A soft measurement method and readable storage medium for titanium dioxide grain size in a rotary kiln during the sulfuric acid process.

Abstract

This invention provides a soft measurement method and a readable storage medium for measuring the titanium dioxide grain size in a rotary kiln during the sulfuric acid process. The soft measurement method combines the flow model of the rotary kiln, the mass conservation equation, the energy conservation equation, the chemical reaction model of the rotary kiln, and the titanium dioxide grain size growth kinetic model. This allows for the calculation of the axial distribution of titanium dioxide grain size within the rotary kiln under different operating conditions. This method is of great significance for optimizing and controlling operating conditions such as fuel flow rate, air flow rate, material flow rate, and kiln speed in the rotary kiln reactor, thereby obtaining high-quality titanium dioxide products.

Description

Technical Field

[0001] This invention relates to the field of titanium dioxide production technology using the sulfuric acid process, and more particularly to a soft measurement method and readable storage medium for titanium dioxide grain size in a rotary kiln during the sulfuric acid process. Background Technology

[0002] Titanium dioxide (commonly known as titanium white) is an important raw material in industries such as architectural coatings, papermaking, and cosmetics. In the sulfuric acid process for producing titanium dioxide, titanium-containing minerals undergo leaching, hydrolysis, calcination, and pulverization to obtain rutile titanium dioxide. Rotary kiln calcination is the most crucial step in the entire process. The residence time and temperature field of the material in the rotary kiln significantly influence the rutile content and grain size of the titanium dioxide. However, the flow, heat transfer, reaction, and grain growth processes within the rotary kiln are highly complex, making it difficult to accurately predict the flow field, temperature field, rutile conversion rate, and grain size. Controlling operating conditions such as hot air flow rate, hot air temperature, material mass flow rate, and rotary kiln speed relies heavily on practical production experience, lacking reliable theoretical calculations. This poses a significant challenge to optimizing operating conditions to obtain high-quality titanium dioxide products.

[0003] In actual industrial production, the titanium dioxide raw material obtained in a rotary kiln needs to undergo cooling and depolymerization before its grain size is measured using methods such as X-ray diffraction and laser particle size analyzers. When the operating parameters in the rotary kiln change, the material residence time, temperature field distribution, rutile conversion rate, and grain size all change accordingly. However, the time interval between changing the operating parameters and obtaining the grain size under the new operating parameters is typically 10–20 hours, making it impossible to obtain timely feedback data. Secondly, industrial experimental methods can only obtain the grain size at the rotary kiln outlet, not the distribution of the grain size along the axial direction inside the kiln. Furthermore, considering safety and cost factors in actual production, it is difficult to conduct numerous industrial experiments under different operating parameters, especially to change the operating conditions in the rotary kiln over a large range.

[0004] In the laboratory, experiments involving heating metatitanic acid in a small muffle furnace can be conducted. Differential thermal analysis, combined with X-ray diffraction and laser particle size analysis, can be used to obtain information on the reaction process, rutile conversion rate, and grain size growth during titanium dioxide calcination. For example, Eastman studied the microstructure development of nano-titanium dioxide grains during annealing using high-temperature in-situ X-ray diffraction and proposed a kinetic model for titanium dioxide grain growth. Wang et al. further determined the apparent activation energy in the grain growth kinetic model when B2O3, K2O, and Li2O were used as salt treatment agents, respectively. However, due to the significant differences between the flow and temperature fields in a small muffle furnace and those in an actual industrial rotary kiln, and the strong coupling between grain size growth and flow, heat transfer, and reaction processes, the grain size growth patterns explored in the laboratory cannot be directly used to predict grain size growth in actual industrial rotary kilns.

[0005] With the development of numerical simulation technology, numerical simulation of rotary kiln reactors is increasingly being applied to the prediction of multiphysics fields in rotary kilns, the development of new rotary kiln processes, and the design, scale-up, and optimization of operating conditions of rotary kilns. Ginsberg and Modigell used the finite difference method to perform one-dimensional steady-state and dynamic numerical simulations of a rotary kiln device in the sulfuric acid process for titanium dioxide production, obtaining the axial distribution of the temperature field in the rotary kiln. Agrawal et al. used a three-dimensional simulation of the gas phase field to obtain the convective heat transfer coefficient between the gas phase and the kiln wall and the material, and coupled this heat transfer coefficient with a one-dimensional steady-state model to calculate the temperature field and material component concentration field in the rotary kiln. However, these methods are limited to obtaining the temperature field and material component concentration field in the rotary kiln through simulation calculations, and cannot calculate the distribution of grain size along the axial position in the rotary kiln. Summary of the Invention

[0006] In view of the problems existing in the prior art, the present invention provides a soft measurement method and readable storage medium for the titanium dioxide grain size in a rotary kiln during the sulfuric acid process. This method can obtain the distribution of titanium dioxide grain size along the axial position of the rotary kiln in a timely and accurate manner when the operating parameters such as hot air flow rate, hot air temperature, material flow rate and kiln speed change. This provides a new technical means to optimize the operating conditions of the rotary kiln and obtain higher quality titanium dioxide products.

[0007] To achieve this objective, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a soft measurement method for the grain size of titanium dioxide in a rotary kiln during the sulfuric acid process for producing titanium dioxide. The soft measurement method includes the following steps:

[0009] (1) Construct and solve the flow model of the rotary kiln to obtain the material layer thickness distribution, material axial velocity distribution and material residence time distribution at the axial position inside the rotary kiln;

[0010] (2) Based on the material layer thickness distribution, material axial velocity distribution and material residence time distribution obtained in step (1), construct and solve the mass conservation equation and energy conservation equation of the rotary kiln to obtain the one-dimensional temperature field in the rotary kiln.

[0011] (3) Construct a rotary kiln chemical reaction model for the production of titanium dioxide by the sulfuric acid process, and couple the flow model in step (1) and the energy conservation equation in step (2) to calculate the one-dimensional component concentration field of the gas phase and materials in the rotary kiln.

[0012] (4) Based on the material residence time distribution, one-dimensional temperature field and one-dimensional component concentration field, the axial distribution of titanium dioxide grain size in the rotary kiln is calculated by solving the titanium dioxide grain size growth kinetic model.

[0013] This invention combines a flow model, a chemical reaction model, and a titanium dioxide grain size growth kinetics model of a rotary kiln. It can directly calculate the axial distribution of titanium dioxide grains in the rotary kiln in real time based on operating conditions. It is applicable to different hot air flow rates, hot air temperatures, material flow rates, and kiln speeds, and has a wide range of applications and timely predictions.

[0014] It is worth noting that the titanium dioxide grain growth process is quite complex, involving both chemical reaction and grain growth processes. The purpose of this invention is not to predict the actual particle size of titanium dioxide, but rather to predict the grain size inside the titanium dioxide. This grain size data has a significant impact on the quality of subsequent titanium dioxide products and therefore requires strict control. The method provided by this invention can monitor different operating conditions in real time, and it obtains not only the titanium dioxide grain size at the rotary kiln outlet, but also the distribution of titanium dioxide grain size along the rotary kiln axis. Based on the axial distribution, it can also determine whether there are overheating, hot spots, or large-scale particle agglomeration in the rotary kiln, which is beneficial for real-time monitoring of the reaction and grain growth in the rotary kiln.

[0015] Preferably, the soft measurement method further includes setting the design parameters, physical property parameters and operating parameters of the rotary kiln before step (1).

[0016] Preferably, the flow model in step (1) is a simplified one-dimensional flow model, preferably the Seaman model. This model can take into account the cofferdam factor in the rotary kiln, thereby enabling a more accurate prediction of the residence time of titanium dioxide grains.

[0017] Preferably, the flow model is as shown in equation (1):

[0018]

[0019] The D mentioned in equation (1) i The inner diameter of the rotary kiln is represented by θ, the dynamic angle of repose by ω, and the rotational speed by α. inc : Indicates the tilt angle of the rotary kiln, V s H represents the volumetric flow rate of the solid phase, and H represents the height of the material bed.

[0020] The distribution of the residence time τ of the solid phase along the axial position z of the rotary kiln is shown in equation (2):

[0021]

[0022] In equation (2) v s S represents the axial flow velocity of the material. bed This indicates the cross-sectional area occupied by the material.

[0023] Preferably, the mass conservation equation in step (2) is a one-dimensional mass conservation equation.

[0024] Preferably, the one-dimensional mass conservation equation is shown in equations (3) to (4):

[0025]

[0026]

[0027] In equations (3) to (4), m represents the mass flow rate of each component in the gas phase and the material, and the subscripts i = 1 to 5 represent the five components in the gas phase: N2, O2, CO2, SO2 and H2O(g), respectively. g in parentheses represents the gaseous state.

[0028] The subscripts j = 1 to 6 represent the six components in the material: H2O(l), TiO(OH)2, TiOSO4·H2O, TiOSO4, TiO2(a), and TiO2(r), respectively. The symbols in parentheses l represent liquid, a represent anatase TiO2, and r represent rutile TiO2. This represents the change in the mass flow rate of a component caused by a chemical reaction process.

[0029] Preferably, the energy conservation equation is a one-dimensional energy conservation equation.

[0030] Preferably, the one-dimensional energy conservation equation includes the energy conservation equation for the gas phase, the energy conservation equation for the material, the energy conservation equation for the gas phase sidewall, the energy conservation equation for the solid phase sidewall, and the energy conservation equation for the outer wall.

[0031] Preferably, the energy conservation equation for the gas phase is as shown in equation (5):

[0032]

[0033] Preferably, the energy conservation equation for the material is as shown in the following equation:

[0034]

[0035] Preferably, the energy conservation equation for the gas phase sidewall is as follows:

[0036] 0 = Q G,WG -Q WG,S -Q WG,WS -Q WG,WO Equation (7)

[0037] Preferably, the energy conservation equation for the solid sidewall is as follows:

[0038] 0 = Q WG,WS -Q WS,S -Q WS,WO Equation (8)

[0039] Preferably, the energy conservation equation for the outer wall surface is as follows:

[0040] 0 = Q WG,WO +Q WG,WO -Q WO,A Equation (9)

[0041] In equations (5) to (9), T G T represents the temperature of the gas phase. S The temperature of the material, c i M represents the molar heat capacity of component i. i c represents the molar mass of component i. j M represents the molar heat capacity of component j; j Represents the molar mass of component j;

[0042] Q G,S Q G,WG Q WG,S and Q WS,S These represent the heat exchange between the gas phase and the solid phase, between the gas phase and the gas phase sidewall, between the gas phase sidewall and the solid phase, and between the solid phase sidewall and the solid phase, respectively; Q WG,WS Q WG,WO Q WS,WO and Q WO,A These represent the heat exchange between the gas phase sidewall and the solid phase sidewall, the gas phase sidewall and the outer wall, the solid phase sidewall and the outer wall, and the outer wall and the environment, respectively; Q Mass and Q Reac These represent energy transfer and heat of chemical reaction caused by mass exchange, respectively.

[0043] The heat exchange term Q inside the rotary kiln G,SQ G,WG Q WG,S and Q WS,S The closure relations are expressed as follows:

[0044]

[0045]

[0046]

[0047] Q WS,S =h WS,S L WS,S (T WS -T S )

[0048] Where h G,S h G,WG and h WS,S L represents the convective heat transfer coefficients between the gas phase and the material, between the gas phase and the gas phase sidewall, and between the material and the material sidewall, respectively. G,S L G,WG L WS,S These represent the convective heat transfer areas per unit axial length between the gas phase and the material, between the gas phase and the gas phase sidewall, and between the material and the material sidewall. G,S e G,WG e WG,S T represents the radiative heat exchange coefficients between the gas phase and the material, between the gas phase and the gas phase sidewall, and between the gas phase sidewall and the material, respectively. WG and T WS These represent the temperatures of the gas phase sidewall and the solid phase sidewall, respectively. σ represents the Stefan-Boltzmann constant.

[0049] Heat exchange term Q on the rotary kiln wall WG,WS Q WG,WO Q WS,WO and Q WO,A The closure relations are expressed as follows:

[0050]

[0051]

[0052]

[0053]

[0054] Where λ W ρ W and c W These represent the thermal conductivity, density, and heat capacity of the wall surface (i.e., the refractory brick), respectively. α fillD represents the material's filling rate. O T represents the diameter of the outer wall of the rotary kiln. WO and T A These represent the external wall surface temperature and the ambient temperature, respectively. WO,A L WO,A and e WO,A These represent the convective heat transfer coefficient between the outer wall surface and the environment, the heat transfer area per unit axial length, and the radiative heat transfer coefficient, respectively.

[0055] During the drying and chemical reaction process inside the rotary kiln, the closed-loop relationships of energy transfer due to mass exchange and reaction heat are expressed as follows:

[0056]

[0057]

[0058] Where h k The enthalpy of reaction k represents the chemical reaction k.

[0059] Preferably, the rotary kiln chemical reaction model in step (3) includes 5 steps, denoted as R. k k is 1 to 5.

[0060] k=1:H2O(l)→H2O(g);

[0061] k=2: TiO(OH)2→TiO2(a)+H2O(g);

[0062] k=3: TiOSO4·H2O→TiOSO4+H2O(g);

[0063] k=4: TiOSO4→TiO2(a)+SO2(g)+1 / 2O2(g);

[0064] k=5:TiO2(a)→TiO2(r).

[0065] Preferably, the reaction kinetic equations for k = 2 to 5 are expressed using Arrhenius's law:

[0066]

[0067] Where ζ k A k E k and n k These represent the conversion rate, pre-exponential factor, activation energy, and reaction order of reaction k, respectively; R is the molar gas constant; and t represents time.

[0068] The mass source terms of each component in the material are shown in equations (10) to (15):

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] Where x H2O Indicates the moisture content of the material;

[0076] The mass source terms of each component in the gas phase are shown in equations (16) to (20), respectively:

[0077]

[0078]

[0079]

[0080]

[0081]

[0082] Preferably, the growth kinetic model of titanium dioxide grain size in step (4) is shown in equation (20):

[0083]

[0084] Where d grain d represents the grain size. grain,0 α is the initial grain size. grain n is a proportionality constant. grain For the dynamic series, E grain This is the activation energy for grain growth.

[0085] Preferably, the value of the grain growth activation energy is related to the type and formulation of the seed crystals and salt treatment agent used in the sulfuric acid process for producing titanium dioxide.

[0086] Preferably, the soft sensing method uses boundary values ​​at both ends of the rotary kiln for solution. Compared to the traditional method that only uses boundary values ​​at the outlet end, the soft sensing method provided by this invention can fully consider the material changes before and after the reaction, significantly improving the prediction results.

[0087] In a second aspect, the present invention provides a readable storage medium storing a program written for a soft measurement method of titanium dioxide grain size in a rotary kiln during the sulfuric acid process for producing titanium dioxide, as described in the first aspect.

[0088] The computer-readable storage medium provided by the present invention stores a program written according to the soft measurement method for titanium dioxide grain size in a rotary kiln during the sulfuric acid process as described in the first aspect. The computer storage medium can interface with existing commercial software to achieve prediction of titanium dioxide grain size.

[0089] Compared with the prior art, the present invention has at least the following beneficial effects:

[0090] (1) The soft measurement method for measuring the size of titanium dioxide grains in the rotary kiln during the sulfuric acid process provided by this invention calculates the size of titanium dioxide grains in less than 10 seconds, thus allowing timely acquisition of the size of titanium dioxide grains after changes in operating conditions.

[0091] (2) The soft measurement method for titanium dioxide grain size in rotary kiln in the sulfuric acid process for titanium dioxide production provided by the present invention can not only calculate the titanium dioxide grain size at the outlet of the rotary kiln, but also calculate the change of titanium dioxide grain size along the axial position of the rotary kiln, thereby providing feedback on the temperature rise of hot spots and calcination stability inside the rotary kiln.

[0092] (3) The soft measurement method for titanium dioxide grain size in rotary kiln in the sulfuric acid process for titanium dioxide production provided by the present invention is applicable to different operating conditions and rotary kilns. For example, it is applicable to rotary kilns in the sulfuric acid process for titanium dioxide production with different design parameters. These parameters are not limited to the length, diameter, refractory brick thickness, tilt angle, and refractory brick material of the rotary kiln. It is applicable to rotary kilns in the sulfuric acid process for titanium dioxide production with different operating conditions, including hot air flow rate, different hot air temperature, different material flow rate, and kiln rotation speed. It is applicable to sulfuric acid process for titanium dioxide production with different salt treatment agent types and different salt treatment agent formulations. Attached Figure Description

[0093] Figure 1 This is an operation flowchart of the soft measurement method for titanium dioxide grain size in the rotary kiln during the sulfuric acid process of titanium dioxide production, provided in a specific embodiment of the present invention.

[0094] Figure 2 This is a graph showing the variation of material thickness and residence time with the axial position of the rotary kiln, as provided in Embodiment 1 of the present invention.

[0095] Figure 3 This is a diagram showing the temperature distribution and solid phase composition as a function of the axial position of the rotary kiln, provided in Embodiment 1 of the present invention.

[0096] Figure 4 This is a distribution diagram of the titanium dioxide grain size predicted by Embodiment 1 of the present invention as a function of the axial position of the rotary kiln.

[0097] Figure 5 This is the effect of different operating conditions on the grain size of titanium dioxide predicted in Example 1 of the present invention. Detailed Implementation

[0098] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0099] The present invention will now be described in further detail. However, the examples described below are merely simplified examples of the present invention and do not represent or limit the scope of protection of the present invention. The scope of protection of the present invention is determined by the claims.

[0100] As a specific embodiment of the present invention, a soft measurement method for the grain size of titanium dioxide in a rotary kiln during the sulfuric acid process is provided. The soft measurement method includes the following steps:

[0101] The design parameters, physical property parameters, and operating parameters of the rotary kiln are set. Specifically, the design parameters include the inner diameter of the rotary kiln, the thickness of the refractory bricks, the kiln length, and the kiln inclination angle. The physical property parameters include refractory density, heat capacity, thermal conductivity, and emissivity. The operating parameters include hot air flow rate, hot air temperature, hot air inlet composition and ratio, material inlet flow rate, material inlet composition and ratio, and kiln rotation speed.

[0102] (1) Construct and solve the flow model of the rotary kiln (Seaman model) to obtain the material layer thickness distribution, material axial velocity distribution and material residence time distribution at the axial position inside the rotary kiln;

[0103] The flow model is shown in equation (1):

[0104]

[0105] The D mentioned in equation (1) i The inner diameter of the rotary kiln is represented by θ, the dynamic angle of repose by ω, and the rotational speed by α. inc : Indicates the tilt angle of the rotary kiln, V s H represents the volumetric flow rate of the solid phase, and H represents the height of the material bed.

[0106] The distribution of the residence time τ of the solid phase along the axial position z of the rotary kiln is shown in equation (2):

[0107]

[0108] In equation (2) v s S represents the axial flow velocity of the material. bed This indicates the cross-sectional area occupied by the material.

[0109] (2) Based on the material layer thickness distribution, material axial velocity distribution and material residence time distribution obtained in step (1), construct and solve the mass conservation equation and energy conservation equation of the rotary kiln to obtain the one-dimensional temperature field in the rotary kiln.

[0110] Specifically, the mass conservation equation in step (2) is a one-dimensional mass conservation equation.

[0111] The one-dimensional mass conservation equation is shown in equations (3) to (4):

[0112]

[0113]

[0114] In equations (3) to (4), m represents the mass flow rate of each component in the gas phase and the material, and the subscripts i = 1 to 5 represent the five components in the gas phase: N2, O2, CO2, SO2 and H2O(g), respectively. g in parentheses represents the gaseous state.

[0115] The subscripts j = 1 to 6 represent the six components in the material: H2O(l), TiO(OH)2, TiOSO4·H2O, TiOSO4, TiO2(a), and TiO2(r), respectively. The symbols in parentheses l represent liquid, a represent anatase TiO2, and r represent rutile TiO2. This represents the change in the mass flow rate of a component caused by a chemical reaction process.

[0116] The energy conservation equation is a one-dimensional energy conservation equation.

[0117] The one-dimensional energy conservation equations include the energy conservation equations for the gas phase, the material phase, the gas phase sidewalls, the solid phase sidewalls, and the outer wall.

[0118] The energy conservation equation for the gas phase is shown in equation (5):

[0119]

[0120] The energy conservation equation for the material is shown in the following equation:

[0121]

[0122] The energy conservation equation for the gas-phase sidewall is shown below:

[0123] 0 = Q G,WG -Q WG,S -Q WG,WS -Q WG,WO Equation (7)

[0124] The energy conservation equation for the solid sidewall is shown below:

[0125] 0 = Q WG,WS -Q WS,S -Q WS,WO Equation (8)

[0126] The energy conservation equation for the outer wall surface is shown below:

[0127] 0 = Q WG,WO +Q WG,WO -Q WO,A Equation (9)

[0128] In equations (5) to (9), T G T represents the temperature of the gas phase. S The temperature of the material, c i M represents the molar heat capacity of component i. i c represents the molar mass of component i. j M represents the molar heat capacity of component j; j Represents the molar mass of component j;

[0129] Q G,S Q G,WG Q WG,S and Q WS,S These represent the heat exchange between the gas phase and the solid phase, between the gas phase and the gas phase sidewall, between the gas phase sidewall and the solid phase, and between the solid phase sidewall and the solid phase, respectively; Q WG,WS Q WG,WO Q WS,WO and Q WO,A These represent the heat exchange between the gas phase sidewall and the solid phase sidewall, the gas phase sidewall and the outer wall, the solid phase sidewall and the outer wall, and the outer wall and the environment, respectively; Q Mass and Q Reac These represent energy transfer and heat of chemical reaction caused by mass exchange, respectively.

[0130] The heat exchange term Q inside the rotary kiln G,S Q G,WG Q WG,S and Q WS,S The closure relations are expressed as follows:

[0131]

[0132]

[0133]

[0134] Q WS,S =h WS,S L WS,S (T WS -TS )

[0135] Where h G,S h G,WG and h WS,S L represents the convective heat transfer coefficients between the gas phase and the material, between the gas phase and the gas phase sidewall, and between the material and the material sidewall, respectively. G,S L G,WG L WS,S These represent the convective heat transfer areas per unit axial length between the gas phase and the material, between the gas phase and the gas phase sidewall, and between the material and the material sidewall. G,S e G,WG e WG,S T represents the radiative heat exchange coefficients between the gas phase and the material, between the gas phase and the gas phase sidewall, and between the gas phase sidewall and the material, respectively. WG and T WS These represent the temperatures of the gas phase sidewall and the solid phase sidewall, respectively. σ represents the Stefan-Boltzmann constant.

[0136] Heat exchange term Q on the rotary kiln wall WG,WS Q WG,WO Q WS,WO and Q WO,A The closure relations are expressed as follows:

[0137]

[0138]

[0139]

[0140]

[0141] Where λ W ρ W and c W These represent the thermal conductivity, density, and heat capacity of the wall surface (i.e., the refractory brick), respectively. α fill D represents the material's filling rate. O T represents the diameter of the outer wall of the rotary kiln. WO and T A These represent the external wall surface temperature and the ambient temperature, respectively. WO,A L WO,A and e WO,A These represent the convective heat transfer coefficient between the outer wall surface and the environment, the heat transfer area per unit axial length, and the radiative heat transfer coefficient, respectively.

[0142] During the drying and chemical reaction process inside the rotary kiln, the closed-loop relationships of energy transfer due to mass exchange and reaction heat are expressed as follows:

[0143]

[0144]

[0145] Where h k The enthalpy of reaction k represents the chemical reaction k.

[0146] (3) Construct a rotary kiln chemical reaction model for the production of titanium dioxide by the sulfuric acid process, and couple the flow model in step (1) and the energy conservation equation in step (2) to calculate the one-dimensional component concentration field of the gas phase and materials in the rotary kiln.

[0147] The rotary kiln chemical reaction model includes 5 steps, denoted as R. k k is 1 to 5.

[0148] k=1:H2O(l)→H2O(g);

[0149] k=2: TiO(OH)2→TiO2(a)+H2O(g);

[0150] k=3: TiOSO4·H2O→TiOSO4+H2O(g);

[0151] k=4: TiOSO4→TiO2(a)+SO2(g)+1 / 2O2(g);

[0152] k=5:TiO2(a)→TiO2(r).

[0153] The reaction kinetic equations for k = 2 to 5 are expressed using Arrhenius's law:

[0154]

[0155] Where ζ k A k E k and n k These represent the conversion rate, pre-exponential factor, activation energy, and reaction order of reaction k, respectively; R is the molar gas constant; and t represents time.

[0156] The mass source terms of each component in the material are shown in equations (10) to (15):

[0157]

[0158]

[0159]

[0160]

[0161]

[0162]

[0163] Where x H2O Indicates the moisture content of the material;

[0164] The mass source terms of each component in the gas phase are shown in equations (16) to (20), respectively:

[0165]

[0166]

[0167]

[0168]

[0169]

[0170] (4) Based on the material residence time distribution, one-dimensional temperature field and one-dimensional component concentration field, the axial distribution of titanium dioxide grain size in the rotary kiln is calculated by solving the titanium dioxide grain size growth kinetic model.

[0171] The growth kinetics model for titanium dioxide grain size is shown in equation (20):

[0172]

[0173] Where d grain d represents the grain size. grain,0 α is the initial grain size. grain n is a proportionality constant. grain For the dynamic series, E grain This is the activation energy for grain growth.

[0174] The value of the grain growth activation energy is related to the type and formulation of the seed crystals and salt treatment agent used in the sulfuric acid process for titanium dioxide production.

[0175] Example 1

[0176] This embodiment provides a soft measurement method for the grain size of titanium dioxide in a rotary kiln during the sulfuric acid process for titanium dioxide production. The soft measurement method includes:

[0177] Specifically, the rotary kiln is 65m long, has an inner diameter of 3.3m, and the refractory bricks are 0.25m thick. The rotary kiln rotates at 0.195 rpm.

[0178] The volumetric flow rates of primary air, secondary air, and natural gas in the rotary kiln are 9000, 14200, and 1200 standard cubic meters per hour, respectively, with temperatures of 15, 156, and 15°C, respectively. The inlet mass flow rate of the material in the rotary kiln is 12 tons per hour, the inlet temperature of the material is 35°C, and the composition of the material is TiO2·0.0652·SO3·4.0572H2O.

[0179] This embodiment calculates the changes in material thickness and material residence time with the axial position of the rotary kiln through step (1) in the specific implementation method, such as Figure 2 As shown. From Figure 2 It can be seen that the material bed height in the rotary kiln remains basically consistent. However, at a distance of 15m from the kiln head, the material bed height increases as the distance from the kiln head decreases, until it reaches the height of the cofferdam. The changes in the temperature of the gas phase, material, and outer wall surface, as well as the composition of the material, with respect to the axial position of the rotary kiln, are obtained through steps (2) and (3). Figure 3 As shown. From Figure 3 It can be seen that the simulation results reasonably predict the temperature change history of the solid phase in the preheating section, constant-rate drying section, falling-rate drying section, and desulfurization process, as well as the change history of solid phase component concentration due to drying and reaction, and the changes in gas phase temperature and outer wall temperature from the kiln head to the kiln tail. By using the boundary values ​​at both ends of the rotary kiln for solution in step (4), the change of grain size with the axis of the rotary kiln is calculated, such as Figure 4 As shown. From Figure 4 It can be seen that the grain size in the rotary kiln begins to grow at a distance of about 15m from the kiln head, and the grain size is about 380μm when it reaches the kiln head.

[0180] Example 2

[0181] In this embodiment, except that the primary air volume in Example 1 is changed to 7000 standard cubic meters / hour, 8000 standard cubic meters / hour, and 1000 standard cubic meters / hour, all other conditions remain the same as in Example 1. From steps (1) to (5), the change in grain size with the axial position of the rotary kiln can be calculated, such as... Figure 5 As shown in (a).

[0182] Example 3

[0183] In this embodiment, except that the hot air temperature in Example 1 is changed to 960℃, 980℃, and 1020℃, all other conditions remain the same as in Example 1. From steps (1) to (5), the change in grain size with the axial position of the rotary kiln can be calculated, such as... Figure 5 As shown in (b).

[0184] Example 4

[0185] In this embodiment, except that the material inlet mass flow rate in Example 1 is changed to 11, 13, and 14 tons / hour, all other conditions remain the same as in Example 1. From steps (1) to (5), the change in grain size with the axial position of the rotary kiln can be calculated, such as... Figure 5 As shown in (c).

[0186] Example 5

[0187] In this embodiment, except that the kiln rotation speed in Example 1 is changed to 0.3, 0.5, and 2.0 rpm, all other conditions remain the same as in Example 1. From steps (1) to (5), the change in grain size with the axial position of the rotary kiln can be calculated, such as... Figure 5 As shown in (d).

[0188] from Figure 5 It can be seen that the grain size growth region in the rotary kiln advances with increasing hot air temperature and flow rate, and the corresponding grain size increases accordingly. Conversely, the grain size growth region is delayed with increasing material mass flow rate, and the corresponding grain size decreases accordingly. Increasing the rotary kiln rotation speed does not affect the starting position of grain growth, but it reduces the grain size due to shortened particle residence time. This indicates that the grain size predicted and calculated by this invention has the same growth trend as the actual grain size, and the prediction method is accurate and applicable to different operating conditions.

[0189] Example 6

[0190] In this embodiment, except that the boundary value limitation at both ends of the rotary kiln is replaced in Embodiment 1, the boundary value limitation at the outlet end is used only, the other conditions remain the same as in Embodiment 1. From steps (1) to (5), the change of grain size with the axial position of the rotary kiln can be calculated.

[0191] In this embodiment, only the boundary value at the outlet is set. However, in actual operation, the front-end control can only control the temperature and feed rate at the inlet. That is, only the boundary conditions at the inlet are the actual operating conditions. Using the boundary value constraint in Embodiment 6 requires obtaining the boundary conditions at the outlet first. Obtaining these boundary conditions is difficult in real-time production. Therefore, when using the method in Embodiment 6, the requirements for setting the initial parameters are quite strict. If the parameters are not set reasonably, the calculation error can easily exceed 50%. This shows that the present invention, by using a double-ended boundary value condition solution, has lower requirements for parameter settings. Even with relatively arbitrary initial parameter settings, it can obtain relatively accurate calculation results, resulting in better performance in actual production applications.

[0192] The actual size of titanium dioxide grains at the rotary kiln outlet of the above embodiment was measured and compared with the calculated grain size. It was found that the average grain size calculated by the present invention using Example 1 was 0.377 μm, while the average grain size actually measured under the same operating conditions was 0.375 μm, with an average error of only 0.53%. This shows that the prediction calculation method provided by the present invention is accurate and highly reliable.

[0193] The present invention has been illustrated with the above embodiments to illustrate its detailed structural features. However, the present invention is not limited to the above detailed structural features, that is, it does not mean that the present invention must rely on the above detailed structural features to be implemented. Those skilled in the art should understand that any improvements to the present invention, equivalent substitutions for the components used in the present invention, additions of auxiliary components, and selection of specific methods, etc., all fall within the protection scope and disclosure scope of the present invention.

Claims

1. A soft-sensing method for the size of titanium dioxide crystal grains in a rotary kiln in the production of titanium dioxide by the sulfuric acid method, characterized in that, The soft measurement method comprises the following steps: (1) constructing and solving a flow model of the rotary kiln to obtain a material layer thickness distribution, a material axial velocity distribution and a material residence time distribution at an axial position in the rotary kiln; (2) constructing and solving a mass conservation equation and an energy conservation equation of the rotary kiln according to the material layer thickness distribution, the material axial velocity distribution and the material residence time distribution obtained in step (1) to obtain a one-dimensional temperature field in the rotary kiln; (3) constructing a chemical reaction model of the rotary kiln for titanium dioxide production by the sulfuric acid method, and coupling the flow model in step (1) and the energy conservation equation in step (2) to calculate a one-dimensional component concentration field of the gas phase and the material in the rotary kiln; (4) according to the material residence time distribution, the one-dimensional temperature field and the one-dimensional component concentration field, a titanium dioxide grain size growth kinetics model is solved to calculate an axial distribution of the titanium dioxide grain size in the rotary kiln; The energy conservation equation is a one-dimensional energy conservation equation; The one-dimensional energy conservation equation comprises an energy conservation equation of the gas phase, an energy conservation equation of the material, an energy conservation equation of a gas phase side wall, an energy conservation equation of a solid phase side wall and an energy conservation equation of an outer wall; The energy conservation equation of the gas phase is shown as formula (5): The energy conservation equation of the material is shown as formula (6): wherein, Tgas represents the temperature of the gas phase, Tmat represents the temperature of the material, Cpimol represents the molar heat capacity of component i; Mimol represents the molar mass of component i, Cpjmol represents the molar heat capacity of component j; Mjmol represents the molar mass of component j; where Q G,S , Q G,WG , Q WG,S and Q WS,S represent the heat exchange between gas phase and solid phase, gas phase and gas phase side wall, gas phase side wall and solid phase, solid phase side wall and solid phase, respectively; Q Mass and Q Reac represent the energy transfer caused by mass exchange and chemical reaction heat, respectively. where m represents the mass flow rate of each component in the gas phase and the feedstock, the subscripts , respectively, represent the five components in the gas phase: N2, O2, CO2, SO2, and H2O(g), where g in parentheses represents gaseous; the subscript j = 1-6, respectively, represent the six components in the feedstock: H2O(l), TiO(OH)2, TiOSO4·H2O, TiOSO4, TiO2(a), and TiO2(r), where l in parentheses represents liquid.

2. The soft-sensing method according to claim 1, characterized by, The soft measurement method further comprises, before step (1), setting design parameters, physical property parameters and operation parameters of the rotary kiln.

3. The soft-sensing method according to claim 1 or 2, characterized by, The flow model in step (1) is a simplified one-dimensional flow model; The flow model is shown as formula (1): D in formula (1) i represents the inner diameter of the rotary kiln, represents the dynamic angle of repose, represents the rotational speed, represents the inclination angle of the rotary kiln, represents the volume flow of the solid phase, H represents the material bed height; where the residence time of the solids The distribution along the axial position z of the rotary kiln is given by equation (2): In formula (2) The expression material axial flow velocity, S bed Indicates the cross-sectional area occupied by the material.

4. The soft-sensing method according to claim 1, characterized in that, The mass conservation equation in step (2) is a one-dimensional mass conservation equation; The one-dimensional mass conservation equation is shown as formula (3)-(4): where m represents the mass flow rate of each component in the gas phase and the material, the subscripts , represent the five components in the gas phase: N2, O2, CO2, SO2, and H2O(g), where g in the parentheses represents the gaseous state; The subscript j = 1 ~ 6 respectively represents 6 components in the material: H2O(l), TiO(OH)2, TiOSO4·H2O, TiOSO4, TiO2(a) and TiO2(r), the symbol l in the bracket represents liquid, a represents anatase TiO2, and r represents rutile TiO2, represents the change of the mass flow rate of the component caused by the chemical reaction process.

5. The soft-sensing method according to claim 1, characterized in that, The energy conservation equation of the gas phase side wall is shown as formula (7): wherein Q WG,WS and Q WG,WO represent the heat exchange between the gas phase side wall surface and the solid phase side wall surface, and between the gas phase side wall surface and the outer wall surface, respectively.

6. The soft-sensing method according to claim 5, characterized in that, The energy conservation equation of the solid phase side wall is shown as formula (8): where Q WS,WO represents the heat exchange between the solid side wall and the outer wall.

7. The soft-sensing method according to claim 5, characterized in that, The energy conservation equation of the outer wall is shown as formula (9): where Q WO,A represents the heat exchange between the outer wall surface and the environment.

8. The soft-sensing method according to claim 1, characterized by, The rotary kiln chemical reaction model in step (3) includes 5 steps, respectively denoted as R k k is 1-5; 9. The soft-sensing method according to claim 8, characterized in that, The reaction kinetics equation of k = 2 ~ 5 is expressed by Arrhenius law: ; wherein 、 、 and n k represent the conversion, pre-exponential factor, activation energy and reaction order of reaction k, respectively, R is the molar gas constant; denotes time; The mass source terms of each component in the material are shown as formula (10)-(15): wherein h represents the moisture content in the material k ΔHkrepresents the reaction enthalpy of the chemical reaction k; The mass source terms of each component in the gas phase are shown as formula (16)-(20):

10. The soft-sensing method according to claim 9, characterized in that, The titanium dioxide grain size growth kinetics model in step (4) is shown as formula (21): wherein D is the grain size, D0 is the initial grain size, K is a proportionality constant, n is the kinetic order, Q is the grain growth activation energy.

11. A readable storage medium, characterized by, The readable storage medium stores a program written according to the soft measurement method of the titanium dioxide grain size in the rotary kiln for titanium dioxide production by the sulfuric acid method according to any one of claims 1-10.

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