Soft measurement method for titanium dioxide grain size in rotary kiln in process of preparing titanium dioxide through sulfuric acid method and readable storage medium

Abstract

The invention provides a soft measurement method for the grain size of titanium dioxide in a rotary kiln in the process of preparing titanium dioxide through a sulfuric acid method and a readable storage medium, and the soft measurement method combines a flow model, a mass conservation equation, an energy conservation equation, a rotary kiln chemical reaction model and a titanium dioxide grain size growth kinetic model of the rotary kiln. According to the method, the axial distribution of the titanium dioxide grain size in the rotary kiln can be calculated according to different operation conditions, and the method has important significance in obtaining high-quality titanium dioxide products by optimizing and regulating the operation conditions such as fuel flow, air flow, material flow and kiln rotating speed in a rotary kiln reactor.

Description

Technical Field

[0001] The invention relates to the technical field of titanium dioxide produced by sulfuric acid process, and in particular to a soft measurement method and a readable storage medium for the size of titanium dioxide grains in a rotary kiln in titanium dioxide produced by sulfuric acid process. Background Art

[0002] Titanium dioxide (commonly known as titanium dioxide) is an important raw material for industries such as architectural coatings, papermaking and cosmetics. In the process of producing titanium dioxide by sulfuric acid method, titanium-containing minerals undergo leaching, hydrolysis, calcination and crushing to obtain rutile titanium dioxide, of which rotary kiln calcination is the most important link in the whole process. The residence time and temperature field of the material in the rotary kiln have an important influence on the quality factors such as the rutile rate of titanium dioxide and the grain size of the product. However, the flow, heat transfer, reaction and grain growth processes in the rotary kiln are very complicated, and the flow field, temperature field, rutile conversion rate and grain size in the rotary kiln are difficult to accurately predict. The control of operating conditions such as hot air flow, hot air temperature, material mass flow and rotary kiln speed in the rotary kiln can only rely on production practice experience, lack of reliable theoretical calculation guidance, which has caused great difficulties in optimizing and controlling the operating conditions to obtain high-quality titanium dioxide products.

[0003] In the actual industrial production process, the titanium dioxide primary product obtained in the rotary kiln needs to be cooled and depolymerized, and then the grain size of the titanium dioxide product is measured by means of X-ray diffraction, laser particle size analyzer, etc. When the operating parameters in the rotary kiln are changed, the material residence time, temperature field distribution, rutile conversion rate and grain size in the rotary kiln will change accordingly. However, the time period from the change of operating parameters to the measurement of the grain size under the new operating parameters usually takes 10 to 20 hours, and feedback data cannot be obtained in time. Secondly, the industrial experimental method can only obtain the grain size at the outlet of the rotary kiln, and cannot obtain the distribution of the grain size inside the rotary kiln along the axial position of the rotary kiln. In addition, considering the safety factors and cost factors in the actual production process, it is difficult to carry out a large number of industrial experiments under different operating parameters, especially the inability to change the operating conditions in the rotary kiln within a large range.

[0004] In the laboratory, the reaction process, rutile conversion rate and grain size growth law of titanium dioxide calcination process can be obtained by heating metatitanic acid in a small muffle furnace, and by means of differential thermal analysis technology, combined with X-ray diffraction, laser particle size analyzer and other means. For example, Eastman studied the microstructural development of nano-titanium dioxide grains during annealing by high-temperature in-situ X-ray diffraction, and proposed a kinetic model for the growth of titanium dioxide grains. 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 huge difference between the flow field and temperature field in the small muffle furnace and the flow field and temperature field in the actual industrial rotary kiln, the grain size growth is strongly coupled with the flow, heat transfer and reaction process. Therefore, the grain size growth law explored in the laboratory cannot be directly used to predict the grain size growth in the actual industrial rotary kiln.

[0005] With the development of numerical simulation technology, numerical simulation of rotary kiln reactors has been increasingly applied to the prediction of multi-physical fields in rotary kilns, the development of new processes for rotary kilns, and the design, amplification, 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 on the rotary kiln device in the sulfuric acid process for titanium dioxide, and obtained the axial distribution of the temperature field of the rotary kiln. Agrawal et al. used a three-dimensional simulated gas 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 the grain size in the rotary kiln 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 for the titanium dioxide grain size in a rotary kiln in the sulfuric acid process for producing titanium dioxide and a readable storage medium, which can timely and accurately obtain the distribution of the titanium dioxide grain size in the rotary kiln along the axial position of the rotary kiln when the operating parameters such as hot air flow, hot air temperature, material flow and kiln speed in the rotary kiln change, thereby providing a new technical means for optimizing the operating conditions of the rotary kiln and obtaining higher quality titanium dioxide products.

[0007] To achieve this object, the present invention adopts the following technical solutions:

[0008] In a first aspect, the present invention provides a soft measurement method for the grain size of titanium dioxide in a rotary kiln in the process of producing titanium dioxide by sulfuric acid method, the soft measurement method comprising 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 in the rotary kiln;

[0010] (2) constructing and solving the mass conservation equation and energy conservation equation of the rotary kiln according to the material layer thickness distribution, material axial velocity distribution and material residence time distribution obtained in step (1) to obtain a one-dimensional temperature field in the rotary kiln;

[0011] (3) constructing a rotary kiln chemical reaction model for producing titanium dioxide by sulfuric acid process, and coupling 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 the material in the rotary kiln;

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

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

[0014] It is worth noting that the titanium dioxide grain growth process is relatively complicated, which includes a chemical reaction process on the one hand and a grain growth process on the other hand. The purpose of the present invention is not to predict the actual particle size of titanium dioxide, but to predict the grain size inside titanium dioxide. This grain size data has a high impact on the quality of subsequent titanium dioxide products, so it needs to be strictly controlled. The method provided by the present invention can be monitored in real time for different operating conditions, and not only the titanium dioxide grain size at the outlet of the rotary kiln is obtained, but also the distribution of the titanium dioxide grain size in the axial direction of the rotary kiln. It can also be judged whether there is a temperature rise, hot spot or large-scale agglomeration of particles in the rotary kiln according to the axial distribution, which is conducive to real-time monitoring of the reaction and grain growth in the rotary kiln.

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

[0016] Preferably, the flow model in step (1) is a simplified one-dimensional flow model, preferably a Seaman model, which can take the cofferdam factor in the rotary kiln into account, thereby being able to more accurately predict the residence time of titanium dioxide grains.

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

[0018]

[0019] In formula (1), D i represents the inner diameter of the rotary kiln, θ represents the dynamic repose angle, ω represents the rotation speed, α inc : Indicates the inclination angle of the rotary kiln, V s represents the volume flow rate of the solid phase, and H represents the material bed height.

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

[0021]

[0022] In formula (2), v s Express the axial flow velocity of the material, S bed Represents 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 as shown in equations (3) to (4):

[0025]

[0026]

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

[0028] Subscript j = 1 to 6, representing the six components in the material: H2O(l), TiO(OH)2, TiOSO4·H2O, TiOSO4, TiO2(a) and TiO2(r), the symbol l in the brackets represents liquid, a represents anatase TiO2, r represents rutile TiO2, Represents the change in component mass flow rate caused by the 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 of the gas phase, the energy conservation equation of the material, the energy conservation equation of the gas phase side wall, the energy conservation equation of the solid phase side wall and the energy conservation equation of the outer wall.

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

[0032]

[0033] Preferably, the energy conservation equation of the material is as shown in the formula:

[0034]

[0035] Preferably, the energy conservation equation of the gas phase side wall is as shown below:

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

[0037] Preferably, the energy conservation equation of the solid phase side wall is as shown below:

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

[0039] Preferably, the energy conservation equation of the outer wall is as shown:

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

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

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

[0043] Heat exchange item Q inside the rotary kiln G,S, Q G,WG , Q WG,S and Q WS,S The closed 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 They represent the convective heat transfer coefficients between the gas phase and the material, between the gas phase and the gas phase side wall, and between the material and the material side wall. G,S , L G,WG , L WS,S Respectively represent the convection heat transfer area between gas phase and material, gas phase and gas phase side wall, material and material side wall per unit axial length. G,S 、e G,WG 、e WG,S They represent the radiation heat exchange coefficients between the gas phase and the material, between the gas phase and the gas phase side wall, and between the gas phase side wall and the material. WG and T WS are the temperatures of the gas phase side wall and the solid phase side wall, respectively. σ is 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 closed relations are expressed as follows:

[0050]

[0051]

[0052]

[0053]

[0054] where λ W , W and c W Represent the thermal conductivity, density and heat capacity of the wall (i.e. refractory bricks) respectively. fillRepresents the filling rate of the material. O Represents the diameter of the outer wall of the rotary kiln. WO and T A Represent the outer wall temperature and the ambient temperature respectively. WO,A , L WO,A and e WO,A They represent the convective heat transfer coefficient between the outer wall and the environment, the heat transfer area per unit axial length, and the radiation heat exchange coefficient respectively.

[0055] During the drying and chemical reaction process in the rotary kiln, the closed relationship between energy migration and reaction heat caused by mass exchange is shown below:

[0056]

[0057]

[0058] where h k Represents the reaction enthalpy of the chemical reaction k.

[0059] Preferably, the rotary kiln chemical reaction model in step (3) includes 5 steps, which are respectively represented by 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 equation for k=2-5 is expressed using the Arrhenius law:

[0066]

[0067] where ζ k , A k 、E k and n k Respectively represent the conversion rate, pre-exponential factor, activation energy and reaction order of reaction k, R is the molar gas constant; 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 in the material;

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

[0077]

[0078]

[0079]

[0080]

[0081]

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

[0083]

[0084] where d grain is the grain size, d grain,0 is the initial grain size, α grain is the proportionality constant, n grain is the kinetic order, E grain is the activation energy of grain growth.

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

[0086] Preferably, the soft measurement method uses boundary value limits at both ends of the rotary kiln to solve the problem. Compared with the traditional method of only using boundary value limits at the outlet end, the soft measurement method provided by the present invention can fully take into account the material changes before and after the reaction, and the prediction results are significantly improved.

[0087] In a second aspect, the present invention provides a readable storage medium storing a program written for the soft measurement method of the titanium dioxide grain size in the rotary kiln in 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 of the titanium dioxide grain size in the rotary kiln in the sulfuric acid process for producing titanium dioxide as described in the first aspect, and the computer storage medium can be connected to existing commercial software to achieve the prediction of the 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 the titanium dioxide grain size in the rotary kiln in the sulfuric acid process of titanium dioxide provided by the present invention calculates the titanium dioxide grain size within 10 seconds, so the titanium dioxide grain size after the operating conditions are changed can be obtained in time;

[0091] (2) The soft measurement method of the titanium dioxide grain size in the rotary kiln in the sulfuric acid process of titanium dioxide 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 the titanium dioxide grain size along the axial position of the rotary kiln, thereby providing feedback on the hot spot temperature rise and calcination stability inside the rotary kiln;

[0092] (3) The soft measurement method for the grain size of titanium dioxide in the rotary kiln during the sulfuric acid process for titanium dioxide provided by the present invention can be applied to different operating conditions and rotary kilns, for example, it is applicable to rotary kilns for the sulfuric acid process for titanium dioxide with different design parameters, and these parameters are not limited to the length, diameter, thickness of refractory bricks, inclination angle of the rotary kiln, and refractory brick materials of the rotary kiln; it is applicable to rotary kilns for the sulfuric acid process for titanium dioxide with different operating conditions, hot air flow rate, different hot air temperatures, different material flow rates, and different kiln speeds; it is applicable to titanium dioxide for the sulfuric acid process with different types of salt treatment agents and different salt treatment agent preparation methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 It is an operation flow chart of a soft measurement method for the size of titanium dioxide grains in a rotary kiln in the sulfuric acid process for producing titanium dioxide according to a specific embodiment of the present invention.

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

[0095] Figure 3 This is a diagram showing the temperature distribution and solid phase components changing with the axial position of the rotary kiln provided in Example 1 of the present invention.

[0096] Figure 4 This is a distribution diagram of the titanium dioxide grain size predicted by Example 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 titanium dioxide grain size predicted by Example 1 of the present invention. DETAILED DESCRIPTION

[0098] The technical solution of the present invention is further described below with reference to the accompanying drawings and through specific implementation methods.

[0099] The present invention is further described in detail below. However, the following examples are only 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 subject to 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 in the sulfuric acid process for producing titanium dioxide is provided, and the soft measurement method comprises the following steps:

[0101] The design parameters, physical 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 length of the kiln, and the inclination of the kiln; the physical parameters include the density of the refractory bricks, the heat capacity, the thermal conductivity, the radiation emissivity, etc.; the operating parameters include the hot air flow rate, the hot air temperature, the composition and proportion of the hot air inlet, the material inlet flow rate, the material inlet composition and proportion, and the kiln rotation speed.

[0102] (1) Construct and solve the flow model (Seaman 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 in the rotary kiln;

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

[0104]

[0105] In formula (1), D i represents the inner diameter of the rotary kiln, θ represents the dynamic repose angle, ω represents the rotation speed, α inc : Indicates the inclination angle of the rotary kiln, V s represents the volume flow rate of the solid phase, and H represents the material bed height.

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

[0107]

[0108] In formula (2), v s Express the axial flow velocity of the material, S bed Represents the cross-sectional area occupied by the material.

[0109] (2) constructing and solving the mass conservation equation and energy conservation equation of the rotary kiln according to the material layer thickness distribution, material axial velocity distribution and material residence time distribution obtained in step (1) to obtain a 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 formula (3) to formula (4), m represents the mass flow rate of each component in the gas phase and the material, and the subscript i = 1 to 5, respectively represents the five components in the gas phase: N2, O2, CO2, SO2 and H2O (g), and the g in the brackets represents the gas state.

[0115] Subscript j = 1 to 6, representing the six components in the material: H2O(l), TiO(OH)2, TiOSO4·H2O, TiOSO4, TiO2(a) and TiO2(r), the symbol l in the brackets represents liquid, a represents anatase TiO2, r represents rutile TiO2, Represents the change in component mass flow rate caused by the chemical reaction process.

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

[0117] The one-dimensional energy conservation equation includes the energy conservation equation of the gas phase, the energy conservation equation of the material, the energy conservation equation of the gas phase side wall, the energy conservation equation of the solid phase side wall and the energy conservation equation of the outer wall.

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

[0119]

[0120] The energy conservation equation of the material is shown as follows:

[0121]

[0122] The energy conservation equation of the gas phase side wall is shown as follows:

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

[0124] The energy conservation equation of the solid side wall is shown as follows:

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

[0126] The energy conservation equation of the outer wall is shown as follows:

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

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

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

[0130] Heat exchange item Q inside the rotary kiln G,S , Q G,WG , Q WG,S and Q WS,S The closed 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 They represent the convective heat transfer coefficients between the gas phase and the material, between the gas phase and the gas phase side wall, and between the material and the material side wall. G,S , L G,WG , L WS,S Respectively represent the convection heat transfer area between gas phase and material, gas phase and gas phase side wall, material and material side wall per unit axial length. G,S 、e G,WG 、e WG,S They represent the radiation heat exchange coefficients between the gas phase and the material, between the gas phase and the gas phase side wall, and between the gas phase side wall and the material. WG and T WS are the temperatures of the gas phase side wall and the solid phase side wall, respectively. σ is 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 closed relations are expressed as follows:

[0137]

[0138]

[0139]

[0140]

[0141] where λ W , W and c W Represent the thermal conductivity, density and heat capacity of the wall (i.e. refractory bricks) respectively. fill Represents the filling rate of the material. O Represents the diameter of the outer wall of the rotary kiln. WO and T A Represent the outer wall temperature and the ambient temperature respectively. WO,A , L WO,A and e WO,A They represent the convective heat transfer coefficient between the outer wall and the environment, the heat transfer area per unit axial length, and the radiation heat exchange coefficient respectively.

[0142] During the drying and chemical reaction process in the rotary kiln, the closed relationship between energy migration and reaction heat caused by mass exchange is shown below:

[0143]

[0144]

[0145] where h k Represents the reaction enthalpy of the chemical reaction k.

[0146] (3) constructing a rotary kiln chemical reaction model for producing titanium dioxide by sulfuric acid process, and coupling 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 the material in the rotary kiln;

[0147] The rotary kiln chemical reaction model includes five steps, which are respectively represented by 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 equation for k=2-5 is expressed using the Arrhenius law:

[0154]

[0155] where ζ k , A k 、E k and n k Respectively represent the conversion rate, pre-exponential factor, activation energy and reaction order of reaction k, R is the molar gas constant; 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 in the material;

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

[0165]

[0166]

[0167]

[0168]

[0169]

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

[0171] The titanium dioxide grain size growth kinetic model is shown in formula (20):

[0172]

[0173] where d grain is the grain size, d grain,0 is the initial grain size, α grain is the proportionality constant, n grain is the kinetic order, E grain is the activation energy of grain growth.

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

[0175] Example 1

[0176] This embodiment provides a soft measurement method for the size of titanium dioxide grains in a rotary kiln in the production of titanium dioxide by sulfuric acid process, and the soft measurement method comprises:

[0177] Specifically, the length of the rotary kiln is 65m, the inner diameter is 3.3m, the thickness of the refractory brick is 0.25m, and the rotation speed of the rotary kiln is 0.195rpm.

[0178] The volume 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, and the temperatures are 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] In this embodiment, the material thickness and material residence time are calculated and obtained according to the change of the axial position of the rotary kiln through step (1) in the specific implementation mode, such as Figure 2 As shown. Figure 2 It can be seen that the material bed height in the rotary kiln remains basically the same. 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. Steps (2) and (3) are used to calculate the changes in the temperature of the gas phase, material, and outer wall surface, and the components in the material with the axial position of the rotary kiln, as shown in Figure 2. Figure 3 As shown. Figure 3 It can be seen that the simulation results reasonably predict the temperature change history of the solid phase in the preheating stage, constant speed drying stage, speed reduction drying stage and desulfurization process, the change history of the solid phase component concentration caused by drying and reaction, and the change of the gas phase temperature and the outer wall temperature from the kiln head to the kiln tail. Step (4) is solved by using the boundary value limit at both ends of the rotary kiln to calculate the change of the grain size along the axial direction of the rotary kiln, such as Figure 4 As shown. Figure 4 It can be seen that the grain size in the rotary kiln starts to grow at about 15 m from the kiln head, and the grain size is about 380 μm 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, other conditions remain the same as those in Example 1. From steps (1) to (5), the change of the grain size with the axial position of the rotary kiln can be calculated, as shown in FIG. Figure 5 (a) shown.

[0182] Example 3

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

[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, other conditions remain the same as in Example 1. From steps (1) to (5), the change of grain size with the axial position of the rotary kiln can be calculated, such as Figure 5 (c) as shown.

[0186] Example 5

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

[0188] from Figure 5 It can be seen that the grain size growth area in the rotary kiln is advanced with the increase of hot air temperature and hot air flow, and the grain size at the corresponding position is also increased accordingly. On the contrary, the grain size growth area is delayed with the increase of material mass flow rate, and the grain size at the corresponding position is also reduced accordingly. The increase in the rotation speed of the rotary kiln does not affect the position where the grains start to grow, but the grain size is reduced due to the shortened residence time of the particles. It shows that the growth trend of the grain size predicted and calculated by the present invention is the same as that of the actual grown 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 constraints at both ends of the rotary kiln are replaced by the boundary value constraints at the outlet end, other conditions remain the same as those in embodiment 1. From steps (1) to (5), the change of the grain size with the axial position of the rotary kiln can be calculated.

[0191] In this embodiment, since only the boundary value of the outlet is set, the front-end control can only control the temperature and feed amount of the inlet in the actual operation process, that is, only the boundary condition of the inlet is the real operating condition, and the boundary value limit in Example 6 is adopted, and the boundary condition of the outlet needs to be obtained first. The acquisition of this boundary condition is relatively difficult in the real-time operation of actual production. Therefore, when the method of Example 6 is used for solving, the setting requirements for the early parameters are relatively strict. When the parameter setting is unreasonable, the calculation error is likely to exceed 50%. This shows that the present invention uses the double-end boundary value condition to solve, and the parameter setting requirements are relatively low. Even if the original parameter setting is relatively random, the calculation result of relative accuracy can be obtained, and the effect is better in actual production application.

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

[0193] The present invention illustrates the detailed structural features of the present invention through the above embodiments, but 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 improvement of the present invention, equivalent replacement of the components selected by the present invention, addition of auxiliary components, selection of specific methods, etc., all fall within the protection scope and disclosure scope of the present invention.

Claims

1. A soft measurement method for the grain size of titanium dioxide in a rotary kiln during the sulfuric acid process for producing titanium dioxide, characterized in that: The soft measurement method comprises the following steps: (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 in the rotary kiln; (2) constructing and solving the mass conservation equation and energy conservation equation of the rotary kiln according to the material layer thickness distribution, material axial velocity distribution and material residence time distribution obtained in step (1) to obtain a one-dimensional temperature field in the rotary kiln; (3) constructing a rotary kiln chemical reaction model for producing titanium dioxide by sulfuric acid process, and coupling 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 the material in the rotary kiln; (4) According to the material residence time distribution, one-dimensional temperature field and one-dimensional component concentration field, the axial distribution of the titanium dioxide grain size in the rotary kiln is calculated by solving the titanium dioxide grain size growth kinetic model.

2. The soft sensing method according to claim 1, characterized in that: 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 in that: The flow model in step (1) is a simplified one-dimensional flow model; Preferably, the flow model is as shown in formula (1): In formula (1), D i represents the inner diameter of the rotary kiln, θ represents the dynamic repose angle, ω represents the rotation speed, α inc : Indicates the inclination angle of the rotary kiln, V s represents the volume flow rate of the solid phase, and H represents the height of the material bed; The distribution of the residence time τ of the solid phase along the axial position z of the rotary kiln is shown in formula (2): In formula (2), v s Express the axial flow velocity of the material, S bed Represents the cross-sectional area occupied by the material.

4. The soft sensing method according to any one of claims 1 to 3, characterized in that: The mass conservation equation in step (2) is a one-dimensional mass conservation equation; Preferably, the one-dimensional mass conservation equation is as shown in equations (3) to (4): In formula (3) to formula (4), m represents the mass flow rate of each component in the gas phase and the material, and the subscript i=1 to 5 represents the five components in the gas phase: N2, O2, CO2, SO2 and H2O (g), and the g in the bracket represents the gas phase; Subscript j = 1 to 6, representing the six components in the material: H2O(l), TiO(OH)2, TiOSO4·H2O, TiOSO4, TiO2(a) and TiO2(r), the symbol l in the brackets represents liquid, a represents anatase TiO2, r represents rutile TiO2, Represents the change in component mass flow rate caused by the chemical reaction process.

5. The soft sensing method according to any one of claims 1 to 4, characterized in that: The energy conservation equation is a one-dimensional energy conservation equation; Preferably, the one-dimensional energy conservation equation includes the energy conservation equation of the gas phase, the energy conservation equation of the material, the energy conservation equation of the gas phase side wall, the energy conservation equation of the solid phase side wall and the energy conservation equation of the outer wall.

6. The soft sensing method according to claim 5, characterized in that: The energy conservation equation of the gas phase is shown in formula (5): Preferably, the energy conservation equation of the material is as shown in the formula: Preferably, the energy conservation equation of the gas phase side wall is as shown below: 0=Q G,WG -Q WG,S -Q WG,WS -Q WG,WO Formula (7) Preferably, the energy conservation equation of the solid phase side wall is as shown below: 0=Q WG,WS -Q WS,S -Q WS,WO Formula (8) Preferably, the energy conservation equation of the outer wall is as shown: 0=Q WG,WO +Q WG,WO -Q WO,A Formula (9) In formula (5) to formula (9), T G represents the temperature of the gas phase, T S Indicates the temperature of the material, c i represents the molar heat capacity of component i; M i represents the molar mass of component i, c j represents the molar heat capacity of component j; M j represents the molar mass of component j; Where Q G,S , Q G,WG , Q WG,S and Q WS,S They represent the heat exchange between gas phase and solid phase, gas phase and gas phase side wall, gas phase side wall and solid phase, and solid phase side wall and solid phase respectively; Q WG,WS , Q WG,WO , Q WS,WO and Q WO,A They represent the heat exchange between the gas phase side wall and the solid phase side wall, the gas phase side wall and the outer wall, the solid phase side wall and the outer wall, and the outer wall and the environment respectively; Q Mass and Q Reac They represent the energy transfer caused by mass exchange and the heat of chemical reaction respectively.

7. The soft sensing method according to any one of claims 1 to 6, characterized in that: The rotary kiln chemical reaction model in step (3) includes 5 steps, which are respectively represented by R k , k is 1 to 5; k=1:H2O(l)→H2O(g); k=2: TiO(OH)2→TiO2(a)+H2O(g); k=3: TiOSO4·H2O→TiOSO4+H2O(g); k=4: TiOSO4→TiO2(a)+SO2(g)+1 / 2O2(g); k=5:TiO2(a)→TiO2(r).

8. The soft sensing method according to claim 7, characterized in that: The reaction kinetic equation for k=2-5 is expressed using the Arrhenius law: where ζ k , A k 、E k and n k Respectively represent the conversion rate, pre-exponential factor, activation energy and reaction order of reaction k, R is the molar gas constant; t represents time; The mass source terms of each component in the material are shown in equations (10) to (15): where x H2O Indicates the moisture content in the material; The mass source terms of each component in the gas phase are shown in equations (16) to (20):

9. The soft sensing method according to any one of claims 1 to 8, characterized in that: The titanium dioxide grain size growth kinetic model in step (4) is shown in formula (20): where d grain is the grain size, d grain,0 is the initial grain size, α grain is the proportionality constant, n grain is the kinetic order, E grain is the activation energy of grain growth.

10. A readable storage medium, characterized in that: The readable storage medium stores a program written according to the soft measurement method of the titanium dioxide grain size in the rotary kiln in the sulfuric acid process of titanium dioxide as described in any one of claims 1 to 9.

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