Comprehensive recovery and utilization method of ferrophosphorus slag resources after lithium extraction with integrated quality control

Abstract

The invention relates to the technical field of recycling and utilizing waste lithium-ion batteries, and discloses a comprehensive recycling and utilizing method for ferrophosphorus slag resources after lithium extraction with integrated quality control; the method realizes integrated quality control of the entire process by adopting a variety of new technical means such as ultrasonic assistance, online monitoring and optimization control for processes such as alkalization reaction, solid-liquid separation, purification and crystallization, and significantly improves product quality stability and production efficiency; the method comprehensively utilizes multidisciplinary knowledge such as physical fields, chemical kinetics, and optimization algorithms, and provides a new technical route for high-value utilization of ferrophosphorus slag resources.

Description

Technical Field

[0001] The invention relates to the technical field of recycling waste lithium-ion batteries, and more specifically to a method for comprehensive recycling and utilization of phosphorus iron slag resources after lithium extraction with integrated quality control. Background Art

[0002] Lithium iron phosphate batteries have been widely used in the field of new energy due to their high specific capacity, stable structure, high safety, good cycle performance, and long service life. The rapid development of new energy vehicles in my country in recent years has led to a sharp increase in the number of lithium iron phosphate batteries. According to the current general use cycle of lithium batteries of 4-6 years, a large number of scrapped batteries are in urgent need of recycling. The positive electrode powder of disassembled waste lithium iron phosphate batteries is treated by a wet process (sulfuric acid method or hydrochloric acid method). The process of recovering the lithium in the positive electrode powder into a high-value lithium carbonate product is relatively mature, but a large amount of iron phosphate slag will remain. As a by-product of the lithium extraction process, the comprehensive utilization of iron phosphate slag resources has always attracted much attention. Traditional methods have certain defects and cannot fully realize the high-value utilization of iron phosphate slag resources, which is mainly reflected in the following aspects:

[0003] The recycling efficiency is low. The traditional recycling process is complicated, takes a long time to process, consumes a lot of energy, and has unstable recycling efficiency. New technologies are needed to speed up the processing, reduce energy consumption, and improve the efficiency of resource recycling.

[0004] Secondary pollution problem: harmful gases or wastewater may be generated during the treatment process, causing secondary pollution to the environment. It is necessary to develop more environmentally friendly recycling technologies to reduce the discharge of waste gas and wastewater during the treatment process and reduce the environmental burden;

[0005] Due to insufficient quality control, existing technologies make it difficult to achieve precise control of product quality throughout the entire recycling process, resulting in unstable quality and purity of the final product. There is an urgent need for a method to achieve full-process quality control from raw material pretreatment to final product generation to ensure high quality and high purity of the product. Summary of the invention

[0006] In order to overcome the above-mentioned defects of the prior art, the present invention proposes a comprehensive recovery and utilization method of ferrophosphorus slag resources after lithium extraction with integrated quality control. The method realizes full-process quality control from raw material processing to final product generation by introducing a variety of new technical means such as ultrasonic assistance, online monitoring and optimization control, and significantly improves the quality stability of the product; by optimizing process parameters and reaction conditions, such as using multiple pH and conductivity sensor arrays, efficient operation of the process is achieved, significantly reducing processing time and energy consumption; the use of optimized control in the solid-liquid separation and purification crystallization process reduces the generation of wastewater and waste gas, and reduces the impact on the environment.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A comprehensive recovery and utilization method of ferrophosphorus slag resources after lithium extraction with integrated quality control, including:

[0009] S10: performing particle size screening and magnetic separation on the ferrophosphorus slag after lithium extraction to obtain pretreated ferrophosphorus slag;

[0010] S20: putting the pretreated ferrophosphorus slag and alkali solution into a reactor to perform an alkalization reaction under controlled temperature and stirring conditions to generate an alkalization reaction product;

[0011] S30: performing solid-liquid separation on the alkalization reaction product to obtain a phosphate solution and iron hydroxide precipitate, wherein the solid-liquid separation process comprises: obtaining impedance spectrum data of the filter cake during the solid-liquid separation process, and optimizing and controlling the filter cake washing process based on the impedance spectrum data;

[0012] S40: purifying the separated phosphate solution, adjusting different pH values, and obtaining trisodium phosphate, disodium hydrogen phosphate and sodium dihydrogen phosphate products, wherein the purification process includes: constructing a dynamic equation for the distribution of crystal groups, and optimizing and controlling the crystallization process of the phosphate solution;

[0013] S50: oxidizing the ferric hydroxide precipitate under controlled temperature and oxidation conditions to generate a polyferric sulfate product.

[0014] Furthermore, the alkalization reaction is divided into two stages: a rapid reaction stage and a slow reaction stage.

[0015] Furthermore, the rapid reaction section includes introducing ultrasonic assistance in the rapid reaction section, utilizing ultrasonic cavitation effect to break up particles, peel off the surface passivation layer, and obtain ultrasonic power density;

[0016] The alkali solution is a sodium hydroxide solution; the rapid reaction section also includes obtaining a real-time concentration value of the sodium hydroxide solution, generating a reaction kinetic model according to the reaction temperature, stirring rate, feed ratio and ultrasonic power density in the alkalization reaction process, and adjusting the alkalization process parameters according to the reaction kinetic model, wherein the reaction kinetic equation of the rapid reaction section with the addition of ultrasonic assistance is:

[0017]

[0018] In the formula, is the reaction rate, A is the rate constant, r is the stirring rate, T is the reaction temperature, T abis the absolute temperature, c is the concentration of sodium hydroxide solution, F is the feed ratio, I is the ultrasonic power density, m is the reaction order of the reactants, α is the empirical parameter describing the stirring rate, β is the empirical parameter describing the feed ratio, γ is the empirical parameter describing the reaction temperature, δ is the empirical parameter describing the effect of ultrasound on the reaction rate, E is the activation energy of the reaction, and R′ is the gas constant.

[0019] Furthermore, the slow reaction section includes: arranging a plurality of pH and conductivity sensor arrays in the reactor to monitor the reaction progress of each area in real time, and constructing a deviation function J based on the target set pH value and conductivity value:

[0020]

[0021] J is the deviation function, pH(i,t) is the actual pH value measured at time t in the same pH sensor i, pH target is the target pH value, EC(i′,t′) is the actual conductivity value measured at time t′ in the same conductivity sensor i′; EC target is the conductivity value set as the target, ω1 is the pH value weight coefficient, ω2 is the conductivity weight coefficient, n is the total number of pH sensors, n′ is the total number of conductivity sensors, i is the serial number of the pH sensor, i′ is the serial number of the conductivity sensor, t represents the time when the pH sensor collects the actual pH value, and t′ represents the time when the conductivity sensor collects the actual conductivity value;

[0022] By adjusting the feed ratio F and the reaction temperature T, the deviation function J is minimized, wherein the method for calculating the adjustment amounts ΔF and ΔT of the feed ratio and the reaction temperature is:

[0023]

[0024]

[0025] Among them, k1 is the adaptive gain coefficient of the feed ratio adjustment, k2 is the adaptive gain coefficient of the reaction temperature adjustment, F is the feed ratio, T is the reaction temperature, ΔF is the feed ratio adjustment, and ΔT is the reaction temperature adjustment.

[0026] Furthermore, the slow reaction section also includes real-time acquisition of near-infrared spectral data of the alkalization reaction product, using a partial least squares regression algorithm to establish a soft measurement model of the near-infrared spectral data of the alkalization reaction product and the reaction conversion rate and product composition, and real-time estimation of the alkalization reaction conversion rate and product composition.

[0027] Furthermore, the method for optimizing and controlling the filter cake washing process based on impedance spectrum data includes:

[0028] Define the filter cake impedance spectrum as Z, the washing water flow rate as q, the impedance spectrum characteristic parameter as R, and the target impedance spectrum characteristic parameter as R target , the optimization goal is to minimize the integral of the square of the difference between the characteristic parameters of the impedance spectrum and the characteristic parameters of the target impedance spectrum;

[0029] Optimization goal: min∫(RR target ) 2 dt;

[0030] The constraints are:

[0031]

[0032] Among them, k3 and k4 are washing kinetic constants, Z eq is the equilibrium impedance spectrum, R eq is the characteristic parameter of the balanced impedance spectrum, is the derivative of time, and this formula is used to describe the change of characteristic parameters of impedance spectrum with time;

[0033] Introduce the Hamiltonian function H:

[0034] H=(RR target ) 2 +λ×(-k3×q×(ZZ eq )-k4×(RR eq ));

[0035] The Hamiltonian function H combines the optimization objective and constraints, including the Lagrange multiplier λ, which is used to integrate the constraints into the optimization objective. According to the Pontryagin minimum principle, the Hamiltonian function H is minimized and the optimal value of the washing water flow rate q is solved.

[0036] Furthermore, the purification process comprises:

[0037] Construct the dynamic equation of grain group distribution:

[0038]

[0039] Where f is the spatial distribution function of the grain group, is the partial derivative of time, G is the crystal growth rate, B is the crystal nucleation rate, D is the crystal dissolution rate, and L is the grain diameter;

[0040] Crystal growth kinetics equation:

[0041]

[0042] Where k g is the crystal growth rate constant, E g is the activation energy of crystal growth, R′ is the gas constant, Tab is the absolute temperature, S represents the saturation of the solution, n g is the index of supersaturation in crystal growth kinetics, and G is the crystal growth rate;

[0043] Nucleation kinetic equation:

[0044]

[0045] In this equation, k b is the nucleation rate constant, E b is the activation energy of nucleation, n b is the index of supersaturation in crystal formation kinetics, and B is the rate of nucleation;

[0046] The finite element method is used to discretize the equations, solve the dynamic evolution of the grain group distribution, control the spatiotemporal distribution of the grain group, and achieve optimal control of the phosphate solution crystallization process.

[0047] Furthermore, the process of performing solid-liquid separation on the alkalization reaction product includes: introducing ultrasonic assistance, constructing a centrifugal separation optimization model with ultrasonic assistance, and performing centrifugal separation optimization control.

[0048] Furthermore, the method for constructing the centrifugal separation optimization model with ultrasound assistance includes:

[0049]

[0050] Where vpar is the sedimentation velocity of the crystal, Δρ is the density difference between the crystal and the liquid, β′ is the proportionality coefficient, I is the ultrasonic power density, γ′ is the exponent of I, and n speed is the rotation speed, r rad is the centrifugal radius and η is the viscosity of the liquid.

[0051] Furthermore, the method further comprises: constructing a comprehensive optimization model to optimize the filter cake washing and phosphate solution crystallization processes during the solid-liquid separation and purification process;

[0052] The method for constructing the comprehensive optimization model includes:

[0053]

[0054] Where f is the spatial distribution function of the grain group, G is the crystal growth rate, B is the crystal nucleation rate, D is the crystal dissolution rate, k w is the washing rate constant, c w is the impurity concentration in the washing water, c s is the impurity concentration on the filter cake surface, δ′ is the exponent of the washing water flow rate q, E cis the activation energy of the crystallization process, S is the supersaturation of the solution, ψ is the index of the impurity removal rate of the filter cake, R′ is the gas constant, T ab is the absolute temperature, is the partial derivative with respect to time, and L is the grain diameter.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] This application introduces ultrasonic assistance in the fast reaction section, using the ultrasonic cavitation effect to break up the grains and peel off the surface passivation layer, greatly improving the interfacial mass transfer rate and reaction conversion rate. Multiple pH and conductivity sensor arrays are arranged in the slow reaction section to monitor the reaction progress of each area in real time, construct a deviation function, and achieve dynamic optimization control by adjusting the feed ratio and reaction temperature.

[0057] In the solid-liquid separation, the present application adopts a rotary sedimentation centrifuge and a plate-and-frame filter press in series, and optimizes the rotation speed, liquid pool depth and other parameters in the centrifuge to achieve rapid sedimentation and separation of sludge. The filter cake washing process introduces electrochemical impedance spectroscopy online detection, combined with a model predictive control algorithm, to optimize the washing water flow and time, and improve the purity of ferric hydroxide.

[0058] In the purification crystallization, the present application adopts a four-effect falling film evaporator to optimize and adjust the supersaturation of the mother liquor in each effect to prevent scaling; a uniform nucleating agent is introduced into the multi-stage forced circulation crystallizer to optimize the cooling temperature difference and the circulation rate, control the crystal nucleation and growth rate, and obtain an ideal crystal particle size distribution.

[0059] This application established a dynamic model of grain group distribution, an alkalization reaction kinetic model, a filter cake impedance spectrum model, etc. Through digital modeling and optimized control, intelligent and refined quality control was achieved throughout the entire process. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0061] Figure 1 The present invention is a flow chart of the steps of the method for comprehensive recovery and utilization of ferrophosphorus slag resources after lithium extraction with integrated quality control. DETAILED DESCRIPTION

[0062] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0063] Example 1

[0064] See also Figure 1 As shown, this embodiment provides a method for comprehensive recovery and utilization of ferrophosphorus slag resources after lithium extraction with integrated quality control, comprising:

[0065] S10: performing particle size screening and magnetic separation on the ferrophosphorus slag after lithium extraction to obtain pretreated ferrophosphorus slag.

[0066] According to production requirements and equipment characteristics, set the appropriate sieve size and magnetic field strength to remove large particle impurities and magnetic substances. Large particle impurities mainly include incompletely reacted lithium iron phosphate particles, electrode matrix residues, incompletely dissolved particles of ion conductive agents, and impurity particles; magnetic substances mainly include incompletely reduced iron-containing magnetic minerals such as magnetite and hematite, and ferromagnetic particles from battery casings or other metal parts.

[0067] This step helps to improve the purity and uniformity of the raw materials, thereby ensuring the stability of the reaction process and the consistency of product quality, and also reducing energy and resource consumption in subsequent processing processes.

[0068] S20: putting the pretreated ferrophosphorus slag and alkali solution into a reactor, and performing an alkalization reaction under controlled temperature and stirring conditions to generate an alkalization reaction product; the alkali solution is a sodium hydroxide solution.

[0069] The alkalization reaction process is divided into two stages: a rapid reaction stage and a slow reaction stage, and the rapid reaction stage and the slow reaction stage are controlled and optimized respectively.

[0070] Ultrasonic assistance is introduced in the rapid reaction stage to obtain ultrasonic power density, and the ultrasonic cavitation effect is used to break up particles and peel off the surface passivation layer to overcome the passivation effect, thereby improving the interfacial mass transfer rate and reaction conversion rate. The ultrasonic cavitation effect refers to the formation of tiny holes in the liquid, which expand and disintegrate in a very short time, creating a local environment of high temperature and high pressure, which is conducive to particle breakage and mass transfer acceleration.

[0071] The concentration of the sodium hydroxide solution is monitored online to obtain the real-time concentration value of the sodium hydroxide solution. A reaction kinetic model is generated according to the reaction temperature, stirring rate, feed ratio and ultrasonic power density during the alkalization reaction. The alkalization process parameters are adjusted according to the reaction kinetic model.

[0072] The reaction kinetic equation of the rapid reaction section with the addition of ultrasound assistance is:

[0073]

[0074] In the formula, is the reaction rate, A is the rate constant, r is the stirring rate, T is the reaction temperature, T ab is the absolute temperature, c is the concentration of sodium hydroxide solution, F is the feed ratio, I is the ultrasonic power density, m is the reaction order of the reactants, α is the empirical parameter describing the stirring rate, β is the empirical parameter describing the feed ratio, γ is the empirical parameter describing the reaction temperature, δ is the empirical parameter describing the effect of ultrasound on the reaction rate, E is the activation energy of the reaction, and R′ is the gas constant.

[0075] The main purpose of the rapid reaction stage is to quickly start and strengthen the reaction process. Usually, a continuous high-shear mixing reactor is used to accelerate the mixing and dispersion of reactants by using high shear force. By adjusting the feed ratio of alkali solution to slurry, stirring rate and reaction temperature, a high reaction speed and efficiency can be achieved in a short time. Online monitoring of the concentration of sodium hydroxide solution requires online concentration monitoring equipment, such as ion selective electrodes or measuring instruments. During the production process, the concentration of sodium hydroxide solution is monitored in real time, and the alkali concentration is adjusted in time to ensure the stability of the alkali concentration, which helps to control the reaction conditions, prevent product quality changes caused by fluctuations in solution concentration, and improve the stability of product quality.

[0076] It can be understood that the feed ratio of alkali solution and ferrophosphorus slag slurry is adjusted to ensure the material concentration required for the reaction; high-speed stirring can improve the mixing degree of the reactants and accelerate the reaction. Temperature is an important factor affecting the reaction rate. Properly increasing the temperature can accelerate the reaction. By online monitoring of the concentration of sodium hydroxide solution and the alkalization process parameters, a reaction kinetics model is generated, and the alkalization parameters are adjusted in real time according to the model to keep the reaction process in the optimal state and achieve a higher reaction rate and conversion rate.

[0077] The signs for judging the end of the rapid reaction phase and the entry into the slow reaction phase can be:

[0078] Monitor the concentration changes of the reactants. When the concentration changes tend to be flat, it means that the rapid reaction stage is over;

[0079] Monitor the reaction heat release. When the reaction heat release rate decreases, it indicates that the rapid reaction stage is over.

[0080] In order to achieve dynamic optimization control in the slow reaction section, multiple pH and conductivity sensor arrays are arranged in the reactor to monitor the reaction progress in each area in real time. Based on the target pH and conductivity values, the deviation function J is constructed:

[0081]

[0082] J is the deviation function, which is a comprehensive evaluation index used to quantify the degree of deviation between the actual measured value and the target set value; pH(i,t) is the actual pH value measured at time t in the same pH sensor i; pH target is the target pH value, that is, the pH level expected to be maintained or achieved during the reaction; EC(i′,t′) is the actual conductivity value measured at time t′ in the same conductivity sensor i′; EC target is the target conductivity value, that is, the conductivity level expected to be maintained or achieved during the reaction; ω1 is the pH value weight coefficient, which is used to adjust the relative importance of pH value in the deviation function; ω2 is the conductivity weight coefficient, which is used to adjust the relative importance of conductivity in the deviation function; n is the total number of pH sensors, n′ is the total number of conductivity sensors, i is the serial number of the pH sensor, i′ is the serial number of the conductivity sensor, t represents the time when the pH sensor collects the actual pH value, and t′ represents the time when the conductivity sensor collects the actual conductivity value.

[0083] By adjusting the feed ratio F and the reaction temperature T, the deviation function J is minimized, wherein the method for calculating the adjustment amounts ΔF and ΔT of the feed ratio and the reaction temperature is:

[0084]

[0085]

[0086] Among them, k1 is the adaptive gain coefficient of the feed ratio adjustment, k2 is the adaptive gain coefficient of the reaction temperature adjustment, which can be estimated and adjusted online according to the actual reaction situation. F is the feed ratio, T is the reaction temperature, ΔF is the feed ratio adjustment, and ΔT is the reaction temperature adjustment.

[0087] The increase in the conductivity of the alkalization reaction product indicates that the reaction is relatively complete, and the phosphate and iron ions in the ferrophosphorus slag are more converted into ions and enter the solution phase. The decrease in conductivity indicates that the reaction is not complete, and a large number of reactants have not been converted into ions or the ionic species have undergone crystallization, precipitation and other processes and have been removed from the solution phase; the appropriate conductivity value indicates that the reaction has reached a certain stage, most of the reactants have been converted into ions, but the ions have not all been crystallized or precipitated. Therefore, multiple pH and conductivity sensor arrays are set in the slow reaction section to monitor the reaction progress in different areas in real time, and the feed ratio and reaction temperature are adjusted in combination with the deviation function to achieve dynamic optimization of the reaction process.

[0088] In the slow reaction section, the near infrared spectrum data of the alkalization reaction product is obtained in real time, and the soft measurement model of the near infrared spectrum, reaction conversion rate and product composition is established by using the partial least squares regression algorithm. The specific method includes:

[0089] Independent Variable Represents the spectrum absorption value matrix of l wavelength sampling points, where l represents the number of sampling points of the spectrum data, x1 represents the spectrum absorption value of the first wavelength sampling point, and x l represents the spectral absorption value of the lth wavelength sampling point; dependent variable represents the concentration matrix of h components to be measured, where h represents the number of components to be measured, y1 represents the concentration of the first component to be measured, and y h Represents the concentration of the hth component to be measured.

[0090] The specific partial least squares regression model can be expressed as:

[0091] For the independent variable X:

[0092] X = T′P + E′;

[0093] For the dependent variable Y:

[0094] Y = UQ + F′;

[0095] Among them, T′ is the latent variable matrix of X, U is the latent variable matrix of Y, P is the wavelength loading matrix, which describes the weight of each wavelength on the latent variable, Q is the component loading matrix to be tested, which reflects the weight of each component to be tested on the latent variable, E′ is the residual matrix of X, and F′ is the residual matrix of Y.

[0096] The goal of the partial least squares regression algorithm is to maximize the correlation between X and Y in the latent variable space by solving T′, P, U, and Q, while minimizing the residuals E′ and F′.

[0097] Near-infrared spectroscopy can reflect the presence of different chemical substances in the solution and their concentration changes. An increase in the concentration of reaction products will lead to an increase in the near-infrared spectral absorption peak, and a decrease in the concentration of reactants will lead to a decrease in the near-infrared spectral absorption peak. Through this model, we can use the real-time near-infrared spectral data to solve the latent variables and the corresponding loading matrix, and then estimate the reaction conversion rate and product composition in real time, providing a reference for solid-liquid separation optimization.

[0098] S30: performing solid-liquid separation on the alkalization reaction product to obtain a phosphate solution and iron hydroxide precipitate, wherein the solid-liquid separation process includes: obtaining impedance spectrum data of the filter cake during the solid-liquid separation process, and optimizing and controlling the filter cake washing process based on the impedance spectrum data.

[0099] The specific sub-steps of S30 include S31-S33:

[0100] S31: A solid-liquid separation process using a rotary sedimentation centrifuge and a plate and frame filter press in series is used to achieve rapid sedimentation and separation of sludge by adjusting parameters such as the rotation speed and liquid pool depth in the rotary sedimentation centrifuge.

[0101] S32: The slag discharged from the centrifuge is further dehydrated by a plate and frame filter press, and the filter press pressure and time are optimized and controlled to obtain a ferric hydroxide filter cake with a low liquid content. At the same time, the clear liquid of the filter press filtrate is returned to the centrifuge to form a closed-loop circulation.

[0102] S33: Metering and controlling the filter cake washing water, combined with online measurement of the filter cake impedance spectrum, to optimize and control the washing water dosage and washing time, and balance the impurity removal rate and washing loss.

[0103] The impedance spectrum data can reflect the dynamic changes of the internal state of the filter cake in real time. The increase of impedance spectrum data indicates that impurities have accumulated inside the filter cake, increasing the resistance; the decrease of impedance spectrum data indicates that impurities have been effectively washed away and the internal resistance has been reduced; when the impedance spectrum data is close to the ideal equilibrium value, it indicates that the filter cake has been cleaned and the desired purity requirements have been achieved. By monitoring the impedance spectrum and comparing it with the target value, it can be determined whether the current washing is sufficient, and the washing water flow rate can be adjusted according to the deviation so that the impedance spectrum data tends to the equilibrium value, thereby achieving optimized control of the washing process.

[0104] The methods for optimizing the control of the filter cake washing process based on impedance spectroscopy data include:

[0105] Define the filter cake impedance spectrum as Z, the washing water flow rate as q, the impedance spectrum characteristic parameter as R, and the target impedance spectrum characteristic parameter as R target The optimization goal is to minimize the integral of the square of the difference between the characteristic parameters of the impedance spectrum and the characteristic parameters of the target impedance spectrum, in order to make the actual impedance spectrum characteristics during the filter cake washing process as close to the preset values ​​as possible.

[0106] Optimization goal: min∫(RR target ) 2 dt;

[0107] The constraints are:

[0108]

[0109] Among them, k3 and k4 are washing kinetic constants, Z eq is the equilibrium impedance spectrum, R eq This formula is used to describe how the characteristic parameters of the impedance spectrum change over time in order to balance the characteristic parameters of the impedance spectrum. The balanced impedance spectrum refers to the impedance spectrum data measured during the filter cake washing process when a certain degree of cleaning is reached and the internal structure and resistance state of the filter cake tend to be stable.

[0110] Next, the Hamiltonian function H is introduced:

[0111] H=(RR target ) 2 +λ×(-k3×q×(ZZ eq )-k4×(RR eq ));

[0112] The Hamiltonian function H combines the optimization objective and constraints, including the Lagrange multiplier λ, which is used to integrate the constraints into the optimization objective. According to the Pontryagin minimum principle, the Hamiltonian function H is minimized and the optimal value of the washing water flow rate q is solved.

[0113] In actual control, the filter cake impedance spectrum Z is obtained through EIS (electrochemical impedance spectroscopy) test, the characteristic parameter R is extracted, and the washing water flow is optimized in real time in combination with the model predictive control algorithm to achieve intelligent optimization control of the filter cake washing process. The filter cake washing water is metered and controlled, combined with the online measurement of the filter cake point impedance spectrum, to optimize the control of the washing water dosage and washing time, balance the impurity removal rate and washing loss, and improve the purity of iron hydroxide.

[0114] This step effectively improves the solid-liquid separation efficiency by connecting a rotary sedimentation centrifuge and a plate-and-frame filter press in series, optimizes and controls the filter press parameters to obtain a low-liquid iron hydroxide filter cake, and simultaneously realizes closed-loop circulating water utilization, improves production and resource utilization, and uses filter cake impedance spectrum data to optimize the amount of washing water in real time, balancing the removal of impurities and the reduction of washing losses, thereby improving product purity and production. These measures not only improve production efficiency, but also ensure the steady improvement of product quality.

[0115] S40: purifying the separated phosphate solution, adjusting different pH values, and obtaining trisodium phosphate, disodium hydrogen phosphate and sodium dihydrogen phosphate products. The purification process includes: constructing a dynamic equation for the distribution of crystal groups, and optimizing and controlling the crystallization process of the phosphate solution.

[0116] The specific steps of S40 include S41-S44:

[0117] S41: Adopt four-effect falling film evaporator, optimize and adjust evaporation temperature and pressure, control supersaturation of mother liquor in each effect, inhibit crystallization and reduce the risk of equipment scaling.

[0118] S42: The evaporation tailings enter the multi-stage forced circulation crystallizer, and by adjusting the circulation rate, cooling temperature difference and other parameters, the crystal nucleation and crystal growth rate are controlled to optimize the crystal particle size distribution.

[0119] S43: Introducing a uniform nucleating agent into the crystallizer provides a large number of nucleation sites, promotes the formation of a large number of fine nuclei, and inhibits abnormal crystal growth.

[0120] S44: Use push-type centrifuge for separation and multi-stage countercurrent washing to reduce intercrystalline impurities and mother liquor adhesion and improve product purity.

[0121] During the crystallization process, dynamic modeling of grain group distribution is performed to optimize crystallization operation parameters, control the spatiotemporal distribution of grain groups, and achieve efficient optimization control of the crystallization process; the dynamic modeling and optimization methods of grain group distribution include:

[0122] First, construct the dynamic equation of grain group distribution:

[0123]

[0124] Where f is the spatial distribution function of the grain group, is the partial derivative with respect to time, G is the crystal growth rate, B is the nucleation rate, D is the crystal dissolution rate, and L is the grain diameter; this equation describes the evolution of the grain population distribution function f in time and space, which includes the influence of multiple dynamic processes such as crystal growth, nucleation, and crystal dissolution.

[0125] Crystal growth kinetics equation:

[0126]

[0127] In this equation, k g is the crystal growth rate constant, E g is the activation energy of crystal growth, R′ is the gas constant, T ab is the absolute temperature, S represents the saturation of the solution, n g is the index of supersaturation in crystal growth kinetics, and G is the crystal growth rate.

[0128] Nucleation kinetic equation:

[0129]

[0130] In this equation, k b is the nucleation rate constant, E b is the activation energy of nucleation, n b is the index of supersaturation in the crystal formation kinetics, and B is the crystal nucleation rate.

[0131] The crystal growth kinetic equation and the nucleation kinetic equation quantitatively describe the relationship between the crystal growth rate G and the nucleation rate B and the environmental conditions, respectively. The environmental conditions include temperature, solution saturation, etc., and provide necessary sub-models for solving the dynamic equation of grain population distribution.

[0132] The finite element method is used to discretize the equations, solve the dynamic evolution of the grain group distribution, control the spatiotemporal distribution of the grain group, and achieve optimal control of the phosphate solution crystallization process.

[0133] The crystallization process of phosphate is greatly affected by the pH value of the solution. By controlling the pH value of the solution, the form of phosphate ions can be changed to obtain different phosphate products:

[0134] Under higher pH conditions (such as pH>12), phosphate mainly exists in the form of PO43-, and the product obtained by crystallization is mainly trisodium phosphate (Na3PO4).

[0135] Under neutral or weakly alkaline conditions (such as pH between 7-11), phosphate mainly exists in the form of HPO42-, and the product obtained by crystallization is mainly disodium hydrogen phosphate (Na2HPO4).

[0136] Under weakly acidic conditions (such as pH between 4-6), phosphate mainly exists in the form of H2PO4-, and the product obtained by crystallization is mainly sodium dihydrogen phosphate (NaH2PO4).

[0137] By optimizing and controlling the crystallization process of phosphate solution through the dynamic equation of grain group distribution, different pH values ​​can be adjusted to obtain different phosphate products such as trisodium phosphate, disodium hydrogen phosphate, sodium dihydrogen phosphate, etc., thereby improving the comprehensive utilization efficiency of phosphorus resources and the added value of products.

[0138] It is understandable that in the four-effect falling film evaporator, by optimizing and adjusting the evaporation temperature and pressure, the supersaturation of each effect mother liquor is accurately controlled, the occurrence of crystallization is effectively avoided, the risk of equipment scaling is reduced, and the smooth operation is ensured. Subsequently, the evaporation tail enters the multi-stage forced circulation crystallizer, and by adjusting the circulation rate, cooling temperature difference and other parameters, the crystal nucleation and crystal growth rate are precisely controlled, thereby optimizing the crystal size distribution and improving the quality of the product. At the same time, the introduction of a uniform nucleating agent into the crystallizer promotes the formation of a large number of fine crystal nuclei and effectively inhibits the abnormal growth of crystals. Finally, the use of push-type centrifuge separation and multi-stage countercurrent washing not only reduces the adhesion of intercrystalline impurities and mother liquor, but also improves the purity of the product, ensuring the efficiency and thoroughness of the crystal separation process. By constructing a dynamic equation for the distribution of grain groups and combining the measured slurry flow field and temperature field data, the spatiotemporal distribution of the grain group is further optimized, thereby realizing efficient optimization control of the entire crystallization process, providing reliable guarantee for production.

[0139] S50: oxidizing the ferric hydroxide precipitate under controlled temperature and oxidation conditions to generate a polyferric sulfate product.

[0140] The specific sub-steps of S50 include S51-S54:

[0141] S51: Pre-treating the separated iron hydroxide precipitate, such as washing, drying, etc., to remove impurities and improve purity.

[0142] S52: Adding the pretreated iron hydroxide precipitate into a reaction kettle or a reactor.

[0143] S53: Add a certain amount of sulfuric acid solution to the reactor, strictly control the temperature, stirring rate and other parameters of the reactor, so that the reaction proceeds under optimal conditions to obtain a liquid polyferric sulfate product.

[0144] S54: The liquid polyferric sulfate product is evaporated, dried, and the like to be made into a final product that meets industrial grade requirements.

[0145] By strictly controlling the reaction conditions and post-treatment process, not only the quality and purity of the product are improved, but also the production efficiency and process stability are improved, providing reliable guarantees for the production process and realizing the efficient production of polyferric sulfate products.

[0146] Example 2

[0147] This embodiment provides a comprehensive recovery and utilization method of ferrophosphorus slag resources after lithium extraction with integrated quality control on the basis of embodiment 1, comprising:

[0148] S10: performing particle size screening and magnetic separation on the ferrophosphorus slag after lithium extraction to obtain pretreated ferrophosphorus slag.

[0149] S20: adding the pretreated ferrophosphorus slag and alkali solution into a reactor in a certain proportion, and performing an alkalization reaction under controlled temperature and stirring conditions to generate an alkalization reaction product.

[0150] S30: performing solid-liquid separation on the alkalization reaction product to obtain a phosphate solution and iron hydroxide precipitate, wherein the solid-liquid separation process includes: obtaining impedance spectrum data of the filter cake during the solid-liquid separation process, and optimizing and controlling the filter cake washing process based on the impedance spectrum data.

[0151] The specific sub-steps of S30 include S31-S33:

[0152] S31: A solid-liquid separation process using a rotary sedimentation centrifuge and a plate and frame filter press in series is used to achieve rapid sedimentation and separation of sludge by adjusting parameters such as the rotation speed and liquid pool depth in the rotary sedimentation centrifuge.

[0153] S32: The slag discharged from the centrifuge is further dehydrated by a plate and frame filter press, and the filter press pressure and time are optimized and controlled to obtain a ferric hydroxide filter cake with a low liquid content. At the same time, the clear liquid of the filter press filtrate is returned to the centrifuge to form a closed-loop circulation.

[0154] S33: Metering and controlling the filter cake washing water, combined with online measurement of the filter cake impedance spectrum, to optimize and control the washing water dosage and washing time, and balance the impurity removal rate and washing loss.

[0155] The ultrasonic cavitation effect can not only accelerate the alkalization reaction, but also promote particle crushing and dispersion, which is helpful for the subsequent solid-liquid separation. In this embodiment, ultrasonic assistance is introduced in the sludge sedimentation separation process of step S31 to construct a centrifugal separation optimization model with ultrasonic assistance. The specific construction method includes:

[0156] In the alkalization reaction process, ultrasonic assistance is introduced to utilize the ultrasonic cavitation effect to improve the mass transfer rate and reaction conversion rate. The reaction rate constant is related to the ultrasonic power density. The quantitative relationship between the ultrasonic power density and the reaction conversion rate is expressed as:

[0157]

[0158] k5 is the reaction rate constant, A' is the pre-exponential factor, E a is the apparent activation energy, R′ is the gas constant, T ab is the absolute temperature, and α′ is the exponent of the ultrasonic power density I.

[0159] The quantitative relationship between ultrasonic power density and reaction conversion rate can help understand the effect of ultrasound on chemical reaction rate and can be used to optimize chemical reaction processes assisted by ultrasound.

[0160] In the solid-liquid separation process, a rotary sedimentation centrifuge is used to optimize the rotation speed and liquid pool depth to increase the sedimentation velocity and separation efficiency of the crystals. The formula for calculating the sedimentation velocity of the crystals is:

[0161]

[0162] v par is the sedimentation velocity of the grains, Δρ is the density difference between the grains and the liquid, L is the grain diameter, n speed is the rotation speed, r rad is the centrifugal radius and η is the viscosity of the liquid.

[0163] This formula can help understand the effect of centrifuge operating parameters on the particle settling velocity, thereby optimizing the separation efficiency.

[0164] The relationship between ultrasonic power density and grain diameter:

[0165] L = β′ × Iγ′;

[0166] β′ is the proportionality coefficient, and γ′ is the exponent of the ultrasonic power density I.

[0167] The relationship between ultrasonic power density and grain diameter is established to explore the effect of ultrasound on grain size. The regulation effect of ultrasound on grain size can be understood through the proportional coefficient and the index of ultrasonic power density.

[0168] The optimization model considering ultrasonic-assisted and centrifugal separation is:

[0169]

[0170] The formula is used to optimize the sedimentation velocity of the grains to improve the separation efficiency. The sedimentation velocity of the grains is used as the objective function, and the ultrasonic power density and rotation speed are used as decision variables to solve the optimization model and obtain the optimal operating parameter combination.

[0171] The introduction of ultrasonic assistance and optimized centrifugal separation model has shown significant benefits in the chemical reaction process. First, the ultrasonic cavitation effect accelerates the mass transfer rate and reaction conversion rate in the alkalization reaction. Through the quantitative relationship formula, we can deeply understand the influence of ultrasound on the reaction rate, and then optimize the chemical reaction process, improve the reaction efficiency and product purity. Secondly, in the solid-liquid separation stage, a rotary sedimentation centrifuge was used. By optimizing the rotation speed and liquid pool depth, the sedimentation rate and separation efficiency of the grains were effectively improved. This series of operations not only reduced the reaction time, but also improved the purity and yield of the product, providing strong support for the optimization of the process flow. The optimization model that comprehensively considers ultrasonic assistance and centrifugal separation provides a scientific basis for achieving the optimal combination of operating parameters, further improving production efficiency and product quality.

[0172] S40: purifying the separated phosphate solution and adjusting different pH values ​​to obtain different products such as trisodium phosphate, disodium hydrogen phosphate, and sodium dihydrogen phosphate. The purification process includes: constructing a dynamic equation for the distribution of grain groups and optimizing the control of the crystallization process of the phosphate solution.

[0173] The specific steps of S40 include S41-S44:

[0174] S41: Adopt four-effect falling film evaporator, optimize and adjust evaporation temperature and pressure, control supersaturation of mother liquor in each effect, inhibit crystallization and reduce the risk of equipment scaling.

[0175] S42: The evaporation tailings enter the multi-stage forced circulation crystallizer, and by adjusting the circulation rate, cooling temperature difference and other parameters, the crystal nucleation and crystal growth rate are controlled to optimize the crystal particle size distribution.

[0176] S43: Introducing a uniform nucleating agent into the crystallizer provides a large number of nucleation sites, promotes the formation of a large number of fine nuclei, and inhibits abnormal crystal growth.

[0177] S44: Use push-type centrifuge for separation and multi-stage countercurrent washing to reduce intercrystalline impurities and mother liquor adhesion and improve product purity.

[0178] Optimized control of the filter cake washing process can significantly reduce the impurity content in the filter cake, providing a better raw material basis for subsequent phosphate solution purification; at the same time, the improvement of the purity of the phosphate solution also helps to reduce the interference of impurities on crystal growth during the crystallization process.

[0179] In this embodiment, during the filter cake washing process, online measurement of filter cake impedance spectrum is introduced to optimize the washing water flow rate. The specific method includes:

[0180] Quantitative relationship between wash water flow rate and impurity removal rate in filter cake:

[0181]

[0182] k w is the washing rate constant, c w is the impurity concentration in the washing water, c s is the impurity concentration on the filter cake surface, and δ′ is the exponent of the washing water flow rate q.

[0183] This formula describes the quantitative relationship between the wash water flow rate and the impurity removal rate in the filter cake, which can assist in optimizing the use of wash water and improving the impurity removal efficiency.

[0184] Dynamic equation of grain group distribution:

[0185]

[0186] Among them, f is the spatial distribution function of the grain group, G is the crystal growth rate, B is the crystal nucleation rate, and D is the crystal dissolution rate.

[0187] This equation describes the change of grain population density with time and grain size. By combining the measured slurry flow field and temperature field data, the dynamic evolution of grain population distribution can be solved and crystallization operation parameters such as temperature and supersaturation can be optimized. It can help understand the influence of factors such as crystal growth, agglomeration, fragmentation and diffusion on grain population distribution, thereby optimizing the crystallization process and improving product quality.

[0188] Relationship between filter cake impurity removal efficiency and crystallization operating parameters:

[0189]

[0190] E c is the activation energy of the crystallization process, S is the supersaturation, ψ is the index of the impurity removal rate of the filter cake, is the impurity removal efficiency of the filter cake, and δ′ is the exponent of the wash water flow rate q.

[0191] This formula reflects the influence of crystallization operating parameters on the filter cake washing process. Through this relationship, the impurity removal efficiency in the crystallization process can be better controlled, thereby improving the purity and quality of the product.

[0192] The comprehensive optimization model considering both filter cake washing and crystallization processes is:

[0193]

[0194] The relationship between the washing water flow rate and impurity removal efficiency in the filter cake washing process and the dynamic equation of crystal group distribution in the phosphate solution crystallization process are combined to establish an optimization model that comprehensively considers the filter cake washing and crystallization processes. This model describes the dynamic changes in crystal formation, growth, agglomeration, crushing and impurity removal during the filter cake washing and crystallization processes, which can help to more comprehensively understand and optimize the entire process.

[0195] The introduction of optimized control of filter cake washing and crystallization processes has shown significant benefits in the production of phosphate products. First, through the optimized control of the filter cake washing process, the impurity content in the filter cake can be effectively reduced, providing a higher quality raw material basis for the subsequent purification of phosphate solution. This not only improves the purity of the product, but also reduces the interference of impurities on crystal growth during the crystallization process, thereby improving the quality and yield of the product. Secondly, combined with the optimization model of the filter cake washing and crystallization process, the entire process can be understood and controlled more comprehensively. By measuring the filter cake impedance spectrum online in real time and combining the dynamic equation of the grain group distribution, the washing water flow rate and crystallization operation parameters can be accurately controlled, the impurity removal efficiency and the crystal growth process can be optimized, and the purity and quality of the product can be further improved. The optimization model that comprehensively considers the filter cake washing and crystallization processes provides a scientific basis for the production of phosphate products and improves production efficiency.

[0196] S50: oxidizing the ferric hydroxide precipitate under controlled temperature and oxidation conditions to generate a polyferric sulfate product.

[0197] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

[0198] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A comprehensive recovery and utilization method of ferrophosphorus slag resources after lithium extraction with integrated quality control, characterized in that: include: S10: performing particle size screening and magnetic separation on the ferrophosphorus slag after lithium extraction to obtain pretreated ferrophosphorus slag; S20: putting the pretreated ferrophosphorus slag and alkali solution into a reactor to perform an alkalization reaction under controlled temperature and stirring conditions to generate an alkalization reaction product; S30: performing solid-liquid separation on the alkalization reaction product to obtain a phosphate solution and iron hydroxide precipitate, wherein the solid-liquid separation process comprises: obtaining impedance spectrum data of the filter cake during the solid-liquid separation process, and optimizing and controlling the filter cake washing process based on the impedance spectrum data; S40: purifying the separated phosphate solution, adjusting different pH values, and obtaining trisodium phosphate, disodium hydrogen phosphate and sodium dihydrogen phosphate products, wherein the purification process includes: constructing a dynamic equation for the distribution of crystal groups, and optimizing and controlling the crystallization process of the phosphate solution; S50: oxidizing the ferric hydroxide precipitate under controlled temperature and oxidation conditions to generate a polyferric sulfate product; The alkalization reaction is divided into two stages: a rapid reaction stage and a slow reaction stage; The rapid reaction section includes introducing ultrasonic assistance in the rapid reaction section, utilizing ultrasonic cavitation effect to break up particles, peel off the surface passivation layer, and obtain ultrasonic power density; The alkali solution is a sodium hydroxide solution; the rapid reaction section also includes obtaining a real-time concentration value of the sodium hydroxide solution, generating a reaction kinetic model according to the reaction temperature, stirring rate, feed ratio and ultrasonic power density in the alkalization reaction process, and adjusting the alkalization process parameters according to the reaction kinetic model, wherein the reaction kinetic equation of the rapid reaction section with the addition of ultrasonic assistance is: In the formula, is the reaction rate, A is the rate constant, r is the stirring rate, T is the reaction temperature, T ab is the absolute temperature, c is the concentration of sodium hydroxide solution, F is the feed ratio, I is the ultrasonic power density, m is the reaction order of the reactants, α is the empirical parameter describing the stirring rate, β is the empirical parameter describing the feed ratio, γ is the empirical parameter describing the reaction temperature, δ is the empirical parameter describing the effect of ultrasound on the reaction rate, E is the activation energy of the reaction, and R′ is the gas constant.

2. The method for comprehensive recovery and utilization of phosphorus iron slag resources after lithium extraction with integrated quality control according to claim 1, characterized in that: The slow reaction section includes: arranging multiple pH and conductivity sensor arrays in the reactor to monitor the reaction progress of each area in real time, and constructing a deviation function J based on the target pH value and conductivity value: J is the deviation function, pH(i,t) is the actual pH value measured at time t in the same pH sensor i, pH target is the target pH value, EC(i′,t′) is the actual conductivity value measured at time t′ in the same conductivity sensor i′; EC target is the conductivity value set as the target, ω1 is the pH value weight coefficient, ω2 is the conductivity weight coefficient, n is the total number of pH sensors, n′ is the total number of conductivity sensors, i is the serial number of the pH sensor, i′ is the serial number of the conductivity sensor, t represents the time when the pH sensor collects the actual pH value, and t′ represents the time when the conductivity sensor collects the actual conductivity value; By adjusting the feed ratio F and the reaction temperature T, the deviation function J is minimized, wherein the method for calculating the adjustment amounts ΔF and ΔT of the feed ratio and the reaction temperature is: Wherein, k1 is the adaptive gain coefficient of the feed ratio adjustment, k2 is the adaptive gain coefficient of the reaction temperature adjustment, ΔF is the feed ratio adjustment, and ΔT is the reaction temperature adjustment.

3. The method for comprehensive recovery and utilization of ferrophosphorus slag resources after lithium extraction with integrated quality control according to claim 1, characterized in that: The slow reaction section also includes real-time acquisition of near-infrared spectral data of the alkalization reaction product, establishment of a soft measurement model of the near-infrared spectral data of the alkalization reaction product, reaction conversion rate, and product composition using a partial least squares regression algorithm, and real-time estimation of the alkalization reaction conversion rate and product composition.

4. The method for comprehensive recovery and utilization of phosphorus iron slag resources after lithium extraction with integrated quality control according to claim 1, characterized in that: The method for optimizing and controlling the filter cake washing process based on impedance spectrum data comprises: Define the filter cake impedance spectrum as Z, the washing water flow rate as q, the impedance spectrum characteristic parameter as R, and the target impedance spectrum characteristic parameter as R target , the optimization goal is to minimize the integral of the square of the difference between the characteristic parameters of the impedance spectrum and the characteristic parameters of the target impedance spectrum; Optimization goal: min∫(RR target ) 2 dt; The constraints are: Among them, k3 and k4 are washing kinetic constants, Z eq is the equilibrium impedance spectrum, R eq is the characteristic parameter of the balanced impedance spectrum, is the derivative of time, and this formula is used to describe the change of characteristic parameters of impedance spectrum with time; Introduce the Hamiltonian function H: H=(R-R target ) 2 +λ×(-k3×q×(Z-Z eq )-k4×(R-R eq )); The Hamiltonian function H combines the optimization objective and constraints, including the Lagrange multiplier λ, which is used to integrate the constraints into the optimization objective. According to the Pontryagin minimum principle, the Hamiltonian function H is minimized and the optimal value of the washing water flow rate q is solved.

5. The method for comprehensive recovery and utilization of phosphorus iron slag resources after lithium extraction with integrated quality control according to claim 1, characterized in that: The purification process comprises: Construct the dynamic equation of grain group distribution: Where f is the spatial distribution function of the grain group, is the partial derivative of time, G is the crystal growth rate, B is the crystal nucleation rate, D is the crystal dissolution rate, and L is the grain diameter; Crystal growth kinetics equation: Where k g is the crystal growth rate constant, E g is the activation energy of crystal growth, R′ is the gas constant, T ab is the absolute temperature, S represents the saturation of the solution, n g It is an index of supersaturation in crystal growth kinetics; Nucleation kinetic equation: In this equation, k b is the nucleation rate constant, E b is the activation energy of nucleation, n b It is an index of supersaturation in crystal formation kinetics; The finite element method is used to discretize the equations, solve the dynamic evolution of the grain group distribution, control the spatiotemporal distribution of the grain group, and achieve optimal control of the phosphate solution crystallization process.

6. The method for comprehensive recovery and utilization of phosphorus iron slag resources after lithium extraction with integrated quality control according to claim 1, characterized in that: The process of solid-liquid separation of the alkalization reaction product includes: introducing ultrasonic assistance, constructing a centrifugal separation optimization model with ultrasonic assistance, and performing centrifugal separation optimization control.

7. The method for comprehensive recovery and utilization of phosphorus iron slag resources after lithium extraction with integrated quality control according to claim 6, characterized in that: The method for constructing the centrifugal separation optimization model with ultrasonic assistance includes: Where vpar is the sedimentation velocity of the crystal, Δρ is the density difference between the crystal and the liquid, β′ is the proportionality coefficient, I is the ultrasonic power density, γ′ is the exponent of I, and n speed is the rotation speed, r rad is the centrifugal radius and η is the viscosity of the liquid.

8. The method for comprehensive recovery and utilization of ferrophosphorus slag resources after lithium extraction with integrated quality control according to claim 1, characterized in that: The method further comprises: constructing a comprehensive optimization model to optimize the filter cake washing and phosphate solution crystallization processes during solid-liquid separation and purification treatment; The method for constructing the comprehensive optimization model includes: Where f is the spatial distribution function of the grain group, G is the crystal growth rate, B is the crystal nucleation rate, D is the crystal dissolution rate, k w is the washing rate constant, c w is the impurity concentration in the washing water, c s is the impurity concentration on the filter cake surface, δ′ is the exponent of the washing water flow rate q, E c is the activation energy of the crystallization process, S is the supersaturation of the solution, ψ is the index of the impurity removal rate of the filter cake, R′ is the gas constant, T ab is the absolute temperature, is the partial derivative with respect to time, and L is the grain diameter.

Images