value P in the future. target Avoid excessively drastic or frequent changes in the control inputs (flow rate, spray parameters, stirring rate, etc.).

[0115] Specifically, state optimization based on the predicted output to obtain candidate process parameters can include constructing a target convergence function based on the predicted output using the following formula: Where J represents the target approach function, H represents the total sampling step size, y(k+j) represents the predicted output, and P target Let λ represent the target value, and let λ represent the weighting factor used to balance the state deviation and the change amplitude of the control quantity; Δu(k+j) represents the control quantity; under the input constraints, solve for the optimal control increment; the constraint condition is: u_min≤u≤u_max; based on the optimal control increment and the current process parameters, obtain the candidate process parameters.

[0116] Step S306: Atomization fusion processing is performed using candidate process parameters, and the equation of state is adjusted in real time until the target nano-calcium carbonate is generated.

[0117] In this process, the candidate process parameters are optimized in real time by adjusting the equation of state in real time. The optimized candidate process parameters are then atomized and fused and monitored in real time to adjust the equation of state in real time, thus forming a closed-loop control. This reduces the fluctuation of conversion rate and makes the particle size distribution of nano-calcium carbonate products more uniform.

[0118] For ease of understanding, the following are several simulated operating conditions:

[0119] Operating Condition 1: Baseline (Conventional Control): CO gas flow rate (Q) g Fixed at 25m 3 / hr, calcium hydroxide solution flow rate (Q) l Fixed at 2.0m 3 / hr, forming a fixed gas-liquid flow ratio (12.5). Spray pressure (P spray The pressure was set at a relatively low fixed value of 0.3 MPa, which resulted in a relatively large estimated initial droplet size (d0), approximately 150 μm. The reaction temperature (T...) rxn The temperature was also maintained at a constant 35°C, and no crystal form control agent was added under these conditions (H = none).

[0120] Operating Condition 2: MPC Control (Target 80nm): Demonstrates how the proposed system uses MPC to achieve a target average particle size of 80nm.

[0121] Operating Condition 3: MPC Control (Target 40nm): Displays the system's ability to produce finer particles by setting a 40nm target.

[0122] Operating Condition 4: MPC Control (Disturbance Response): Starting from Operating Condition 3 (target 40nm), a disturbance of a sudden drop in inlet CO concentration (e.g., -15%) is introduced. Demonstrate how MPC adjusts other parameters to maintain the target particle size.

[0123] Condition 5: MPC Control + Crystal Form Control Agent (Target 30nm): Simulates Condition 3 conditions, but adds crystal form control agent 'A' to achieve a smaller target particle size of 30nm. This utilizes the model's... The control agent effect captured by the fmorph(H) term.

[0124] Table 1 shows the simulation results for the above working conditions.

[0125] Table 1: Simulation Results

[0126]

[0127]

[0128] Notes to Table 1:

[0129] [1] Spray pressure is an example controllable parameter that affects the initial droplet size (d0). MPC may directly control the pressure or nozzle settings.

[0130] [2]d0 is estimated based on spray pressure / conditions; a smaller d0 is generally advantageous for obtaining a smaller final particle size p.

[0131] [3]σ p The standard deviation or similar metric represents the particle size distribution. A lower value indicates higher uniformity.

[0132] Interpretation of the above results:

[0133] 1. Baseline vs. MPC: Condition 1 (baseline) showed larger, more uneven particles and lower conversion rate than conditions (2 and 3) controlled by MPC, demonstrating the limitations of the fixed parameter method.

[0134] 2. MPC Target Achieved: Conditions 2 and 3 demonstrate that MPC successfully adjusted the input parameters (Q). g Q l P spray T rxn This improved the average particle size (p) to be close to the desired target (80 nm and 40 nm, respectively), while also improving the uniformity (σ). p And conversion rate (XCO2). Producing smaller particles (condition 3 vs condition 2) usually requires more stringent conditions (higher gas flow rate, higher spray pressure).

[0135] 3. Disturbance Suppression: Operating condition 4 demonstrates the robustness of the MPC. When the inlet CO concentration decreases (disturbance), the controller detects the deviation (possibly through intermediate measurements or predicted output drift) and increases Q. g and Q lCompensation was performed to restore the particle size (p) to the target of close to 40 nm, although the conversion efficiency decreased slightly temporarily.

[0136] 4. Effect of Crystal Form Control Agent: Condition 5 shows that the addition of the crystal form control agent (H = Type A) enables the system to achieve a smaller target particle size (30nm) and exhibits excellent uniformity (σ). p =6nm) and high conversion / yield, which is likely due to the influence of the MPC model. The nucleation / growth kinetics captured by the project are realized.

[0137] In this embodiment of the invention, sensor data is monitored in real time, and the state equation is updated in real time to accurately reflect changes in actual operating conditions. Then, the optimal control input is solved by MPC to achieve fine control of the gas-liquid ratio, spray parameters, and stirring rate. This closed-loop control not only enables the formation of an optimal gas-liquid interface in the reactor, significantly improving mass transfer and reaction rates, but also ensures that the product particle size and quality indicators remain stable within the predetermined target range.

[0138] Example 4

[0139] Corresponding to the above method embodiments, this invention provides a nano-calcium carbonate preparation device based on a dynamic mathematical model. Figure 5 A schematic diagram of a nano-calcium carbonate preparation device based on a dynamic mathematical model is provided in an embodiment of the present invention, as shown below. Figure 4 As shown, the nano-calcium carbonate preparation device based on a dynamic mathematical model may include:

[0140] The exhaust gas acquisition module 401 is used to acquire the exhaust gas emitted by the combustion power plant.

[0141] The exhaust gas treatment module 402 is used to compress, pretreat, and atomize the exhaust gas to obtain a liquid droplet gas mixture system.

[0142] The state equation output module 403 is used to input the current process parameters of the droplet-gas mixing system into a pre-established dynamic mathematical model for parameter coupling and correlation, and output the state equation.

[0143] The prediction and optimization module 404 is used to perform state prediction and optimization based on the state equation to obtain candidate process parameters.

[0144] The target nano-calcium carbonate generation module 405 is used to perform atomization fusion processing through candidate process parameters and adjust the equation of state in real time until the target nano-calcium carbonate is generated.

[0145] The nano-calcium carbonate preparation device based on a dynamic mathematical model provided in this invention can obtain exhaust gas from a combustion power plant, compress, pretreat, and atomize it to obtain a droplet-gas mixture system. The current process parameters of this system are input into a pre-established dynamic mathematical model for parameter coupling and correlation, outputting a state equation. Based on this equation, state prediction and optimization are performed to obtain candidate process parameters. These parameters are then used for atomization and fusion processing, with the state equation adjusted in real time until the target nano-calcium carbonate is generated. This method accurately reflects changes in actual operating conditions, updating process parameters in real time to ensure a more uniform particle size distribution in the nano-calcium carbonate product, thereby reducing conversion rate fluctuations.

[0146] In some embodiments, the exhaust gas treatment module is further configured to compress and collect the exhaust gas into a carbon dioxide tank via an air compressor; the outlet pipe of the carbon dioxide tank is connected to a water washing bottle to remove sulfur dioxide and dust from the exhaust gas; the outlet pipe of the water washing bottle is connected to a carbon dioxide pressure swing adsorber to concentrate the carbon dioxide gas in the exhaust gas; the outlet pipe of the carbon dioxide pressure swing adsorber is connected to an air compressor to compress the carbon dioxide gas; the outlet pipe of the air compressor is connected to a pressure stabilizing tank, and the outlet pipe of the pressure stabilizing tank is connected to the bottom of the spray reaction tank to deliver carbon dioxide gas; the top of the spray reaction tank is provided with multiple spray heads, a pressure reducing valve, and a liquid inlet pipe; the Ca(OH) solution obtained by filtration is atomized through the spray heads to obtain droplets; the droplets and the carbon dioxide gas delivered from the outlet pipe of the pressure stabilizing tank are mixed to obtain a droplet gas mixture system.

[0147] In some embodiments, the state equation output module is further configured to input the current process parameters of the droplet-gas mixing system into a pre-established dynamic mathematical model, determine the correspondence between the current process parameters and the product parameters, perform parameter coupling association based on the correspondence, and output the state equation.

[0148] In some embodiments, the product parameters include: average droplet diameter, average particle size of CaCO3 product, and final product particle size. The state equation output module is also used to determine the correspondence between the current process parameters and the average droplet diameter based on the following formula: Where d represents the average droplet diameter, σ represents the liquid surface tension, and ρ g Let represent gas density, U represent the characteristic relative velocity between the gas and liquid phases, α1 represent the scaling factor, and β1 represent the scaling exponent; the correspondence between the current process parameters and the average particle size of the CaCO3 product is determined based on the following formula: Where p represents the average particle size of the CaCO3 product; k r A represents the reaction rate constant. contact V represents the gas-liquid contact area, and C represents the reactor volume.CO and C eq These represent the initial and equilibrium concentrations of carbon dioxide gas in the reaction, respectively. The relationship between the current process parameters and the final product particle size is determined based on the following formula: Where p represents the final product particle size, d represents the initial reactant droplet size, and Q... g Q represents the flow rate of carbon dioxide gas. l The flow rate of Ca(OH)2 liquid is represented by N, the stirring rate by p0, and the reference or initial value of the target particle size by d. * This indicates the droplet size under preset operating conditions. N represents the gas-liquid flow ratio under preset operating conditions. * α1 represents the stirring rate under preset operating conditions, α2 represents the sensitivity of the final product particle size to changes in the initial reactant droplet size, α3 represents the sensitivity of the final product particle size to changes in the gas-liquid flow ratio, and α4 represents the sensitivity of the final product particle size to changes in the stirring rate.

[0149] In some embodiments, the state equation output module is further configured to perform parameter coupling association based on the following formula correspondence to obtain the state vector and the input vector: z(t) represents the state vector, d(t) represents the droplet size, p(t) represents the product particle size, u(t) represents the input vector, and Q... g (t) represents the carbon dioxide gas flow rate, Q l (t) represents the liquid flow rate of Ca(OH)2, U spray (t) represents the adjustable parameters of the spray device, and N(t) represents the stirring rate; the state equation is obtained based on the state vector and input vector using the following formula: x(k+1)=A·x(k)+B·Δu(k); where, Δu(k)=u(k)-u ref , representing the adjustment amount relative to the reference operating condition, u ref Represents the steady-state condition; A represents matrix A, B represents matrix B, and matrix A ∈ R. 2×2 It is used to describe the dynamic coupling relationship between state variables; matrix B∈R 2×4 This indicates the regulatory effect of the input on the state variable.

[0150] In some embodiments, the prediction and optimization module is further configured to predict the state within the next H sampling steps based on the state equation using the following formula: x(k+j+1)=A·x(k+j)+B·Δu(k+j), j=0,1,…,H; where j represents the number of sampling steps and H represents the total sampling step length; Δu(k)=u(k)-u ref , representing the adjustment amount relative to the reference operating condition, u refThe steady-state condition is represented by A and B, which represent matrices A and B, respectively. y(k+j)=C·x(k+j) represents the predicted output. Based on the predicted output, state optimization is performed to obtain candidate process parameters.

[0151] In some embodiments, the prediction and optimization module is further configured to construct a target convergence function based on the prediction output using the following formula: Where J represents the target approach function, H represents the total sampling step size, y(k+j) represents the predicted output, and P target Let λ represent the target value, and let λ represent the weighting factor used to balance the state deviation and the change amplitude of the control quantity; Δu(k+j) represents the control quantity; under the input constraints, solve for the optimal control increment; the constraint condition is: u_min≤u≤u_max; based on the optimal control increment and the current process parameters, obtain the candidate process parameters.

[0152] The device provided in this embodiment of the invention has the same implementation principle and technical effect as the aforementioned method embodiment. For the sake of brevity, any parts not mentioned in the device embodiment can be referred to the corresponding content in the aforementioned method embodiment.

[0153] Example 5

[0154] This invention also provides an electronic device for running the above-described method for preparing nano-calcium carbonate based on a dynamic mathematical model; see also Figure 6 The diagram shows the structure of an electronic device, which includes a memory 500 and a processor 501. The memory 500 is used to store one or more computer instructions, which are executed by the processor 501 to realize the above-mentioned method for preparing nano-calcium carbonate based on a dynamic mathematical model.

[0155] Furthermore, Figure 6 The electronic device shown also includes a bus 502 and a communication interface 503. The processor 501, the communication interface 503 and the memory 500 are connected via the bus 502.

[0156] The memory 500 may include high-speed random access memory (RAM) or non-volatile memory, such as at least one disk storage device. Communication between this system network element and at least one other network element is achieved through at least one communication interface 503 (which can be wired or wireless), such as the Internet, wide area network, local area network, or metropolitan area network. The bus 502 may be an ISA bus, PCI bus, or EISA bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 6The symbol is represented by a single double-headed arrow, but this does not mean that there is only one bus or one type of bus.

[0157] Processor 501 may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by the integrated logic circuitry in the hardware of processor 501 or by instructions in software form. Processor 501 can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this invention can be directly manifested as execution by a hardware decoding processor, or execution by a combination of hardware and software modules in the decoding processor. The software module can reside in a readily available storage medium in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory 500, and processor 501 reads information from memory 500 and, in conjunction with its hardware, completes the steps of the method described in the foregoing embodiments.

[0158] This invention also provides a computer-readable storage medium storing computer-executable instructions. When these computer-executable instructions are called and executed by a processor, they cause the processor to implement the above-described method for preparing nano-calcium carbonate based on a dynamic mathematical model. For specific implementation details, please refer to the method embodiments, which will not be repeated here.

[0159] The computer program product for the preparation method of nano-calcium carbonate based on a dynamic mathematical model provided in this embodiment of the invention includes a computer-readable storage medium storing non-volatile program code executable by a processor. The instructions included in the program code can be used to execute the methods described in the preceding method embodiments. For specific implementation, please refer to the method embodiments, which will not be repeated here.

[0160] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0161] In the several embodiments provided by this invention, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the coupling or direct coupling or communication connection shown or discussed may be through some communication interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0162] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0163] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0164] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0165] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for preparing nano-calcium carbonate based on a dynamic mathematical model, characterized in that, The method includes: Obtain exhaust gases from combustion power plants; The exhaust gas is compressed, pretreated, and atomized to obtain a droplet gas mixture system. The current process parameters of the droplet-gas mixing system are input into a pre-established dynamic mathematical model for parameter coupling and correlation, and the state equation is output. Based on the state equation, state prediction and optimization are performed to obtain candidate process parameters; The candidate process parameters are used for atomization and fusion processing, and the equation of state is adjusted in real time until the target nano-calcium carbonate is generated.

2. The method according to claim 1, characterized in that, The process of compressing, pretreating, and atomizing the exhaust gas to obtain a droplet-gas mixture system includes: The exhaust gas is compressed and collected into a carbon dioxide tank using an air compressor; The outlet pipe of the carbon dioxide tank is connected to a water washing bottle to remove sulfur dioxide and dust from the exhaust gas. The outlet pipe of the washing bottle is connected to a carbon dioxide pressure swing adsorber to concentrate the carbon dioxide gas in the exhaust gas. The outlet pipe of the carbon dioxide pressure swing adsorber is connected to an air compressor to compress the carbon dioxide gas; The air compressor's outlet pipe is connected to a pressure stabilizing tank, and the pressure stabilizing tank's outlet pipe is connected to the bottom of the spray reaction tank to deliver the carbon dioxide gas; the top of the spray reaction tank is equipped with multiple spray heads, a pressure reducing valve, and a liquid inlet pipe; The Ca(OH) solution obtained by filtration is atomized through the spray head to obtain droplets; The droplets and the carbon dioxide gas supplied from the outlet pipe of the pressure stabilizing tank are mixed to obtain the droplet-gas mixing system.

3. The method according to claim 1, characterized in that, The process of inputting the current process parameters of the droplet-gas mixing system into a pre-established dynamic mathematical model for parameter coupling and correlation, and outputting a state equation, includes: The current process parameters of the droplet-gas mixing system are input into a pre-established dynamic mathematical model to determine the correspondence between the current process parameters and the product parameters. Based on the aforementioned correspondence, parameter coupling and association are performed to output the state equation.

4. The method according to claim 3, characterized in that, The product parameters include: average droplet diameter, average particle size of CaCO3 product, and final product particle size. Determining the correspondence between the current process parameters and the product parameters includes: The correspondence between the current process parameters and the average droplet diameter is determined based on the following formula: Where d represents the average droplet diameter, σ represents the liquid surface tension, and ρ g α1 represents the gas density, U represents the characteristic relative velocity between the gas and liquid phases, α1 represents the scaling coefficient, and β1 represents the scaling exponent. The correspondence between the current process parameters and the average particle size of the CaCO3 product is determined based on the following formula: Where p represents the average particle size of the CaCO3 product; k r A represents the reaction rate constant. contact V represents the gas-liquid contact area, and C represents the reactor volume. CO and C eq These represent the initial and equilibrium concentrations of carbon dioxide gas in the gas, respectively. The correspondence between the current process parameters and the final product particle size is determined based on the following formula: Where p represents the final product particle size, d represents the initial reactant droplet size, and Q g Q represents the flow rate of carbon dioxide gas. l The flow rate of Ca(OH)2 liquid is represented by N, the stirring rate by p0, and the reference or initial value of the target particle size by d. * This indicates the droplet size under preset operating conditions. N represents the gas-liquid flow ratio under preset operating conditions. * α1 represents the stirring rate under preset operating conditions, α2 represents the sensitivity of the final product particle size to changes in the initial reactant droplet size, α3 represents the sensitivity of the final product particle size to changes in the gas-liquid flow ratio, and α4 represents the sensitivity of the final product particle size to changes in the stirring rate.

5. The method according to claim 4, characterized in that, The parameter coupling association based on the correspondence, and the output of the state equation, includes: The state vector and input vector are obtained by coupling parameters based on the correspondence of the following formulas: z(t) represents the state vector, d(t) represents the droplet size, p(t) represents the product particle size, u(t) represents the input vector, and Q... g (t) represents the carbon dioxide gas flow rate, Q l (t) represents the liquid flow rate of Ca(OH)2, U spray (t) represents the adjustable parameters of the spray device, and N(t) represents the stirring rate; The state equation is obtained based on the state vector and the input vector using the following formula: x(k+1)=A·x(k)+B·Δu(k); where, Δu(k)=u(k)-u ref , representing the adjustment amount relative to the reference operating condition, u ref Represents the steady-state condition; A represents matrix A, B represents matrix B, and matrix A ∈ R. 2×2 It is used to describe the dynamic coupling relationship between state variables; matrix B∈R 2×4 This indicates the regulatory effect of the input on the state variable.

6. The method according to claim 5, characterized in that, include: The process of predicting and optimizing the state based on the state equation to obtain candidate process parameters includes: The state prediction for the next H sampling steps is performed based on the state equation using the following formula: x(k+j+1)=A·x(k+j)+B·Δu(k+j), j=0,1,…,H; where j represents the number of sampling steps and H represents the total sampling step length; Δu(k)=u(k)-u ref , representing the adjustment amount relative to the reference operating condition, u ref This represents the steady-state condition; A and B represent matrices A and B respectively; y(k+j)=C·x(k+j) represents the predicted output; Based on the predicted output, state optimization is performed to obtain candidate process parameters.

7. The method according to claim 6, characterized in that, The process of optimizing the state based on the predicted output to obtain candidate process parameters includes: The target approximation function is constructed based on the predicted output using the following formula: Where J represents the target approach function, H represents the total sampling step size, y(k+j) represents the prediction output, and P target λ represents the target value, λ represents the weighting factor used to balance the state deviation and the magnitude of the control quantity change; Δu(k+j) represents the control quantity. Under the input constraints, solve for the optimal control increment; the constraints are: u_min≤u≤u_max; Candidate process parameters are obtained based on the optimal control increment and the current process parameters.

8. A device for preparing nano-calcium carbonate based on a dynamic mathematical model, characterized in that, The device includes: Exhaust gas acquisition module, used to acquire exhaust gas emitted from combustion power plants; The exhaust gas treatment module is used to compress, pretreat, and atomize the exhaust gas to obtain a droplet gas mixture system. The state equation output module is used to input the current process parameters of the droplet-gas mixing system into a pre-established dynamic mathematical model for parameter coupling and correlation, and output the state equation. The prediction and optimization module is used to predict and optimize the state based on the state equation to obtain candidate process parameters. The target nano-calcium carbonate generation module is used to perform atomization fusion processing using the candidate process parameters and adjust the equation of state in real time until the target nano-calcium carbonate is generated.

9. An electronic device, characterized in that, The method includes a processor and a memory, the memory storing computer-executable instructions that can be executed by the processor, the processor executing the computer-executable instructions to implement the method for preparing nano-calcium carbonate based on a dynamic mathematical model as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the method for preparing nano-calcium carbonate based on a dynamic mathematical model as described in any one of claims 1 to 7.

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